spbrfs(l) [redhat man page]

SPBRFS(l)								 )								 SPBRFS(l)

NAME

       SPBRFS  -  improve  the	computed  solution  to a system of linear equations when the coefficient matrix is symmetric positive definite and
       banded, and provides error bounds and backward error estimates for the solution

SYNOPSIS

       SUBROUTINE SPBRFS( UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )

	   CHARACTER	  UPLO

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

	   INTEGER	  IWORK( * )

	   REAL 	  AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE

       SPBRFS improves the computed solution to a system of linear equations when the  coefficient  matrix  is	symmetric  positive  definite  and
       banded, and provides error bounds and backward error estimates for the solution.

ARGUMENTS

       UPLO    (input) CHARACTER*1
	       = 'U':  Upper triangle of A is stored;
	       = 'L':  Lower triangle of A is stored.

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

       KD      (input) INTEGER
	       The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'.  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) REAL array, dimension (LDAB,N)
	       The  upper  or  lower triangle of the symmetric 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).

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

       AFB     (input) REAL array, dimension (LDAFB,N)
	       The  triangular	factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T of the band matrix A as computed by SPBTRF,
	       in the same storage format as A (see AB).

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

       B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
	       On entry, the solution matrix X, as computed by SPBTRS.	On exit, the improved 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 estimate is as reliable as the estimate  for  RCOND,  and	is  almost
	       always a slight overestimate 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 solution).

       WORK    (workspace) REAL 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

PARAMETERS

       ITMAX is the maximum number of steps of iterative refinement.

LAPACK version 3.0						   15 June 2000 							 SPBRFS(l)

spbrfs.f(3)							      LAPACK							       spbrfs.f(3)

NAME

       spbrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine spbrfs (UPLO, N, KD, NRHS, AB, LDAB, AFB, LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO)
	   SPBRFS

Function/Subroutine Documentation
   subroutine spbrfs (characterUPLO, integerN, integerKD, integerNRHS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB,
       integerLDAFB, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( *
       )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
       SPBRFS

       Purpose:

	    SPBRFS improves the computed solution to a system of linear
	    equations when the coefficient matrix is symmetric positive definite
	    and banded, and provides error bounds and backward error estimates
	    for the solution.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.

	   N

		     N is INTEGER
		     The order of the matrix A.  N >= 0.

	   KD

		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

	   NRHS

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

	   AB

		     AB is REAL array, dimension (LDAB,N)
		     The upper or lower triangle of the symmetric 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).

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   AFB

		     AFB is REAL array, dimension (LDAFB,N)
		     The triangular factor U or L from the Cholesky factorization
		     A = U**T*U or A = L*L**T of the band matrix A as computed by
		     SPBTRF, in the same storage format as A (see AB).

	   LDAFB

		     LDAFB is INTEGER
		     The leading dimension of the array AFB.  LDAFB >= KD+1.

	   B

		     B is REAL array, dimension (LDB,NRHS)
		     The right hand side matrix B.

	   LDB

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

	   X

		     X is REAL array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by SPBTRS.
		     On exit, the improved solution matrix X.

	   LDX

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

	   FERR

		     FERR is 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 estimate is as reliable as
		     the estimate for RCOND, and is almost always a slight
		     overestimate of the true error.

	   BERR

		     BERR is 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 solution).

	   WORK

		     WORK is REAL array, dimension (3*N)

	   IWORK

		     IWORK is INTEGER array, dimension (N)

	   INFO

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

       Internal Parameters:

	     ITMAX is the maximum number of steps of iterative refinement.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 189 of file spbrfs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       spbrfs.f(3)