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/* ========================================================================== */
/* === UMFPACK_get_determinant ============================================== */
/* ========================================================================== */
/* -------------------------------------------------------------------------- */
/* UMFPACK Version 4.6, Copyright (c) 2005 by Timothy A. Davis. CISE Dept, */
/* Univ. of Florida. All Rights Reserved. See ../Doc/License for License. */
/* web: http://www.cise.ufl.edu/research/sparse/umfpack */
/* UMFPACK_get_determinant contributed by David Bateman, Motorola, Paris. */
/* -------------------------------------------------------------------------- */
int umfpack_di_get_determinant
(
double *Mx,
double *Ex,
void *NumericHandle,
double User_Info [UMFPACK_INFO]
) ;
long umfpack_dl_get_determinant
(
double *Mx,
double *Ex,
void *NumericHandle,
double User_Info [UMFPACK_INFO]
) ;
int umfpack_zi_get_determinant
(
double *Mx,
double *Mz,
double *Ex,
void *NumericHandle,
double User_Info [UMFPACK_INFO]
) ;
long umfpack_zl_get_determinant
(
double *Mx,
double *Mz,
double *Ex,
void *NumericHandle,
double User_Info [UMFPACK_INFO]
) ;
/*
double int Syntax:
#include "umfpack.h"
void *Numeric ;
int status ;
double Mx, Ex, Info [UMFPACK_INFO] ;
status = umfpack_di_get_determinant (&Mx, &Ex, Numeric, Info) ;
double long Syntax:
#include "umfpack.h"
void *Numeric ;
long status ;
double Mx, Ex, Info [UMFPACK_INFO] ;
status = umfpack_dl_get_determinant (&Mx, &Ex, Numeric, Info) ;
complex int Syntax:
#include "umfpack.h"
void *Numeric ;
int status ;
double Mx, Mz, Ex, Info [UMFPACK_INFO] ;
status = umfpack_zi_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
complex int Syntax:
#include "umfpack.h"
void *Numeric ;
long status ;
double *Mx, *Mz, *Ex, Info [UMFPACK_INFO] ;
status = umfpack_zl_get_determinant (&Mx, &Mz, &Ex, Numeric, Info) ;
packed complex int Syntax:
Same as above, except Mz is NULL.
Author: Contributed by David Bateman, Motorola, Paris
Purpose:
Using the LU factors and the permutation vectors contained in the Numeric
object, calculate the determinant of the matrix A.
The value of the determinant can be returned in two forms, depending on
whether Ex is NULL or not. If Ex is NULL then the value of the determinant
is returned on Mx and Mz for the real and imaginary parts. However, to
avoid over- or underflows, the determinant can be split into a mantissa
and exponent, and the parts returned separately, in which case Ex is not
NULL. The actual determinant is then given by
double det ;
det = Mx * pow (10.0, Ex) ;
for the double case, or
double det [2] ;
det [0] = Mx * pow (10.0, Ex) ; // real part
det [1] = Mz * pow (10.0, Ex) ; // imaginary part
for the complex case. Information on if the determinant will or has
over or under-flowed is given by Info [UMFPACK_STATUS].
In the "packed complex" syntax, Mx [0] holds the real part and Mx [1]
holds the imaginary part. Mz is not used (it is NULL).
Returns:
Returns UMFPACK_OK if sucessful. Returns UMFPACK_ERROR_out_of_memory if
insufficient memory is available for the n_row integer workspace that
umfpack_*_get_determinant allocates to construct pivots from the
permutation vectors. Returns UMFPACK_ERROR_invalid_Numeric_object if the
Numeric object provided as input is invalid. Returns
UMFPACK_WARNING_singular_matrix if the determinant is zero. Returns
UMFPACK_WARNING_determinant_underflow or
UMFPACK_WARNING_determinant_overflow if the determinant has underflowed
overflowed (for the case when Ex is NULL), or will overflow if Ex is not
NULL and det is computed (see above) in the user program.
Arguments:
double *Mx ; Output argument (array of size 1, or size 2 if Mz is NULL)
double *Mz ; Output argument (optional)
double *Ex ; Output argument (optional)
The determinant returned in mantissa/exponent form, as discussed above.
If Mz is NULL, then both the original and imaginary parts will be
returned in Mx. If Ex is NULL then the determinant is returned directly
in Mx and Mz (or Mx [0] and Mx [1] if Mz is NULL), rather than in
mantissa/exponent form.
void *Numeric ; Input argument, not modified.
Numeric must point to a valid Numeric object, computed by
umfpack_*_numeric.
double Info [UMFPACK_INFO] ; Output argument.
Contains information about the calculation of the determinant. If a
(double *) NULL pointer is passed, then no statistics are returned in
Info (this is not an error condition). The following statistics are
computed in umfpack_*_determinant:
Info [UMFPACK_STATUS]: status code. This is also the return value,
whether or not Info is present.
UMFPACK_OK
The determinant was successfully found.
UMFPACK_ERROR_out_of_memory
Insufficient memory to solve the linear system.
UMFPACK_ERROR_argument_missing
Mx is missing (NULL).
UMFPACK_ERROR_invalid_Numeric_object
The Numeric object is not valid.
UMFPACK_ERROR_invalid_system
The matrix is rectangular. Only square systems can be
handled.
UMFPACK_WARNING_singluar_matrix
The determinant is zero or NaN. The matrix is singular.
UMFPACK_WARNING_determinant_underflow
When passing from mantissa/exponent form to the determinant
an underflow has or will occur. If the mantissa/exponent from
of obtaining the determinant is used, the underflow will occur
in the user program. If the single argument method of
obtaining the determinant is used, the underflow has already
occurred.
UMFPACK_WARNING_determinant_overflow
When passing from mantissa/exponent form to the determinant
an overflow has or will occur. If the mantissa/exponent from
of obtaining the determinant is used, the overflow will occur
in the user program. If the single argument method of
obtaining the determinant is used, the overflow has already
occurred.
*/
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