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|
RECURSIVE SUBROUTINE PSLAQR3( WANTT, WANTZ, N, KTOP, KBOT, NW, H,
$ DESCH, ILOZ, IHIZ, Z, DESCZ, NS, ND,
$ SR, SI, V, DESCV, NH, T, DESCT, NV,
$ WV, DESCW, WORK, LWORK, IWORK,
$ LIWORK, RECLEVEL )
*
* Contribution from the Department of Computing Science and HPC2N,
* Umea University, Sweden
*
* -- ScaLAPACK auxiliary routine (version 2.0.1) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* Univ. of Colorado Denver and University of California, Berkeley.
* January, 2012
*
IMPLICIT NONE
*
* .. Scalar Arguments ..
INTEGER IHIZ, ILOZ, KBOT, KTOP, LWORK, N, ND, NH, NS,
$ NV, NW, LIWORK, RECLEVEL
LOGICAL WANTT, WANTZ
* ..
* .. Array Arguments ..
INTEGER DESCH( * ), DESCZ( * ), DESCT( * ), DESCV( * ),
$ DESCW( * ), IWORK( * )
REAL H( * ), SI( KBOT ), SR( KBOT ), T( * ),
$ V( * ), WORK( * ), WV( * ),
$ Z( * )
* ..
*
* Purpose
* =======
*
* Aggressive early deflation:
*
* This subroutine accepts as input an upper Hessenberg matrix H and
* performs an orthogonal similarity transformation designed to detect
* and deflate fully converged eigenvalues from a trailing principal
* submatrix. On output H has been overwritten by a new Hessenberg
* matrix that is a perturbation of an orthogonal similarity
* transformation of H. It is to be hoped that the final version of H
* has many zero subdiagonal entries.
*
* 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
* =========
*
* WANTT (global input) LOGICAL
* If .TRUE., then the Hessenberg matrix H is fully updated
* so that the quasi-triangular Schur factor may be
* computed (in cooperation with the calling subroutine).
* If .FALSE., then only enough of H is updated to preserve
* the eigenvalues.
*
* WANTZ (global input) LOGICAL
* If .TRUE., then the orthogonal matrix Z is updated so
* so that the orthogonal Schur factor may be computed
* (in cooperation with the calling subroutine).
* If .FALSE., then Z is not referenced.
*
* N (global input) INTEGER
* The order of the matrix H and (if WANTZ is .TRUE.) the
* order of the orthogonal matrix Z.
*
* KTOP (global input) INTEGER
* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.
* KBOT and KTOP together determine an isolated block
* along the diagonal of the Hessenberg matrix.
*
* KBOT (global input) INTEGER
* It is assumed without a check that either
* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together
* determine an isolated block along the diagonal of the
* Hessenberg matrix.
*
* NW (global input) INTEGER
* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).
*
* H (local input/output) REAL array, dimension
* (DESCH(LLD_),*)
* On input the initial N-by-N section of H stores the
* Hessenberg matrix undergoing aggressive early deflation.
* On output H has been transformed by an orthogonal
* similarity transformation, perturbed, and the returned
* to Hessenberg form that (it is to be hoped) has some
* zero subdiagonal entries.
*
* DESCH (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix H.
*
* ILOZ (global input) INTEGER
* IHIZ (global input) INTEGER
* Specify the rows of Z to which transformations must be
* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.
*
* Z (input/output) REAL array, dimension
* (DESCH(LLD_),*)
* IF WANTZ is .TRUE., then on output, the orthogonal
* similarity transformation mentioned above has been
* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.
* If WANTZ is .FALSE., then Z is unreferenced.
*
* DESCZ (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix Z.
*
* NS (global output) INTEGER
* The number of unconverged (ie approximate) eigenvalues
* returned in SR and SI that may be used as shifts by the
* calling subroutine.
*
* ND (global output) INTEGER
* The number of converged eigenvalues uncovered by this
* subroutine.
*
* SR (global output) REAL array, dimension KBOT
* SI (global output) REAL array, dimension KBOT
* On output, the real and imaginary parts of approximate
* eigenvalues that may be used for shifts are stored in
* SR(KBOT-ND-NS+1) through SR(KBOT-ND) and
* SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.
* The real and imaginary parts of converged eigenvalues
* are stored in SR(KBOT-ND+1) through SR(KBOT) and
* SI(KBOT-ND+1) through SI(KBOT), respectively.
*
* V (global workspace) REAL array, dimension
* (DESCV(LLD_),*)
* An NW-by-NW distributed work array.
*
* DESCV (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix V.
*
* NH (input) INTEGER scalar
* The number of columns of T. NH.GE.NW.
*
* T (global workspace) REAL array, dimension
* (DESCV(LLD_),*)
*
* DESCT (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix T.
*
* NV (global input) INTEGER
* The number of rows of work array WV available for
* workspace. NV.GE.NW.
*
* WV (global workspace) REAL array, dimension
* (DESCW(LLD_),*)
*
* DESCW (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix WV.
*
* WORK (local workspace) REAL array, dimension LWORK.
* On exit, WORK(1) is set to an estimate of the optimal value
* of LWORK for the given values of N, NW, KTOP and KBOT.
*
* LWORK (local input) INTEGER
* The dimension of the work array WORK. LWORK = 2*NW
* suffices, but greater efficiency may result from larger
* values of LWORK.
*
* If LWORK = -1, then a workspace query is assumed; PSLAQR3
* only estimates the optimal workspace size for the given
* values of N, NW, KTOP and KBOT. The estimate is returned
* in WORK(1). No error message related to LWORK is issued
* by XERBLA. Neither H nor Z are accessed.
*
* IWORK (local workspace) INTEGER array, dimension (LIWORK)
*
* LIWORK (local input) INTEGER
* The length of the workspace array IWORK
*
* ================================================================
* Based on contributions by
* Robert Granat and Meiyue Shao,
* Department of Computing Science and HPC2N,
* Umea University, Sweden
*
* ================================================================
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
INTEGER RECMAX
LOGICAL SORTGRAD
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, RECMAX = 3,
$ SORTGRAD = .FALSE. )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0, ONE = 1.0 )
* ..
* .. Local Scalars ..
REAL AA, BB, BETA, CC, CS, DD, EVI, EVK, FOO, S,
$ SAFMAX, SAFMIN, SMLNUM, SN, TAU, ULP,
$ ELEM, ELEM1, ELEM2, ELEM3, R1, ANORM, RNORM,
$ RESAED
INTEGER I, IFST, ILST, INFO, INFQR, J, JW, K, KCOL,
$ KEND, KLN, KROW, KWTOP, LTOP, LWK1, LWK2, LWK3,
$ LWKOPT, NMIN, LLDH, LLDZ, LLDT, LLDV, LLDWV,
$ ICTXT, NPROW, NMAX, NPCOL, MYROW, MYCOL, NB,
$ IROFFH, M, RCOLS, TAUROWS, RROWS, TAUCOLS,
$ ITAU, IR, IPW, NPROCS, MLOC, IROFFHH,
$ ICOFFHH, HHRSRC, HHCSRC, HHROWS, HHCOLS,
$ IROFFZZ, ICOFFZZ, ZZRSRC, ZZCSRC, ZZROWS,
$ ZZCOLS, IERR, TZROWS0, TZCOLS0, IERR0, IPT0,
$ IPZ0, IPW0, NB2, ROUND, LILST, KK, LILST0,
$ IWRK1, RSRC, CSRC, LWK4, LWK5, IWRK2, LWK6,
$ LWK7, LWK8, ILWKOPT, TZROWS, TZCOLS, NSEL,
$ NPMIN, ICTXT_NEW, MYROW_NEW, MYCOL_NEW
LOGICAL BULGE, SORTED, LQUERY
* ..
* .. Local Arrays ..
INTEGER PAR( 6 ), DESCR( DLEN_ ),
$ DESCTAU( DLEN_ ), DESCHH( DLEN_ ),
$ DESCZZ( DLEN_ ), DESCTZ0( DLEN_ ),
$ PMAP( 64*64 )
REAL DDUM( 1 )
* ..
* .. External Functions ..
REAL SLAMCH, PSLANGE
INTEGER PILAENVX, NUMROC, INDXG2P, ICEIL, BLACS_PNUM
EXTERNAL SLAMCH, PILAENVX, NUMROC, INDXG2P, PSLANGE,
$ ICEIL, BLACS_PNUM
* ..
* .. External Subroutines ..
EXTERNAL PSCOPY, PSGEHRD, PSGEMM, SLABAD, PSLACPY,
$ PSLAQR1, SLANV2, PSLAQR0, PSLARF, PSLARFG,
$ PSLASET, PSTRORD, PSELGET, PSELSET,
$ PSLAMVE, BLACS_GRIDINFO, BLACS_GRIDMAP,
$ BLACS_GRIDEXIT, PSGEMR2D
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, FLOAT, INT, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
ICTXT = DESCH( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
NPROCS = NPROW*NPCOL
*
* Extract local leading dimensions, blockfactors, offset for
* keeping the alignment requirements and size of deflation window.
*
LLDH = DESCH( LLD_ )
LLDZ = DESCZ( LLD_ )
LLDT = DESCT( LLD_ )
LLDV = DESCV( LLD_ )
LLDWV = DESCW( LLD_ )
NB = DESCH( MB_ )
IROFFH = MOD( KTOP - 1, NB )
JW = MIN( NW, KBOT-KTOP+1 )
NSEL = NB+JW
*
* Extract environment variables for parallel eigenvalue reordering.
*
PAR(1) = PILAENVX(ICTXT, 17, 'PSLAQR3', 'SV', JW, NB, -1, -1)
PAR(2) = PILAENVX(ICTXT, 18, 'PSLAQR3', 'SV', JW, NB, -1, -1)
PAR(3) = PILAENVX(ICTXT, 19, 'PSLAQR3', 'SV', JW, NB, -1, -1)
PAR(4) = PILAENVX(ICTXT, 20, 'PSLAQR3', 'SV', JW, NB, -1, -1)
PAR(5) = PILAENVX(ICTXT, 21, 'PSLAQR3', 'SV', JW, NB, -1, -1)
PAR(6) = PILAENVX(ICTXT, 22, 'PSLAQR3', 'SV', JW, NB, -1, -1)
*
* Check if workspace query.
*
LQUERY = LWORK.EQ.-1 .OR. LIWORK.EQ.-1
*
* Estimate optimal workspace.
*
IF( JW.LE.2 ) THEN
LWKOPT = 1
ELSE
*
* Workspace query calls to PSGEHRD and PSORMHR.
*
TAUROWS = NUMROC( 1, 1, MYCOL, DESCV(RSRC_), NPROW )
TAUCOLS = NUMROC( JW+IROFFH, NB, MYCOL, DESCV(CSRC_),
$ NPCOL )
CALL PSGEHRD( JW, 1, JW, T, 1, 1, DESCT, WORK, WORK, -1,
$ INFO )
LWK1 = INT( WORK( 1 ) ) + TAUROWS*TAUCOLS
*
* Workspace query call to PSORMHR.
*
CALL PSORMHR( 'Right', 'No', JW, JW, 1, JW, T, 1, 1, DESCT,
$ WORK, V, 1, 1, DESCV, WORK, -1, INFO )
LWK2 = INT( WORK( 1 ) )
*
* Workspace query call to PSLAQR0.
*
NMIN = PILAENVX( ICTXT, 12, 'PSLAQR3', 'SV', JW, 1, JW, LWORK )
NMAX = ( N-1 ) / 3
IF( JW+IROFFH.GT.NMIN .AND. JW+IROFFH.LE.NMAX
$ .AND. RECLEVEL.LT.RECMAX ) THEN
CALL PSLAQR0( .TRUE., .TRUE., JW+IROFFH, 1+IROFFH,
$ JW+IROFFH, T, DESCT, SR, SI, 1, JW, V, DESCV,
$ WORK, -1, IWORK, LIWORK-NSEL, INFQR,
$ RECLEVEL+1 )
LWK3 = INT( WORK( 1 ) )
IWRK1 = IWORK( 1 )
ELSE
RSRC = DESCT( RSRC_ )
CSRC = DESCT( CSRC_ )
DESCT( RSRC_ ) = 0
DESCT( CSRC_ ) = 0
CALL PSLAQR1( .TRUE., .TRUE., JW+IROFFH, 1, JW+IROFFH, T,
$ DESCT, SR, SI, 1, JW+IROFFH, V, DESCV, WORK, -1,
$ IWORK, LIWORK-NSEL, INFQR )
DESCT( RSRC_ ) = RSRC
DESCT( CSRC_ ) = CSRC
LWK3 = INT( WORK( 1 ) )
IWRK1 = IWORK( 1 )
END IF
*
* Workspace in case of alignment problems.
*
TZROWS0 = NUMROC( JW+IROFFH, NB, MYROW, 0, NPROW )
TZCOLS0 = NUMROC( JW+IROFFH, NB, MYCOL, 0, NPCOL )
LWK4 = 2 * TZROWS0*TZCOLS0
*
* Workspace check for reordering.
*
CALL PSTRORD( 'Vectors', IWORK, PAR, JW+IROFFH, T, 1, 1,
$ DESCT, V, 1, 1, DESCV, DDUM, DDUM, MLOC, WORK, -1,
$ IWORK, LIWORK-NSEL, INFO )
LWK5 = INT( WORK( 1 ) )
IWRK2 = IWORK( 1 )
*
* Extra workspace for reflecting back spike
* (workspace for PSLARF approximated for simplicity).
*
RROWS = NUMROC( N+IROFFH, NB, MYROW, DESCV(RSRC_), NPROW )
RCOLS = NUMROC( 1, 1, MYCOL, DESCV(CSRC_), NPCOL )
LWK6 = RROWS*RCOLS + TAUROWS*TAUCOLS +
$ 2*ICEIL(ICEIL(JW+IROFFH,NB),NPROW)*NB
$ *ICEIL(ICEIL(JW+IROFFH,NB),NPCOL)*NB
*
* Extra workspace needed by PBLAS update calls
* (also estimated for simplicity).
*
LWK7 = MAX( ICEIL(ICEIL(JW,NB),NPROW)*NB *
$ ICEIL(ICEIL(N-KBOT,NB),NPCOL)*NB,
$ ICEIL(ICEIL(IHIZ-ILOZ+1,NB),NPROW)*NB *
$ ICEIL(ICEIL(JW,NB),NPCOL)*NB,
$ ICEIL(ICEIL(KBOT-JW,NB),NPROW)*NB *
$ ICEIL(ICEIL(JW,NB),NPCOL)*NB )
*
* Residual check workspace.
*
TZROWS = NUMROC( JW+IROFFH, NB, MYROW, DESCT(RSRC_), NPROW )
TZCOLS = NUMROC( JW+IROFFH, NB, MYCOL, DESCT(CSRC_), NPCOL )
LWK8 = 2*TZROWS*TZCOLS
*
* Optimal workspace.
*
LWKOPT = MAX( LWK1, LWK2, LWK3+LWK4, LWK5, LWK6, LWK7, LWK8 )
ILWKOPT = MAX( IWRK1, IWRK2 )
END IF
*
* Quick return in case of workspace query.
*
WORK( 1 ) = FLOAT( LWKOPT )
*
* IWORK(1:NSEL) is used as the array SELECT for PSTRORD.
*
IWORK( 1 ) = ILWKOPT + NSEL
IF( LQUERY )
$ RETURN
*
* Nothing to do for an empty active block ...
NS = 0
ND = 0
IF( KTOP.GT.KBOT )
$ RETURN
* ... nor for an empty deflation window.
*
IF( NW.LT.1 )
$ RETURN
*
* Machine constants.
*
SAFMIN = SLAMCH( 'SAFE MINIMUM' )
SAFMAX = ONE / SAFMIN
CALL SLABAD( SAFMIN, SAFMAX )
ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( FLOAT( N ) / ULP )
*
* Setup deflation window.
*
JW = MIN( NW, KBOT-KTOP+1 )
KWTOP = KBOT - JW + 1
IF( KWTOP.EQ.KTOP ) THEN
S = ZERO
ELSE
CALL PSELGET( 'All', '1-Tree', S, H, KWTOP, KWTOP-1, DESCH )
END IF
*
IF( KBOT.EQ.KWTOP ) THEN
*
* 1-by-1 deflation window: not much to do.
*
CALL PSELGET( 'All', '1-Tree', SR( KWTOP ), H, KWTOP, KWTOP,
$ DESCH )
SI( KWTOP ) = ZERO
NS = 1
ND = 0
IF( ABS( S ).LE.MAX( SMLNUM, ULP*ABS( SR( KWTOP ) ) ) )
$ THEN
NS = 0
ND = 1
IF( KWTOP.GT.KTOP )
$ CALL PSELSET( H, KWTOP, KWTOP-1 , DESCH, ZERO )
END IF
RETURN
END IF
*
IF( KWTOP.EQ.KTOP .AND. KBOT-KWTOP.EQ.1 ) THEN
*
* 2-by-2 deflation window: a little more to do.
*
CALL PSELGET( 'All', '1-Tree', AA, H, KWTOP, KWTOP, DESCH )
CALL PSELGET( 'All', '1-Tree', BB, H, KWTOP, KWTOP+1, DESCH )
CALL PSELGET( 'All', '1-Tree', CC, H, KWTOP+1, KWTOP, DESCH )
CALL PSELGET( 'All', '1-Tree', DD, H, KWTOP+1, KWTOP+1, DESCH )
CALL SLANV2( AA, BB, CC, DD, SR(KWTOP), SI(KWTOP),
$ SR(KWTOP+1), SI(KWTOP+1), CS, SN )
NS = 0
ND = 2
IF( CC.EQ.ZERO ) THEN
I = KWTOP
IF( I+2.LE.N .AND. WANTT )
$ CALL PSROT( N-I-1, H, I, I+2, DESCH, DESCH(M_), H, I+1,
$ I+2, DESCH, DESCH(M_), CS, SN, WORK, LWORK, INFO )
IF( I.GT.1 )
$ CALL PSROT( I-1, H, 1, I, DESCH, 1, H, 1, I+1, DESCH, 1,
$ CS, SN, WORK, LWORK, INFO )
IF( WANTZ )
$ CALL PSROT( IHIZ-ILOZ+1, Z, ILOZ, I, DESCZ, 1, Z, ILOZ,
$ I+1, DESCZ, 1, CS, SN, WORK, LWORK, INFO )
CALL PSELSET( H, I, I, DESCH, AA )
CALL PSELSET( H, I, I+1, DESCH, BB )
CALL PSELSET( H, I+1, I, DESCH, CC )
CALL PSELSET( H, I+1, I+1, DESCH, DD )
END IF
WORK( 1 ) = FLOAT( LWKOPT )
RETURN
END IF
*
* Calculate new value for IROFFH in case deflation window
* was adjusted.
*
IROFFH = MOD( KWTOP - 1, NB )
*
* Adjust number of rows and columns of T matrix descriptor
* to prepare for call to PDBTRORD.
*
DESCT( M_ ) = JW+IROFFH
DESCT( N_ ) = JW+IROFFH
*
* Convert to spike-triangular form. (In case of a rare QR failure,
* this routine continues to do aggressive early deflation using that
* part of the deflation window that converged using INFQR here and
* there to keep track.)
*
* Copy the trailing submatrix to the working space.
*
CALL PSLASET( 'All', IROFFH, JW+IROFFH, ZERO, ONE, T, 1, 1,
$ DESCT )
CALL PSLASET( 'All', JW, IROFFH, ZERO, ZERO, T, 1+IROFFH, 1,
$ DESCT )
CALL PSLACPY( 'All', 1, JW, H, KWTOP, KWTOP, DESCH, T, 1+IROFFH,
$ 1+IROFFH, DESCT )
CALL PSLACPY( 'Upper', JW-1, JW-1, H, KWTOP+1, KWTOP, DESCH, T,
$ 1+IROFFH+1, 1+IROFFH, DESCT )
IF( JW.GT.2 )
$ CALL PSLASET( 'Lower', JW-2, JW-2, ZERO, ZERO, T, 1+IROFFH+2,
$ 1+IROFFH, DESCT )
CALL PSLACPY( 'All', JW-1, 1, H, KWTOP+1, KWTOP+JW-1, DESCH, T,
$ 1+IROFFH+1, 1+IROFFH+JW-1, DESCT )
*
* Initialize the working orthogonal matrix.
*
CALL PSLASET( 'All', JW+IROFFH, JW+IROFFH, ZERO, ONE, V, 1, 1,
$ DESCV )
*
* Compute the Schur form of T.
*
NPMIN = PILAENVX( ICTXT, 23, 'PSLAQR3', 'SV', JW, NB, NPROW,
$ NPCOL )
NMIN = PILAENVX( ICTXT, 12, 'PSLAQR3', 'SV', JW, 1, JW, LWORK )
NMAX = ( N-1 ) / 3
IF( MIN(NPROW, NPCOL).LE.NPMIN+1 .OR. RECLEVEL.GE.1 ) THEN
*
* The AED window is large enough.
* Compute the Schur decomposition with all processors.
*
IF( JW+IROFFH.GT.NMIN .AND. JW+IROFFH.LE.NMAX
$ .AND. RECLEVEL.LT.RECMAX ) THEN
CALL PSLAQR0( .TRUE., .TRUE., JW+IROFFH, 1+IROFFH,
$ JW+IROFFH, T, DESCT, SR( KWTOP-IROFFH ),
$ SI( KWTOP-IROFFH ), 1+IROFFH, JW+IROFFH, V, DESCV,
$ WORK, LWORK, IWORK(NSEL+1), LIWORK-NSEL, INFQR,
$ RECLEVEL+1 )
ELSE
IF( DESCT(RSRC_).EQ.0 .AND. DESCT(CSRC_).EQ.0 ) THEN
IF( JW+IROFFH.GT.DESCT( MB_ ) ) THEN
CALL PSLAQR1( .TRUE., .TRUE., JW+IROFFH, 1,
$ JW+IROFFH, T, DESCT, SR( KWTOP-IROFFH ),
$ SI( KWTOP-IROFFH ), 1, JW+IROFFH, V,
$ DESCV, WORK, LWORK, IWORK(NSEL+1), LIWORK-NSEL,
$ INFQR )
ELSE
IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
CALL SLAHQR( .TRUE., .TRUE., JW+IROFFH, 1+IROFFH,
$ JW+IROFFH, T, DESCT(LLD_),
$ SR( KWTOP-IROFFH ), SI( KWTOP-IROFFH ),
$ 1+IROFFH, JW+IROFFH, V, DESCV(LLD_), INFQR )
ELSE
INFQR = 0
END IF
IF( NPROCS.GT.1 )
$ CALL IGAMN2D( ICTXT, 'All', '1-Tree', 1, 1, INFQR,
$ 1, -1, -1, -1, -1, -1 )
END IF
ELSEIF( JW+IROFFH.LE.DESCT( MB_ ) ) THEN
IF( MYROW.EQ.DESCT(RSRC_) .AND. MYCOL.EQ.DESCT(CSRC_) )
$ THEN
CALL SLAHQR( .TRUE., .TRUE., JW+IROFFH, 1+IROFFH,
$ JW+IROFFH, T, DESCT(LLD_),
$ SR( KWTOP-IROFFH ), SI( KWTOP-IROFFH ),
$ 1+IROFFH, JW+IROFFH, V, DESCV(LLD_), INFQR )
ELSE
INFQR = 0
END IF
IF( NPROCS.GT.1 )
$ CALL IGAMN2D( ICTXT, 'All', '1-Tree', 1, 1, INFQR,
$ 1, -1, -1, -1, -1, -1 )
ELSE
TZROWS0 = NUMROC( JW+IROFFH, NB, MYROW, 0, NPROW )
TZCOLS0 = NUMROC( JW+IROFFH, NB, MYCOL, 0, NPCOL )
CALL DESCINIT( DESCTZ0, JW+IROFFH, JW+IROFFH, NB, NB, 0,
$ 0, ICTXT, MAX(1,TZROWS0), IERR0 )
IPT0 = 1
IPZ0 = IPT0 + MAX(1,TZROWS0)*TZCOLS0
IPW0 = IPZ0 + MAX(1,TZROWS0)*TZCOLS0
CALL PSLAMVE( 'All', JW+IROFFH, JW+IROFFH, T, 1, 1,
$ DESCT, WORK(IPT0), 1, 1, DESCTZ0, WORK(IPW0) )
CALL PSLASET( 'All', JW+IROFFH, JW+IROFFH, ZERO, ONE,
$ WORK(IPZ0), 1, 1, DESCTZ0 )
CALL PSLAQR1( .TRUE., .TRUE., JW+IROFFH, 1,
$ JW+IROFFH, WORK(IPT0), DESCTZ0,
$ SR( KWTOP-IROFFH ), SI( KWTOP-IROFFH ),
$ 1, JW+IROFFH, WORK(IPZ0),
$ DESCTZ0, WORK(IPW0), LWORK-IPW0+1, IWORK(NSEL+1),
$ LIWORK-NSEL, INFQR )
CALL PSLAMVE( 'All', JW+IROFFH, JW+IROFFH, WORK(IPT0), 1,
$ 1, DESCTZ0, T, 1, 1, DESCT, WORK(IPW0) )
CALL PSLAMVE( 'All', JW+IROFFH, JW+IROFFH, WORK(IPZ0), 1,
$ 1, DESCTZ0, V, 1, 1, DESCV, WORK(IPW0) )
END IF
END IF
ELSE
*
* The AED window is too small.
* Redistribute the AED window to a subgrid
* and do the computation on the subgrid.
*
ICTXT_NEW = ICTXT
DO 20 I = 0, NPMIN-1
DO 10 J = 0, NPMIN-1
PMAP( J+1+I*NPMIN ) = BLACS_PNUM( ICTXT, I, J )
10 CONTINUE
20 CONTINUE
CALL BLACS_GRIDMAP( ICTXT_NEW, PMAP, NPMIN, NPMIN, NPMIN )
CALL BLACS_GRIDINFO( ICTXT_NEW, NPMIN, NPMIN, MYROW_NEW,
$ MYCOL_NEW )
IF( MYROW.GE.NPMIN .OR. MYCOL.GE.NPMIN ) ICTXT_NEW = -1
IF( ICTXT_NEW.GE.0 ) THEN
TZROWS0 = NUMROC( JW, NB, MYROW_NEW, 0, NPMIN )
TZCOLS0 = NUMROC( JW, NB, MYCOL_NEW, 0, NPMIN )
CALL DESCINIT( DESCTZ0, JW, JW, NB, NB, 0,
$ 0, ICTXT_NEW, MAX(1,TZROWS0), IERR0 )
IPT0 = 1
IPZ0 = IPT0 + MAX(1,TZROWS0)*MAX(1,TZCOLS0)
IPW0 = IPZ0 + MAX(1,TZROWS0)*MAX(1,TZCOLS0)
ELSE
IPT0 = 1
IPZ0 = 2
IPW0 = 3
DESCTZ0( CTXT_ ) = -1
INFQR = 0
END IF
CALL PSGEMR2D( JW, JW, T, 1+IROFFH, 1+IROFFH, DESCT,
$ WORK(IPT0), 1, 1, DESCTZ0, ICTXT )
IF( ICTXT_NEW.GE.0 ) THEN
CALL PSLASET( 'All', JW, JW, ZERO, ONE, WORK(IPZ0), 1, 1,
$ DESCTZ0 )
NMIN = PILAENVX( ICTXT_NEW, 12, 'PSLAQR3', 'SV', JW, 1, JW,
$ LWORK )
IF( JW.GT.NMIN .AND. JW.LE.NMAX .AND. RECLEVEL.LT.1 ) THEN
CALL PSLAQR0( .TRUE., .TRUE., JW, 1, JW, WORK(IPT0),
$ DESCTZ0, SR( KWTOP ), SI( KWTOP ), 1, JW,
$ WORK(IPZ0), DESCTZ0, WORK(IPW0), LWORK-IPW0+1,
$ IWORK(NSEL+1), LIWORK-NSEL, INFQR,
$ RECLEVEL+1 )
ELSE
CALL PSLAQR1( .TRUE., .TRUE., JW, 1, JW, WORK(IPT0),
$ DESCTZ0, SR( KWTOP ), SI( KWTOP ), 1, JW,
$ WORK(IPZ0), DESCTZ0, WORK(IPW0), LWORK-IPW0+1,
$ IWORK(NSEL+1), LIWORK-NSEL, INFQR )
END IF
END IF
CALL PSGEMR2D( JW, JW, WORK(IPT0), 1, 1, DESCTZ0, T, 1+IROFFH,
$ 1+IROFFH, DESCT, ICTXT )
CALL PSGEMR2D( JW, JW, WORK(IPZ0), 1, 1, DESCTZ0, V, 1+IROFFH,
$ 1+IROFFH, DESCV, ICTXT )
IF( ICTXT_NEW.GE.0 )
$ CALL BLACS_GRIDEXIT( ICTXT_NEW )
IF( MYROW+MYCOL.GT.0 ) THEN
DO 40 J = 0, JW-1
SR( KWTOP+J ) = ZERO
SI( KWTOP+J ) = ZERO
40 CONTINUE
END IF
CALL IGAMN2D( ICTXT, 'All', '1-Tree', 1, 1, INFQR, 1, -1, -1,
$ -1, -1, -1 )
CALL SGSUM2D( ICTXT, 'All', ' ', JW, 1, SR(KWTOP), JW, -1, -1 )
CALL SGSUM2D( ICTXT, 'All', ' ', JW, 1, SI(KWTOP), JW, -1, -1 )
END IF
*
* Adjust INFQR for offset from block border in submatrices.
*
IF( INFQR.NE.0 )
$ INFQR = INFQR - IROFFH
*
* PSTRORD needs a clean margin near the diagonal.
*
DO 50 J = 1, JW - 3
CALL PSELSET( T, J+2, J, DESCT, ZERO )
CALL PSELSET( T, J+3, J, DESCT, ZERO )
50 CONTINUE
IF( JW.GT.2 )
$ CALL PSELSET( T, JW, JW-2, DESCT, ZERO )
*
* Check local residual for AED Schur decomposition.
*
RESAED = 0.0
*
* Clean up the array SELECT for PSTRORD.
*
DO 60 J = 1, NSEL
IWORK( J ) = 0
60 CONTINUE
*
* Set local M counter to zero.
*
MLOC = 0
*
* Outer deflation detection loop (label 80).
* In this loop a bunch of undeflatable eigenvalues
* are moved simultaneously.
*
DO 70 J = 1, IROFFH + INFQR
IWORK( J ) = 1
70 CONTINUE
*
NS = JW
ILST = INFQR + 1 + IROFFH
IF( ILST.GT.1 ) THEN
CALL PSELGET( 'All', '1-Tree', ELEM, T, ILST, ILST-1, DESCT )
BULGE = ELEM.NE.ZERO
IF( BULGE ) ILST = ILST+1
END IF
*
80 CONTINUE
IF( ILST.LE.NS+IROFFH ) THEN
*
* Find the top-left corner of the local window.
*
LILST = MAX(ILST,NS+IROFFH-NB+1)
IF( LILST.GT.1 ) THEN
CALL PSELGET( 'All', '1-Tree', ELEM, T, LILST, LILST-1,
$ DESCT )
BULGE = ELEM.NE.ZERO
IF( BULGE ) LILST = LILST+1
END IF
*
* Lock all eigenvalues outside the local window.
*
DO 90 J = IROFFH+1, LILST-1
IWORK( J ) = 1
90 CONTINUE
LILST0 = LILST
*
* Inner deflation detection loop (label 100).
* In this loop, the undeflatable eigenvalues are moved to the
* top-left corner of the local window.
*
100 CONTINUE
IF( LILST.LE.NS+IROFFH ) THEN
IF( NS.EQ.1 ) THEN
BULGE = .FALSE.
ELSE
CALL PSELGET( 'All', '1-Tree', ELEM, T, NS+IROFFH,
$ NS+IROFFH-1, DESCT )
BULGE = ELEM.NE.ZERO
END IF
*
* Small spike tip test for deflation.
*
IF( .NOT.BULGE ) THEN
*
* Real eigenvalue.
*
CALL PSELGET( 'All', '1-Tree', ELEM, T, NS+IROFFH,
$ NS+IROFFH, DESCT )
FOO = ABS( ELEM )
IF( FOO.EQ.ZERO )
$ FOO = ABS( S )
CALL PSELGET( 'All', '1-Tree', ELEM, V, 1+IROFFH,
$ NS+IROFFH, DESCV )
IF( ABS( S*ELEM ).LE.MAX( SMLNUM, ULP*FOO ) ) THEN
*
* Deflatable.
*
NS = NS - 1
ELSE
*
* Undeflatable: move it up out of the way.
*
IFST = NS
DO 110 J = LILST, JW+IROFFH
IWORK( J ) = 0
110 CONTINUE
IWORK( IFST+IROFFH ) = 1
CALL PSTRORD( 'Vectors', IWORK, PAR, JW+IROFFH, T, 1,
$ 1, DESCT, V, 1, 1, DESCV, WORK,
$ WORK(JW+IROFFH+1), MLOC,
$ WORK(2*(JW+IROFFH)+1), LWORK-2*(JW+IROFFH),
$ IWORK(NSEL+1), LIWORK-NSEL, INFO )
*
* Adjust the array SELECT explicitly so that it does not
* rely on the output of PSTRORD.
*
IWORK( IFST+IROFFH ) = 0
IWORK( LILST ) = 1
LILST = LILST + 1
*
* In case of a rare exchange failure, adjust the
* pointers ILST and LILST to the current place to avoid
* unexpected behaviors.
*
IF( INFO.NE.0 ) THEN
LILST = MAX(INFO, LILST)
ILST = MAX(INFO, ILST)
END IF
END IF
ELSE
*
* Complex conjugate pair.
*
CALL PSELGET( 'All', '1-Tree', ELEM1, T, NS+IROFFH,
$ NS+IROFFH, DESCT )
CALL PSELGET( 'All', '1-Tree', ELEM2, T, NS+IROFFH,
$ NS+IROFFH-1, DESCT )
CALL PSELGET( 'All', '1-Tree', ELEM3, T, NS+IROFFH-1,
$ NS+IROFFH, DESCT )
FOO = ABS( ELEM1 ) + SQRT( ABS( ELEM2 ) )*
$ SQRT( ABS( ELEM3 ) )
IF( FOO.EQ.ZERO )
$ FOO = ABS( S )
CALL PSELGET( 'All', '1-Tree', ELEM1, V, 1+IROFFH,
$ NS+IROFFH, DESCV )
CALL PSELGET( 'All', '1-Tree', ELEM2, V, 1+IROFFH,
$ NS+IROFFH-1, DESCV )
IF( MAX( ABS( S*ELEM1 ), ABS( S*ELEM2 ) ).LE.
$ MAX( SMLNUM, ULP*FOO ) ) THEN
*
* Deflatable.
*
NS = NS - 2
ELSE
*
* Undeflatable: move them up out of the way.
*
IFST = NS
DO 120 J = LILST, JW+IROFFH
IWORK( J ) = 0
120 CONTINUE
IWORK( IFST+IROFFH ) = 1
IWORK( IFST+IROFFH-1 ) = 1
CALL PSTRORD( 'Vectors', IWORK, PAR, JW+IROFFH, T, 1,
$ 1, DESCT, V, 1, 1, DESCV, WORK,
$ WORK(JW+IROFFH+1), MLOC,
$ WORK(2*(JW+IROFFH)+1), LWORK-2*(JW+IROFFH),
$ IWORK(NSEL+1), LIWORK-NSEL, INFO )
*
* Adjust the array SELECT explicitly so that it does not
* rely on the output of PSTRORD.
*
IWORK( IFST+IROFFH ) = 0
IWORK( IFST+IROFFH-1 ) = 0
IWORK( LILST ) = 1
IWORK( LILST+1 ) = 1
LILST = LILST + 2
*
* In case of a rare exchange failure, adjust the
* pointers ILST and LILST to the current place to avoid
* unexpected behaviors.
*
IF( INFO.NE.0 ) THEN
LILST = MAX(INFO, LILST)
ILST = MAX(INFO, ILST)
END IF
END IF
END IF
*
* End of inner deflation detection loop.
*
GO TO 100
END IF
*
* Unlock the eigenvalues outside the local window.
* Then undeflatable eigenvalues are moved to the proper position.
*
DO 130 J = ILST, LILST0-1
IWORK( J ) = 0
130 CONTINUE
CALL PSTRORD( 'Vectors', IWORK, PAR, JW+IROFFH, T, 1, 1,
$ DESCT, V, 1, 1, DESCV, WORK, WORK(JW+IROFFH+1),
$ M, WORK(2*(JW+IROFFH)+1), LWORK-2*(JW+IROFFH),
$ IWORK(NSEL+1), LIWORK-NSEL, INFO )
ILST = M + 1
*
* In case of a rare exchange failure, adjust the pointer ILST to
* the current place to avoid unexpected behaviors.
*
IF( INFO.NE.0 )
$ ILST = MAX(INFO, ILST)
*
* End of outer deflation detection loop.
*
GO TO 80
END IF
*
* Post-reordering step: copy output eigenvalues to output.
*
CALL SCOPY( JW, WORK(1+IROFFH), 1, SR( KWTOP ), 1 )
CALL SCOPY( JW, WORK(JW+2*IROFFH+1), 1, SI( KWTOP ), 1 )
*
* Check local residual for reordered AED Schur decomposition.
*
RESAED = 0.0
*
* Return to Hessenberg form.
*
IF( NS.EQ.0 )
$ S = ZERO
*
IF( NS.LT.JW .AND. SORTGRAD ) THEN
*
* Sorting diagonal blocks of T improves accuracy for
* graded matrices. Bubble sort deals well with exchange
* failures. Eigenvalues/shifts from T are also restored.
*
ROUND = 0
SORTED = .FALSE.
I = NS + 1 + IROFFH
140 CONTINUE
IF( SORTED )
$ GO TO 180
SORTED = .TRUE.
ROUND = ROUND + 1
*
KEND = I - 1
I = INFQR + 1 + IROFFH
IF( I.EQ.NS+IROFFH ) THEN
K = I + 1
ELSE IF( SI( KWTOP-IROFFH + I-1 ).EQ.ZERO ) THEN
K = I + 1
ELSE
K = I + 2
END IF
150 CONTINUE
IF( K.LE.KEND ) THEN
IF( K.EQ.I+1 ) THEN
EVI = ABS( SR( KWTOP-IROFFH+I-1 ) )
ELSE
EVI = ABS( SR( KWTOP-IROFFH+I-1 ) ) +
$ ABS( SI( KWTOP-IROFFH+I-1 ) )
END IF
*
IF( K.EQ.KEND ) THEN
EVK = ABS( SR( KWTOP-IROFFH+K-1 ) )
ELSEIF( SI( KWTOP-IROFFH+K-1 ).EQ.ZERO ) THEN
EVK = ABS( SR( KWTOP-IROFFH+K-1 ) )
ELSE
EVK = ABS( SR( KWTOP-IROFFH+K-1 ) ) +
$ ABS( SI( KWTOP-IROFFH+K-1 ) )
END IF
*
IF( EVI.GE.EVK ) THEN
I = K
ELSE
MLOC = 0
SORTED = .FALSE.
IFST = I
ILST = K
DO 160 J = 1, I-1
IWORK( J ) = 1
MLOC = MLOC + 1
160 CONTINUE
IF( K.EQ.I+2 ) THEN
IWORK( I ) = 0
IWORK(I+1) = 0
ELSE
IWORK( I ) = 0
END IF
IF( K.NE.KEND .AND. SI( KWTOP-IROFFH+K-1 ).NE.ZERO ) THEN
IWORK( K ) = 1
IWORK(K+1) = 1
MLOC = MLOC + 2
ELSE
IWORK( K ) = 1
IF( K.LT.KEND ) IWORK(K+1) = 0
MLOC = MLOC + 1
END IF
DO 170 J = K+2, JW+IROFFH
IWORK( J ) = 0
170 CONTINUE
CALL PSTRORD( 'Vectors', IWORK, PAR, JW+IROFFH, T, 1, 1,
$ DESCT, V, 1, 1, DESCV, WORK, WORK(JW+IROFFH+1), M,
$ WORK(2*(JW+IROFFH)+1), LWORK-2*(JW+IROFFH),
$ IWORK(NSEL+1), LIWORK-NSEL, IERR )
CALL SCOPY( JW, WORK(1+IROFFH), 1, SR( KWTOP ), 1 )
CALL SCOPY( JW, WORK(JW+2*IROFFH+1), 1, SI( KWTOP ), 1 )
IF( IERR.EQ.0 ) THEN
I = ILST
ELSE
I = K
END IF
END IF
IF( I.EQ.KEND ) THEN
K = I + 1
ELSE IF( SI( KWTOP-IROFFH+I-1 ).EQ.ZERO ) THEN
K = I + 1
ELSE
K = I + 2
END IF
GO TO 150
END IF
GO TO 140
180 CONTINUE
END IF
*
* Restore number of rows and columns of T matrix descriptor.
*
DESCT( M_ ) = NW+IROFFH
DESCT( N_ ) = NH+IROFFH
*
IF( NS.LT.JW .OR. S.EQ.ZERO ) THEN
IF( NS.GT.1 .AND. S.NE.ZERO ) THEN
*
* Reflect spike back into lower triangle.
*
RROWS = NUMROC( NS+IROFFH, NB, MYROW, DESCV(RSRC_), NPROW )
RCOLS = NUMROC( 1, 1, MYCOL, DESCV(CSRC_), NPCOL )
CALL DESCINIT( DESCR, NS+IROFFH, 1, NB, 1, DESCV(RSRC_),
$ DESCV(CSRC_), ICTXT, MAX(1, RROWS), INFO )
TAUROWS = NUMROC( 1, 1, MYCOL, DESCV(RSRC_), NPROW )
TAUCOLS = NUMROC( JW+IROFFH, NB, MYCOL, DESCV(CSRC_),
$ NPCOL )
CALL DESCINIT( DESCTAU, 1, JW+IROFFH, 1, NB, DESCV(RSRC_),
$ DESCV(CSRC_), ICTXT, MAX(1, TAUROWS), INFO )
*
IR = 1
ITAU = IR + DESCR( LLD_ ) * RCOLS
IPW = ITAU + DESCTAU( LLD_ ) * TAUCOLS
*
CALL PSLASET( 'All', NS+IROFFH, 1, ZERO, ZERO, WORK(ITAU),
$ 1, 1, DESCTAU )
*
CALL PSCOPY( NS, V, 1+IROFFH, 1+IROFFH, DESCV, DESCV(M_),
$ WORK(IR), 1+IROFFH, 1, DESCR, 1 )
CALL PSLARFG( NS, BETA, 1+IROFFH, 1, WORK(IR), 2+IROFFH, 1,
$ DESCR, 1, WORK(ITAU+IROFFH) )
CALL PSELSET( WORK(IR), 1+IROFFH, 1, DESCR, ONE )
*
CALL PSLASET( 'Lower', JW-2, JW-2, ZERO, ZERO, T, 3+IROFFH,
$ 1+IROFFH, DESCT )
*
CALL PSLARF( 'Left', NS, JW, WORK(IR), 1+IROFFH, 1, DESCR,
$ 1, WORK(ITAU+IROFFH), T, 1+IROFFH, 1+IROFFH,
$ DESCT, WORK( IPW ) )
CALL PSLARF( 'Right', NS, NS, WORK(IR), 1+IROFFH, 1, DESCR,
$ 1, WORK(ITAU+IROFFH), T, 1+IROFFH, 1+IROFFH,
$ DESCT, WORK( IPW ) )
CALL PSLARF( 'Right', JW, NS, WORK(IR), 1+IROFFH, 1, DESCR,
$ 1, WORK(ITAU+IROFFH), V, 1+IROFFH, 1+IROFFH,
$ DESCV, WORK( IPW ) )
*
ITAU = 1
IPW = ITAU + DESCTAU( LLD_ ) * TAUCOLS
CALL PSGEHRD( JW+IROFFH, 1+IROFFH, NS+IROFFH, T, 1, 1,
$ DESCT, WORK(ITAU), WORK( IPW ), LWORK-IPW+1, INFO )
END IF
*
* Copy updated reduced window into place.
*
IF( KWTOP.GT.1 ) THEN
CALL PSELGET( 'All', '1-Tree', ELEM, V, 1+IROFFH,
$ 1+IROFFH, DESCV )
CALL PSELSET( H, KWTOP, KWTOP-1, DESCH, S*ELEM )
END IF
CALL PSLACPY( 'Upper', JW-1, JW-1, T, 1+IROFFH+1, 1+IROFFH,
$ DESCT, H, KWTOP+1, KWTOP, DESCH )
CALL PSLACPY( 'All', 1, JW, T, 1+IROFFH, 1+IROFFH, DESCT, H,
$ KWTOP, KWTOP, DESCH )
CALL PSLACPY( 'All', JW-1, 1, T, 1+IROFFH+1, 1+IROFFH+JW-1,
$ DESCT, H, KWTOP+1, KWTOP+JW-1, DESCH )
*
* Accumulate orthogonal matrix in order to update
* H and Z, if requested.
*
IF( NS.GT.1 .AND. S.NE.ZERO ) THEN
CALL PSORMHR( 'Right', 'No', JW+IROFFH, NS+IROFFH, 1+IROFFH,
$ NS+IROFFH, T, 1, 1, DESCT, WORK(ITAU), V, 1,
$ 1, DESCV, WORK( IPW ), LWORK-IPW+1, INFO )
END IF
*
* Update vertical slab in H.
*
IF( WANTT ) THEN
LTOP = 1
ELSE
LTOP = KTOP
END IF
KLN = MAX( 0, KWTOP-LTOP )
IROFFHH = MOD( LTOP-1, NB )
ICOFFHH = MOD( KWTOP-1, NB )
HHRSRC = INDXG2P( LTOP, NB, MYROW, DESCH(RSRC_), NPROW )
HHCSRC = INDXG2P( KWTOP, NB, MYCOL, DESCH(CSRC_), NPCOL )
HHROWS = NUMROC( KLN+IROFFHH, NB, MYROW, HHRSRC, NPROW )
HHCOLS = NUMROC( JW+ICOFFHH, NB, MYCOL, HHCSRC, NPCOL )
CALL DESCINIT( DESCHH, KLN+IROFFHH, JW+ICOFFHH, NB, NB,
$ HHRSRC, HHCSRC, ICTXT, MAX(1, HHROWS), IERR )
CALL PSGEMM( 'No', 'No', KLN, JW, JW, ONE, H, LTOP,
$ KWTOP, DESCH, V, 1+IROFFH, 1+IROFFH, DESCV, ZERO,
$ WORK, 1+IROFFHH, 1+ICOFFHH, DESCHH )
CALL PSLACPY( 'All', KLN, JW, WORK, 1+IROFFHH, 1+ICOFFHH,
$ DESCHH, H, LTOP, KWTOP, DESCH )
*
* Update horizontal slab in H.
*
IF( WANTT ) THEN
KLN = N-KBOT
IROFFHH = MOD( KWTOP-1, NB )
ICOFFHH = MOD( KBOT, NB )
HHRSRC = INDXG2P( KWTOP, NB, MYROW, DESCH(RSRC_), NPROW )
HHCSRC = INDXG2P( KBOT+1, NB, MYCOL, DESCH(CSRC_), NPCOL )
HHROWS = NUMROC( JW+IROFFHH, NB, MYROW, HHRSRC, NPROW )
HHCOLS = NUMROC( KLN+ICOFFHH, NB, MYCOL, HHCSRC, NPCOL )
CALL DESCINIT( DESCHH, JW+IROFFHH, KLN+ICOFFHH, NB, NB,
$ HHRSRC, HHCSRC, ICTXT, MAX(1, HHROWS), IERR )
CALL PSGEMM( 'Tr', 'No', JW, KLN, JW, ONE, V,
$ 1+IROFFH, 1+IROFFH, DESCV, H, KWTOP, KBOT+1,
$ DESCH, ZERO, WORK, 1+IROFFHH, 1+ICOFFHH, DESCHH )
CALL PSLACPY( 'All', JW, KLN, WORK, 1+IROFFHH, 1+ICOFFHH,
$ DESCHH, H, KWTOP, KBOT+1, DESCH )
END IF
*
* Update vertical slab in Z.
*
IF( WANTZ ) THEN
KLN = IHIZ-ILOZ+1
IROFFZZ = MOD( ILOZ-1, NB )
ICOFFZZ = MOD( KWTOP-1, NB )
ZZRSRC = INDXG2P( ILOZ, NB, MYROW, DESCZ(RSRC_), NPROW )
ZZCSRC = INDXG2P( KWTOP, NB, MYCOL, DESCZ(CSRC_), NPCOL )
ZZROWS = NUMROC( KLN+IROFFZZ, NB, MYROW, ZZRSRC, NPROW )
ZZCOLS = NUMROC( JW+ICOFFZZ, NB, MYCOL, ZZCSRC, NPCOL )
CALL DESCINIT( DESCZZ, KLN+IROFFZZ, JW+ICOFFZZ, NB, NB,
$ ZZRSRC, ZZCSRC, ICTXT, MAX(1, ZZROWS), IERR )
CALL PSGEMM( 'No', 'No', KLN, JW, JW, ONE, Z, ILOZ,
$ KWTOP, DESCZ, V, 1+IROFFH, 1+IROFFH, DESCV,
$ ZERO, WORK, 1+IROFFZZ, 1+ICOFFZZ, DESCZZ )
CALL PSLACPY( 'All', KLN, JW, WORK, 1+IROFFZZ, 1+ICOFFZZ,
$ DESCZZ, Z, ILOZ, KWTOP, DESCZ )
END IF
END IF
*
* Return the number of deflations (ND) and the number of shifts (NS).
* (Subtracting INFQR from the spike length takes care of the case of
* a rare QR failure while calculating eigenvalues of the deflation
* window.)
*
ND = JW - NS
NS = NS - INFQR
*
* Return optimal workspace.
*
WORK( 1 ) = FLOAT( LWKOPT )
IWORK( 1 ) = ILWKOPT + NSEL
*
* End of PSLAQR3
*
END
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