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SUBROUTINE PSLAGGE( M, N, 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, LWORK, M, N, ORDER
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), ISEED( 4 )
REAL A( * ), D( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSLAGGE generates a real symmetric matrix A, by pre- and post-
* multiplying a real diagonal matrix D with a random orthogonal
* matrices: A = U*D*VT.
*
* This is just a quick implementation which will be replaced in the
* future. The random matrix A1(m,n) is generated and random left
* orthogonal matrix U(m,m) is obtained by running QR on A1:
* A1(m,n) = U(m,m)*R,
* where U(m,m) is a product of min(m,n) Householder rotations.
* Afterwards the space of A1 is reused for a second random matrix
* A2(m,n), which is used to obtain the right orthogonal matrix VT(n,n)
* by running LQ on A2:
* A2(m,n) = L*VT(n,n).
* This requires vastly more computation than necessary, but not
* significantly more communication than is used in the rest of this
* routine, and hence is not that much slower than an efficient
* solution.
*
* 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
* =========
*
* M (global input) INTEGER
* Number of rows of the matrix A. M >= 0.
*
* N (global input) INTEGER
* Number of columns of matrix A. N >= 0.
*
* D (local input) REAL array, dimension (N)
* The diagonal elements of the diagonal matrix D.
*
* A (local output) REAL array
* Global dimension (M, N), local dimension (MP, NQ)
*
* IA (global input) INTEGER
* The global row index of the submatrix of the distributed
* matrix A to operate on.
*
* JA (global input) INTEGER
* The global column index of the submatrix of the distributed
* matrix A to operate 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) REAL array, dimension (LWORK)
*
* LWORK (local input) INTEGER dimension of WORK
* LWORK >= MAX( QR_WORK, LQ_WORK )
* QR_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU1 ) +
* MAX( SIZEMQRLEFT, SIZEQRF)
* LQ_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU2) +
* MAX( SIZEMLQRIGHT, SIZEQRF )
* Where:
* LDAA = DESCA( LLD_ )
* MB_A = DESCA( MB_ )
* NB_A = DESCA( NB_ )
* RSRC_A = DESCA( RSRC_ )
* CSRC_A = DESCA( CSRC_ )
* LCM = ILCM( NPROW, NPCOL )
* LCMQ = LCM / NPCOL
* IROFFA = MOD( IA-1, MB_A )
* ICOFFA = MOD( JA-1, NB_A )
* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW )
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL )
* MP = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW )
* NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL )
* DTAU1 = NUMROC( JA + SIZE- 1, NB_A, MYCOL, IACOL, NPROW )
* DTAU2 = NUMROC( IA + SIZE- 1, MB_A, MYROW, IAROW, NPROW )
* SIZEMQRLEFT = MAX( (MB_A*(MB_A-1))/2, ( MP + NQ ) * MB_A )
* + ( MP + NB_A ) * NB_A
* SIZEMLQRIGHT = MAX( (MB_A*(MB_A-1))/2, (MP + NQ)*MB_A ) +
* MB_A * MB_A
* SIZEQRF = NB_A*NP + MB_A*NQ + NB_A*NB_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, 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 )
REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER CSRC_A, DTAU1, DTAU2, I, IACOL, IAROW, ICOFFA,
$ IROFFA, LCM, LCMQ, LDAA, LQ_WORK, LWMIN, MB_A,
$ MP, MYCOL, MYROW, NB_A, NPCOL, NPROW, NQ,
$ PTR2AA, PTR2TAU, PTR2WORK, QR_WORK, RSRC_A,
$ SIZE, SIZELQF, SIZEMLQRIGHT, SIZEMQRLEFT,
$ SIZEQRF
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PSELSET, PSGELQF,
$ PSGEQRF, PSLASET, PSMATGEN, PSORMLQ, PSORMQR,
$ PXERBLA
* ..
* .. External Functions ..
INTEGER ILCM, INDXG2P, NUMROC
EXTERNAL ILCM, INDXG2P, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
* This is just to keep ftnchek happy
IF( BLOCK_CYCLIC_2D*DLEN_*DTYPE_*M_*N_.LT.0 )RETURN
*
* Initialize grid information.
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
* Check LWORK.
*
INFO = 0
SIZE = MIN( M, N )
IF( NPROW.EQ.-1 ) THEN
INFO = -607
ELSE
CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 8, INFO )
END IF
* Calculation of a minimum workspace.
LDAA = DESCA( LLD_ )
MB_A = DESCA( MB_ )
NB_A = DESCA( NB_ )
RSRC_A = DESCA( RSRC_ )
CSRC_A = DESCA( CSRC_ )
LCM = ILCM( NPROW, NPCOL )
LCMQ = LCM / NPCOL
IROFFA = MOD( IA-1, MB_A )
ICOFFA = MOD( JA-1, NB_A )
IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW )
IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL )
DTAU1 = NUMROC( JA+SIZE-1, NB_A, MYCOL, IACOL, NPCOL )
DTAU2 = NUMROC( IA+SIZE-1, MB_A, MYROW, IAROW, NPROW )
MP = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL )
*
SIZEMQRLEFT = MAX( ( MB_A*( MB_A-1 ) ) / 2, ( MP+NQ )*MB_A ) +
$ ( MP+NB_A )*NB_A
SIZEMLQRIGHT = MAX( ( MB_A*( MB_A-1 ) ) / 2, ( MP+NQ )*MB_A ) +
$ MB_A*MB_A
SIZEQRF = NB_A*MP + MB_A*NQ + NB_A*NB_A + 100
SIZELQF = NB_A*( MP+NQ+NB_A ) + 100
*
QR_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU1 ) +
$ MAX( SIZEMQRLEFT, SIZEQRF )
LQ_WORK = LDAA*MAX( 1, NQ ) + 200 + MAX( 1, DTAU2 ) +
$ MAX( SIZEMLQRIGHT, SIZELQF )
LWMIN = MAX( QR_WORK, LQ_WORK )
WORK( 1 ) = LWMIN
IF( LWORK.EQ.-1 )
$ GO TO 20
*
* Test the input arguments.
*
IF( INFO.EQ.0 ) THEN
IF( SIZE.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_ ), 'PSLAGGE', -INFO )
RETURN
END IF
*
* Build a diagonal matrix A with the eigenvalues specified in D.
*
CALL PSLASET( 'Full', M, N, ZERO, ZERO, A, IA, JA, DESCA )
DO 10 I = 1, SIZE
CALL PSELSET( A, I, I, DESCA, D( I ) )
10 CONTINUE
*
* Local dimension of array TAU in tis case is LOCc(JA+MIN(M,N)-1).
*
PTR2AA = 2
PTR2TAU = PTR2AA + LDAA*MAX( 1, NQ ) + 100
PTR2WORK = PTR2TAU + MAX( 1, DTAU1 ) + 100
*
CALL PSLASET( 'All', M, N, ZERO, ZERO, WORK( PTR2AA ), IA, JA,
$ DESCA )
*
* Build a random matrix AA1.
*
CALL PSMATGEN( DESCA( CTXT_ ), 'N', 'N', M, N, DESCA( MB_ ),
$ DESCA( NB_ ), WORK( PTR2AA ), DESCA( LLD_ ),
$ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED( 1 ), 0, MP,
$ 0, NQ, MYROW, MYCOL, NPROW, NPCOL )
*
* Produce QR decomposition AA1 -> U*R.
*
CALL PSGEQRF( M, N, WORK( PTR2AA ), IA, JA, DESCA,
$ WORK( PTR2TAU ), WORK( PTR2WORK ), SIZEQRF, INFO )
*
* A = U*A.
*
CALL PSORMQR( 'L', 'N', M, N, SIZE, WORK( PTR2AA ), IA, JA, DESCA,
$ WORK( PTR2TAU ), A, IA, JA, DESCA, WORK( PTR2WORK ),
$ SIZEMQRLEFT, INFO )
*
* Reinitialize pointer to WORK array. Dimension of array TAU in
* this case is LOCr(IA+MIN(M,N)-1).
*
PTR2WORK = PTR2TAU + MAX( 1, DTAU2 ) + 100
*
* Use the same workspace to generate a random matrix AA2.
*
CALL PSMATGEN( DESCA( CTXT_ ), 'N', 'N', M, N, DESCA( MB_ ),
$ DESCA( NB_ ), WORK( PTR2AA ), DESCA( LLD_ ),
$ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED( 2 ), 0, MP,
$ 0, NQ, MYROW, MYCOL, NPROW, NPCOL )
*
* Produce LQ decomposition of random matrix AA2 -> L*VT.
*
CALL PSGELQF( M, N, WORK( PTR2AA ), IA, JA, DESCA,
$ WORK( PTR2TAU ), WORK( PTR2WORK ), SIZELQF, INFO )
*
* Calculate A = A*VT.
*
CALL PSORMLQ( 'R', 'N', M, N, SIZE, WORK( PTR2AA ), IA, JA, DESCA,
$ WORK( PTR2TAU ), A, IA, JA, DESCA, WORK( PTR2WORK ),
$ SIZEMLQRIGHT, INFO )
*
* End of PSLAGGE
*
20 CONTINUE
RETURN
END
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