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SUBROUTINE PSLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, A, DESCA,
$ ILOZ, IHIZ, Z, DESCZ, NS, ND, SR, SI, T, LDT,
$ V, LDV, WR, WI, WORK, LWORK )
*
* Contribution from the Department of Computing Science and HPC2N,
* Umea University, Sweden
*
* -- ScaLAPACK routine (version 2.0.2) --
* Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
* May 1 2012
*
IMPLICIT NONE
*
* .. Scalar Arguments ..
INTEGER IHIZ, ILOZ, KBOT, KTOP, LDT, LDV, LWORK, N, ND,
$ NS, NW
LOGICAL WANTT, WANTZ
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCZ( * )
REAL A( * ), SI( KBOT ), SR( KBOT ), T( LDT, * ),
$ V( LDV, * ), WORK( * ), WI( * ), WR( * ),
$ Z( * )
* ..
*
* Purpose
* =======
*
* Aggressive early deflation:
*
* PSLAQR2 accepts as input an upper Hessenberg matrix A and performs an
* orthogonal similarity transformation designed to detect and deflate
* fully converged eigenvalues from a trailing principal submatrix. On
* output A has been overwritten by a new Hessenberg matrix that is a
* perturbation of an orthogonal similarity transformation of A. It is
* to be hoped that the final version of H has many zero subdiagonal
* entries.
*
* This routine handles small deflation windows which is affordable by
* one processor. Normally, it is called by PSLAQR1. All the inputs are
* assumed to be valid without checking.
*
* 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
* 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. However, H(KTOP,KTOP-1)=0 is not
* essentially necessary if WANTT is .TRUE. .
*
* NW (global input) INTEGER
* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).
* Normally NW .GE. 3 if PSLAQR2 is called by PSLAQR1.
*
* A (local input/output) REAL array, dimension
* (DESCH(LLD_),*)
* On input the initial N-by-N section of A stores the
* Hessenberg matrix undergoing aggressive early deflation.
* On output A 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.
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* 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.
* On proc #0, 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. On other
* processors, these entries are set to zero.
*
* T (local workspace) REAL array, dimension LDT*NW.
*
* LDT (local input) INTEGER
* The leading dimension of the array T.
* LDT >= NW.
*
* V (local workspace) REAL array, dimension LDV*NW.
*
* LDV (local input) INTEGER
* The leading dimension of the array V.
* LDV >= NW.
*
* WR (local workspace) REAL array, dimension KBOT.
* WI (local workspace) REAL array, dimension KBOT.
*
* WORK (local workspace) REAL array, dimension LWORK.
*
* LWORK (local input) INTEGER
* WORK(LWORK) is a local array and LWORK is assumed big enough
* so that LWORK >= NW*NW.
*
* ================================================================
* Implemented by
* Meiyue Shao, Department of Computing Science and HPC2N,
* Umea University, Sweden
*
* ================================================================
* References:
* B. Kagstrom, D. Kressner, and M. Shao,
* On Aggressive Early Deflation in Parallel Variants of the QR
* Algorithm.
* Para 2010, to appear.
*
* ================================================================
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
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
PARAMETER ( ZERO = 0.0, ONE = 1.0 )
* ..
* .. Local Scalars ..
INTEGER CONTXT, HBL, I, I1, I2, IAFIRST, ICOL, ICOL1,
$ ICOL2, INFO, II, IROW, IROW1, IROW2, ITMP1,
$ ITMP2, J, JAFIRST, JJ, K, L, LDA, LDZ, LLDTMP,
$ MYCOL, MYROW, NODE, NPCOL, NPROW, DBLK,
$ HSTEP, VSTEP, KKROW, KKCOL, KLN, LTOP, LEFT,
$ RIGHT, UP, DOWN, D1, D2
* ..
* .. Local Arrays ..
INTEGER DESCT( 9 ), DESCV( 9 ), DESCWH( 9 ),
$ DESCWV( 9 )
* ..
* .. External Functions ..
INTEGER NUMROC
EXTERNAL NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, SLASET,
$ SLAQR3, DESCINIT, PSGEMM, PSGEMR2D, SGEMM,
$ SLAMOV, SGESD2D, SGERV2D, SGEBS2D, SGEBR2D,
$ IGEBS2D, IGEBR2D
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
INFO = 0
*
IF( N.EQ.0 )
$ RETURN
*
* NODE (IAFIRST,JAFIRST) OWNS A(1,1)
*
HBL = DESCA( MB_ )
CONTXT = DESCA( CTXT_ )
LDA = DESCA( LLD_ )
IAFIRST = DESCA( RSRC_ )
JAFIRST = DESCA( CSRC_ )
LDZ = DESCZ( LLD_ )
CALL BLACS_GRIDINFO( CONTXT, NPROW, NPCOL, MYROW, MYCOL )
NODE = MYROW*NPCOL + MYCOL
LEFT = MOD( MYCOL+NPCOL-1, NPCOL )
RIGHT = MOD( MYCOL+1, NPCOL )
UP = MOD( MYROW+NPROW-1, NPROW )
DOWN = MOD( MYROW+1, NPROW )
*
* I1 and I2 are the indices of the first row and last column of A
* to which transformations must be applied.
*
I = KBOT
L = KTOP
IF( WANTT ) THEN
I1 = 1
I2 = N
LTOP = 1
ELSE
I1 = L
I2 = I
LTOP = L
END IF
*
* Begin Aggressive Early Deflation.
*
DBLK = NW
CALL INFOG2L( I-DBLK+1, I-DBLK+1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF ( MYROW .EQ. II ) THEN
CALL DESCINIT( DESCT, DBLK, DBLK, DBLK, DBLK, II, JJ, CONTXT,
$ LDT, INFO )
CALL DESCINIT( DESCV, DBLK, DBLK, DBLK, DBLK, II, JJ, CONTXT,
$ LDV, INFO )
ELSE
CALL DESCINIT( DESCT, DBLK, DBLK, DBLK, DBLK, II, JJ, CONTXT,
$ 1, INFO )
CALL DESCINIT( DESCV, DBLK, DBLK, DBLK, DBLK, II, JJ, CONTXT,
$ 1, INFO )
END IF
CALL PSGEMR2D( DBLK, DBLK, A, I-DBLK+1, I-DBLK+1, DESCA, T, 1, 1,
$ DESCT, CONTXT )
IF ( MYROW .EQ. II .AND. MYCOL .EQ. JJ ) THEN
CALL SLASET( 'All', DBLK, DBLK, ZERO, ONE, V, LDV )
CALL SLAQR3( .TRUE., .TRUE., DBLK, 1, DBLK, DBLK-1, T, LDT, 1,
$ DBLK, V, LDV, NS, ND, WR, WI, WORK, DBLK, DBLK,
$ WORK( DBLK*DBLK+1 ), DBLK, DBLK, WORK( 2*DBLK*DBLK+1 ),
$ DBLK, WORK( 3*DBLK*DBLK+1 ), LWORK-3*DBLK*DBLK )
CALL SGEBS2D( CONTXT, 'All', ' ', DBLK, DBLK, V, LDV )
CALL IGEBS2D( CONTXT, 'All', ' ', 1, 1, ND, 1 )
ELSE
CALL SGEBR2D( CONTXT, 'All', ' ', DBLK, DBLK, V, LDV, II, JJ )
CALL IGEBR2D( CONTXT, 'All', ' ', 1, 1, ND, 1, II, JJ )
END IF
*
IF( ND .GT. 0 ) THEN
*
* Copy the local matrix back to the diagonal block.
*
CALL PSGEMR2D( DBLK, DBLK, T, 1, 1, DESCT, A, I-DBLK+1,
$ I-DBLK+1, DESCA, CONTXT )
*
* Update T and Z.
*
IF( MOD( I-DBLK, HBL )+DBLK .LE. HBL ) THEN
*
* Simplest case: the deflation window is located on one
* processor.
* Call SGEMM directly to perform the update.
*
HSTEP = LWORK / DBLK
VSTEP = HSTEP
*
* Update horizontal slab in A.
*
IF( WANTT ) THEN
CALL INFOG2L( I-DBLK+1, I+1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYROW .EQ. II ) THEN
ICOL1 = NUMROC( N, HBL, MYCOL, JAFIRST, NPCOL )
DO 10 KKCOL = ICOL, ICOL1, HSTEP
KLN = MIN( HSTEP, ICOL1-KKCOL+1 )
CALL SGEMM( 'T', 'N', DBLK, KLN, DBLK, ONE, V,
$ LDV, A( IROW+(KKCOL-1)*LDA ), LDA, ZERO, WORK,
$ DBLK )
CALL SLAMOV( 'A', DBLK, KLN, WORK, DBLK,
$ A( IROW+(KKCOL-1)*LDA ), LDA )
10 CONTINUE
END IF
END IF
*
* Update vertical slab in A.
*
CALL INFOG2L( LTOP, I-DBLK+1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( I-DBLK, I-DBLK+1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 20 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA, V, LDV, ZERO, WORK,
$ KLN )
CALL SLAMOV( 'A', KLN, DBLK, WORK, KLN,
$ A( KKROW+(ICOL-1)*LDA ), LDA )
20 CONTINUE
END IF
*
* Update vertical slab in Z.
*
IF( WANTZ ) THEN
CALL INFOG2L( ILOZ, I-DBLK+1, DESCZ, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( IHIZ, I-DBLK+1, DESCZ, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 30 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ, V, LDV, ZERO,
$ WORK, KLN )
CALL SLAMOV( 'A', KLN, DBLK, WORK, KLN,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ )
30 CONTINUE
END IF
END IF
*
ELSE IF( MOD( I-DBLK, HBL )+DBLK .LE. 2*HBL ) THEN
*
* More complicated case: the deflation window lay on a 2x2
* processor mesh.
* Call SGEMM locally and communicate by pair.
*
D1 = HBL - MOD( I-DBLK, HBL )
D2 = DBLK - D1
HSTEP = LWORK / DBLK
VSTEP = HSTEP
*
* Update horizontal slab in A.
*
IF( WANTT ) THEN
CALL INFOG2L( I-DBLK+1, I+1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYROW .EQ. UP ) THEN
IF( MYROW .EQ. II ) THEN
ICOL1 = NUMROC( N, HBL, MYCOL, JAFIRST, NPCOL )
DO 40 KKCOL = ICOL, ICOL1, HSTEP
KLN = MIN( HSTEP, ICOL1-KKCOL+1 )
CALL SGEMM( 'T', 'N', DBLK, KLN, DBLK, ONE, V,
$ DBLK, A( IROW+(KKCOL-1)*LDA ), LDA, ZERO,
$ WORK, DBLK )
CALL SLAMOV( 'A', DBLK, KLN, WORK, DBLK,
$ A( IROW+(KKCOL-1)*LDA ), LDA )
40 CONTINUE
END IF
ELSE
IF( MYROW .EQ. II ) THEN
ICOL1 = NUMROC( N, HBL, MYCOL, JAFIRST, NPCOL )
DO 50 KKCOL = ICOL, ICOL1, HSTEP
KLN = MIN( HSTEP, ICOL1-KKCOL+1 )
CALL SGEMM( 'T', 'N', D2, KLN, D1, ONE,
$ V( 1, D1+1 ), LDV, A( IROW+(KKCOL-1)*LDA ),
$ LDA, ZERO, WORK( D1+1 ), DBLK )
CALL SGESD2D( CONTXT, D2, KLN, WORK( D1+1 ),
$ DBLK, DOWN, MYCOL )
CALL SGERV2D( CONTXT, D1, KLN, WORK, DBLK, DOWN,
$ MYCOL )
CALL SGEMM( 'T', 'N', D1, KLN, D1, ONE,
$ V, LDV, A( IROW+(KKCOL-1)*LDA ), LDA, ONE,
$ WORK, DBLK )
CALL SLAMOV( 'A', D1, KLN, WORK, DBLK,
$ A( IROW+(KKCOL-1)*LDA ), LDA )
50 CONTINUE
ELSE IF( UP .EQ. II ) THEN
ICOL1 = NUMROC( N, HBL, MYCOL, JAFIRST, NPCOL )
DO 60 KKCOL = ICOL, ICOL1, HSTEP
KLN = MIN( HSTEP, ICOL1-KKCOL+1 )
CALL SGEMM( 'T', 'N', D1, KLN, D2, ONE,
$ V( D1+1, 1 ), LDV, A( IROW+(KKCOL-1)*LDA ),
$ LDA, ZERO, WORK, DBLK )
CALL SGESD2D( CONTXT, D1, KLN, WORK, DBLK, UP,
$ MYCOL )
CALL SGERV2D( CONTXT, D2, KLN, WORK( D1+1 ),
$ DBLK, UP, MYCOL )
CALL SGEMM( 'T', 'N', D2, KLN, D2, ONE,
$ V( D1+1, D1+1 ), LDV,
$ A( IROW+(KKCOL-1)*LDA ), LDA, ONE,
$ WORK( D1+1 ), DBLK )
CALL SLAMOV( 'A', D2, KLN, WORK( D1+1 ), DBLK,
$ A( IROW+(KKCOL-1)*LDA ), LDA )
60 CONTINUE
END IF
END IF
END IF
*
* Update vertical slab in A.
*
CALL INFOG2L( LTOP, I-DBLK+1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYCOL .EQ. LEFT ) THEN
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( I-DBLK, I-DBLK+1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 70 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA, V, LDV, ZERO,
$ WORK, KLN )
CALL SLAMOV( 'A', KLN, DBLK, WORK, KLN,
$ A( KKROW+(ICOL-1)*LDA ), LDA )
70 CONTINUE
END IF
ELSE
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( I-DBLK, I-DBLK+1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 80 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, D2, D1, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA,
$ V( 1, D1+1 ), LDV, ZERO, WORK( 1+D1*KLN ),
$ KLN )
CALL SGESD2D( CONTXT, KLN, D2, WORK( 1+D1*KLN ),
$ KLN, MYROW, RIGHT )
CALL SGERV2D( CONTXT, KLN, D1, WORK, KLN, MYROW,
$ RIGHT )
CALL SGEMM( 'N', 'N', KLN, D1, D1, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA, V, LDV, ONE,
$ WORK, KLN )
CALL SLAMOV( 'A', KLN, D1, WORK, KLN,
$ A( KKROW+(ICOL-1)*LDA ), LDA )
80 CONTINUE
ELSE IF ( LEFT .EQ. JJ ) THEN
CALL INFOG2L( I-DBLK, I-DBLK+1, DESCA, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 90 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, D1, D2, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA, V( D1+1, 1 ),
$ LDV, ZERO, WORK, KLN )
CALL SGESD2D( CONTXT, KLN, D1, WORK, KLN, MYROW,
$ LEFT )
CALL SGERV2D( CONTXT, KLN, D2, WORK( 1+D1*KLN ),
$ KLN, MYROW, LEFT )
CALL SGEMM( 'N', 'N', KLN, D2, D2, ONE,
$ A( KKROW+(ICOL-1)*LDA ), LDA, V( D1+1, D1+1 ),
$ LDV, ONE, WORK( 1+D1*KLN ), KLN )
CALL SLAMOV( 'A', KLN, D2, WORK( 1+D1*KLN ), KLN,
$ A( KKROW+(ICOL-1)*LDA ), LDA )
90 CONTINUE
END IF
END IF
*
* Update vertical slab in Z.
*
IF( WANTZ ) THEN
CALL INFOG2L( ILOZ, I-DBLK+1, DESCZ, NPROW, NPCOL, MYROW,
$ MYCOL, IROW, ICOL, II, JJ )
IF( MYCOL .EQ. LEFT ) THEN
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( IHIZ, I-DBLK+1, DESCZ, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 100 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ, V, LDV, ZERO,
$ WORK, KLN )
CALL SLAMOV( 'A', KLN, DBLK, WORK, KLN,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ )
100 CONTINUE
END IF
ELSE
IF( MYCOL .EQ. JJ ) THEN
CALL INFOG2L( IHIZ, I-DBLK+1, DESCZ, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 110 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, D2, D1, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ,
$ V( 1, D1+1 ), LDV, ZERO, WORK( 1+D1*KLN ),
$ KLN )
CALL SGESD2D( CONTXT, KLN, D2, WORK( 1+D1*KLN ),
$ KLN, MYROW, RIGHT )
CALL SGERV2D( CONTXT, KLN, D1, WORK, KLN, MYROW,
$ RIGHT )
CALL SGEMM( 'N', 'N', KLN, D1, D1, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ, V, LDV, ONE,
$ WORK, KLN )
CALL SLAMOV( 'A', KLN, D1, WORK, KLN,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ )
110 CONTINUE
ELSE IF( LEFT .EQ. JJ ) THEN
CALL INFOG2L( IHIZ, I-DBLK+1, DESCZ, NPROW, NPCOL,
$ MYROW, MYCOL, IROW1, ICOL1, ITMP1, ITMP2 )
IF( MYROW .NE. ITMP1 ) IROW1 = IROW1-1
DO 120 KKROW = IROW, IROW1, VSTEP
KLN = MIN( VSTEP, IROW1-KKROW+1 )
CALL SGEMM( 'N', 'N', KLN, D1, D2, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ,
$ V( D1+1, 1 ), LDV, ZERO, WORK, KLN )
CALL SGESD2D( CONTXT, KLN, D1, WORK, KLN, MYROW,
$ LEFT )
CALL SGERV2D( CONTXT, KLN, D2, WORK( 1+D1*KLN ),
$ KLN, MYROW, LEFT )
CALL SGEMM( 'N', 'N', KLN, D2, D2, ONE,
$ Z( KKROW+(ICOL-1)*LDZ ), LDZ,
$ V( D1+1, D1+1 ), LDV, ONE,
$ WORK( 1+D1*KLN ), KLN )
CALL SLAMOV( 'A', KLN, D2, WORK( 1+D1*KLN ),
$ KLN, Z( KKROW+(ICOL-1)*LDZ ), LDZ )
120 CONTINUE
END IF
END IF
END IF
*
ELSE
*
* Most complicated case: the deflation window lay across the
* border of the processor mesh.
* Treat V as a distributed matrix and call PSGEMM.
*
HSTEP = LWORK / DBLK * NPCOL
VSTEP = LWORK / DBLK * NPROW
LLDTMP = NUMROC( DBLK, DBLK, MYROW, 0, NPROW )
LLDTMP = MAX( 1, LLDTMP )
CALL DESCINIT( DESCV, DBLK, DBLK, DBLK, DBLK, 0, 0, CONTXT,
$ LLDTMP, INFO )
CALL DESCINIT( DESCWH, DBLK, HSTEP, DBLK, LWORK / DBLK, 0,
$ 0, CONTXT, LLDTMP, INFO )
*
* Update horizontal slab in A.
*
IF( WANTT ) THEN
DO 130 KKCOL = I+1, N, HSTEP
KLN = MIN( HSTEP, N-KKCOL+1 )
CALL PSGEMM( 'T', 'N', DBLK, KLN, DBLK, ONE, V, 1, 1,
$ DESCV, A, I-DBLK+1, KKCOL, DESCA, ZERO, WORK, 1,
$ 1, DESCWH )
CALL PSGEMR2D( DBLK, KLN, WORK, 1, 1, DESCWH, A,
$ I-DBLK+1, KKCOL, DESCA, CONTXT )
130 CONTINUE
END IF
*
* Update vertical slab in A.
*
DO 140 KKROW = LTOP, I-DBLK, VSTEP
KLN = MIN( VSTEP, I-DBLK-KKROW+1 )
LLDTMP = NUMROC( KLN, LWORK / DBLK, MYROW, 0, NPROW )
LLDTMP = MAX( 1, LLDTMP )
CALL DESCINIT( DESCWV, KLN, DBLK, LWORK / DBLK, DBLK, 0,
$ 0, CONTXT, LLDTMP, INFO )
CALL PSGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE, A, KKROW,
$ I-DBLK+1, DESCA, V, 1, 1, DESCV, ZERO, WORK, 1, 1,
$ DESCWV )
CALL PSGEMR2D( KLN, DBLK, WORK, 1, 1, DESCWV, A, KKROW,
$ I-DBLK+1, DESCA, CONTXT )
140 CONTINUE
*
* Update vertical slab in Z.
*
IF( WANTZ ) THEN
DO 150 KKROW = ILOZ, IHIZ, VSTEP
KLN = MIN( VSTEP, IHIZ-KKROW+1 )
LLDTMP = NUMROC( KLN, LWORK / DBLK, MYROW, 0, NPROW )
LLDTMP = MAX( 1, LLDTMP )
CALL DESCINIT( DESCWV, KLN, DBLK, LWORK / DBLK, DBLK,
$ 0, 0, CONTXT, LLDTMP, INFO )
CALL PSGEMM( 'N', 'N', KLN, DBLK, DBLK, ONE, Z, KKROW,
$ I-DBLK+1, DESCZ, V, 1, 1, DESCV, ZERO, WORK, 1,
$ 1, DESCWV )
CALL PSGEMR2D( KLN, DBLK, WORK, 1, 1, DESCWV, Z,
$ KKROW, I-DBLK+1, DESCZ, CONTXT )
150 CONTINUE
END IF
END IF
*
* Extract converged eigenvalues.
*
II = 0
160 CONTINUE
IF( II .EQ. ND-1 .OR. WI( DBLK-II ) .EQ. ZERO ) THEN
IF( NODE .EQ. 0 ) THEN
SR( I-II ) = WR( DBLK-II )
ELSE
SR( I-II ) = ZERO
END IF
SI( I-II ) = ZERO
II = II + 1
ELSE
IF( NODE .EQ. 0 ) THEN
SR( I-II-1 ) = WR( DBLK-II-1 )
SR( I-II ) = WR( DBLK-II )
SI( I-II-1 ) = WI( DBLK-II-1 )
SI( I-II ) = WI( DBLK-II )
ELSE
SR( I-II-1 ) = ZERO
SR( I-II ) = ZERO
SI( I-II-1 ) = ZERO
SI( I-II ) = ZERO
END IF
II = II + 2
END IF
IF( II .LT. ND ) GOTO 160
END IF
*
* END OF PSLAQR2
*
END
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