PZHEGST  reduce a complex Hermitiandefinite generalized eigenproblem to
standard form
 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( * )
PZHEGST reduces a complex Hermitiandefinite generalized eigenproblem to
standard form. In the following sub( A ) denotes A( IA:IA+N1, JA:JA+N1 ) and
sub( B ) denotes B( IB:IB+N1, JB:JB+N1 ).
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
 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+N1)). On entry,
this array contains the local pieces of the NbyN Hermitian distributed
matrix sub( A ). If UPLO = 'U', the leading NbyN 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 NbyN 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+N1)). 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 ith argument is an array and the jentry had an illegal
value, then INFO = (i*100+j), if the ith argument is a scalar and had an
illegal value, then INFO = i.