csprfs.f(3)							      LAPACK							       csprfs.f(3)

NAME

       csprfs.f -

SYNOPSIS

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

Function/Subroutine Documentation
   subroutine csprfs (characterUPLO, integerN, integerNRHS, complex, dimension( * )AP, complex, dimension( * )AFP, integer, dimension( * )IPIV,
       complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR,
       complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)
       CSPRFS

       Purpose:

	    CSPRFS 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 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 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 CSPTRF, 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 CSPTRF.

	   B

		     B is COMPLEX 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 array, dimension (LDX,NRHS)
		     On entry, the solution matrix X, as computed by CSPTRS.
		     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 COMPLEX array, dimension (2*N)

	   RWORK

		     RWORK is REAL 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 csprfs.f.

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

Version 3.4.1							  Sun May 26 2013						       csprfs.f(3)