- 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, * )
PURPOSEZHPRFS 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.
- 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
PARAMETERSITMAX is the maximum number of steps of iterative refinement.