PZHEGST(l)

NAME
PZHEGST - reduce a complex Hermitian-definite generalized eigenproblem to standard form

SYNOPSIS

SUBROUTINE PZHEGST(
    IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, DESCB, SCALE, INFO )

CHARACTER
    UPLO

INTEGER
    IA, IB, IBTYPE, INFO, JA, JB, N

DOUBLE
    PRECISION SCALE

INTEGER
    DESCA( * ), DESCB( * )

COMPLEX*16
    A( * ), B( * )

PURPOSE
PZHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form.

In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ).

If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, and sub( A ) is overwritten by inv(U**H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L**H)

If IBTYPE = 2 or 3, the problem is sub( A )*sub( B )*x = lambda*x or sub( B )*sub( A )*x = lambda*x, and sub( A ) is overwritten by U*sub( A )*U**H or L**H*sub( A )*L.

sub( B ) must have been previously factorized as U**H*U or L*L**H by PZPOTRF.

Notes
=====

Each global data object is described by an associated description vector. This vector stores the information required to establish the mapping between an object element and its corresponding process and memory location.

Let A be a generic term for any 2D block cyclicly distributed array. Such a global array has an associated description vector DESCA. In the following comments, the character _ should be read as "of the global array".

NOTATION STORED IN EXPLANATION
--------------- -------------- -------------------------------------- DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
                        DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
                        the BLACS process grid A is distribu-
                        ted over. The context itself is glo-
                        bal, but the handle (the integer
                        value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
                        array A.
N_A (global) DESCA( N_ ) The number of columns in the global
                        array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
                        the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
                        the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
                        row of the array A is distributed. CSRC_A (global) DESCA( CSRC_ ) The process column over which the
                        first column of the array A is
                        distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
                        array. LLD_A >= MAX(1,LOCr(M_A)).

Let K be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process would receive if K were distributed over the p processes of its process column.
Similarly, LOCc( K ) denotes the number of elements of K that a process would receive if K were distributed over the q processes of its process row.
The values of LOCr() and LOCc() may be determined via a call to the ScaLAPACK tool function, NUMROC:
        LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
        LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). An upper bound for these quantities may be computed by:
        LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
        LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A

ARGUMENTS

IBTYPE   (global input) INTEGER
    = 1: compute inv(U**H)*sub( A )*inv(U) or inv(L)*sub( A )*inv(L**H); = 2 or 3: compute U*sub( A )*U**H or L**H*sub( A )*L.

UPLO    (global input) CHARACTER
    = 'U': Upper triangle of sub( A ) is stored and sub( B ) is factored as U**H*U; = 'L': Lower triangle of sub( A ) is stored and sub( B ) is factored as L*L**H.

N       (global input) INTEGER
    The order of the matrices sub( A ) and sub( B ). N >= 0.

A       (local input/local output) COMPLEX*16 pointer into the
    local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). On entry, this array contains the local pieces of the N-by-N Hermitian distributed matrix sub( A ). If UPLO = 'U', the leading N-by-N upper triangular part of sub( A ) contains the upper triangular part of the matrix, and its strictly lower triangular part is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of sub( A ) contains the lower triangular part of the matrix, and its strictly upper triangular part is not referenced.

    On exit, if INFO = 0, the transformed matrix, stored in the same format as sub( A ).

IA      (global input) INTEGER
    A's global row index, which points to the beginning of the submatrix which is to be operated on.

JA      (global input) INTEGER
    A's global column index, which points to the beginning of the submatrix which is to be operated on.

DESCA   (global and local input) INTEGER array of dimension DLEN_.
    The array descriptor for the distributed matrix A.

B       (local input) COMPLEX*16 pointer into the local memory
    to an array of dimension (LLD_B, LOCc(JB+N-1)). On entry, this array contains the local pieces of the triangular factor from the Cholesky factorization of sub( B ), as returned by PZPOTRF.

IB      (global input) INTEGER
    B's global row index, which points to the beginning of the submatrix which is to be operated on.

JB      (global input) INTEGER
    B's global column index, which points to the beginning of the submatrix which is to be operated on.

DESCB   (global and local input) INTEGER array of dimension DLEN_.
    The array descriptor for the distributed matrix B.

SCALE   (global output) DOUBLE PRECISION
    Amount by which the eigenvalues should be scaled to compensate for the scaling performed in this routine. At present, SCALE is always returned as 1.0, it is returned here to allow for future enhancement.

INFO    (global output) INTEGER
    = 0: successful exit
    < 0: If the i-th argument is an array and the j-entry had an illegal value, then INFO = -(i*100+j), if the i-th argument is a scalar and had an illegal value, then INFO = -i.