dtbrfs man page on YellowDog

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DTBRFS(l)			       )			     DTBRFS(l)

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, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
			  LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

	   INTEGER	  INFO, KD, LDAB, LDB, LDX, N, NRHS

	   INTEGER	  IWORK( * )

	   DOUBLE	  PRECISION AB( LDAB, * ), B( LDB, *  ),  BERR(	 *  ),
			  FERR( * ), WORK( * ), X( LDX, * )

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) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       TRANS   (input) CHARACTER*1
	       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)

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

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

       KD      (input) INTEGER
	       The  number of superdiagonals or subdiagonals of the triangular
	       band matrix A.  KD >= 0.

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

       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
	       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 AB as follows: if UPLO = 'U',
	       AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO  =  'L',
	       AB(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.

       LDAB    (input) INTEGER
	       The leading dimension of the array AB.  LDAB >= KD+1.

       B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
	       The right hand side matrix B.

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

       X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
	       The solution matrix X.

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

       FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
	       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) DOUBLE PRECISION array, dimension (NRHS)
	       The componentwise relative backward error of each solution vec‐
	       tor X(j) (i.e., the smallest relative change in any element  of
	       A or B that makes X(j) an exact solution).

       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)

       IWORK   (workspace) INTEGER array, dimension (N)

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

LAPACK version 3.0		 15 June 2000			     DTBRFS(l)
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