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zsprfs.f(3)				      LAPACK				      zsprfs.f(3)

NAME
       zsprfs.f -

SYNOPSIS
   Functions/Subroutines
       subroutine zsprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
	   INFO)
	   ZSPRFS

Function/Subroutine Documentation
   subroutine zsprfs (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP,
       complex*16, dimension( * )AFP, integer, dimension( * )IPIV, complex*16, dimension( ldb, *
       )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension(
       * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double
       precision, dimension( * )RWORK, integerINFO)
       ZSPRFS

       Purpose:

	    ZSPRFS improves the computed solution to a system of linear
	    equations when the coefficient matrix is symmetric indefinite
	    and packed, 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.

	   NRHS

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

	   AP

		     AP is COMPLEX*16 array, dimension (N*(N+1)/2)
		     The upper or lower triangle of the symmetric matrix A, packed
		     columnwise in a linear array.  The j-th column of A is stored
		     in the array AP as follows:
		     if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
		     if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

	   AFP

		     AFP is COMPLEX*16 array, dimension (N*(N+1)/2)
		     The factored form of the matrix A.  AFP contains the block
		     diagonal matrix D and the multipliers used to obtain the
		     factor U or L from the factorization A = U*D*U**T or
		     A = L*D*L**T as computed by ZSPTRF, stored as a packed
		     triangular matrix.

	   IPIV

		     IPIV is INTEGER array, dimension (N)
		     Details of the interchanges and the block structure of D
		     as determined by ZSPTRF.

	   B

		     B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by ZSPTRS.
		     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 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

		     BERR is 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 solution).

	   WORK

		     WORK is COMPLEX*16 array, dimension (2*N)

	   RWORK

		     RWORK is DOUBLE PRECISION 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 180 of file zsprfs.f.

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

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