NAME
PDGETRI - compute the inverse of a distributed matrix using the LU
factorization computed by PDGETRF
SYNOPSIS
SUBROUTINE PDGETRI( N, A, IA, JA, DESCA, IPIV, WORK, LWORK, IWORK,
LIWORK, INFO )
INTEGER IA, INFO, JA, LIWORK, LWORK, N
INTEGER DESCA( * ), IPIV( * ), IWORK( * )
DOUBLE PRECISION A( * ), WORK( * )
PURPOSE
PDGETRI computes the inverse of a distributed matrix using the LU
factorization computed by PDGETRF. This method inverts U and then
computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA
by solving the system InvA*L = inv(U) for InvA.
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
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) DOUBLE PRECISION pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). On
entry, the local pieces of the L and U obtained by the
factorization sub( A ) = P*L*U computed by PDGETRF. On exit, if
INFO = 0, sub( A ) contains the inverse of the original
distributed matrix sub( A ).
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.
IPIV (local input) INTEGER array, dimension LOCr(M_A)+MB_A
keeps track of the pivoting information. IPIV(i) is the global
row index the local row i was swapped with. This array is tied
to the distributed matrix A.
WORK (local workspace/local output) DOUBLE PRECISION 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 = LOCr(N+MOD(IA-1,MB_A))*NB_A. WORK is used
to keep a copy of at most an entire column block of sub( A ).
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.
IWORK (local workspace/local output) INTEGER array,
dimension (LIWORK) On exit, IWORK(1) returns the minimal and
optimal LIWORK.
LIWORK (local or global input) INTEGER
The dimension of the array IWORK used as workspace for
physically transposing the pivots. LIWORK is local input and
must be at least if NPROW == NPCOL then LIWORK = LOCc( N_A +
MOD(JA-1, NB_A) ) + NB_A, else LIWORK = LOCc( N_A + MOD(JA-1,
NB_A) ) + MAX( CEIL(CEIL(LOCr(M_A)/MB_A)/(LCM/NPROW)), NB_A )
where LCM is the least common multiple of process rows and
columns (NPROW and NPCOL). end if
If LIWORK = -1, then LIWORK 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. > 0: If
INFO = K, U(IA+K-1,IA+K-1) is exactly zero; the matrix is
singular and its inverse could not be computed.