spprfs(3F)

NAME
     SPPRFS - improve the computed solution to a system of linear equations
     when the coefficient matrix is symmetric positive definite and packed,
     and provides error bounds and backward error estimates for the solution

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

         CHARACTER      UPLO

         INTEGER        INFO, LDB, LDX, N, NRHS

         INTEGER        IWORK( * )

         REAL           AFP( * ), AP( * ), B( LDB, * ), BERR( * ), FERR( * ),
                        WORK( * ), X( LDX, * )

PURPOSE
     SPPRFS improves the computed solution to a system of linear equations
     when the coefficient matrix is symmetric 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) REAL array, dimension (N*(N+1)/2)
             The upper or lower triangle of the symmetric 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) REAL array, dimension (N*(N+1)/2)
             The triangular factor U or L from the Cholesky factorization A =
             U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed
             columnwise in a linear array in the same format as A (see AP).

     B       (input) REAL 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) REAL array, dimension (LDX,NRHS)
             On entry, the solution matrix X, as computed by SPPTRS.  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 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) REAL array, dimension (3*N)

     IWORK   (workspace) INTEGER 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.