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RedHat 9 (Linux i386) - man page for ctbrfs (redhat section l)

CTBRFS(l)					)					CTBRFS(l)

NAME
       CTBRFS - provide error bounds and backward error estimates for the solution to a system of
       linear equations with a triangular band coefficient matrix

SYNOPSIS
       SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX,  FERR,  BERR,
			  WORK, RWORK, INFO )

	   CHARACTER	  DIAG, TRANS, UPLO

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

	   REAL 	  BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX	  AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

PURPOSE
       CTBRFS  provides error bounds and backward error estimates for the solution to a system of
       linear equations with a triangular band coefficient matrix.  The solution matrix X must be
       computed  by  CTBTRS or some other means before entering this routine.  CTBRFS 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)

       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) COMPLEX 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 fol-
	       lows: 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 ele-
	       ments 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) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
	       The solution matrix X.

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

       FERR    (output) REAL 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 esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       BERR    (output) REAL array, dimension (NRHS)
	       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  solu-
	       tion).

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL 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 				CTBRFS(l)


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