Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  the  factorization of a complex Hermitian matrix A using the Bunch-
       Kaufman diagonal pivoting method

SYNOPSIS

       SUBROUTINE ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )

           CHARACTER      UPLO

           INTEGER        INFO, LDA, LWORK, N

           INTEGER        IPIV( * )

           COMPLEX*16     A( LDA, * ), WORK( * )

PURPOSE

       ZHETRF computes the factorization of a complex Hermitian matrix A using the  Bunch-Kaufman
       diagonal pivoting method.  The form of the
        factorization is
           A = U*D*U**H  or  A = L*D*L**H
        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.
        This is the blocked version of the algorithm, calling Level 3 BLAS.

ARGUMENTS

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangle of A is stored;
                = 'L':  Lower triangle of A is stored.

        N       (input) INTEGER
                The order of the matrix A.  N >= 0.

        A       (input/output) 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, the block diagonal matrix D and the multipliers used
                to obtain the factor U or L (see below for further details).

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

        IPIV    (output) INTEGER array, dimension (N)
                Details of the interchanges and the block structure of D.
                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.

        WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The length of WORK.  LWORK >=1.  For best performance
                LWORK >= N*NB, where NB is the block size returned by ILAENV.

        INFO    (output) 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, and division by zero will occur if it
                is used to solve a system of equations.

FURTHER DETAILS

        If UPLO = 'U', then A = U*D*U**H, where
           U = P(n)*U(n)* ... *P(k)U(k)* ...,
        i.e., U is a product of terms P(k)*U(k), where k decreases from n to
        1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    v    0   )   k-s
           U(k) =  (   0    I    0   )   s
                   (   0    0    I   )   n-k
                      k-s   s   n-k
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
        If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
        and A(k,k), and v overwrites A(1:k-2,k-1:k).
        If UPLO = 'L', then A = L*D*L**H, where
           L = P(1)*L(1)* ... *P(k)*L(k)* ...,
        i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
        n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
        and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
        defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
        that if the diagonal block D(k) is of order s (s = 1 or 2), then
                   (   I    0     0   )  k-1
           L(k) =  (   0    I     0   )  s
                   (   0    v     I   )  n-k-s+1
                      k-1   s  n-k-s+1
        If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
        If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
        and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

 LAPACK routine (version 3.3.1)             April 2011                            ZHETRF(3lapack)