public static double[] pds_random(int n, ref typeMethods.r8NormalData data, ref int seed)
//****************************************************************************80
//
// Purpose:
//
// PDS_RANDOM returns the PDS_RANDOM matrix.
//
// Discussion:
//
// The matrix is a "random" positive definite symmetric matrix.
//
// The matrix returned will have eigenvalues in the range [0,1].
//
// Properties:
//
// A is symmetric: A' = A.
//
// A is positive definite: 0 < x'*A*x for nonzero x.
//
// The eigenvalues of A will be real.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 15 June 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the order of the matrix.
//
// Input/output, int &SEED, a seed for the random
// number generator.
//
// Output, double PDS_RANDOM[N*N], the matrix.
//
{
int j;
double[] a = new double[n * n];
//
// Get a random set of eigenvalues.
//
double[] lambda = UniformRNG.r8vec_uniform_01_new(n, ref seed);
//
// Get a random orthogonal matrix Q.
//
double[] q = Orthogonal.orth_random(n, ref data, ref seed);
//
// Set A = Q * Lambda * Q'.
//
for (j = 0; j < n; j++)
{
int i;
for (i = 0; i < n; i++)
{
a[i + j * n] = 0.0;
int k;
for (k = 0; k < n; k++)
{
a[i + j * n] += q[i + k * n] * lambda[k] * q[j + k * n];
}
}
}
return(a);
}
