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

ZSPRFS(l)					)					ZSPRFS(l)

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

SYNOPSIS
       SUBROUTINE ZSPRFS( UPLO,  N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK,
			  INFO )

	   CHARACTER	  UPLO

	   INTEGER	  INFO, LDB, LDX, N, NRHS

	   INTEGER	  IPIV( * )

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

	   COMPLEX*16	  AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )

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.

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.

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

       AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
	       The upper or lower triangle of the symmetric matrix A, packed columnwise in a lin-
	       ear 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     (input) 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    (input) INTEGER array, dimension (N)
	       Details of the interchanges and the block structure of D as determined by ZSPTRF.

       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 ZSPTRS.  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 				ZSPRFS(l)


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