# CentOS 7.0 - man page for dsprfs (centos section 3)

dsprfs.f(3) LAPACK dsprfs.f(3)dsprfs.fNAME-Functions/Subroutines subroutine dsprfs (UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO) DSPRFSSYNOPSISFunction/Subroutine Documentation subroutine dsprfs (characterUPLO, integerN, integerNRHS, double precision, dimension( * )AP, double precision, dimension( * )AFP, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO) DSPRFS 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. Parameters: UPLO UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N N is INTEGER The order of the matrix A. N >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0. AP AP is 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 = '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 AFP is 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. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSPTRF. B B is DOUBLE PRECISION array, dimension (LDB,NRHS) The right hand side matrix B. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). X X is DOUBLE PRECISION array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by DSPTRS. On exit, the improved solution matrix X. LDX LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N). FERR FERR is 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. BERR BERR is 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). WORK WORK is DOUBLE PRECISION array, dimension (3*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value Internal Parameters: ITMAX is the maximum number of steps of iterative refinement. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 179 of file dsprfs.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 dsprfs.f(3)