CPPRFS(3)                  MathKeisan LAPACK routine                 CPPRFS(3)



NAME
       CPPRFS - the computed solution to a system of linear equations when the
       coefficient matrix is Hermitian positive definite and packed, and  pro-
       vides error bounds and backward error estimates for the solution

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

           CHARACTER      UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

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

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

PURPOSE
       CPPRFS  improves  the computed solution to a system of linear equations
       when the coefficient matrix is Hermitian positive definite and  packed,
       and  provides  error  bounds and backward error estimates for the solu-
       tion.


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 array, dimension (N*(N+1)/2)
               The  upper  or lower triangle of the Hermitian 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)*(2n-j)/2)  =
               A(i,j) for j<=i<=n.

       AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
               The  triangular factor U or L from the Cholesky factorization A
               = U**H*U or A = L*L**H, as computed  by  SPPTRF/CPPTRF,  packed
               columnwise  in a linear array in the same format as A (see AP).

       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  CPPTRS.   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 3.1)    November 2006                       CPPRFS(3)