/**
* Creates a new random symmetric matrix that will have the specified real eigenvalues.
*
* @param num Dimension of the resulting matrix.
* @param rand Random number generator.
* @param eigenvalues Set of real eigenvalues that the matrix will have.
* @return A random matrix with the specified eigenvalues.
*/
public static DMatrixRMaj symmetricWithEigenvalues(int num, IMersenneTwister rand, double[] eigenvalues)
{
DMatrixRMaj V = RandomMatrices_DDRM.orthogonal(num, num, rand);
DMatrixRMaj D = CommonOps_DDRM.diag(eigenvalues);
DMatrixRMaj temp = new DMatrixRMaj(num, num);
CommonOps_DDRM.mult(V, D, temp);
CommonOps_DDRM.multTransB(temp, V, D);
return(D);
}
/**
* <p>
* Creates a random matrix which will have the provided singular values. The length of sv
* is assumed to be the rank of the matrix. This can be useful for testing purposes when one
* needs to ensure that a matrix is not singular but randomly generated.
* </p>
*
* @param numRows Number of rows in generated matrix.
* @param numCols NUmber of columns in generated matrix.
* @param rand Random number generator.
* @param sv Singular values of the matrix.
* @return A new matrix with the specified singular values.
*/
public static DMatrixRMaj singleValues(int numRows, int numCols,
IMersenneTwister rand, double[] sv)
{
DMatrixRMaj U = RandomMatrices_DDRM.orthogonal(numRows, numRows, rand);
DMatrixRMaj V = RandomMatrices_DDRM.orthogonal(numCols, numCols, rand);
DMatrixRMaj S = new DMatrixRMaj(numRows, numCols);
int min = Math.Min(numRows, numCols);
min = Math.Min(min, sv.Length);
for (int i = 0; i < min; i++)
{
S.set(i, i, sv[i]);
}
DMatrixRMaj tmp = new DMatrixRMaj(numRows, numCols);
CommonOps_DDRM.mult(U, S, tmp);
CommonOps_DDRM.multTransB(tmp, V, S);
return(S);
}