public void testSpareMatrixReference()
{
int rows = 10;
int columns = 10;
int nMatrices = 5;
int nElements = 50;
MersenneTwisterUniformRng rng = new MersenneTwisterUniformRng(1234);
SparseMatrix expected = new SparseMatrix(rows, columns);
List <SparseMatrix> refs = new List <SparseMatrix>();
for (int i = 0; i < nMatrices; ++i)
{
SparseMatrix m = new SparseMatrix(rows, columns);
for (int j = 0; j < nElements; ++j)
{
int row = Convert.ToInt32(rng.next().value *rows);
int column = Convert.ToInt32(rng.next().value *columns);
double value = rng.next().value;
m[row, column] += value;
expected[row, column] += value;
}
refs.Add(m);
}
SparseMatrix calculated = refs.accumulate(1, refs.Count, refs[0], (a, b) => a + b);
for (int i = 0; i < rows; ++i)
{
for (int j = 0; j < columns; ++j)
{
if (Math.Abs(calculated[i, j] - expected[i, j]) > 100 * Const.QL_EPSILON)
{
QAssert.Fail("Error using sparse matrix references in " +
"Element (" + i + ", " + j + ")" +
"\n expected : " + expected[i, j] +
"\n calculated: " + calculated[i, j]);
}
}
}
}
public void testQRSolve()
{
// Testing QR solve...
setup();
double tol = 1.0e-12;
MersenneTwisterUniformRng rng = new MersenneTwisterUniformRng(1234);
Matrix bigM = new Matrix(50, 100, 0.0);
for (int i = 0; i < Math.Min(bigM.rows(), bigM.columns()); ++i)
{
bigM[i, i] = i + 1.0;
}
Matrix[] testMatrices = { M1, M2, M3, Matrix.transpose(M3),
M4, Matrix.transpose(M4), M5, I, M7,bigM, Matrix.transpose(bigM) };
for (int j = 0; j < testMatrices.Length; j++)
{
Matrix A = testMatrices[j];
Vector b = new Vector(A.rows());
for (int k = 0; k < 10; ++k)
{
for (int i = 0; i < b.Count; ++i)
{
b[i] = rng.next().value;
}
Vector x = MatrixUtilities.qrSolve(A, b, true);
if (A.columns() >= A.rows())
{
if (norm(A * x - b) > tol)
{
QAssert.Fail("A*x does not match vector b (norm = "
+ norm(A * x - b) + ")");
}
}
else
{
// use the SVD to calculate the reference values
int n = A.columns();
Vector xr = new Vector(n, 0.0);
SVD svd = new SVD(A);
Matrix V = svd.V();
Matrix U = svd.U();
Vector w = svd.singularValues();
double threshold = n * Const.QL_EPSILON;
for (int i = 0; i < n; ++i)
{
if (w[i] > threshold)
{
double u = 0;
int zero = 0;
for (int kk = 0; kk < U.rows(); kk++)
{
u += (U[kk, i] * b[zero++]) / w[i];
}
for (int jj = 0; jj < n; ++jj)
{
xr[jj] += u * V[jj, i];
}
}
}
if (norm(xr - x) > tol)
{
QAssert.Fail("least square solution does not match (norm = "
+ norm(x - xr) + ")");
}
}
}
}
}
