Go to main content
Oracle Developer Studio 12.5 Man Pages

Exit Print View

Updated: June 2017
 
 

sgbrfs (3p)

Name

sgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution

Synopsis

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

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

SUBROUTINE SGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

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

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

SUBROUTINE GBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA,
AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
WORK2, INFO)

CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, KL, KU, 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 sgbrfs(char transa, int n, int kl, int ku, 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  sgbrfs_64(char transa, long n, long kl, long ku, 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                           sgbrfs(3P)



NAME
       sgbrfs  - improve the computed solution to a system of linear equations
       when the coefficient matrix is banded, and  provide  error  bounds  and
       backward error estimates for the solution


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

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

       SUBROUTINE SGBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA, AF, LDAF,
             IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

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

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

       SUBROUTINE GBRFS_64(TRANSA, N, KL, KU, NRHS, A, LDA,
              AF, LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK,
              WORK2, INFO)

       CHARACTER(LEN=1) :: TRANSA
       INTEGER(8) :: N, KL, KU, 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 sgbrfs(char transa, int n, int kl, int ku, 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  sgbrfs_64(char transa, long n, long kl, long ku, 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
       sgbrfs improves the computed solution to a system of  linear  equations
       when  the  coefficient  matrix is banded, and provides error bounds and
       backward error estimates for the solution.


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.


       KL (input)
                 The number of subdiagonals within the band of A.  KL >= 0.


       KU (input)
                 The number of superdiagonals within the band of A.  KU >=  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 band matrix A, stored in rows 1 to KL+KU+1.  The
                 j-th  column of A is stored in the j-th column of the array A
                 as   follows:   A(ku+1+i-j,j)   =   A(i,j)    for    max(1,j-
                 ku)<=i<=min(n,j+kl).


       LDA (input)
                 The leading dimension of the array A.  LDA >= KL+KU+1.


       AF (input)
                 Details of the LU factorization of the band matrix A, as com-
                 puted by SGBTRF.  U is stored as  an  upper  triangular  band
                 matrix  with  KL+KU  superdiagonals in rows 1 to KL+KU+1, and
                 the multipliers used during the factorization are  stored  in
                 rows KL+KU+2 to 2*KL+KU+1.


       LDAF (input)
                 The leading dimension of the array AF.  LDAF >= 2*KL*KU+1.


       IPIVOT (input)
                 The  pivot  indices  from  SGBTRF;  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  SGBTRS.   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                        sgbrfs(3P)