SRC/chesv_aa_2stage.f(3)   Library Functions Manual   SRC/chesv_aa_2stage.f(3)

NAME
       SRC/chesv_aa_2stage.f

SYNOPSIS
   Functions/Subroutines
       subroutine chesv_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv,
           ipiv2, b, ldb, work, lwork, info)
            CHESV_AA_2STAGE computes the solution to system of linear
           equations A * X = B for HE matrices

Function/Subroutine Documentation
   subroutine chesv_aa_2stage (character uplo, integer n, integer nrhs,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( * )
       tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
       ipiv2, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
       * ) work, integer lwork, integer info)
        CHESV_AA_2STAGE computes the solution to system of linear equations A
       * X = B for HE matrices

       Purpose:


            CHESV_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 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 array, dimension (LTB)
                     On exit, details of the LU factorization of the band matrix.

           LTB

                     LTB is INTEGER
                     The size of the array TB. LTB >= 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 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 workspace of size LWORK

           LWORK

                     LWORK is INTEGER
                     The size of WORK. LWORK >= 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 183 of file chesv_aa_2stage.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0        SRC/chesv_aa_2stage.f(3)