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SUBROUTINE PZTRTRI( UPLO, DIAG, N, A, IA, JA, DESCA, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* 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*16 A( * )
* ..
*
* Purpose
* =======
*
* PZTRTRI computes the inverse of a upper or lower triangular
* distributed matrix sub( A ) = 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
* =========
*
* UPLO (global input) CHARACTER
* Specifies whether the distributed matrix sub( A ) is upper
* or lower triangular:
* = 'U': Upper triangular,
* = 'L': Lower triangular.
*
* DIAG (global input) CHARACTER
* Specifies whether or not the distributed matrix sub( A )
* is unit triangular:
* = 'N': Non-unit triangular,
* = 'U': 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*16 pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* On entry, 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 to be inverted, 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.
* On exit, the (triangular) inverse of the original matrix.
*
* 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 (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, A(IA+K-1,JA+K-1) is exactly zero. The
* triangular matrix sub( A ) is singular and its
* inverse can not be computed.
*
* ====================================================================
*
* .. 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*16 ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER I, ICOFF, ICTXT, IROFF, ICURCOL, ICURROW,
$ IDUMMY, II, IOFFA, J, JB, JJ, JN, LDA, MYCOL,
$ MYROW, NN, NPCOL, NPROW
* ..
* .. Local Arrays ..
INTEGER IDUM1( 2 ), IDUM2( 2 )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, IGAMX2D, INFOG2L,
$ PCHK1MAT, PXERBLA, PZTRTI2, PZTRMM,
$ PZTRSM
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL
EXTERNAL ICEIL, LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC ICHAR, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test input parameters
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -(700+CTXT_)
ELSE
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
*
CALL CHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, INFO )
IF( INFO.EQ.0 ) THEN
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
ELSE IF( IROFF.NE.ICOFF .OR. IROFF.NE.0 ) THEN
INFO = -6
ELSE IF( DESCA( MB_ ).NE.DESCA( NB_ ) ) THEN
INFO = -(700+NB_)
END IF
END IF
*
IF( UPPER ) THEN
IDUM1( 1 ) = ICHAR( 'U' )
ELSE
IDUM1( 1 ) = ICHAR( 'L' )
END IF
IDUM2( 1 ) = 1
IF( NOUNIT ) THEN
IDUM1( 2 ) = ICHAR( 'N' )
ELSE
IDUM1( 2 ) = ICHAR( 'U' )
END IF
IDUM2( 2 ) = 2
*
CALL PCHK1MAT( N, 3, N, 3, IA, JA, DESCA, 7, 2, IDUM1, IDUM2,
$ INFO )
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PZTRTRI', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check for singularity if non-unit.
*
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
IF( NOUNIT ) THEN
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL,
$ II, JJ, ICURROW, ICURCOL )
*
* Handle first block separately
*
JB = JN-JA+1
LDA = DESCA( LLD_ )
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
IOFFA = II+(JJ-1)*LDA
DO 10 I = 0, JB-1
IF( A( IOFFA ).EQ.ZERO .AND. INFO.EQ.0 )
$ INFO = I + 1
IOFFA = IOFFA + LDA + 1
10 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ II = II + JB
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over remaining blocks of columns
*
DO 30 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
IF( MYROW.EQ.ICURROW .AND. MYCOL.EQ.ICURCOL ) THEN
IOFFA = II+(JJ-1)*LDA
DO 20 I = 0, JB-1
IF( A( IOFFA ).EQ.ZERO .AND. INFO.EQ.0 )
$ INFO = J + I - JA + 1
IOFFA = IOFFA + LDA + 1
20 CONTINUE
END IF
IF( MYROW.EQ.ICURROW )
$ II = II + JB
IF( MYCOL.EQ.ICURCOL )
$ JJ = JJ + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
30 CONTINUE
CALL IGAMX2D( ICTXT, 'All', ' ', 1, 1, INFO, 1, IDUMMY,
$ IDUMMY, -1, -1, MYCOL )
IF( INFO.NE.0 )
$ RETURN
END IF
*
* Use blocked code
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix
*
JB = JN-JA+1
*
* Handle first block of column separately
*
CALL PZTRTI2( UPLO, DIAG, JB, A, IA, JA, DESCA, INFO )
*
* Loop over remaining block of columns
*
DO 40 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( DESCA( NB_ ), JA+N-J )
I = IA + J - JA
*
* Compute rows 1:j-1 of current block column
*
CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG, J-JA, JB,
$ ONE, A, IA, JA, DESCA, A, IA, J, DESCA )
CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG, J-JA,
$ JB, -ONE, A, I, J, DESCA, A, IA, J, DESCA )
*
* Compute inverse of current diagonal block
*
CALL PZTRTI2( UPLO, DIAG, JB, A, I, J, DESCA, INFO )
*
40 CONTINUE
*
ELSE
*
* Compute inverse of lower triangular matrix
*
NN = ( ( JA+N-2 ) / DESCA( NB_ ) )*DESCA( NB_ ) + 1
DO 50 J = NN, JN+1, -DESCA( NB_ )
JB = MIN( DESCA( NB_ ), JA+N-J )
I = IA + J - JA
IF( J+JB.LE.JA+N-1 ) THEN
*
* Compute rows j+jb:ja+n-1 of current block column
*
CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG,
$ JA+N-J-JB, JB, ONE, A, I+JB, J+JB, DESCA,
$ A, I+JB, J, DESCA )
CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG,
$ JA+N-J-JB, JB, -ONE, A, I, J, DESCA,
$ A, I+JB, J, DESCA )
END IF
*
* Compute inverse of current diagonal block
*
CALL PZTRTI2( UPLO, DIAG, JB, A, I, J, DESCA, INFO )
*
50 CONTINUE
*
* Handle the last block of columns separately
*
JB = JN-JA+1
IF( JA+JB.LE.JA+N-1 ) THEN
*
* Compute rows ja+jb:ja+n-1 of current block column
*
CALL PZTRMM( 'Left', UPLO, 'No transpose', DIAG, N-JB, JB,
$ ONE, A, IA+JB, JA+JB, DESCA, A, IA+JB, JA,
$ DESCA )
CALL PZTRSM( 'Right', UPLO, 'No transpose', DIAG, N-JB, JB,
$ -ONE, A, IA, JA, DESCA, A, IA+JB, JA, DESCA )
END IF
*
* Compute inverse of current diagonal block
*
CALL PZTRTI2( UPLO, DIAG, JB, A, IA, JA, DESCA, INFO )
*
END IF
*
RETURN
*
* End PZTRTRI
*
END
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