CPPRFS - improve the computed solution to a system of lin­
       ear equations when the  coefficient  matrix  is  Hermitian
       positive  definite  and  packed, and provides 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  lin­
       ear  equations  when  the  coefficient matrix is Hermitian
       positive definite 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 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  com­
               puted  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.

               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 solu­
               tion vector X(j) (the j-th column of the  solution
               matrix  X).   If XTRUE is the true solution corre­
               sponding 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 reli­
               able 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 vector 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 ille­
               gal value


PARAMETERS

       ITMAX  is the maximum number of steps of iterative refine­
       ment.


Man(1) output converted with man2html