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dtbrfs(3P)		    Sun Performance Library		    dtbrfs(3P)

NAME
       dtbrfs  -  provide  error  bounds  and backward error estimates for the
       solution to a system of linear equations with a triangular band coeffi‐
       cient matrix

SYNOPSIS
       SUBROUTINE DTBRFS(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B, LDB,
	     X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER * 1 UPLO, TRANSA, DIAG
       INTEGER N, KD, NRHS, LDA, LDB, LDX, INFO
       INTEGER WORK2(*)
       DOUBLE	PRECISION  A(LDA,*),  B(LDB,*),	 X(LDX,*),  FERR(*),  BERR(*),
       WORK(*)

       SUBROUTINE DTBRFS_64(UPLO, TRANSA, DIAG, N, KD, NRHS, A, LDA, B,
	     LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)

       CHARACTER * 1 UPLO, TRANSA, DIAG
       INTEGER*8 N, KD, NRHS, LDA, LDB, LDX, INFO
       INTEGER*8 WORK2(*)
       DOUBLE  PRECISION  A(LDA,*),  B(LDB,*),	X(LDX,*),  FERR(*),   BERR(*),
       WORK(*)

   F95 INTERFACE
       SUBROUTINE TBRFS(UPLO, [TRANSA], DIAG, N, KD, NRHS, A, [LDA], B,
	      [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])

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

       SUBROUTINE TBRFS_64(UPLO, [TRANSA], DIAG, N, KD, NRHS, A, [LDA],
	      B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])

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

   C INTERFACE
       #include <sunperf.h>

       void dtbrfs(char uplo, char transa, char diag, int n, int kd, int nrhs,
		 double *a, int lda, double *b, int ldb, double *x,  int  ldx,
		 double *ferr, double *berr, int *info);

       void dtbrfs_64(char uplo, char transa, char diag, long n, long kd, long
		 nrhs, double *a, long lda, double *b, long  ldb,  double  *x,
		 long ldx, double *ferr, double *berr, long *info);

PURPOSE
       dtbrfs provides error bounds and backward error estimates for the solu‐
       tion to a system of linear equations with a triangular band coefficient
       matrix.

       The  solution  matrix  X must be computed by DTBTRS or some other means
       before entering this routine.  DTBRFS does not do iterative  refinement
       because doing so cannot improve the backward error.

ARGUMENTS
       UPLO (input)
		 = 'U':	 A is upper triangular;
		 = 'L':	 A is lower triangular.

       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.

       DIAG (input)
		 = 'N':	 A is non-unit triangular;
		 = 'U':	 A is unit triangular.

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

       KD (input)
		 The  number of superdiagonals or subdiagonals of the triangu‐
		 lar band matrix A.  KD >= 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  upper  or	 lower triangular band matrix A, stored in the
		 first kd+1 rows of the array. The j-th column of A is	stored
		 in  the j-th column of the array A as follows: if UPLO = 'U',
		 A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO =  'L',
		 A(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).	If DIAG = 'U',
		 the diagonal elements of A are not referenced and are assumed
		 to be 1.

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

       B (input) The right hand side matrix B.

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

       X (input) The 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			    dtbrfs(3P)
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