Routine: PDORM2L()  File: SRC\pdorm2l.f

 
 
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..
     .. Array Arguments ..
     ..
  Purpose
  =======
  PDORM2L overwrites the general real M-by-N distributed matrix
  sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with
                      SIDE = 'L'            SIDE = 'R'
  TRANS = 'N':      Q * sub( C )          sub( C ) * Q
  TRANS = 'T':      Q**T * sub( C )       sub( C ) * Q**T
  where Q is a real orthogonal distributed matrix defined as the
  product of K elementary reflectors
        Q = H(k) . . . H(2) H(1)
  as returned by PDGEQLF. Q is of order M if SIDE = 'L' and of order N
  if SIDE = 'R'.
  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
  =========
  SIDE    (global input) CHARACTER
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.
  TRANS   (global input) CHARACTER
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.
  M       (global input) INTEGER
          The number of rows to be operated on i.e the number of rows
          of the distributed submatrix sub( C ). M >= 0.
  N       (global input) INTEGER
          The number of columns to be operated on i.e the number of
          columns of the distributed submatrix sub( C ). N >= 0.
  K       (global input) INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q.  If SIDE = 'L', M >= K >= 0, if SIDE = 'R',
          N >= K >= 0.
  A       (local input) DOUBLE PRECISION pointer into the local memory
          to an array of dimension (LLD_A,LOCc(JA+K-1)). On entry, the
          j-th column must contain the vector which defines the elemen-
          tary reflector H(j), JA <= j <= JA+K-1, as returned by
          PDGEQLF in the K columns of its distributed matrix
          argument A(IA:*,JA:JA+K-1). A(IA:*,JA:JA+K-1) is modified by
          the routine but restored on exit.
          If SIDE = 'L', LLD_A >= MAX( 1, LOCr(IA+M-1) ),
          if SIDE = 'R', LLD_A >= MAX( 1, LOCr(IA+N-1) ).
  IA      (global input) INTEGER
          The row index in the global array A indicating the first
          row of sub( A ).
  JA      (global input) INTEGER
          The column index in the global array A indicating the
          first column of sub( A ).
  DESCA   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix A.
  TAU     (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
          This array contains the scalar factors TAU(j) of the
          elementary reflectors H(j) as returned by PDGEQLF.
          TAU is tied to the distributed matrix A.
  C       (local input/local output) DOUBLE PRECISION pointer into the
          local memory to an array of dimension (LLD_C,LOCc(JC+N-1)).
          On entry, the local pieces of the distributed matrix sub(C).
          On exit, sub( C ) is overwritten by Q*sub( C ) or Q'*sub( C )
          or sub( C )*Q' or sub( C )*Q.
  IC      (global input) INTEGER
          The row index in the global array C indicating the first
          row of sub( C ).
  JC      (global input) INTEGER
          The column index in the global array C indicating the
          first column of sub( C ).
  DESCC   (global and local input) INTEGER array of dimension DLEN_.
          The array descriptor for the distributed matrix C.
  WORK    (local workspace/local output) DOUBLE PRECISION array,
                                                    dimension (LWORK)
          On exit, WORK(1) returns the minimal and optimal LWORK.
  LWORK   (local or global input) INTEGER
          The dimension of the array WORK.
          LWORK is local input and must be at least
          If SIDE = 'L', LWORK >= MpC0 + MAX( 1, NqC0 );
          if SIDE = 'R', LWORK >= NqC0 + MAX( MAX( 1, MpC0 ), NUMROC(
                   NUMROC( N+ICOFFC,NB_A,0,0,NPCOL ),NB_A,0,0,LCMQ ) );
          where LCMQ = LCM / NPCOL with LCM = ICLM( NPROW, NPCOL ),
          IROFFC = MOD( IC-1, MB_C ), ICOFFC = MOD( JC-1, NB_C ),
          ICROW = INDXG2P( IC, MB_C, MYROW, RSRC_C, NPROW ),
          ICCOL = INDXG2P( JC, NB_C, MYCOL, CSRC_C, NPCOL ),
          MpC0 = NUMROC( M+IROFFC, MB_C, MYROW, ICROW, NPROW ),
          NqC0 = NUMROC( N+ICOFFC, NB_C, MYCOL, ICCOL, NPCOL ),
          ILCM, INDXG2P and NUMROC are ScaLAPACK tool functions;
          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
          the subroutine BLACS_GRIDINFO.
          If LWORK = -1, then LWORK is global input and a workspace
          query is assumed; the routine only calculates the minimum
          and optimal size for all work arrays. Each of these
          values is returned in the first entry of the corresponding
          work array, and no error message is issued by PXERBLA.
  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.
  Alignment requirements
  ======================
  The distributed submatrices A(IA:*, JA:*) and C(IC:IC+M-1,JC:JC+N-1)
  must verify some alignment properties, namely the following
  expressions should be true:
  If SIDE = 'L',
    ( MB_A.EQ.MB_C .AND. IROFFA.EQ.IROFFC .AND. IAROW.EQ.ICROW )
  If SIDE = 'R',
    ( MB_A.EQ.NB_C .AND. IROFFA.EQ.ICOFFC )
  =====================================================================
     .. Parameters ..

 
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001        SUBROUTINE PDORM2L( SIDE , TRANS , M , N , K , A , IA , JA , DESCA , TAU ,
002       $C , IC , JC , DESCC , WORK , LWORK , INFO )
003  
004  *     -- ScaLAPACK routine(version 1.7) --
005  *     University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006  *     and University of California , Berkeley.
007  *     May 25 , 2001
008  
009  *     .. Scalar Arguments ..
010        CHARACTER SIDE , TRANS
011        INTEGER IA , IC , INFO , JA , JC , K , LWORK , M , N
012        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
013       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
014        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
015       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
016       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
017        DOUBLE PRECISION ONE
018        PARAMETER( ONE = 1.0D + 0 )
019  *     ..
020  *     .. Local Scalars ..
021        LOGICAL LEFT , LQUERY , NOTRAN
022        CHARACTER COLBTOP , ROWBTOP
023        INTEGER IACOL , IAROW , ICCOL , ICOFFC , ICROW , ICTXT , ICC ,
024       $II , IROFFA , IROFFC , J , J1 , J2 , J3 , JCC , JJ ,
025       $LCM , LCMQ , LWMIN , MI , MP , MPC0 , MYCOL , MYROW ,
026       $NI , NPCOL , NPROW , NQ , NQC0
027        DOUBLE PRECISION AJJ
028  *     ..
029  *     .. External Subroutines ..
030        EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , CHK1MAT , DGEBR2D ,
031       $DGEBS2D , DGERV2D , DGESD2D , DSCAL ,
032       $INFOG2L , PDELSET , PDELSET2 , PDLARF ,
033       $PB_TOPGET , PB_TOPSET , PXERBLA
034  *     ..
035  *     .. External Functions ..
036        LOGICAL LSAME
037        INTEGER ILCM , INDXG2P , NUMROC
038        EXTERNAL ILCM , INDXG2P , LSAME , NUMROC
039  *     ..
040  *     .. Intrinsic Functions ..
041        INTRINSIC DBLE , MAX , MOD
042  *     ..
043  *     .. Executable Statements ..
044  
045  *     Get grid parameters
046  
047        ICTXT = DESCA( CTXT_ )
048        CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
049  
050  *     Test the input parameters
051  
052        INFO = 0
053        IF( NPROW.EQ. - 1 ) THEN
054            INFO = - (900 + CTXT_)
055        ELSE
056            LEFT = LSAME( SIDE , 'L' )
057            NOTRAN = LSAME( TRANS , 'N' )
058  
059  *         NQ is the order of Q
060  
061            IF( LEFT ) THEN
062                NQ = M
063                CALL CHK1MAT( M , 3 , K , 5 , IA , JA , DESCA , 9 , INFO )
064            ELSE
065                NQ = N
066                CALL CHK1MAT( N , 4 , K , 5 , IA , JA , DESCA , 9 , INFO )
067            END IF
068            CALL CHK1MAT( M , 3 , N , 4 , IC , JC , DESCC , 14 , INFO )
069            IF( INFO.EQ.0 ) THEN
070                IROFFA = MOD( IA - 1 , DESCA( MB_ ) )
071                IROFFC = MOD( IC - 1 , DESCC( MB_ ) )
072                ICOFFC = MOD( JC - 1 , DESCC( NB_ ) )
073                IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
074       $        NPROW )
075                ICROW = INDXG2P( IC , DESCC( MB_ ) , MYROW , DESCC( RSRC_ ) ,
076       $        NPROW )
077                ICCOL = INDXG2P( JC , DESCC( NB_ ) , MYCOL , DESCC( CSRC_ ) ,
078       $        NPCOL )
079                MPC0 = NUMROC( M + IROFFC , DESCC( MB_ ) , MYROW , ICROW , NPROW )
080                NQC0 = NUMROC( N + ICOFFC , DESCC( NB_ ) , MYCOL , ICCOL , NPCOL )
081  
082                IF( LEFT ) THEN
083                    LWMIN = MPC0 + MAX( 1 , NQC0 )
084                ELSE
085                    LCM = ILCM( NPROW , NPCOL )
086                    LCMQ = LCM / NPCOL
087                    LWMIN = NQC0 + MAX( MAX( 1 , MPC0 ) , NUMROC( NUMROC(
088       $            N + ICOFFC , DESCA( NB_ ) , 0 , 0 , NPCOL ) ,
089       $            DESCA( NB_ ) , 0 , 0 , LCMQ ) )
090                END IF
091  
092                WORK( 1 ) = DBLE( LWMIN )
093                LQUERY =( LWORK.EQ. - 1 )
094                IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE , 'R' ) ) THEN
095                    INFO = - 1
096                ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS , 'T' ) ) THEN
097                    INFO = - 2
098                ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
099                    INFO = - 5
100                ELSE IF( .NOT.LEFT .AND. DESCA( MB_ ).NE.DESCC( NB_ ) ) THEN
101                    INFO = - (900 + NB_)
102                ELSE IF( LEFT .AND. IROFFA.NE.IROFFC ) THEN
103                    INFO = - 12
104                ELSE IF( LEFT .AND. IAROW.NE.ICROW ) THEN
105                    INFO = - 12
106                ELSE IF( .NOT.LEFT .AND. IROFFA.NE.ICOFFC ) THEN
107                    INFO = - 13
108                ELSE IF( LEFT .AND. DESCA( MB_ ).NE.DESCC( MB_ ) ) THEN
109                    INFO = - (1400 + MB_)
110                ELSE IF( ICTXT.NE.DESCC( CTXT_ ) ) THEN
111                    INFO = - (1400 + CTXT_)
112                ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
113                    INFO = - 16
114                END IF
115            END IF
116        END IF
117        IF( INFO.NE.0 ) THEN
118            CALL PXERBLA( ICTXT , 'PDORM2L' , - INFO )
119            CALL BLACS_ABORT( ICTXT , 1 )
120            RETURN
121        ELSE IF( LQUERY ) THEN
122            RETURN
123        END IF
124  
125  *     Quick return if possible
126  
127        IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
128       $    RETURN
129  
130            IF( DESCA( M_ ).EQ.1 ) THEN
131                CALL INFOG2L( IA , JA , DESCA , NPROW , NPCOL , MYROW , MYCOL , II ,
132       $        JJ , IAROW , IACOL )
133                CALL INFOG2L( IC , JC , DESCC , NPROW , NPCOL , MYROW , MYCOL , ICC ,
134       $        JCC , ICROW , ICCOL )
135                IF( LEFT ) THEN
136                    IF( MYROW.EQ.IAROW ) THEN
137                        NQ = NUMROC( JC + N - 1 , DESCC( NB_ ) , MYCOL , DESCC( CSRC_ ) ,
138       $                NPCOL )
139                        IF( MYCOL.EQ.IACOL ) THEN
140                            AJJ = ONE - TAU( JJ )
141                            CALL DGEBS2D( ICTXT , 'Rowwise' , ' ' , 1 , 1 , AJJ , 1 )
142                            CALL DSCAL( NQ - JCC + 1 , AJJ ,
143       $                    C( ICC + (JCC - 1)*DESCC( LLD_ ) ) ,
144       $                    DESCC( LLD_ ) )
145                        ELSE
146                            CALL DGEBR2D( ICTXT , 'Rowwise' , ' ' , 1 , 1 , AJJ , 1 ,
147       $                    IAROW , IACOL )
148                            CALL DSCAL( NQ - JCC + 1 , AJJ ,
149       $                    C( ICC + (JCC - 1)*DESCC( LLD_ ) ) ,
150       $                    DESCC( LLD_ ) )
151                        END IF
152                    END IF
153                ELSE
154                    IF( MYCOL.EQ.IACOL ) THEN
155                        AJJ = ONE - TAU( JJ )
156                    END IF
157  
158                    IF( IACOL.NE.ICCOL ) THEN
159                        IF( MYCOL.EQ.IACOL )
160       $                    CALL DGESD2D( ICTXT , 1 , 1 , AJJ , 1 , MYROW , ICCOL )
161                            IF( MYCOL.EQ.ICCOL )
162       $                        CALL DGERV2D( ICTXT , 1 , 1 , AJJ , 1 , MYROW , IACOL )
163                            END IF
164  
165                            IF( MYCOL.EQ.ICCOL ) THEN
166                                MP = NUMROC( IC + M - 1 , DESCC( MB_ ) , MYROW , DESCC( RSRC_ ) ,
167       $                        NPROW )
168                                CALL DSCAL( MP - ICC + 1 , AJJ , C( ICC + (JCC - 1)*
169       $                        DESCC( LLD_ ) ) , 1 )
170                            END IF
171  
172                        END IF
173  
174                    ELSE
175  
176                        CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
177                        CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
178  
179                        IF( LEFT .AND. NOTRAN .OR. .NOT.LEFT .AND. .NOT.NOTRAN ) THEN
180                            J1 = JA
181                            J2 = JA + K - 1
182                            J3 = 1
183                        ELSE
184                            J1 = JA + K - 1
185                            J2 = JA
186                            J3 = - 1
187                        END IF
188  
189                        IF( LEFT ) THEN
190                            NI = N
191                            IF( NOTRAN ) THEN
192                                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'I - ring' )
193                            ELSE
194                                CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , 'D - ring' )
195                            END IF
196                            CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , ' ' )
197                        ELSE
198                            MI = M
199                        END IF
200  
201                        DO 10 J = J1 , J2 , J3
202  
203                            IF( LEFT ) THEN
204  
205  *                             H(j) or H(j)' is applied to C(ic : ic + m - k + j - ja , jc : jc + n - 1)
206  
207                                MI = M - K + J - JA + 1
208                            ELSE
209  
210  *                             H(j) or H(j)' is applied to C(ic : ic + m - 1 , jc : jc + n - k + j - ja)
211  
212                                NI = N - K + J - JA + 1
213                            END IF
214  
215  *                         Apply H(j) or H(j)'
216  
217                            CALL PDELSET2( AJJ , A , IA + NQ - K + J - JA , J , DESCA , ONE )
218                            CALL PDLARF ( SIDE , MI , NI , A , IA , J , DESCA , 1 , TAU , C , IC ,
219       $                    JC , DESCC , WORK )
220                            CALL PDELSET( A , IA + NQ - K + J - JA , J , DESCA , AJJ )
221  
222     10                 CONTINUE
223  
224                        CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
225                        CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
226  
227                    END IF
228  
229                    WORK( 1 ) = DBLE( LWMIN )
230  
231                    RETURN
232  
233  *                 End of PDORM2L
234  
235                END