SRC/zhesv_aa_2stage.f(3) Library Functions Manual SRC/zhesv_aa_2stage.f(3)

SRC/zhesv_aa_2stage.f


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

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.

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