sla_gercond (3p)

Name

sla_gercond - estimate the Skeel condition number for a general matrix

Synopsis

REAL  FUNCTION SLA_GERCOND (TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C,
INFO, WORK, IWORK)


CHARACTER*1 TRANS

INTEGER N, LDA, LDAF, INFO, CMODE

INTEGER IPIV(*), IWORK(*)

REAL A(LDA,*), AF(LDAF,*), WORK(*), C(*)


REAL FUNCTION SLA_GERCOND_64 (TRANS, N, A, LDA, AF, LDAF, IPIV,  CMODE,
C, INFO, WORK, IWORK)


CHARACTER*1 TRANS

INTEGER*8 N, LDA, LDAF, INFO, CMODE

INTEGER*8 IPIV(*), IWORK(*)

REAL A(LDA,*), AF(LDAF,*), WORK(*), C(*)


F95 INTERFACE
REAL  FUNCTION  LA_GERCOND (TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C,
INFO, WORK, IWORK)


REAL, DIMENSION(:,:) :: A, AF

INTEGER :: N, LDA, LDAF, CMODE, INFO

CHARACTER(LEN=1) :: TRANS

INTEGER, DIMENSION(:) :: IPIV, IWORK

REAL, DIMENSION(:) :: C, WORK


REAL FUNCTION LA_GERCOND_64 (TRANS, N, A, LDA, AF, LDAF,  IPIV,  CMODE,
C, INFO, WORK, IWORK)


REAL, DIMENSION(:,:) :: A, AF

INTEGER(8) :: N, LDA, LDAF, CMODE, INFO

CHARACTER(LEN=1) :: TRANS

INTEGER(8), DIMENSION(:) :: IPIV, IWORK

REAL, DIMENSION(:) :: C, WORK


C INTERFACE
#include <sunperf.h>

float sla_gercond (char trans, int n, float *a, int lda, float *af, int
ldaf, int *ipiv, int cmode, float *c, int *info);

float sla_gercond_64 (char trans, long n, float  *a,  long  lda,  float
*af,  long  ldaf,  long  *ipiv,  long  cmode,  float *c, long
*info);

Description

Oracle Solaris Studio Performance Library                      sla_gercond(3P)



NAME
       sla_gercond - estimate the Skeel condition number for a general matrix


SYNOPSIS
       REAL  FUNCTION SLA_GERCOND (TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C,
                 INFO, WORK, IWORK)


       CHARACTER*1 TRANS

       INTEGER N, LDA, LDAF, INFO, CMODE

       INTEGER IPIV(*), IWORK(*)

       REAL A(LDA,*), AF(LDAF,*), WORK(*), C(*)


       REAL FUNCTION SLA_GERCOND_64 (TRANS, N, A, LDA, AF, LDAF, IPIV,  CMODE,
                 C, INFO, WORK, IWORK)


       CHARACTER*1 TRANS

       INTEGER*8 N, LDA, LDAF, INFO, CMODE

       INTEGER*8 IPIV(*), IWORK(*)

       REAL A(LDA,*), AF(LDAF,*), WORK(*), C(*)


   F95 INTERFACE
       REAL  FUNCTION  LA_GERCOND (TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C,
                 INFO, WORK, IWORK)


       REAL, DIMENSION(:,:) :: A, AF

       INTEGER :: N, LDA, LDAF, CMODE, INFO

       CHARACTER(LEN=1) :: TRANS

       INTEGER, DIMENSION(:) :: IPIV, IWORK

       REAL, DIMENSION(:) :: C, WORK


       REAL FUNCTION LA_GERCOND_64 (TRANS, N, A, LDA, AF, LDAF,  IPIV,  CMODE,
                 C, INFO, WORK, IWORK)


       REAL, DIMENSION(:,:) :: A, AF

       INTEGER(8) :: N, LDA, LDAF, CMODE, INFO

       CHARACTER(LEN=1) :: TRANS

       INTEGER(8), DIMENSION(:) :: IPIV, IWORK

       REAL, DIMENSION(:) :: C, WORK


   C INTERFACE
       #include <sunperf.h>

       float sla_gercond (char trans, int n, float *a, int lda, float *af, int
                 ldaf, int *ipiv, int cmode, float *c, int *info);

       float sla_gercond_64 (char trans, long n, float  *a,  long  lda,  float
                 *af,  long  ldaf,  long  *ipiv,  long  cmode,  float *c, long
                 *info);


PURPOSE
       sla_gercond estimates the Skeel condition number of op(A)*op2(C)  where
       op2 is determined by CMODE as follows
       CMODE =  1    op2(C) = C
       CMODE =  0    op2(C) = I
       CMODE = -1    op2(C) = inv(C)
       The  Skeel condition number cond(A)=norminf(|inv(A)||A|) is computed by
       computing scaling factors R such that diag(R)*A*op2(C) is  row  equili-
       brated and computing the standard infinity-norm condition number.


ARGUMENTS
       TRANS (input)
                 TRANS is CHARACTER*1
                 Specifies the form of the system of equations:
                 = 'N':  A * X = B     (No transpose)
                 = 'T':  A**T * X = B  (Transpose)
                 = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)


       N (input)
                 N is INTEGER
                 The number of linear equations, i.e., the order of the matrix
                 A. N >= 0.


       A (input)
                 A is REAL array, dimension (LDA,N)
                 On entry, the N-by-N matrix A.


       LDA (input)
                 LDA is INTEGER
                 The leading dimension of the array A.
                 LDA >= max(1,N).


       AF (input)
                 AF is REAL array, dimension (LDAF,N)
                 The factors L and U from the factorization
                 A = P*L*U as computed by SGETRF.


       LDAF (input)
                 LDAF is INTEGER
                 The leading dimension of the array AF.
                 LDAF >= max(1,N).


       IPIV (input)
                 IPIV is INTEGER array, dimension (N)
                 The pivot indices from the factorization A=P*L*U as  computed
                 by  SGETRF;  row  i  of  the matrix was interchanged with row
                 IPIV(i).


       CMODE (input)
                 CMODE is INTEGER
                 Determines op2(C) in the formula op(A) * op2(C) as follows:
                 CMODE =  1    op2(C) = C
                 CMODE =  0    op2(C) = I
                 CMODE = -1    op2(C) = inv(C)


       C (input)
                 C is REAL array, dimension (N)
                 The vector C in the formula op(A) * op2(C).


       INFO (output)
                 INFO is INTEGER
                 = 0:  Successful exit.
                 i > 0:  The ith argument is invalid.


       WORK (input)
                 WORK is REAL array, dimension (3*N).
                 Workspace.


       IWORK (input)
                 IWORK is INTEGER array, dimension (N).
                 Workspace.2




                                  7 Nov 2015                   sla_gercond(3P)