sgerfs (3p)

Name

sgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution

Synopsis

SUBROUTINE SGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB,
X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER*1 TRANSA
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
REAL  A(LDA,*),  AF(LDAF,*),  B(LDB,*),  X(LDX,*),  FERR(*),   BERR(*),
WORK(*)

SUBROUTINE SGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER*1 TRANSA
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
REAL   A(LDA,*),  AF(LDAF,*),  B(LDB,*),  X(LDX,*),  FERR(*),  BERR(*),
WORK(*)




F95 INTERFACE
SUBROUTINE GERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT,
B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER(LEN=1) :: TRANSA
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X

SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X




C INTERFACE
#include <sunperf.h>

void sgerfs(char transa, int n, int nrhs, float *a, int lda, float *af,
int  ldaf, int *ipivot, float *b, int ldb, float *x, int ldx,
float *ferr, float *berr, int *info);

void sgerfs_64(char transa, long n, long  nrhs,  float  *a,  long  lda,
float *af, long ldaf, long *ipivot, float *b, long ldb, float
*x, long ldx, float *ferr, float *berr, long *info);

Description

Oracle Solaris Studio Performance Library                           sgerfs(3P)



NAME
       sgerfs  - improve the computed solution to a system of linear equations
       and provide error bounds and backward error estimates for the solution


SYNOPSIS
       SUBROUTINE SGERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B, LDB,
             X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER*1 TRANSA
       INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
       INTEGER IPIVOT(*), WORK2(*)
       REAL  A(LDA,*),  AF(LDAF,*),  B(LDB,*),  X(LDX,*),  FERR(*),   BERR(*),
       WORK(*)

       SUBROUTINE SGERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
             LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER*1 TRANSA
       INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
       INTEGER*8 IPIVOT(*), WORK2(*)
       REAL   A(LDA,*),  AF(LDAF,*),  B(LDB,*),  X(LDX,*),  FERR(*),  BERR(*),
       WORK(*)




   F95 INTERFACE
       SUBROUTINE GERFS(TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT,
              B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER(LEN=1) :: TRANSA
       INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
       INTEGER, DIMENSION(:) :: IPIVOT, WORK2
       REAL, DIMENSION(:) :: FERR, BERR, WORK
       REAL, DIMENSION(:,:) :: A, AF, B, X

       SUBROUTINE GERFS_64(TRANSA, N, NRHS, A, LDA, AF, LDAF,
              IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER(LEN=1) :: TRANSA
       INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
       INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
       REAL, DIMENSION(:) :: FERR, BERR, WORK
       REAL, DIMENSION(:,:) :: A, AF, B, X




   C INTERFACE
       #include <sunperf.h>

       void sgerfs(char transa, int n, int nrhs, float *a, int lda, float *af,
                 int  ldaf, int *ipivot, float *b, int ldb, float *x, int ldx,
                 float *ferr, float *berr, int *info);

       void sgerfs_64(char transa, long n, long  nrhs,  float  *a,  long  lda,
                 float *af, long ldaf, long *ipivot, float *b, long ldb, float
                 *x, long ldx, float *ferr, float *berr, long *info);



PURPOSE
       sgerfs improves the computed solution to a system of  linear  equations
       and  provides  error  bounds and backward error estimates for the solu-
       tion.


ARGUMENTS
       TRANSA (input)
                 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) The order of the matrix A.  N >= 0.


       NRHS (input)
                 The number of right hand sides, i.e., the number  of  columns
                 of the matrices B and X.  NRHS >= 0.


       A (input) The original N-by-N matrix A.


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


       AF (input)
                 The  factors L and U from the factorization A = P*L*U as com-
                 puted by SGETRF.


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


       IPIVOT (input)
                 The pivot indices from SGETRF; for  1<=i<=N,  row  i  of  the
                 matrix was interchanged with row IPIVOT(i).


       B (input) The right hand side matrix B.


       LDB (input)
                 The leading dimension of the array B.  LDB >= max(1,N).


       X (input/output)
                 On  entry,  the solution matrix X, as computed by SGETRS.  On
                 exit, the improved solution matrix X.


       LDX (input)
                 The leading dimension of the array X.  LDX >= max(1,N).


       FERR (output)
                 The estimated forward error bound for  each  solution  vector
                 X(j) (the j-th column of the solution matrix X).  If XTRUE is
                 the true solution corresponding to X(j), FERR(j) is an  esti-
                 mated upper bound for the magnitude of the largest element in
                 (X(j) - XTRUE) divided by the magnitude of the  largest  ele-
                 ment  in  X(j).   The estimate is as reliable as the estimate
                 for RCOND, and is almost always a slight overestimate of  the
                 true error.


       BERR (output)
                 The  componentwise  relative  backward error of each solution
                 vector X(j) (i.e., the smallest relative change in  any  ele-
                 ment of A or B that makes X(j) an exact solution).


       WORK (workspace)
                 dimension(3*N)

       WORK2 (workspace)
                 dimension(N)


       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value




                                  7 Nov 2015                        sgerfs(3P)