/// <summary>
/// N(mu, sigma)
/// </summary>
/// <param name="l">lower bound</param>
/// <param name="u">upper bound</param>
public MultivariateNormalDistribution(PZMath_vector m, PZMath_matrix s)
{
dimension = m.Size;
mu = new PZMath_vector(dimension);
mu.MemCopyFrom(m);
sigma = new PZMath_matrix(dimension, dimension);
sigma.MemCopyFrom(s);
if (dimension != sigma.RowCount || dimension != sigma.ColumnCount)
throw new ApplicationException("MultivariateNormalDistribution::MultivariateNormalDistribution(), mu and sigma in different dimension!");
Init();
}
// calculate covar
public void Covar(double epsrel, PZMath_matrix covar)
{
double tolr;
int i, j, k;
int kmax = 0;
PZMath_matrix r;
PZMath_vector tau;
PZMath_vector norm;
PZMath_permutation perm;
int m = J.RowCount;
int n = J.ColumnCount ;
if (m < n)
PZMath_errno.ERROR ("PZMath_multifit_fdfsolver::Covar(), Jacobian be rectangular M x N with M >= N", PZMath_errno.PZMath_EBADLEN);
if (covar.ColumnCount != covar.RowCount || covar.RowCount != n)
PZMath_errno.ERROR ("PZMath_multifit_fdfsolver::Covar(), covariance matrix must be square and match second dimension of jacobian", PZMath_errno.PZMath_EBADLEN);
r = new PZMath_matrix(m, n);
tau = new PZMath_vector(n);
perm = new PZMath_permutation(n);
norm = new PZMath_vector(n);
{
int signum = 0;
r.MemCopyFrom(J);
PZMath_linalg.QRPTDecomp(r, tau, perm, out signum, norm);
}
/* Form the inverse of R in the full upper triangle of R */
tolr = epsrel * System.Math.Abs(r[0, 0]);
for (k = 0 ; k < n ; k++)
{
double rkk = r[k, k];
if (System.Math.Abs(rkk) <= tolr)
{
break;
}
r[k, k] = 1.0 / rkk;
for (j = 0; j < k ; j++)
{
double t = r[j, k] / rkk;
r[j, k] = 0.0;
for (i = 0; i <= j; i++)
{
double rik = r[i, k];
double rij = r[i, j];
r[i, k] = rik - t * rij;
}
}
kmax = k;
}
/* Form the full upper triangle of the inverse of R^T R in the full
upper triangle of R */
for (k = 0; k <= kmax ; k++)
{
for (j = 0; j < k; j++)
{
double rjk = r[j, k];
for (i = 0; i <= j ; i++)
{
double rij = r[i, j];
double rik = r[i, k];
r[i, j] = rij + rjk * rik;
}
}
{
double t = r[k, k];
for (i = 0; i <= k; i++)
{
double rik = r[i, k];
r[i, k] = t * rik;
}
}
}
/* Form the full lower triangle of the covariance matrix in the
strict lower triangle of R and in w */
for (j = 0 ; j < n ; j++)
{
int pj = (int) perm[j];
for (i = 0; i <= j; i++)
{
int pi = (int) perm[i];
double rij;
if (j > kmax)
{
r[i, j] = 0.0;
rij = 0.0 ;
}
else
{
rij = r[i, j];
}
if (pi > pj)
{
r[pi, pj] = rij;
}
else if (pi < pj)
{
r[pj, pi] = rij;
}
}
{
double rjj = r[j, j];
covar[pj, pj] = rjj;
}
}
/* symmetrize the covariance matrix */
for (j = 0 ; j < n ; j++)
{
for (i = 0; i < j ; i++)
{
double rji = r[j, i];
covar[j, i] = rji;
covar[i, j] = rji;
}
}
}