• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

zgbrfs - improve 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

SYNOPSIS

  SUBROUTINE ZGBRFS( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF, LDAF, 
 *      IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

  SUBROUTINE ZGBRFS_64( TRANSA, N, NSUB, NSUPER, NRHS, A, LDA, AF, 
 *      LDAF, IPIVOT, B, LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 TRANSA
  DOUBLE COMPLEX A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER*8 IPIVOT(*)
  DOUBLE PRECISION FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE GBRFS( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA], AF, 
 *       [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
  INTEGER :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2

  SUBROUTINE GBRFS_64( [TRANSA], [N], NSUB, NSUPER, [NRHS], A, [LDA], 
 *       AF, [LDAF], IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: TRANSA
  COMPLEX(8), DIMENSION(:) :: WORK
  COMPLEX(8), DIMENSION(:,:) :: A, AF, B, X
  INTEGER(8) :: N, NSUB, NSUPER, NRHS, LDA, LDAF, LDB, LDX, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL(8), DIMENSION(:) :: FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void zgbrfs(char transa, int n, int nsub, int nsuper, int nrhs, doublecomplex *a, int lda, doublecomplex *af, int ldaf, int *ipivot, doublecomplex *b, int ldb, doublecomplex *x, int ldx, double *ferr, double *berr, int *info);

void zgbrfs_64(char transa, long n, long nsub, long nsuper, long nrhs, doublecomplex *a, long lda, doublecomplex *af, long ldaf, long *ipivot, doublecomplex *b, long ldb, doublecomplex *x, long ldx, double *ferr, double *berr, long *info);

PURPOSE

zgbrfs 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)

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

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

• NSUPER (input)
  The number of superdiagonals within the band of A. NSUPER > = 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 NSUB+NSUPER+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 > = NSUB+NSUPER+1.

• AF (input)
  Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and the multipliers used during the factorization are stored in rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1.

• LDAF (input)
  The leading dimension of the array AF. LDAF > = 2*NSUB*NSUPER+1.

• IPIVOT (input)
  The pivot indices from CGBTRF; 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 CGBTRS. 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 estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element 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 element of A or B that makes X(j) an exact solution).

• WORK (workspace)
  dimension(2*N)

• WORK2 (workspace)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value