# man pzhegs2 (Fonctions bibliothèques) - reduce a complex Hermitian-definite generalized eigenproblem to standard form

## NAME

PZHEGS2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form

## SYNOPSIS

- SUBROUTINE PZHEGS2(
- IBTYPE, UPLO, N, A, IA, JA, DESCA, B, IB, JB, DESCB, INFO )
- CHARACTER UPLO
- INTEGER IA, IB, IBTYPE, INFO, JA, JB, N
- INTEGER DESCA( * ), DESCB( * )
- COMPLEX*16 A( * ), B( * )

## PURPOSE

PZHEGS2 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.
- 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.