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|
*
*
SUBROUTINE PSSQPSUBTST( WKNOWN, JOBZ, UPLO, N, THRESH, ABSTOL, A,
$ COPYA, Z, IA, JA, DESCA, WIN, WNEW,
$ IPREPAD, IPOSTPAD, WORK, LWORK, LWORK1,
$ RESULT, TSTNRM, QTQNRM, NOUT )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* November 15, 1997
*
* .. Scalar Arguments ..
LOGICAL WKNOWN
CHARACTER JOBZ, UPLO
INTEGER IA, IPOSTPAD, IPREPAD, JA, LWORK, LWORK1, N,
$ NOUT, RESULT
REAL ABSTOL, QTQNRM, THRESH, TSTNRM
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * ), COPYA( * ), WIN( * ), WNEW( * ),
$ WORK( * ), Z( * )
* ..
*
* Purpose
* =======
*
* PSSQPSUBTST calls PSSYEV and then tests the output of
* PSSYEV
* If JOBZ = 'V' then the following two tests are performed:
* |AQ -QL| / (abstol + eps * norm(A) ) < N*THRESH
* |QT * Q - I| / eps * norm(A) < N*THRESH
* If WKNOWN then
* we check to make sure that the eigenvalues match expectations
* i.e. |WIN - WNEW(1+IPREPAD)| / (eps * |WIN|) < THRESH
* where WIN is the array of eigenvalues as computed by
* PSSYEV when eigenvectors are requested
*
* Arguments
* =========
*
* NP = the number of rows local to a given process.
* NQ = the number of columns local to a given process.
*
* WKNOWN (global input) INTEGER
* .FALSE.: WIN does not contain the eigenvalues
* .TRUE.: WIN does contain the eigenvalues
*
* JOBZ (global input) CHARACTER*1
* Specifies whether or not to compute the eigenvectors:
* = 'N': Compute eigenvalues only.
* = 'V': Compute eigenvalues and eigenvectors.
* Must be 'V' on first call to PSSQPSUBTST
*
* UPLO (global input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrix A is stored:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (global input) INTEGER
* Size of the matrix to be tested. (global size)
*
* 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.
*
* ABSTOL (global input) REAL
* The absolute tolerance for the eigenvalues. An
* eigenvalue is considered to be located if it has
* been determined to lie in an interval whose width
* is "abstol" or less. If "abstol" is less than or equal
* to zero, then ulp*|T| will be used, where |T| is
* the 1-norm of the matrix.
*
* A (local workspace) REAL array
* global dimension (N, N), local dimension (DESCA(DLEN_), NQ)
* A is distributed in a block cyclic manner over both rows
* and columns.
* See PSSYEV for a description of block cyclic layout.
* The test matrix, which is then modified by PSSYEV
* A has already been padded front and back, use A(1+IPREPAD)
*
* COPYA (local input) REAL array, dimension(N*N)
* COPYA holds a copy of the original matrix A
* identical in both form and content to A
*
* Z (local workspace) REAL array, dim (N*N)
* Z is distributed in the same manner as A
* Z contains the eigenvector matrix
* Z is used as workspace by the test routines
* PSSEPCHK and PSSEPQTQ.
* Z has already been padded front and back, use Z(1+IPREPAD)
*
* IA (global input) INTEGER
* On entry, IA specifies the global row index of the submatrix
* of the global matrix A, COPYA and Z to operate on.
*
* JA (global input) INTEGER
* On entry, IA specifies the global column index of the submat
* of the global matrix A, COPYA and Z to operate on.
*
* DESCA (global/local input) INTEGER array of dimension 8
* The array descriptor for the matrix A, COPYA and Z.
*
* WIN (global input) REAL array, dimension (N)
* If .not. WKNOWN, WIN is ignored on input
* Otherwise, WIN() is taken as the standard by which the
* eigenvalues are to be compared against.
*
* WNEW (global workspace) REAL array, dimension (N)
* The eigenvalues as computed by this call to PSSYEV.
* WNEW has already been padded front and back,
* use WNEW(1+IPREPAD)
*
* WORK (local workspace) REAL array, dimension (LWORK)
* WORK has already been padded front and back,
* use WORK(1+IPREPAD)
*
* LWORK (local input) INTEGER
* The actual length of the array WORK after padding.
*
*
* LWORK1 (local input) INTEGER
* The amount of real workspace to pass to PSSYEV
*
* RESULT (global output) INTEGER
* The result of this call to PSSYEV
* RESULT = -3 => This process did not participate
* RESULT = 0 => All tests passed
* RESULT = 1 => ONe or more tests failed
*
* TSTNRM (global output) REAL
* |AQ- QL| / (ABSTOL+EPS*|A|)*N
*
* QTQNRM (global output) REAL
* |QTQ -I| / N*EPS
*
* .. Parameters ..
*
INTEGER BLOCK_CYCLIC_2D, DLEN_, DT_, CTXT_, M_, N_,
$ MB_, NB_, RSRC_, CSRC_, LLD_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DT_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
REAL FIVE, NEGONE, PADVAL, ZERO
PARAMETER ( PADVAL = 13.5285E+0, FIVE = 5.0E+0,
$ NEGONE = -1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, IAM, INFO, ISIZESUBTST, ISIZESYEVX,
$ ISIZETST, J, EIGS, MINSIZE, MQ, MYCOL, MYROW,
$ NP, NPCOL, NPROW, NQ, RESAQ, RESQTQ,
$ SIZECHK, SIZEMQRLEFT, SIZEMQRRIGHT, SIZEQRF,
$ SIZEQTQ, SIZESUBTST, SIZESYEV, SIZESYEVX,
$ SIZETMS, SIZETST, SIZESYEVD, ISIZESYEVD
REAL EPS, EPSNORMA, ERROR, MAXERROR, MINERROR,
$ NORMWIN, SAFMIN
* ..
* .. Local Arrays ..
INTEGER DESCZ( DLEN_ ), ITMP( 2 ),
$ IWORK( 2 )
* ..
* .. External Functions ..
*
LOGICAL LSAME
INTEGER NUMROC
REAL PSLAMCH, PSLANSY
EXTERNAL LSAME, NUMROC, PSLAMCH, PSLANSY
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCINIT, IGAMN2D, IGAMX2D,
$ PSCHEKPAD, PSELSET, PSFILLPAD, PSLASIZESQP,
$ PSSEPCHK, PSSEPQTQ, PSSYEV, SGAMN2D, SGAMX2D,
$ SLACPY, SLBOOT, SLTIMER
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD
* ..
* .. Executable Statements ..
* This is just to keep ftnchek happy
IF( BLOCK_CYCLIC_2D*CSRC_*CTXT_*DLEN_*DT_*LLD_*MB_*M_*NB_*N_*
$ RSRC_.LT.0 )RETURN
CALL PSLASIZESQP( DESCA, IPREPAD, IPOSTPAD, SIZEMQRLEFT,
$ SIZEMQRRIGHT, SIZEQRF, SIZETMS, SIZEQTQ,
$ SIZECHK, SIZESYEVX, ISIZESYEVX, SIZESYEV,
$ SIZESYEVD, ISIZESYEVD, SIZESUBTST, ISIZESUBTST,
$ SIZETST, ISIZETST )
*
TSTNRM = NEGONE
QTQNRM = NEGONE
EPS = PSLAMCH( DESCA( CTXT_ ), 'Eps' )
SAFMIN = PSLAMCH( DESCA( CTXT_ ), 'Safe min' )
*
NORMWIN = SAFMIN / EPS
IF( N.GE.1 )
$ NORMWIN = MAX( ABS( WIN( 1+IPREPAD ) ),
$ ABS( WIN( N+IPREPAD ) ), NORMWIN )
*
* Make sure that we aren't using information from previous calls
*
DO 10 I = 1, LWORK1, 1
WORK( I+IPREPAD ) = 14.3E+0
10 CONTINUE
*
DO 30 I = 1, N
WNEW( I+IPREPAD ) = 3.14159E+0
30 CONTINUE
*
DO 40 I = 1, 2
IWORK( I ) = 0
40 CONTINUE
*
IF( LSAME( JOBZ, 'N' ) ) THEN
EIGS = 0
ELSE
EIGS = N
END IF
*
*
CALL DESCINIT( DESCZ, DESCA( M_ ), DESCA( N_ ), DESCA( MB_ ),
$ DESCA( NB_ ), DESCA( RSRC_ ), DESCA( CSRC_ ),
$ DESCA( CTXT_ ), DESCA( LLD_ ), INFO )
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
IAM = 1
IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 )
$ IAM = 0
*
* If this process is not involved in this test, bail out now
*
RESULT = -3
IF( MYROW.GE.NPROW .OR. MYROW.LT.0 )
$ GO TO 150
RESULT = 0
*
NP = NUMROC( N, DESCA( MB_ ), MYROW, 0, NPROW )
NQ = NUMROC( N, DESCA( NB_ ), MYCOL, 0, NPCOL )
MQ = NUMROC( EIGS, DESCA( NB_ ), MYCOL, 0, NPCOL )
*
* Find the amount of workspace needed with or without eigenvectors.
*
CALL PSLASIZESYEV( JOBZ, N, DESCA, MINSIZE )
*
CALL SLACPY( 'A', NP, NQ, COPYA, DESCA( LLD_ ), A( 1+IPREPAD ),
$ DESCA( LLD_ ) )
*
CALL PSFILLPAD( DESCA( CTXT_ ), NP, NQ, A, DESCA( LLD_ ), IPREPAD,
$ IPOSTPAD, PADVAL )
*
CALL PSFILLPAD( DESCZ( CTXT_ ), NP, MQ, Z, DESCZ( LLD_ ), IPREPAD,
$ IPOSTPAD, PADVAL+1.0E+0 )
*
CALL PSFILLPAD( DESCA( CTXT_ ), N, 1, WNEW, N, IPREPAD, IPOSTPAD,
$ PADVAL+2.0E+0 )
*
CALL PSFILLPAD( DESCA( CTXT_ ), LWORK1, 1, WORK, LWORK1, IPREPAD,
$ IPOSTPAD, PADVAL+4.0E+0 )
*
* Make sure that PSSYEV does not cheat (i.e. use answers
* already computed.)
*
DO 60 I = 1, N, 1
DO 50 J = 1, EIGS, 1
CALL PSELSET( Z( 1+IPREPAD ), I, J, DESCA, 13.0E+0 )
50 CONTINUE
60 CONTINUE
*
CALL SLBOOT
CALL SLTIMER( 1 )
CALL SLTIMER( 6 )
CALL PSSYEV( JOBZ, UPLO, N, A( 1+IPREPAD ), IA, JA, DESCA,
$ WNEW( 1+IPREPAD ), Z( 1+IPREPAD ), IA, JA, DESCA,
$ WORK( 1+IPREPAD ), LWORK1, INFO )
CALL SLTIMER( 6 )
CALL SLTIMER( 1 )
*
IF( THRESH.LE.0 ) THEN
RESULT = 0
ELSE
CALL PSCHEKPAD( DESCA( CTXT_ ), 'PSSYEV-A', NP, NQ, A,
$ DESCA( LLD_ ), IPREPAD, IPOSTPAD, PADVAL )
*
CALL PSCHEKPAD( DESCZ( CTXT_ ), 'PSSYEV-Z', NP, MQ, Z,
$ DESCZ( LLD_ ), IPREPAD, IPOSTPAD,
$ PADVAL+1.0E+0 )
*
CALL PSCHEKPAD( DESCA( CTXT_ ), 'PSSYEV-WNEW', N, 1, WNEW, N,
$ IPREPAD, IPOSTPAD, PADVAL+2.0E+0 )
*
CALL PSCHEKPAD( DESCA( CTXT_ ), 'PSSYEV-WORK', LWORK1, 1,
$ WORK, LWORK1, IPREPAD, IPOSTPAD,
$ PADVAL+4.0E+0 )
*
* Check INFO
*
*
* Make sure that all processes return the same value of INFO
*
ITMP( 1 ) = INFO
ITMP( 2 ) = INFO
*
CALL IGAMN2D( DESCA( CTXT_ ), 'a', ' ', 1, 1, ITMP, 1, 1, 1,
$ -1, -1, 0 )
CALL IGAMX2D( DESCA( CTXT_ ), 'a', ' ', 1, 1, ITMP( 2 ), 1, 1,
$ 1, -1, -1, 0 )
*
*
IF( ITMP( 1 ).NE.ITMP( 2 ) ) THEN
IF( IAM.EQ.0 )
$ WRITE( NOUT, FMT = * )
$ 'Different processes return different INFO'
RESULT = 1
ELSE IF( INFO.NE.0 ) THEN
IF( IAM.EQ.0 ) THEN
WRITE( NOUT, FMT = 9999 )INFO
IF( INFO.EQ.(N+1) )
$ WRITE( NOUT, FMT = 9994 )
RESULT = 1
END IF
ELSE IF( INFO.EQ.14 .AND. LWORK1.GE.MINSIZE ) THEN
IF( IAM.EQ.0 )
$ WRITE( NOUT, FMT = 9996 )INFO
RESULT = 1
END IF
*
IF( RESULT.EQ.0 .OR. INFO.GT.N ) THEN
*
* Make sure that different processes return the same eigenvalues.
* This is a more exhaustive check that provided by PSSYEV.
*
DO 70 I = 1, N
WORK( I ) = WNEW( I+IPREPAD )
WORK( I+N ) = WNEW( I+IPREPAD )
70 CONTINUE
*
CALL SGAMN2D( DESCA( CTXT_ ), 'a', ' ', N, 1, WORK, N, 1,
$ 1, -1, -1, 0 )
CALL SGAMX2D( DESCA( CTXT_ ), 'a', ' ', N, 1,
$ WORK( 1+N ), N, 1, 1, -1, -1, 0 )
*
DO 80 I = 1, N
*
IF( ABS( WORK( I )-WORK( N+I ) ).GT.ZERO ) THEN
IF( IAM.EQ.0 )
$ WRITE( NOUT, FMT = 9995 )
RESULT = 1
GO TO 90
END IF
80 CONTINUE
90 CONTINUE
END IF
*
CALL IGAMX2D( DESCA( CTXT_ ), 'a', ' ', 1, 1, RESULT, 1, 1, 1,
$ -1, -1, 0 )
*
* Compute eps * norm(A)
*
IF( N.EQ.0 ) THEN
EPSNORMA = EPS
ELSE
EPSNORMA = PSLANSY( 'I', UPLO, N, COPYA, IA, JA, DESCA,
$ WORK )*EPS
END IF
*
* Note that a couple key variables get redefined in PSSEPCHK
* as described by this table:
*
* PSSEPTST name PSSEPCHK name
* ------------- -------------
* COPYA A
* Z Q
* A C
*
*
IF( LSAME( JOBZ, 'V' ) ) THEN
*
* Perform the |AQ - QE| test
*
CALL PSFILLPAD( DESCA( CTXT_ ), SIZECHK, 1, WORK, SIZECHK,
$ IPREPAD, IPOSTPAD, 4.3E+0 )
*
RESAQ = 0
*
CALL PSSEPCHK( N, N, COPYA, IA, JA, DESCA,
$ MAX( ABSTOL+EPSNORMA, SAFMIN ), THRESH,
$ Z( 1+IPREPAD ), IA, JA, DESCZ,
$ A( 1+IPREPAD ), IA, JA, DESCA,
$ WNEW( 1+IPREPAD ), WORK( 1+IPREPAD ),
$ SIZECHK, TSTNRM, RESAQ )
*
CALL PSCHEKPAD( DESCA( CTXT_ ), 'PSSEPCHK-WORK', SIZECHK, 1,
$ WORK, SIZECHK, IPREPAD, IPOSTPAD, 4.3E+0 )
*
IF( RESAQ.NE.0 ) THEN
RESULT = 1
WRITE( NOUT, FMT = 9993 )
END IF
*
* Perform the |QTQ - I| test
*
CALL PSFILLPAD( DESCA( CTXT_ ), SIZEQTQ, 1, WORK, SIZEQTQ,
$ IPREPAD, IPOSTPAD, 4.3E+0 )
*
RESQTQ = 0
*
CALL PSSEPQTQ( N, N, THRESH, Z( 1+IPREPAD ), IA, JA, DESCZ,
$ A( 1+IPREPAD ), IA, JA, DESCA,
$ IWORK( 1 ), IWORK( 1 ), WORK( 1 ),
$ WORK( IPREPAD+1 ), SIZEQTQ, QTQNRM, INFO,
$ RESQTQ )
*
CALL PSCHEKPAD( DESCA( CTXT_ ), 'PSSEPQTQ-WORK', SIZEQTQ, 1,
$ WORK, SIZEQTQ, IPREPAD, IPOSTPAD, 4.3E+0 )
*
IF( RESQTQ.NE.0 ) THEN
RESULT = 1
WRITE( NOUT, FMT = 9992 )
END IF
*
IF( INFO.NE.0 ) THEN
IF( IAM.EQ.0 )
$ WRITE( NOUT, FMT = 9998 )INFO
RESULT = 1
END IF
END IF
*
* Check to make sure that we have the right eigenvalues
*
IF( WKNOWN .AND. N.GT.0 ) THEN
*
* Find the largest difference between the computed
* and expected eigenvalues
*
MINERROR = NORMWIN
MAXERROR = 0
*
DO 140 I = 1, N
ERROR = ABS( WIN( I+IPREPAD )-WNEW( I+IPREPAD ) )
MAXERROR = MAX( MAXERROR, ERROR )
140 CONTINUE
MINERROR = MIN( MAXERROR, MINERROR )
*
IF( MINERROR.GT.NORMWIN*FIVE*THRESH*EPS ) THEN
IF( IAM.EQ.0 )
$ WRITE( NOUT, FMT = 9997 )MINERROR, NORMWIN
RESULT = 1
END IF
END IF
END IF
*
* All processes should report the same result
*
CALL IGAMX2D( DESCA( CTXT_ ), 'a', ' ', 1, 1, RESULT, 1, 1, 1, -1,
$ -1, 0 )
*
150 CONTINUE
*
*
RETURN
*
9999 FORMAT( 'PSSYEV returned INFO=', I7 )
9998 FORMAT( 'PSSEPQTQ in PSSQPSUBTST returned INFO=', I7 )
9997 FORMAT( 'PSSQPSUBTST minerror =', D11.2, ' normwin=', D11.2 )
9996 FORMAT( 'PSSYEV returned INFO=', I7,
$ ' despite adequate workspace' )
9995 FORMAT( 'Different processes return different eigenvalues' )
9994 FORMAT( 'Heterogeneity detected by PSSYEV' )
9993 FORMAT( 'PSSYEV failed the |AQ -QE| test' )
9992 FORMAT( 'PSSYEV failed the |QTQ -I| test' )
*
* End of PSSQPSUBTST
*
END
|
