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## man page of LAPACK-3

### LAPACK-3: improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and

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## NAME

LAPACK-3 - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provides error bounds and backward error estimates for the solution## SYNOPSIS

SUBROUTINE ZHPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDB, LDX, N, NRHS INTEGER IPIV( * ) DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) COMPLEX*16 AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )PURPOSE

ZHPRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian 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) COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the Hermitian 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) COMPLEX*16 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**H or A = L*D*L**H as computed by ZHPTRF, 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 ZHPTRF. B (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZHPTRS. On exit, the improved solution matrix X. LDX (input) INTEGER The leading dimension of the array X. LDX >= max(1,N). 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. 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). WORK (workspace) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION 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 3.2) March 2011 LAPACK-3(3)

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