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241 lines
9.1 KiB
C++
241 lines
9.1 KiB
C++
/*
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* Copyright (c) Contributors to the Open 3D Engine Project. For complete copyright and license terms please see the LICENSE at the root of this distribution.
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*
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* SPDX-License-Identifier: Apache-2.0 OR MIT
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*
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*/
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#include <Tests/Environment.h>
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#include <AzTest/AzTest.h>
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#include <LinearAlgebra.h>
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namespace NumericalMethods
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{
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TEST(LinearAlgebraTest, VectorVariableAccessors_AccessingElements_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 2.0, 5.0, -3.0 });
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EXPECT_NEAR(v1[0], 2.0, 1e-3);
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EXPECT_NEAR(v1[2], -3.0, 1e-3);
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EXPECT_NEAR(v1[1], 5.0, 1e-3);
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}
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TEST(LinearAlgebraTest, VectorVariable_GetDimension_CorrectDimension)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 3.0, -4.0, 12.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ -7.0, -24.0 });
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VectorVariable v3 = VectorVariable::CreateFromVector({ 17.0 });
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VectorVariable v4;
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VectorVariable v5 = VectorVariable::CreateFromVector({ 3.0, 10.0, -5.0, 7.0, -8.0, 3.0 });
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VectorVariable v6(5);
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EXPECT_EQ(v1.GetDimension(), 3);
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EXPECT_EQ(v2.GetDimension(), 2);
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EXPECT_EQ(v3.GetDimension(), 1);
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EXPECT_EQ(v4.GetDimension(), 0);
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EXPECT_EQ(v5.GetDimension(), 6);
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EXPECT_EQ(v6.GetDimension(), 5);
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}
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TEST(LinearAlgebraTest, VectorVariableArithmetic_AddingVectors_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 1.0, 2.0, 3.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ 2.0, 6.0, -4.0 });
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VectorVariable v3 = v1 + v2;
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ExpectClose(v3.GetValues(), { 3.0, 8.0, -1.0 }, 1e-3);
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v3 += v1;
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ExpectClose(v3.GetValues(), { 4.0, 10.0, 2.0 }, 1e-3);
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}
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TEST(LinearAlgebraTest, VectorVariableArithmetic_SubtractingVectors_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 1.0, 2.0, 3.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ 2.0, 6.0, -4.0 });
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VectorVariable v3 = v1 - v2;
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ExpectClose(v3.GetValues(), { -1.0, -4.0, 7.0 }, 1e-3);
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v3 = v2 - v1;
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ExpectClose(v3.GetValues(), { 1.0, 4.0, -7.0 }, 1e-3);
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VectorVariable v4 = -v3;
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ExpectClose(v4.GetValues(), { -1.0, -4.0, 7.0 }, 1e-3);
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v4 -= v2;
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ExpectClose(v4.GetValues(), { -3.0, -10.0, 11.0 }, 1e-3);
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}
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TEST(LinearAlgebraTest, VectorVariableArithmetic_ScalarVectorMultiplication_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 1.0, 2.0, 3.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ 2.0, 6.0, -4.0 });
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VectorVariable v3 = 3.0 * v1;
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ExpectClose(v3.GetValues(), { 3.0, 6.0, 9.0 }, 1e-3);
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v3 = v2 * 0.5;
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ExpectClose(v3.GetValues(), { 1.0, 3.0, -2.0 }, 1e-3);
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}
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TEST(LinearAlgebraTest, VectorVariableArithmetic_Norm_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 3.0, -4.0, 12.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ -7.0, -24.0 });
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VectorVariable v3 = VectorVariable::CreateFromVector({ 17.0 });
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VectorVariable v4;
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VectorVariable v5 = VectorVariable::CreateFromVector({ 3.0, 10.0, -5.0, 7.0, -8.0, 3.0 });
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VectorVariable v6(5);
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EXPECT_NEAR(v1.Norm(), 13.0, 1e-3);
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EXPECT_NEAR(v2.Norm(), 25.0, 1e-3);
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EXPECT_NEAR(v3.Norm(), 17.0, 1e-3);
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EXPECT_NEAR(v4.Norm(), 0, 1e-3);
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EXPECT_NEAR(v5.Norm(), 16, 1e-3);
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EXPECT_NEAR(v6.Norm(), 0, 1e-3);
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}
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TEST(LinearAlgebraTest, VectorVariableArithmetic_DotProduct_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 6.0, -5.0, 8.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ -7.0, -4.0, 2.0 });
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VectorVariable v3 = VectorVariable::CreateFromVector({ 3.0, 7.0, -5.0 });
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EXPECT_NEAR(v1.Dot(v2), -6.0, 1e-3);
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EXPECT_NEAR(v2.Dot(v1), -6.0, 1e-3);
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EXPECT_NEAR(v1.Dot(v3), -57.0, 1e-3);
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EXPECT_NEAR(v2.Dot(v3), -59.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_AddingMatrices_CorrectResults)
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{
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MatrixVariable m1(2, 3);
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MatrixVariable m2(2, 3);
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for (AZ::u32 row = 0; row < 2; row++)
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{
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for (AZ::u32 col = 0; col < 3; col++)
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{
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m1.Element(row, col) = row * row + col; // [[0, 1, 2], [1, 2, 3]]
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m2.Element(row, col) = row + col * 2.0; // [[0, 2, 4], [1, 3, 5]]
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}
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}
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MatrixVariable m3 = m1 + m2; // [[0, 3, 6], [2, 5, 8]]
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EXPECT_EQ(m3.GetNumRows(), 2);
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EXPECT_EQ(m3.GetNumColumns(), 3);
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EXPECT_NEAR(m3.Element(0, 0), 0.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 2), 8.0, 1e-3);
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EXPECT_NEAR(m3.Element(0, 1), 3.0, 1e-3);
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m3 += m1; // [[0, 4, 8], [3, 7, 11]]
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EXPECT_NEAR(m3.Element(0, 2), 8.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 1), 7.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_SubtractingMatrices_CorrectResults)
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{
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MatrixVariable m1(2, 3);
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MatrixVariable m2(2, 3);
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for (AZ::u32 row = 0; row < 2; row++)
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{
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for (AZ::u32 col = 0; col < 3; col++)
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{
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m1.Element(row, col) = row * row + col; // [[0, 1, 2], [1, 2, 3]]
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m2.Element(row, col) = row + col * 2.0; // [[0, 2, 4], [1, 3, 5]]
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}
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}
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MatrixVariable m3 = m2 - m1; // [[0, 1, 2], [0, 1, 2]]
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EXPECT_EQ(m3.GetNumRows(), 2);
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EXPECT_EQ(m3.GetNumColumns(), 3);
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EXPECT_NEAR(m3.Element(0, 2), 2.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 1), 1.0, 1e-3);
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EXPECT_NEAR(m3.Element(0, 1), 1.0, 1e-3);
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m3 = m1 - m3; // [[0, 0, 0], [1, 1, 1]]
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EXPECT_NEAR(m3.Element(0, 1), 0.0, 1e-3);
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EXPECT_NEAR(m3.Element(0, 0), 0.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 2), 1.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_MatrixScalarDivision_CorrectResults)
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{
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MatrixVariable m1(2, 2);
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m1.Element(0, 0) = 3.0;
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m1.Element(0, 1) = 9.0;
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m1.Element(1, 0) = -6.0;
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m1.Element(1, 1) = 3.0;
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MatrixVariable m2 = m1 / 3.0;
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EXPECT_NEAR(m2.Element(0, 0), 1.0, 1e-3);
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EXPECT_NEAR(m2.Element(1, 0), -2.0, 1e-3);
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MatrixVariable m3 = m2 / 0.5;
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EXPECT_NEAR(m3.Element(1, 1), 2.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 0), -4.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_MatrixScalarMultiplication_CorrectResults)
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{
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MatrixVariable m1(3, 2);
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m1.Element(0, 0) = 7.0;
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m1.Element(0, 1) = 5.0;
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m1.Element(1, 0) = -3.0;
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m1.Element(1, 1) = 4.0;
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m1.Element(2, 0) = 6.0;
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m1.Element(2, 1) = -2.0;
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MatrixVariable m2 = 4.0 * m1;
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EXPECT_NEAR(m2.Element(2, 0), 24.0, 1e-3);
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EXPECT_NEAR(m2.Element(1, 0), -12.0, 1e-3);
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EXPECT_NEAR(m2.Element(0, 1), 20.0, 1e-3);
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MatrixVariable m3 = 0.5 * m2;
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EXPECT_NEAR(m3.Element(1, 1), 8.0, 1e-3);
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EXPECT_NEAR(m3.Element(2, 1), -4.0, 1e-3);
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EXPECT_NEAR(m3.Element(0, 0), 14.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_MatrixMatrixMultiplication_CorrectResults)
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{
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MatrixVariable m1(3, 2);
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m1.Element(0, 0) = 1.0;
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m1.Element(0, 1) = 7.0;
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m1.Element(1, 0) = -2.0;
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m1.Element(1, 1) = -4.0;
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m1.Element(2, 0) = -3.0;
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m1.Element(2, 1) = 5.0;
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MatrixVariable m2(2, 2);
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m2.Element(0, 0) = 4.0;
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m2.Element(0, 1) = -3.0;
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m2.Element(1, 0) = 5.0;
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m2.Element(1, 1) = 2.0;
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MatrixVariable m3 = m1 * m2;
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EXPECT_EQ(m3.GetNumRows(), 3);
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EXPECT_EQ(m3.GetNumColumns(), 2);
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EXPECT_NEAR(m3.Element(0, 0), 39.0, 1e-3);
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EXPECT_NEAR(m3.Element(0, 1), 11.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 0), -28.0, 1e-3);
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EXPECT_NEAR(m3.Element(1, 1), -2.0, 1e-3);
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EXPECT_NEAR(m3.Element(2, 0), 13.0, 1e-3);
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EXPECT_NEAR(m3.Element(2, 1), 19.0, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_MatrixVectorMultiplication_CorrectResults)
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{
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MatrixVariable m(3, 2);
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m.Element(0, 0) = 1.0;
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m.Element(0, 1) = 7.0;
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m.Element(1, 0) = -2.0;
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m.Element(1, 1) = -4.0;
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m.Element(2, 0) = -3.0;
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m.Element(2, 1) = 5.0;
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VectorVariable v1 = VectorVariable::CreateFromVector({ 2.0, -3.0 });
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VectorVariable v2 = m * v1;
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EXPECT_EQ(v2.GetDimension(), 3);
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ExpectClose(v2.GetValues(), { -19.0, 8.0, -21.0 }, 1e-3);
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}
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TEST(LinearAlgebraTest, MatrixArithmetic_OuterProduct_CorrectResults)
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{
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VectorVariable v1 = VectorVariable::CreateFromVector({ 1.0, -2.0, 2.0 });
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VectorVariable v2 = VectorVariable::CreateFromVector({ -2.0, 3.0, 1.0 });
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MatrixVariable m = OuterProduct(v1, v2);
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EXPECT_NEAR(m.Element(0, 1), 3.0, 1e-3);
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EXPECT_NEAR(m.Element(1, 2), -2.0, 1e-3);
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EXPECT_NEAR(m.Element(1, 1), -6.0, 1e-3);
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EXPECT_NEAR(m.Element(0, 2), 1.0, 1e-3);
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EXPECT_NEAR(m.Element(2, 1), 6.0, 1e-3);
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}
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} // namespace NumericalMethods::Optimization
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