cporfs man page on Scientific

```CPORFS(1)		 LAPACK routine (version 3.2)		     CPORFS(1)

NAME
CPORFS - improves the computed solution to a system of linear equations
when the coefficient matrix is Hermitian positive definite,

SYNOPSIS
SUBROUTINE CPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF,  B,	LDB,  X,  LDX,
FERR, BERR, WORK, RWORK, INFO )

CHARACTER	  UPLO

INTEGER	  INFO, LDA, LDAF, LDB, LDX, N, NRHS

REAL		  BERR( * ), FERR( * ), RWORK( * )

COMPLEX	  A(  LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
X( LDX, * )

PURPOSE
CPORFS improves the computed solution to a system of  linear  equations
when  the  coefficient  matrix is Hermitian positive definite, and pro‐
vides 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.

A       (input) COMPLEX array, dimension (LDA,N)
The  Hermitian  matrix  A.   If	UPLO = 'U', the leading N-by-N
upper triangular part of A contains the upper  triangular  part
of the matrix A, and the strictly lower triangular part of A is
not referenced.	If UPLO = 'L', the leading N-by-N lower trian‐
gular  part  of	A  contains  the  lower triangular part of the
matrix A, and the strictly upper triangular part of  A  is  not
referenced.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

AF      (input) COMPLEX array, dimension (LDAF,N)
The  triangular factor U or L from the Cholesky factorization A
= U**H*U or A = L*L**H, as computed by CPOTRF.

LDAF    (input) INTEGER
The leading dimension of the array AF.  LDAF >= max(1,N).

B       (input) COMPLEX 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 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as  computed  by  CPOTRS.   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 vec‐
tor X(j) (i.e., the smallest relative change in any element  of
A or B that makes X(j) an exact solution).

WORK    (workspace) COMPLEX array, dimension (2*N)

RWORK   (workspace) REAL 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 routine (version 3.2)	 November 2008			     CPORFS(1)
```
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