inverse.cpp
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#include "test_macros.hpp"
#include <matrix/math.hpp>
using namespace matrix;
static const size_t n_large = 50;
int main()
{
float data[9] = {0, 2, 3,
4, 5, 6,
7, 8, 10
};
float data_check[9] = {
-0.4f, -0.8f, 0.6f,
-0.4f, 4.2f, -2.4f,
0.6f, -2.8f, 1.6f
};
SquareMatrix<float, 3> A(data);
SquareMatrix<float, 3> A_I = inv(A);
SquareMatrix<float, 3> A_I_check(data_check);
TEST((A_I - A_I_check).abs().max() < 1e-6f);
float data_2x2[4] = {12, 2,
-7, 5
};
float data_2x2_check[4] = {
0.0675675675f, -0.02702702f,
0.0945945945f, 0.162162162f
};
SquareMatrix<float, 2> A2x2(data_2x2);
SquareMatrix<float, 2> A2x2_I = inv(A2x2);
SquareMatrix<float, 2> A2x2_I_check(data_2x2_check);
TEST(isEqual(A2x2_I, A2x2_I_check));
SquareMatrix<float, 2> A2x2_sing = ones<float, 2, 2>();
SquareMatrix<float, 2> A2x2_sing_I;
TEST(inv(A2x2_sing, A2x2_sing_I) == false);
SquareMatrix<float, 3> A3x3_sing = ones<float, 3, 3>();
SquareMatrix<float, 3> A3x3_sing_I;
TEST(inv(A3x3_sing, A3x3_sing_I) == false)
// stess test
SquareMatrix<float, n_large> A_large;
A_large.setIdentity();
SquareMatrix<float, n_large> A_large_I;
A_large_I.setZero();
for (size_t i = 0; i < n_large; i++) {
A_large_I = inv(A_large);
TEST(isEqual(A_large, A_large_I));
}
SquareMatrix<float, 3> zero_test = zeros<float, 3, 3>();
TEST(isEqual(inv(zero_test), zeros<float, 3, 3>()));
// test pivotting
float data2[81] = {
-2, 1, 1, -1, -5, 1, 2, -1, 0,
-3, 2, -1, 0, 2, 2, -1, -5, 3,
0, 0, 0, 1, 4, -3, 3, 0, -2,
2, 2, -1, -2, -1, 0, 3, 0, 1,
-1, 2, -1, -1, -3, 3, 0, -2, 3,
0, 1, 1, -3, 3, -2, 0, -4, 0,
1, 0, 0, 0, 0, 0, -2, 4, -3,
1, -1, 0, -1, -1, 1, -1, -3, 4,
0, 3, -1, -2, 2, 1, -2, 0, -1
};
float data2_check[81] = {
6, -4, 3, -3, -9, -8, -10, 8, 14,
-2, -7, -5, -3, -2, -2, -16, -5, 8,
-2, 0, -23, 7, -24, -5, -28, -14, 9,
3, -7, 2, -5, -4, -6, -13, 4, 13,
-1, 4, -8, 5, -8, 0, -3, -5, -2,
6, 7, -7, 7, -21, -7, -5, 3, 6,
1, 4, -4, 4, -7, -1, 0, -1, -1,
-7, 3, -11, 5, 1, 6, -1, -13, -10,
-8, 0, -11, 3, 3, 6, -5, -14, -8
};
SquareMatrix<float, 9> A2(data2);
SquareMatrix<float, 9> A2_I = inv(A2);
SquareMatrix<float, 9> A2_I_check(data2_check);
TEST((A2_I - A2_I_check).abs().max() < 1e-3f);
float data3[9] = {
0, 1, 2,
3, 4, 5,
6, 7, 9
};
float data3_check[9] = {
-0.3333333f, -1.6666666f, 1,
-1, 4, -2,
1, -2, 1
};
SquareMatrix<float, 3> A3(data3);
SquareMatrix<float, 3> A3_I = inv(A3);
SquareMatrix<float, 3> A3_I_check(data3_check);
TEST(isEqual(inv(A3), A3_I_check));
TEST(isEqual(A3_I, A3_I_check));
TEST(A3.I(A3_I));
TEST(isEqual(A3_I, A3_I_check));
// cover singular matrices
A3(0, 0) = 0;
A3(0, 1) = 0;
A3(0, 2) = 0;
A3_I = inv(A3);
SquareMatrix<float, 3> Z3 = zeros<float, 3, 3>();
TEST(!A3.I(A3_I));
TEST(!Z3.I(A3_I));
TEST(isEqual(A3_I, Z3));
TEST(isEqual(A3.I(), Z3));
for(size_t i = 0; i < 9; i++) {
A2(0, i) = 0;
}
A2_I = inv(A2);
SquareMatrix<float, 9> Z9 = zeros<float, 9, 9>();
TEST(!A2.I(A2_I));
TEST(!Z9.I(A2_I));
TEST(isEqual(A2_I, Z9));
TEST(isEqual(A2.I(), Z9));
// cover NaN
A3(0, 0) = NAN;
A3(0, 1) = 0;
A3(0, 2) = 0;
A3_I = inv(A3);
TEST(isEqual(A3_I, Z3));
TEST(isEqual(A3.I(), Z3));
A2(0, 0) = NAN;
A2_I = inv(A2);
TEST(isEqual(A2_I, Z9));
TEST(isEqual(A2.I(), Z9));
float data4[9] = {
1.33471626f, 0.74946721f, -0.0531679f,
0.74946721f, 1.07519593f, 0.08036323f,
-0.0531679f, 0.08036323f, 1.01618474f
};
SquareMatrix<float, 3> A4(data4);
float data4_cholesky[9] = {
1.15529921f, 0.f, 0.f,
0.6487213f, 0.80892311f, 0.f,
-0.04602089f, 0.13625271f, 0.99774847f
};
SquareMatrix<float, 3> A4_cholesky_check(data4_cholesky);
SquareMatrix<float, 3> A4_cholesky = cholesky(A4);
TEST(isEqual(A4_cholesky_check, A4_cholesky));
SquareMatrix<float, 3> I3;
I3.setIdentity();
TEST(isEqual(choleskyInv(A4)*A4, I3));
TEST(isEqual(cholesky(Z3), Z3));
return 0;
}
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