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DSPRFS(1) LAPACK routine (version 3.2) DSPRFS(1)

NAME

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

SYNOPSIS

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

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.

ARGUMENTS

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
The order of the matrix A. N >= 0.
The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
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.
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.
Details of the interchanges and the block structure of D as determined by DSPTRF.
The right hand side matrix B.
The leading dimension of the array B. LDB >= max(1,N).
On entry, the solution matrix X, as computed by DSPTRS. On exit, the improved solution matrix X.
The leading dimension of the array X. LDX >= max(1,N).
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.
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).
= 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.

November 2008 LAPACK routine (version 3.2)