SSPRFS(3)                  MathKeisan LAPACK routine                 SSPRFS(3)



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

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

           CHARACTER      UPLO

           INTEGER        INFO, LDB, LDX, N, NRHS

           INTEGER        IPIV( * ), IWORK( * )

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

PURPOSE
       SSPRFS  improves  the computed solution to a system of linear equations
       when the coefficient matrix is symmetric  indefinite  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)*(2*n-j)/2) =
               A(i,j) for j<=i<=n.

       AFP     (input) REAL array, dimension (N*(N+1)/2)
               The factored form of the matrix  A.   AFP  contains  the  block
               diagonal matrix D and the multipliers used to obtain the factor
               U or L from the factorization A = U*D*U**T or A =  L*D*L**T  as
               computed by SSPTRF, stored as a packed triangular matrix.

       IPIV    (input) INTEGER array, dimension (N)
               Details  of  the  interchanges  and the block structure of D as
               determined by SSPTRF.

       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  SSPTRS.   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) 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 3.1)    November 2006                       SSPRFS(3)