CPPRFS(3)      LAPACK routine of NEC Numeric Library Collection      CPPRFS(3)



NAME
       CPPRFS

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



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 solution.




ARGUMENTS
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

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

           AP        (input)
                     AP is 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)
                     AFP is 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)
                     B is COMPLEX array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB       (input)
                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           X         (input/output)
                     X is COMPLEX array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by CPPTRS.
                     On exit, the improved solution matrix X.

           LDX       (input)
                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           FERR      (output)
                     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      (output)
                     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      (output)
                     WORK is COMPLEX array, dimension (2*N)

           RWORK     (output)
                     RWORK is REAL array, dimension (N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                      CPPRFS(3)