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

//

// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas

// Digital Ltd. LLC

// 

// All rights reserved.

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

#include <testMatrix.h>

#include "ImathMatrix.h"

#include "ImathMatrixAlgo.h"

#include "ImathVec.h"

#include "ImathLimits.h"

#include "ImathMath.h"

#include "ImathInt64.h"

#include "ImathRandom.h"

#include <iostream>

#include <assert.h>

using namespace std;

using IMATH_INTERNAL_NAMESPACE::Int64;

//

// This file is not currently intended to exhaustively test

// the Imath Matrix33<T> and Matrix44<T> classes.  We leave

// that to PyImathTest.

//

// Instead, in this file we test only those aspects of the

// Imath Matrix33<T> and Matrix44<T> classes that must be 

// or are more convenient to test from C++.

//

void

testMatrix ()

{

    cout << "Testing functions in ImathMatrix.h" << endl;

    union {float f; int i;} nanf;

    nanf.i = 0x7f800001; //  NAN

    union {double d; Int64 i;} nand;

    nand.i = 0x7ff0000000000001ULL; //  NAN

    {

	cout << "Imath::M33f shear functions" << endl;

	IMATH_INTERNAL_NAMESPACE::M33f m1, m2;

	m1.setShear (2.0f);

	assert

	   (m1[0][0] == 1.0f  &&  m1[0][1] == 0.0f  &&  m1[0][2] == 0.0f  &&

	    m1[1][0] == 2.0f  &&  m1[1][1] == 1.0f  &&  m1[1][2] == 0.0f  &&

	    m1[2][0] == 0.0f  &&  m1[2][1] == 0.0f  &&  m1[2][2] == 1.0f);

	m2.setShear (IMATH_INTERNAL_NAMESPACE::V2f (3.0f, 4.0f));

	assert

	   (m2[0][0] == 1.0f  &&  m2[0][1] == 4.0f  &&  m2[0][2] == 0.0f  &&

	    m2[1][0] == 3.0f  &&  m2[1][1] == 1.0f  &&  m2[1][2] == 0.0f  &&

	    m2[2][0] == 0.0f  &&  m2[2][1] == 0.0f  &&  m2[2][2] == 1.0f);

	m1.shear (IMATH_INTERNAL_NAMESPACE::V2f (5.0f, 6.0f));

	assert

	   (m1[0][0] == 13.0f  &&  m1[0][1] == 6.0f  &&  m1[0][2] == 0.0f  &&

	    m1[1][0] ==  7.0f  &&  m1[1][1] == 1.0f  &&  m1[1][2] == 0.0f  &&

	    m1[2][0] ==  0.0f  &&  m1[2][1] == 0.0f  &&  m1[2][2] == 1.0f);

	m2.shear (7.0f);

	assert

	   (m2[0][0] ==  1.0f  &&  m2[0][1] ==  4.0f  &&  m2[0][2] == 0.0f  &&

	    m2[1][0] == 10.0f  &&  m2[1][1] == 29.0f  &&  m2[1][2] == 0.0f  &&

	    m2[2][0] ==  0.0f  &&  m2[2][1] ==  0.0f  &&  m2[2][2] == 1.0f);

	cout << "M33f constructors and equality operators" << endl;

	IMATH_INTERNAL_NAMESPACE::M33f test(m2);

	assert(test == m2);

	IMATH_INTERNAL_NAMESPACE::M33f test2;

	assert(test != test2);

	IMATH_INTERNAL_NAMESPACE::M33f test3;

	test3.makeIdentity();

	assert(test2 == test3);

    }

    {

	cout << "M33d constructors and equality operators" << endl;

	IMATH_INTERNAL_NAMESPACE::M33d m2;

	m2[0][0] = 99.0f;

	m2[1][2] = 101.0f;

	IMATH_INTERNAL_NAMESPACE::M33d test(m2);

	assert(test == m2);

	IMATH_INTERNAL_NAMESPACE::M33d test2;

	assert(test != test2);

	IMATH_INTERNAL_NAMESPACE::M33d test3;

	test3.makeIdentity();

	assert(test2 == test3);

        IMATH_INTERNAL_NAMESPACE::M33f test4 (1.0f, 2.0f, 3.0f,

                           4.0f, 5.0f, 6.0f,

                           7.0f, 8.0f, 9.0f);

        IMATH_INTERNAL_NAMESPACE::M33d test5 = IMATH_INTERNAL_NAMESPACE::M33d (test4);

        assert (test5[0][0] == 1.0);

        assert (test5[0][1] == 2.0);

        assert (test5[0][2] == 3.0);

        assert (test5[1][0] == 4.0);

        assert (test5[1][1] == 5.0);

        assert (test5[1][2] == 6.0);

        assert (test5[2][0] == 7.0);

        assert (test5[2][1] == 8.0);

        assert (test5[2][2] == 9.0);

    }

    {

	IMATH_INTERNAL_NAMESPACE::M44f m2;

	m2[0][0] = 99.0f;

	m2[1][2] = 101.0f;

	cout << "M44f constructors and equality operators" << endl;

	IMATH_INTERNAL_NAMESPACE::M44f test(m2);

	assert(test == m2);

	IMATH_INTERNAL_NAMESPACE::M44f test2;

	assert(test != test2);

	IMATH_INTERNAL_NAMESPACE::M44f test3;

	test3.makeIdentity();

	assert(test2 == test3);

	//

	// Test non-equality when a NAN is in the same

	// place in two identical matrices

	//

	test2[0][0] = nanf.f;

	test3 = test2;

	assert(test2 != test3);

    }

    {

	IMATH_INTERNAL_NAMESPACE::M44d m2;

	m2[0][0] = 99.0f;

	m2[1][2] = 101.0f;

	cout << "M44d constructors and equality operators" << endl;

	IMATH_INTERNAL_NAMESPACE::M44d test(m2);

	assert(test == m2);

	IMATH_INTERNAL_NAMESPACE::M44d test2;

	assert(test != test2);

	IMATH_INTERNAL_NAMESPACE::M44d test3;

	test3.makeIdentity();

	assert(test2 == test3);

	//

	// Test non-equality when a NAN is in the same

	// place in two identical matrices

	//

	test2[0][0] = nand.d;

	test3 = test2;

	assert(test2 != test3);

        IMATH_INTERNAL_NAMESPACE::M44f test4 ( 1.0f,  2.0f,  3.0f,  4.0f,

                            5.0f,  6.0f,  7.0f,  8.0f,

                            9.0f, 10.0f, 11.0f, 12.0f,

                           13.0f, 14.0f, 15.0f, 16.0f);

        IMATH_INTERNAL_NAMESPACE::M44d test5 = IMATH_INTERNAL_NAMESPACE::M44d (test4);

        assert (test5[0][0] ==  1.0);

        assert (test5[0][1] ==  2.0);

        assert (test5[0][2] ==  3.0);

        assert (test5[0][3] ==  4.0);

        assert (test5[1][0] ==  5.0);

        assert (test5[1][1] ==  6.0);

        assert (test5[1][2] ==  7.0);

        assert (test5[1][3] ==  8.0);

        assert (test5[2][0] ==  9.0);

        assert (test5[2][1] == 10.0);

        assert (test5[2][2] == 11.0);

        assert (test5[2][3] == 12.0);

        assert (test5[3][0] == 13.0);

        assert (test5[3][1] == 14.0);

        assert (test5[3][2] == 15.0);

        assert (test5[3][3] == 16.0);

    }

    {

	cout << "Converting between M33 and M44" << endl;

	IMATH_INTERNAL_NAMESPACE::M44d m1;

	m1[0][0] = 99;

	IMATH_INTERNAL_NAMESPACE::M44f m2;

	m2.setValue(m1);

	assert(m2[0][0] == (float)m1[0][0]);

	m1[0][0] = 101;

	m1.setValue(m2);

	assert(m2[0][0] == (float)m1[0][0]);

    }

    // Matrix minors

    {

        cout << "3x3 Matrix minors" << endl;

        IMATH_INTERNAL_NAMESPACE::M33f a(1,2,3,4,5,6,7,8,9);

        assert (a.minorOf(0,0) == a.fastMinor(1,2,1,2));

        assert (a.minorOf(0,1) == a.fastMinor(1,2,0,2));

        assert (a.minorOf(0,2) == a.fastMinor(1,2,0,1));

        assert (a.minorOf(1,0) == a.fastMinor(0,2,1,2));

        assert (a.minorOf(1,1) == a.fastMinor(0,2,0,2));

        assert (a.minorOf(1,2) == a.fastMinor(0,2,0,1));

        assert (a.minorOf(2,0) == a.fastMinor(0,1,1,2));

        assert (a.minorOf(2,1) == a.fastMinor(0,1,0,2));

        assert (a.minorOf(2,2) == a.fastMinor(0,1,0,1));

    }

    {

        IMATH_INTERNAL_NAMESPACE::M33d a(1,2,3,4,5,6,7,8,9);

        assert (a.minorOf(0,0) == a.fastMinor(1,2,1,2));

        assert (a.minorOf(0,1) == a.fastMinor(1,2,0,2));

        assert (a.minorOf(0,2) == a.fastMinor(1,2,0,1));

        assert (a.minorOf(1,0) == a.fastMinor(0,2,1,2));

        assert (a.minorOf(1,1) == a.fastMinor(0,2,0,2));

        assert (a.minorOf(1,2) == a.fastMinor(0,2,0,1));

        assert (a.minorOf(2,0) == a.fastMinor(0,1,1,2));

        assert (a.minorOf(2,1) == a.fastMinor(0,1,0,2));

        assert (a.minorOf(2,2) == a.fastMinor(0,1,0,1));

    }

    // Determinants (by building a random singular value decomposition)

    {

        cout << "3x3 determinant" << endl;

        IMATH_INTERNAL_NAMESPACE::Rand32 random;

        IMATH_INTERNAL_NAMESPACE::M33f u;

        IMATH_INTERNAL_NAMESPACE::M33f v;

        IMATH_INTERNAL_NAMESPACE::M33f s;

        u.setRotation( random.nextf() );

        v.setRotation( random.nextf() );

        s[0][0] = random.nextf();

        s[1][1] = random.nextf();

        s[2][2] = random.nextf();

        IMATH_INTERNAL_NAMESPACE::M33f c = u * s * v.transpose();

        assert (fabsf(c.determinant() - s[0][0]*s[1][1]*s[2][2]) <= u.baseTypeEpsilon());

    }

    {

        IMATH_INTERNAL_NAMESPACE::Rand32 random;

        IMATH_INTERNAL_NAMESPACE::M33d u;

        IMATH_INTERNAL_NAMESPACE::M33d v;

        IMATH_INTERNAL_NAMESPACE::M33d s;

        u.setRotation( (double)random.nextf() );

        v.setRotation( (double)random.nextf() );

        s[0][0] = (double)random.nextf();

        s[1][1] = (double)random.nextf();

        s[2][2] = (double)random.nextf();

        IMATH_INTERNAL_NAMESPACE::M33d c = u * s * v.transpose();

        assert (fabs(c.determinant() - s[0][0]*s[1][1]*s[2][2]) <= u.baseTypeEpsilon());

    }

    // Outer product of two 3D vectors

    {

        cout << "Outer product of two 3D vectors" << endl;

        IMATH_INTERNAL_NAMESPACE::V3f a(1,2,3);

        IMATH_INTERNAL_NAMESPACE::V3f b(4,5,6);

        IMATH_INTERNAL_NAMESPACE::M33f  p = IMATH_INTERNAL_NAMESPACE::outerProduct(a,b);

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

        {

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

            {

                assert (p[i][j] == a[i]*b[j]);

            }

        }

    }

    {

        IMATH_INTERNAL_NAMESPACE::V3d a(1,2,3);

        IMATH_INTERNAL_NAMESPACE::V3d b(4,5,6);

        IMATH_INTERNAL_NAMESPACE::M33d  p = IMATH_INTERNAL_NAMESPACE::outerProduct(a,b);

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

        {

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

            {

                assert (p[i][j] == a[i]*b[j]);

            }

        }

    }

    // Determinants (by building a random singular value decomposition)

    {

        cout << "4x4 determinants" << endl;

        IMATH_INTERNAL_NAMESPACE::Rand32 random;

        IMATH_INTERNAL_NAMESPACE::M44f u = IMATH_INTERNAL_NAMESPACE::rotationMatrix

            ( IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize(),

              IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize() );

        IMATH_INTERNAL_NAMESPACE::M44f v = IMATH_INTERNAL_NAMESPACE::rotationMatrix

            ( IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize(),

              IMATH_INTERNAL_NAMESPACE::V3f(random.nextf(),random.nextf(),random.nextf()).normalize() );

        IMATH_INTERNAL_NAMESPACE::M44f s;

        s[0][0] = random.nextf();

        s[1][1] = random.nextf();

        s[2][2] = random.nextf();

        s[3][3] = random.nextf();

        IMATH_INTERNAL_NAMESPACE::M44f c = u * s * v.transpose();

        assert (fabsf(c.determinant() - s[0][0]*s[1][1]*s[2][2]*s[3][3]) <= u.baseTypeEpsilon());

    }

    {

        IMATH_INTERNAL_NAMESPACE::Rand32 random;

        IMATH_INTERNAL_NAMESPACE::M44d u = IMATH_INTERNAL_NAMESPACE::rotationMatrix

            ( IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize(),

              IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize() );

        IMATH_INTERNAL_NAMESPACE::M44d v = IMATH_INTERNAL_NAMESPACE::rotationMatrix

            ( IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize(),

              IMATH_INTERNAL_NAMESPACE::V3d(random.nextf(),random.nextf(),random.nextf()).normalize() );

        IMATH_INTERNAL_NAMESPACE::M44d s;

        s[0][0] = random.nextf();

        s[1][1] = random.nextf();

        s[2][2] = random.nextf();

        s[3][3] = random.nextf();

        IMATH_INTERNAL_NAMESPACE::M44d c = u * s * v.transpose();

        assert (fabs(c.determinant() - s[0][0]*s[1][1]*s[2][2]*s[3][3]) <= u.baseTypeEpsilon());

    }

    // Matrix minors

    {

        cout << "4x4 matrix minors" << endl;

        IMATH_INTERNAL_NAMESPACE::M44d a(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);

        assert (a.minorOf(0,0) == a.fastMinor(1,2,3,1,2,3));

        assert (a.minorOf(0,1) == a.fastMinor(1,2,3,0,2,3));

        assert (a.minorOf(0,2) == a.fastMinor(1,2,3,0,1,3));

        assert (a.minorOf(0,3) == a.fastMinor(1,2,3,0,1,2));

        assert (a.minorOf(1,0) == a.fastMinor(0,2,3,1,2,3));

        assert (a.minorOf(1,1) == a.fastMinor(0,2,3,0,2,3));

        assert (a.minorOf(1,2) == a.fastMinor(0,2,3,0,1,3));

        assert (a.minorOf(1,3) == a.fastMinor(0,2,3,0,1,2));

        assert (a.minorOf(2,0) == a.fastMinor(0,1,3,1,2,3));

        assert (a.minorOf(2,1) == a.fastMinor(0,1,3,0,2,3));

        assert (a.minorOf(2,2) == a.fastMinor(0,1,3,0,1,3));

        assert (a.minorOf(2,3) == a.fastMinor(0,1,3,0,1,2));

        assert (a.minorOf(3,0) == a.fastMinor(0,1,2,1,2,3));

        assert (a.minorOf(3,1) == a.fastMinor(0,1,2,0,2,3));

        assert (a.minorOf(3,2) == a.fastMinor(0,1,2,0,1,3));

        assert (a.minorOf(3,3) == a.fastMinor(0,1,2,0,1,2));

    }

    {

        IMATH_INTERNAL_NAMESPACE::M44f a(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16);

        assert (a.minorOf(0,0) == a.fastMinor(1,2,3,1,2,3));

        assert (a.minorOf(0,1) == a.fastMinor(1,2,3,0,2,3));

        assert (a.minorOf(0,2) == a.fastMinor(1,2,3,0,1,3));

        assert (a.minorOf(0,3) == a.fastMinor(1,2,3,0,1,2));

        assert (a.minorOf(1,0) == a.fastMinor(0,2,3,1,2,3));

        assert (a.minorOf(1,1) == a.fastMinor(0,2,3,0,2,3));

        assert (a.minorOf(1,2) == a.fastMinor(0,2,3,0,1,3));

        assert (a.minorOf(1,3) == a.fastMinor(0,2,3,0,1,2));

        assert (a.minorOf(2,0) == a.fastMinor(0,1,3,1,2,3));

        assert (a.minorOf(2,1) == a.fastMinor(0,1,3,0,2,3));

        assert (a.minorOf(2,2) == a.fastMinor(0,1,3,0,1,3));

        assert (a.minorOf(2,3) == a.fastMinor(0,1,3,0,1,2));

        assert (a.minorOf(3,0) == a.fastMinor(0,1,2,1,2,3));

        assert (a.minorOf(3,1) == a.fastMinor(0,1,2,0,2,3));

        assert (a.minorOf(3,2) == a.fastMinor(0,1,2,0,1,3));

        assert (a.minorOf(3,3) == a.fastMinor(0,1,2,0,1,2));

    }

    // VC 2005 64 bits compiler has a bug with __restrict keword.

    // Pointers with __restrict should not alias the same symbol.

    // But, with optimization on, VC removes intermediate temp variable

    // and ignores __restrict.

    {

        cout << "M44 multiplicaftion test" << endl;

        IMATH_INTERNAL_NAMESPACE::M44f M ( 1.0f,  2.0f,  3.0f,  4.0f,

                        5.0f,  6.0f,  7.0f,  8.0f,

                        9.0f, 10.0f, 11.0f, 12.0f,

                        13.0f, 14.0f, 15.0f, 16.0f);

        IMATH_INTERNAL_NAMESPACE::M44f N; N.makeIdentity();

        // N should be equal to M

        // This typical test fails

        // when __restrict is used for pointers in "multiply" function.

        N = N * M;

        assert(N == M);

        if (N != M) {

            cout << "M44 multiplication test has failed, error." << endl

                 << "M" << endl << M << endl

                 << "N" << endl << N << endl;

        }

    }

    cout << "ok\n" << endl;

}