public static int solverTest(double eps)
{
int success = 0;
Write("\n ===== Solver Test =====\n");
Write("Performed by calculating the difference: Ax - b = 0. \n");
for (int i = 2; i < 6; i++)
{
matrix A = rndMat.randomMatrix(i, i);
vector b = rndMat.randomVector(i);
var gkl = new bidiag(A);
vector diff = A * gkl.solver(b) - b;
for (int m = 0; m < i; m++)
{
if (Abs(diff[m]) > eps)
{
success = 1;
}
}
}
if (success == 0)
{
Write("Solver test PASSED!\n");
}
else
{
Write("Solver test FAILED!\n");
}
return(success);
}//solverTest
}//solverTest
public static int inverseTest(double eps)
{
int success = 0;
Write("\n ===== Inverse Test =====\n");
Write("Performed by calculating the difference: A*A^-1 - I = 0. \n");
for (int i = 2; i < 6; i++)
{
matrix A = rndMat.randomMatrix(i, i);
matrix I = new matrix(i, i);
I.set_identity();
var gkl = new bidiag(A);
matrix diff = A * gkl.inverse() - I;
for (int m = 0; m < i; m++)
{
for (int n = 0; n < i; n++)
{
if (Abs(diff[m, n]) > eps)
{
success = 1;
}
}
}
}
if (success == 0)
{
Write("Inverse test PASSED!\n");
}
else
{
Write("Inverse test FAILED!\n");
}
return(success);
}//inverseTest
}//inverseTest
public static int differenceTest(double eps)
{
Write("\n ===== Difference Test =====\n");
Write("Performed by calculating the difference: A - U*B*V^T = 0. \n");
int successSquare = 0;
for (int i = 2; i < 6; i++)
{
matrix A = rndMat.randomMatrix(i, i);
var gkl = new bidiag(A);
matrix diff = A - gkl.U * gkl.B * gkl.V.transpose();
for (int m = 0; m < i; m++)
{
for (int n = 0; n < i; n++)
{
if (Abs(diff[m, n]) > eps)
{
successSquare = 1;
}
}
}
}
if (successSquare == 0)
{
Write("Square matrix difference test PASSED!\n");
}
else
{
Write("Square matrix difference test FAILED!\n");
}
int successTall = 0;
for (int i = 3; i < 6; i++)
{
for (int j = 2; j < i; j++)
{
matrix A = rndMat.randomMatrix(i, j);
var gkl = new bidiag(A);
matrix diff = A - gkl.U * gkl.B * gkl.V.transpose();
for (int m = 0; m < i; m++)
{
for (int n = 0; n < j; n++)
{
if (Abs(diff[m, n]) > eps)
{
successTall = 1;
}
}
}
}
}
if (successTall == 0)
{
Write("Tall matrix difference test PASSED!\n");
}
else
{
Write("Tall matrix difference test FAILED!\n");
}
return(successSquare + successTall);
} //differenceTest
public static void Main()
{
matrix A = rndMat.randomMatrix(5, 3);
Write("Example of Golub-Kahan-Lanczos bidiagonalization on tall matrix:\n");
Write("The matrix A is written as A = UBV^T. Example for random A given as:\n");
A.print("A =");
var gkl = new bidiag(A);
Write("The found matrix U and V are: \n");
gkl.U.print("\n U = ");
gkl.V.print("\n V = ");
matrix B_calc = gkl.U.transpose() * A * gkl.V;
Write("The bidiogonal matrix calculated via U and V, and directly from the method is given below: \n");
B_calc.print("\n U^T * A * V = ");
gkl.B.print("\n B = ");
Write("The difference between A and the representation of A through B:\n");
(A - gkl.U * gkl.B * gkl.V.transpose()).print("\n 0 = A - U*B*V^T =");
Write("\n Use bidiagonalization to solve Ax=b equation for square random matrix matrix A:\n");
A = rndMat.randomMatrix(3, 3);
A.print("A = ");
Write("With random vector b:\n");
vector b = rndMat.randomVector(3);
b.print("b =");
gkl = new bidiag(A);
vector x = gkl.solver(b);
Write("Solution to equation:\n");
x.print("x =");
vector diff = A * x - b;
Write("Check if solution is correct: \n");
diff.print("0 = A*x - b =");
Write("\n Determinant (found as product of diagonal of B) and inverse:\n");
Write($"|Det(A)| = {gkl.determinant()}\n");
gkl.inverse().print("A^-1 = ");
Write("Check if inverse is correct: \n");
(gkl.inverse() * A).print("1 = A^-1 * A = ");
int success = 0;
double eps = 1e-7;
success = tests.differenceTest(eps);
success += tests.solverTest(eps);
success += tests.inverseTest(eps);
Write("\n ===== Tests result =====\n");
if (success == 0)
{
Write("All test PASSED! \n");
}
else
{
Write("One or several test FAILED! \n");
}
} //Main