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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LAPACK                          Version 3.12.0        SRC/zhesv_aa_2stage.f(3)