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#define PY_SSIZE_T_CLEAN
#ifndef CYTHON_USE_PYLONG_INTERNALS
#ifdef PYLONG_BITS_IN_DIGIT
#define CYTHON_USE_PYLONG_INTERNALS 0
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#include "pyconfig.h"
#ifdef PYLONG_BITS_IN_DIGIT
#define CYTHON_USE_PYLONG_INTERNALS 1
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#define CYTHON_USE_PYLONG_INTERNALS 0
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#include "Python.h"
#ifndef Py_PYTHON_H
    #error Python headers needed to compile C extensions, please install development version of Python.
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    #error Cython requires Python 2.6+ or Python 3.2+.
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#define CYTHON_ABI "0_21_1"
#include <stddef.h>
#ifndef offsetof
#define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
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#ifndef PY_LONG_LONG
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#ifndef Py_HUGE_VAL
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#define CYTHON_COMPILING_IN_PYPY 1
#define CYTHON_COMPILING_IN_CPYTHON 0
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#define CYTHON_COMPILING_IN_PYPY 0
#define CYTHON_COMPILING_IN_CPYTHON 1
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#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600
#define Py_OptimizeFlag 0
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#define __PYX_BUILD_PY_SSIZE_T "n"
#define CYTHON_FORMAT_SSIZE_T "z"
#if PY_MAJOR_VERSION < 3
  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos) \
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#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
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  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ? \
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  #define CYTHON_PEP393_ENABLED 0
  #define __Pyx_PyUnicode_READY(op)       (0)
  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
#endif
#if CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
  #define __Pyx_PyFrozenSet_Size(s)         PyObject_Size(s)
#else
  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ? \
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
  #define __Pyx_PyFrozenSet_Size(s)         PySet_Size(s)
#endif
#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
#else
  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBaseString_Type            PyUnicode_Type
  #define PyStringObject               PyUnicodeObject
  #define PyString_Type                PyUnicode_Type
  #define PyString_Check               PyUnicode_Check
  #define PyString_CheckExact          PyUnicode_CheckExact
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
#else
  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
#endif
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#if PY_MAJOR_VERSION >= 3
  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
  #define PyInt_Check(op)              PyLong_Check(op)
  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
  #define PyInt_FromString             PyLong_FromString
  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
  #define PyInt_AsLong                 PyLong_AsLong
  #define PyInt_AS_LONG                PyLong_AS_LONG
  #define PyInt_AsSsize_t              PyLong_AsSsize_t
  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
  #define PyNumber_Int                 PyNumber_Long
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
#endif
#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
  #ifndef PyUnicode_InternFromString
    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
  #endif
#endif
#if PY_VERSION_HEX < 0x030200A4
  typedef long Py_hash_t;
  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
#else
  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
#else
  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
#endif
#ifndef CYTHON_INLINE
  #if defined(__GNUC__)
    #define CYTHON_INLINE __inline__
  #elif defined(_MSC_VER)
    #define CYTHON_INLINE __inline
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_INLINE inline
  #else
    #define CYTHON_INLINE
  #endif
#endif
#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
  #elif defined(_MSC_VER) && _MSC_VER >= 1400
    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
  #else
    #define CYTHON_RESTRICT
  #endif
#endif
#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  /* Initialize NaN. The sign is irrelevant, an exponent with all bits 1 and
   a nonzero mantissa means NaN. If the first bit in the mantissa is 1, it is
   a quiet NaN. */
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
#endif
#ifdef __cplusplus
template<typename T>
void __Pyx_call_destructor(T* x) {
    x->~T();
}
#endif


#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
#else
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
#endif

#ifndef __PYX_EXTERN_C
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#if defined(WIN32) || defined(MS_WINDOWS)
#define _USE_MATH_DEFINES
#endif
#include <math.h>
#define __PYX_HAVE__dipy__align__transforms
#define __PYX_HAVE_API__dipy__align__transforms
#include "string.h"
#include "stdio.h"
#include "stdlib.h"
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#include "dpy_math.h"
#include "pythread.h"
#include "pystate.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#ifdef PYREX_WITHOUT_ASSERTIONS
#define CYTHON_WITHOUT_ASSERTIONS
#endif

#ifndef CYTHON_UNUSED
# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
#   else
#     define CYTHON_UNUSED
#   endif
# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
# else
#   define CYTHON_UNUSED
# endif
#endif
typedef struct {PyObject **p; char *s; const Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (    \
    (sizeof(type) < sizeof(Py_ssize_t))  ||             \
    (sizeof(type) > sizeof(Py_ssize_t) &&               \
          likely(v < (type)PY_SSIZE_T_MAX ||            \
                 v == (type)PY_SSIZE_T_MAX)  &&         \
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||       \
                                v == (type)PY_SSIZE_T_MIN)))  ||  \
    (sizeof(type) == sizeof(Py_ssize_t) &&              \
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||        \
                               v == (type)PY_SSIZE_T_MAX)))  )
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if PY_MAJOR_VERSION < 3
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#else
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
#endif
#define __Pyx_PyObject_AsSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromUString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromUString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromUString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromUString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromUString(s) __Pyx_PyUnicode_FromString((const char*)s)
#if PY_MAJOR_VERSION < 3
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u)
{
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#else
#define __Pyx_Py_UNICODE_strlen Py_UNICODE_strlen
#endif
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#define __Pyx_Owned_Py_None(b) (Py_INCREF(Py_None), Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? (Py_INCREF(Py_True), Py_True) : (Py_INCREF(Py_False), Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x);
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_COMPILING_IN_CPYTHON
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    if (strcmp(default_encoding_c, "ascii") == 0) {
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
    } else {
        char ascii_chars[128];
        int c;
        for (c = 0; c < 128; c++) {
            ascii_chars[c] = c;
        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif


/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */

static PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #define CYTHON_CCOMPLEX 1
  #else
    #define CYTHON_CCOMPLEX 0
  #endif
#endif
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #include <complex>
  #else
    #include <complex.h>
  #endif
#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
#endif


static const char *__pyx_f[] = {
  "dipy/align/transforms.pyx",
  "__init__.pxd",
  "stringsource",
  "type.pxd",
};
struct __pyx_memoryview_obj;
typedef struct {
  struct __pyx_memoryview_obj *memview;
  char *data;
  Py_ssize_t shape[8];
  Py_ssize_t strides[8];
  Py_ssize_t suboffsets[8];
} __Pyx_memviewslice;

#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  size_t fmt_offset;
  size_t new_count, enc_count;
  size_t struct_alignment;
  int is_complex;
  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;

#include <pythread.h>
#ifndef CYTHON_ATOMICS
    #define CYTHON_ATOMICS 1
#endif
#define __pyx_atomic_int_type int
#if CYTHON_ATOMICS && __GNUC__ >= 4 && (__GNUC_MINOR__ > 1 ||           \
                    (__GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL >= 2)) && \
                    !defined(__i386__)
    #define __pyx_atomic_incr_aligned(value, lock) __sync_fetch_and_add(value, 1)
    #define __pyx_atomic_decr_aligned(value, lock) __sync_fetch_and_sub(value, 1)
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Using GNU atomics"
    #endif
#elif CYTHON_ATOMICS && MSC_VER
    #include <Windows.h>
    #define __pyx_atomic_int_type LONG
    #define __pyx_atomic_incr_aligned(value, lock) InterlockedIncrement(value)
    #define __pyx_atomic_decr_aligned(value, lock) InterlockedDecrement(value)
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Using MSVC atomics"
    #endif
#elif CYTHON_ATOMICS && (defined(__ICC) || defined(__INTEL_COMPILER)) && 0
    #define __pyx_atomic_incr_aligned(value, lock) _InterlockedIncrement(value)
    #define __pyx_atomic_decr_aligned(value, lock) _InterlockedDecrement(value)
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Using Intel atomics"
    #endif
#else
    #undef CYTHON_ATOMICS
    #define CYTHON_ATOMICS 0
    #ifdef __PYX_DEBUG_ATOMICS
        #warning "Not using atomics"
    #endif
#endif
typedef volatile __pyx_atomic_int_type __pyx_atomic_int;
#if CYTHON_ATOMICS
    #define __pyx_add_acquisition_count(memview) \
             __pyx_atomic_incr_aligned(__pyx_get_slice_count_pointer(memview), memview->lock)
    #define __pyx_sub_acquisition_count(memview) \
            __pyx_atomic_decr_aligned(__pyx_get_slice_count_pointer(memview), memview->lock)
#else
    #define __pyx_add_acquisition_count(memview) \
            __pyx_add_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock)
    #define __pyx_sub_acquisition_count(memview) \
            __pyx_sub_acquisition_count_locked(__pyx_get_slice_count_pointer(memview), memview->lock)
#endif


/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":723
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 */
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":724
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
 */
typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":725
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":726
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":730
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":731
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
 */
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":732
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * #ctypedef npy_uint96     uint96_t
 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":733
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":737
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":738
 * 
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
 * #ctypedef npy_float128   float128_t
 */
typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":747
 * # The int types are mapped a bit surprising --
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":748
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   longlong_t
 * 
 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":749
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_ulong      uint_t
 */
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":751
 * ctypedef npy_longlong   longlong_t
 * 
 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t
 */
typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":752
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":753
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
 */
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":755
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":756
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":758
 * ctypedef npy_uintp      uintp_t
 * 
 * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t
 */
typedef npy_double __pyx_t_5numpy_float_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":759
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":760
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
 */
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< float > __pyx_t_float_complex;
  #else
    typedef float _Complex __pyx_t_float_complex;
  #endif
#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
#endif

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
  #endif
#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif


/*--- Type declarations ---*/
struct __pyx_obj_4dipy_5align_10transforms_Transform;
struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D;
struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D;
struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D;
struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D;
struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D;
struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D;
struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D;
struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D;
struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D;
struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D;
struct __pyx_array_obj;
struct __pyx_MemviewEnum_obj;
struct __pyx_memoryview_obj;
struct __pyx_memoryviewslice_obj;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":762
 * ctypedef npy_longdouble longdouble_t
 * 
 * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t
 */
typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":763
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":764
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cdouble     complex_t
 */
typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../../../../../usr/lib/python2.7/dist-packages/Cython/Includes/numpy/__init__.pxd":766
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;

/* "dipy/align/transforms.pyx":15
 *     double log(double)
 * 
 * cdef class Transform:             # <<<<<<<<<<<<<<
 *     r""" Base class (contract) for all transforms for affine image registration.
 *     Each transform must define the following (fast, nogil) methods:
 */
struct __pyx_obj_4dipy_5align_10transforms_Transform {
  PyObject_HEAD
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform *__pyx_vtab;
  int number_of_parameters;
  int dim;
};


/* "dipy/align/transforms.pyx":121
 * 
 * 
 * cdef class TranslationTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Translation transform in 2D
 */
struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":190
 * 
 * 
 * cdef class TranslationTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Translation transform in 3D
 */
struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":261
 * 
 * 
 * cdef class RotationTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rotation transform in 2D
 */
struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":335
 * 
 * 
 * cdef class RotationTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rotation transform in 3D
 */
struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":428
 * 
 * 
 * cdef class RigidTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rigid transform in 2D (rotation + translation)
 */
struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":515
 * 
 * 
 * cdef class RigidTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rigid transform in 3D (rotation + translation)
 */
struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":634
 * 
 * 
 * cdef class ScalingTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Scaling transform in 2D
 */
struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":697
 * 
 * 
 * cdef class ScalingTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Scaling transform in 3D
 */
struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":761
 * 
 * 
 * cdef class AffineTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Affine transform in 2D
 */
struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "dipy/align/transforms.pyx":846
 * 
 * 
 * cdef class AffineTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Affine transform in 3D
 */
struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D {
  struct __pyx_obj_4dipy_5align_10transforms_Transform __pyx_base;
};


/* "View.MemoryView":99
 * 
 * @cname("__pyx_array")
 * cdef class array:             # <<<<<<<<<<<<<<
 * 
 *     cdef:
 */
struct __pyx_array_obj {
  PyObject_HEAD
  char *data;
  Py_ssize_t len;
  char *format;
  int ndim;
  Py_ssize_t *_shape;
  Py_ssize_t *_strides;
  Py_ssize_t itemsize;
  PyObject *mode;
  PyObject *_format;
  void (*callback_free_data)(void *);
  int free_data;
  int dtype_is_object;
};


/* "View.MemoryView":269
 * 
 * @cname('__pyx_MemviewEnum')
 * cdef class Enum(object):             # <<<<<<<<<<<<<<
 *     cdef object name
 *     def __init__(self, name):
 */
struct __pyx_MemviewEnum_obj {
  PyObject_HEAD
  PyObject *name;
};


/* "View.MemoryView":302
 * 
 * @cname('__pyx_memoryview')
 * cdef class memoryview(object):             # <<<<<<<<<<<<<<
 * 
 *     cdef object obj
 */
struct __pyx_memoryview_obj {
  PyObject_HEAD
  struct __pyx_vtabstruct_memoryview *__pyx_vtab;
  PyObject *obj;
  PyObject *_size;
  PyObject *_array_interface;
  PyThread_type_lock lock;
  __pyx_atomic_int acquisition_count[2];
  __pyx_atomic_int *acquisition_count_aligned_p;
  Py_buffer view;
  int flags;
  int dtype_is_object;
  __Pyx_TypeInfo *typeinfo;
};


/* "View.MemoryView":922
 * 
 * @cname('__pyx_memoryviewslice')
 * cdef class _memoryviewslice(memoryview):             # <<<<<<<<<<<<<<
 *     "Internal class for passing memoryview slices to Python"
 * 
 */
struct __pyx_memoryviewslice_obj {
  struct __pyx_memoryview_obj __pyx_base;
  __Pyx_memviewslice from_slice;
  PyObject *from_object;
  PyObject *(*to_object_func)(char *);
  int (*to_dtype_func)(char *, PyObject *);
};



/* "dipy/align/transforms.pyx":15
 *     double log(double)
 * 
 * cdef class Transform:             # <<<<<<<<<<<<<<
 *     r""" Base class (contract) for all transforms for affine image registration.
 *     Each transform must define the following (fast, nogil) methods:
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform {
  int (*_jacobian)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice);
  void (*_get_identity_parameters)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice);
  void (*_param_to_matrix)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice);
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform *__pyx_vtabptr_4dipy_5align_10transforms_Transform;


/* "dipy/align/transforms.pyx":121
 * 
 * 
 * cdef class TranslationTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Translation transform in 2D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform2D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform2D *__pyx_vtabptr_4dipy_5align_10transforms_TranslationTransform2D;


/* "dipy/align/transforms.pyx":190
 * 
 * 
 * cdef class TranslationTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Translation transform in 3D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform3D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform3D *__pyx_vtabptr_4dipy_5align_10transforms_TranslationTransform3D;


/* "dipy/align/transforms.pyx":261
 * 
 * 
 * cdef class RotationTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rotation transform in 2D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform2D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform2D *__pyx_vtabptr_4dipy_5align_10transforms_RotationTransform2D;


/* "dipy/align/transforms.pyx":335
 * 
 * 
 * cdef class RotationTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rotation transform in 3D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform3D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform3D *__pyx_vtabptr_4dipy_5align_10transforms_RotationTransform3D;


/* "dipy/align/transforms.pyx":428
 * 
 * 
 * cdef class RigidTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rigid transform in 2D (rotation + translation)
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform2D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform2D *__pyx_vtabptr_4dipy_5align_10transforms_RigidTransform2D;


/* "dipy/align/transforms.pyx":515
 * 
 * 
 * cdef class RigidTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Rigid transform in 3D (rotation + translation)
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform3D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform3D *__pyx_vtabptr_4dipy_5align_10transforms_RigidTransform3D;


/* "dipy/align/transforms.pyx":634
 * 
 * 
 * cdef class ScalingTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Scaling transform in 2D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_ScalingTransform2D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_ScalingTransform2D *__pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform2D;


/* "dipy/align/transforms.pyx":697
 * 
 * 
 * cdef class ScalingTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Scaling transform in 3D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_ScalingTransform3D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_ScalingTransform3D *__pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform3D;


/* "dipy/align/transforms.pyx":761
 * 
 * 
 * cdef class AffineTransform2D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Affine transform in 2D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_AffineTransform2D {
  struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_base;
};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_AffineTransform2D *__pyx_vtabptr_4dipy_5align_10transforms_AffineTransform2D;


/* "dipy/align/transforms.pyx":846
 * 
 * 
 * cdef class AffineTransform3D(Transform):             # <<<<<<<<<<<<<<
 *     def __init__(self):
 *         r""" Affine transform in 3D
 */

struct __pyx_vtabstruct_4dipy_5align_10transforms_AffineTransform3D {
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};
static struct __pyx_vtabstruct_4dipy_5align_10transforms_AffineTransform3D *__pyx_vtabptr_4dipy_5align_10transforms_AffineTransform3D;


/* "View.MemoryView":302
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 *     cdef object obj
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struct __pyx_vtabstruct_memoryview {
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  PyObject *(*setitem_slice_assignment)(struct __pyx_memoryview_obj *, PyObject *, PyObject *);
  PyObject *(*setitem_slice_assign_scalar)(struct __pyx_memoryview_obj *, struct __pyx_memoryview_obj *, PyObject *);
  PyObject *(*setitem_indexed)(struct __pyx_memoryview_obj *, PyObject *, PyObject *);
  PyObject *(*convert_item_to_object)(struct __pyx_memoryview_obj *, char *);
  PyObject *(*assign_item_from_object)(struct __pyx_memoryview_obj *, char *, PyObject *);
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static struct __pyx_vtabstruct_memoryview *__pyx_vtabptr_memoryview;


/* "View.MemoryView":922
 * 
 * @cname('__pyx_memoryviewslice')
 * cdef class _memoryviewslice(memoryview):             # <<<<<<<<<<<<<<
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 * 
 */

struct __pyx_vtabstruct__memoryviewslice {
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static PyObject *__Pyx_GetBuiltinName(PyObject *name);

static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
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static CYTHON_INLINE int __Pyx_CheckKeywordStrings(PyObject *kwdict, const char* function_name, int kw_allowed);

static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[], \
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static CYTHON_INLINE void __Pyx_ErrRestore(PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetch(PyObject **type, PyObject **value, PyObject **tb);

static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
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static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

static CYTHON_INLINE int  __Pyx_GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
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static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);

#define __Pyx_BUF_MAX_NDIMS %(BUF_MAX_NDIMS)d
#define __Pyx_MEMVIEW_DIRECT   1
#define __Pyx_MEMVIEW_PTR      2
#define __Pyx_MEMVIEW_FULL     4
#define __Pyx_MEMVIEW_CONTIG   8
#define __Pyx_MEMVIEW_STRIDED  16
#define __Pyx_MEMVIEW_FOLLOW   32
#define __Pyx_IS_C_CONTIG 1
#define __Pyx_IS_F_CONTIG 2
static int __Pyx_init_memviewslice(
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static CYTHON_INLINE int __pyx_add_acquisition_count_locked(
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static CYTHON_INLINE int __pyx_sub_acquisition_count_locked(
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#define __pyx_get_slice_count(memview) (*__pyx_get_slice_count_pointer(memview))
#define __PYX_INC_MEMVIEW(slice, have_gil) __Pyx_INC_MEMVIEW(slice, have_gil, __LINE__)
#define __PYX_XDEC_MEMVIEW(slice, have_gil) __Pyx_XDEC_MEMVIEW(slice, have_gil, __LINE__)
static CYTHON_INLINE void __Pyx_INC_MEMVIEW(__Pyx_memviewslice *, int, int);
static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *, int, int);

static void __Pyx_WriteUnraisable(const char *name, int clineno,
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static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
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#include <string.h>

static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals);

static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals);

#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyString_Equals __Pyx_PyUnicode_Equals
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#define __Pyx_PyString_Equals __Pyx_PyBytes_Equals
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#ifndef __PYX_FORCE_INIT_THREADS
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#define UNARY_NEG_WOULD_OVERFLOW(x)            (((x) < 0) & ((unsigned long)(x) == 0-(unsigned long)(x)))

static CYTHON_UNUSED int __pyx_array_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
static PyObject *get_memview(PyObject *__pyx_v_self); /*proto*/
static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *, PyObject *);

static CYTHON_INLINE PyObject* __Pyx_decode_c_string(
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static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb);
static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb);

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);

static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);

#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck) \
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
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static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
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static CYTHON_UNUSED int __pyx_memoryview_getbuffer(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
static PyObject *__pyx_memoryview_transpose(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview__get__base(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_shape(PyObject *__pyx_v_self); /*proto*/
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
    PyListObject* L = (PyListObject*) list;
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static PyObject *__pyx_memoryview_get_strides(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_suboffsets(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_ndim(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_itemsize(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_nbytes(PyObject *__pyx_v_self); /*proto*/
static PyObject *__pyx_memoryview_get_size(PyObject *__pyx_v_self); /*proto*/
static CYTHON_INLINE int __Pyx_PyList_Extend(PyObject* L, PyObject* v) {
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#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE int __Pyx_PyList_Append(PyObject* list, PyObject* x) {
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#define __Pyx_PyList_Append(L,x) PyList_Append(L,x)
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static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname);

static PyObject *__pyx_memoryviewslice__get__base(PyObject *__pyx_v_self); /*proto*/
static int __Pyx_SetVtable(PyObject *dict, void *vtable);

typedef struct {
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struct __Pyx_CodeObjectCache {
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static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static PyCodeObject *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);

static void __Pyx_AddTraceback(const char *funcname, int c_line,
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typedef struct {
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typedef struct {
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  Py_buffer pybuffer;
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static Py_ssize_t __Pyx_zeros[] = {0, 0, 0, 0, 0, 0, 0, 0};
static Py_ssize_t __Pyx_minusones[] = {-1, -1, -1, -1, -1, -1, -1, -1};

static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

static int __pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b);

static int __Pyx_ValidateAndInit_memviewslice(
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static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *);

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);

static PyObject *__pyx_memview_get_double(const char *itemp);
static int __pyx_memview_set_double(const char *itemp, PyObject *obj);

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *);

#if CYTHON_CCOMPLEX
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    #define __Pyx_CREAL(z) ((z).real())
    #define __Pyx_CIMAG(z) ((z).imag())
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    #define __Pyx_CREAL(z) (__real__(z))
    #define __Pyx_CIMAG(z) (__imag__(z))
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    #define __Pyx_CREAL(z) ((z).real)
    #define __Pyx_CIMAG(z) ((z).imag)
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#if (defined(_WIN32) || defined(__clang__)) && defined(__cplusplus) && CYTHON_CCOMPLEX
    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
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    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
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static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

#if CYTHON_CCOMPLEX
    #define __Pyx_c_eqf(a, b)   ((a)==(b))
    #define __Pyx_c_sumf(a, b)  ((a)+(b))
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    #define __Pyx_c_is_zerof(z) ((z)==(float)0)
    #define __Pyx_c_conjf(z)    (::std::conj(z))
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        #define __Pyx_c_absf(z)     (::std::abs(z))
        #define __Pyx_c_powf(a, b)  (::std::pow(a, b))
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    #define __Pyx_c_conjf(z)    (conjf(z))
    #if 1
        #define __Pyx_c_absf(z)     (cabsf(z))
        #define __Pyx_c_powf(a, b)  (cpowf(a, b))
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    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex);
    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex);
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        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex, __pyx_t_float_complex);
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static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);

#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq(a, b)   ((a)==(b))
    #define __Pyx_c_sum(a, b)  ((a)+(b))
    #define __Pyx_c_diff(a, b) ((a)-(b))
    #define __Pyx_c_prod(a, b) ((a)*(b))
    #define __Pyx_c_quot(a, b) ((a)/(b))
    #define __Pyx_c_neg(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero(z) ((z)==(double)0)
    #define __Pyx_c_conj(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs(z)     (::std::abs(z))
        #define __Pyx_c_pow(a, b)  (::std::pow(a, b))
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  #else
    #define __Pyx_c_is_zero(z) ((z)==0)
    #define __Pyx_c_conj(z)    (conj(z))
    #if 1
        #define __Pyx_c_abs(z)     (cabs(z))
        #define __Pyx_c_pow(a, b)  (cpow(a, b))
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    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex, __pyx_t_double_complex);
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static int __pyx_f_4dipy_5align_10transforms_9Transform__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_x, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_9Transform__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_9Transform__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_T); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_22TranslationTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_22TranslationTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_19RotationTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_19RotationTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_19RotationTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_16RigidTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_16RigidTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_16RigidTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_16RigidTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_16RigidTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_16RigidTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_17AffineTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_17AffineTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_17AffineTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
static int __pyx_f_4dipy_5align_10transforms_17AffineTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self, CYTHON_UNUSED __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_17AffineTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta); /* proto*/
static void __pyx_f_4dipy_5align_10transforms_17AffineTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R); /* proto*/
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static int __pyx_pf_4dipy_5align_10transforms_9Transform___cinit__(struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self); /* proto */
static PyObject *__pyx_pf_4dipy_5align_10transforms_9Transform_2jacobian(struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x); /* proto */
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static PyObject *__pyx_pf_4dipy_5align_10transforms_9Transform_8get_number_of_parameters(struct __pyx_obj_4dipy_5align_10transforms_Transform *__pyx_v_self); /* proto */
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static int __pyx_pf_4dipy_5align_10transforms_22TranslationTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_22TranslationTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_19RotationTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_19RotationTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_16RigidTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_16RigidTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_18ScalingTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform2D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_18ScalingTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_17AffineTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_AffineTransform2D *__pyx_v_self); /* proto */
static int __pyx_pf_4dipy_5align_10transforms_17AffineTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self); /* proto */
static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static int __pyx_array_MemoryView_5array___cinit__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_shape, Py_ssize_t __pyx_v_itemsize, PyObject *__pyx_v_format, PyObject *__pyx_v_mode, int __pyx_v_allocate_buffer); /* proto */
static int __pyx_array_getbuffer_MemoryView_5array_2__getbuffer__(struct __pyx_array_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_array_MemoryView_5array_4__dealloc__(struct __pyx_array_obj *__pyx_v_self); /* proto */
static PyObject *get_memview_MemoryView_5array_7memview___get__(struct __pyx_array_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_array_MemoryView_5array_6__getattr__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_attr); /* proto */
static PyObject *__pyx_array_MemoryView_5array_8__getitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item); /* proto */
static int __pyx_array_MemoryView_5array_10__setitem__(struct __pyx_array_obj *__pyx_v_self, PyObject *__pyx_v_item, PyObject *__pyx_v_value); /* proto */
static int __pyx_MemviewEnum_MemoryView_4Enum___init__(struct __pyx_MemviewEnum_obj *__pyx_v_self, PyObject *__pyx_v_name); /* proto */
static PyObject *__pyx_MemviewEnum_MemoryView_4Enum_2__repr__(struct __pyx_MemviewEnum_obj *__pyx_v_self); /* proto */
static int __pyx_memoryview_MemoryView_10memoryview___cinit__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_obj, int __pyx_v_flags, int __pyx_v_dtype_is_object); /* proto */
static void __pyx_memoryview_MemoryView_10memoryview_2__dealloc__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_4__getitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index); /* proto */
static int __pyx_memoryview_MemoryView_10memoryview_6__setitem__(struct __pyx_memoryview_obj *__pyx_v_self, PyObject *__pyx_v_index, PyObject *__pyx_v_value); /* proto */
static int __pyx_memoryview_getbuffer_MemoryView_10memoryview_8__getbuffer__(struct __pyx_memoryview_obj *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static PyObject *__pyx_memoryview_transpose_MemoryView_10memoryview_1T___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview__get__base_MemoryView_10memoryview_4base___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_shape_MemoryView_10memoryview_5shape___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_strides_MemoryView_10memoryview_7strides___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_suboffsets_MemoryView_10memoryview_10suboffsets___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_ndim_MemoryView_10memoryview_4ndim___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_itemsize_MemoryView_10memoryview_8itemsize___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_nbytes_MemoryView_10memoryview_6nbytes___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_get_size_MemoryView_10memoryview_4size___get__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static Py_ssize_t __pyx_memoryview_MemoryView_10memoryview_10__len__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_12__repr__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_14__str__(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_16is_c_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_18is_f_contig(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_20copy(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryview_MemoryView_10memoryview_22copy_fortran(struct __pyx_memoryview_obj *__pyx_v_self); /* proto */
static void __pyx_memoryviewslice_MemoryView_16_memoryviewslice___dealloc__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_memoryviewslice__get__base_MemoryView_16_memoryviewslice_4base___get__(struct __pyx_memoryviewslice_obj *__pyx_v_self); /* proto */
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_Transform(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_TranslationTransform2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_TranslationTransform3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RotationTransform2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RotationTransform3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RigidTransform2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RigidTransform3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_ScalingTransform2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_ScalingTransform3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_AffineTransform2D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_4dipy_5align_10transforms_AffineTransform3D(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_array(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_Enum(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
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static char __pyx_k_np[] = "np";
static char __pyx_k_eye[] = "eye";
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static char __pyx_k_memview[] = "memview";
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static char __pyx_k_MemoryError[] = "MemoryError";
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static char __pyx_k_MemoryView_of_r_at_0x_x[] = "<MemoryView of %r at 0x%x>";
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static char __pyx_k_Invalid_shape_in_axis_d_d[] = "Invalid shape in axis %d: %d.";
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static PyObject *__pyx_n_s_unpack;
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/* "dipy/align/transforms.pyx":46
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  Py_ssize_t __pyx_t_19;
  Py_ssize_t __pyx_t_20;
  Py_ssize_t __pyx_t_21;

  /* "dipy/align/transforms.pyx":227
 *             (independent of x)
 *         """
 *         J[0, 0], J[0, 1], J[0, 2] = 1.0, 0.0, 0.0             # <<<<<<<<<<<<<<
 *         J[1, 0], J[1, 1], J[1, 2] = 0.0, 1.0, 0.0
 *         J[2, 0], J[2, 1], J[2, 2] = 0.0, 0.0, 1.0
 */
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  __pyx_t_2 = 0.0;
  __pyx_t_3 = 0.0;
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  __pyx_t_5 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_4 * __pyx_v_J.strides[0]) ) + __pyx_t_5 * __pyx_v_J.strides[1]) )) = __pyx_t_1;
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  __pyx_t_7 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_6 * __pyx_v_J.strides[0]) ) + __pyx_t_7 * __pyx_v_J.strides[1]) )) = __pyx_t_2;
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  __pyx_t_9 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_8 * __pyx_v_J.strides[0]) ) + __pyx_t_9 * __pyx_v_J.strides[1]) )) = __pyx_t_3;

  /* "dipy/align/transforms.pyx":228
 *         """
 *         J[0, 0], J[0, 1], J[0, 2] = 1.0, 0.0, 0.0
 *         J[1, 0], J[1, 1], J[1, 2] = 0.0, 1.0, 0.0             # <<<<<<<<<<<<<<
 *         J[2, 0], J[2, 1], J[2, 2] = 0.0, 0.0, 1.0
 *         # This Jacobian does not depend on x (it's constant): return 1
 */
  __pyx_t_3 = 0.0;
  __pyx_t_2 = 1.0;
  __pyx_t_1 = 0.0;
  __pyx_t_10 = 1;
  __pyx_t_11 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_10 * __pyx_v_J.strides[0]) ) + __pyx_t_11 * __pyx_v_J.strides[1]) )) = __pyx_t_3;
  __pyx_t_12 = 1;
  __pyx_t_13 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_12 * __pyx_v_J.strides[0]) ) + __pyx_t_13 * __pyx_v_J.strides[1]) )) = __pyx_t_2;
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  __pyx_t_15 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_14 * __pyx_v_J.strides[0]) ) + __pyx_t_15 * __pyx_v_J.strides[1]) )) = __pyx_t_1;

  /* "dipy/align/transforms.pyx":229
 *         J[0, 0], J[0, 1], J[0, 2] = 1.0, 0.0, 0.0
 *         J[1, 0], J[1, 1], J[1, 2] = 0.0, 1.0, 0.0
 *         J[2, 0], J[2, 1], J[2, 2] = 0.0, 0.0, 1.0             # <<<<<<<<<<<<<<
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 *         return 1
 */
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  __pyx_t_2 = 0.0;
  __pyx_t_3 = 1.0;
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  __pyx_t_17 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_16 * __pyx_v_J.strides[0]) ) + __pyx_t_17 * __pyx_v_J.strides[1]) )) = __pyx_t_1;
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  __pyx_t_19 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_18 * __pyx_v_J.strides[0]) ) + __pyx_t_19 * __pyx_v_J.strides[1]) )) = __pyx_t_2;
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  __pyx_t_21 = 2;
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  /* "dipy/align/transforms.pyx":231
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 */
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  /* "dipy/align/transforms.pyx":197
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 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
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  /* function exit code */
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/* "dipy/align/transforms.pyx":233
 *         return 1
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
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 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
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  /* "dipy/align/transforms.pyx":243
 *             buffer to write the parameters of the 3D translation transform
 *         """
 *         theta[:3] = 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
 */
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  __pyx_t_1.memview = __pyx_v_theta.memview;
  __PYX_INC_MEMVIEW(&__pyx_t_1, 0);
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  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);

  /* "dipy/align/transforms.pyx":233
 *         return 1
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
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 *         Sets in theta the parameter values corresponding to the identity
 */

  /* function exit code */
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/* "dipy/align/transforms.pyx":245
 *         theta[:3] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 3D translation transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_22TranslationTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
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  double __pyx_t_2;
  double __pyx_t_3;
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  Py_ssize_t __pyx_t_21;
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  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;

  /* "dipy/align/transforms.pyx":255
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 *         """
 *         R[0, 0], R[0, 1], R[0, 2], R[0, 3] = 1, 0, 0, theta[0]             # <<<<<<<<<<<<<<
 *         R[1, 0], R[1, 1], R[1, 2], R[1, 3] = 0, 1, 0, theta[1]
 *         R[2, 0], R[2, 1], R[2, 2], R[2, 3] = 0, 0, 1, theta[2]
 */
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  __pyx_t_2 = 0.0;
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  /* "dipy/align/transforms.pyx":256
 *         """
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 *         R[1, 0], R[1, 1], R[1, 2], R[1, 3] = 0, 1, 0, theta[1]             # <<<<<<<<<<<<<<
 *         R[2, 0], R[2, 1], R[2, 2], R[2, 3] = 0, 0, 1, theta[2]
 *         R[3, 0], R[3, 1], R[3, 2], R[3, 3] = 0, 0, 0, 1
 */
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  __pyx_t_16 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_15 * __pyx_v_R.strides[0]) ) + __pyx_t_16 * __pyx_v_R.strides[1]) )) = __pyx_t_5;
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  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_17 * __pyx_v_R.strides[0]) ) + __pyx_t_18 * __pyx_v_R.strides[1]) )) = __pyx_t_3;
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 *         R[1, 0], R[1, 1], R[1, 2], R[1, 3] = 0, 1, 0, theta[1]
 *         R[2, 0], R[2, 1], R[2, 2], R[2, 3] = 0, 0, 1, theta[2]             # <<<<<<<<<<<<<<
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  /* "dipy/align/transforms.pyx":258
 *         R[1, 0], R[1, 1], R[1, 2], R[1, 3] = 0, 1, 0, theta[1]
 *         R[2, 0], R[2, 1], R[2, 2], R[2, 3] = 0, 0, 1, theta[2]
 *         R[3, 0], R[3, 1], R[3, 2], R[3, 3] = 0, 0, 0, 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
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  /* function exit code */
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/* "dipy/align/transforms.pyx":262
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/* "dipy/align/transforms.pyx":268
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  double __pyx_v_px;
  double __pyx_v_py;
  int __pyx_r;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;
  Py_ssize_t __pyx_t_6;
  Py_ssize_t __pyx_t_7;
  Py_ssize_t __pyx_t_8;

  /* "dipy/align/transforms.pyx":296
 *         '''
 *         cdef:
 *             double st = sin(theta[0])             # <<<<<<<<<<<<<<
 *             double ct = cos(theta[0])
 *             double px = x[0], py = x[1]
 */
  __pyx_t_1 = 0;
  __pyx_v_st = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":297
 *         cdef:
 *             double st = sin(theta[0])
 *             double ct = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double px = x[0], py = x[1]
 * 
 */
  __pyx_t_2 = 0;
  __pyx_v_ct = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_2 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":298
 *             double st = sin(theta[0])
 *             double ct = cos(theta[0])
 *             double px = x[0], py = x[1]             # <<<<<<<<<<<<<<
 * 
 *         J[0, 0] = -px * st - py * ct
 */
  __pyx_t_3 = 0;
  __pyx_v_px = (*((double *) ( /* dim=0 */ (__pyx_v_x.data + __pyx_t_3 * __pyx_v_x.strides[0]) )));
  __pyx_t_4 = 1;
  __pyx_v_py = (*((double *) ( /* dim=0 */ (__pyx_v_x.data + __pyx_t_4 * __pyx_v_x.strides[0]) )));

  /* "dipy/align/transforms.pyx":300
 *             double px = x[0], py = x[1]
 * 
 *         J[0, 0] = -px * st - py * ct             # <<<<<<<<<<<<<<
 *         J[1, 0] = px * ct - py * st
 *         # This Jacobian depends on x (it's not constant): return 0
 */
  __pyx_t_5 = 0;
  __pyx_t_6 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_5 * __pyx_v_J.strides[0]) ) + __pyx_t_6 * __pyx_v_J.strides[1]) )) = (((-__pyx_v_px) * __pyx_v_st) - (__pyx_v_py * __pyx_v_ct));

  /* "dipy/align/transforms.pyx":301
 * 
 *         J[0, 0] = -px * st - py * ct
 *         J[1, 0] = px * ct - py * st             # <<<<<<<<<<<<<<
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0
 */
  __pyx_t_7 = 1;
  __pyx_t_8 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_7 * __pyx_v_J.strides[0]) ) + __pyx_t_8 * __pyx_v_J.strides[1]) )) = ((__pyx_v_px * __pyx_v_ct) - (__pyx_v_py * __pyx_v_st));

  /* "dipy/align/transforms.pyx":303
 *         J[1, 0] = px * ct - py * st
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:
 */
  __pyx_r = 0;
  goto __pyx_L0;

  /* "dipy/align/transforms.pyx":268
 *         self.number_of_parameters = 1
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
 *         r''' Jacobian matrix of a 2D rotation with parameter theta, at x
 * 
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "dipy/align/transforms.pyx":305
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_19RotationTransform2D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
  Py_ssize_t __pyx_t_1;

  /* "dipy/align/transforms.pyx":315
 *             buffer to write the parameters of the 2D rotation transform
 *         """
 *         theta[0] = 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
 */
  __pyx_t_1 = 0;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) )) = 0.0;

  /* "dipy/align/transforms.pyx":305
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

  /* function exit code */
}

/* "dipy/align/transforms.pyx":317
 *         theta[0] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 2D rotation transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_19RotationTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
  double __pyx_v_ct;
  double __pyx_v_st;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  double __pyx_t_3;
  double __pyx_t_4;
  double __pyx_t_5;
  Py_ssize_t __pyx_t_6;
  Py_ssize_t __pyx_t_7;
  Py_ssize_t __pyx_t_8;
  Py_ssize_t __pyx_t_9;
  Py_ssize_t __pyx_t_10;
  Py_ssize_t __pyx_t_11;
  Py_ssize_t __pyx_t_12;
  Py_ssize_t __pyx_t_13;
  Py_ssize_t __pyx_t_14;
  Py_ssize_t __pyx_t_15;
  Py_ssize_t __pyx_t_16;
  Py_ssize_t __pyx_t_17;
  Py_ssize_t __pyx_t_18;
  Py_ssize_t __pyx_t_19;
  Py_ssize_t __pyx_t_20;
  Py_ssize_t __pyx_t_21;
  Py_ssize_t __pyx_t_22;
  Py_ssize_t __pyx_t_23;

  /* "dipy/align/transforms.pyx":328
 *         """
 *         cdef:
 *             double ct = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, 0
 */
  __pyx_t_1 = 0;
  __pyx_v_ct = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":329
 *         cdef:
 *             double ct = cos(theta[0])
 *             double st = sin(theta[0])             # <<<<<<<<<<<<<<
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, 0
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, 0
 */
  __pyx_t_2 = 0;
  __pyx_v_st = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_2 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":330
 *             double ct = cos(theta[0])
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, 0             # <<<<<<<<<<<<<<
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, 0
 *         R[2, 0], R[2, 1], R[2, 2] = 0, 0, 1
 */
  __pyx_t_3 = __pyx_v_ct;
  __pyx_t_4 = (-__pyx_v_st);
  __pyx_t_5 = 0.0;
  __pyx_t_6 = 0;
  __pyx_t_7 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_6 * __pyx_v_R.strides[0]) ) + __pyx_t_7 * __pyx_v_R.strides[1]) )) = __pyx_t_3;
  __pyx_t_8 = 0;
  __pyx_t_9 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_8 * __pyx_v_R.strides[0]) ) + __pyx_t_9 * __pyx_v_R.strides[1]) )) = __pyx_t_4;
  __pyx_t_10 = 0;
  __pyx_t_11 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_10 * __pyx_v_R.strides[0]) ) + __pyx_t_11 * __pyx_v_R.strides[1]) )) = __pyx_t_5;

  /* "dipy/align/transforms.pyx":331
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, 0
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, 0             # <<<<<<<<<<<<<<
 *         R[2, 0], R[2, 1], R[2, 2] = 0, 0, 1
 * 
 */
  __pyx_t_5 = __pyx_v_st;
  __pyx_t_4 = __pyx_v_ct;
  __pyx_t_3 = 0.0;
  __pyx_t_12 = 1;
  __pyx_t_13 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_12 * __pyx_v_R.strides[0]) ) + __pyx_t_13 * __pyx_v_R.strides[1]) )) = __pyx_t_5;
  __pyx_t_14 = 1;
  __pyx_t_15 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_14 * __pyx_v_R.strides[0]) ) + __pyx_t_15 * __pyx_v_R.strides[1]) )) = __pyx_t_4;
  __pyx_t_16 = 1;
  __pyx_t_17 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_16 * __pyx_v_R.strides[0]) ) + __pyx_t_17 * __pyx_v_R.strides[1]) )) = __pyx_t_3;

  /* "dipy/align/transforms.pyx":332
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, 0
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, 0
 *         R[2, 0], R[2, 1], R[2, 2] = 0, 0, 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_t_3 = 0.0;
  __pyx_t_4 = 0.0;
  __pyx_t_5 = 1.0;
  __pyx_t_18 = 2;
  __pyx_t_19 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_18 * __pyx_v_R.strides[0]) ) + __pyx_t_19 * __pyx_v_R.strides[1]) )) = __pyx_t_3;
  __pyx_t_20 = 2;
  __pyx_t_21 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_20 * __pyx_v_R.strides[0]) ) + __pyx_t_21 * __pyx_v_R.strides[1]) )) = __pyx_t_4;
  __pyx_t_22 = 2;
  __pyx_t_23 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_22 * __pyx_v_R.strides[0]) ) + __pyx_t_23 * __pyx_v_R.strides[1]) )) = __pyx_t_5;

  /* "dipy/align/transforms.pyx":317
 *         theta[0] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 2D rotation transform
 * 
 */

  /* function exit code */
}

/* "dipy/align/transforms.pyx":336
 * 
 * cdef class RotationTransform3D(Transform):
 *     def __init__(self):             # <<<<<<<<<<<<<<
 *         r""" Rotation transform in 3D
 *         """
 */

/* Python wrapper */
static int __pyx_pw_4dipy_5align_10transforms_19RotationTransform3D_1__init__(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static char __pyx_doc_4dipy_5align_10transforms_19RotationTransform3D___init__[] = " Rotation transform in 3D\n        ";
#if CYTHON_COMPILING_IN_CPYTHON
struct wrapperbase __pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform3D___init__;
#endif
static int __pyx_pw_4dipy_5align_10transforms_19RotationTransform3D_1__init__(PyObject *__pyx_v_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
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  if (unlikely(__pyx_kwds) && unlikely(PyDict_Size(__pyx_kwds) > 0) && unlikely(!__Pyx_CheckKeywordStrings(__pyx_kwds, "__init__", 0))) return -1;
  __pyx_r = __pyx_pf_4dipy_5align_10transforms_19RotationTransform3D___init__(((struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *)__pyx_v_self));

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static int __pyx_pf_4dipy_5align_10transforms_19RotationTransform3D___init__(struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self) {
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__init__", 0);

  /* "dipy/align/transforms.pyx":339
 *         r""" Rotation transform in 3D
 *         """
 *         self.dim = 3             # <<<<<<<<<<<<<<
 *         self.number_of_parameters = 3
 * 
 */
  __pyx_v_self->__pyx_base.dim = 3;

  /* "dipy/align/transforms.pyx":340
 *         """
 *         self.dim = 3
 *         self.number_of_parameters = 3             # <<<<<<<<<<<<<<
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:
 */
  __pyx_v_self->__pyx_base.number_of_parameters = 3;

  /* "dipy/align/transforms.pyx":336
 * 
 * cdef class RotationTransform3D(Transform):
 *     def __init__(self):             # <<<<<<<<<<<<<<
 *         r""" Rotation transform in 3D
 *         """
 */

  /* function exit code */
  __pyx_r = 0;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
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/* "dipy/align/transforms.pyx":342
 *         self.number_of_parameters = 3
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
 *         r''' Jacobian matrix of a 3D rotation with parameters theta, at x
 * 
 */

static int __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J) {
  double __pyx_v_sa;
  double __pyx_v_ca;
  double __pyx_v_sb;
  double __pyx_v_cb;
  double __pyx_v_sc;
  double __pyx_v_cc;
  double __pyx_v_px;
  double __pyx_v_py;
  double __pyx_v_pz;
  int __pyx_r;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;
  Py_ssize_t __pyx_t_6;
  Py_ssize_t __pyx_t_7;
  Py_ssize_t __pyx_t_8;
  Py_ssize_t __pyx_t_9;
  Py_ssize_t __pyx_t_10;
  Py_ssize_t __pyx_t_11;
  Py_ssize_t __pyx_t_12;
  Py_ssize_t __pyx_t_13;
  Py_ssize_t __pyx_t_14;
  Py_ssize_t __pyx_t_15;
  Py_ssize_t __pyx_t_16;
  Py_ssize_t __pyx_t_17;
  Py_ssize_t __pyx_t_18;
  Py_ssize_t __pyx_t_19;
  Py_ssize_t __pyx_t_20;
  Py_ssize_t __pyx_t_21;
  Py_ssize_t __pyx_t_22;
  Py_ssize_t __pyx_t_23;
  Py_ssize_t __pyx_t_24;
  Py_ssize_t __pyx_t_25;
  Py_ssize_t __pyx_t_26;
  Py_ssize_t __pyx_t_27;

  /* "dipy/align/transforms.pyx":361
 *         '''
 *         cdef:
 *             double sa = sin(theta[0])             # <<<<<<<<<<<<<<
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 */
  __pyx_t_1 = 0;
  __pyx_v_sa = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":362
 *         cdef:
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 */
  __pyx_t_2 = 0;
  __pyx_v_ca = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_2 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":363
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])             # <<<<<<<<<<<<<<
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 */
  __pyx_t_3 = 1;
  __pyx_v_sb = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_3 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":364
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])             # <<<<<<<<<<<<<<
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])
 */
  __pyx_t_4 = 1;
  __pyx_v_cb = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_4 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":365
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])             # <<<<<<<<<<<<<<
 *             double cc = cos(theta[2])
 *             double px = x[0], py = x[1], pz = x[2]
 */
  __pyx_t_5 = 2;
  __pyx_v_sc = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_5 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":366
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])             # <<<<<<<<<<<<<<
 *             double px = x[0], py = x[1], pz = x[2]
 * 
 */
  __pyx_t_6 = 2;
  __pyx_v_cc = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_6 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":367
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])
 *             double px = x[0], py = x[1], pz = x[2]             # <<<<<<<<<<<<<<
 * 
 *         J[0, 0] = (-sc * ca * sb) * px + (sc * sa) * py + (sc * ca * cb) * pz
 */
  __pyx_t_7 = 0;
  __pyx_v_px = (*((double *) ( /* dim=0 */ (__pyx_v_x.data + __pyx_t_7 * __pyx_v_x.strides[0]) )));
  __pyx_t_8 = 1;
  __pyx_v_py = (*((double *) ( /* dim=0 */ (__pyx_v_x.data + __pyx_t_8 * __pyx_v_x.strides[0]) )));
  __pyx_t_9 = 2;
  __pyx_v_pz = (*((double *) ( /* dim=0 */ (__pyx_v_x.data + __pyx_t_9 * __pyx_v_x.strides[0]) )));

  /* "dipy/align/transforms.pyx":369
 *             double px = x[0], py = x[1], pz = x[2]
 * 
 *         J[0, 0] = (-sc * ca * sb) * px + (sc * sa) * py + (sc * ca * cb) * pz             # <<<<<<<<<<<<<<
 *         J[1, 0] = (cc * ca * sb) * px + (-cc * sa) * py + (-cc * ca * cb) * pz
 *         J[2, 0] = (sa * sb) * px + ca * py + (-sa * cb) * pz
 */
  __pyx_t_10 = 0;
  __pyx_t_11 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_10 * __pyx_v_J.strides[0]) ) + __pyx_t_11 * __pyx_v_J.strides[1]) )) = ((((((-__pyx_v_sc) * __pyx_v_ca) * __pyx_v_sb) * __pyx_v_px) + ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_py)) + (((__pyx_v_sc * __pyx_v_ca) * __pyx_v_cb) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":370
 * 
 *         J[0, 0] = (-sc * ca * sb) * px + (sc * sa) * py + (sc * ca * cb) * pz
 *         J[1, 0] = (cc * ca * sb) * px + (-cc * sa) * py + (-cc * ca * cb) * pz             # <<<<<<<<<<<<<<
 *         J[2, 0] = (sa * sb) * px + ca * py + (-sa * cb) * pz
 * 
 */
  __pyx_t_12 = 1;
  __pyx_t_13 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_12 * __pyx_v_J.strides[0]) ) + __pyx_t_13 * __pyx_v_J.strides[1]) )) = (((((__pyx_v_cc * __pyx_v_ca) * __pyx_v_sb) * __pyx_v_px) + (((-__pyx_v_cc) * __pyx_v_sa) * __pyx_v_py)) + ((((-__pyx_v_cc) * __pyx_v_ca) * __pyx_v_cb) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":371
 *         J[0, 0] = (-sc * ca * sb) * px + (sc * sa) * py + (sc * ca * cb) * pz
 *         J[1, 0] = (cc * ca * sb) * px + (-cc * sa) * py + (-cc * ca * cb) * pz
 *         J[2, 0] = (sa * sb) * px + ca * py + (-sa * cb) * pz             # <<<<<<<<<<<<<<
 * 
 *         J[0, 1] = (-cc * sb - sc * sa * cb) * px + (cc * cb - sc * sa * sb) * pz
 */
  __pyx_t_14 = 2;
  __pyx_t_15 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_14 * __pyx_v_J.strides[0]) ) + __pyx_t_15 * __pyx_v_J.strides[1]) )) = ((((__pyx_v_sa * __pyx_v_sb) * __pyx_v_px) + (__pyx_v_ca * __pyx_v_py)) + (((-__pyx_v_sa) * __pyx_v_cb) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":373
 *         J[2, 0] = (sa * sb) * px + ca * py + (-sa * cb) * pz
 * 
 *         J[0, 1] = (-cc * sb - sc * sa * cb) * px + (cc * cb - sc * sa * sb) * pz             # <<<<<<<<<<<<<<
 *         J[1, 1] = (-sc * sb + cc * sa * cb) * px + (sc * cb + cc * sa * sb) * pz
 *         J[2, 1] = (-ca * cb) * px + (-ca * sb) * pz
 */
  __pyx_t_16 = 0;
  __pyx_t_17 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_16 * __pyx_v_J.strides[0]) ) + __pyx_t_17 * __pyx_v_J.strides[1]) )) = (((((-__pyx_v_cc) * __pyx_v_sb) - ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_cb)) * __pyx_v_px) + (((__pyx_v_cc * __pyx_v_cb) - ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_sb)) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":374
 * 
 *         J[0, 1] = (-cc * sb - sc * sa * cb) * px + (cc * cb - sc * sa * sb) * pz
 *         J[1, 1] = (-sc * sb + cc * sa * cb) * px + (sc * cb + cc * sa * sb) * pz             # <<<<<<<<<<<<<<
 *         J[2, 1] = (-ca * cb) * px + (-ca * sb) * pz
 * 
 */
  __pyx_t_18 = 1;
  __pyx_t_19 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_18 * __pyx_v_J.strides[0]) ) + __pyx_t_19 * __pyx_v_J.strides[1]) )) = (((((-__pyx_v_sc) * __pyx_v_sb) + ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_cb)) * __pyx_v_px) + (((__pyx_v_sc * __pyx_v_cb) + ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_sb)) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":375
 *         J[0, 1] = (-cc * sb - sc * sa * cb) * px + (cc * cb - sc * sa * sb) * pz
 *         J[1, 1] = (-sc * sb + cc * sa * cb) * px + (sc * cb + cc * sa * sb) * pz
 *         J[2, 1] = (-ca * cb) * px + (-ca * sb) * pz             # <<<<<<<<<<<<<<
 * 
 *         J[0, 2] = (-sc * cb - cc * sa * sb) * px + (-cc * ca) * py + \
 */
  __pyx_t_20 = 2;
  __pyx_t_21 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_20 * __pyx_v_J.strides[0]) ) + __pyx_t_21 * __pyx_v_J.strides[1]) )) = ((((-__pyx_v_ca) * __pyx_v_cb) * __pyx_v_px) + (((-__pyx_v_ca) * __pyx_v_sb) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":377
 *         J[2, 1] = (-ca * cb) * px + (-ca * sb) * pz
 * 
 *         J[0, 2] = (-sc * cb - cc * sa * sb) * px + (-cc * ca) * py + \             # <<<<<<<<<<<<<<
 *                   (-sc * sb + cc * sa * cb) * pz
 *         J[1, 2] = (cc * cb - sc * sa * sb) * px + (-sc * ca) * py + \
 */
  __pyx_t_22 = 0;
  __pyx_t_23 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_22 * __pyx_v_J.strides[0]) ) + __pyx_t_23 * __pyx_v_J.strides[1]) )) = ((((((-__pyx_v_sc) * __pyx_v_cb) - ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_sb)) * __pyx_v_px) + (((-__pyx_v_cc) * __pyx_v_ca) * __pyx_v_py)) + ((((-__pyx_v_sc) * __pyx_v_sb) + ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_cb)) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":379
 *         J[0, 2] = (-sc * cb - cc * sa * sb) * px + (-cc * ca) * py + \
 *                   (-sc * sb + cc * sa * cb) * pz
 *         J[1, 2] = (cc * cb - sc * sa * sb) * px + (-sc * ca) * py + \             # <<<<<<<<<<<<<<
 *                   (cc * sb + sc * sa * cb) * pz
 *         J[2, 2] = 0
 */
  __pyx_t_24 = 1;
  __pyx_t_25 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_24 * __pyx_v_J.strides[0]) ) + __pyx_t_25 * __pyx_v_J.strides[1]) )) = (((((__pyx_v_cc * __pyx_v_cb) - ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_sb)) * __pyx_v_px) + (((-__pyx_v_sc) * __pyx_v_ca) * __pyx_v_py)) + (((__pyx_v_cc * __pyx_v_sb) + ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_cb)) * __pyx_v_pz));

  /* "dipy/align/transforms.pyx":381
 *         J[1, 2] = (cc * cb - sc * sa * sb) * px + (-sc * ca) * py + \
 *                   (cc * sb + sc * sa * cb) * pz
 *         J[2, 2] = 0             # <<<<<<<<<<<<<<
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0
 */
  __pyx_t_26 = 2;
  __pyx_t_27 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_26 * __pyx_v_J.strides[0]) ) + __pyx_t_27 * __pyx_v_J.strides[1]) )) = 0.0;

  /* "dipy/align/transforms.pyx":383
 *         J[2, 2] = 0
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:
 */
  __pyx_r = 0;
  goto __pyx_L0;

  /* "dipy/align/transforms.pyx":342
 *         self.number_of_parameters = 3
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
 *         r''' Jacobian matrix of a 3D rotation with parameters theta, at x
 * 
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "dipy/align/transforms.pyx":385
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
  __Pyx_memviewslice __pyx_t_1 = { 0, 0, { 0 }, { 0 }, { 0 } };
  int __pyx_t_2;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;

  /* "dipy/align/transforms.pyx":395
 *             buffer to write the parameters of the 3D rotation transform
 *         """
 *         theta[:3] = 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
 */
  __pyx_t_2 = -1;
  __pyx_t_1.data = __pyx_v_theta.data;
  __pyx_t_1.memview = __pyx_v_theta.memview;
  __PYX_INC_MEMVIEW(&__pyx_t_1, 0);
  if (unlikely(__pyx_memoryview_slice_memviewslice(
    &__pyx_t_1,
    __pyx_v_theta.shape[0], __pyx_v_theta.strides[0], __pyx_v_theta.suboffsets[0],
    0,
    0,
    &__pyx_t_2,
    0,
    3,
    0,
    0,
    1,
    0,
    1) < 0))
{
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 395; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}

{
      double __pyx_temp_scalar = 0.0;
      {
          Py_ssize_t __pyx_temp_extent_0 = __pyx_t_1.shape[0];
          Py_ssize_t __pyx_temp_stride_0 = __pyx_t_1.strides[0];
          char *__pyx_temp_pointer_0;
          Py_ssize_t __pyx_temp_idx_0;
          __pyx_temp_pointer_0 = __pyx_t_1.data;
          for (__pyx_temp_idx_0 = 0; __pyx_temp_idx_0 < __pyx_temp_extent_0; __pyx_temp_idx_0++) {
            *((double *) __pyx_temp_pointer_0) = __pyx_temp_scalar;
            __pyx_temp_pointer_0 += __pyx_temp_stride_0;
          }
      }
  }
  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);

  /* "dipy/align/transforms.pyx":385
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

  /* function exit code */
  goto __pyx_L0;
  __pyx_L1_error:;
  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);
  __Pyx_WriteUnraisable("dipy.align.transforms.RotationTransform3D._get_identity_parameters", __pyx_clineno, __pyx_lineno, __pyx_filename, 0);
  __pyx_L0:;
}

/* "dipy/align/transforms.pyx":397
 *         theta[:3] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 3D rotation transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_19RotationTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
  double __pyx_v_sa;
  double __pyx_v_ca;
  double __pyx_v_sb;
  double __pyx_v_cb;
  double __pyx_v_sc;
  double __pyx_v_cc;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;
  Py_ssize_t __pyx_t_6;
  double __pyx_t_7;
  double __pyx_t_8;
  double __pyx_t_9;
  double __pyx_t_10;
  Py_ssize_t __pyx_t_11;
  Py_ssize_t __pyx_t_12;
  Py_ssize_t __pyx_t_13;
  Py_ssize_t __pyx_t_14;
  Py_ssize_t __pyx_t_15;
  Py_ssize_t __pyx_t_16;
  Py_ssize_t __pyx_t_17;
  Py_ssize_t __pyx_t_18;
  Py_ssize_t __pyx_t_19;
  Py_ssize_t __pyx_t_20;
  Py_ssize_t __pyx_t_21;
  Py_ssize_t __pyx_t_22;
  Py_ssize_t __pyx_t_23;
  Py_ssize_t __pyx_t_24;
  Py_ssize_t __pyx_t_25;
  Py_ssize_t __pyx_t_26;
  Py_ssize_t __pyx_t_27;
  Py_ssize_t __pyx_t_28;
  Py_ssize_t __pyx_t_29;
  Py_ssize_t __pyx_t_30;
  Py_ssize_t __pyx_t_31;
  Py_ssize_t __pyx_t_32;
  Py_ssize_t __pyx_t_33;
  Py_ssize_t __pyx_t_34;
  Py_ssize_t __pyx_t_35;
  Py_ssize_t __pyx_t_36;
  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;
  Py_ssize_t __pyx_t_40;
  Py_ssize_t __pyx_t_41;
  Py_ssize_t __pyx_t_42;

  /* "dipy/align/transforms.pyx":415
 *         """
 *         cdef:
 *             double sa = sin(theta[0])             # <<<<<<<<<<<<<<
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 */
  __pyx_t_1 = 0;
  __pyx_v_sa = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":416
 *         cdef:
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 */
  __pyx_t_2 = 0;
  __pyx_v_ca = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_2 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":417
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])             # <<<<<<<<<<<<<<
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 */
  __pyx_t_3 = 1;
  __pyx_v_sb = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_3 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":418
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])             # <<<<<<<<<<<<<<
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])
 */
  __pyx_t_4 = 1;
  __pyx_v_cb = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_4 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":419
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])             # <<<<<<<<<<<<<<
 *             double cc = cos(theta[2])
 * 
 */
  __pyx_t_5 = 2;
  __pyx_v_sc = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_5 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":420
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])             # <<<<<<<<<<<<<<
 * 
 *         R[0,0], R[0,1], R[0,2], R[0, 3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, 0
 */
  __pyx_t_6 = 2;
  __pyx_v_cc = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_6 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":422
 *             double cc = cos(theta[2])
 * 
 *         R[0,0], R[0,1], R[0,2], R[0, 3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, 0             # <<<<<<<<<<<<<<
 *         R[1,0], R[1,1], R[1,2], R[1, 3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, 0
 *         R[2,0], R[2,1], R[2,2], R[2, 3] = -ca*sb, sa, ca*cb, 0
 */
  __pyx_t_7 = ((__pyx_v_cc * __pyx_v_cb) - ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_sb));
  __pyx_t_8 = ((-__pyx_v_sc) * __pyx_v_ca);
  __pyx_t_9 = ((__pyx_v_cc * __pyx_v_sb) + ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_cb));
  __pyx_t_10 = 0.0;
  __pyx_t_11 = 0;
  __pyx_t_12 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_11 * __pyx_v_R.strides[0]) ) + __pyx_t_12 * __pyx_v_R.strides[1]) )) = __pyx_t_7;
  __pyx_t_13 = 0;
  __pyx_t_14 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_13 * __pyx_v_R.strides[0]) ) + __pyx_t_14 * __pyx_v_R.strides[1]) )) = __pyx_t_8;
  __pyx_t_15 = 0;
  __pyx_t_16 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_15 * __pyx_v_R.strides[0]) ) + __pyx_t_16 * __pyx_v_R.strides[1]) )) = __pyx_t_9;
  __pyx_t_17 = 0;
  __pyx_t_18 = 3;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_17 * __pyx_v_R.strides[0]) ) + __pyx_t_18 * __pyx_v_R.strides[1]) )) = __pyx_t_10;

  /* "dipy/align/transforms.pyx":423
 * 
 *         R[0,0], R[0,1], R[0,2], R[0, 3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, 0
 *         R[1,0], R[1,1], R[1,2], R[1, 3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, 0             # <<<<<<<<<<<<<<
 *         R[2,0], R[2,1], R[2,2], R[2, 3] = -ca*sb, sa, ca*cb, 0
 *         R[3,0], R[3,1], R[3,2], R[3, 3] = 0, 0, 0, 1
 */
  __pyx_t_10 = ((__pyx_v_sc * __pyx_v_cb) + ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_sb));
  __pyx_t_9 = (__pyx_v_cc * __pyx_v_ca);
  __pyx_t_8 = ((__pyx_v_sc * __pyx_v_sb) - ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_cb));
  __pyx_t_7 = 0.0;
  __pyx_t_19 = 1;
  __pyx_t_20 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_19 * __pyx_v_R.strides[0]) ) + __pyx_t_20 * __pyx_v_R.strides[1]) )) = __pyx_t_10;
  __pyx_t_21 = 1;
  __pyx_t_22 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_21 * __pyx_v_R.strides[0]) ) + __pyx_t_22 * __pyx_v_R.strides[1]) )) = __pyx_t_9;
  __pyx_t_23 = 1;
  __pyx_t_24 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_23 * __pyx_v_R.strides[0]) ) + __pyx_t_24 * __pyx_v_R.strides[1]) )) = __pyx_t_8;
  __pyx_t_25 = 1;
  __pyx_t_26 = 3;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_25 * __pyx_v_R.strides[0]) ) + __pyx_t_26 * __pyx_v_R.strides[1]) )) = __pyx_t_7;

  /* "dipy/align/transforms.pyx":424
 *         R[0,0], R[0,1], R[0,2], R[0, 3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, 0
 *         R[1,0], R[1,1], R[1,2], R[1, 3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, 0
 *         R[2,0], R[2,1], R[2,2], R[2, 3] = -ca*sb, sa, ca*cb, 0             # <<<<<<<<<<<<<<
 *         R[3,0], R[3,1], R[3,2], R[3, 3] = 0, 0, 0, 1
 * 
 */
  __pyx_t_7 = ((-__pyx_v_ca) * __pyx_v_sb);
  __pyx_t_8 = __pyx_v_sa;
  __pyx_t_9 = (__pyx_v_ca * __pyx_v_cb);
  __pyx_t_10 = 0.0;
  __pyx_t_27 = 2;
  __pyx_t_28 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_27 * __pyx_v_R.strides[0]) ) + __pyx_t_28 * __pyx_v_R.strides[1]) )) = __pyx_t_7;
  __pyx_t_29 = 2;
  __pyx_t_30 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_29 * __pyx_v_R.strides[0]) ) + __pyx_t_30 * __pyx_v_R.strides[1]) )) = __pyx_t_8;
  __pyx_t_31 = 2;
  __pyx_t_32 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_31 * __pyx_v_R.strides[0]) ) + __pyx_t_32 * __pyx_v_R.strides[1]) )) = __pyx_t_9;
  __pyx_t_33 = 2;
  __pyx_t_34 = 3;
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 * 
 * 
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 * 
 */

  /* function exit code */
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/* "dipy/align/transforms.pyx":429
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 */

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static int __pyx_pf_4dipy_5align_10transforms_16RigidTransform2D___init__(struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self) {
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  /* "dipy/align/transforms.pyx":437
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 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:
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  /* "dipy/align/transforms.pyx":429
 * 
 * cdef class RigidTransform2D(Transform):
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 *         The parameter vector theta of length 3 is interpreted as follows:
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/* "dipy/align/transforms.pyx":439
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 *         r''' Jacobian matrix of a 2D rigid transform (rotation + translation)
 * 
 */

static int __pyx_f_4dipy_5align_10transforms_16RigidTransform2D__jacobian(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_x, __Pyx_memviewslice __pyx_v_J) {
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  /* "dipy/align/transforms.pyx":470
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 *         cdef:
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 *             double ct = cos(theta[0])
 *             double px = x[0], py = x[1]
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  /* "dipy/align/transforms.pyx":471
 *         cdef:
 *             double st = sin(theta[0])
 *             double ct = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double px = x[0], py = x[1]
 * 
 */
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  /* "dipy/align/transforms.pyx":472
 *             double st = sin(theta[0])
 *             double ct = cos(theta[0])
 *             double px = x[0], py = x[1]             # <<<<<<<<<<<<<<
 * 
 *         J[0, 0], J[0, 1], J[0, 2] = -px * st - py * ct, 1, 0
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  /* "dipy/align/transforms.pyx":474
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 * 
 *         J[0, 0], J[0, 1], J[0, 2] = -px * st - py * ct, 1, 0             # <<<<<<<<<<<<<<
 *         J[1, 0], J[1, 1], J[1, 2] = px * ct - py * st, 0, 1
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  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_12 * __pyx_v_J.strides[0]) ) + __pyx_t_13 * __pyx_v_J.strides[1]) )) = __pyx_t_7;

  /* "dipy/align/transforms.pyx":475
 * 
 *         J[0, 0], J[0, 1], J[0, 2] = -px * st - py * ct, 1, 0
 *         J[1, 0], J[1, 1], J[1, 2] = px * ct - py * st, 0, 1             # <<<<<<<<<<<<<<
 *         # This Jacobian depends on x (it's not constant): return 0
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 */
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  __pyx_t_6 = 0.0;
  __pyx_t_5 = 1.0;
  __pyx_t_14 = 1;
  __pyx_t_15 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_14 * __pyx_v_J.strides[0]) ) + __pyx_t_15 * __pyx_v_J.strides[1]) )) = __pyx_t_7;
  __pyx_t_16 = 1;
  __pyx_t_17 = 1;
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 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
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 */

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/* "dipy/align/transforms.pyx":479
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 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
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 *         Sets in theta the parameter values corresponding to the identity
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  /* "dipy/align/transforms.pyx":492
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 *         """
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 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
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  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);

  /* "dipy/align/transforms.pyx":479
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

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/* "dipy/align/transforms.pyx":494
 *         theta[:3] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 2D rigid transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_16RigidTransform2D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
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  Py_ssize_t __pyx_t_24;
  Py_ssize_t __pyx_t_25;

  /* "dipy/align/transforms.pyx":508
 *         """
 *         cdef:
 *             double ct = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, theta[1]
 */
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  /* "dipy/align/transforms.pyx":509
 *         cdef:
 *             double ct = cos(theta[0])
 *             double st = sin(theta[0])             # <<<<<<<<<<<<<<
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, theta[1]
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, theta[2]
 */
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  /* "dipy/align/transforms.pyx":510
 *             double ct = cos(theta[0])
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, theta[1]             # <<<<<<<<<<<<<<
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, theta[2]
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 */
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  /* "dipy/align/transforms.pyx":511
 *             double st = sin(theta[0])
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, theta[1]
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, theta[2]             # <<<<<<<<<<<<<<
 *         R[2, 0], R[2, 1], R[2, 2] = 0, 0, 1
 * 
 */
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  __pyx_t_13 = 2;
  __pyx_t_3 = (*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_13 * __pyx_v_theta.strides[0]) )));
  __pyx_t_14 = 1;
  __pyx_t_15 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_14 * __pyx_v_R.strides[0]) ) + __pyx_t_15 * __pyx_v_R.strides[1]) )) = __pyx_t_6;
  __pyx_t_16 = 1;
  __pyx_t_17 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_16 * __pyx_v_R.strides[0]) ) + __pyx_t_17 * __pyx_v_R.strides[1]) )) = __pyx_t_4;
  __pyx_t_18 = 1;
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  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_18 * __pyx_v_R.strides[0]) ) + __pyx_t_19 * __pyx_v_R.strides[1]) )) = __pyx_t_3;

  /* "dipy/align/transforms.pyx":512
 *         R[0, 0], R[0, 1], R[0, 2] = ct, -st, theta[1]
 *         R[1, 0], R[1, 1], R[1, 2] = st, ct, theta[2]
 *         R[2, 0], R[2, 1], R[2, 2] = 0, 0, 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
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 *             double cb = cos(theta[1])
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 *             double cb = cos(theta[1])             # <<<<<<<<<<<<<<
 *             double sc = sin(theta[2])
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 *             double sc = sin(theta[2])             # <<<<<<<<<<<<<<
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 *             double cc = cos(theta[2])
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 *         J[1, 1] = (-sc * sb + cc * sa * cb) * px + (sc * cb + cc * sa * sb) * pz
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            PyGILState_Release(__pyx_gilstate_save);
            #endif
        {__pyx_filename = __pyx_f[0]; __pyx_lineno = 577; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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if (unlikely(__pyx_memoryview_slice_memviewslice(
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{
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 577; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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{
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  __PYX_XDEC_MEMVIEW(&__pyx_t_30, 0);

  /* "dipy/align/transforms.pyx":578
 *         J[0, 3:6] = 0
 *         J[1, 3:6] = 0
 *         J[2, 3:6] = 0             # <<<<<<<<<<<<<<
 *         J[0, 3], J[1, 4], J[2, 5] = 1, 1, 1
 *         # This Jacobian depends on x (it's not constant): return 0
 */
  __pyx_t_29 = -1;
  __pyx_t_31.data = __pyx_v_J.data;
  __pyx_t_31.memview = __pyx_v_J.memview;
  __PYX_INC_MEMVIEW(&__pyx_t_31, 0);
  {
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        __pyx_tmp_idx += __pyx_tmp_shape;
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            PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
            #endif
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            PyGILState_Release(__pyx_gilstate_save);
            #endif
        {__pyx_filename = __pyx_f[0]; __pyx_lineno = 578; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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        __pyx_t_31.data += __pyx_tmp_idx * __pyx_tmp_stride;
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if (unlikely(__pyx_memoryview_slice_memviewslice(
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{
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 578; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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{
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  /* "dipy/align/transforms.pyx":579
 *         J[1, 3:6] = 0
 *         J[2, 3:6] = 0
 *         J[0, 3], J[1, 4], J[2, 5] = 1, 1, 1             # <<<<<<<<<<<<<<
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0
 */
  __pyx_t_32 = 1.0;
  __pyx_t_33 = 1.0;
  __pyx_t_34 = 1.0;
  __pyx_t_35 = 0;
  __pyx_t_36 = 3;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_35 * __pyx_v_J.strides[0]) ) + __pyx_t_36 * __pyx_v_J.strides[1]) )) = __pyx_t_32;
  __pyx_t_37 = 1;
  __pyx_t_38 = 4;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_37 * __pyx_v_J.strides[0]) ) + __pyx_t_38 * __pyx_v_J.strides[1]) )) = __pyx_t_33;
  __pyx_t_39 = 2;
  __pyx_t_40 = 5;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_39 * __pyx_v_J.strides[0]) ) + __pyx_t_40 * __pyx_v_J.strides[1]) )) = __pyx_t_34;

  /* "dipy/align/transforms.pyx":581
 *         J[0, 3], J[1, 4], J[2, 5] = 1, 1, 1
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:
 */
  __pyx_r = 0;
  goto __pyx_L0;

  /* "dipy/align/transforms.pyx":529
 *         self.number_of_parameters = 6
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
 *         r''' Jacobian matrix of a 3D rigid transform (rotation + translation)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __PYX_XDEC_MEMVIEW(&__pyx_t_28, 0);
  __PYX_XDEC_MEMVIEW(&__pyx_t_30, 0);
  __PYX_XDEC_MEMVIEW(&__pyx_t_31, 0);
  __Pyx_WriteUnraisable("dipy.align.transforms.RigidTransform3D._jacobian", __pyx_clineno, __pyx_lineno, __pyx_filename, 0);
  __pyx_r = 0;
  __pyx_L0:;
  return __pyx_r;
}

/* "dipy/align/transforms.pyx":583
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_16RigidTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
  __Pyx_memviewslice __pyx_t_1 = { 0, 0, { 0 }, { 0 }, { 0 } };
  int __pyx_t_2;
  int __pyx_lineno = 0;
  const char *__pyx_filename = NULL;
  int __pyx_clineno = 0;

  /* "dipy/align/transforms.pyx":599
 *             theta[5] : translation along the z axis
 *         """
 *         theta[:6] = 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
 */
  __pyx_t_2 = -1;
  __pyx_t_1.data = __pyx_v_theta.data;
  __pyx_t_1.memview = __pyx_v_theta.memview;
  __PYX_INC_MEMVIEW(&__pyx_t_1, 0);
  if (unlikely(__pyx_memoryview_slice_memviewslice(
    &__pyx_t_1,
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    &__pyx_t_2,
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{
    {__pyx_filename = __pyx_f[0]; __pyx_lineno = 599; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
}

{
      double __pyx_temp_scalar = 0.0;
      {
          Py_ssize_t __pyx_temp_extent_0 = __pyx_t_1.shape[0];
          Py_ssize_t __pyx_temp_stride_0 = __pyx_t_1.strides[0];
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          for (__pyx_temp_idx_0 = 0; __pyx_temp_idx_0 < __pyx_temp_extent_0; __pyx_temp_idx_0++) {
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          }
      }
  }
  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);

  /* "dipy/align/transforms.pyx":583
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

  /* function exit code */
  goto __pyx_L0;
  __pyx_L1_error:;
  __PYX_XDEC_MEMVIEW(&__pyx_t_1, 0);
  __Pyx_WriteUnraisable("dipy.align.transforms.RigidTransform3D._get_identity_parameters", __pyx_clineno, __pyx_lineno, __pyx_filename, 0);
  __pyx_L0:;
}

/* "dipy/align/transforms.pyx":601
 *         theta[:6] = 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with the 3D rigid transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_16RigidTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_RigidTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
  double __pyx_v_sa;
  double __pyx_v_ca;
  double __pyx_v_sb;
  double __pyx_v_cb;
  double __pyx_v_sc;
  double __pyx_v_cc;
  double __pyx_v_dx;
  double __pyx_v_dy;
  double __pyx_v_dz;
  Py_ssize_t __pyx_t_1;
  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;
  Py_ssize_t __pyx_t_6;
  Py_ssize_t __pyx_t_7;
  Py_ssize_t __pyx_t_8;
  Py_ssize_t __pyx_t_9;
  double __pyx_t_10;
  double __pyx_t_11;
  double __pyx_t_12;
  double __pyx_t_13;
  Py_ssize_t __pyx_t_14;
  Py_ssize_t __pyx_t_15;
  Py_ssize_t __pyx_t_16;
  Py_ssize_t __pyx_t_17;
  Py_ssize_t __pyx_t_18;
  Py_ssize_t __pyx_t_19;
  Py_ssize_t __pyx_t_20;
  Py_ssize_t __pyx_t_21;
  Py_ssize_t __pyx_t_22;
  Py_ssize_t __pyx_t_23;
  Py_ssize_t __pyx_t_24;
  Py_ssize_t __pyx_t_25;
  Py_ssize_t __pyx_t_26;
  Py_ssize_t __pyx_t_27;
  Py_ssize_t __pyx_t_28;
  Py_ssize_t __pyx_t_29;
  Py_ssize_t __pyx_t_30;
  Py_ssize_t __pyx_t_31;
  Py_ssize_t __pyx_t_32;
  Py_ssize_t __pyx_t_33;
  Py_ssize_t __pyx_t_34;
  Py_ssize_t __pyx_t_35;
  Py_ssize_t __pyx_t_36;
  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;
  Py_ssize_t __pyx_t_40;
  Py_ssize_t __pyx_t_41;
  Py_ssize_t __pyx_t_42;
  Py_ssize_t __pyx_t_43;
  Py_ssize_t __pyx_t_44;
  Py_ssize_t __pyx_t_45;

  /* "dipy/align/transforms.pyx":618
 *         """
 *         cdef:
 *             double sa = sin(theta[0])             # <<<<<<<<<<<<<<
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 */
  __pyx_t_1 = 0;
  __pyx_v_sa = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_1 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":619
 *         cdef:
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])             # <<<<<<<<<<<<<<
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 */
  __pyx_t_2 = 0;
  __pyx_v_ca = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_2 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":620
 *             double sa = sin(theta[0])
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])             # <<<<<<<<<<<<<<
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 */
  __pyx_t_3 = 1;
  __pyx_v_sb = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_3 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":621
 *             double ca = cos(theta[0])
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])             # <<<<<<<<<<<<<<
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])
 */
  __pyx_t_4 = 1;
  __pyx_v_cb = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_4 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":622
 *             double sb = sin(theta[1])
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])             # <<<<<<<<<<<<<<
 *             double cc = cos(theta[2])
 *             double dx = theta[3]
 */
  __pyx_t_5 = 2;
  __pyx_v_sc = sin((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_5 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":623
 *             double cb = cos(theta[1])
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])             # <<<<<<<<<<<<<<
 *             double dx = theta[3]
 *             double dy = theta[4]
 */
  __pyx_t_6 = 2;
  __pyx_v_cc = cos((*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_6 * __pyx_v_theta.strides[0]) ))));

  /* "dipy/align/transforms.pyx":624
 *             double sc = sin(theta[2])
 *             double cc = cos(theta[2])
 *             double dx = theta[3]             # <<<<<<<<<<<<<<
 *             double dy = theta[4]
 *             double dz = theta[5]
 */
  __pyx_t_7 = 3;
  __pyx_v_dx = (*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_7 * __pyx_v_theta.strides[0]) )));

  /* "dipy/align/transforms.pyx":625
 *             double cc = cos(theta[2])
 *             double dx = theta[3]
 *             double dy = theta[4]             # <<<<<<<<<<<<<<
 *             double dz = theta[5]
 * 
 */
  __pyx_t_8 = 4;
  __pyx_v_dy = (*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_8 * __pyx_v_theta.strides[0]) )));

  /* "dipy/align/transforms.pyx":626
 *             double dx = theta[3]
 *             double dy = theta[4]
 *             double dz = theta[5]             # <<<<<<<<<<<<<<
 * 
 *         R[0,0], R[0,1], R[0,2], R[0,3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, dx
 */
  __pyx_t_9 = 5;
  __pyx_v_dz = (*((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_9 * __pyx_v_theta.strides[0]) )));

  /* "dipy/align/transforms.pyx":628
 *             double dz = theta[5]
 * 
 *         R[0,0], R[0,1], R[0,2], R[0,3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, dx             # <<<<<<<<<<<<<<
 *         R[1,0], R[1,1], R[1,2], R[1,3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, dy
 *         R[2,0], R[2,1], R[2,2], R[2,3] = -ca*sb, sa, ca*cb, dz
 */
  __pyx_t_10 = ((__pyx_v_cc * __pyx_v_cb) - ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_sb));
  __pyx_t_11 = ((-__pyx_v_sc) * __pyx_v_ca);
  __pyx_t_12 = ((__pyx_v_cc * __pyx_v_sb) + ((__pyx_v_sc * __pyx_v_sa) * __pyx_v_cb));
  __pyx_t_13 = __pyx_v_dx;
  __pyx_t_14 = 0;
  __pyx_t_15 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_14 * __pyx_v_R.strides[0]) ) + __pyx_t_15 * __pyx_v_R.strides[1]) )) = __pyx_t_10;
  __pyx_t_16 = 0;
  __pyx_t_17 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_16 * __pyx_v_R.strides[0]) ) + __pyx_t_17 * __pyx_v_R.strides[1]) )) = __pyx_t_11;
  __pyx_t_18 = 0;
  __pyx_t_19 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_18 * __pyx_v_R.strides[0]) ) + __pyx_t_19 * __pyx_v_R.strides[1]) )) = __pyx_t_12;
  __pyx_t_20 = 0;
  __pyx_t_21 = 3;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_20 * __pyx_v_R.strides[0]) ) + __pyx_t_21 * __pyx_v_R.strides[1]) )) = __pyx_t_13;

  /* "dipy/align/transforms.pyx":629
 * 
 *         R[0,0], R[0,1], R[0,2], R[0,3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, dx
 *         R[1,0], R[1,1], R[1,2], R[1,3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, dy             # <<<<<<<<<<<<<<
 *         R[2,0], R[2,1], R[2,2], R[2,3] = -ca*sb, sa, ca*cb, dz
 *         R[3,0], R[3,1], R[3,2], R[3,3] = 0, 0, 0, 1
 */
  __pyx_t_13 = ((__pyx_v_sc * __pyx_v_cb) + ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_sb));
  __pyx_t_12 = (__pyx_v_cc * __pyx_v_ca);
  __pyx_t_11 = ((__pyx_v_sc * __pyx_v_sb) - ((__pyx_v_cc * __pyx_v_sa) * __pyx_v_cb));
  __pyx_t_10 = __pyx_v_dy;
  __pyx_t_22 = 1;
  __pyx_t_23 = 0;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_22 * __pyx_v_R.strides[0]) ) + __pyx_t_23 * __pyx_v_R.strides[1]) )) = __pyx_t_13;
  __pyx_t_24 = 1;
  __pyx_t_25 = 1;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_24 * __pyx_v_R.strides[0]) ) + __pyx_t_25 * __pyx_v_R.strides[1]) )) = __pyx_t_12;
  __pyx_t_26 = 1;
  __pyx_t_27 = 2;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_26 * __pyx_v_R.strides[0]) ) + __pyx_t_27 * __pyx_v_R.strides[1]) )) = __pyx_t_11;
  __pyx_t_28 = 1;
  __pyx_t_29 = 3;
  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_R.data + __pyx_t_28 * __pyx_v_R.strides[0]) ) + __pyx_t_29 * __pyx_v_R.strides[1]) )) = __pyx_t_10;

  /* "dipy/align/transforms.pyx":630
 *         R[0,0], R[0,1], R[0,2], R[0,3] = cc*cb-sc*sa*sb, -sc*ca, cc*sb+sc*sa*cb, dx
 *         R[1,0], R[1,1], R[1,2], R[1,3] = sc*cb+cc*sa*sb, cc*ca, sc*sb-cc*sa*cb, dy
 *         R[2,0], R[2,1], R[2,2], R[2,3] = -ca*sb, sa, ca*cb, dz             # <<<<<<<<<<<<<<
 *         R[3,0], R[3,1], R[3,2], R[3,3] = 0, 0, 0, 1
 * 
 */
  __pyx_t_10 = ((-__pyx_v_ca) * __pyx_v_sb);
  __pyx_t_11 = __pyx_v_sa;
  __pyx_t_12 = (__pyx_v_ca * __pyx_v_cb);
  __pyx_t_13 = __pyx_v_dz;
  __pyx_t_30 = 2;
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/* "dipy/align/transforms.pyx":670
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/* "dipy/align/transforms.pyx":682
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 *         self.number_of_parameters = 1
 * 
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  /* function exit code */
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/* "dipy/align/transforms.pyx":733
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_ScalingTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
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 *             buffer to write the parameters of the 3D scale transform
 *         """
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 * 
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  /* "dipy/align/transforms.pyx":733
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 *         r""" Parameter values corresponding to the identity
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  /* function exit code */
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/* "dipy/align/transforms.pyx":745
 *         theta[0] = 1
 * 
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 *         r""" Matrix associated with the 3D (isotropic) scaling transform
 * 
 */

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  /* function exit code */
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  /* "dipy/align/transforms.pyx":900
 *             J[j, :12] = 0
 *         J[0, :3] = x[:3]
 *         J[0, 3] = 1             # <<<<<<<<<<<<<<
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 *         J[0, 3] = 1
 *         J[1, 4:7] = x[:3]             # <<<<<<<<<<<<<<
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 *         J[2, 8:11] = x[:3]
 */
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  /* "dipy/align/transforms.pyx":902
 *         J[0, 3] = 1
 *         J[1, 4:7] = x[:3]
 *         J[1, 7] = 1             # <<<<<<<<<<<<<<
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 */
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  /* "dipy/align/transforms.pyx":903
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 *         J[1, 7] = 1
 *         J[2, 8:11] = x[:3]             # <<<<<<<<<<<<<<
 *         J[2, 11] = 1
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 */
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  /* "dipy/align/transforms.pyx":904
 *         J[1, 7] = 1
 *         J[2, 8:11] = x[:3]
 *         J[2, 11] = 1             # <<<<<<<<<<<<<<
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0
 */
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  *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_J.data + __pyx_t_14 * __pyx_v_J.strides[0]) ) + __pyx_t_15 * __pyx_v_J.strides[1]) )) = 1.0;

  /* "dipy/align/transforms.pyx":906
 *         J[2, 11] = 1
 *         # This Jacobian depends on x (it's not constant): return 0
 *         return 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:
 */
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  /* "dipy/align/transforms.pyx":853
 *         self.number_of_parameters = 12
 * 
 *     cdef int _jacobian(self, double[:] theta, double[:] x, double[:, :] J)nogil:             # <<<<<<<<<<<<<<
 *         r""" Jacobian matrix of the 3D affine transform
 *         The transformation is given by:
 */

  /* function exit code */
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}

/* "dipy/align/transforms.pyx":908
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

static void __pyx_f_4dipy_5align_10transforms_17AffineTransform3D__get_identity_parameters(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta) {
  double __pyx_t_1;
  double __pyx_t_2;
  double __pyx_t_3;
  double __pyx_t_4;
  Py_ssize_t __pyx_t_5;
  Py_ssize_t __pyx_t_6;
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  Py_ssize_t __pyx_t_15;
  Py_ssize_t __pyx_t_16;

  /* "dipy/align/transforms.pyx":918
 *             buffer to write the parameters of the 3D affine transform
 *         """
 *         theta[0], theta[1], theta[2], theta[3] = 1, 0, 0, 0             # <<<<<<<<<<<<<<
 *         theta[4], theta[5], theta[6], theta[7] = 0, 1, 0, 0
 *         theta[8], theta[9], theta[10], theta[11] = 0, 0, 1, 0
 */
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  __pyx_t_2 = 0.0;
  __pyx_t_3 = 0.0;
  __pyx_t_4 = 0.0;
  __pyx_t_5 = 0;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_5 * __pyx_v_theta.strides[0]) )) = __pyx_t_1;
  __pyx_t_6 = 1;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_6 * __pyx_v_theta.strides[0]) )) = __pyx_t_2;
  __pyx_t_7 = 2;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_7 * __pyx_v_theta.strides[0]) )) = __pyx_t_3;
  __pyx_t_8 = 3;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_8 * __pyx_v_theta.strides[0]) )) = __pyx_t_4;

  /* "dipy/align/transforms.pyx":919
 *         """
 *         theta[0], theta[1], theta[2], theta[3] = 1, 0, 0, 0
 *         theta[4], theta[5], theta[6], theta[7] = 0, 1, 0, 0             # <<<<<<<<<<<<<<
 *         theta[8], theta[9], theta[10], theta[11] = 0, 0, 1, 0
 * 
 */
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  __pyx_t_3 = 1.0;
  __pyx_t_2 = 0.0;
  __pyx_t_1 = 0.0;
  __pyx_t_9 = 4;
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  __pyx_t_10 = 5;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_10 * __pyx_v_theta.strides[0]) )) = __pyx_t_3;
  __pyx_t_11 = 6;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_11 * __pyx_v_theta.strides[0]) )) = __pyx_t_2;
  __pyx_t_12 = 7;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_12 * __pyx_v_theta.strides[0]) )) = __pyx_t_1;

  /* "dipy/align/transforms.pyx":920
 *         theta[0], theta[1], theta[2], theta[3] = 1, 0, 0, 0
 *         theta[4], theta[5], theta[6], theta[7] = 0, 1, 0, 0
 *         theta[8], theta[9], theta[10], theta[11] = 0, 0, 1, 0             # <<<<<<<<<<<<<<
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:
 */
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  __pyx_t_3 = 1.0;
  __pyx_t_4 = 0.0;
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  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_14 * __pyx_v_theta.strides[0]) )) = __pyx_t_2;
  __pyx_t_15 = 10;
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  __pyx_t_16 = 11;
  *((double *) ( /* dim=0 */ (__pyx_v_theta.data + __pyx_t_16 * __pyx_v_theta.strides[0]) )) = __pyx_t_4;

  /* "dipy/align/transforms.pyx":908
 *         return 0
 * 
 *     cdef void _get_identity_parameters(self, double[:] theta) nogil:             # <<<<<<<<<<<<<<
 *         r""" Parameter values corresponding to the identity
 *         Sets in theta the parameter values corresponding to the identity
 */

  /* function exit code */
}

/* "dipy/align/transforms.pyx":922
 *         theta[8], theta[9], theta[10], theta[11] = 0, 0, 1, 0
 * 
 *     cdef void _param_to_matrix(self, double[:] theta, double[:, :] R) nogil:             # <<<<<<<<<<<<<<
 *         r""" Matrix associated with a general 3D affine transform
 * 
 */

static void __pyx_f_4dipy_5align_10transforms_17AffineTransform3D__param_to_matrix(CYTHON_UNUSED struct __pyx_obj_4dipy_5align_10transforms_AffineTransform3D *__pyx_v_self, __Pyx_memviewslice __pyx_v_theta, __Pyx_memviewslice __pyx_v_R) {
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      /* "View.MemoryView":715
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      /* "View.MemoryView":731
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 *     cdef bint have_start, have_stop, have_step
 * 
 *     for dim, index in enumerate(indices):             # <<<<<<<<<<<<<<
 *         if PyIndex_Check(index):
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 * 
 *     if isinstance(memview, _memoryviewslice):             # <<<<<<<<<<<<<<
 *         return memoryview_fromslice(dst, new_ndim,
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    /* "View.MemoryView":734
 * 
 *     if isinstance(memview, _memoryviewslice):
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 *                                     memviewsliceobj.to_object_func,
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 */
    __Pyx_XDECREF(((PyObject *)__pyx_r));

    /* "View.MemoryView":735
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 *                                     memviewsliceobj.to_dtype_func,
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    /* "View.MemoryView":736
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    /* "View.MemoryView":734
 * 
 *     if isinstance(memview, _memoryviewslice):
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 *                                     memviewsliceobj.to_object_func,
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 */
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    /* "View.MemoryView":739
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 *                                     memview.dtype_is_object)
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 */
    __Pyx_XDECREF(((PyObject *)__pyx_r));

    /* "View.MemoryView":740
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 * 
 */
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    /* "View.MemoryView":739
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 *                                     memview.dtype_is_object)
 * 
 */
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 * 
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  /* function exit code */
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}

/* "View.MemoryView":764
 * 
 * @cname('__pyx_memoryview_slice_memviewslice')
 * cdef int slice_memviewslice(             # <<<<<<<<<<<<<<
 *         __Pyx_memviewslice *dst,
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 */

static int __pyx_memoryview_slice_memviewslice(__Pyx_memviewslice *__pyx_v_dst, Py_ssize_t __pyx_v_shape, Py_ssize_t __pyx_v_stride, Py_ssize_t __pyx_v_suboffset, int __pyx_v_dim, int __pyx_v_new_ndim, int *__pyx_v_suboffset_dim, Py_ssize_t __pyx_v_start, Py_ssize_t __pyx_v_stop, Py_ssize_t __pyx_v_step, int __pyx_v_have_start, int __pyx_v_have_stop, int __pyx_v_have_step, int __pyx_v_is_slice) {
  Py_ssize_t __pyx_v_new_shape;
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  int __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
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 * 
 *         if start < 0:
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 */
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 * 
 *         if start < 0:
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 */
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    /* "View.MemoryView":788
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 */
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      /* "View.MemoryView":789
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 *     else:
 * 
 */
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 * 
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 * 
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    /* "View.MemoryView":794
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 * 
 *         if have_step and step == 0:             # <<<<<<<<<<<<<<
 *             _err_dim(ValueError, "Step may not be zero (axis %d)", dim)
 * 
 */
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    } else {
      __pyx_t_2 = __pyx_t_1;
      goto __pyx_L9_bool_binop_done;
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    __pyx_t_1 = ((__pyx_v_step == 0) != 0);
    __pyx_t_2 = __pyx_t_1;
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      /* "View.MemoryView":795
 * 
 *         if have_step and step == 0:
 *             _err_dim(ValueError, "Step may not be zero (axis %d)", dim)             # <<<<<<<<<<<<<<
 * 
 * 
 */
      __pyx_t_3 = __pyx_memoryview_err_dim(__pyx_builtin_ValueError, __pyx_k_Step_may_not_be_zero_axis_d, __pyx_v_dim); if (unlikely(__pyx_t_3 == -1)) {__pyx_filename = __pyx_f[2]; __pyx_lineno = 795; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
      goto __pyx_L8;
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    __pyx_L8:;

    /* "View.MemoryView":798
 * 
 * 
 *         if have_start:             # <<<<<<<<<<<<<<
 *             if start < 0:
 *                 start += shape
 */
    __pyx_t_2 = (__pyx_v_have_start != 0);
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      /* "View.MemoryView":799
 * 
 *         if have_start:
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 *                 start += shape
 *                 if start < 0:
 */
      __pyx_t_2 = ((__pyx_v_start < 0) != 0);
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        /* "View.MemoryView":800
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 *                 start += shape             # <<<<<<<<<<<<<<
 *                 if start < 0:
 *                     start = 0
 */
        __pyx_v_start = (__pyx_v_start + __pyx_v_shape);

        /* "View.MemoryView":801
 *             if start < 0:
 *                 start += shape
 *                 if start < 0:             # <<<<<<<<<<<<<<
 *                     start = 0
 *             elif start >= shape:
 */
        __pyx_t_2 = ((__pyx_v_start < 0) != 0);
        if (__pyx_t_2) {

          /* "View.MemoryView":802
 *                 start += shape
 *                 if start < 0:
 *                     start = 0             # <<<<<<<<<<<<<<
 *             elif start >= shape:
 *                 if negative_step:
 */
          __pyx_v_start = 0;
          goto __pyx_L13;
        }
        __pyx_L13:;
        goto __pyx_L12;
      }

      /* "View.MemoryView":803
 *                 if start < 0:
 *                     start = 0
 *             elif start >= shape:             # <<<<<<<<<<<<<<
 *                 if negative_step:
 *                     start = shape - 1
 */
      __pyx_t_2 = ((__pyx_v_start >= __pyx_v_shape) != 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":804
 *                     start = 0
 *             elif start >= shape:
 *                 if negative_step:             # <<<<<<<<<<<<<<
 *                     start = shape - 1
 *                 else:
 */
        __pyx_t_2 = (__pyx_v_negative_step != 0);
        if (__pyx_t_2) {

          /* "View.MemoryView":805
 *             elif start >= shape:
 *                 if negative_step:
 *                     start = shape - 1             # <<<<<<<<<<<<<<
 *                 else:
 *                     start = shape
 */
          __pyx_v_start = (__pyx_v_shape - 1);
          goto __pyx_L14;
        }
        /*else*/ {

          /* "View.MemoryView":807
 *                     start = shape - 1
 *                 else:
 *                     start = shape             # <<<<<<<<<<<<<<
 *         else:
 *             if negative_step:
 */
          __pyx_v_start = __pyx_v_shape;
        }
        __pyx_L14:;
        goto __pyx_L12;
      }
      __pyx_L12:;
      goto __pyx_L11;
    }
    /*else*/ {

      /* "View.MemoryView":809
 *                     start = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 start = shape - 1
 *             else:
 */
      __pyx_t_2 = (__pyx_v_negative_step != 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":810
 *         else:
 *             if negative_step:
 *                 start = shape - 1             # <<<<<<<<<<<<<<
 *             else:
 *                 start = 0
 */
        __pyx_v_start = (__pyx_v_shape - 1);
        goto __pyx_L15;
      }
      /*else*/ {

        /* "View.MemoryView":812
 *                 start = shape - 1
 *             else:
 *                 start = 0             # <<<<<<<<<<<<<<
 * 
 *         if have_stop:
 */
        __pyx_v_start = 0;
      }
      __pyx_L15:;
    }
    __pyx_L11:;

    /* "View.MemoryView":814
 *                 start = 0
 * 
 *         if have_stop:             # <<<<<<<<<<<<<<
 *             if stop < 0:
 *                 stop += shape
 */
    __pyx_t_2 = (__pyx_v_have_stop != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":815
 * 
 *         if have_stop:
 *             if stop < 0:             # <<<<<<<<<<<<<<
 *                 stop += shape
 *                 if stop < 0:
 */
      __pyx_t_2 = ((__pyx_v_stop < 0) != 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":816
 *         if have_stop:
 *             if stop < 0:
 *                 stop += shape             # <<<<<<<<<<<<<<
 *                 if stop < 0:
 *                     stop = 0
 */
        __pyx_v_stop = (__pyx_v_stop + __pyx_v_shape);

        /* "View.MemoryView":817
 *             if stop < 0:
 *                 stop += shape
 *                 if stop < 0:             # <<<<<<<<<<<<<<
 *                     stop = 0
 *             elif stop > shape:
 */
        __pyx_t_2 = ((__pyx_v_stop < 0) != 0);
        if (__pyx_t_2) {

          /* "View.MemoryView":818
 *                 stop += shape
 *                 if stop < 0:
 *                     stop = 0             # <<<<<<<<<<<<<<
 *             elif stop > shape:
 *                 stop = shape
 */
          __pyx_v_stop = 0;
          goto __pyx_L18;
        }
        __pyx_L18:;
        goto __pyx_L17;
      }

      /* "View.MemoryView":819
 *                 if stop < 0:
 *                     stop = 0
 *             elif stop > shape:             # <<<<<<<<<<<<<<
 *                 stop = shape
 *         else:
 */
      __pyx_t_2 = ((__pyx_v_stop > __pyx_v_shape) != 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":820
 *                     stop = 0
 *             elif stop > shape:
 *                 stop = shape             # <<<<<<<<<<<<<<
 *         else:
 *             if negative_step:
 */
        __pyx_v_stop = __pyx_v_shape;
        goto __pyx_L17;
      }
      __pyx_L17:;
      goto __pyx_L16;
    }
    /*else*/ {

      /* "View.MemoryView":822
 *                 stop = shape
 *         else:
 *             if negative_step:             # <<<<<<<<<<<<<<
 *                 stop = -1
 *             else:
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      __pyx_t_2 = (__pyx_v_negative_step != 0);
      if (__pyx_t_2) {

        /* "View.MemoryView":823
 *         else:
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 *                 stop = -1             # <<<<<<<<<<<<<<
 *             else:
 *                 stop = shape
 */
        __pyx_v_stop = -1;
        goto __pyx_L19;
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      /*else*/ {

        /* "View.MemoryView":825
 *                 stop = -1
 *             else:
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 * 
 *         if not have_step:
 */
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    /* "View.MemoryView":827
 *                 stop = shape
 * 
 *         if not have_step:             # <<<<<<<<<<<<<<
 *             step = 1
 * 
 */
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      /* "View.MemoryView":828
 * 
 *         if not have_step:
 *             step = 1             # <<<<<<<<<<<<<<
 * 
 * 
 */
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      goto __pyx_L20;
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    __pyx_L20:;

    /* "View.MemoryView":832
 * 
 *         with cython.cdivision(True):
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 *             if (stop - start) - step * new_shape:
 */
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    /* "View.MemoryView":834
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 */
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      /* "View.MemoryView":835
 * 
 *             if (stop - start) - step * new_shape:
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 *         if new_shape < 0:
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    /* "View.MemoryView":837
 *                 new_shape += 1
 * 
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 */
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      /* "View.MemoryView":838
 * 
 *         if new_shape < 0:
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 * 
 * 
 */
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    /* "View.MemoryView":841
 * 
 * 
 *         dst.strides[new_ndim] = stride * step             # <<<<<<<<<<<<<<
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 * 
 *         dst.strides[new_ndim] = stride * step
 *         dst.shape[new_ndim] = new_shape             # <<<<<<<<<<<<<<
 *         dst.suboffsets[new_ndim] = suboffset
 * 
 */
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    /* "View.MemoryView":843
 *         dst.strides[new_ndim] = stride * step
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 * 
 */
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  /* "View.MemoryView":846
 * 
 * 
 *     if suboffset_dim[0] < 0:             # <<<<<<<<<<<<<<
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    /* "View.MemoryView":847
 * 
 *     if suboffset_dim[0] < 0:
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  /*else*/ {

    /* "View.MemoryView":849
 *         dst.data += start * stride
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 * 
 *     if suboffset >= 0:
 */
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  /* "View.MemoryView":851
 *         dst.suboffsets[suboffset_dim[0]] += start * stride
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 *     if suboffset >= 0:             # <<<<<<<<<<<<<<
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    /* "View.MemoryView":852
 * 
 *     if suboffset >= 0:
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 *             if new_ndim == 0:
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      /* "View.MemoryView":853
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      __pyx_t_2 = ((__pyx_v_new_ndim == 0) != 0);
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        /* "View.MemoryView":854
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 *                 _err_dim(IndexError, "All dimensions preceding dimension %d "
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        /* "View.MemoryView":856
 *                 dst.data = (<char **> dst.data)[0] + suboffset
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      /* "View.MemoryView":859
 *                                      "must be indexed and not sliced", dim)
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 *     return 0
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 * 
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 * 
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/* "View.MemoryView":867
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static char *__pyx_pybuffer_index(Py_buffer *__pyx_v_view, char *__pyx_v_bufp, Py_ssize_t __pyx_v_index, Py_ssize_t __pyx_v_dim) {
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 *     cdef char *resultp
 */
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  /* "View.MemoryView":870
 *                           Py_ssize_t dim) except NULL:
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 */
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  /* "View.MemoryView":873
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 * 
 *     if view.ndim == 0:             # <<<<<<<<<<<<<<
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 *         stride = itemsize
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    /* "View.MemoryView":874
 * 
 *     if view.ndim == 0:
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 *     else:
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      PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
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      PyErr_SetString(PyExc_ZeroDivisionError, "integer division or modulo by zero");
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 *     if isinstance(memview, _memoryviewslice):             # <<<<<<<<<<<<<<
 *         to_object_func = (<_memoryviewslice> memview).to_object_func
 *         to_dtype_func = (<_memoryviewslice> memview).to_dtype_func
 */
  __pyx_t_1 = __Pyx_TypeCheck(((PyObject *)__pyx_v_memview), ((PyObject *)__pyx_memoryviewslice_type)); 
  __pyx_t_2 = (__pyx_t_1 != 0);
  if (__pyx_t_2) {

    /* "View.MemoryView":1048
 * 
 *     if isinstance(memview, _memoryviewslice):
 *         to_object_func = (<_memoryviewslice> memview).to_object_func             # <<<<<<<<<<<<<<
 *         to_dtype_func = (<_memoryviewslice> memview).to_dtype_func
 *     else:
 */
    __pyx_t_3 = ((struct __pyx_memoryviewslice_obj *)__pyx_v_memview)->to_object_func;
    __pyx_v_to_object_func = __pyx_t_3;

    /* "View.MemoryView":1049
 *     if isinstance(memview, _memoryviewslice):
 *         to_object_func = (<_memoryviewslice> memview).to_object_func
 *         to_dtype_func = (<_memoryviewslice> memview).to_dtype_func             # <<<<<<<<<<<<<<
 *     else:
 *         to_object_func = NULL
 */
    __pyx_t_4 = ((struct __pyx_memoryviewslice_obj *)__pyx_v_memview)->to_dtype_func;
    __pyx_v_to_dtype_func = __pyx_t_4;
    goto __pyx_L3;
  }
  /*else*/ {

    /* "View.MemoryView":1051
 *         to_dtype_func = (<_memoryviewslice> memview).to_dtype_func
 *     else:
 *         to_object_func = NULL             # <<<<<<<<<<<<<<
 *         to_dtype_func = NULL
 * 
 */
    __pyx_v_to_object_func = NULL;

    /* "View.MemoryView":1052
 *     else:
 *         to_object_func = NULL
 *         to_dtype_func = NULL             # <<<<<<<<<<<<<<
 * 
 *     return memoryview_fromslice(memviewslice[0], memview.view.ndim,
 */
    __pyx_v_to_dtype_func = NULL;
  }
  __pyx_L3:;

  /* "View.MemoryView":1054
 *         to_dtype_func = NULL
 * 
 *     return memoryview_fromslice(memviewslice[0], memview.view.ndim,             # <<<<<<<<<<<<<<
 *                                 to_object_func, to_dtype_func,
 *                                 memview.dtype_is_object)
 */
  __Pyx_XDECREF(__pyx_r);

  /* "View.MemoryView":1056
 *     return memoryview_fromslice(memviewslice[0], memview.view.ndim,
 *                                 to_object_func, to_dtype_func,
 *                                 memview.dtype_is_object)             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_t_5 = __pyx_memoryview_fromslice((__pyx_v_memviewslice[0]), __pyx_v_memview->view.ndim, __pyx_v_to_object_func, __pyx_v_to_dtype_func, __pyx_v_memview->dtype_is_object); if (unlikely(!__pyx_t_5)) {__pyx_filename = __pyx_f[2]; __pyx_lineno = 1054; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_r = __pyx_t_5;
  __pyx_t_5 = 0;
  goto __pyx_L0;

  /* "View.MemoryView":1040
 * 
 * @cname('__pyx_memoryview_copy_object_from_slice')
 * cdef memoryview_copy_from_slice(memoryview memview, __Pyx_memviewslice *memviewslice):             # <<<<<<<<<<<<<<
 *     """
 *     Create a new memoryview object from a given memoryview object and slice.
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("View.MemoryView.memoryview_copy_from_slice", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "View.MemoryView":1062
 * 
 * 
 * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) nogil:             # <<<<<<<<<<<<<<
 *     if arg < 0:
 *         return -arg
 */

static Py_ssize_t abs_py_ssize_t(Py_ssize_t __pyx_v_arg) {
  Py_ssize_t __pyx_r;
  int __pyx_t_1;

  /* "View.MemoryView":1063
 * 
 * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) nogil:
 *     if arg < 0:             # <<<<<<<<<<<<<<
 *         return -arg
 *     else:
 */
  __pyx_t_1 = ((__pyx_v_arg < 0) != 0);
  if (__pyx_t_1) {

    /* "View.MemoryView":1064
 * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) nogil:
 *     if arg < 0:
 *         return -arg             # <<<<<<<<<<<<<<
 *     else:
 *         return arg
 */
    __pyx_r = (-__pyx_v_arg);
    goto __pyx_L0;
  }
  /*else*/ {

    /* "View.MemoryView":1066
 *         return -arg
 *     else:
 *         return arg             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_get_best_slice_order')
 */
    __pyx_r = __pyx_v_arg;
    goto __pyx_L0;
  }

  /* "View.MemoryView":1062
 * 
 * 
 * cdef Py_ssize_t abs_py_ssize_t(Py_ssize_t arg) nogil:             # <<<<<<<<<<<<<<
 *     if arg < 0:
 *         return -arg
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1069
 * 
 * @cname('__pyx_get_best_slice_order')
 * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Figure out the best memory access order for a given slice.
 */

static char __pyx_get_best_slice_order(__Pyx_memviewslice *__pyx_v_mslice, int __pyx_v_ndim) {
  int __pyx_v_i;
  Py_ssize_t __pyx_v_c_stride;
  Py_ssize_t __pyx_v_f_stride;
  char __pyx_r;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "View.MemoryView":1074
 *     """
 *     cdef int i
 *     cdef Py_ssize_t c_stride = 0             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t f_stride = 0
 * 
 */
  __pyx_v_c_stride = 0;

  /* "View.MemoryView":1075
 *     cdef int i
 *     cdef Py_ssize_t c_stride = 0
 *     cdef Py_ssize_t f_stride = 0             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim - 1, -1, -1):
 */
  __pyx_v_f_stride = 0;

  /* "View.MemoryView":1077
 *     cdef Py_ssize_t f_stride = 0
 * 
 *     for i in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]
 */
  for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) {
    __pyx_v_i = __pyx_t_1;

    /* "View.MemoryView":1078
 * 
 *     for i in range(ndim - 1, -1, -1):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             c_stride = mslice.strides[i]
 *             break
 */
    __pyx_t_2 = (((__pyx_v_mslice->shape[__pyx_v_i]) > 1) != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":1079
 *     for i in range(ndim - 1, -1, -1):
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]             # <<<<<<<<<<<<<<
 *             break
 * 
 */
      __pyx_v_c_stride = (__pyx_v_mslice->strides[__pyx_v_i]);

      /* "View.MemoryView":1080
 *         if mslice.shape[i] > 1:
 *             c_stride = mslice.strides[i]
 *             break             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim):
 */
      goto __pyx_L4_break;
    }
  }
  __pyx_L4_break:;

  /* "View.MemoryView":1082
 *             break
 * 
 *     for i in range(ndim):             # <<<<<<<<<<<<<<
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]
 */
  __pyx_t_1 = __pyx_v_ndim;
  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_1; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "View.MemoryView":1083
 * 
 *     for i in range(ndim):
 *         if mslice.shape[i] > 1:             # <<<<<<<<<<<<<<
 *             f_stride = mslice.strides[i]
 *             break
 */
    __pyx_t_2 = (((__pyx_v_mslice->shape[__pyx_v_i]) > 1) != 0);
    if (__pyx_t_2) {

      /* "View.MemoryView":1084
 *     for i in range(ndim):
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]             # <<<<<<<<<<<<<<
 *             break
 * 
 */
      __pyx_v_f_stride = (__pyx_v_mslice->strides[__pyx_v_i]);

      /* "View.MemoryView":1085
 *         if mslice.shape[i] > 1:
 *             f_stride = mslice.strides[i]
 *             break             # <<<<<<<<<<<<<<
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):
 */
      goto __pyx_L7_break;
    }
  }
  __pyx_L7_break:;

  /* "View.MemoryView":1087
 *             break
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):             # <<<<<<<<<<<<<<
 *         return 'C'
 *     else:
 */
  __pyx_t_2 = ((abs_py_ssize_t(__pyx_v_c_stride) <= abs_py_ssize_t(__pyx_v_f_stride)) != 0);
  if (__pyx_t_2) {

    /* "View.MemoryView":1088
 * 
 *     if abs_py_ssize_t(c_stride) <= abs_py_ssize_t(f_stride):
 *         return 'C'             # <<<<<<<<<<<<<<
 *     else:
 *         return 'F'
 */
    __pyx_r = 'C';
    goto __pyx_L0;
  }
  /*else*/ {

    /* "View.MemoryView":1090
 *         return 'C'
 *     else:
 *         return 'F'             # <<<<<<<<<<<<<<
 * 
 * @cython.cdivision(True)
 */
    __pyx_r = 'F';
    goto __pyx_L0;
  }

  /* "View.MemoryView":1069
 * 
 * @cname('__pyx_get_best_slice_order')
 * cdef char get_best_order(__Pyx_memviewslice *mslice, int ndim) nogil:             # <<<<<<<<<<<<<<
 *     """
 *     Figure out the best memory access order for a given slice.
 */

  /* function exit code */
  __pyx_L0:;
  return __pyx_r;
}

/* "View.MemoryView":1093
 * 
 * @cython.cdivision(True)
 * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides,             # <<<<<<<<<<<<<<
 *                                    char *dst_data, Py_ssize_t *dst_strides,
 *                                    Py_ssize_t *src_shape, Py_ssize_t *dst_shape,
 */

static void _copy_strided_to_strided(char *__pyx_v_src_data, Py_ssize_t *__pyx_v_src_strides, char *__pyx_v_dst_data, Py_ssize_t *__pyx_v_dst_strides, Py_ssize_t *__pyx_v_src_shape, Py_ssize_t *__pyx_v_dst_shape, int __pyx_v_ndim, size_t __pyx_v_itemsize) {
  CYTHON_UNUSED Py_ssize_t __pyx_v_i;
  CYTHON_UNUSED Py_ssize_t __pyx_v_src_extent;
  Py_ssize_t __pyx_v_dst_extent;
  Py_ssize_t __pyx_v_src_stride;
  Py_ssize_t __pyx_v_dst_stride;
  int __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;
  Py_ssize_t __pyx_t_4;
  Py_ssize_t __pyx_t_5;

  /* "View.MemoryView":1100
 * 
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t src_extent = src_shape[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]
 */
  __pyx_v_src_extent = (__pyx_v_src_shape[0]);

  /* "View.MemoryView":1101
 *     cdef Py_ssize_t i
 *     cdef Py_ssize_t src_extent = src_shape[0]
 *     cdef Py_ssize_t dst_extent = dst_shape[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t src_stride = src_strides[0]
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 */
  __pyx_v_dst_extent = (__pyx_v_dst_shape[0]);

  /* "View.MemoryView":1102
 *     cdef Py_ssize_t src_extent = src_shape[0]
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]             # <<<<<<<<<<<<<<
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 * 
 */
  __pyx_v_src_stride = (__pyx_v_src_strides[0]);

  /* "View.MemoryView":1103
 *     cdef Py_ssize_t dst_extent = dst_shape[0]
 *     cdef Py_ssize_t src_stride = src_strides[0]
 *     cdef Py_ssize_t dst_stride = dst_strides[0]             # <<<<<<<<<<<<<<
 * 
 *     if ndim == 1:
 */
  __pyx_v_dst_stride = (__pyx_v_dst_strides[0]);

  /* "View.MemoryView":1105
 *     cdef Py_ssize_t dst_stride = dst_strides[0]
 * 
 *     if ndim == 1:             # <<<<<<<<<<<<<<
 *        if (src_stride > 0 and dst_stride > 0 and
 *            <size_t> src_stride == itemsize == <size_t> dst_stride):
 */
  __pyx_t_1 = ((__pyx_v_ndim == 1) != 0);
  if (__pyx_t_1) {

    /* "View.MemoryView":1106
 * 
 *     if ndim == 1:
 *        if (src_stride > 0 and dst_stride > 0 and             # <<<<<<<<<<<<<<
 *            <size_t> src_stride == itemsize == <size_t> dst_stride):
 *            memcpy(dst_data, src_data, itemsize * dst_extent)
 */
    __pyx_t_2 = ((__pyx_v_src_stride > 0) != 0);
    if (__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L5_bool_binop_done;
    }
    __pyx_t_2 = ((__pyx_v_dst_stride > 0) != 0);
    if (__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L5_bool_binop_done;
    }

    /* "View.MemoryView":1107
 *     if ndim == 1:
 *        if (src_stride > 0 and dst_stride > 0 and
 *            <size_t> src_stride == itemsize == <size_t> dst_stride):             # <<<<<<<<<<<<<<
 *            memcpy(dst_data, src_data, itemsize * dst_extent)
 *        else:
 */
    __pyx_t_2 = (((size_t)__pyx_v_src_stride) == __pyx_v_itemsize);
    if (__pyx_t_2) {
      __pyx_t_2 = (__pyx_v_itemsize == ((size_t)__pyx_v_dst_stride));
    }
    __pyx_t_3 = (__pyx_t_2 != 0);
    __pyx_t_1 = __pyx_t_3;
    __pyx_L5_bool_binop_done:;
    if (__pyx_t_1) {

      /* "View.MemoryView":1108
 *        if (src_stride > 0 and dst_stride > 0 and
 *            <size_t> src_stride == itemsize == <size_t> dst_stride):
 *            memcpy(dst_data, src_data, itemsize * dst_extent)             # <<<<<<<<<<<<<<
 *        else:
 *            for i in range(dst_extent):
 */
      memcpy(__pyx_v_dst_data, __pyx_v_src_data, (__pyx_v_itemsize * __pyx_v_dst_extent));
      goto __pyx_L4;
    }
    /*else*/ {

      /* "View.MemoryView":1110
 *            memcpy(dst_data, src_data, itemsize * dst_extent)
 *        else:
 *            for i in range(dst_extent):             # <<<<<<<<<<<<<<
 *                memcpy(dst_data, src_data, itemsize)
 *                src_data += src_stride
 */
      __pyx_t_4 = __pyx_v_dst_extent;
      for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) {
        __pyx_v_i = __pyx_t_5;

        /* "View.MemoryView":1111
 *        else:
 *            for i in range(dst_extent):
 *                memcpy(dst_data, src_data, itemsize)             # <<<<<<<<<<<<<<
 *                src_data += src_stride
 *                dst_data += dst_stride
 */
        memcpy(__pyx_v_dst_data, __pyx_v_src_data, __pyx_v_itemsize);

        /* "View.MemoryView":1112
 *            for i in range(dst_extent):
 *                memcpy(dst_data, src_data, itemsize)
 *                src_data += src_stride             # <<<<<<<<<<<<<<
 *                dst_data += dst_stride
 *     else:
 */
        __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);

        /* "View.MemoryView":1113
 *                memcpy(dst_data, src_data, itemsize)
 *                src_data += src_stride
 *                dst_data += dst_stride             # <<<<<<<<<<<<<<
 *     else:
 *         for i in range(dst_extent):
 */
        __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
      }
    }
    __pyx_L4:;
    goto __pyx_L3;
  }
  /*else*/ {

    /* "View.MemoryView":1115
 *                dst_data += dst_stride
 *     else:
 *         for i in range(dst_extent):             # <<<<<<<<<<<<<<
 *             _copy_strided_to_strided(src_data, src_strides + 1,
 *                                      dst_data, dst_strides + 1,
 */
    __pyx_t_4 = __pyx_v_dst_extent;
    for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) {
      __pyx_v_i = __pyx_t_5;

      /* "View.MemoryView":1116
 *     else:
 *         for i in range(dst_extent):
 *             _copy_strided_to_strided(src_data, src_strides + 1,             # <<<<<<<<<<<<<<
 *                                      dst_data, dst_strides + 1,
 *                                      src_shape + 1, dst_shape + 1,
 */
      _copy_strided_to_strided(__pyx_v_src_data, (__pyx_v_src_strides + 1), __pyx_v_dst_data, (__pyx_v_dst_strides + 1), (__pyx_v_src_shape + 1), (__pyx_v_dst_shape + 1), (__pyx_v_ndim - 1), __pyx_v_itemsize);

      /* "View.MemoryView":1120
 *                                      src_shape + 1, dst_shape + 1,
 *                                      ndim - 1, itemsize)
 *             src_data += src_stride             # <<<<<<<<<<<<<<
 *             dst_data += dst_stride
 * 
 */
      __pyx_v_src_data = (__pyx_v_src_data + __pyx_v_src_stride);

      /* "View.MemoryView":1121
 *                                      ndim - 1, itemsize)
 *             src_data += src_stride
 *             dst_data += dst_stride             # <<<<<<<<<<<<<<
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,
 */
      __pyx_v_dst_data = (__pyx_v_dst_data + __pyx_v_dst_stride);
    }
  }
  __pyx_L3:;

  /* "View.MemoryView":1093
 * 
 * @cython.cdivision(True)
 * cdef void _copy_strided_to_strided(char *src_data, Py_ssize_t *src_strides,             # <<<<<<<<<<<<<<
 *                                    char *dst_data, Py_ssize_t *dst_strides,
 *                                    Py_ssize_t *src_shape, Py_ssize_t *dst_shape,
 */

  /* function exit code */
}

/* "View.MemoryView":1123
 *             dst_data += dst_stride
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) nogil:
 */

static void copy_strided_to_strided(__Pyx_memviewslice *__pyx_v_src, __Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize) {

  /* "View.MemoryView":1126
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) nogil:
 *     _copy_strided_to_strided(src.data, src.strides, dst.data, dst.strides,             # <<<<<<<<<<<<<<
 *                              src.shape, dst.shape, ndim, itemsize)
 * 
 */
  _copy_strided_to_strided(__pyx_v_src->data, __pyx_v_src->strides, __pyx_v_dst->data, __pyx_v_dst->strides, __pyx_v_src->shape, __pyx_v_dst->shape, __pyx_v_ndim, __pyx_v_itemsize);

  /* "View.MemoryView":1123
 *             dst_data += dst_stride
 * 
 * cdef void copy_strided_to_strided(__Pyx_memviewslice *src,             # <<<<<<<<<<<<<<
 *                                   __Pyx_memviewslice *dst,
 *                                   int ndim, size_t itemsize) nogil:
 */

  /* function exit code */
}

/* "View.MemoryView":1130
 * 
 * @cname('__pyx_memoryview_slice_get_size')
 * cdef Py_ssize_t slice_get_size(__Pyx_memviewslice *src, int ndim) nogil:             # <<<<<<<<<<<<<<
 *     "Return the size of the memory occupied by the slice in number of bytes"
 *     cdef int i
 */

static Py_ssize_t __pyx_memoryview_slice_get_size(__Pyx_memviewslice *__pyx_v_src, int __pyx_v_ndim) {
  int __pyx_v_i;
  Py_ssize_t __pyx_v_size;
  Py_ssize_t __pyx_r;
  Py_ssize_t __pyx_t_1;
  int __pyx_t_2;
  int __pyx_t_3;

  /* "View.MemoryView":1133
 *     "Return the size of the memory occupied by the slice in number of bytes"
 *     cdef int i
 *     cdef Py_ssize_t size = src.memview.view.itemsize             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim):
 */
  __pyx_t_1 = __pyx_v_src->memview->view.itemsize;
  __pyx_v_size = __pyx_t_1;

  /* "View.MemoryView":1135
 *     cdef Py_ssize_t size = src.memview.view.itemsize
 * 
 *     for i in range(ndim):             # <<<<<<<<<<<<<<
 *         size *= src.shape[i]
 * 
 */
  __pyx_t_2 = __pyx_v_ndim;
  for (__pyx_t_3 = 0; __pyx_t_3 < __pyx_t_2; __pyx_t_3+=1) {
    __pyx_v_i = __pyx_t_3;

    /* "View.MemoryView":1136
 * 
 *     for i in range(ndim):
 *         size *= src.shape[i]             # <<<<<<<<<<<<<<
 * 
 *     return size
 */
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 *             free(tmpdata)
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 */
      __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);

      /* "View.MemoryView":1277
 *             memcpy(dst.data, src.data, slice_get_size(&src, ndim))
 *             refcount_copying(&dst, dtype_is_object, ndim, True)
 *             free(tmpdata)             # <<<<<<<<<<<<<<
 *             return 0
 * 
 */
      free(__pyx_v_tmpdata);

      /* "View.MemoryView":1278
 *             refcount_copying(&dst, dtype_is_object, ndim, True)
 *             free(tmpdata)
 *             return 0             # <<<<<<<<<<<<<<
 * 
 *     if order == 'F' == get_best_order(&dst, ndim):
 */
      __pyx_r = 0;
      goto __pyx_L0;
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    goto __pyx_L11;
  }
  __pyx_L11:;

  /* "View.MemoryView":1280
 *             return 0
 * 
 *     if order == 'F' == get_best_order(&dst, ndim):             # <<<<<<<<<<<<<<
 * 
 * 
 */
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  if (__pyx_t_2) {
    __pyx_t_2 = ('F' == __pyx_get_best_slice_order((&__pyx_v_dst), __pyx_v_ndim));
  }
  __pyx_t_7 = (__pyx_t_2 != 0);
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    /* "View.MemoryView":1283
 * 
 * 
 *         transpose_memslice(&src)             # <<<<<<<<<<<<<<
 *         transpose_memslice(&dst)
 * 
 */
    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_src)); if (unlikely(__pyx_t_5 == 0)) {__pyx_filename = __pyx_f[2]; __pyx_lineno = 1283; __pyx_clineno = __LINE__; goto __pyx_L1_error;}

    /* "View.MemoryView":1284
 * 
 *         transpose_memslice(&src)
 *         transpose_memslice(&dst)             # <<<<<<<<<<<<<<
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, False)
 */
    __pyx_t_5 = __pyx_memslice_transpose((&__pyx_v_dst)); if (unlikely(__pyx_t_5 == 0)) {__pyx_filename = __pyx_f[2]; __pyx_lineno = 1284; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    goto __pyx_L14;
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  __pyx_L14:;

  /* "View.MemoryView":1286
 *         transpose_memslice(&dst)
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, False)             # <<<<<<<<<<<<<<
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
 *     refcount_copying(&dst, dtype_is_object, ndim, True)
 */
  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 0);

  /* "View.MemoryView":1287
 * 
 *     refcount_copying(&dst, dtype_is_object, ndim, False)
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)             # <<<<<<<<<<<<<<
 *     refcount_copying(&dst, dtype_is_object, ndim, True)
 * 
 */
  copy_strided_to_strided((&__pyx_v_src), (&__pyx_v_dst), __pyx_v_ndim, __pyx_v_itemsize);

  /* "View.MemoryView":1288
 *     refcount_copying(&dst, dtype_is_object, ndim, False)
 *     copy_strided_to_strided(&src, &dst, ndim, itemsize)
 *     refcount_copying(&dst, dtype_is_object, ndim, True)             # <<<<<<<<<<<<<<
 * 
 *     free(tmpdata)
 */
  __pyx_memoryview_refcount_copying((&__pyx_v_dst), __pyx_v_dtype_is_object, __pyx_v_ndim, 1);

  /* "View.MemoryView":1290
 *     refcount_copying(&dst, dtype_is_object, ndim, True)
 * 
 *     free(tmpdata)             # <<<<<<<<<<<<<<
 *     return 0
 * 
 */
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  /* "View.MemoryView":1291
 * 
 *     free(tmpdata)
 *     return 0             # <<<<<<<<<<<<<<
 * 
 * @cname('__pyx_memoryview_broadcast_leading')
 */
  __pyx_r = 0;
  goto __pyx_L0;

  /* "View.MemoryView":1222
 * 
 * @cname('__pyx_memoryview_copy_contents')
 * cdef int memoryview_copy_contents(__Pyx_memviewslice src,             # <<<<<<<<<<<<<<
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    PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();
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/* "View.MemoryView":1294
 * 
 * @cname('__pyx_memoryview_broadcast_leading')
 * cdef void broadcast_leading(__Pyx_memviewslice *slice,             # <<<<<<<<<<<<<<
 *                             int ndim,
 *                             int ndim_other) nogil:
 */

static void __pyx_memoryview_broadcast_leading(__Pyx_memviewslice *__pyx_v_slice, int __pyx_v_ndim, int __pyx_v_ndim_other) {
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  int __pyx_t_2;

  /* "View.MemoryView":1298
 *                             int ndim_other) nogil:
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 *     cdef int offset = ndim_other - ndim             # <<<<<<<<<<<<<<
 * 
 *     for i in range(ndim - 1, -1, -1):
 */
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  /* "View.MemoryView":1300
 *     cdef int offset = ndim_other - ndim
 * 
 *     for i in range(ndim - 1, -1, -1):             # <<<<<<<<<<<<<<
 *         slice.shape[i + offset] = slice.shape[i]
 *         slice.strides[i + offset] = slice.strides[i]
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  for (__pyx_t_1 = (__pyx_v_ndim - 1); __pyx_t_1 > -1; __pyx_t_1-=1) {
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    /* "View.MemoryView":1301
 * 
 *     for i in range(ndim - 1, -1, -1):
 *         slice.shape[i + offset] = slice.shape[i]             # <<<<<<<<<<<<<<
 *         slice.strides[i + offset] = slice.strides[i]
 *         slice.suboffsets[i + offset] = slice.suboffsets[i]
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    (__pyx_v_slice->shape[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_slice->shape[__pyx_v_i]);

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 *     for i in range(ndim - 1, -1, -1):
 *         slice.shape[i + offset] = slice.shape[i]
 *         slice.strides[i + offset] = slice.strides[i]             # <<<<<<<<<<<<<<
 *         slice.suboffsets[i + offset] = slice.suboffsets[i]
 * 
 */
    (__pyx_v_slice->strides[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_slice->strides[__pyx_v_i]);

    /* "View.MemoryView":1303
 *         slice.shape[i + offset] = slice.shape[i]
 *         slice.strides[i + offset] = slice.strides[i]
 *         slice.suboffsets[i + offset] = slice.suboffsets[i]             # <<<<<<<<<<<<<<
 * 
 *     for i in range(offset):
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    (__pyx_v_slice->suboffsets[(__pyx_v_i + __pyx_v_offset)]) = (__pyx_v_slice->suboffsets[__pyx_v_i]);
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 *         slice.suboffsets[i + offset] = slice.suboffsets[i]
 * 
 *     for i in range(offset):             # <<<<<<<<<<<<<<
 *         slice.shape[i] = 1
 *         slice.strides[i] = slice.strides[0]
 */
  __pyx_t_1 = __pyx_v_offset;
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    /* "View.MemoryView":1306
 * 
 *     for i in range(offset):
 *         slice.shape[i] = 1             # <<<<<<<<<<<<<<
 *         slice.strides[i] = slice.strides[0]
 *         slice.suboffsets[i] = -1
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    /* "View.MemoryView":1307
 *     for i in range(offset):
 *         slice.shape[i] = 1
 *         slice.strides[i] = slice.strides[0]             # <<<<<<<<<<<<<<
 *         slice.suboffsets[i] = -1
 * 
 */
    (__pyx_v_slice->strides[__pyx_v_i]) = (__pyx_v_slice->strides[0]);

    /* "View.MemoryView":1308
 *         slice.shape[i] = 1
 *         slice.strides[i] = slice.strides[0]
 *         slice.suboffsets[i] = -1             # <<<<<<<<<<<<<<
 * 
 * 
 */
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 * 
 * @cname('__pyx_memoryview_broadcast_leading')
 * cdef void broadcast_leading(__Pyx_memviewslice *slice,             # <<<<<<<<<<<<<<
 *                             int ndim,
 *                             int ndim_other) nogil:
 */

  /* function exit code */
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/* "View.MemoryView":1316
 * 
 * @cname('__pyx_memoryview_refcount_copying')
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object,             # <<<<<<<<<<<<<<
 *                            int ndim, bint inc) nogil:
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static void __pyx_memoryview_refcount_copying(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_dtype_is_object, int __pyx_v_ndim, int __pyx_v_inc) {
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 * 
 * 
 *     if dtype_is_object:             # <<<<<<<<<<<<<<
 *         refcount_objects_in_slice_with_gil(dst.data, dst.shape,
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 * 
 *     if dtype_is_object:
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 *                                            dst.strides, ndim, inc)
 * 
 */
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 * 
 * @cname('__pyx_memoryview_refcount_copying')
 * cdef void refcount_copying(__Pyx_memviewslice *dst, bint dtype_is_object,             # <<<<<<<<<<<<<<
 *                            int ndim, bint inc) nogil:
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 */

  /* function exit code */
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/* "View.MemoryView":1325
 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil')
 * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape,             # <<<<<<<<<<<<<<
 *                                              Py_ssize_t *strides, int ndim,
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 */

static void __pyx_memoryview_refcount_objects_in_slice_with_gil(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) {
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 *                                              Py_ssize_t *strides, int ndim,
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 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice')
 */
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 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice_with_gil')
 * cdef void refcount_objects_in_slice_with_gil(char *data, Py_ssize_t *shape,             # <<<<<<<<<<<<<<
 *                                              Py_ssize_t *strides, int ndim,
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/* "View.MemoryView":1331
 * 
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 * cdef void refcount_objects_in_slice(char *data, Py_ssize_t *shape,             # <<<<<<<<<<<<<<
 *                                     Py_ssize_t *strides, int ndim, bint inc):
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static void __pyx_memoryview_refcount_objects_in_slice(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, int __pyx_v_inc) {
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    /* "View.MemoryView":1336
 * 
 *     for i in range(shape[0]):
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 *     for i in range(shape[0]):
 *         if ndim == 1:
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 *                 Py_INCREF((<PyObject **> data)[0])
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      __pyx_t_3 = (__pyx_v_inc != 0);
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        /* "View.MemoryView":1338
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 *                 Py_INCREF((<PyObject **> data)[0])             # <<<<<<<<<<<<<<
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 *                 Py_DECREF((<PyObject **> data)[0])             # <<<<<<<<<<<<<<
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 *                 Py_DECREF((<PyObject **> data)[0])
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 *                                       ndim - 1, inc)
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 */
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 *         data += strides[0]             # <<<<<<<<<<<<<<
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 * 
 * @cname('__pyx_memoryview_refcount_objects_in_slice')
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/* "View.MemoryView":1351
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 * @cname('__pyx_memoryview_slice_assign_scalar')
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 *                               size_t itemsize, void *item,
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static void __pyx_memoryview_slice_assign_scalar(__Pyx_memviewslice *__pyx_v_dst, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item, int __pyx_v_dtype_is_object) {

  /* "View.MemoryView":1354
 *                               size_t itemsize, void *item,
 *                               bint dtype_is_object) nogil:
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  /* "View.MemoryView":1355
 *                               bint dtype_is_object) nogil:
 *     refcount_copying(dst, dtype_is_object, ndim, False)
 *     _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim,             # <<<<<<<<<<<<<<
 *                          itemsize, item)
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  /* "View.MemoryView":1357
 *     _slice_assign_scalar(dst.data, dst.shape, dst.strides, ndim,
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 * 
 * 
 */
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  /* "View.MemoryView":1351
 * 
 * @cname('__pyx_memoryview_slice_assign_scalar')
 * cdef void slice_assign_scalar(__Pyx_memviewslice *dst, int ndim,             # <<<<<<<<<<<<<<
 *                               size_t itemsize, void *item,
 *                               bint dtype_is_object) nogil:
 */

  /* function exit code */
}

/* "View.MemoryView":1361
 * 
 * @cname('__pyx_memoryview__slice_assign_scalar')
 * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape,             # <<<<<<<<<<<<<<
 *                               Py_ssize_t *strides, int ndim,
 *                               size_t itemsize, void *item) nogil:
 */

static void __pyx_memoryview__slice_assign_scalar(char *__pyx_v_data, Py_ssize_t *__pyx_v_shape, Py_ssize_t *__pyx_v_strides, int __pyx_v_ndim, size_t __pyx_v_itemsize, void *__pyx_v_item) {
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  Py_ssize_t __pyx_t_2;
  Py_ssize_t __pyx_t_3;

  /* "View.MemoryView":1365
 *                               size_t itemsize, void *item) nogil:
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 *     cdef Py_ssize_t extent = shape[0]
 * 
 */
  __pyx_v_stride = (__pyx_v_strides[0]);

  /* "View.MemoryView":1366
 *     cdef Py_ssize_t i
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 *     cdef Py_ssize_t extent = shape[0]             # <<<<<<<<<<<<<<
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 *     if ndim == 1:
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  /* "View.MemoryView":1368
 *     cdef Py_ssize_t extent = shape[0]
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 *     if ndim == 1:             # <<<<<<<<<<<<<<
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  __pyx_t_1 = ((__pyx_v_ndim == 1) != 0);
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    /* "View.MemoryView":1369
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 *     if ndim == 1:
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 *             memcpy(data, item, itemsize)
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      /* "View.MemoryView":1370
 *     if ndim == 1:
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      /* "View.MemoryView":1371
 *         for i in range(extent):
 *             memcpy(data, item, itemsize)
 *             data += stride             # <<<<<<<<<<<<<<
 *     else:
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 */
      __pyx_v_data = (__pyx_v_data + __pyx_v_stride);
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    /* "View.MemoryView":1373
 *             data += stride
 *     else:
 *         for i in range(extent):             # <<<<<<<<<<<<<<
 *             _slice_assign_scalar(data, shape + 1, strides + 1,
 *                                 ndim - 1, itemsize, item)
 */
    __pyx_t_2 = __pyx_v_extent;
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      __pyx_v_i = __pyx_t_3;

      /* "View.MemoryView":1374
 *     else:
 *         for i in range(extent):
 *             _slice_assign_scalar(data, shape + 1, strides + 1,             # <<<<<<<<<<<<<<
 *                                 ndim - 1, itemsize, item)
 *             data += stride
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      /* "View.MemoryView":1376
 *             _slice_assign_scalar(data, shape + 1, strides + 1,
 *                                 ndim - 1, itemsize, item)
 *             data += stride             # <<<<<<<<<<<<<<
 * 
 * 
 */
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  /* "View.MemoryView":1361
 * 
 * @cname('__pyx_memoryview__slice_assign_scalar')
 * cdef void _slice_assign_scalar(char *data, Py_ssize_t *shape,             # <<<<<<<<<<<<<<
 *                               Py_ssize_t *strides, int ndim,
 *                               size_t itemsize, void *item) nogil:
 */

  /* function exit code */
}
static struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform __pyx_vtable_4dipy_5align_10transforms_Transform;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_Transform(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
  struct __pyx_obj_4dipy_5align_10transforms_Transform *p;
  PyObject *o;
  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_Transform *)o);
  p->__pyx_vtab = __pyx_vtabptr_4dipy_5align_10transforms_Transform;
  if (unlikely(__pyx_pw_4dipy_5align_10transforms_9Transform_1__cinit__(o, __pyx_empty_tuple, NULL) < 0)) {
    Py_DECREF(o); o = 0;
  }
  return o;
}

static void __pyx_tp_dealloc_4dipy_5align_10transforms_Transform(PyObject *o) {
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  if (unlikely(Py_TYPE(o)->tp_finalize) && (!PyType_IS_GC(Py_TYPE(o)) || !_PyGC_FINALIZED(o))) {
    if (PyObject_CallFinalizerFromDealloc(o)) return;
  }
  #endif
  (*Py_TYPE(o)->tp_free)(o);
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_Transform[] = {
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  {"param_to_matrix", (PyCFunction)__pyx_pw_4dipy_5align_10transforms_9Transform_7param_to_matrix, METH_O, __pyx_doc_4dipy_5align_10transforms_9Transform_6param_to_matrix},
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  {"get_dim", (PyCFunction)__pyx_pw_4dipy_5align_10transforms_9Transform_11get_dim, METH_NOARGS, 0},
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_Transform = {
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  sizeof(struct __pyx_obj_4dipy_5align_10transforms_Transform), /*tp_basicsize*/
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  __pyx_tp_dealloc_4dipy_5align_10transforms_Transform, /*tp_dealloc*/
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  0, /*tp_compare*/
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  " Base class (contract) for all transforms for affine image registration.\n    Each transform must define the following (fast, nogil) methods:\n\n    1. _jacobian(theta, x, J): receives a parameter vector theta, a point in\n       x, and a matrix J with shape (dim, len(theta)). It must writes in J, the\n       Jacobian of the transform with parameters theta evaluated at x.\n\n    2. _get_identity_parameters(theta): receives a vector theta whose length is\n       the number of parameters of the transform and sets in theta the values\n       that define the identity transform.\n\n    3. _param_to_matrix(theta, T): receives a parameter vector theta, and a\n       matrix T of shape (dim + 1, dim + 1) and writes in T the matrix\n       representation of the transform with parameters theta\n\n    This base class defines the (slow, convenient) python wrappers for each\n    of the above functions, which also do parameter checking and raise\n    a ValueError in case the provided parameters are invalid.\n    ", /*tp_doc*/
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform2D __pyx_vtable_4dipy_5align_10transforms_TranslationTransform2D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_TranslationTransform2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *p;
  PyObject *o = __pyx_tp_new_4dipy_5align_10transforms_Transform(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform2D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform*)__pyx_vtabptr_4dipy_5align_10transforms_TranslationTransform2D;
  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_TranslationTransform2D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_TranslationTransform2D = {
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_TranslationTransform3D __pyx_vtable_4dipy_5align_10transforms_TranslationTransform3D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_TranslationTransform3D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *p;
  PyObject *o = __pyx_tp_new_4dipy_5align_10transforms_Transform(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_TranslationTransform3D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform*)__pyx_vtabptr_4dipy_5align_10transforms_TranslationTransform3D;
  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_TranslationTransform3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_TranslationTransform3D = {
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform2D __pyx_vtable_4dipy_5align_10transforms_RotationTransform2D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RotationTransform2D(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *p;
  PyObject *o = __pyx_tp_new_4dipy_5align_10transforms_Transform(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_RotationTransform2D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform*)__pyx_vtabptr_4dipy_5align_10transforms_RotationTransform2D;
  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_RotationTransform2D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_RotationTransform2D = {
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_RotationTransform3D __pyx_vtable_4dipy_5align_10transforms_RotationTransform3D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RotationTransform3D(PyTypeObject *t, PyObject *a, PyObject *k) {
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  PyObject *o = __pyx_tp_new_4dipy_5align_10transforms_Transform(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_RotationTransform3D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform*)__pyx_vtabptr_4dipy_5align_10transforms_RotationTransform3D;
  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_RotationTransform3D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_RotationTransform3D = {
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform2D __pyx_vtable_4dipy_5align_10transforms_RigidTransform2D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RigidTransform2D(PyTypeObject *t, PyObject *a, PyObject *k) {
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  PyObject *o = __pyx_tp_new_4dipy_5align_10transforms_Transform(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_obj_4dipy_5align_10transforms_RigidTransform2D *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_4dipy_5align_10transforms_Transform*)__pyx_vtabptr_4dipy_5align_10transforms_RigidTransform2D;
  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_RigidTransform2D[] = {
  {0, 0, 0, 0}
};

static PyTypeObject __pyx_type_4dipy_5align_10transforms_RigidTransform2D = {
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static struct __pyx_vtabstruct_4dipy_5align_10transforms_RigidTransform3D __pyx_vtable_4dipy_5align_10transforms_RigidTransform3D;

static PyObject *__pyx_tp_new_4dipy_5align_10transforms_RigidTransform3D(PyTypeObject *t, PyObject *a, PyObject *k) {
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  return o;
}

static PyMethodDef __pyx_methods_4dipy_5align_10transforms_RigidTransform3D[] = {
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static PyTypeObject __pyx_type_4dipy_5align_10transforms_RigidTransform3D = {
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  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  0, /*tp_doc*/
  __pyx_tp_traverse_Enum, /*tp_traverse*/
  __pyx_tp_clear_Enum, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_Enum, /*tp_methods*/
  0, /*tp_members*/
  0, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  __pyx_MemviewEnum___init__, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_Enum, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct_memoryview __pyx_vtable_memoryview;

static PyObject *__pyx_tp_new_memoryview(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_memoryview_obj *p;
  PyObject *o;
  if (likely((t->tp_flags & Py_TPFLAGS_IS_ABSTRACT) == 0)) {
    o = (*t->tp_alloc)(t, 0);
  } else {
    o = (PyObject *) PyBaseObject_Type.tp_new(t, __pyx_empty_tuple, 0);
  }
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_memoryview_obj *)o);
  p->__pyx_vtab = __pyx_vtabptr_memoryview;
  p->obj = Py_None; Py_INCREF(Py_None);
  p->_size = Py_None; Py_INCREF(Py_None);
  p->_array_interface = Py_None; Py_INCREF(Py_None);
  p->view.obj = NULL;
  if (unlikely(__pyx_memoryview___cinit__(o, a, k) < 0)) {
    Py_DECREF(o); o = 0;
  }
  return o;
}

static void __pyx_tp_dealloc_memoryview(PyObject *o) {
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  #if PY_VERSION_HEX >= 0x030400a1
  if (unlikely(Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) {
    if (PyObject_CallFinalizerFromDealloc(o)) return;
  }
  #endif
  PyObject_GC_UnTrack(o);
  {
    PyObject *etype, *eval, *etb;
    PyErr_Fetch(&etype, &eval, &etb);
    ++Py_REFCNT(o);
    __pyx_memoryview___dealloc__(o);
    --Py_REFCNT(o);
    PyErr_Restore(etype, eval, etb);
  }
  Py_CLEAR(p->obj);
  Py_CLEAR(p->_size);
  Py_CLEAR(p->_array_interface);
  (*Py_TYPE(o)->tp_free)(o);
}

static int __pyx_tp_traverse_memoryview(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  if (p->obj) {
    e = (*v)(p->obj, a); if (e) return e;
  }
  if (p->_size) {
    e = (*v)(p->_size, a); if (e) return e;
  }
  if (p->_array_interface) {
    e = (*v)(p->_array_interface, a); if (e) return e;
  }
  if (p->view.obj) {
    e = (*v)(p->view.obj, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_memoryview(PyObject *o) {
  PyObject* tmp;
  struct __pyx_memoryview_obj *p = (struct __pyx_memoryview_obj *)o;
  tmp = ((PyObject*)p->obj);
  p->obj = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_size);
  p->_size = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->_array_interface);
  p->_array_interface = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  Py_CLEAR(p->view.obj);
  return 0;
}
static PyObject *__pyx_sq_item_memoryview(PyObject *o, Py_ssize_t i) {
  PyObject *r;
  PyObject *x = PyInt_FromSsize_t(i); if(!x) return 0;
  r = Py_TYPE(o)->tp_as_mapping->mp_subscript(o, x);
  Py_DECREF(x);
  return r;
}

static int __pyx_mp_ass_subscript_memoryview(PyObject *o, PyObject *i, PyObject *v) {
  if (v) {
    return __pyx_memoryview___setitem__(o, i, v);
  }
  else {
    PyErr_Format(PyExc_NotImplementedError,
      "Subscript deletion not supported by %.200s", Py_TYPE(o)->tp_name);
    return -1;
  }
}

static PyObject *__pyx_getprop___pyx_memoryview_T(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_transpose(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_base(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview__get__base(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_shape(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_shape(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_strides(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_strides(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_suboffsets(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_suboffsets(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_ndim(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_ndim(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_itemsize(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_itemsize(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_nbytes(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_nbytes(o);
}

static PyObject *__pyx_getprop___pyx_memoryview_size(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryview_get_size(o);
}

static PyMethodDef __pyx_methods_memoryview[] = {
  {"is_c_contig", (PyCFunction)__pyx_memoryview_is_c_contig, METH_NOARGS, 0},
  {"is_f_contig", (PyCFunction)__pyx_memoryview_is_f_contig, METH_NOARGS, 0},
  {"copy", (PyCFunction)__pyx_memoryview_copy, METH_NOARGS, 0},
  {"copy_fortran", (PyCFunction)__pyx_memoryview_copy_fortran, METH_NOARGS, 0},
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets_memoryview[] = {
  {(char *)"T", __pyx_getprop___pyx_memoryview_T, 0, 0, 0},
  {(char *)"base", __pyx_getprop___pyx_memoryview_base, 0, 0, 0},
  {(char *)"shape", __pyx_getprop___pyx_memoryview_shape, 0, 0, 0},
  {(char *)"strides", __pyx_getprop___pyx_memoryview_strides, 0, 0, 0},
  {(char *)"suboffsets", __pyx_getprop___pyx_memoryview_suboffsets, 0, 0, 0},
  {(char *)"ndim", __pyx_getprop___pyx_memoryview_ndim, 0, 0, 0},
  {(char *)"itemsize", __pyx_getprop___pyx_memoryview_itemsize, 0, 0, 0},
  {(char *)"nbytes", __pyx_getprop___pyx_memoryview_nbytes, 0, 0, 0},
  {(char *)"size", __pyx_getprop___pyx_memoryview_size, 0, 0, 0},
  {0, 0, 0, 0, 0}
};

static PySequenceMethods __pyx_tp_as_sequence_memoryview = {
  __pyx_memoryview___len__, /*sq_length*/
  0, /*sq_concat*/
  0, /*sq_repeat*/
  __pyx_sq_item_memoryview, /*sq_item*/
  0, /*sq_slice*/
  0, /*sq_ass_item*/
  0, /*sq_ass_slice*/
  0, /*sq_contains*/
  0, /*sq_inplace_concat*/
  0, /*sq_inplace_repeat*/
};

static PyMappingMethods __pyx_tp_as_mapping_memoryview = {
  __pyx_memoryview___len__, /*mp_length*/
  __pyx_memoryview___getitem__, /*mp_subscript*/
  __pyx_mp_ass_subscript_memoryview, /*mp_ass_subscript*/
};

static PyBufferProcs __pyx_tp_as_buffer_memoryview = {
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getreadbuffer*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getwritebuffer*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getsegcount*/
  #endif
  #if PY_MAJOR_VERSION < 3
  0, /*bf_getcharbuffer*/
  #endif
  __pyx_memoryview_getbuffer, /*bf_getbuffer*/
  0, /*bf_releasebuffer*/
};

static PyTypeObject __pyx_type___pyx_memoryview = {
  PyVarObject_HEAD_INIT(0, 0)
  "dipy.align.transforms.memoryview", /*tp_name*/
  sizeof(struct __pyx_memoryview_obj), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_memoryview, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #else
  0, /*reserved*/
  #endif
  __pyx_memoryview___repr__, /*tp_repr*/
  0, /*tp_as_number*/
  &__pyx_tp_as_sequence_memoryview, /*tp_as_sequence*/
  &__pyx_tp_as_mapping_memoryview, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  __pyx_memoryview___str__, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  &__pyx_tp_as_buffer_memoryview, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  0, /*tp_doc*/
  __pyx_tp_traverse_memoryview, /*tp_traverse*/
  __pyx_tp_clear_memoryview, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods_memoryview, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets_memoryview, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_memoryview, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};
static struct __pyx_vtabstruct__memoryviewslice __pyx_vtable__memoryviewslice;

static PyObject *__pyx_tp_new__memoryviewslice(PyTypeObject *t, PyObject *a, PyObject *k) {
  struct __pyx_memoryviewslice_obj *p;
  PyObject *o = __pyx_tp_new_memoryview(t, a, k);
  if (unlikely(!o)) return 0;
  p = ((struct __pyx_memoryviewslice_obj *)o);
  p->__pyx_base.__pyx_vtab = (struct __pyx_vtabstruct_memoryview*)__pyx_vtabptr__memoryviewslice;
  p->from_object = Py_None; Py_INCREF(Py_None);
  p->from_slice.memview = NULL;
  return o;
}

static void __pyx_tp_dealloc__memoryviewslice(PyObject *o) {
  struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o;
  #if PY_VERSION_HEX >= 0x030400a1
  if (unlikely(Py_TYPE(o)->tp_finalize) && !_PyGC_FINALIZED(o)) {
    if (PyObject_CallFinalizerFromDealloc(o)) return;
  }
  #endif
  PyObject_GC_UnTrack(o);
  {
    PyObject *etype, *eval, *etb;
    PyErr_Fetch(&etype, &eval, &etb);
    ++Py_REFCNT(o);
    __pyx_memoryviewslice___dealloc__(o);
    --Py_REFCNT(o);
    PyErr_Restore(etype, eval, etb);
  }
  Py_CLEAR(p->from_object);
  PyObject_GC_Track(o);
  __pyx_tp_dealloc_memoryview(o);
}

static int __pyx_tp_traverse__memoryviewslice(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o;
  e = __pyx_tp_traverse_memoryview(o, v, a); if (e) return e;
  if (p->from_object) {
    e = (*v)(p->from_object, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear__memoryviewslice(PyObject *o) {
  PyObject* tmp;
  struct __pyx_memoryviewslice_obj *p = (struct __pyx_memoryviewslice_obj *)o;
  __pyx_tp_clear_memoryview(o);
  tmp = ((PyObject*)p->from_object);
  p->from_object = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  __PYX_XDEC_MEMVIEW(&p->from_slice, 1);
  return 0;
}

static PyObject *__pyx_getprop___pyx_memoryviewslice_base(PyObject *o, CYTHON_UNUSED void *x) {
  return __pyx_memoryviewslice__get__base(o);
}

static PyMethodDef __pyx_methods__memoryviewslice[] = {
  {0, 0, 0, 0}
};

static struct PyGetSetDef __pyx_getsets__memoryviewslice[] = {
  {(char *)"base", __pyx_getprop___pyx_memoryviewslice_base, 0, 0, 0},
  {0, 0, 0, 0, 0}
};

static PyTypeObject __pyx_type___pyx_memoryviewslice = {
  PyVarObject_HEAD_INIT(0, 0)
  "dipy.align.transforms._memoryviewslice", /*tp_name*/
  sizeof(struct __pyx_memoryviewslice_obj), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc__memoryviewslice, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #else
  0, /*reserved*/
  #endif
  #if CYTHON_COMPILING_IN_PYPY
  __pyx_memoryview___repr__, /*tp_repr*/
  #else
  0, /*tp_repr*/
  #endif
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  #if CYTHON_COMPILING_IN_PYPY
  __pyx_memoryview___str__, /*tp_str*/
  #else
  0, /*tp_str*/
  #endif
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_BASETYPE|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  "Internal class for passing memoryview slices to Python", /*tp_doc*/
  __pyx_tp_traverse__memoryviewslice, /*tp_traverse*/
  __pyx_tp_clear__memoryviewslice, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  __pyx_methods__memoryviewslice, /*tp_methods*/
  0, /*tp_members*/
  __pyx_getsets__memoryviewslice, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new__memoryviewslice, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};

static PyMethodDef __pyx_methods[] = {
  {0, 0, 0, 0}
};

#if PY_MAJOR_VERSION >= 3
static struct PyModuleDef __pyx_moduledef = {
  #if PY_VERSION_HEX < 0x03020000
    { PyObject_HEAD_INIT(NULL) NULL, 0, NULL },
  #else
    PyModuleDef_HEAD_INIT,
  #endif
    "transforms",
    0, /* m_doc */
    -1, /* m_size */
    __pyx_methods /* m_methods */,
    NULL, /* m_reload */
    NULL, /* m_traverse */
    NULL, /* m_clear */
    NULL /* m_free */
};
#endif

static __Pyx_StringTabEntry __pyx_string_tab[] = {
  {&__pyx_n_s_AFFINE, __pyx_k_AFFINE, sizeof(__pyx_k_AFFINE), 0, 0, 1, 1},
  {&__pyx_kp_s_Buffer_view_does_not_expose_stri, __pyx_k_Buffer_view_does_not_expose_stri, sizeof(__pyx_k_Buffer_view_does_not_expose_stri), 0, 0, 1, 0},
  {&__pyx_kp_s_Can_only_create_a_buffer_that_is, __pyx_k_Can_only_create_a_buffer_that_is, sizeof(__pyx_k_Can_only_create_a_buffer_that_is), 0, 0, 1, 0},
  {&__pyx_kp_s_Cannot_index_with_type_s, __pyx_k_Cannot_index_with_type_s, sizeof(__pyx_k_Cannot_index_with_type_s), 0, 0, 1, 0},
  {&__pyx_n_s_Ellipsis, __pyx_k_Ellipsis, sizeof(__pyx_k_Ellipsis), 0, 0, 1, 1},
  {&__pyx_kp_s_Empty_shape_tuple_for_cython_arr, __pyx_k_Empty_shape_tuple_for_cython_arr, sizeof(__pyx_k_Empty_shape_tuple_for_cython_arr), 0, 0, 1, 0},
  {&__pyx_kp_u_Format_string_allocated_too_shor, __pyx_k_Format_string_allocated_too_shor, sizeof(__pyx_k_Format_string_allocated_too_shor), 0, 1, 0, 0},
  {&__pyx_kp_u_Format_string_allocated_too_shor_2, __pyx_k_Format_string_allocated_too_shor_2, sizeof(__pyx_k_Format_string_allocated_too_shor_2), 0, 1, 0, 0},
  {&__pyx_n_s_IndexError, __pyx_k_IndexError, sizeof(__pyx_k_IndexError), 0, 0, 1, 1},
  {&__pyx_kp_s_Indirect_dimensions_not_supporte, __pyx_k_Indirect_dimensions_not_supporte, sizeof(__pyx_k_Indirect_dimensions_not_supporte), 0, 0, 1, 0},
  {&__pyx_kp_s_Invalid_mode_expected_c_or_fortr, __pyx_k_Invalid_mode_expected_c_or_fortr, sizeof(__pyx_k_Invalid_mode_expected_c_or_fortr), 0, 0, 1, 0},
  {&__pyx_kp_s_Invalid_number_of_parameters_d, __pyx_k_Invalid_number_of_parameters_d, sizeof(__pyx_k_Invalid_number_of_parameters_d), 0, 0, 1, 0},
  {&__pyx_kp_s_Invalid_point_dimension_d, __pyx_k_Invalid_point_dimension_d, sizeof(__pyx_k_Invalid_point_dimension_d), 0, 0, 1, 0},
  {&__pyx_kp_s_Invalid_shape_in_axis_d_d, __pyx_k_Invalid_shape_in_axis_d_d, sizeof(__pyx_k_Invalid_shape_in_axis_d_d), 0, 0, 1, 0},
  {&__pyx_kp_s_Invalid_transform, __pyx_k_Invalid_transform, sizeof(__pyx_k_Invalid_transform), 0, 0, 1, 0},
  {&__pyx_n_s_MemoryError, __pyx_k_MemoryError, sizeof(__pyx_k_MemoryError), 0, 0, 1, 1},
  {&__pyx_kp_s_MemoryView_of_r_at_0x_x, __pyx_k_MemoryView_of_r_at_0x_x, sizeof(__pyx_k_MemoryView_of_r_at_0x_x), 0, 0, 1, 0},
  {&__pyx_kp_s_MemoryView_of_r_object, __pyx_k_MemoryView_of_r_object, sizeof(__pyx_k_MemoryView_of_r_object), 0, 0, 1, 0},
  {&__pyx_kp_u_Non_native_byte_order_not_suppor, __pyx_k_Non_native_byte_order_not_suppor, sizeof(__pyx_k_Non_native_byte_order_not_suppor), 0, 1, 0, 0},
  {&__pyx_n_b_O, __pyx_k_O, sizeof(__pyx_k_O), 0, 0, 0, 1},
  {&__pyx_kp_s_Out_of_bounds_on_buffer_access_a, __pyx_k_Out_of_bounds_on_buffer_access_a, sizeof(__pyx_k_Out_of_bounds_on_buffer_access_a), 0, 0, 1, 0},
  {&__pyx_n_s_RIGID, __pyx_k_RIGID, sizeof(__pyx_k_RIGID), 0, 0, 1, 1},
  {&__pyx_n_s_ROTATION, __pyx_k_ROTATION, sizeof(__pyx_k_ROTATION), 0, 0, 1, 1},
  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
  {&__pyx_n_s_SCALING, __pyx_k_SCALING, sizeof(__pyx_k_SCALING), 0, 0, 1, 1},
  {&__pyx_n_s_TRANSLATION, __pyx_k_TRANSLATION, sizeof(__pyx_k_TRANSLATION), 0, 0, 1, 1},
  {&__pyx_n_s_TypeError, __pyx_k_TypeError, sizeof(__pyx_k_TypeError), 0, 0, 1, 1},
  {&__pyx_kp_s_Unable_to_convert_item_to_object, __pyx_k_Unable_to_convert_item_to_object, sizeof(__pyx_k_Unable_to_convert_item_to_object), 0, 0, 1, 0},
  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
  {&__pyx_n_s_allocate_buffer, __pyx_k_allocate_buffer, sizeof(__pyx_k_allocate_buffer), 0, 0, 1, 1},
  {&__pyx_n_s_base, __pyx_k_base, sizeof(__pyx_k_base), 0, 0, 1, 1},
  {&__pyx_n_s_c, __pyx_k_c, sizeof(__pyx_k_c), 0, 0, 1, 1},
  {&__pyx_n_u_c, __pyx_k_c, sizeof(__pyx_k_c), 0, 1, 0, 1},
  {&__pyx_n_s_class, __pyx_k_class, sizeof(__pyx_k_class), 0, 0, 1, 1},
  {&__pyx_kp_s_contiguous_and_direct, __pyx_k_contiguous_and_direct, sizeof(__pyx_k_contiguous_and_direct), 0, 0, 1, 0},
  {&__pyx_kp_s_contiguous_and_indirect, __pyx_k_contiguous_and_indirect, sizeof(__pyx_k_contiguous_and_indirect), 0, 0, 1, 0},
  {&__pyx_n_s_dtype_is_object, __pyx_k_dtype_is_object, sizeof(__pyx_k_dtype_is_object), 0, 0, 1, 1},
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  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_TranslationTransform3D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 190; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_22TranslationTransform3D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_22TranslationTransform3D___init__.doc = __pyx_doc_4dipy_5align_10transforms_22TranslationTransform3D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_22TranslationTransform3D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_TranslationTransform3D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_TranslationTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 190; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "TranslationTransform3D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_TranslationTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 190; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_TranslationTransform3D = &__pyx_type_4dipy_5align_10transforms_TranslationTransform3D;
  __pyx_vtabptr_4dipy_5align_10transforms_RotationTransform2D = &__pyx_vtable_4dipy_5align_10transforms_RotationTransform2D;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform2D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform2D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform2D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform2D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform2D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform2D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform2D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_RotationTransform2D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_RotationTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 261; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_RotationTransform2D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_RotationTransform2D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 261; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform2D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform2D___init__.doc = __pyx_doc_4dipy_5align_10transforms_19RotationTransform2D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform2D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_RotationTransform2D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_RotationTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 261; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "RotationTransform2D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_RotationTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 261; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_RotationTransform2D = &__pyx_type_4dipy_5align_10transforms_RotationTransform2D;
  __pyx_vtabptr_4dipy_5align_10transforms_RotationTransform3D = &__pyx_vtable_4dipy_5align_10transforms_RotationTransform3D;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform3D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform3D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform3D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform3D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform3D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_RotationTransform3D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_19RotationTransform3D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_RotationTransform3D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_RotationTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 335; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_RotationTransform3D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_RotationTransform3D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 335; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform3D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform3D___init__.doc = __pyx_doc_4dipy_5align_10transforms_19RotationTransform3D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_19RotationTransform3D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_RotationTransform3D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_RotationTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 335; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "RotationTransform3D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_RotationTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 335; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_RotationTransform3D = &__pyx_type_4dipy_5align_10transforms_RotationTransform3D;
  __pyx_vtabptr_4dipy_5align_10transforms_RigidTransform2D = &__pyx_vtable_4dipy_5align_10transforms_RigidTransform2D;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform2D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform2D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform2D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform2D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform2D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform2D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform2D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_RigidTransform2D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_RigidTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 428; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_RigidTransform2D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_RigidTransform2D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 428; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform2D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform2D___init__.doc = __pyx_doc_4dipy_5align_10transforms_16RigidTransform2D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform2D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_RigidTransform2D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_RigidTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 428; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "RigidTransform2D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_RigidTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 428; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_RigidTransform2D = &__pyx_type_4dipy_5align_10transforms_RigidTransform2D;
  __pyx_vtabptr_4dipy_5align_10transforms_RigidTransform3D = &__pyx_vtable_4dipy_5align_10transforms_RigidTransform3D;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform3D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform3D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform3D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform3D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform3D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_RigidTransform3D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_16RigidTransform3D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_RigidTransform3D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_RigidTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 515; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_RigidTransform3D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_RigidTransform3D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 515; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform3D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform3D___init__.doc = __pyx_doc_4dipy_5align_10transforms_16RigidTransform3D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_16RigidTransform3D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_RigidTransform3D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_RigidTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 515; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "RigidTransform3D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_RigidTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 515; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_RigidTransform3D = &__pyx_type_4dipy_5align_10transforms_RigidTransform3D;
  __pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform2D = &__pyx_vtable_4dipy_5align_10transforms_ScalingTransform2D;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform2D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform2D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform2D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform2D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform2D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_ScalingTransform2D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_ScalingTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 634; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_ScalingTransform2D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_ScalingTransform2D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 634; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform2D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform2D___init__.doc = __pyx_doc_4dipy_5align_10transforms_18ScalingTransform2D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform2D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_ScalingTransform2D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 634; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "ScalingTransform2D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_ScalingTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 634; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_ScalingTransform2D = &__pyx_type_4dipy_5align_10transforms_ScalingTransform2D;
  __pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform3D = &__pyx_vtable_4dipy_5align_10transforms_ScalingTransform3D;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform3D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform3D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform3D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_ScalingTransform3D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_18ScalingTransform3D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_ScalingTransform3D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_ScalingTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 697; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_ScalingTransform3D.tp_print = 0;
  #if CYTHON_COMPILING_IN_CPYTHON
  {
    PyObject *wrapper = PyObject_GetAttrString((PyObject *)&__pyx_type_4dipy_5align_10transforms_ScalingTransform3D, "__init__"); if (unlikely(!wrapper)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 697; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
    if (Py_TYPE(wrapper) == &PyWrapperDescr_Type) {
      __pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform3D___init__ = *((PyWrapperDescrObject *)wrapper)->d_base;
      __pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform3D___init__.doc = __pyx_doc_4dipy_5align_10transforms_18ScalingTransform3D___init__;
      ((PyWrapperDescrObject *)wrapper)->d_base = &__pyx_wrapperbase_4dipy_5align_10transforms_18ScalingTransform3D___init__;
    }
  }
  #endif
  if (__Pyx_SetVtable(__pyx_type_4dipy_5align_10transforms_ScalingTransform3D.tp_dict, __pyx_vtabptr_4dipy_5align_10transforms_ScalingTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 697; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  if (PyObject_SetAttrString(__pyx_m, "ScalingTransform3D", (PyObject *)&__pyx_type_4dipy_5align_10transforms_ScalingTransform3D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 697; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_ptype_4dipy_5align_10transforms_ScalingTransform3D = &__pyx_type_4dipy_5align_10transforms_ScalingTransform3D;
  __pyx_vtabptr_4dipy_5align_10transforms_AffineTransform2D = &__pyx_vtable_4dipy_5align_10transforms_AffineTransform2D;
  __pyx_vtable_4dipy_5align_10transforms_AffineTransform2D.__pyx_base = *__pyx_vtabptr_4dipy_5align_10transforms_Transform;
  __pyx_vtable_4dipy_5align_10transforms_AffineTransform2D.__pyx_base._jacobian = (int (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_17AffineTransform2D__jacobian;
  __pyx_vtable_4dipy_5align_10transforms_AffineTransform2D.__pyx_base._get_identity_parameters = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_17AffineTransform2D__get_identity_parameters;
  __pyx_vtable_4dipy_5align_10transforms_AffineTransform2D.__pyx_base._param_to_matrix = (void (*)(struct __pyx_obj_4dipy_5align_10transforms_Transform *, __Pyx_memviewslice, __Pyx_memviewslice))__pyx_f_4dipy_5align_10transforms_17AffineTransform2D__param_to_matrix;
  __pyx_type_4dipy_5align_10transforms_AffineTransform2D.tp_base = __pyx_ptype_4dipy_5align_10transforms_Transform;
  if (PyType_Ready(&__pyx_type_4dipy_5align_10transforms_AffineTransform2D) < 0) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 761; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_type_4dipy_5align_10transforms_AffineTransform2D.tp_print = 0;
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            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (PyExceptionClass_Check(type)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                if (PyObject_IsSubclass(instance_class, type)) {
                    type = instance_class;
                } else {
                    instance_class = NULL;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
#if PY_VERSION_HEX >= 0x03030000
    if (cause) {
#else
    if (cause && cause != Py_None) {
#endif
        PyObject *fixed_cause;
        if (cause == Py_None) {
            fixed_cause = NULL;
        } else if (PyExceptionClass_Check(cause)) {
            fixed_cause = PyObject_CallObject(cause, NULL);
            if (fixed_cause == NULL)
                goto bad;
        } else if (PyExceptionInstance_Check(cause)) {
            fixed_cause = cause;
            Py_INCREF(fixed_cause);
        } else {
            PyErr_SetString(PyExc_TypeError,
                            "exception causes must derive from "
                            "BaseException");
            goto bad;
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
#if CYTHON_COMPILING_IN_PYPY
        PyObject *tmp_type, *tmp_value, *tmp_tb;
        PyErr_Fetch(tmp_type, tmp_value, tmp_tb);
        Py_INCREF(tb);
        PyErr_Restore(tmp_type, tmp_value, tb);
        Py_XDECREF(tmp_tb);
#else
        PyThreadState *tstate = PyThreadState_GET();
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}
#endif

static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if CYTHON_COMPILING_IN_CPYTHON
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = PyCFunction_GET_FUNCTION(func);
    self = PyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

#if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || PyObject_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject* args = PyTuple_Pack(1, arg);
    return (likely(args)) ? __Pyx_PyObject_Call(func, args, NULL) : NULL;
}
#endif

static CYTHON_INLINE int __Pyx_IsLittleEndian(void) {
  unsigned int n = 1;
  return *(unsigned char*)(&n) != 0;
}
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static CYTHON_INLINE PyObject *
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number;
    int ndim = ctx->head->field->type->ndim;
;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return NULL;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return NULL;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
            return PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
        if (*ts != ',' && *ts != ')')
            return PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim)
        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return NULL;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return Py_None;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_IsLittleEndian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
            ctx->enc_packmode == ctx->new_packmode) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}
static CYTHON_INLINE void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}
static CYTHON_INLINE int __Pyx_GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  if (obj == Py_None || obj == NULL) {
    __Pyx_ZeroBuffer(buf);
    return 0;
  }
  buf->buf = NULL;
  if (__Pyx_GetBuffer(obj, buf, flags) == -1) goto fail;
  if (buf->ndim != nd) {
    PyErr_Format(PyExc_ValueError,
                 "Buffer has wrong number of dimensions (expected %d, got %d)",
                 nd, buf->ndim);
    goto fail;
  }
  if (!cast) {
    __Pyx_BufFmt_Context ctx;
    __Pyx_BufFmt_Init(&ctx, stack, dtype);
    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
  }
  if ((unsigned)buf->itemsize != dtype->size) {
    PyErr_Format(PyExc_ValueError,
      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_ZeroBuffer(buf);
  return -1;
}
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (info->buf == NULL) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}

static int
__Pyx_init_memviewslice(struct __pyx_memoryview_obj *memview,
                        int ndim,
                        __Pyx_memviewslice *memviewslice,
                        int memview_is_new_reference)
{
    __Pyx_RefNannyDeclarations
    int i, retval=-1;
    Py_buffer *buf = &memview->view;
    __Pyx_RefNannySetupContext("init_memviewslice", 0);
    if (!buf) {
        PyErr_SetString(PyExc_ValueError,
            "buf is NULL.");
        goto fail;
    } else if (memviewslice->memview || memviewslice->data) {
        PyErr_SetString(PyExc_ValueError,
            "memviewslice is already initialized!");
        goto fail;
    }
    if (buf->strides) {
        for (i = 0; i < ndim; i++) {
            memviewslice->strides[i] = buf->strides[i];
        }
    } else {
        Py_ssize_t stride = buf->itemsize;
        for (i = ndim - 1; i >= 0; i--) {
            memviewslice->strides[i] = stride;
            stride *= buf->shape[i];
        }
    }
    for (i = 0; i < ndim; i++) {
        memviewslice->shape[i]   = buf->shape[i];
        if (buf->suboffsets) {
            memviewslice->suboffsets[i] = buf->suboffsets[i];
        } else {
            memviewslice->suboffsets[i] = -1;
        }
    }
    memviewslice->memview = memview;
    memviewslice->data = (char *)buf->buf;
    if (__pyx_add_acquisition_count(memview) == 0 && !memview_is_new_reference) {
        Py_INCREF(memview);
    }
    retval = 0;
    goto no_fail;
fail:
    memviewslice->memview = 0;
    memviewslice->data = 0;
    retval = -1;
no_fail:
    __Pyx_RefNannyFinishContext();
    return retval;
}
static CYTHON_INLINE void __pyx_fatalerror(const char *fmt, ...) {
    va_list vargs;
    char msg[200];
    va_start(vargs, fmt);
#ifdef HAVE_STDARG_PROTOTYPES
    va_start(vargs, fmt);
#else
    va_start(vargs);
#endif
    vsnprintf(msg, 200, fmt, vargs);
    Py_FatalError(msg);
    va_end(vargs);
}
static CYTHON_INLINE int
__pyx_add_acquisition_count_locked(__pyx_atomic_int *acquisition_count,
                                   PyThread_type_lock lock)
{
    int result;
    PyThread_acquire_lock(lock, 1);
    result = (*acquisition_count)++;
    PyThread_release_lock(lock);
    return result;
}
static CYTHON_INLINE int
__pyx_sub_acquisition_count_locked(__pyx_atomic_int *acquisition_count,
                                   PyThread_type_lock lock)
{
    int result;
    PyThread_acquire_lock(lock, 1);
    result = (*acquisition_count)--;
    PyThread_release_lock(lock);
    return result;
}
static CYTHON_INLINE void
__Pyx_INC_MEMVIEW(__Pyx_memviewslice *memslice, int have_gil, int lineno)
{
    int first_time;
    struct __pyx_memoryview_obj *memview = memslice->memview;
    if (!memview || (PyObject *) memview == Py_None)
        return;
    if (__pyx_get_slice_count(memview) < 0)
        __pyx_fatalerror("Acquisition count is %d (line %d)",
                         __pyx_get_slice_count(memview), lineno);
    first_time = __pyx_add_acquisition_count(memview) == 0;
    if (first_time) {
        if (have_gil) {
            Py_INCREF((PyObject *) memview);
        } else {
            PyGILState_STATE _gilstate = PyGILState_Ensure();
            Py_INCREF((PyObject *) memview);
            PyGILState_Release(_gilstate);
        }
    }
}
static CYTHON_INLINE void __Pyx_XDEC_MEMVIEW(__Pyx_memviewslice *memslice,
                                             int have_gil, int lineno) {
    int last_time;
    struct __pyx_memoryview_obj *memview = memslice->memview;
    if (!memview ) {
        return;
    } else if ((PyObject *) memview == Py_None) {
        memslice->memview = NULL;
        return;
    }
    if (__pyx_get_slice_count(memview) <= 0)
        __pyx_fatalerror("Acquisition count is %d (line %d)",
                         __pyx_get_slice_count(memview), lineno);
    last_time = __pyx_sub_acquisition_count(memview) == 1;
    memslice->data = NULL;
    if (last_time) {
        if (have_gil) {
            Py_CLEAR(memslice->memview);
        } else {
            PyGILState_STATE _gilstate = PyGILState_Ensure();
            Py_CLEAR(memslice->memview);
            PyGILState_Release(_gilstate);
        }
    } else {
        memslice->memview = NULL;
    }
}

static void __Pyx_WriteUnraisable(const char *name, CYTHON_UNUSED int clineno,
                                  CYTHON_UNUSED int lineno, CYTHON_UNUSED const char *filename,
                                  int full_traceback) {
    PyObject *old_exc, *old_val, *old_tb;
    PyObject *ctx;
    __Pyx_ErrFetch(&old_exc, &old_val, &old_tb);
    if (full_traceback) {
        Py_XINCREF(old_exc);
        Py_XINCREF(old_val);
        Py_XINCREF(old_tb);
        __Pyx_ErrRestore(old_exc, old_val, old_tb);
        PyErr_PrintEx(1);
    }
    #if PY_MAJOR_VERSION < 3
    ctx = PyString_FromString(name);
    #else
    ctx = PyUnicode_FromString(name);
    #endif
    __Pyx_ErrRestore(old_exc, old_val, old_tb);
    if (!ctx) {
        PyErr_WriteUnraisable(Py_None);
    } else {
        PyErr_WriteUnraisable(ctx);
        Py_DECREF(ctx);
    }
}

static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(PyObject_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    return 0;
}

static void __Pyx_RaiseArgumentTypeInvalid(const char* name, PyObject *obj, PyTypeObject *type) {
    PyErr_Format(PyExc_TypeError,
        "Argument '%.200s' has incorrect type (expected %.200s, got %.200s)",
        name, type->tp_name, Py_TYPE(obj)->tp_name);
}
static CYTHON_INLINE int __Pyx_ArgTypeTest(PyObject *obj, PyTypeObject *type, int none_allowed,
    const char *name, int exact)
{
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (none_allowed && obj == Py_None) return 1;
    else if (exact) {
        if (likely(Py_TYPE(obj) == type)) return 1;
        #if PY_MAJOR_VERSION == 2
        else if ((type == &PyBaseString_Type) && likely(__Pyx_PyBaseString_CheckExact(obj))) return 1;
        #endif
    }
    else {
        if (likely(PyObject_TypeCheck(obj, type))) return 1;
    }
    __Pyx_RaiseArgumentTypeInvalid(name, obj, type);
    return 0;
}

static CYTHON_INLINE int __Pyx_PyBytes_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
    if (s1 == s2) {
        return (equals == Py_EQ);
    } else if (PyBytes_CheckExact(s1) & PyBytes_CheckExact(s2)) {
        const char *ps1, *ps2;
        Py_ssize_t length = PyBytes_GET_SIZE(s1);
        if (length != PyBytes_GET_SIZE(s2))
            return (equals == Py_NE);
        ps1 = PyBytes_AS_STRING(s1);
        ps2 = PyBytes_AS_STRING(s2);
        if (ps1[0] != ps2[0]) {
            return (equals == Py_NE);
        } else if (length == 1) {
            return (equals == Py_EQ);
        } else {
            int result = memcmp(ps1, ps2, (size_t)length);
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & PyBytes_CheckExact(s2)) {
        return (equals == Py_NE);
    } else if ((s2 == Py_None) & PyBytes_CheckExact(s1)) {
        return (equals == Py_NE);
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
#endif
}

static CYTHON_INLINE int __Pyx_PyUnicode_Equals(PyObject* s1, PyObject* s2, int equals) {
#if CYTHON_COMPILING_IN_PYPY
    return PyObject_RichCompareBool(s1, s2, equals);
#else
#if PY_MAJOR_VERSION < 3
    PyObject* owned_ref = NULL;
#endif
    int s1_is_unicode, s2_is_unicode;
    if (s1 == s2) {
        goto return_eq;
    }
    s1_is_unicode = PyUnicode_CheckExact(s1);
    s2_is_unicode = PyUnicode_CheckExact(s2);
#if PY_MAJOR_VERSION < 3
    if ((s1_is_unicode & (!s2_is_unicode)) && PyString_CheckExact(s2)) {
        owned_ref = PyUnicode_FromObject(s2);
        if (unlikely(!owned_ref))
            return -1;
        s2 = owned_ref;
        s2_is_unicode = 1;
    } else if ((s2_is_unicode & (!s1_is_unicode)) && PyString_CheckExact(s1)) {
        owned_ref = PyUnicode_FromObject(s1);
        if (unlikely(!owned_ref))
            return -1;
        s1 = owned_ref;
        s1_is_unicode = 1;
    } else if (((!s2_is_unicode) & (!s1_is_unicode))) {
        return __Pyx_PyBytes_Equals(s1, s2, equals);
    }
#endif
    if (s1_is_unicode & s2_is_unicode) {
        Py_ssize_t length;
        int kind;
        void *data1, *data2;
        if (unlikely(__Pyx_PyUnicode_READY(s1) < 0) || unlikely(__Pyx_PyUnicode_READY(s2) < 0))
            return -1;
        length = __Pyx_PyUnicode_GET_LENGTH(s1);
        if (length != __Pyx_PyUnicode_GET_LENGTH(s2)) {
            goto return_ne;
        }
        kind = __Pyx_PyUnicode_KIND(s1);
        if (kind != __Pyx_PyUnicode_KIND(s2)) {
            goto return_ne;
        }
        data1 = __Pyx_PyUnicode_DATA(s1);
        data2 = __Pyx_PyUnicode_DATA(s2);
        if (__Pyx_PyUnicode_READ(kind, data1, 0) != __Pyx_PyUnicode_READ(kind, data2, 0)) {
            goto return_ne;
        } else if (length == 1) {
            goto return_eq;
        } else {
            int result = memcmp(data1, data2, (size_t)(length * kind));
            #if PY_MAJOR_VERSION < 3
            Py_XDECREF(owned_ref);
            #endif
            return (equals == Py_EQ) ? (result == 0) : (result != 0);
        }
    } else if ((s1 == Py_None) & s2_is_unicode) {
        goto return_ne;
    } else if ((s2 == Py_None) & s1_is_unicode) {
        goto return_ne;
    } else {
        int result;
        PyObject* py_result = PyObject_RichCompare(s1, s2, equals);
        if (!py_result)
            return -1;
        result = __Pyx_PyObject_IsTrue(py_result);
        Py_DECREF(py_result);
        return result;
    }
return_eq:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_EQ);
return_ne:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(owned_ref);
    #endif
    return (equals == Py_NE);
#endif
}

static CYTHON_INLINE PyObject *__Pyx_GetAttr(PyObject *o, PyObject *n) {
#if CYTHON_COMPILING_IN_CPYTHON
#if PY_MAJOR_VERSION >= 3
    if (likely(PyUnicode_Check(n)))
#else
    if (likely(PyString_Check(n)))
#endif
        return __Pyx_PyObject_GetAttrStr(o, n);
#endif
    return PyObject_GetAttr(o, n);
}

static CYTHON_INLINE PyObject* __Pyx_decode_c_string(
         const char* cstring, Py_ssize_t start, Py_ssize_t stop,
         const char* encoding, const char* errors,
         PyObject* (*decode_func)(const char *s, Py_ssize_t size, const char *errors)) {
    Py_ssize_t length;
    if (unlikely((start < 0) | (stop < 0))) {
        length = strlen(cstring);
        if (start < 0) {
            start += length;
            if (start < 0)
                start = 0;
        }
        if (stop < 0)
            stop += length;
    }
    length = stop - start;
    if (unlikely(length <= 0))
        return PyUnicode_FromUnicode(NULL, 0);
    cstring += start;
    if (decode_func) {
        return decode_func(cstring, length, errors);
    } else {
        return PyUnicode_Decode(cstring, length, encoding, errors);
    }
}

static CYTHON_INLINE void __Pyx_ExceptionSave(PyObject **type, PyObject **value, PyObject **tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
#else
    PyErr_GetExcInfo(type, value, tb);
#endif
}
static void __Pyx_ExceptionReset(PyObject *type, PyObject *value, PyObject *tb) {
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(type, value, tb);
#endif
}

static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyThreadState *tstate = PyThreadState_GET();
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_COMPILING_IN_CPYTHON
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
#if CYTHON_COMPILING_IN_CPYTHON
    PyThreadState *tstate = PyThreadState_GET();
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = *type;
    tstate->exc_value = *value;
    tstate->exc_traceback = *tb;
#else
    PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
    PyErr_SetExcInfo(*type, *value, *tb);
#endif
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}

static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyList_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (wraparound & unlikely(i < 0)) i += PyTuple_GET_SIZE(o);
    if ((!boundscheck) || likely((0 <= i) & (i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
                                                     int is_list, int wraparound, int boundscheck) {
#if CYTHON_COMPILING_IN_CPYTHON
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (PyErr_ExceptionMatches(PyExc_OverflowError))
                        PyErr_Clear();
                    else
                        return NULL;
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

static CYTHON_INLINE void __Pyx_RaiseUnboundLocalError(const char *varname) {
    PyErr_Format(PyExc_UnboundLocalError, "local variable '%s' referenced before assignment", varname);
}

static int __Pyx_SetVtable(PyObject *dict, void *vtable) {
#if PY_VERSION_HEX >= 0x02070000
    PyObject *ob = PyCapsule_New(vtable, 0, 0);
#else
    PyObject *ob = PyCObject_FromVoidPtr(vtable, 0);
#endif
    if (!ob)
        goto bad;
    if (PyDict_SetItem(dict, __pyx_n_s_pyx_vtable, ob) < 0)
        goto bad;
    Py_DECREF(ob);
    return 0;
bad:
    Py_XDECREF(ob);
    return -1;
}

static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = (start + end) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_code_cache.count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

#include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        0,
        0,
        0,
        0,
        0,
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple, /*PyObject *consts,*/
        __pyx_empty_tuple, /*PyObject *names,*/
        __pyx_empty_tuple, /*PyObject *varnames,*/
        __pyx_empty_tuple, /*PyObject *freevars,*/
        __pyx_empty_tuple, /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        py_line,
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    py_code = __pyx_find_code_object(c_line ? c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        PyThreadState_GET(), /*PyThreadState *tstate,*/
        py_code,             /*PyCodeObject *code,*/
        __pyx_d,      /*PyObject *globals,*/
        0                    /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    py_frame->f_lineno = py_line;
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_array_type)) return __pyx_array_getbuffer(obj, view, flags);
        if (PyObject_TypeCheck(obj, __pyx_memoryview_type)) return __pyx_memoryview_getbuffer(obj, view, flags);
    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
    return -1;
}
static void __Pyx_ReleaseBuffer(Py_buffer *view) {
    PyObject *obj = view->obj;
    if (!obj) return;
    if (PyObject_CheckBuffer(obj)) {
        PyBuffer_Release(view);
        return;
    }
        if (PyObject_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) { __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view); return; }
    Py_DECREF(obj);
    view->obj = NULL;
}
#endif


        static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_VERSION_HEX < 0x03030000
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    {
        #if PY_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                #if PY_VERSION_HEX < 0x03030000
                PyObject *py_level = PyInt_FromLong(1);
                if (!py_level)
                    goto bad;
                module = PyObject_CallFunctionObjArgs(py_import,
                    name, global_dict, empty_dict, list, py_level, NULL);
                Py_DECREF(py_level);
                #else
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                #endif
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_VERSION_HEX < 0x03030000
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
            #else
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_VERSION_HEX < 0x03030000
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

static int
__pyx_typeinfo_cmp(__Pyx_TypeInfo *a, __Pyx_TypeInfo *b)
{
    int i;
    if (!a || !b)
        return 0;
    if (a == b)
        return 1;
    if (a->size != b->size || a->typegroup != b->typegroup ||
            a->is_unsigned != b->is_unsigned || a->ndim != b->ndim) {
        if (a->typegroup == 'H' || b->typegroup == 'H') {
            return a->size == b->size;
        } else {
            return 0;
        }
    }
    if (a->ndim) {
        for (i = 0; i < a->ndim; i++)
            if (a->arraysize[i] != b->arraysize[i])
                return 0;
    }
    if (a->typegroup == 'S') {
        if (a->flags != b->flags)
            return 0;
        if (a->fields || b->fields) {
            if (!(a->fields && b->fields))
                return 0;
            for (i = 0; a->fields[i].type && b->fields[i].type; i++) {
                __Pyx_StructField *field_a = a->fields + i;
                __Pyx_StructField *field_b = b->fields + i;
                if (field_a->offset != field_b->offset ||
                    !__pyx_typeinfo_cmp(field_a->type, field_b->type))
                    return 0;
            }
            return !a->fields[i].type && !b->fields[i].type;
        }
    }
    return 1;
}

static int
__pyx_check_strides(Py_buffer *buf, int dim, int ndim, int spec)
{
    if (buf->shape[dim] <= 1)
        return 1;
    if (buf->strides) {
        if (spec & __Pyx_MEMVIEW_CONTIG) {
            if (spec & (__Pyx_MEMVIEW_PTR|__Pyx_MEMVIEW_FULL)) {
                if (buf->strides[dim] != sizeof(void *)) {
                    PyErr_Format(PyExc_ValueError,
                                 "Buffer is not indirectly contiguous "
                                 "in dimension %d.", dim);
                    goto fail;
                }
            } else if (buf->strides[dim] != buf->itemsize) {
                PyErr_SetString(PyExc_ValueError,
                                "Buffer and memoryview are not contiguous "
                                "in the same dimension.");
                goto fail;
            }
        }
        if (spec & __Pyx_MEMVIEW_FOLLOW) {
            Py_ssize_t stride = buf->strides[dim];
            if (stride < 0)
                stride = -stride;
            if (stride < buf->itemsize) {
                PyErr_SetString(PyExc_ValueError,
                                "Buffer and memoryview are not contiguous "
                                "in the same dimension.");
                goto fail;
            }
        }
    } else {
        if (spec & __Pyx_MEMVIEW_CONTIG && dim != ndim - 1) {
            PyErr_Format(PyExc_ValueError,
                         "C-contiguous buffer is not contiguous in "
                         "dimension %d", dim);
            goto fail;
        } else if (spec & (__Pyx_MEMVIEW_PTR)) {
            PyErr_Format(PyExc_ValueError,
                         "C-contiguous buffer is not indirect in "
                         "dimension %d", dim);
            goto fail;
        } else if (buf->suboffsets) {
            PyErr_SetString(PyExc_ValueError,
                            "Buffer exposes suboffsets but no strides");
            goto fail;
        }
    }
    return 1;
fail:
    return 0;
}
static int
__pyx_check_suboffsets(Py_buffer *buf, int dim, CYTHON_UNUSED int ndim, int spec)
{
    if (spec & __Pyx_MEMVIEW_DIRECT) {
        if (buf->suboffsets && buf->suboffsets[dim] >= 0) {
            PyErr_Format(PyExc_ValueError,
                         "Buffer not compatible with direct access "
                         "in dimension %d.", dim);
            goto fail;
        }
    }
    if (spec & __Pyx_MEMVIEW_PTR) {
        if (!buf->suboffsets || (buf->suboffsets && buf->suboffsets[dim] < 0)) {
            PyErr_Format(PyExc_ValueError,
                         "Buffer is not indirectly accessible "
                         "in dimension %d.", dim);
            goto fail;
        }
    }
    return 1;
fail:
    return 0;
}
static int
__pyx_verify_contig(Py_buffer *buf, int ndim, int c_or_f_flag)
{
    int i;
    if (c_or_f_flag & __Pyx_IS_F_CONTIG) {
        Py_ssize_t stride = 1;
        for (i = 0; i < ndim; i++) {
            if (stride * buf->itemsize != buf->strides[i] &&
                    buf->shape[i] > 1)
            {
                PyErr_SetString(PyExc_ValueError,
                    "Buffer not fortran contiguous.");
                goto fail;
            }
            stride = stride * buf->shape[i];
        }
    } else if (c_or_f_flag & __Pyx_IS_C_CONTIG) {
        Py_ssize_t stride = 1;
        for (i = ndim - 1; i >- 1; i--) {
            if (stride * buf->itemsize != buf->strides[i] &&
                    buf->shape[i] > 1) {
                PyErr_SetString(PyExc_ValueError,
                    "Buffer not C contiguous.");
                goto fail;
            }
            stride = stride * buf->shape[i];
        }
    }
    return 1;
fail:
    return 0;
}
static int __Pyx_ValidateAndInit_memviewslice(
                int *axes_specs,
                int c_or_f_flag,
                int buf_flags,
                int ndim,
                __Pyx_TypeInfo *dtype,
                __Pyx_BufFmt_StackElem stack[],
                __Pyx_memviewslice *memviewslice,
                PyObject *original_obj)
{
    struct __pyx_memoryview_obj *memview, *new_memview;
    __Pyx_RefNannyDeclarations
    Py_buffer *buf;
    int i, spec = 0, retval = -1;
    __Pyx_BufFmt_Context ctx;
    int from_memoryview = __pyx_memoryview_check(original_obj);
    __Pyx_RefNannySetupContext("ValidateAndInit_memviewslice", 0);
    if (from_memoryview && __pyx_typeinfo_cmp(dtype, ((struct __pyx_memoryview_obj *)
                                                            original_obj)->typeinfo)) {
        memview = (struct __pyx_memoryview_obj *) original_obj;
        new_memview = NULL;
    } else {
        memview = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
                                            original_obj, buf_flags, 0, dtype);
        new_memview = memview;
        if (unlikely(!memview))
            goto fail;
    }
    buf = &memview->view;
    if (buf->ndim != ndim) {
        PyErr_Format(PyExc_ValueError,
                "Buffer has wrong number of dimensions (expected %d, got %d)",
                ndim, buf->ndim);
        goto fail;
    }
    if (new_memview) {
        __Pyx_BufFmt_Init(&ctx, stack, dtype);
        if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
    }
    if ((unsigned) buf->itemsize != dtype->size) {
        PyErr_Format(PyExc_ValueError,
                     "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "u byte%s) "
                     "does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "u byte%s)",
                     buf->itemsize,
                     (buf->itemsize > 1) ? "s" : "",
                     dtype->name,
                     dtype->size,
                     (dtype->size > 1) ? "s" : "");
        goto fail;
    }
    for (i = 0; i < ndim; i++) {
        spec = axes_specs[i];
        if (!__pyx_check_strides(buf, i, ndim, spec))
            goto fail;
        if (!__pyx_check_suboffsets(buf, i, ndim, spec))
            goto fail;
    }
    if (buf->strides && !__pyx_verify_contig(buf, ndim, c_or_f_flag))
        goto fail;
    if (unlikely(__Pyx_init_memviewslice(memview, ndim, memviewslice,
                                         new_memview != NULL) == -1)) {
        goto fail;
    }
    retval = 0;
    goto no_fail;
fail:
    Py_XDECREF(new_memview);
    retval = -1;
no_fail:
    __Pyx_RefNannyFinishContext();
    return retval;
}

static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_ds_double(PyObject *obj) {
    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
    __Pyx_BufFmt_StackElem stack[1];
    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
    int retcode;
    if (obj == Py_None) {
        result.memview = (struct __pyx_memoryview_obj *) Py_None;
        return result;
    }
    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
                                                 PyBUF_RECORDS, 1,
                                                 &__Pyx_TypeInfo_double, stack,
                                                 &result, obj);
    if (unlikely(retcode == -1))
        goto __pyx_fail;
    return result;
__pyx_fail:
    result.memview = NULL;
    result.data = NULL;
    return result;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(int) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

static PyObject *__pyx_memview_get_double(const char *itemp) {
    return (PyObject *) PyFloat_FromDouble(*(double *) itemp);
}
static int __pyx_memview_set_double(const char *itemp, PyObject *obj) {
    double value = __pyx_PyFloat_AsDouble(obj);
    if ((value == (double)-1) && PyErr_Occurred())
        return 0;
    *(double *) itemp = value;
    return 1;
}

static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
        } else if (sizeof(long) <= sizeof(unsigned long long)) {
            return PyLong_FromUnsignedLongLong((unsigned long long) value);
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(long long)) {
            return PyLong_FromLongLong((long long) value);
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

#define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)       \
    {                                                                     \
        func_type value = func_value;                                     \
        if (sizeof(target_type) < sizeof(func_type)) {                    \
            if (unlikely(value != (func_type) (target_type) value)) {     \
                func_type zero = 0;                                       \
                if (is_unsigned && unlikely(value < zero))                \
                    goto raise_neg_overflow;                              \
                else                                                      \
                    goto raise_overflow;                                  \
            }                                                             \
        }                                                                 \
        return (target_type) value;                                       \
    }

#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
 #endif
#endif

static CYTHON_INLINE Py_intptr_t __Pyx_PyInt_As_Py_intptr_t(PyObject *x) {
    const Py_intptr_t neg_one = (Py_intptr_t) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(Py_intptr_t) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (Py_intptr_t) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(Py_intptr_t) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(Py_intptr_t) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(Py_intptr_t,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(Py_intptr_t, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(Py_intptr_t) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, long, PyLong_AsLong(x))
            } else if (sizeof(Py_intptr_t) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(Py_intptr_t, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            Py_intptr_t val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (Py_intptr_t) -1;
        }
    } else {
        Py_intptr_t val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (Py_intptr_t) -1;
        val = __Pyx_PyInt_As_Py_intptr_t(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to Py_intptr_t");
    return (Py_intptr_t) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to Py_intptr_t");
    return (Py_intptr_t) -1;
}

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return ::std::complex< float >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return x + y*(__pyx_t_float_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      __pyx_t_float_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eqf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sumf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_difff(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prodf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quotf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        float denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_negf(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zerof(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conjf(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE float __Pyx_c_absf(__pyx_t_float_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtf(z.real*z.real + z.imag*z.imag);
          #else
            return hypotf(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_powf(__pyx_t_float_complex a, __pyx_t_float_complex b) {
            __pyx_t_float_complex z;
            float r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    float denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(a, a);
                    case 3:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, a);
                    case 4:
                        z = __Pyx_c_prodf(a, a);
                        return __Pyx_c_prodf(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_absf(a);
                theta = atan2f(a.imag, a.real);
            }
            lnr = logf(r);
            z_r = expf(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosf(z_theta);
            z.imag = z_r * sinf(z_theta);
            return z;
        }
    #endif
#endif

#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return ::std::complex< double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return x + y*(__pyx_t_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      __pyx_t_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

#if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq(__pyx_t_double_complex a, __pyx_t_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        double denom = b.real * b.real + b.imag * b.imag;
        z.real = (a.real * b.real + a.imag * b.imag) / denom;
        z.imag = (a.imag * b.real - a.real * b.imag) / denom;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(a, a);
                    case 3:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, a);
                    case 4:
                        z = __Pyx_c_prod(a, a);
                        return __Pyx_c_prod(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                }
                r = a.real;
                theta = 0;
            } else {
                r = __Pyx_c_abs(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(int) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(int, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(int, long, PyLong_AsLong(x))
            } else if (sizeof(int) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(int, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

static int
__pyx_memviewslice_is_contig(const __Pyx_memviewslice *mvs,
                             char order, int ndim)
{
    int i, index, step, start;
    Py_ssize_t itemsize = mvs->memview->view.itemsize;
    if (order == 'F') {
        step = 1;
        start = 0;
    } else {
        step = -1;
        start = ndim - 1;
    }
    for (i = 0; i < ndim; i++) {
        index = start + step * i;
        if (mvs->suboffsets[index] >= 0 || mvs->strides[index] != itemsize)
            return 0;
        itemsize *= mvs->shape[index];
    }
    return 1;
}

static void
__pyx_get_array_memory_extents(__Pyx_memviewslice *slice,
                               void **out_start, void **out_end,
                               int ndim, size_t itemsize)
{
    char *start, *end;
    int i;
    start = end = slice->data;
    for (i = 0; i < ndim; i++) {
        Py_ssize_t stride = slice->strides[i];
        Py_ssize_t extent = slice->shape[i];
        if (extent == 0) {
            *out_start = *out_end = start;
            return;
        } else {
            if (stride > 0)
                end += stride * (extent - 1);
            else
                start += stride * (extent - 1);
        }
    }
    *out_start = start;
    *out_end = end + itemsize;
}
static int
__pyx_slices_overlap(__Pyx_memviewslice *slice1,
                     __Pyx_memviewslice *slice2,
                     int ndim, size_t itemsize)
{
    void *start1, *end1, *start2, *end2;
    __pyx_get_array_memory_extents(slice1, &start1, &end1, ndim, itemsize);
    __pyx_get_array_memory_extents(slice2, &start2, &end2, ndim, itemsize);
    return (start1 < end2) && (start2 < end1);
}

static __Pyx_memviewslice
__pyx_memoryview_copy_new_contig(const __Pyx_memviewslice *from_mvs,
                                 const char *mode, int ndim,
                                 size_t sizeof_dtype, int contig_flag,
                                 int dtype_is_object)
{
    __Pyx_RefNannyDeclarations
    int i;
    __Pyx_memviewslice new_mvs = { 0, 0, { 0 }, { 0 }, { 0 } };
    struct __pyx_memoryview_obj *from_memview = from_mvs->memview;
    Py_buffer *buf = &from_memview->view;
    PyObject *shape_tuple = NULL;
    PyObject *temp_int = NULL;
    struct __pyx_array_obj *array_obj = NULL;
    struct __pyx_memoryview_obj *memview_obj = NULL;
    __Pyx_RefNannySetupContext("__pyx_memoryview_copy_new_contig", 0);
    for (i = 0; i < ndim; i++) {
        if (from_mvs->suboffsets[i] >= 0) {
            PyErr_Format(PyExc_ValueError, "Cannot copy memoryview slice with "
                                           "indirect dimensions (axis %d)", i);
            goto fail;
        }
    }
    shape_tuple = PyTuple_New(ndim);
    if (unlikely(!shape_tuple)) {
        goto fail;
    }
    __Pyx_GOTREF(shape_tuple);
    for(i = 0; i < ndim; i++) {
        temp_int = PyInt_FromSsize_t(from_mvs->shape[i]);
        if(unlikely(!temp_int)) {
            goto fail;
        } else {
            PyTuple_SET_ITEM(shape_tuple, i, temp_int);
            temp_int = NULL;
        }
    }
    array_obj = __pyx_array_new(shape_tuple, sizeof_dtype, buf->format, (char *) mode, NULL);
    if (unlikely(!array_obj)) {
        goto fail;
    }
    __Pyx_GOTREF(array_obj);
    memview_obj = (struct __pyx_memoryview_obj *) __pyx_memoryview_new(
                                    (PyObject *) array_obj, contig_flag,
                                    dtype_is_object,
                                    from_mvs->memview->typeinfo);
    if (unlikely(!memview_obj))
        goto fail;
    if (unlikely(__Pyx_init_memviewslice(memview_obj, ndim, &new_mvs, 1) < 0))
        goto fail;
    if (unlikely(__pyx_memoryview_copy_contents(*from_mvs, new_mvs, ndim, ndim,
                                                dtype_is_object) < 0))
        goto fail;
    goto no_fail;
fail:
    __Pyx_XDECREF(new_mvs.memview);
    new_mvs.memview = NULL;
    new_mvs.data = NULL;
no_fail:
    __Pyx_XDECREF(shape_tuple);
    __Pyx_XDECREF(temp_int);
    __Pyx_XDECREF(array_obj);
    __Pyx_RefNannyFinishContext();
    return new_mvs;
}

static CYTHON_INLINE PyObject *
__pyx_capsule_create(void *p, CYTHON_UNUSED const char *sig)
{
    PyObject *cobj;
#if PY_VERSION_HEX >= 0x02070000
    cobj = PyCapsule_New(p, sig, NULL);
#else
    cobj = PyCObject_FromVoidPtr(p, NULL);
#endif
    return cobj;
}

static CYTHON_INLINE char __Pyx_PyInt_As_char(PyObject *x) {
    const char neg_one = (char) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(char) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(char, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (char) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(char, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(char) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(char, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(char) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(char, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(char,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(char, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(char) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(char, long, PyLong_AsLong(x))
            } else if (sizeof(char) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(char, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            char val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (char) -1;
        }
    } else {
        char val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (char) -1;
        val = __Pyx_PyInt_As_char(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to char");
    return (char) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to char");
    return (char) -1;
}

static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long, PyLong_AsUnsignedLong(x))
            } else if (sizeof(long) <= sizeof(unsigned long long)) {
                __PYX_VERIFY_RETURN_INT(long, unsigned long long, PyLong_AsUnsignedLongLong(x))
            }
        } else {
#if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
 #if CYTHON_USE_PYLONG_INTERNALS
            switch (Py_SIZE(x)) {
                case  0: return 0;
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +(((PyLongObject*)x)->ob_digit[0]));
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, -(sdigit) ((PyLongObject*)x)->ob_digit[0]);
            }
 #endif
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT(long, long, PyLong_AsLong(x))
            } else if (sizeof(long) <= sizeof(long long)) {
                __PYX_VERIFY_RETURN_INT(long, long long, PyLong_AsLongLong(x))
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_Int(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_Int(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

static CYTHON_INLINE __Pyx_memviewslice __Pyx_PyObject_to_MemoryviewSlice_dsds_double(PyObject *obj) {
    __Pyx_memviewslice result = { 0, 0, { 0 }, { 0 }, { 0 } };
    __Pyx_BufFmt_StackElem stack[1];
    int axes_specs[] = { (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED), (__Pyx_MEMVIEW_DIRECT | __Pyx_MEMVIEW_STRIDED) };
    int retcode;
    if (obj == Py_None) {
        result.memview = (struct __pyx_memoryview_obj *) Py_None;
        return result;
    }
    retcode = __Pyx_ValidateAndInit_memviewslice(axes_specs, 0,
                                                 PyBUF_RECORDS, 2,
                                                 &__Pyx_TypeInfo_double, stack,
                                                 &result, obj);
    if (unlikely(retcode == -1))
        goto __pyx_fail;
    return result;
__pyx_fail:
    result.memview = NULL;
    result.data = NULL;
    return result;
}

static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

#ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

#ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility",
            module_name, class_name);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling",
            module_name, class_name);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        ++t;
    }
    return 0;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
static CYTHON_INLINE char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
#if PY_VERSION_HEX < 0x03030000
        char* defenc_c;
        PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
        if (!defenc) return NULL;
        defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        {
            char* end = defenc_c + PyBytes_GET_SIZE(defenc);
            char* c;
            for (c = defenc_c; c < end; c++) {
                if ((unsigned char) (*c) >= 128) {
                    PyUnicode_AsASCIIString(o);
                    return NULL;
                }
            }
        }
#endif
        *length = PyBytes_GET_SIZE(defenc);
        return defenc_c;
#else
        if (__Pyx_PyUnicode_READY(o) == -1) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
        if (PyUnicode_IS_ASCII(o)) {
            *length = PyUnicode_GET_LENGTH(o);
            return PyUnicode_AsUTF8(o);
        } else {
            PyUnicode_AsASCIIString(o);
            return NULL;
        }
#else
        return PyUnicode_AsUTF8AndSize(o, length);
#endif
#endif
    } else
#endif
#if !CYTHON_COMPILING_IN_PYPY
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_Int(PyObject* x) {
  PyNumberMethods *m;
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (PyInt_Check(x) || PyLong_Check(x))
#else
  if (PyLong_Check(x))
#endif
    return Py_INCREF(x), x;
  m = Py_TYPE(x)->tp_as_number;
#if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = PyNumber_Long(x);
  }
#else
  if (m && m->nb_int) {
    name = "int";
    res = PyNumber_Long(x);
  }
#endif
  if (res) {
#if PY_MAJOR_VERSION < 3
    if (!PyInt_Check(res) && !PyLong_Check(res)) {
#else
    if (!PyLong_Check(res)) {
#endif
      PyErr_Format(PyExc_TypeError,
                   "__%.4s__ returned non-%.4s (type %.200s)",
                   name, name, Py_TYPE(res)->tp_name);
      Py_DECREF(res);
      return NULL;
    }
  }
  else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_TypeError,
                    "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b)))
      return PyInt_AS_LONG(b);
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_COMPILING_IN_CPYTHON && PY_MAJOR_VERSION >= 3
     #if CYTHON_USE_PYLONG_INTERNALS
       switch (Py_SIZE(b)) {
       case -1: return -(sdigit)((PyLongObject*)b)->ob_digit[0];
       case  0: return 0;
       case  1: return ((PyLongObject*)b)->ob_digit[0];
       }
     #endif
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
