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dgbrfs(3P)		    Sun Performance Library		    dgbrfs(3P)

NAME
       dgbrfs  - 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 DGBRFS(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(*)
       DOUBLE  PRECISION  A(LDA,*),  AF(LDAF,*),  B(LDB,*), X(LDX,*), FERR(*),
       BERR(*), WORK(*)

       SUBROUTINE DGBRFS_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(*)
       DOUBLE PRECISION 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(8), DIMENSION(:) :: FERR, BERR, WORK
       REAL(8), 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(8), DIMENSION(:) :: FERR, BERR, WORK
       REAL(8), DIMENSION(:,:) :: A, AF, B, X

   C INTERFACE
       #include <sunperf.h>

       void  dgbrfs(char  transa,  int n, int kl, int ku, int nrhs, double *a,
		 int lda, double *af, int ldaf, int *ipivot,  double  *b,  int
		 ldb,  double  *x,  int	 ldx,  double *ferr, double *berr, int
		 *info);

       void dgbrfs_64(char transa, long n, long kl, long ku, long nrhs, double
		 *a, long lda, double *af, long ldaf, long *ipivot, double *b,
		 long ldb, double *x, long ldx, double	*ferr,	double	*berr,
		 long *info);

PURPOSE
       dgbrfs  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)

		 TRANSA is defaulted to 'N' for F95 INTERFACE.

       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 DGBTRF.  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  DGBTRF;  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  DGBTRS.   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

				  6 Mar 2009			    dgbrfs(3P)
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