Provided by: scalapack-doc_1.5-10_all 
NAME
PZTRCON - estimate the reciprocal of the condition number of a triangular distributed
matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm
SYNOPSIS
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( * )
PURPOSE
PZTRCON estimates the reciprocal of the condition number of a triangular distributed
matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm.
The norm of A(IA:IA+N-1,JA:JA+N-1) is computed and an estimate is obtained for
norm(inv(A(IA:IA+N-1,JA:JA+N-1))), then the reciprocal of the condition number is computed
as
RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
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
NORM (global input) CHARACTER
Specifies whether the 1-norm condition number or the infinity-norm condition
number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
UPLO (global input) CHARACTER
= 'U': A(IA:IA+N-1,JA:JA+N-1) is upper triangular;
= 'L': A(IA:IA+N-1,JA:JA+N-1) is lower triangular.
DIAG (global input) CHARACTER
= 'N': A(IA:IA+N-1,JA:JA+N-1) is non-unit triangular;
= 'U': A(IA:IA+N-1,JA:JA+N-1) is unit triangular.
N (global input) INTEGER
The order of the distributed matrix A(IA:IA+N-1,JA:JA+N-1). N >= 0.
A (local input) COMPLEX*16 pointer into the local memory
to an array of dimension ( LLD_A, LOCc(JA+N-1) ). This array contains the local
pieces of the triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1). If UPLO = 'U',
the leading N-by-N 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 N-by-N 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+N-1,JA:JA+N-1) 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+N-1,JA:JA+N-1), computed as
RCOND = 1 / ( norm( A(IA:IA+N-1,JA:JA+N-1) ) *
norm( inv(A(IA:IA+N-1,JA:JA+N-1)) ) ).
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(IA-1,MB_A)) + MAX( 2, MAX(NB_A*CEIL(P-1,Q),LOCc(N+MOD(JA-1,NB_A))
+ NB_A*CEIL(Q-1,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(JA-1,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 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.