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*
*
SUBROUTINE PSSEPQTQ( MS, NV, THRESH, Q, IQ, JQ, DESCQ, C, IC, JC,
$ DESCC, PROCDIST, ICLUSTR, GAP, WORK, LWORK,
$ QTQNRM, INFO, RES )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IC, INFO, IQ, JC, JQ, LWORK, MS, NV, RES
REAL QTQNRM, THRESH
* ..
* .. Array Arguments ..
*
INTEGER DESCC( * ), DESCQ( * ), ICLUSTR( * ),
$ PROCDIST( * )
REAL C( * ), GAP( * ), Q( * ), 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
* =======
*
* Compute |I - QT * Q| / (ulp * n)
*
* Arguments
* =========
*
* NP = number of local rows in C
* NQ = number of local columns in C and Q
*
* MS (global input) INTEGER
* Matrix size.
* The number of global rows in Q
*
* NV (global input) INTEGER
* Number of eigenvectors
* The number of global columns in C and Q
*
* THRESH (global input) REAL
* A test will count as "failed" if the "error", computed as
* described below, exceeds THRESH. Note that the error
* is scaled to be O(1), so THRESH should be a reasonably
* small multiple of 1, e.g., 10 or 100. In particular,
* it should not depend on the precision (single vs. double)
* or the size of the matrix. It must be at least zero.
*
* Q (local input) REAL array,
* global dimension (MS, NV), local dimension (LDQ, NQ)
*
* Contains the eigenvectors as computed by PSSTEIN
*
* IQ (global input) INTEGER
* Q's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JQ (global input) INTEGER
* Q's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCQ (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix Q.
*
* C (local workspace) REAL array,
* global dimension (NV, NV), local dimension (DESCC(DLEN_), NQ)
*
* Accumulator for computing I - QT * Q
*
* IC (global input) INTEGER
* C's global row index, which points to the beginning of the
* submatrix which is to be operated on.
*
* JC (global input) INTEGER
* C's global column index, which points to the beginning of
* the submatrix which is to be operated on.
*
* DESCC (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix C.
*
* W (input) REAL array, dimension (NV)
* All procesors have an identical copy of W()
*
* Contains the computed eigenvalues
*
* PROCDIST (global input) INTEGER array dimension (NPROW*NPCOL+1)
* Identifies which eigenvectors are the last to be computed
* by a given process
*
* ICLUSTR (global input) INTEGER array dimension (2*P)
* This input array contains indices of eigenvectors
* corresponding to a cluster of eigenvalues that could not be
* orthogonalized due to insufficient workspace.
* This should be the output of PSSTEIN.
*
* GAP (global input) REAL array, dimension (P)
* This input array contains the gap between eigenvalues whose
* eigenvectors could not be orthogonalized.
*
* WORK (local workspace) REAL array, dimension (LWORK)
*
* LWORK (local input) INTEGER
* The length of the array WORK.
* LWORK >= 2 + MAX( DESCC( MB_ ), 2 )*( 2*NP0+MQ0 )
* Where:
* NP0 = NUMROC( NV, DESCC( MB_ ), 0, 0, NPROW )
* MQ0 = NUMROC( NV, DESCC( NB_ ), 0, 0, NPCOL )
*
* QTQNRM (global output) REAL
* |QTQ -I| / EPS
*
* RES (global output) INTEGER
* 0 if the test passes i.e. |I - QT * Q| / (ulp * n) <= THRESH
* 1 if the test fails i.e. |I - QT * Q| / (ulp * n) > THRESH
*
*
* .. 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, ONE, NEGONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0,
$ NEGONE = -1.0E+0 )
* ..
* .. Intrinsic Functions ..
*
INTRINSIC MAX, REAL
* ..
* .. Local Scalars ..
INTEGER CLUSTER, FIRSTP, IMAX, IMIN, JMAX, JMIN, LWMIN,
$ MQ0, MYCOL, MYROW, NEXTP, NP0, NPCOL, NPROW
REAL NORM, QTQNRM2, ULP
* ..
* .. External Functions ..
INTEGER NUMROC
REAL PSLAMCH, PSLANGE
EXTERNAL NUMROC, PSLAMCH, PSLANGE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, PSGEMM, PSLASET,
$ PSMATADD, PXERBLA
* ..
* .. 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
*
*
RES = 0
ULP = PSLAMCH( DESCC( CTXT_ ), 'P' )
*
CALL BLACS_GRIDINFO( DESCC( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
INFO = 0
CALL CHK1MAT( MS, 1, MS, 2, IQ, JQ, DESCQ, 7, INFO )
CALL CHK1MAT( NV, 1, MS, 2, IC, JC, DESCC, 11, INFO )
*
IF( INFO.EQ.0 ) THEN
NP0 = NUMROC( NV, DESCC( MB_ ), 0, 0, NPROW )
MQ0 = NUMROC( NV, DESCC( NB_ ), 0, 0, NPCOL )
*
LWMIN = 2 + MAX( DESCC( MB_ ), 2 )*( 2*NP0+MQ0 )
*
IF( IQ.NE.1 ) THEN
INFO = -5
ELSE IF( JQ.NE.1 ) THEN
INFO = -6
ELSE IF( IC.NE.1 ) THEN
INFO = -9
ELSE IF( JC.NE.1 ) THEN
INFO = -10
ELSE IF( LWORK.LT.LWMIN ) THEN
INFO = -16
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( DESCC( CTXT_ ), 'PSSEPQTQ', -INFO )
RETURN
END IF
*
* C = Identity matrix
*
CALL PSLASET( 'A', NV, NV, ZERO, ONE, C, IC, JC, DESCC )
*
* C = C - QT * Q
*
IF( NV*MS.GT.0 ) THEN
CALL PSGEMM( 'Transpose', 'N', NV, NV, MS, NEGONE, Q, 1, 1,
$ DESCQ, Q, 1, 1, DESCQ, ONE, C, 1, 1, DESCC )
END IF
*
* Allow for poorly orthogonalized eigenvectors for large clusters
*
NORM = PSLANGE( '1', NV, NV, C, 1, 1, DESCC, WORK )
QTQNRM = NORM / ( REAL( MAX( MS, 1 ) )*ULP )
*
CLUSTER = 1
10 CONTINUE
DO 20 FIRSTP = 1, NPROW*NPCOL
IF( PROCDIST( FIRSTP ).GE.ICLUSTR( 2*( CLUSTER-1 )+1 ) )
$ GO TO 30
20 CONTINUE
30 CONTINUE
*
IMIN = ICLUSTR( 2*CLUSTER-1 )
JMAX = ICLUSTR( 2*CLUSTER )
*
*
IF( IMIN.EQ.0 )
$ GO TO 60
*
DO 40 NEXTP = FIRSTP, NPROW*NPCOL
IMAX = PROCDIST( NEXTP )
JMIN = IMAX + 1
*
*
CALL PSMATADD( IMAX-IMIN+1, JMAX-JMIN+1, ZERO, C, IMIN, JMIN,
$ DESCC, GAP( CLUSTER ) / 0.01E+0, C, IMIN, JMIN,
$ DESCC )
CALL PSMATADD( JMAX-JMIN+1, IMAX-IMIN+1, ZERO, C, JMIN, IMIN,
$ DESCC, GAP( CLUSTER ) / 0.01E+0, C, JMIN, IMIN,
$ DESCC )
IMIN = IMAX
*
IF( ICLUSTR( 2*CLUSTER ).LT.PROCDIST( NEXTP+1 ) )
$ GO TO 50
40 CONTINUE
50 CONTINUE
*
CLUSTER = CLUSTER + 1
GO TO 10
60 CONTINUE
*
* Compute the norm of C
*
NORM = PSLANGE( '1', NV, NV, C, 1, 1, DESCC, WORK )
*
QTQNRM2 = NORM / ( REAL( MAX( MS, 1 ) )*ULP )
*
IF( QTQNRM2.GT.THRESH ) THEN
RES = 1
QTQNRM = QTQNRM2
END IF
RETURN
*
* End of PSSEPQTQ
*
END
|
