#include <catch2/catch_approx.hpp> #include <catch2/catch_test_macros.hpp> #include <catch2/matchers/catch_matchers_all.hpp> #include <Kokkos_Core.hpp> #include <utils/PugsAssert.hpp> #include <utils/Types.hpp> #include <algebra/TinyMatrix.hpp> #include <sstream> // Instantiate to ensure full coverage is performed template class TinyMatrix<1, 1, int>; template class TinyMatrix<2, 2, int>; template class TinyMatrix<3, 4, int>; template class TinyMatrix<4, 4, double>; // clazy:excludeall=non-pod-global-static TEST_CASE("TinyMatrix", "[algebra]") { REQUIRE(TinyMatrix<1, 1, int>::Dimension == 1); REQUIRE(TinyMatrix<1, 1, int>::NumberOfRows == 1); REQUIRE(TinyMatrix<1, 1, int>::NumberOfColumns == 1); REQUIRE(TinyMatrix<2, 3, int>::Dimension == 6); REQUIRE(TinyMatrix<2, 3, int>::NumberOfRows == 2); REQUIRE(TinyMatrix<2, 3, int>::NumberOfColumns == 3); REQUIRE(TinyMatrix<5, 4, int>::Dimension == 20); REQUIRE(TinyMatrix<5, 4, int>::NumberOfRows == 5); REQUIRE(TinyMatrix<5, 4, int>::NumberOfColumns == 4); TinyMatrix<3, 4, int> A(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12); TinyVector<3, int> x1(1, 5, 9); TinyVector<3, int> x2(2, 6, 10); TinyVector<3, int> x3(3, 7, 11); TinyVector<3, int> x4(4, 8, 12); REQUIRE(((A(0, 0) == 1) and (A(0, 1) == 2) and (A(0, 2) == 3) and (A(0, 3) == 4) and // (A(1, 0) == 5) and (A(1, 1) == 6) and (A(1, 2) == 7) and (A(1, 3) == 8) and // (A(2, 0) == 9) and (A(2, 1) == 10) and (A(2, 2) == 11) and (A(2, 3) == 12))); REQUIRE(A == TinyMatrix<3, 4, int>(x1, x2, x3, x4)); TinyMatrix<3, 4, int> B(6, 5, 3, 8, 34, 6, 35, 6, 7, 1, 3, 6); SECTION("checking for opposed matrix") { const TinyMatrix minus_A = -A; REQUIRE( ((minus_A(0, 0) == -1) and (minus_A(0, 1) == -2) and (minus_A(0, 2) == -3) and (minus_A(0, 3) == -4) and // (minus_A(1, 0) == -5) and (minus_A(1, 1) == -6) and (minus_A(1, 2) == -7) and (minus_A(1, 3) == -8) and // (minus_A(2, 0) == -9) and (minus_A(2, 1) == -10) and (minus_A(2, 2) == -11) and (minus_A(2, 3) == -12))); } SECTION("checking for equality and difference tests") { const TinyMatrix copy_A = A; REQUIRE(((copy_A(0, 0) == 1) and (copy_A(0, 1) == 2) and (copy_A(0, 2) == 3) and (copy_A(0, 3) == 4) and // (copy_A(1, 0) == 5) and (copy_A(1, 1) == 6) and (copy_A(1, 2) == 7) and (copy_A(1, 3) == 8) and // (copy_A(2, 0) == 9) and (copy_A(2, 1) == 10) and (copy_A(2, 2) == 11) and (copy_A(2, 3) == 12))); REQUIRE(copy_A == A); REQUIRE_FALSE(copy_A != A); TinyMatrix<3, 4, int> affected_A; affected_A = A; REQUIRE(affected_A == A); REQUIRE_FALSE(affected_A != A); REQUIRE(A != B); REQUIRE_FALSE(A == B); } SECTION("checking for scalar left product") { const int a = 2; const TinyMatrix<3, 4, int> aA = a * A; REQUIRE(aA == TinyMatrix<3, 4, int>(2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24)); } SECTION("checking for scalar seft product") { const int a = 2; TinyMatrix copy_A = A; REQUIRE((copy_A *= a) == TinyMatrix<3, 4, int>(2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24)); } SECTION("checking for null matrix management") { TinyMatrix<4, 3, int> Z = zero; REQUIRE(Z == TinyMatrix<4, 3, int>(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)); TinyMatrix<4, 3, int> affected_Z; affected_Z = zero; REQUIRE(affected_Z == Z); } SECTION("checking for identity management") { TinyMatrix<3, 3, int> I = identity; REQUIRE(I == TinyMatrix<3, 3, int>(1, 0, 0, 0, 1, 0, 0, 0, 1)); TinyMatrix<3, 3, int> affected_I; affected_I = identity; REQUIRE(affected_I == I); } SECTION("checking for matrices sum") { REQUIRE(A + B == TinyMatrix<3, 4, int>(7, 7, 6, 12, 39, 12, 42, 14, 16, 11, 14, 18)); TinyMatrix<3, 4, int> ApB = A; ApB += B; REQUIRE(ApB == A + B); TinyMatrix<3, 4, int> Ap2B = A + 2 * B; REQUIRE(Ap2B == ApB + B); } SECTION("checking for matrices difference ") { REQUIRE(A - B == TinyMatrix<3, 4, int>(-5, -3, 0, -4, -29, 0, -28, 2, 2, 9, 8, 6)); TinyMatrix<3, 4, int> AmB = A; AmB -= B; REQUIRE(AmB == A - B); TinyMatrix<3, 4, int> Am2B = A - 2 * B; REQUIRE(Am2B == AmB - B); } SECTION("checking for matrices product") { TinyMatrix<4, 2, int> C{3, -2, 2, 6, -2, 5, 7, 2}; REQUIRE(A * C == TinyMatrix<3, 2, int>(29, 33, 69, 77, 109, 121)); TinyMatrix<2, 3, int> D{-3, 2, 3, 2, 5, -7}; REQUIRE(D * A == TinyMatrix<2, 4, int>(34, 36, 38, 40, -36, -36, -36, -36)); } SECTION("checking for matrix-vector product") { REQUIRE(A * TinyVector<4, int>(2, -3, 5, 2) == TinyVector<3, int>(19, 43, 67)); } SECTION("checking for tensor product") { const TinyVector<4, int> u(1, 3, 7, 5); const TinyVector<3, int> v(6, 2, -3); REQUIRE(tensorProduct(u, v) == TinyMatrix<4, 3, int>(6, 2, -3, 18, 6, -9, 42, 14, -21, 30, 10, -15)); } SECTION("checking for minor calculation") { REQUIRE(getMinor(A, 0, 0) == TinyMatrix<2, 3, int>(6, 7, 8, 10, 11, 12)); REQUIRE(getMinor(A, 1, 0) == TinyMatrix<2, 3, int>(2, 3, 4, 10, 11, 12)); REQUIRE(getMinor(A, 2, 0) == TinyMatrix<2, 3, int>(2, 3, 4, 6, 7, 8)); REQUIRE(getMinor(A, 0, 1) == TinyMatrix<2, 3, int>(5, 7, 8, 9, 11, 12)); REQUIRE(getMinor(A, 1, 1) == TinyMatrix<2, 3, int>(1, 3, 4, 9, 11, 12)); REQUIRE(getMinor(A, 2, 1) == TinyMatrix<2, 3, int>(1, 3, 4, 5, 7, 8)); REQUIRE(getMinor(A, 0, 2) == TinyMatrix<2, 3, int>(5, 6, 8, 9, 10, 12)); REQUIRE(getMinor(A, 1, 2) == TinyMatrix<2, 3, int>(1, 2, 4, 9, 10, 12)); REQUIRE(getMinor(A, 2, 2) == TinyMatrix<2, 3, int>(1, 2, 4, 5, 6, 8)); REQUIRE(getMinor(A, 0, 3) == TinyMatrix<2, 3, int>(5, 6, 7, 9, 10, 11)); REQUIRE(getMinor(A, 1, 3) == TinyMatrix<2, 3, int>(1, 2, 3, 9, 10, 11)); REQUIRE(getMinor(A, 2, 3) == TinyMatrix<2, 3, int>(1, 2, 3, 5, 6, 7)); } SECTION("checking for cofactors") { TinyMatrix<3, 3, int> A(1, 2, 3, 4, 5, 6, 7, 8, 9); REQUIRE(cofactor(A, 0, 0) == (5 * 9 - 8 * 6)); REQUIRE(cofactor(A, 1, 0) == -(2 * 9 - 8 * 3)); REQUIRE(cofactor(A, 2, 0) == (2 * 6 - 5 * 3)); REQUIRE(cofactor(A, 0, 1) == -(4 * 9 - 7 * 6)); REQUIRE(cofactor(A, 1, 1) == (1 * 9 - 7 * 3)); REQUIRE(cofactor(A, 2, 1) == -(1 * 6 - 4 * 3)); REQUIRE(cofactor(A, 0, 2) == (4 * 8 - 5 * 7)); REQUIRE(cofactor(A, 1, 2) == -(1 * 8 - 7 * 2)); REQUIRE(cofactor(A, 2, 2) == (1 * 5 - 4 * 2)); } SECTION("checking for determinant calculations") { REQUIRE(det(TinyMatrix<1, 1, int>(6)) == 6); REQUIRE(det(TinyMatrix<2, 2, int>(3, 1, -3, 6)) == 21); REQUIRE(det(TinyMatrix<3, 3, int>(1, 1, 1, 1, 2, 1, 2, 1, 3)) == 1); REQUIRE(det(TinyMatrix<3, 3, int>(6, 5, 3, 8, 34, 6, 35, 6, 7)) == -1444); REQUIRE(det(TinyMatrix<4>(1, 2.3, 7, -6.2, 3, 4, 9, 1, 4.1, 5, 2, -3, 2, 27, 3, 17.5)) == Catch::Approx(6661.455).epsilon(1E-14)); REQUIRE(det(TinyMatrix<4>(1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 2, 2)) == 0); } SECTION("checking for trace calculations") { REQUIRE(trace(TinyMatrix<1, 1, int>(6)) == 6); REQUIRE(trace(TinyMatrix<2, 2, int>(5, 1, -3, 6)) == 5 + 6); REQUIRE(trace(TinyMatrix<3, 3, int>(1, 1, 1, 1, 2, 1, 2, 1, 3)) == 1 + 2 + 3); REQUIRE(trace(TinyMatrix<3, 3, int>(6, 5, 3, 8, 34, 6, 35, 6, 7)) == 6 + 34 + 7); REQUIRE(trace(TinyMatrix<4>(1, 2.3, 7, -6.2, 3, 4, 9, 1, 4.1, 5, 2, -3, 2, 27, 3, 17.5)) == Catch::Approx(1 + 4 + 2 + 17.5).epsilon(1E-14)); REQUIRE(trace(TinyMatrix<4>(1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 2, 2)) == 1 + 0 + 1 + 2); } SECTION("checking for inverse calculations") { { const TinyMatrix<1> A1(2); REQUIRE(inverse(A1)(0, 0) == Catch::Approx(0.5).epsilon(1E-14)); } { const TinyMatrix<2> A2(2, 3, 4, 1); const TinyMatrix<2> I = inverse(A2) * A2; REQUIRE(I(0, 0) == Catch::Approx(1).epsilon(1E-14)); REQUIRE(I(0, 1) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(1, 0) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(1, 1) == Catch::Approx(1).epsilon(1E-14)); } { const TinyMatrix<3> A3(2, 3, 1, 4, -1, 5, -2, 3, 4); const TinyMatrix<3> I = inverse(A3) * A3; REQUIRE(I(0, 0) == Catch::Approx(1).epsilon(1E-14)); REQUIRE(I(0, 1) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(0, 2) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(1, 0) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(1, 1) == Catch::Approx(1).epsilon(1E-14)); REQUIRE(I(1, 2) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(2, 0) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(2, 1) == Catch::Approx(0).margin(1E-14)); REQUIRE(I(2, 2) == Catch::Approx(1).epsilon(1E-14)); } } SECTION("checking for sizes") { REQUIRE(TinyMatrix<1>{}.numberOfRows() == 1); REQUIRE(TinyMatrix<1>{}.numberOfColumns() == 1); REQUIRE(TinyMatrix<1>{}.dimension() == 1); REQUIRE(TinyMatrix<1>{}.numberOfValues() == 1); REQUIRE(TinyMatrix<2>{}.numberOfRows() == 2); REQUIRE(TinyMatrix<2>{}.numberOfColumns() == 2); REQUIRE(TinyMatrix<2>{}.numberOfValues() == 4); REQUIRE(TinyMatrix<3>{}.numberOfRows() == 3); REQUIRE(TinyMatrix<3>{}.numberOfColumns() == 3); REQUIRE(TinyMatrix<3>{}.dimension() == 9); REQUIRE(TinyMatrix<3>{}.numberOfValues() == 9); REQUIRE(TinyMatrix<3, 4>{}.numberOfRows() == 3); REQUIRE(TinyMatrix<3, 4>{}.numberOfColumns() == 4); REQUIRE(TinyMatrix<3, 4>{}.dimension() == 12); REQUIRE(TinyMatrix<3, 4>{}.numberOfValues() == 12); } SECTION("is square matrix") { REQUIRE(TinyMatrix<1>{}.isSquare()); REQUIRE(TinyMatrix<2>{}.isSquare()); REQUIRE(TinyMatrix<3>{}.isSquare()); REQUIRE_FALSE(TinyMatrix<3, 4>{}.isSquare()); } SECTION("transpose") { TinyMatrix tA = transpose(A); REQUIRE(((tA(0, 0) == 1) and (tA(1, 0) == 2) and (tA(2, 0) == 3) and (tA(3, 0) == 4) and // (tA(0, 1) == 5) and (tA(1, 1) == 6) and (tA(2, 1) == 7) and (tA(3, 1) == 8) and // (tA(0, 2) == 9) and (tA(1, 2) == 10) and (tA(2, 2) == 11) and (tA(3, 2) == 12))); TinyMatrix ttA = transpose(tA); REQUIRE(ttA == A); } SECTION("checking for matrices output") { REQUIRE(Catch::Detail::stringify(A) == "[[1,2,3,4],[5,6,7,8],[9,10,11,12]]"); REQUIRE(Catch::Detail::stringify(TinyMatrix<1, 1, int>(7)) == "[[7]]"); } SECTION("checking scalarProduct") { TinyMatrix<3, 4, int> B(0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1); // TinyMatrix<3, 4, int> A(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12); REQUIRE(scalarProduct(A, B) == -7); } SECTION("checking norm") { TinyMatrix<3, 4, int> B(0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1); // TinyMatrix<3, 4, int> A(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12); REQUIRE(norm(B) == 3); } #ifndef NDEBUG SECTION("output with signaling NaN") { TinyMatrix<2, 3> A; A(0, 0) = 1; A(0, 2) = 3; A(1, 0) = 2; std::ostringstream A_ost; A_ost << A; std::ostringstream ref_ost; ref_ost << "[[1,nan,3],[2,nan,nan]]"; REQUIRE(A_ost.str() == ref_ost.str()); } SECTION("checking for bounds violation") { REQUIRE_THROWS_AS(A(3, 0), AssertError); REQUIRE_THROWS_AS(A(0, 4), AssertError); REQUIRE_THROWS_AS(getMinor(A, 3, 0), AssertError); REQUIRE_THROWS_AS(getMinor(A, 0, 4), AssertError); const TinyMatrix<3, 4, int>& constA = A; REQUIRE_THROWS_AS(constA(3, 0), AssertError); REQUIRE_THROWS_AS(constA(0, 4), AssertError); } SECTION("checking for nan initialization") { TinyMatrix<3, 4, double> B; for (size_t i = 0; i < B.numberOfRows(); ++i) { for (size_t j = 0; j < B.numberOfColumns(); ++j) { REQUIRE(std::isnan(B(i, j))); } } } SECTION("checking for bad initialization") { TinyMatrix<3, 4, int> B; for (size_t i = 0; i < B.numberOfRows(); ++i) { for (size_t j = 0; j < B.numberOfColumns(); ++j) { REQUIRE(B(i, j) == std::numeric_limits<int>::max() / 2); } } } SECTION("checking for bad initialization") { TinyMatrix<3, 4, int> B; for (size_t i = 0; i < B.numberOfRows(); ++i) { for (size_t j = 0; j < B.numberOfColumns(); ++j) { REQUIRE(B(i, j) == std::numeric_limits<int>::max() / 2); } } } #endif // NDEBUG }