MPSolve 3.2.1
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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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
nThe size of the matrix.
outputThe 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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
shiftThe value of $\lambda$.
nThe size of the matrix.
outputThe 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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
nThe size of the matrix.
outputThe 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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
shiftThe value of $\lambda$.
nThe size of the matrix.
outputThe 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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
nThe size of the matrix.
outputThe storage for the result.
errorA 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
ctxThe current mps_context
hessenberg_matrixThe hessenberg matrix whose determinant should be computed.
shiftThe value of $\lambda$.
nThe size of the matrix.
outputThe storage for the result.
errorA bound on the error.