spprfs(3)

NAME

SPPRFS - improve the computed solution to a system of lin

ear 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 lin

ear 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 ma

trix 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 SPP

TRF/CPPTRF, packed columnwise in a linear array in the same for

mat 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 solu

tion 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 ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

SPPRFS(3)