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NAME

```       PCPOTF2  -  compute  the  Cholesky factorization of a complex hermitian
positive definite distributed matrix sub( A )=A(IA:IA+N-1,JA:JA+N-1)

```

SYNOPSIS

```       SUBROUTINE PCPOTF2( UPLO, N, A, IA, JA, DESCA, INFO )

CHARACTER       UPLO

INTEGER         IA, INFO, JA, N

INTEGER         DESCA( * )

COMPLEX         A( * )

```

PURPOSE

```       PCPOTF2 computes the Cholesky  factorization  of  a  complex  hermitian
positive definite distributed matrix sub( A )=A(IA:IA+N-1,JA:JA+N-1).

The factorization has the form

sub( A ) = U’ * U ,  if UPLO = ’U’, or

sub( A ) = L  * L’,  if UPLO = ’L’,

where U is an upper triangular matrix and L is lower triangular.

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

This routine requires  N  <=  NB_A-MOD(JA-1,  NB_A)  and  square  block
decomposition ( MB_A = NB_A ).

```

ARGUMENTS

```       UPLO    (global input) CHARACTER
= ’U’:  Upper triangle of sub( A ) is stored;
= ’L’:  Lower triangle of sub( A ) is stored.

N       (global input) INTEGER
The  number  of  rows  and  columns to be operated on, i.e. the
order of the distributed submatrix sub( A ). N >= 0.

A       (local input/local output) COMPLEX 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
symmetric distributed matrix sub( A ) to be factored.  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 distribu- ted matrix,
and its strictly upper triangular part is not  referenced.   On
exit,  if  UPLO  =  ’U’,  the  upper  triangular  part  of  the
distributed matrix contains the Cholesky factor U,  if  UPLO  =
’L’,  the  lower  triangular  part  of the distribu- ted matrix
contains the Cholesky factor L.

IA      (global input) INTEGER
The row index in the global array A indicating the first row of
sub( A ).

JA      (global input) INTEGER
The  column  index  in  the global array A indicating the first
column of sub( A ).

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

INFO    (local 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.   >  0:   If
INFO = K, the leading minor of order K,
A(IA:IA+K-1,JA:JA+K-1)   is  not  positive  definite,  and  the
factorization could not be completed.
```