int GMRFLib_gsl_spd_inverse(gsl_matrix * A)
{
/*
* replace SPD matrix A with its inverse
*/
gsl_matrix *L;
gsl_vector *x;
size_t i, n;
assert(A->size1 == A->size2);
n = A->size1;
x = gsl_vector_calloc(n);
L = GMRFLib_gsl_duplicate_matrix(A);
gsl_linalg_cholesky_decomp(L);
for (i = 0; i < n; i++) {
gsl_vector_set_basis(x, i);
gsl_linalg_cholesky_svx(L, x);
gsl_matrix_set_col(A, i, x);
}
gsl_vector_free(x);
gsl_matrix_free(L);
return GMRFLib_SUCCESS;
}
int
gsl_linalg_cholesky_solve (const gsl_matrix * LLT,
const gsl_vector * b,
gsl_vector * x)
{
if (LLT->size1 != LLT->size2)
{
GSL_ERROR ("cholesky matrix must be square", GSL_ENOTSQR);
}
else if (LLT->size1 != b->size)
{
GSL_ERROR ("matrix size must match b size", GSL_EBADLEN);
}
else if (LLT->size2 != x->size)
{
GSL_ERROR ("matrix size must match solution size", GSL_EBADLEN);
}
else
{
int status;
/* copy x <- b */
gsl_vector_memcpy (x, b);
status = gsl_linalg_cholesky_svx(LLT, x);
return status;
}
}
CAMLprim value ml_gsl_linalg_cholesky_svx(value CHO, value X)
{
_DECLARE_MATRIX(CHO);
_DECLARE_VECTOR(X);
_CONVERT_MATRIX(CHO);
_CONVERT_VECTOR(X);
gsl_linalg_cholesky_svx(&m_CHO, &v_X);
return Val_unit;
}
//inverse of real (symmetric) positive defined matrix
//as a by-product we may obtain the square root of the determinant of A
int InvRPD(Matrix &R, Matrix &A, double *LogDetSqrt, Matrix *ExternChol) {
assert(A.nRow() == A.nCol());
assert(R.nRow() == R.nCol());
assert(A.nRow() == R.nCol());
Matrix *Chol;
//Make the auxiliar matrix equal to A
if (ExternChol == NULL)
Chol = new Matrix( A.nRow(), A.nCol());
else
Chol = ExternChol;
R.Iden(); //Make R the identity
Chol->copy(A);
//Chol->print("A=\n");
gsl_error_handler_t *hand = gsl_set_error_handler_off ();
int res = gsl_linalg_cholesky_decomp(Chol->Ma());
gsl_set_error_handler(hand);
if (res == GSL_EDOM) {
//printf("Matrix::InvRPD: Warning: Non positive definite matrix.\n"); //exit(0);
return 0;
}
assert(res != GSL_EDOM); //Check that everything went well
//solve for the cannonical vectors to obtain the inverse in R
for (int i=0; i<R.nRow(); i++)
{
//R.print("R=\n");
gsl_linalg_cholesky_svx( Chol->Ma(), R.AsColVec(i));
}
if (LogDetSqrt != NULL) {
*LogDetSqrt = 0.0;
for (int i=0; i<Chol->nRow(); i++) {
*LogDetSqrt += log(Chol->ele( i, i)); //multiply the diagonal elements
}
}
if (ExternChol == NULL)
delete Chol;
return 1;
}
/**
* C++ version of gsl_linalg_cholesky_svx().
* @param cholesky A Cholesky decomposition matrix
* @param x A vector
* @return Error code on failure
*/
inline int cholesky_svx( matrix const& cholesky, vector& x ){
return gsl_linalg_cholesky_svx( cholesky.get(), x.get() ); }
