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

ZGBRFS(l)					)					ZGBRFS(l)

NAME
       ZGBRFS  -  improve  the computed solution to a system of linear equations when the coeffi-
       cient matrix is banded, and provides error bounds and backward  error  estimates  for  the
       solution

SYNOPSIS
       SUBROUTINE ZGBRFS( TRANS,  N,  KL,  KU,	NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX,
			  FERR, BERR, WORK, RWORK, INFO )

	   CHARACTER	  TRANS

	   INTEGER	  INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * )

	   DOUBLE	  PRECISION BERR( * ), FERR( * ), RWORK( * )

	   COMPLEX*16	  AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( * ), X( LDX, * )

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
       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)

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

       KL      (input) INTEGER
	       The number of subdiagonals within the band of A.  KL >= 0.

       KU      (input) INTEGER
	       The number of superdiagonals within the band of A.  KU >= 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*16 array, dimension (LDAB,N)
	       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 AB as follows: AB(ku+1+i-j,j) = A(i,j) for
	       max(1,j-ku)<=i<=min(n,j+kl).

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

       AFB     (input) COMPLEX*16 array, dimension (LDAFB,N)
	       Details of the LU factorization of the band matrix A, as computed by ZGBTRF.  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.

       LDAFB   (input) INTEGER
	       The leading dimension of the array AFB.	LDAFB >= 2*KL*KU+1.

       IPIV    (input) INTEGER array, dimension (N)
	       The  pivot  indices from ZGBTRF; for 1<=i<=N, row i of the matrix was interchanged
	       with row IPIV(i).

       B       (input) COMPLEX*16 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/output) COMPLEX*16 array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by ZGBTRS.	 On  exit,  the  improved
	       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 esti-
	       mate is as reliable as the estimate for RCOND, and is almost always a slight over-
	       estimate of the true error.

       BERR    (output) DOUBLE PRECISION 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*16 array, dimension (2*N)

       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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

PARAMETERS
       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0			   15 June 2000 				ZGBRFS(l)


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