Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

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.

 LAPACK routine (version 3.2)               April 2011                            SPPRFS(3lapack)