Provided by: scalapack-doc_1.5-10_all 
NAME
PCTRCON - 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 PCTRCON( 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
REAL RCOND
INTEGER DESCA( * )
REAL RWORK( * )
COMPLEX A( * ), WORK( * )
PURPOSE
PCTRCON 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 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) REAL
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 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) REAL 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.