hessenberg-determinant.h File Reference

Implementation of determinant computation for Hessenberg matrices. More...

#include <mps/mps.h>

Go to the source code of this file.

Functions
MPS_BEGIN_DECLS void	mps_fhessenberg_determinant (mps_context *ctx, cplx_t *hessenberg_matrix, size_t n, cplx_t output, long int *exponent)
	This is the full implementation of the recursive determinant computation.
void	mps_fhessenberg_shifted_determinant (mps_context *ctx, cplx_t *hessenberg_matrix, const cplx_t shift, size_t n, cplx_t output, long int *exponent)
	This is the full implementation of the recursive determinant computation of the Hessnberg - \lambda I matrix.
void	mps_dhessenberg_determinant (mps_context *ctx, cdpe_t *hessenberg_matrix, size_t n, cdpe_t output)
	This is the full implementation of the recursive determinant computation.
void	mps_dhessenberg_shifted_determinant (mps_context *ctx, cdpe_t *hessenberg_matrix, const cdpe_t shift, size_t n, cdpe_t output)
	This is the full implementation of the recursive determinant computation of the Hessenberg - \lambda I matrix.
void	mps_mhessenberg_determinant (mps_context *ctx, mpc_t *hessenberg_matrix, size_t n, mpc_t output, rdpe_t error)
	This is the full implementation of the recursive determinant computation.
void	mps_mhessenberg_shifted_determinant (mps_context *ctx, mpc_t *hessenberg_matrix, mpc_t shift, size_t n, mpc_t output, rdpe_t error)
	This is the full implementation of the recursive determinant computation of the Hessnberg - \lambda I matrix.

Detailed Description

Implementation of determinant computation for Hessenberg matrices.

Function Documentation

mps_dhessenberg_determinant()

void mps_dhessenberg_determinant	(	mps_context *	ctx,
		cdpe_t *	hessenberg_matrix,
		size_t	n,
		cdpe_t	output )

This is the full implementation of the recursive determinant computation.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
n	The size of the matrix.
output	The storage for the result.

mps_dhessenberg_shifted_determinant()

void mps_dhessenberg_shifted_determinant	(	mps_context *	ctx,
		cdpe_t *	hessenberg_matrix,
		const cdpe_t	shift,
		size_t	n,
		cdpe_t	output )

This is the full implementation of the recursive determinant computation of the Hessenberg - \lambda I matrix.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
shift	The value of .
n	The size of the matrix.
output	The storage for the result.

mps_fhessenberg_determinant()

MPS_BEGIN_DECLS void mps_fhessenberg_determinant	(	mps_context *	ctx,
		cplx_t *	hessenberg_matrix,
		size_t	n,
		cplx_t	output,
		long int *	exponent )

This is the full implementation of the recursive determinant computation.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
n	The size of the matrix.
output	The storage for the result.

mps_fhessenberg_shifted_determinant()

void mps_fhessenberg_shifted_determinant	(	mps_context *	ctx,
		cplx_t *	hessenberg_matrix,
		const cplx_t	shift,
		size_t	n,
		cplx_t	output,
		long int *	acc_exponent )

This is the full implementation of the recursive determinant computation of the Hessnberg - \lambda I matrix.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
shift	The value of .
n	The size of the matrix.
output	The storage for the result.

mps_mhessenberg_determinant()

void mps_mhessenberg_determinant	(	mps_context *	ctx,
		mpc_t *	hessenberg_matrix,
		size_t	n,
		mpc_t	output,
		rdpe_t	error )

This is the full implementation of the recursive determinant computation.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
n	The size of the matrix.
output	The storage for the result.
error	A bound on the error.

mps_mhessenberg_shifted_determinant()

void mps_mhessenberg_shifted_determinant	(	mps_context *	ctx,
		mpc_t *	hessenberg_matrix,
		mpc_t	shift,
		size_t	n,
		mpc_t	output,
		rdpe_t	error )

This is the full implementation of the recursive determinant computation of the Hessnberg - \lambda I matrix.

Parameters

ctx	The current mps_context
hessenberg_matrix	The hessenberg matrix whose determinant should be computed.
shift	The value of .
n	The size of the matrix.
output	The storage for the result.
error	A bound on the error.