(S|D|C|Z)GESVX¶

Single, double, single complex, and double complex GESVX.

Description¶

Uses LU decomposition with pivoting to solve one of the equations:

$A \mult X = B$

$\trans{A} \mult X = B$

$\herm{A} \mult X = B$

This interface provides more options than the simplified GESV interface. The matrix A may be provided factored or non-factored on input. Equilibration is configurable. Error estimates for the solution are also provided.

If FACT is ‘F’ then A is supplied both in equilibrated form and in LU factored form with pivots. In this case arguments A, AF, IPIV, EQUED, R, and C are input arguments provided by the caller. Otherwise AF, IPIV, EQUED, R, and C are output arguments.

LAPACK Interface¶

void sgesvx(const char *FACT, const char *TRANS, const qml_long *N,
    const qml_long *NRHS, float *A, const qml_long *LDA, float *AF,
    const qml_long *LDAF, qml_long *IPIV, char *EQUED, float *R, float *C,
    float *B, const qml_long *LDB, float *X, const qml_long *LDX,
    float *RCOND, float *FERR, float *BERR, float *WORK, qml_long *IWORK,
    qml_long *INFO);

void dgesvx(const char *FACT, const char *TRANS, const qml_long *N,
    const qml_long *NRHS, double *A, const qml_long *LDA, double *AF,
    const qml_long *LDAF, qml_long *IPIV, char *EQUED, double *R,
    double *C, double *B, const qml_long *LDB, double *X,
    const qml_long *LDX, double *RCOND, double *FERR, double *BERR,
    double *WORK, qml_long *IWORK, qml_long *INFO);

void cgesvx(const char *FACT, const char *TRANS, const qml_long *N,
    const qml_long *NRHS, qml_single_complex *A, const qml_long *LDA,
    qml_single_complex *AF, const qml_long *LDAF, qml_long *IPIV,
    char *EQUED, float *R, float *C, qml_single_complex *B,
    const qml_long *LDB, qml_single_complex *X, const qml_long *LDX,
    float *RCOND, float *FERR, float *BERR, qml_single_complex *WORK,
    float *RWORK, qml_long *INFO);

void zgesvx(const char *FACT, const char *TRANS, const qml_long *N,
    const qml_long *NRHS, qml_double_complex *A, const qml_long *LDA,
    qml_double_complex *AF, const qml_long *LDAF, qml_long *IPIV,
    char *EQUED, double *R, double *C, qml_double_complex *B,
    const qml_long *LDB, qml_double_complex *X, const qml_long *LDX,
    double *RCOND, double *FERR, double *BERR, qml_double_complex *WORK,
    double *RWORK, qml_long *INFO);

Arguments¶

FACT	One of ‘F’ (factorization provided), ‘N’ (factorization requested), or ‘E’ (equilibration and factorization requested)
TRANS	One of ‘N’ (no tranpose), ‘T’ (transpose), or ‘C’ (Hermitian)
N	Number of linear equations, order of A
NRHS	Number of right hand sides, number of columns of B and X
A	Matrix of size N x N, must be equilibrated if FACT is ‘F’ and EQUED is not ‘N’
LDA	Leading dimension of A
AF	Factored form of A
LDAF	Leading dimension of AF
IPIV	Pivot indices
EQUED	Type of equilibration, ‘N’ (none), ‘R’ (row), ‘C’ (column), ‘B’ (both)
R	Array of size N, row scaling factors of A
C	Array of size N, column scaling factors of A
B	Matrix of size N x NRHS
LDB	Leading dimension of B
X	Matrix of size N x NRHS containing solutions
LDX	Leading dimension of X
RCOND	Estimate of reciprocal of condition number of A after equilibration
FERR	Array of size NRHS, estimate of forward errors for each solution
BERR	Array of size NRHS, relative backward error for each solution
WORK	Workspace of size 4N
RWORK	Workspace of size 2N
IWORK	Integer workspace of size N
INFO	0 on success, <0 for illegal arguments, >0 for factorization problems