SUBROUTINE PCTRTI2( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )
*
* -- ScaLAPACK routine (version 1.5) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER IA, INFO, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
COMPLEX A( * )
* ..
*
* Purpose
* =======
*
* PCTRTI2 computes the inverse of a complex upper or lower triangular
* block matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). This matrix should be
* contained in one and only one process memory space (local operation).
*
* 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
* =========
*
* UPLO (global input) CHARACTER*1
* = 'U': sub( A ) is upper triangular;
* = 'L': sub( A ) is lower triangular.
*
* DIAG (global input) CHARACTER*1
* = 'N': sub( A ) is non-unit triangular
* = 'U': sub( A ) is unit triangular
*
* 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)),
* this array contains the local pieces of the triangular matrix
* sub( A ). If UPLO = 'U', the leading N-by-N upper triangular
* part of the matrix sub( A ) contains the upper triangular
* matrix, and the strictly lower triangular part of sub( A )
* is not referenced. If UPLO = 'L', the leading N-by-N lower
* triangular part of the matrix sub( A ) contains the lower
* triangular matrix, and the strictly upper triangular part
* of sub( A ) is not referenced. If DIAG = 'U', the diagonal
* elements of sub( A ) are also not referenced and are assumed
* to be 1. On exit, the (triangular) inverse of the original
* matrix, in the same storage format.
*
* 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.
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
COMPLEX ONE
PARAMETER ( ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER IACOL, IAROW, ICTXT, ICURR, IDIAG, IIA, IOFFA,
$ JJA, LDA, MYCOL, MYROW, NA, NPCOL, NPROW
COMPLEX AJJ
* ..
* .. External Subroutines ..
EXTERNAL BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, CSCAL,
$ CTRMV, INFOG2L, PXERBLA
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -(700+CTXT_)
ELSE
CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO )
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PCTRTI2', -INFO )
CALL BLACS_ABORT( ICTXT, 1 )
RETURN
END IF
*
* Compute local indexes
*
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
*
IF( MYROW.EQ.IAROW .AND. MYCOL.EQ.IACOL ) THEN
*
LDA = DESCA( LLD_ )
*
IF( UPPER ) THEN
*
IOFFA = IIA + ( JJA - 1 ) * LDA
ICURR = IOFFA + LDA
*
IF( NOUNIT ) THEN
*
* Compute inverse of upper non-unit triangular matrix.
*
A( IOFFA ) = ONE / A( IOFFA )
IDIAG = ICURR + 1
DO 10 NA = 1, N-1
A( IDIAG ) = ONE / A( IDIAG )
AJJ = -A( IDIAG )
*
* Compute elements 1:j-1 of j-th column.
*
CALL CTRMV( 'Upper', 'No transpose', DIAG, NA,
$ A( IOFFA ), LDA, A( ICURR ), 1 )
CALL CSCAL( NA, AJJ, A( ICURR ), 1 )
IDIAG = IDIAG + LDA + 1
ICURR = ICURR + LDA
10 CONTINUE
*
ELSE
*
* Compute inverse of upper unit triangular matrix.
*
DO 20 NA = 1, N-1
*
* Compute elements 1:j-1 of j-th column.
*
CALL CTRMV( 'Upper', 'No transpose', DIAG, NA,
$ A( IOFFA ), LDA, A( ICURR ), 1 )
CALL CSCAL( NA, -ONE, A( ICURR ), 1 )
ICURR = ICURR + LDA
20 CONTINUE
*
END IF
*
ELSE
*
ICURR = IIA + N - 1 + ( JJA + N - 2 ) * LDA
IOFFA = ICURR - LDA
*
IF( NOUNIT ) THEN
*
* Compute inverse of lower non-unit triangular matrix.
*
A( ICURR ) = ONE / A( ICURR )
IDIAG = IOFFA - 1
DO 30 NA = 1, N-1
A( IDIAG ) = ONE / A( IDIAG )
AJJ = -A( IDIAG )
*
* Compute elements j+1:n of j-th column.
*
CALL CTRMV( 'Lower', 'No transpose', DIAG, NA,
$ A( ICURR ), LDA, A( IOFFA ), 1 )
CALL CSCAL( NA, AJJ, A( IOFFA ), 1 )
ICURR = IDIAG
IDIAG = IDIAG - LDA - 1
IOFFA = IDIAG + 1
30 CONTINUE
*
ELSE
*
* Compute inverse of lower unit triangular matrix.
*
DO 40 NA = 1, N-1
*
* Compute elements j+1:n of j-th column.
*
CALL CTRMV( 'Lower', 'No transpose', DIAG, NA,
$ A( ICURR ), LDA, A( IOFFA ), 1 )
CALL CSCAL( NA, -ONE, A( IOFFA ), 1 )
ICURR = ICURR - LDA - 1
IOFFA = ICURR - LDA
40 CONTINUE
*
END IF
*
END IF
*
END IF
*
* End of PCTRTI2
*
END