Visible to Intel only — GUID: GUID-82B40C5D-1ED1-408B-B7CE-7817844879E8
Visible to Intel only — GUID: GUID-82B40C5D-1ED1-408B-B7CE-7817844879E8
?hetrs2
Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix.
Syntax
call chetrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )
call zhetrs2( uplo, n, nrhs, a, lda, ipiv, b, ldb, work, info )
call hetrs2( a, b, ipiv [,uplo] [,info] )
Include Files
- mkl.fi, lapack.f90
Description
The routine solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization of A:
if uplo='U', |
A = U*D*UH |
if uplo='L', |
A = L*D*LH |
where
U and L are upper and lower triangular matrices with unit diagonal
- D is a Hermitian block-diagonal matrix.
The factorization is computed by ?hetrf.
Input Parameters
uplo |
CHARACTER*1. Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', the array a stores the upper triangular factor U of the factorization A = U*D*UH. If uplo = 'L', the array a stores the lower triangular factor L of the factorization A = L*D*LH. |
n |
INTEGER. The order of matrix A; n≥ 0. |
nrhs |
INTEGER. The number of right-hand sides; nrhs≥ 0. |
a, b |
COMPLEX for chetrs2 DOUBLE COMPLEX for zhetrs2 Arrays: a(lda,*), b(ldb,*). The array a contains the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ?hetrf. The array b contains the right-hand side matrix B. The second dimension of a must be at least max(1,n), and the second dimension of b at least max(1,nrhs). |
lda |
INTEGER. The leading dimension of a; lda≥ max(1, n). |
ldb |
INTEGER. The leading dimension of b; ldb≥ max(1, n). |
ipiv |
INTEGER. Array of size n. The ipiv array contains details of the interchanges and the block structure of D as determined by ?hetrf. |
work |
COMPLEX for chetrs2 DOUBLE COMPLEX for zhetrs2 Workspace array, size n. |
Output Parameters
b |
Overwritten by the solution matrix X. |
info |
INTEGER. If info = 0, the execution is successful. If info = -i, the i-th parameter had an illegal value. |
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine hetrs2 interface are as follows:
a |
Holds the matrix A of size (n, n). |
b |
Holds the matrix B of size (n, nrhs). |
ipiv |
Holds the vector of length n. |
uplo |
Must be 'U' or 'L'. The default value is 'U'. |