SRC/zhesv_aa_2stage.f(3) | Library Functions Manual | SRC/zhesv_aa_2stage.f(3) |
NAME
SRC/zhesv_aa_2stage.f
SYNOPSIS
Functions/Subroutines
subroutine zhesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb,
ipiv, ipiv2, b, ldb, work, lwork, info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X
= B for HE matrices
Function/Subroutine Documentation
subroutine zhesv_aa_2stage (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) work, integer lwork, integer info)
ZHESV_AA_2STAGE computes the solution to system of linear equations A * X = B for HE matrices
Purpose:
!> !> ZHESV_AA_2STAGE computes the solution to a complex system of !> linear equations !> A * X = B, !> where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS !> matrices. !> !> Aasen's 2-stage algorithm is used to factor A as !> A = U**H * T * U, if UPLO = 'U', or !> A = L * T * L**H, if UPLO = 'L', !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and T is Hermitian and band. The matrix T is !> then LU-factored with partial pivoting. The factored form of A !> is then used to solve the system of equations A * X = B. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS. !>
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 matrix B. NRHS >= 0. !>
A
!> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the hermitian matrix A. If UPLO = 'U', the leading !> N-by-N upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced. If UPLO = 'L', the !> leading N-by-N lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced. !> !> On exit, L is stored below (or above) the subdiagonal blocks, !> when UPLO is 'L' (or 'U'). !>
LDA
!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !>
TB
!> TB is COMPLEX*16 array, dimension (MAX(1,LTB)). !> On exit, details of the LU factorization of the band matrix. !>
LTB
!> LTB is INTEGER !> The size of the array TB. LTB >= MAX(1,4*N), internally !> used to select NB such that LTB >= (3*NB+1)*N. !> !> If LTB = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of LTB, !> returns this value as the first entry of TB, and !> no error message related to LTB is issued by XERBLA. !>
IPIV
!> IPIV is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of A were interchanged with the !> row and column IPIV(k). !>
IPIV2
!> IPIV2 is INTEGER array, dimension (N) !> On exit, it contains the details of the interchanges, i.e., !> the row and column k of T were interchanged with the !> row and column IPIV(k). !>
B
!> B is COMPLEX*16 array, dimension (LDB,NRHS) !> On entry, the right hand side matrix B. !> On exit, the solution matrix X. !>
LDB
!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
WORK
!> WORK is COMPLEX*16 workspace of size (MAX(1,LWORK)). !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
LWORK
!> LWORK is INTEGER !> The size of WORK. LWORK >= MAX(1,N), internally used to !> select NB such that LWORK >= N*NB. !> !> If LWORK = -1, then a workspace query is assumed; the !> routine only calculates the optimal size of the WORK array, !> returns this value as the first entry of the WORK array, and !> no error message related to LWORK is issued by XERBLA. !>
INFO
!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if INFO = i, band LU factorization failed on i-th column !>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 185 of file zhesv_aa_2stage.f.
Author
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