/**
* 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 randomly generated set of orthonormal vectors. At most it can generate the same
* number of vectors as the dimension of the vectors.
* </p>
*
* <p>
* This is done by creating random vectors then ensuring that they are orthogonal
* to all the ones previously created with reflectors.
* </p>
*
* <p>
* NOTE: This employs a brute force O(N<sup>3</sup>) algorithm.
* </p>
*
* @param dimen dimension of the space which the vectors will span.
* @param numVectors How many vectors it should generate.
* @param rand Used to create random vectors.
* @return Array of N random orthogonal vectors of unit length.
*/
// is there a faster algorithm out there? This one is a bit sluggish
public static DMatrixRMaj[] span(int dimen, int numVectors, IMersenneTwister rand)
{
if (dimen < numVectors)
{
throw new ArgumentException("The number of vectors must be less than or equal to the dimension");
}
DMatrixRMaj[] u = new DMatrixRMaj[numVectors];
u[0] = RandomMatrices_DDRM.rectangle(dimen, 1, -1, 1, rand);
NormOps_DDRM.normalizeF(u[0]);
for (int i = 1; i < numVectors; i++)
{
// Console.WriteLine(" i = "+i);
DMatrixRMaj a = new DMatrixRMaj(dimen, 1);
DMatrixRMaj r = null;
for (int j = 0; j < i; j++)
{
// Console.WriteLine("j = "+j);
if (j == 0)
{
r = RandomMatrices_DDRM.rectangle(dimen, 1, -1, 1, rand);
}
// find a vector that is normal to vector j
// u[i] = (1/2)*(r + Q[j]*r)
a.set(r);
VectorVectorMult_DDRM.householder(-2.0, u[j], r, a);
CommonOps_DDRM.add(r, a, a);
CommonOps_DDRM.scale(0.5, a);
// UtilEjml.print(a);
DMatrixRMaj t = a;
a = r;
r = t;
// normalize it so it doesn't get too small
double val = NormOps_DDRM.normF(r);
if (val == 0 || double.IsNaN(val) || double.IsInfinity(val))
{
throw new InvalidOperationException("Failed sanity check");
}
CommonOps_DDRM.divide(r, val);
}
u[i] = r;
}
return(u);
}
/**
* <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);
}
