Cynopolis
1091bbda32
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616 lines
19 KiB
C++
616 lines
19 KiB
C++
// include the unit test framework first
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#include <catch2/catch_test_macros.hpp>
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#include <catch2/matchers/catch_matchers_floating_point.hpp>
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// include the module you're going to test next
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#include "Matrix.hpp"
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// any other libraries
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#include <array>
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#include <cmath>
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#include <iostream>
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TEST_CASE("Elementary Matrix Operations", "Matrix") {
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std::array<float, 4> arr2{5, 6, 7, 8};
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Matrix<2, 2> mat1{1, 2, 3, 4};
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Matrix<2, 2> mat2{arr2};
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Matrix<2, 2> mat3{};
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SECTION("Initialization") {
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// array initialization
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REQUIRE(mat1.Get(0, 0) == 1);
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REQUIRE(mat1.Get(0, 1) == 2);
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REQUIRE(mat1.Get(1, 0) == 3);
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REQUIRE(mat1.Get(1, 1) == 4);
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// empty initialization
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REQUIRE(mat3.Get(0, 0) == 0);
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REQUIRE(mat3.Get(0, 1) == 0);
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REQUIRE(mat3.Get(1, 0) == 0);
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REQUIRE(mat3.Get(1, 1) == 0);
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// template pack initialization
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REQUIRE(mat2.Get(0, 0) == 5);
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REQUIRE(mat2.Get(0, 1) == 6);
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REQUIRE(mat2.Get(1, 0) == 7);
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REQUIRE(mat2.Get(1, 1) == 8);
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// large matrix
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Matrix<255, 255> mat6{};
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mat6.Fill(4);
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for (uint8_t row{0}; row < 255; row++) {
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for (uint8_t column{0}; column < 255; column++) {
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REQUIRE(mat6.Get(row, column) == 4);
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}
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}
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}
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SECTION("Fill") {
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mat1.Fill(0);
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REQUIRE(mat1.Get(0, 0) == 0);
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REQUIRE(mat1.Get(0, 1) == 0);
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REQUIRE(mat1.Get(1, 0) == 0);
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REQUIRE(mat1.Get(1, 1) == 0);
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mat2.Fill(100000);
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REQUIRE(mat2.Get(0, 0) == 100000);
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REQUIRE(mat2.Get(0, 1) == 100000);
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REQUIRE(mat2.Get(1, 0) == 100000);
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REQUIRE(mat2.Get(1, 1) == 100000);
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mat3.Fill(-20);
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REQUIRE(mat3.Get(0, 0) == -20);
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REQUIRE(mat3.Get(0, 1) == -20);
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REQUIRE(mat3.Get(1, 0) == -20);
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REQUIRE(mat3.Get(1, 1) == -20);
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}
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SECTION("Addition") {
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std::string strBuf1 = "";
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mat1.ToString(strBuf1);
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std::cout << "Matrix 1:\n" << strBuf1 << std::endl;
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mat1.Add(mat2, mat3);
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REQUIRE(mat3.Get(0, 0) == 6);
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REQUIRE(mat3.Get(0, 1) == 8);
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REQUIRE(mat3.Get(1, 0) == 10);
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REQUIRE(mat3.Get(1, 1) == 12);
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// try out addition with overloaded operators
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mat3.Fill(0);
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mat3 = mat1 + mat2;
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REQUIRE(mat3.Get(0, 0) == 6);
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REQUIRE(mat3.Get(0, 1) == 8);
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REQUIRE(mat3.Get(1, 0) == 10);
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REQUIRE(mat3.Get(1, 1) == 12);
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}
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SECTION("Subtraction") {
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mat1.Sub(mat2, mat3);
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REQUIRE(mat3.Get(0, 0) == -4);
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REQUIRE(mat3.Get(0, 1) == -4);
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REQUIRE(mat3.Get(1, 0) == -4);
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REQUIRE(mat3.Get(1, 1) == -4);
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// try out subtraction with operators
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mat3.Fill(0);
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mat3 = mat1 - mat2;
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REQUIRE(mat3.Get(0, 0) == -4);
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REQUIRE(mat3.Get(0, 1) == -4);
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REQUIRE(mat3.Get(1, 0) == -4);
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REQUIRE(mat3.Get(1, 1) == -4);
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}
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SECTION("Multiplication") {
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mat1.Mult(mat2, mat3);
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REQUIRE(mat3.Get(0, 0) == 19);
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REQUIRE(mat3.Get(0, 1) == 22);
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REQUIRE(mat3.Get(1, 0) == 43);
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REQUIRE(mat3.Get(1, 1) == 50);
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// try out multiplication with operators
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mat3.Fill(0);
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mat3 = mat1 * mat2;
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REQUIRE(mat3.Get(0, 0) == 19);
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REQUIRE(mat3.Get(0, 1) == 22);
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REQUIRE(mat3.Get(1, 0) == 43);
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REQUIRE(mat3.Get(1, 1) == 50);
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// Non-square multiplication
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Matrix<2, 4> mat4{1, 2, 3, 4, 5, 6, 7, 8};
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Matrix<4, 2> mat5{9, 10, 11, 12, 13, 14, 15, 16};
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Matrix<2, 2> mat6{};
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mat6 = mat4 * mat5;
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REQUIRE(mat6.Get(0, 0) == 130);
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REQUIRE(mat6.Get(0, 1) == 140);
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REQUIRE(mat6.Get(1, 0) == 322);
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REQUIRE(mat6.Get(1, 1) == 348);
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// One more non-square multiplicaiton
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Matrix<4, 4> mat7{};
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mat7 = mat5 * mat4;
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REQUIRE(mat7.Get(0, 0) == 59);
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REQUIRE(mat7.Get(0, 1) == 78);
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REQUIRE(mat7.Get(0, 2) == 97);
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REQUIRE(mat7.Get(0, 3) == 116);
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REQUIRE(mat7.Get(1, 0) == 71);
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REQUIRE(mat7.Get(1, 1) == 94);
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REQUIRE(mat7.Get(1, 2) == 117);
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REQUIRE(mat7.Get(1, 3) == 140);
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REQUIRE(mat7.Get(2, 0) == 83);
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REQUIRE(mat7.Get(2, 1) == 110);
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REQUIRE(mat7.Get(2, 2) == 137);
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REQUIRE(mat7.Get(2, 3) == 164);
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REQUIRE(mat7.Get(3, 0) == 95);
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REQUIRE(mat7.Get(3, 1) == 126);
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REQUIRE(mat7.Get(3, 2) == 157);
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REQUIRE(mat7.Get(3, 3) == 188);
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}
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SECTION("Scalar Multiplication") {
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mat1.Mult(2, mat3);
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REQUIRE(mat3.Get(0, 0) == 2);
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REQUIRE(mat3.Get(0, 1) == 4);
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REQUIRE(mat3.Get(1, 0) == 6);
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REQUIRE(mat3.Get(1, 1) == 8);
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}
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SECTION("Element Multiply") {
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mat1.ElementMultiply(mat2, mat3);
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REQUIRE(mat3.Get(0, 0) == 5);
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REQUIRE(mat3.Get(0, 1) == 12);
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REQUIRE(mat3.Get(1, 0) == 21);
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REQUIRE(mat3.Get(1, 1) == 32);
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}
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SECTION("Element Divide") {
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mat1.ElementDivide(mat2, mat3);
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REQUIRE_THAT(mat3.Get(0, 0), Catch::Matchers::WithinRel(0.2f, 1e-6f));
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REQUIRE_THAT(mat3.Get(0, 1), Catch::Matchers::WithinRel(0.3333333f, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 0), Catch::Matchers::WithinRel(0.4285714f, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 1), Catch::Matchers::WithinRel(0.5f, 1e-6f));
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}
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SECTION("Minor Matrix") {
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// what about matrices of 0,0 or 1,1?
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// minor matrix for 2x2 matrix
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Matrix<1, 1> minorMat1{};
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mat1.MinorMatrix(minorMat1, 0, 0);
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REQUIRE(minorMat1.Get(0, 0) == 4);
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mat1.MinorMatrix(minorMat1, 0, 1);
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REQUIRE(minorMat1.Get(0, 0) == 3);
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mat1.MinorMatrix(minorMat1, 1, 0);
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REQUIRE(minorMat1.Get(0, 0) == 2);
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mat1.MinorMatrix(minorMat1, 1, 1);
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REQUIRE(minorMat1.Get(0, 0) == 1);
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// minor matrix for 3x3 matrix
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Matrix<3, 3> mat4{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<2, 2> minorMat4{};
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mat4.MinorMatrix(minorMat4, 0, 0);
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REQUIRE(minorMat4.Get(0, 0) == 5);
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REQUIRE(minorMat4.Get(0, 1) == 6);
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REQUIRE(minorMat4.Get(1, 0) == 8);
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REQUIRE(minorMat4.Get(1, 1) == 9);
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mat4.MinorMatrix(minorMat4, 1, 1);
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REQUIRE(minorMat4.Get(0, 0) == 1);
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REQUIRE(minorMat4.Get(0, 1) == 3);
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REQUIRE(minorMat4.Get(1, 0) == 7);
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REQUIRE(minorMat4.Get(1, 1) == 9);
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mat4.MinorMatrix(minorMat4, 2, 2);
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REQUIRE(minorMat4.Get(0, 0) == 1);
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REQUIRE(minorMat4.Get(0, 1) == 2);
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REQUIRE(minorMat4.Get(1, 0) == 4);
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REQUIRE(minorMat4.Get(1, 1) == 5);
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}
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SECTION("Determinant") {
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float det1 = mat1.Det();
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REQUIRE_THAT(det1, Catch::Matchers::WithinRel(-2.0F, 1e-6f));
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Matrix<3, 3> mat4{1, 2, 3, 4, 5, 6, 7, 8, 9};
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float det4 = mat4.Det();
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REQUIRE_THAT(det4, Catch::Matchers::WithinRel(0.0F, 1e-6f));
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Matrix<3, 3> mat5{1, 0, 0, 0, 2, 0, 0, 0, 3};
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float det5 = mat5.Det();
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REQUIRE_THAT(det5, Catch::Matchers::WithinRel(6.0F, 1e-6f));
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}
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SECTION("Matrix of Minors") {
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mat1.MatrixOfMinors(mat3);
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REQUIRE_THAT(mat3.Get(0, 0), Catch::Matchers::WithinRel(4.0F, 1e-6f));
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REQUIRE_THAT(mat3.Get(0, 1), Catch::Matchers::WithinRel(3.0F, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 0), Catch::Matchers::WithinRel(2.0F, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 1), Catch::Matchers::WithinRel(1.0F, 1e-6f));
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Matrix<3, 3> mat4{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<3, 3> mat5{0};
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mat4.MatrixOfMinors(mat5);
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REQUIRE_THAT(mat5.Get(0, 0), Catch::Matchers::WithinRel(-3.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(0, 1), Catch::Matchers::WithinRel(-6.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(0, 2), Catch::Matchers::WithinRel(-3.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(1, 0), Catch::Matchers::WithinRel(-6.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(1, 1), Catch::Matchers::WithinRel(-12.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(1, 2), Catch::Matchers::WithinRel(-6.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(2, 0), Catch::Matchers::WithinRel(-3.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(2, 1), Catch::Matchers::WithinRel(-6.0F, 1e-6f));
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REQUIRE_THAT(mat5.Get(2, 2), Catch::Matchers::WithinRel(-3.0F, 1e-6f));
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}
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SECTION("Invert") {
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mat3 = mat1.Invert();
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REQUIRE_THAT(mat3.Get(0, 0), Catch::Matchers::WithinRel(-2.0F, 1e-6f));
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REQUIRE_THAT(mat3.Get(0, 1), Catch::Matchers::WithinRel(1.0F, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 0), Catch::Matchers::WithinRel(1.5F, 1e-6f));
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REQUIRE_THAT(mat3.Get(1, 1), Catch::Matchers::WithinRel(-0.5F, 1e-6f));
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};
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SECTION("Transpose") {
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// transpose a square matrix
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mat3 = mat1.Transpose();
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REQUIRE(mat3.Get(0, 0) == 1);
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REQUIRE(mat3.Get(0, 1) == 3);
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REQUIRE(mat3.Get(1, 0) == 2);
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REQUIRE(mat3.Get(1, 1) == 4);
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// transpose a non-square matrix
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Matrix<2, 3> mat4{1, 2, 3, 4, 5, 6};
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Matrix<3, 2> mat5{};
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mat5 = mat4.Transpose();
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REQUIRE(mat5.Get(0, 0) == 1);
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REQUIRE(mat5.Get(0, 1) == 4);
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REQUIRE(mat5.Get(1, 0) == 2);
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REQUIRE(mat5.Get(1, 1) == 5);
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REQUIRE(mat5.Get(2, 0) == 3);
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REQUIRE(mat5.Get(2, 1) == 6);
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}
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SECTION("GET ROW") {
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Matrix<1, 2> mat1Rows{};
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mat1.GetRow(0, mat1Rows);
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REQUIRE(mat1Rows.Get(0, 0) == 1);
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REQUIRE(mat1Rows.Get(0, 1) == 2);
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mat1.GetRow(1, mat1Rows);
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REQUIRE(mat1Rows.Get(0, 0) == 3);
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REQUIRE(mat1Rows.Get(0, 1) == 4);
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}
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SECTION("GET COLUMN") {
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Matrix<2, 1> mat1Columns{};
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mat1.GetColumn(0, mat1Columns);
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REQUIRE(mat1Columns.Get(0, 0) == 1);
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REQUIRE(mat1Columns.Get(1, 0) == 3);
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mat1.GetColumn(1, mat1Columns);
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REQUIRE(mat1Columns.Get(0, 0) == 2);
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REQUIRE(mat1Columns.Get(1, 0) == 4);
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}
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SECTION("Get Sub-Matrices") {
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Matrix<3, 3> mat4{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<2, 2> mat5 = mat4.SubMatrix<2, 2, 0, 0>();
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REQUIRE(mat5.Get(0, 0) == 1);
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REQUIRE(mat5.Get(0, 1) == 2);
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REQUIRE(mat5.Get(1, 0) == 4);
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REQUIRE(mat5.Get(1, 1) == 5);
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mat5 = mat4.SubMatrix<2, 2, 1, 1>();
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REQUIRE(mat5.Get(0, 0) == 5);
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REQUIRE(mat5.Get(0, 1) == 6);
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REQUIRE(mat5.Get(1, 0) == 8);
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REQUIRE(mat5.Get(1, 1) == 9);
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Matrix<3, 1> mat6 = mat4.SubMatrix<3, 1, 0, 0>();
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REQUIRE(mat6.Get(0, 0) == 1);
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REQUIRE(mat6.Get(1, 0) == 4);
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REQUIRE(mat6.Get(2, 0) == 7);
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Matrix<1, 3> mat7 = mat4.SubMatrix<1, 3, 0, 0>();
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REQUIRE(mat7.Get(0, 0) == 1);
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REQUIRE(mat7.Get(0, 1) == 2);
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REQUIRE(mat7.Get(0, 2) == 3);
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}
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SECTION("Set Sub-Matrices") {
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Matrix<3, 3> startMatrix{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<3, 3> mat4 = startMatrix;
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Matrix<2, 2> mat5{10, 11, 12, 13};
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mat4.SetSubMatrix(0, 0, mat5);
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REQUIRE(mat4.Get(0, 0) == 10);
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REQUIRE(mat4.Get(0, 1) == 11);
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REQUIRE(mat4.Get(1, 0) == 12);
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REQUIRE(mat4.Get(1, 1) == 13);
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mat4 = startMatrix;
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mat4.SetSubMatrix(1, 1, mat5);
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REQUIRE(mat4.Get(1, 1) == 10);
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REQUIRE(mat4.Get(1, 2) == 11);
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REQUIRE(mat4.Get(2, 1) == 12);
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REQUIRE(mat4.Get(2, 2) == 13);
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Matrix<3, 1> mat6{10, 11, 12};
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mat4.SetSubMatrix(0, 0, mat6);
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REQUIRE(mat4.Get(0, 0) == 10);
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REQUIRE(mat4.Get(1, 0) == 11);
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REQUIRE(mat4.Get(2, 0) == 12);
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Matrix<1, 3> mat7{10, 11, 12};
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mat4.SetSubMatrix(0, 0, mat7);
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REQUIRE(mat4.Get(0, 0) == 10);
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REQUIRE(mat4.Get(0, 1) == 11);
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REQUIRE(mat4.Get(0, 2) == 12);
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}
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}
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template <uint8_t rows, uint8_t columns>
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float matrixSum(const Matrix<rows, columns> &matrix) {
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float sum = 0;
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for (uint32_t i = 0; i < rows * columns; i++) {
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float number = matrix.ToArray()[i];
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sum += number * number;
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}
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return std::sqrt(sum);
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}
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// TODO: Add test for scalar division
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TEST_CASE("Euclidean Norm", "Matrix") {
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SECTION("2x2 Normalize") {
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Matrix<2, 2> mat1{1, 2, 3, 4};
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Matrix<2, 2> mat2{};
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mat2 = mat1 / mat1.EuclideanNorm();
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float sqrt_30{static_cast<float>(sqrt(30.0f))};
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REQUIRE(mat2.Get(0, 0) == 1 / sqrt_30);
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REQUIRE(mat2.Get(0, 1) == 2 / sqrt_30);
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REQUIRE(mat2.Get(1, 0) == 3 / sqrt_30);
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REQUIRE(mat2.Get(1, 1) == 4 / sqrt_30);
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REQUIRE_THAT(matrixSum(mat2), Catch::Matchers::WithinRel(1.0f, 1e-6f));
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}
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SECTION("2x1 (Vector) Normalize") {
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Matrix<2, 1> mat1{-0.878877044, 2.92092276};
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Matrix<2, 1> mat2{};
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mat2 = mat1 / mat1.EuclideanNorm();
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REQUIRE_THAT(mat2.Get(0, 0),
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Catch::Matchers::WithinRel(-0.288129855179f, 1e-6f));
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REQUIRE_THAT(mat2.Get(1, 0),
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Catch::Matchers::WithinRel(0.957591346325f, 1e-6f));
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float sum = matrixSum(mat2);
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REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
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}
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SECTION("Normalized vectors sum to 1") {
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Matrix<9, 1> mat1{1, 2, 3, 4, 5, 6, 7, 8, 9};
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Matrix<9, 1> mat2;
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mat2 = mat1 / mat1.EuclideanNorm();
|
|
float sum = matrixSum(mat2);
|
|
REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
|
|
|
|
Matrix<2, 3> mat3{1, 2, 3, 4, 5, 6};
|
|
Matrix<2, 3> mat4{};
|
|
mat4 = mat3 / mat3.EuclideanNorm();
|
|
sum = matrixSum(mat4);
|
|
REQUIRE_THAT(sum, Catch::Matchers::WithinRel(1.0f, 1e-6f));
|
|
}
|
|
}
|
|
|
|
TEST_CASE("QR Decompositions", "Matrix") {
|
|
SECTION("2x2 QRDecomposition") {
|
|
Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f};
|
|
Matrix<2, 2> Q{}, R{};
|
|
A.QRDecomposition(Q, R);
|
|
|
|
// Check that Q * R ≈ A
|
|
Matrix<2, 2> QR{};
|
|
Q.Mult(R, QR);
|
|
for (int i = 0; i < 2; ++i) {
|
|
for (int j = 0; j < 2; ++j) {
|
|
REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Check that Q is orthonormal: Qᵀ * Q ≈ I
|
|
Matrix<2, 2> Qt = Q.Transpose();
|
|
Matrix<2, 2> QtQ{};
|
|
Qt.Mult(Q, QtQ);
|
|
for (int i = 0; i < 2; ++i) {
|
|
for (int j = 0; j < 2; ++j) {
|
|
if (i == j)
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
|
|
else
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Optional: R should be upper triangular
|
|
REQUIRE(std::fabs(R[1][0]) < 1e-4f);
|
|
|
|
// check that all Q values are correct
|
|
REQUIRE_THAT(Q[0][0], Catch::Matchers::WithinRel(0.3162f, 1e-4f));
|
|
REQUIRE_THAT(Q[0][1], Catch::Matchers::WithinRel(0.94868f, 1e-4f));
|
|
REQUIRE_THAT(Q[1][0], Catch::Matchers::WithinRel(0.94868f, 1e-4f));
|
|
REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(-0.3162f, 1e-4f));
|
|
|
|
// check that all R values are correct
|
|
REQUIRE_THAT(R[0][0], Catch::Matchers::WithinRel(3.16228f, 1e-4f));
|
|
REQUIRE_THAT(R[0][1], Catch::Matchers::WithinRel(4.42719f, 1e-4f));
|
|
REQUIRE_THAT(R[1][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.63246f, 1e-4f));
|
|
}
|
|
|
|
SECTION("3x3 QRDecomposition") {
|
|
// this symmetrix tridiagonal matrix is well behaved for testing
|
|
Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
|
|
uint32_t matrixRank = 2;
|
|
|
|
Matrix<3, 3> Q{}, R{};
|
|
A.QRDecomposition(Q, R);
|
|
|
|
std::string strBuf1 = "";
|
|
Q.ToString(strBuf1);
|
|
std::cout << "Q:\n" << strBuf1 << std::endl;
|
|
strBuf1 = "";
|
|
R.ToString(strBuf1);
|
|
std::cout << "R:\n" << strBuf1 << std::endl;
|
|
|
|
// Check that Q * R ≈ A
|
|
Matrix<3, 3> QR{};
|
|
QR = Q * R;
|
|
for (int i = 0; i < 3; ++i) {
|
|
for (int j = 0; j < 3; ++j) {
|
|
REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Check that Qᵀ * Q ≈ I
|
|
// In this case the A matrix is only rank 2, so the identity matrix given by
|
|
// Qᵀ * Q is actually only going to be 2x2.
|
|
Matrix<3, 3> Qt = Q.Transpose();
|
|
Matrix<3, 3> QtQ{};
|
|
QtQ = Qt * Q;
|
|
for (int i = 0; i < matrixRank; ++i) {
|
|
for (int j = 0; j < matrixRank; ++j) {
|
|
if (i == j)
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
|
|
else
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Optional: Check R is upper triangular
|
|
// The matrix's rank is only 2 so the last row will not be triangular
|
|
for (int i = 1; i < matrixRank; ++i) {
|
|
for (int j = 0; j < i; ++j) {
|
|
REQUIRE(std::fabs(R[i][j]) < 1e-4f);
|
|
}
|
|
}
|
|
|
|
// check that all Q values are correct
|
|
REQUIRE_THAT(Q[0][0], Catch::Matchers::WithinRel(0.1231f, 1e-4f));
|
|
REQUIRE_THAT(Q[0][1], Catch::Matchers::WithinRel(0.904534f, 1e-4f));
|
|
REQUIRE_THAT(Q[0][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(Q[1][0], Catch::Matchers::WithinRel(0.49237f, 1e-4f));
|
|
REQUIRE_THAT(Q[1][1], Catch::Matchers::WithinRel(0.301511f, 1e-4f));
|
|
REQUIRE_THAT(Q[1][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(Q[2][0], Catch::Matchers::WithinRel(0.86164f, 1e-4f));
|
|
REQUIRE_THAT(Q[2][1], Catch::Matchers::WithinRel(-0.30151f, 1e-4f));
|
|
REQUIRE_THAT(Q[2][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
|
|
// check that all R values are correct
|
|
REQUIRE_THAT(R[0][0], Catch::Matchers::WithinRel(8.124038f, 1e-4f));
|
|
REQUIRE_THAT(R[0][1], Catch::Matchers::WithinRel(9.60114f, 1e-4f));
|
|
REQUIRE_THAT(R[0][2], Catch::Matchers::WithinRel(11.07823f, 1e-4f));
|
|
REQUIRE_THAT(R[1][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(R[1][1], Catch::Matchers::WithinRel(0.90453f, 1e-4f));
|
|
REQUIRE_THAT(R[1][2], Catch::Matchers::WithinRel(1.80907f, 1e-4f));
|
|
REQUIRE_THAT(R[2][0], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(R[2][1], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
REQUIRE_THAT(R[2][2], Catch::Matchers::WithinRel(0.0f, 1e-4f));
|
|
}
|
|
|
|
SECTION("4x2 QRDecomposition") {
|
|
// A simple 4x2 matrix
|
|
Matrix<4, 2> A{1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f};
|
|
|
|
Matrix<4, 2> Q{};
|
|
Matrix<2, 2> R{};
|
|
A.QRDecomposition(Q, R);
|
|
|
|
// Check that Q * R ≈ A
|
|
Matrix<4, 2> QR{};
|
|
Q.Mult(R, QR);
|
|
for (int i = 0; i < 4; ++i) {
|
|
for (int j = 0; j < 2; ++j) {
|
|
REQUIRE_THAT(QR[i][j], Catch::Matchers::WithinRel(A[i][j], 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Check that Qᵀ * Q ≈ I₂
|
|
Matrix<2, 4> Qt = Q.Transpose();
|
|
Matrix<2, 2> QtQ{};
|
|
Qt.Mult(Q, QtQ);
|
|
for (int i = 0; i < 2; ++i) {
|
|
for (int j = 0; j < 2; ++j) {
|
|
if (i == j)
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinRel(1.0f, 1e-4f));
|
|
else
|
|
REQUIRE_THAT(QtQ[i][j], Catch::Matchers::WithinAbs(0.0f, 1e-4f));
|
|
}
|
|
}
|
|
|
|
// Check R is upper triangular (i > j ⇒ R[i][j] ≈ 0)
|
|
for (int i = 1; i < 2; ++i) {
|
|
for (int j = 0; j < i; ++j) {
|
|
REQUIRE(std::fabs(R[i][j]) < 1e-4f);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TEST_CASE("Eigenvalues and Vectors", "Matrix") {
|
|
// SECTION("2x2 Eigen") {
|
|
// Matrix<2, 2> A{1.0f, 2.0f, 3.0f, 4.0f};
|
|
// Matrix<2, 2> vectors{};
|
|
// Matrix<2, 1> values{};
|
|
|
|
// A.EigenQR(vectors, values, 1000000, 1e-20f);
|
|
|
|
// REQUIRE_THAT(vectors[0][0], Catch::Matchers::WithinRel(0.41597f, 1e-4f));
|
|
// REQUIRE_THAT(vectors[1][0], Catch::Matchers::WithinRel(0.90938f, 1e-4f));
|
|
// REQUIRE_THAT(values[0][0], Catch::Matchers::WithinRel(5.372282f, 1e-4f));
|
|
// REQUIRE_THAT(values[1][0], Catch::Matchers::WithinRel(-0.372281f,
|
|
// 1e-4f));
|
|
// }
|
|
|
|
// SECTION("3x3 Eigen") {
|
|
// // this symmetrix tridiagonal matrix is well behaved for testing
|
|
// Matrix<3, 3> A{1, 2, 3, 4, 5, 6, 7, 8, 9};
|
|
|
|
// Matrix<3, 3> vectors{};
|
|
// Matrix<3, 1> values{};
|
|
// A.EigenQR(vectors, values, 1000000, 1e-8f);
|
|
|
|
// std::string strBuf1 = "";
|
|
// vectors.ToString(strBuf1);
|
|
// std::cout << "Vectors:\n" << strBuf1 << std::endl;
|
|
// strBuf1 = "";
|
|
// values.ToString(strBuf1);
|
|
// std::cout << "Values:\n" << strBuf1 << std::endl;
|
|
|
|
// REQUIRE_THAT(vectors[0][0], Catch::Matchers::WithinRel(0.23197f, 1e-4f));
|
|
// REQUIRE_THAT(vectors[1][0], Catch::Matchers::WithinRel(0.525322f,
|
|
// 1e-4f)); REQUIRE_THAT(vectors[2][0], Catch::Matchers::WithinRel(0.81867f,
|
|
// 1e-4f)); REQUIRE_THAT(values[0][0], Catch::Matchers::WithinRel(-1.11684f,
|
|
// 1e-4f)); REQUIRE_THAT(values[1][0], Catch::Matchers::WithinRel(0.0f,
|
|
// 1e-4f)); REQUIRE_THAT(values[2][0], Catch::Matchers::WithinRel(16.1168f,
|
|
// 1e-4f));
|
|
// }
|
|
// }
|