NAME

       chesv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine chesv (UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO)
            CHESV computes the solution to system of linear equations A * X = B for HE matrices

Function/Subroutine Documentation

   subroutine chesv (characterUPLO, integerN, integerNRHS, complex, dimension( lda, * )A,
       integerLDA, integer, dimension( * )IPIV, complex, dimension( ldb, * )B, integerLDB,
       complex, dimension( * )WORK, integerLWORK, integerINFO)
        CHESV computes the solution to system of linear equations A * X = B for HE matrices

       Purpose:

            CHESV 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.

            The diagonal pivoting method is used to factor A as
               A = U * D * U**H,  if UPLO = 'U', or
               A = L * D * L**H,  if UPLO = 'L',
            where U (or L) is a product of permutation and unit upper (lower)
            triangular matrices, and D is Hermitian and block diagonal with
            1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
            used to solve the system of equations A * X = B.

       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 number of linear equations, i.e., 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, if INFO = 0, the block diagonal matrix D and the
                     multipliers used to obtain the factor U or L from the
                     factorization A = U*D*U**H or A = L*D*L**H as computed by
                     CHETRF.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D, as
                     determined by CHETRF.  If IPIV(k) > 0, then rows and columns
                     k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
                     diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
                     then rows and columns k-1 and -IPIV(k) were interchanged and
                     D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
                     IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
                     -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
                     diagonal block.

           B

                     B is COMPLEX array, dimension (LDB,NRHS)
                     On entry, the N-by-NRHS right hand side matrix B.
                     On exit, if INFO = 0, the N-by-NRHS solution matrix X.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           WORK

                     WORK is COMPLEX array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK.  LWORK >= 1, and for best performance
                     LWORK >= max(1,N*NB), where NB is the optimal blocksize for
                     CHETRF.
                     for LWORK < N, TRS will be done with Level BLAS 2
                     for LWORK >= N, TRS will be done with Level BLAS 3

                     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, D(i,i) is exactly zero.  The factorization
                          has been completed, but the block diagonal matrix D is
                          exactly singular, so the solution could not be computed.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 171 of file chesv.f.

Author

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