///////////////////////////////////////////////////////////////////////////

//

// Copyright (c) 2010, Industrial Light & Magic, a division of Lucas

// Digital Ltd. LLC

// 

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///////////////////////////////////////////////////////////////////////////

#include "ImathMatrixAlgo.h"

#include <iostream>

#include <assert.h>

#include <cmath>

#include <limits>

#include <algorithm>

template <typename T>

void

verifyOrthonormal (const IMATH_INTERNAL_NAMESPACE::Matrix33<T>& A)

{

    const T valueEps = T(100) * std::numeric_limits<T>::epsilon();

    const IMATH_INTERNAL_NAMESPACE::Matrix33<T> prod = A * A.transposed();

    for (int i = 0; i < 3; ++i)

    {

        for (int j = 0; j < 3; ++j)

        {

            if (i == j)

                assert (std::abs (prod[i][j] - 1) < valueEps);

            else

                assert (std::abs (prod[i][j]) < valueEps);

        }

    }

}

template <typename T>

void

verifyOrthonormal (const IMATH_INTERNAL_NAMESPACE::Matrix44<T>& A)

{

    const T valueEps = T(100) * std::numeric_limits<T>::epsilon();

    const IMATH_INTERNAL_NAMESPACE::Matrix44<T> prod = A * A.transposed();

    for (int i = 0; i < 4; ++i)

    {

        for (int j = 0; j < 4; ++j)

        {

            if (i == j)

                assert (std::abs (prod[i][j] - 1) <= valueEps);

            else

                assert (std::abs (prod[i][j]) <= valueEps);

        }

    }

}

template <typename T>

void

verifyTinySVD_3x3 (const IMATH_INTERNAL_NAMESPACE::Matrix33<T>& A)

{

    T maxEntry = 0;

    for (int i = 0; i < 3; ++i)

        for (int j = 0; j < 3; ++j)

            maxEntry = std::max (maxEntry, std::abs (A[i][j]));

    const T eps = std::numeric_limits<T>::epsilon();

    const T valueEps = maxEntry * T(10) * eps;

    for (int i = 0; i < 2; ++i)

    {

        const bool posDet = (i == 0);

        IMATH_INTERNAL_NAMESPACE::Matrix33<T> U, V;

        IMATH_INTERNAL_NAMESPACE::Vec3<T> S;

        IMATH_INTERNAL_NAMESPACE::jacobiSVD (A, U, S, V, eps, posDet);

        IMATH_INTERNAL_NAMESPACE::Matrix33<T> S_times_Vt;

        for (int i = 0; i < 3; ++i)

            for (int j = 0; j < 3; ++j)

                S_times_Vt[i][j] = S[j] * V[i][j];

        S_times_Vt.transpose();

        // Verify that the product of the matrices is A:

        const IMATH_INTERNAL_NAMESPACE::Matrix33<T> product = U * S_times_Vt;

        for (int i = 0; i < 3; ++i)

            for (int j = 0; j < 3; ++j)

                assert (std::abs (product[i][j] - A[i][j]) <= valueEps);

        // Verify that U and V are orthogonal:

        if (posDet)

        {

            assert (U.determinant() > 0.9);

            assert (V.determinant() > 0.9);

        }

        // Verify that the singular values are sorted:

        for (int i = 0; i < 2; ++i)

            assert (S[i] >= S[i+1]);

        // Verify that all the SVs except maybe the last one are positive:

        for (int i = 0; i < 2; ++i)

            assert (S[i] >= T(0));

        if (!posDet)

            assert (S[2] >= T(0));

        verifyOrthonormal (U);

        verifyOrthonormal (V);

    }

}

template <typename T>

void

verifyTinySVD_4x4 (const IMATH_INTERNAL_NAMESPACE::Matrix44<T>& A)

{

    T maxEntry = 0;

    for (int i = 0; i < 4; ++i)

        for (int j = 0; j < 4; ++j)

            maxEntry = std::max (maxEntry, std::abs (A[i][j]));

    const T eps = std::numeric_limits<T>::epsilon();

    const T valueEps = maxEntry * T(100) * eps;

    for (int i = 0; i < 2; ++i)

    {

        const bool posDet = (i == 0);

        IMATH_INTERNAL_NAMESPACE::Matrix44<T> U, V;

        IMATH_INTERNAL_NAMESPACE::Vec4<T> S;

        IMATH_INTERNAL_NAMESPACE::jacobiSVD (A, U, S, V, eps, posDet);

        IMATH_INTERNAL_NAMESPACE::Matrix44<T> S_times_Vt;

        for (int i = 0; i < 4; ++i)

            for (int j = 0; j < 4; ++j)

                S_times_Vt[i][j] = S[j] * V[i][j];

        S_times_Vt.transpose();

        // Verify that the product of the matrices is A:

        const IMATH_INTERNAL_NAMESPACE::Matrix44<T> product = U * S_times_Vt;

        for (int i = 0; i < 4; ++i)

            for (int j = 0; j < 4; ++j)

                assert (std::abs (product[i][j] - A[i][j]) <= valueEps);

        // Verify that U and V have positive determinant if requested:

        if (posDet)

        {

            assert (U.determinant() > 0.99);

            assert (V.determinant() > 0.99);

        }

        // Verify that the singular values are sorted:

        for (int i = 0; i < 3; ++i)

            assert (S[i] >= S[i+1]);

        // Verify that all the SVs except maybe the last one are positive:

        for (int i = 0; i < 3; ++i)

            assert (S[i] >= T(0));

        if (!posDet)

            assert (S[3] >= T(0));

        verifyOrthonormal (U);

        verifyOrthonormal (V);

    }

}

template <typename T>

void

testTinySVD_3x3 (const IMATH_INTERNAL_NAMESPACE::Matrix33<T>& A)

{

    std::cout << "Verifying SVD for [[" << A[0][0] << ", " << A[0][1] << ", " << A[0][2] << "], "

                                 << "[" << A[1][0] << ", " << A[1][1] << ", " << A[1][2] << "], "

                                 << "[" << A[2][0] << ", " << A[2][1] << ", " << A[2][2] << "]]\n";

    verifyTinySVD_3x3 (A);

    verifyTinySVD_3x3 (A.transposed());

    // Try all different orderings of the columns of A:

    int cols[3] = { 0, 1, 2 };

    do

    {

        IMATH_INTERNAL_NAMESPACE::Matrix33<T> B;

        for (int i = 0; i < 3; ++i)

            for (int j = 0; j < 3; ++j)

                B[i][j] = A[i][cols[j]];

        verifyTinySVD_3x3 (B);

    } while (std::next_permutation (cols, cols + 3));

}

template <typename T>

void

testTinySVD_3x3 (const T a, const T b, const T c,

                 const T d, const T e, const T f,

                 const T g, const T h, const T i)

{

    const IMATH_INTERNAL_NAMESPACE::Matrix33<T> A (a, b, c, d, e, f, g, h, i);

    testTinySVD_3x3 (A);

}

template <typename T>

void

testTinySVD_4x4 (const IMATH_INTERNAL_NAMESPACE::Matrix44<T>& A)

{

    std::cout << "Verifying SVD for [[" << A[0][0] << ", " << A[0][1] << ", " << A[0][2] << ", " << A[0][3] << "], "

                                 << "[" << A[1][0] << ", " << A[1][1] << ", " << A[1][2] << ", " << A[1][3] << "], "

                                 << "[" << A[2][0] << ", " << A[2][1] << ", " << A[2][2] << ", " << A[2][3] << "], "

                                 << "[" << A[3][0] << ", " << A[3][1] << ", " << A[3][2] << ", " << A[3][3] << "]]\n";

    verifyTinySVD_4x4 (A);

    verifyTinySVD_4x4 (A.transposed());

    // Try all different orderings of the columns of A:

    int cols[4] = { 0, 1, 2, 3 };

    do

    {

        IMATH_INTERNAL_NAMESPACE::Matrix44<T> B;

        for (int i = 0; i < 4; ++i)

            for (int j = 0; j < 4; ++j)

                B[i][j] = A[i][cols[j]];

        verifyTinySVD_4x4 (B);

    } while (std::next_permutation (cols, cols + 4));

}

template <typename T>

void

testTinySVD_4x4 (const T a, const T b, const T c, const T d, 

                 const T e, const T f, const T g, const T h, 

                 const T i, const T j, const T k, const T l,

                 const T m, const T n, const T o, const T p)

{

    const IMATH_INTERNAL_NAMESPACE::Matrix44<T> A (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p);

    testTinySVD_4x4 (A);

}

template <typename T>

void

testTinySVDImp()

{

    // Try a bunch of 3x3 matrices:

    testTinySVD_3x3<T> (1, 0, 0, 0, 1, 0, 0, 0, 1);

    testTinySVD_3x3<T> (1, 0, 0, 0, -1, 0, 0, 0, 1);

    testTinySVD_3x3<T> (0, 0, 0, 0, 0, 0, 0, 0, 0);

    testTinySVD_3x3<T> (0, 0, 0, 0, 0, 0, 0, 0, 1);

    testTinySVD_3x3<T> (1, 0, 0, 0, 1, 0, 0, 0, 0);

    testTinySVD_3x3<T> (1, 0, 0, 0, 0, 0, 0, 0, 0);

    testTinySVD_3x3<T> (1, 0, 0, 1e-10, 0, 0, 0, 0, 0);

    testTinySVD_3x3<T> (1, 0, 0, 1e-10, 0, 0, 0, 0, 100000);

    testTinySVD_3x3<T> (1, 2, 3, 4, 5, 6, 7, 8, 9);

    testTinySVD_3x3<T> (1, 2, 3, 4, 5, 6, 7, 8, 9);

    testTinySVD_3x3<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec3<T> (100, 1e-5, 0), IMATH_INTERNAL_NAMESPACE::Vec3<T> (100, 1e-5, 0)));

    testTinySVD_3x3<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec3<T> (245, 20, 1), IMATH_INTERNAL_NAMESPACE::Vec3<T> (256, 300, 20)));

    testTinySVD_3x3<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec3<T> (245, 20, 1), IMATH_INTERNAL_NAMESPACE::Vec3<T> (245, 20, 1)) +

                        outerProduct (IMATH_INTERNAL_NAMESPACE::Vec3<T> (1, 2, 3), IMATH_INTERNAL_NAMESPACE::Vec3<T> (1, 2, 3)));

    // Some problematic matrices from SVDTest:

    testTinySVD_3x3<T> (

            0.0023588321752040036, -0.0096558131480729038, 0.0010959850449366493,

            0.0088671829608044754, 0.0016771794267033666, -0.0043081475729438235,

            0.003976050440932701, 0.0019880497026345716, 0.0089576046614601966);

    testTinySVD_3x3<T> (

            2.3588321752040035e-09, -9.6558131480729038e-09,  1.0959850449366498e-09,

            8.8671829608044748e-09,  1.6771794267033661e-09, -4.3081475729438225e-09,

            3.9760504409327016e-09,  1.9880497026345722e-09,  8.9576046614601957e-09);

    testTinySVD_3x3<T> (

            -0.46673855799602715,  0.67466260360310948,  0.97646986796448998,

            -0.032460753747103721, 0.046584527749418278, 0.067431228641151142,

            -0.088885055229687815, 0.1280389179308779,   0.18532617511453064);

    testTinySVD_3x3<T> (

            1e-8, 0, 0,

            0, 1e-8, 0,

            0, 0, 1e-8);

    testTinySVD_3x3<T> (

            1,     0,      0,

            0,     .00036, 0,

            1e-18, 0,      .00018);

    testTinySVD_3x3<T> (

            1.3,   0,     0,

            0,     .0003, 0,

            1e-17, 0,     0);

    testTinySVD_3x3<T> (

            1, 0,    0,

            0, 1e-2, 0,

            0, 0, 1e-2);

    testTinySVD_3x3<T> (

            1,0,0,

            0,1,0,

            0,0,0);

    testTinySVD_3x3<T> (

            1,  0,     0,

            0,  1e-3,  0,

            0,  0,  1e-6);

    testTinySVD_3x3<T> (

             0.59588638570136332, -0.79761234126107794, -1,

             0.39194500425202045,  0.91763115383440363, -0.341818175044664,

            -0.45056075218951946, -0.71259057727425101,  0.47125008216720271);

    testTinySVD_3x3<T> (

             4.38805348e-09, -2.53189691e-09, -4.65678607e-09,

            -3.23000099e-10,  1.86370294e-10,  3.42781192e-10,

            -4.61572824e-09,  2.6632645e-09,   4.89840346e-09);

    // problematic 2x2 one for lapack on suse (see below), padded with 0's

    testTinySVD_3x3<T> (

            0,  -1.00000003e-22, 0,

            1.00000001e-07,  0, 0,

            0, 0, 0);

    // problematic 2x2 one for lapack on suse (see below), padded with 0's and 1

    testTinySVD_3x3<T> (

            0,  -1.00000003e-22, 0,

            1.00000001e-07,  0, 0,

            0, 0, 1);

    // Now, 4x4 matrices:

    testTinySVD_4x4<T> (1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);

    testTinySVD_4x4<T> (1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);

    testTinySVD_4x4<T> (1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0);

    testTinySVD_4x4<T> (1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);

    testTinySVD_4x4<T> (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);

    testTinySVD_4x4<T> (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);

    testTinySVD_4x4<T> (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16);

    testTinySVD_4x4<T> (0, -1.00000003e-22, 0, 0, 00000001e-07, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);

    testTinySVD_4x4<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec4<T> (100, 1e-5, 0, 0), IMATH_INTERNAL_NAMESPACE::Vec4<T> (100, 1e-5, 0, 0)));

    testTinySVD_4x4<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec4<T> (245, 20, 1, 0.5), IMATH_INTERNAL_NAMESPACE::Vec4<T> (256, 300, 20, 10)));

    testTinySVD_4x4<T> (outerProduct (IMATH_INTERNAL_NAMESPACE::Vec4<T> (245, 20, 1, 0.5), IMATH_INTERNAL_NAMESPACE::Vec4<T> (256, 300, 20, 10)) +

                        outerProduct (IMATH_INTERNAL_NAMESPACE::Vec4<T> (30, 10, 10, 10), IMATH_INTERNAL_NAMESPACE::Vec4<T> (1, 2, 3, 3)));

}

void

testTinySVD ()

{

    std::cout << "Testing TinySVD algorithms in single precision..." << std::endl;

    testTinySVDImp<float>();

    std::cout << "Testing TinySVD algorithms in double precision..." << std::endl;

    testTinySVDImp<double>();

}