PZTRCON  estimate the reciprocal of the condition number of a triangular
distributed matrix A(IA:IA+N1,JA:JA+N1), in either the 1norm or the
infinitynorm
 SUBROUTINE PZTRCON(
 NORM, UPLO, DIAG, N, A, IA, JA, DESCA, RCOND, WORK, LWORK, RWORK, LRWORK,
INFO )
CHARACTER DIAG, NORM, UPLO INTEGER IA, JA, INFO, LRWORK, LWORK, N DOUBLE
PRECISION RCOND INTEGER DESCA( * ) DOUBLE PRECISION RWORK( * ) COMPLEX*16 A( *
), WORK( * )
PZTRCON estimates the reciprocal of the condition number of a triangular
distributed matrix A(IA:IA+N1,JA:JA+N1), in either the 1norm or the
infinitynorm. The norm of A(IA:IA+N1,JA:JA+N1) is computed and an estimate
is obtained for norm(inv(A(IA:IA+N1,JA:JA+N1))), then the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm( A(IA:IA+N1,JA:JA+N1) ) *
norm( inv(A(IA:IA+N1,JA:JA+N1)) ) ).
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
 NORM (global input) CHARACTER
 Specifies whether the 1norm condition number or the infinitynorm
condition number is required:
= '1' or 'O': 1norm;
= 'I': Infinitynorm.
 UPLO (global input) CHARACTER

= 'U': A(IA:IA+N1,JA:JA+N1) is upper triangular;
= 'L': A(IA:IA+N1,JA:JA+N1) is lower triangular.
 DIAG (global input) CHARACTER

= 'N': A(IA:IA+N1,JA:JA+N1) is nonunit triangular;
= 'U': A(IA:IA+N1,JA:JA+N1) is unit triangular.
 N (global input) INTEGER

The order of the distributed matrix A(IA:IA+N1,JA:JA+N1). N >= 0.
 A (local input) COMPLEX*16 pointer into the local memory
 to an array of dimension ( LLD_A, LOCc(JA+N1) ). This array contains the
local pieces of the triangular distributed matrix A(IA:IA+N1,JA:JA+N1).
If UPLO = 'U', the leading NbyN upper triangular part of this
distributed matrix con tains the upper triangular matrix, and its
strictly lower triangular part is not referenced. If UPLO = 'L', the
leading NbyN lower triangular part of this ditributed matrix contains
the lower triangular matrix, and the strictly upper triangular part is not
referenced. If DIAG = 'U', the diagonal elements of A(IA:IA+N1,JA:JA+N1)
are also not referenced and are assumed to be 1.
 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.
 RCOND (global output) DOUBLE PRECISION
 The reciprocal of the condition number of the distributed matrix
A(IA:IA+N1,JA:JA+N1), computed as
RCOND = 1 / ( norm( A(IA:IA+N1,JA:JA+N1) ) *
norm( inv(A(IA:IA+N1,JA:JA+N1)) ) ).
 WORK (local workspace/local output) COMPLEX*16 array,
 dimension (LWORK) On exit, WORK(1) returns the minimal and optimal
LWORK.
 LWORK (local or global input) INTEGER
 The dimension of the array WORK. LWORK is local input and must be at least
LWORK >= 2*LOCr(N+MOD(IA1,MB_A)) + MAX( 2,
MAX(NB_A*CEIL(P1,Q),LOCc(N+MOD(JA1,NB_A)) + NB_A*CEIL(Q1,P)) ).
If LWORK = 1, then LWORK is global input and a workspace query is assumed;
the routine only calculates the minimum and optimal size for all work
arrays. Each of these values is returned in the first entry of the
corresponding work array, and no error message is issued by PXERBLA.
 RWORK (local workspace/local output) DOUBLE PRECISION array,
 dimension (LRWORK) On exit, RWORK(1) returns the minimal and optimal
LRWORK.
 LRWORK (local or global input) INTEGER
 The dimension of the array RWORK. LRWORK is local input and must be at
least LRWORK >= LOCc(N+MOD(JA1,NB_A)).
If LRWORK = 1, then LRWORK is global input and a workspace query is
assumed; the routine only calculates the minimum and optimal size for all
work arrays. Each of these values is returned in the first entry of the
corresponding work array, and no error message is issued by PXERBLA.
 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.