.TH  DSPRFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " 
.SH NAME
DSPRFS - 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
.SH SYNOPSIS
.TP 19
SUBROUTINE DSPRFS(
UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX,
FERR, BERR, WORK, IWORK, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, LDB, LDX, N, NRHS
.TP 19
.ti +4
INTEGER
IPIV( * ), IWORK( * )
.TP 19
.ti +4
DOUBLE
PRECISION AFP( * ), AP( * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
.SH PURPOSE
DSPRFS 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.

.SH ARGUMENTS
.TP 8
UPLO    (input) CHARACTER*1
= \(aqU\(aq:  Upper triangle of A is stored;
.br
= \(aqL\(aq:  Lower triangle of A is stored.
.TP 8
N       (input) INTEGER
The order of the matrix A.  N >= 0.
.TP 8
NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X.  NRHS >= 0.
.TP 8
AP      (input) DOUBLE PRECISION 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
.TP 8
AFP     (input) DOUBLE PRECISION 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 DSPTRF, stored as a packed
triangular matrix.
.TP 8
IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSPTRF.
.TP 8
B       (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
The right hand side matrix B.
.TP 8
LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).
.TP 8
X       (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DSPTRS.
On exit, the improved solution matrix X.
.TP 8
LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
.TP 8
FERR    (output) DOUBLE PRECISION 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.
.TP 8
BERR    (output) DOUBLE PRECISION 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).
.TP 8
WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
.TP 8
IWORK   (workspace) INTEGER array, dimension (N)
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
.SH PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.
