/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell

CppAD is distributed under the terms of the
             Eclipse Public License Version 2.0.

This Source Code may also be made available under the following
Secondary License when the conditions for such availability set forth
in the Eclipse Public License, Version 2.0 are satisfied:
      GNU General Public License, Version 2.0 or later.
---------------------------------------------------------------------------- */

/*
Old sparse Jacobian example
*/

# include <cppad/cppad.hpp>
namespace { // ---------------------------------------------------------

bool rc_tridiagonal(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t i, j, k, ell;
    double eps10 = 10. * CppAD::epsilon<double>();

    // domain space vector
    size_t n = 13; // must be greater than or equal 3 (see n_sweep below)
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    CPPAD_TESTVECTOR(double)        x(n);
    for(j = 0; j < n; j++)
        X[j] = x[j] = double(j+1);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = n;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    CPPAD_TESTVECTOR(double) check(m * n );
    for(ell = 0; ell < m * n; ell++)
        check[ell] = 0.0;

    size_t K = 0;
    for(i = 0; i < n; i++)
    {   ell        = i * n + i;
        Y[i]       = double(ell+1) * 0.5 * X[i] * X[i];
        check[ell] = double(ell+1) * x[i];
        K++;
        if( i < n-1 )
        {   j          = i + 1;
            ell        = i * n + j;
            Y[i]      += double(ell+1) * 0.5 * X[i+1] * X[i+1];
            check[ell] = double(ell+1) * x[i+1];
            K++;
        }
        if(i > 0 )
        {   j          = i - 1;
            ell        = i * n + j;
            Y[i]      += double(ell+1) * 0.5 * X[i-1] * X[i-1];
            check[ell] = double(ell+1) * x[i-1];
        }
    }

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // sparsity pattern
    CppAD::vector< std::set<size_t> > s(m), p(m);
    for(i = 0; i < m; i++)
        s[i].insert(i);
    p   = f.RevSparseJac(m, s);

    // Request the upper triangle of the array
    CPPAD_TESTVECTOR(size_t) r(K), c(K);
    CPPAD_TESTVECTOR(double) jac(K);
    k = 0;
    for(i = 0; i < n; i++)
    {   r[k] = i;
        c[k] = i;
        k++;
        if( i < n-1 )
        {   r[k] = i;
            c[k] = i+1;
            k++;
        }
    }
    ok &= K == k;

    CppAD::sparse_jacobian_work work;
    size_t n_sweep = f.SparseJacobianForward(x, p, r, c, jac, work);
    ok &= n_sweep == 3;
    for(k = 0; k < K; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }
    work.clear();
    n_sweep = f.SparseJacobianReverse(x, p, r, c, jac, work);
    ok &= n_sweep == 3;
    for(k = 0; k < K; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }

    return ok;
}

template <class BaseVector, class SetVector>
bool rc_set(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t i, j, k, ell;
    double eps10 = 10. * CppAD::epsilon<double>();

    // domain space vector
    size_t n = 4;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = 1.0*X[0] + 2.0*X[1];
    Y[1] = 3.0*X[2] + 4.0*X[3];
    Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[3]*X[3]/2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y
    /*
          [ 1 2 0 0    ]
    jac = [ 0 0 3 4    ]
          [ 5 6 0 7*x_3]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1] = 2.; check[2]  = 0.; check[3]  = 0.;
    check[4] = 0.; check[5] = 0.; check[6]  = 3.; check[7]  = 4.;
    check[8] = 5.; check[9] = 6.; check[10] = 0.; check[11] = 7.*x[3];

    // sparsity pattern
    SetVector s(m), p(m);
    for(i = 0; i < m; i++)
        s[i].insert(i);
    p   = f.RevSparseJac(m, s);

    // Use forward mode to compute columns 0 and 2
    // (make sure order of rows and columns does not matter)
    CPPAD_TESTVECTOR(size_t) r(3), c(3);
    BaseVector jac(3);
    r[0] = 2; c[0] = 0;
    r[1] = 1; c[1] = 2;
    r[2] = 0; c[2] = 0;
    CppAD::sparse_jacobian_work work;
    size_t n_sweep = f.SparseJacobianForward(x, p, r, c, jac, work);
    for(k = 0; k < 3; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }
    ok &= (n_sweep == 1);

    // Use reverse mode to compute rows 0 and 1
    // (make sure order of rows and columns does not matter)
    r.resize(4), c.resize(4); jac.resize(4);
    r[0] = 0; c[0] = 0;
    r[1] = 1; c[1] = 2;
    r[2] = 0; c[2] = 1;
    r[3] = 1; c[3] = 3;
    work.clear();
    n_sweep = f.SparseJacobianReverse(x, p, r, c, jac, work);
    for(k = 0; k < 4; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }
    ok &= (n_sweep == 1);

    return ok;
}
template <class BaseVector, class BoolVector>
bool rc_bool(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t j, k, ell;
    double eps10 = 10. * CppAD::epsilon<double>();

    // domain space vector
    size_t n = 4;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = 1.0*X[0] + 2.0*X[1];
    Y[1] = 3.0*X[2] + 4.0*X[3];
    Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[3]*X[3]/2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y
    /*
          [ 1 2 0 0    ]
    jac = [ 0 0 3 4    ]
          [ 5 6 0 7*x_3]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1] = 2.; check[2]  = 0.; check[3]  = 0.;
    check[4] = 0.; check[5] = 0.; check[6]  = 3.; check[7]  = 4.;
    check[8] = 5.; check[9] = 6.; check[10] = 0.; check[11] = 7.*x[3];
    BoolVector s(m * n);
    s[0] = true;   s[1] = true;   s[2] = false;   s[3] = false;
    s[4] = false;  s[5] = false;  s[6] = true;    s[7] = true;
    s[8] = true;   s[9] = true;  s[10] = false;  s[11] = true;

    // Use forward mode to compute columns 0 and 2
    // (make sure order of rows and columns does not matter)
    CPPAD_TESTVECTOR(size_t) r(3), c(3);
    BaseVector jac(3);
    r[0] = 2; c[0] = 0;
    r[1] = 1; c[1] = 2;
    r[2] = 0; c[2] = 0;
    CppAD::sparse_jacobian_work work;
    size_t n_sweep = f.SparseJacobianForward(x, s, r, c, jac, work);
    for(k = 0; k < 3; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }
    ok &= (n_sweep == 1);

    // Use reverse mode to compute rows 0 and 1
    // (make sure order of rows and columns does not matter)
    r.resize(4), c.resize(4); jac.resize(4);
    r[0] = 0; c[0] = 0;
    r[1] = 1; c[1] = 2;
    r[2] = 0; c[2] = 1;
    r[3] = 1; c[3] = 3;
    work.clear();
    n_sweep = f.SparseJacobianReverse(x, s, r, c, jac, work);
    for(k = 0; k < 4; k++)
    {   ell = r[k] * n + c[k];
        ok &=  NearEqual(check[ell], jac[k], eps10, eps10);
    }
    ok &= (n_sweep == 1);

    return ok;
}


template <class BaseVector, class BoolVector>
bool reverse_bool(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t i, j, k;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 4;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = 1.0*X[0] + 2.0*X[1];
    Y[1] = 3.0*X[2] + 4.0*X[3];
    Y[2] = 5.0*X[0] + 6.0*X[1] + 7.0*X[2] + 8.0*X[3]*X[3]/2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y without sparsity pattern
    BaseVector jac(m * n);
    jac = f.SparseJacobian(x);
    /*
          [ 1 2 0 0    ]
    jac = [ 0 0 3 4    ]
          [ 5 6 7 8*x_3]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1] = 2.; check[2]  = 0.; check[3]  = 0.;
    check[4] = 0.; check[5] = 0.; check[6]  = 3.; check[7]  = 4.;
    check[8] = 5.; check[9] = 6.; check[10] = 7.; check[11] = 8.*x[3];
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    // test passing sparsity pattern
    BoolVector s(m * m);
    BoolVector p(m * n);
    for(i = 0; i < m; i++)
    {   for(k = 0; k < m; k++)
            s[i * m + k] = false;
        s[i * m + i] = true;
    }
    p   = f.RevSparseJac(m, s);
    jac = f.SparseJacobian(x, p);
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    return ok;
}

template <class BaseVector, class SetVector>
bool reverse_set(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t i, j, k;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 4;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = X[0] + X[1];
    Y[1] = X[2] + X[3];
    Y[2] = X[0] + X[1] + X[2] + X[3] * X[3] / 2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y without sparsity pattern
    BaseVector jac(m * n);
    jac = f.SparseJacobian(x);
    /*
          [ 1 1 0 0  ]
    jac = [ 0 0 1 1  ]
          [ 1 1 1 x_3]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
    check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
    check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    // test passing sparsity pattern
    SetVector s(m), p(m);
    for(i = 0; i < m; i++)
        s[i].insert(i);
    p   = f.RevSparseJac(m, s);
    jac = f.SparseJacobian(x, p);
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    return ok;
}

template <class BaseVector, class BoolVector>
bool forward_bool(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t j, k;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 3;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 4;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = X[0] + X[2];
    Y[1] = X[0] + X[2];
    Y[2] = X[1] + X[2];
    Y[3] = X[1] + X[2] * X[2] / 2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y without sparsity pattern
    BaseVector jac(m * n);
    jac = f.SparseJacobian(x);
    /*
          [ 1 0 1   ]
    jac = [ 1 0 1   ]
          [ 0 1 1   ]
          [ 0 1 x_2 ]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1]  = 0.; check[2]  = 1.;
    check[3] = 1.; check[4]  = 0.; check[5]  = 1.;
    check[6] = 0.; check[7]  = 1.; check[8]  = 1.;
    check[9] = 0.; check[10] = 1.; check[11] = x[2];
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    // test passing sparsity pattern
    BoolVector r(n * n);
    BoolVector p(m * n);
    for(j = 0; j < n; j++)
    {   for(k = 0; k < n; k++)
            r[j * n + k] = false;
        r[j * n + j] = true;
    }
    p   = f.ForSparseJac(n, r);
    jac = f.SparseJacobian(x, p);
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    return ok;
}

template <class BaseVector, class SetVector>
bool forward_set(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t j, k;
    double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 3;
    CPPAD_TESTVECTOR(AD<double>)  X(n);
    for(j = 0; j < n; j++)
        X[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(X);

    size_t m = 4;
    CPPAD_TESTVECTOR(AD<double>)  Y(m);
    Y[0] = X[0] + X[2];
    Y[1] = X[0] + X[2];
    Y[2] = X[1] + X[2];
    Y[3] = X[1] + X[2] * X[2] / 2.;

    // create f: X -> Y and stop tape recording
    CppAD::ADFun<double> f(X, Y);

    // new value for the independent variable vector
    BaseVector x(n);
    for(j = 0; j < n; j++)
        x[j] = double(j);

    // Jacobian of y without sparsity pattern
    BaseVector jac(m * n);
    jac = f.SparseJacobian(x);
    /*
          [ 1 0 1   ]
    jac = [ 1 0 1   ]
          [ 0 1 1   ]
          [ 0 1 x_2 ]
    */
    BaseVector check(m * n);
    check[0] = 1.; check[1]  = 0.; check[2]  = 1.;
    check[3] = 1.; check[4]  = 0.; check[5]  = 1.;
    check[6] = 0.; check[7]  = 1.; check[8]  = 1.;
    check[9] = 0.; check[10] = 1.; check[11] = x[2];
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    // test passing sparsity pattern
    SetVector r(n), p(m);
    for(j = 0; j < n; j++)
        r[j].insert(j);
    p   = f.ForSparseJac(n, r);
    jac = f.SparseJacobian(x, p);
    for(k = 0; k < 12; k++)
        ok &=  NearEqual(check[k], jac[k], eps99, eps99 );

    return ok;
}

bool multiple_of_n_bit(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::vector;
    size_t i, j;

    // should be the same as the corresponding typedef in
    // cppad/local/sparse_pack.hpp
    typedef size_t Pack;

    // number of bits per packed value
    size_t n_bit = std::numeric_limits<Pack>::digits;

    // check case where number of variables is equal to n_bit
    vector< AD<double> > x(n_bit);
    vector< AD<double> > y(n_bit);

    // create an AD function with domain and range dimension equal to n_bit
    CppAD::Independent(x);
    for(i = 0; i < n_bit; i++)
        y[i] = x[n_bit - i - 1];
    CppAD::ADFun<double> f(x, y);

    // Jacobian sparsity patterns
    vector<bool> r(n_bit * n_bit);
    vector<bool> s(n_bit * n_bit);
    for(i = 0; i < n_bit; i++)
    {   for(j = 0; j < n_bit; j++)
            r[ i * n_bit + j ] = (i == j);
    }
    s = f.ForSparseJac(n_bit, r);

    // check the result
    for(i = 0; i < n_bit; i++)
    {   for(j = 0; j < n_bit; j++)
        {   if( i == n_bit - j - 1 )
                ok = ok & s[ i * n_bit + j ];
            else
                ok = ok & (! s[i * n_bit + j] );
        }
    }

    return ok;
}

// check for a sparse_list bug that was fixed on 2017-04-06
void algo_sparse_list_bug(
    const CppAD::vector < CppAD::AD<double> >& ax ,
    CppAD::vector < CppAD::AD<double> >&       ay )
{
    ay[2] = 1.0;
    ay[0] = 1.0;
    ay[1] = ax[2];
    ay[3] = ax[2];
}
bool sparse_list_bug(void)
{   bool ok  = true;
    using CppAD::AD;
    using CppAD::vector;
    typedef CppAD::vector < std::set<size_t> > sparsity;
    //
    size_t n = 4;
    vector< AD<double> > ay(n), ax(n);
    for(size_t i = 0; i < n; ++i)
        ax[i] = 1.0;
    //
    // sparsity pattern corresponding to identity matrix
    sparsity eye(n);
    for (size_t i = 0; i < n; i++)
        eye[i].insert(i);
    //
    CppAD::checkpoint<double> atom_fun(
        "sparse_list_bug",
        algo_sparse_list_bug,
        ax,
        ay,
        CppAD::atomic_base<double>::set_sparsity_enum
    );
    //
    vector < AD<double> > au(n);
    for (size_t j = 0; j < n; j++)
        au[j] = 1.0;
    //
    // version of function that uses atom_fun
    CppAD::Independent(au);
    vector< AD<double> > av(n);
    atom_fun(au, ay);
    for (size_t j = 0; j < n; j++) {
        av[j] = ay[j] +  au[j];
    }
    CppAD::ADFun<double> yes_atom_fun(au, av);
    //
    // version of function that uses algoright
    CppAD::Independent(au);
    algo_sparse_list_bug(au, ay);
    for (size_t j = 0; j < n; j++) {
        av[j] = ay[j] +  au[j];
    }
    CppAD::ADFun<double> no_atom_fun(au, av);

    //
    sparsity pattern_yes = yes_atom_fun.RevSparseJac(n, eye);
    sparsity pattern_no  = no_atom_fun.RevSparseJac(n, eye);
    //
    for(size_t i = 0; i < n; i++)
        ok &= pattern_yes[i] == pattern_no[i];
    //
    return ok;
}



} // End empty namespace

# include <vector>
# include <valarray>
bool sparse_jacobian(void)
{   bool ok = true;
    ok &= rc_tridiagonal();
    ok &= multiple_of_n_bit();
    ok &= sparse_list_bug();
    // ---------------------------------------------------------------
    // vector of bool cases
    ok &=      rc_bool< CppAD::vector<double>, CppAD::vectorBool   >();
    ok &= forward_bool< CppAD::vector<double>, CppAD::vector<bool> >();
    //
    ok &= reverse_bool< std::vector<double>,   std::vector<bool>   >();
    ok &=      rc_bool< std::vector<double>,   std::valarray<bool> >();
    //
    ok &= forward_bool< std::valarray<double>, CppAD::vectorBool   >();
    ok &= reverse_bool< std::valarray<double>, CppAD::vector<bool> >();
    // ---------------------------------------------------------------
    // vector of set cases
    typedef std::vector< std::set<size_t> >   std_vector_set;
    typedef CppAD::vector< std::set<size_t> > cppad_vector_set;
    //
    ok &=      rc_set< CppAD::vector<double>, std_vector_set   >();
    ok &= forward_set< std::valarray<double>, std_vector_set   >();
    //
    ok &= reverse_set< std::vector<double>,   cppad_vector_set >();
    ok &=      rc_set< CppAD::vector<double>, cppad_vector_set >();
    //
    // According to section 26.3.2.3 of the 1998 C++ standard
    // a const valarray does not return references to its elements.
    // typedef std::valarray< std::set<size_t> > std_valarray_set;
    // ok &= forward_set< std::valarray<double>, std_valarray_set >();
    // ok &= reverse_set< std::valarray<double>, std_valarray_set >();
    // ---------------------------------------------------------------
    //
    return ok;
}
