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*
*
SUBROUTINE PCLAGHE( N, K, D, A, IA, JA, DESCA, ISEED, ORDER, WORK,
$ LWORK, INFO )
*
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IA, INFO, JA, K, LWORK, N, ORDER
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), ISEED( 4 )
REAL D( * )
COMPLEX A( * ), WORK( * )
* ..
*
* 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
*
* Purpose
* =======
*
* PCLAGHE generates a real Hermitian matrix A, by pre- and post-
* multiplying a real diagonal matrix D with a random orthogonal matrix:
* A = U*D*U'.
*
* This is just a quick implementation which will be replaced in the
* future. The random orthogonal matrix is computed by creating a
* random matrix and running QR on it. This requires vastly more
* computation than necessary, but not significantly more communication
* than is used in the rest of this rouinte, and hence is not that much
* slower than an efficient solution.
*
* Arguments
* =========
*
* N (global input) INTEGER
* The size of the matrix A. N >= 0.
*
* K (global input) INTEGER
* The number of nonzero subdiagonals within the band of A.
* 0 <= K <= N-1.
* ### K must be 0 or N-1, 0 < K < N-1 is not supported yet.
*
* D (global input) COMPLEX array, dimension (N)
* The diagonal elements of the diagonal matrix D.
*
* A (local output) COMPLEX array
* Global dimension (N, N), local dimension (NP, NQ)
* The generated n by n Hermitian matrix A (the full matrix is
* stored).
*
* IA (global input) INTEGER
* A's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JA (global input) INTEGER
* A's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* ISEED (global input/output) INTEGER array, dimension (4)
* On entry, the seed of the random number generator; the array
* elements must be between 0 and 4095, and ISEED(4) must be
* odd.
* On exit, the seed is updated and will remain identical on
* all processes in the context.
*
* ORDER (global input) INTEGER
* Number of reflectors in the matrix Q
* At present, ORDER .NE. N is not supported
*
* WORK (local workspace) COMPLEX array, dimension (LWORK)
*
* LWORK (local input) INTEGER dimension of WORK
* LWORK >= SIZETMS as returned by PCLASIZESEP
*
*
* 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, DLEN_, DTYPE_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
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 CZERO
PARAMETER ( CZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER CSRC_A, I, IACOL, IAROW, ICOFFA, II, IIROW,
$ INDAA, INDTAU, INDWORK, IPOSTPAD, IPREPAD,
$ IROFFA, ISIZEHEEVX, ISIZESUBTST, ISIZETST,
$ JJCOL, LDAA, LII, LIII, LJJ, LJJJ, LWMIN, MAXI,
$ MB_A, MYCOL, MYROW, NB_A, NP, NPCOL, NPROW, NQ,
$ RSIZECHK, RSIZEHEEVX, RSIZEQTQ, RSIZESUBTST,
$ RSIZETST, RSRC_A, SIZEHEEVX, SIZEMQRLEFT,
$ SIZEMQRRIGHT, SIZEQRF, SIZESUBTST, SIZETMS,
$ SIZETST, SIZEHEEVD, RSIZEHEEVD, ISIZEHEEVD
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, CLASET, PCGEQRF,
$ PCLASIZESEP, PCMATGEN, PCUNMQR, PXERBLA
* ..
* .. External Functions ..
INTEGER INDXG2P, NUMROC
EXTERNAL INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
*
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
* This is just to keep ftnchek happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DTYPE_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
*
* Initialize grid information
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
* Check LWORK
*
INFO = 0
IF( NPROW.EQ.-1 ) THEN
INFO = -( 700+CTXT_ )
ELSE
CALL CHK1MAT( N, 1, N, 1, IA, JA, DESCA, 7, INFO )
END IF
*
LDAA = DESCA( LLD_ )
MB_A = DESCA( MB_ )
NB_A = DESCA( NB_ )
RSRC_A = DESCA( RSRC_ )
CSRC_A = DESCA( CSRC_ )
IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW )
IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL )
IROFFA = MOD( IA-1, MB_A )
ICOFFA = MOD( JA-1, NB_A )
NP = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL )
IPREPAD = 0
IPOSTPAD = 0
CALL PCLASIZESEP( DESCA, IPREPAD, IPOSTPAD, SIZEMQRLEFT,
$ SIZEMQRRIGHT, SIZEQRF, SIZETMS, RSIZEQTQ,
$ RSIZECHK, SIZEHEEVX, RSIZEHEEVX, ISIZEHEEVX,
$ SIZEHEEVD, RSIZEHEEVD, ISIZEHEEVD,
$ SIZESUBTST, RSIZESUBTST, ISIZESUBTST, SIZETST,
$ RSIZETST, ISIZETST )
LWMIN = SIZETMS
*
* Test the input arguments
*
IF( INFO.EQ.0 ) THEN
IF( K.LT.0 .OR. K.GT.N-1 ) THEN
INFO = -2
ELSE IF( N.NE.ORDER ) THEN
INFO = -9
ELSE IF( LWORK.LT.LWMIN ) THEN
INFO = -11
END IF
END IF
IF( INFO.LT.0 ) THEN
CALL PXERBLA( DESCA( CTXT_ ), 'PCLAGHE', -INFO )
RETURN
END IF
*
INDAA = 1
INDTAU = INDAA + LDAA*MAX( 1, NQ )
INDWORK = INDTAU + MAX( 1, NQ )
*
IF( K.NE.0 ) THEN
CALL CLASET( 'A', LDAA, NQ, CZERO, CZERO, WORK( INDAA ), LDAA )
*
*
* Build a random matrix
*
*
CALL PCMATGEN( DESCA( CTXT_ ), 'N', 'N', N, ORDER,
$ DESCA( MB_ ), DESCA( NB_ ), WORK( INDAA ),
$ DESCA( LLD_ ), DESCA( RSRC_ ), DESCA( CSRC_ ),
$ ISEED( 1 ), 0, NP, 0, NQ, MYROW, MYCOL, NPROW,
$ NPCOL )
CALL PCGEQRF( N, ORDER, WORK( INDAA ), IA, JA, DESCA,
$ WORK( INDTAU ), WORK( INDWORK ), SIZEQRF, INFO )
*
END IF
*
* Build a diagonal matrix A with the eigenvalues specified in D
*
CALL CLASET( 'A', NP, NQ, CZERO, CZERO, A, DESCA( LLD_ ) )
*
IIROW = 0
JJCOL = 0
LII = 1
LJJ = 1
*
DO 20 II = 1, N, DESCA( MB_ )
MAXI = MIN( N, II+DESCA( MB_ )-1 )
IF( ( MYROW.EQ.IIROW ) .AND. ( MYCOL.EQ.JJCOL ) ) THEN
LIII = LII
LJJJ = LJJ
DO 10 I = II, MAXI
A( LIII+( LJJJ-1 )*DESCA( LLD_ ) ) = D( I )
LIII = LIII + 1
LJJJ = LJJJ + 1
10 CONTINUE
END IF
IF( MYROW.EQ.IIROW )
$ LII = LII + DESCA( MB_ )
IF( MYCOL.EQ.JJCOL )
$ LJJ = LJJ + DESCA( MB_ )
IIROW = MOD( IIROW+1, NPROW )
JJCOL = MOD( JJCOL+1, NPCOL )
20 CONTINUE
*
* A = Q * A
*
IF( K.NE.0 ) THEN
*
CALL PCUNMQR( 'L', 'Conjugate transpose', N, N, ORDER,
$ WORK( INDAA ), IA, JA, DESCA, WORK( INDTAU ), A,
$ IA, JA, DESCA, WORK( INDWORK ), SIZEMQRLEFT,
$ INFO )
*
*
* A = A * Q'
*
*
CALL PCUNMQR( 'R', 'N', N, N, ORDER, WORK( INDAA ), IA, JA,
$ DESCA, WORK( INDTAU ), A, IA, JA, DESCA,
$ WORK( INDWORK ), SIZEMQRRIGHT, INFO )
*
END IF
*
* End of PCLAGHE
*
END
|
