int
gsl_linalg_cholesky_decomp (gsl_matrix * A)
{
int status;
status = gsl_linalg_cholesky_decomp1(A);
if (status == GSL_SUCCESS)
{
gsl_matrix_transpose_tricpy('L', 0, A, A);
}
return status;
}
int
gsl_linalg_cholesky_decomp_unit(gsl_matrix * A, gsl_vector * D)
{
const size_t N = A->size1;
size_t i, j;
/* initial Cholesky */
int stat_chol = gsl_linalg_cholesky_decomp1(A);
if(stat_chol == GSL_SUCCESS)
{
/* calculate D from diagonal part of initial Cholesky */
for(i = 0; i < N; ++i)
{
const double C_ii = gsl_matrix_get(A, i, i);
gsl_vector_set(D, i, C_ii*C_ii);
}
/* multiply initial Cholesky by 1/sqrt(D) on the right */
for(i = 0; i < N; ++i)
{
for(j = 0; j < N; ++j)
{
gsl_matrix_set(A, i, j, gsl_matrix_get(A, i, j) / sqrt(gsl_vector_get(D, j)));
}
}
/* Because the initial Cholesky contained both L and transpose(L),
the result of the multiplication is not symmetric anymore;
but the lower triangle _is_ correct. Therefore we reflect
it to the upper triangle and declare victory.
*/
for(i = 0; i < N; ++i)
for(j = i + 1; j < N; ++j)
gsl_matrix_set(A, i, j, gsl_matrix_get(A, j, i));
}
return stat_chol;
}
int
gsl_linalg_cholesky_decomp2(gsl_matrix * A, gsl_vector * S)
{
const size_t M = A->size1;
const size_t N = A->size2;
if (M != N)
{
GSL_ERROR("cholesky decomposition requires square matrix", GSL_ENOTSQR);
}
else if (N != S->size)
{
GSL_ERROR("S must have length N", GSL_EBADLEN);
}
else
{
int status;
/* compute scaling factors to reduce cond(A) */
status = gsl_linalg_cholesky_scale(A, S);
if (status)
return status;
/* apply scaling factors */
status = gsl_linalg_cholesky_scale_apply(A, S);
if (status)
return status;
/* compute Cholesky decomposition of diag(S) A diag(S) */
status = gsl_linalg_cholesky_decomp1(A);
if (status)
return status;
return GSL_SUCCESS;
}
}
