001        SUBROUTINE PSLARF( SIDE , M , N , V , IV , JV , DESCV , INCV , TAU ,
002       $C , IC , JC , DESCC , WORK )
003  
004  *     -- ScaLAPACK auxiliary 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
011        INTEGER IC , INCV , IV , JC , JV , M , N
012  *     ..
013  *     .. Array Arguments ..
014        INTEGER DESCC( * ) , DESCV( * )
015        REAL C( * ) , TAU( * ) , V( * ) , WORK( * )
016  *     ..
017  
018  *     Purpose
019  *     === ====
020  
021  *     PSLARF applies a real elementary reflector Q(or Q**T) to a real
022  *     M-by - N distributed matrix sub( C ) = C(IC : IC + M - 1 , JC : JC + N - 1) , from
023  *     either the left or the right. Q is represented in the form
024  
025  *     Q = I - tau * v * v'
026  
027  *     where tau is a real scalar and v is a real vector.
028  
029  *     If tau = 0 , then Q is taken to be the unit matrix.
030  
031  *     Notes
032  *     === ==
033  
034  *     Each global data object is described by an associated description
035  *     vector. This vector stores the information required to establish
036  *     the mapping between an object element and its corresponding process
037  *     and memory location.
038  
039  *     Let A be a generic term for any 2D block cyclicly distributed array.
040  *     Such a global array has an associated description vector DESCA.
041  *     In the following comments , the character _ should be read as
042  *     "of the global array".
043  
044  *     NOTATION STORED IN EXPLANATION
045  *     --- ------------ -------------- --------------------------------------
046  *     DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case ,
047  *     DTYPE_A = 1.
048  *     CTXT_A(global) DESCA( CTXT_ ) The BLACS context handle , indicating
049  *     the BLACS process grid A is distribu -
050  *     ted over. The context itself is glo -
051  *     bal , but the handle(the integer
052  *     value) may vary.
053  *     M_A(global) DESCA( M_ ) The number of rows in the global
054  *     array A.
055  *     N_A(global) DESCA( N_ ) The number of columns in the global
056  *     array A.
057  *     MB_A(global) DESCA( MB_ ) The blocking factor used to distribute
058  *     the rows of the array.
059  *     NB_A(global) DESCA( NB_ ) The blocking factor used to distribute
060  *     the columns of the array.
061  *     RSRC_A(global) DESCA( RSRC_ ) The process row over which the first
062  *     row of the array A is distributed.
063  *     CSRC_A(global) DESCA( CSRC_ ) The process column over which the
064  *     first column of the array A is
065  *     distributed.
066  *     LLD_A(local) DESCA( LLD_ ) The leading dimension of the local
067  *     array. LLD_A >= MAX(1 , LOCr(M_A)).
068  
069  *     Let K be the number of rows or columns of a distributed matrix ,
070  *     and assume that its process grid has dimension p x q.
071  *     LOCr( K ) denotes the number of elements of K that a process
072  *     would receive if K were distributed over the p processes of its
073  *     process column.
074  *     Similarly , LOCc( K ) denotes the number of elements of K that a
075  *     process would receive if K were distributed over the q processes of
076  *     its process row.
077  *     The values of LOCr() and LOCc() may be determined via a call to the
078  *     ScaLAPACK tool function , NUMROC :
079  *     LOCr( M ) = NUMROC( M , MB_A , MYROW , RSRC_A , NPROW ) ,
080  *     LOCc( N ) = NUMROC( N , NB_A , MYCOL , CSRC_A , NPCOL ).
081  *     An upper bound for these quantities may be computed by :
082  *     LOCr( M ) <= ceil( ceil(M / MB_A) / NPROW )*MB_A
083  *     LOCc( N ) <= ceil( ceil(N / NB_A) / NPCOL )*NB_A
084  
085  *     Because vectors may be viewed as a subclass of matrices , a
086  *     distributed vector is considered to be a distributed matrix.
087  
088  *     Restrictions
089  *     === =========
090  
091  *     If SIDE = 'Left' and INCV = 1 , then the row process having the first
092  *     entry V(IV , JV) must also have the first row of sub( C ). Moreover ,
093  *     MOD(IV - 1 , MB_V) must be equal to MOD(IC - 1 , MB_C) , if INCV = M_V , only
094  *     the last equality must be satisfied.
095  
096  *     If SIDE = 'Right' and INCV = M_V then the column process having the
097  *     first entry V(IV , JV) must also have the first column of sub( C ) and
098  *     MOD(JV - 1 , NB_V) must be equal to MOD(JC - 1 , NB_C) , if INCV = 1 only the
099  *     last equality must be satisfied.
100  
101  *     Arguments
102  *     === ======
103  
104  *     SIDE(global input) CHARACTER
105  *     = 'L' : form Q * sub( C ) ,
106  *     = 'R' : form sub( C ) * Q , Q = Q**T.
107  
108  *     M(global input) INTEGER
109  *     The number of rows to be operated on i.e the number of rows
110  *     of the distributed submatrix sub( C ). M >= 0.
111  
112  *     N(global input) INTEGER
113  *     The number of columns to be operated on i.e the number of
114  *     columns of the distributed submatrix sub( C ). N >= 0.
115  
116  *     V(local input) REAL pointer into the local memory
117  *     to an array of dimension(LLD_V ,*) containing the local
118  *     pieces of the distributed vectors V representing the
119  *     Householder transformation Q ,
120  *     V(IV : IV + M - 1 , JV) if SIDE = 'L' and INCV = 1 ,
121  *     V(IV , JV : JV + M - 1) if SIDE = 'L' and INCV = M_V ,
122  *     V(IV : IV + N - 1 , JV) if SIDE = 'R' and INCV = 1 ,
123  *     V(IV , JV : JV + N - 1) if SIDE = 'R' and INCV = M_V ,
124  
125  *     The vector v in the representation of Q. V is not used if
126  *     TAU = 0.
127  
128  *     IV(global input) INTEGER
129  *     The row index in the global array V indicating the first
130  *     row of sub( V ).
131  
132  *     JV(global input) INTEGER
133  *     The column index in the global array V indicating the
134  *     first column of sub( V ).
135  
136  *     DESCV(global and local input) INTEGER array of dimension DLEN_.
137  *     The array descriptor for the distributed matrix V.
138  
139  *     INCV(global input) INTEGER
140  *     The global increment for the elements of V. Only two values
141  *     of INCV are supported in this version , namely 1 and M_V.
142  *     INCV must not be zero.
143  
144  *     TAU(local input) REAL , array , dimension LOCc(JV) if
145  *     INCV = 1 , and LOCr(IV) otherwise. This array contains the
146  *     Householder scalars related to the Householder vectors.
147  *     TAU is tied to the distributed matrix V.
148  
149  *     C(local input / local output) REAL pointer into the
150  *     local memory to an array of dimension(LLD_C , LOCc(JC + N - 1) ) ,
151  *     containing the local pieces of sub( C ). On exit , sub( C )
152  *     is overwritten by the Q * sub( C ) if SIDE = 'L' , or
153  *     sub( C ) * Q if SIDE = 'R'.
154  
155  *     IC(global input) INTEGER
156  *     The row index in the global array C indicating the first
157  *     row of sub( C ).
158  
159  *     JC(global input) INTEGER
160  *     The column index in the global array C indicating the
161  *     first column of sub( C ).
162  
163  *     DESCC(global and local input) INTEGER array of dimension DLEN_.
164  *     The array descriptor for the distributed matrix C.
165  
166  *     WORK(local workspace) REAL array , dimension(LWORK)
167  *     If INCV = 1 ,
168  *     if SIDE = 'L' ,
169  *     if IVCOL = ICCOL ,
170  *     LWORK >= NqC0
171  *     else
172  *     LWORK >= MpC0 + MAX( 1 , NqC0 )
173  *     end if
174  *     else if SIDE = 'R' ,
175  *     LWORK >= NqC0 + MAX( MAX( 1 , MpC0 ) , NUMROC( NUMROC(
176  *     N + ICOFFC , NB_V , 0 , 0 , NPCOL ) , NB_V , 0 , 0 , LCMQ ) )
177  *     end if
178  *     else if INCV = M_V ,
179  *     if SIDE = 'L' ,
180  *     LWORK >= MpC0 + MAX( MAX( 1 , NqC0 ) , NUMROC( NUMROC(
181  *     M + IROFFC , MB_V , 0 , 0 , NPROW ) , MB_V , 0 , 0 , LCMP ) )
182  *     else if SIDE = 'R' ,
183  *     if IVROW = ICROW ,
184  *     LWORK >= MpC0
185  *     else
186  *     LWORK >= NqC0 + MAX( 1 , MpC0 )
187  *     end if
188  *     end if
189  *     end if
190  
191  *     where LCM is the least common multiple of NPROW and NPCOL and
192  *     LCM = ILCM( NPROW , NPCOL ) , LCMP = LCM / NPROW ,
193  *     LCMQ = LCM / NPCOL ,
194  
195  *     IROFFC = MOD( IC - 1 , MB_C ) , ICOFFC = MOD( JC - 1 , NB_C ) ,
196  *     ICROW = INDXG2P( IC , MB_C , MYROW , RSRC_C , NPROW ) ,
197  *     ICCOL = INDXG2P( JC , NB_C , MYCOL , CSRC_C , NPCOL ) ,
198  *     MpC0 = NUMROC( M + IROFFC , MB_C , MYROW , ICROW , NPROW ) ,
199  *     NqC0 = NUMROC( N + ICOFFC , NB_C , MYCOL , ICCOL , NPCOL ) ,
200  
201  *     ILCM , INDXG2P and NUMROC are ScaLAPACK tool functions ;
202  *     MYROW , MYCOL , NPROW and NPCOL can be determined by calling
203  *     the subroutine BLACS_GRIDINFO.
204  
205  *     Alignment requirements
206  *     === ===================
207  
208  *     The distributed submatrices V(IV : * , JV :*) and C(IC : IC + M - 1 , JC : JC + N - 1)
209  *     must verify some alignment properties , namely the following
210  *     expressions should be true :
211  
212  *     MB_V = NB_V ,
213  
214  *     If INCV = 1 ,
215  *     If SIDE = 'Left' ,
216  *     ( MB_V.EQ.MB_C .AND. IROFFV.EQ.IROFFC .AND. IVROW.EQ.ICROW )
217  *     If SIDE = 'Right' ,
218  *     ( MB_V.EQ.NB_A .AND. MB_V.EQ.NB_C .AND. IROFFV.EQ.ICOFFC )
219  *     else if INCV = M_V ,
220  *     If SIDE = 'Left' ,
221  *     ( MB_V.EQ.NB_V .AND. MB_V.EQ.MB_C .AND. ICOFFV.EQ.IROFFC )
222  *     If SIDE = 'Right' ,
223  *     ( NB_V.EQ.NB_C .AND. ICOFFV.EQ.ICOFFC .AND. IVCOL.EQ.ICCOL )
224  *     end if
225  
226  *     === ==================================================================
227  
228  *     .. Parameters ..
229        INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
230       $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
231        PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
232       $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
233       $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
234        REAL ONE , ZERO
235        PARAMETER( ONE = 1.0E + 0 , ZERO = 0.0E + 0 )
236        CALL SGER( MP , NQ , - TAULOC , WORK( IPW ) , 1 , WORK , 1 ,
237       $C( IOFFC ) , LDC )
238        END IF
239  
240        END IF
241  
242        END IF
243  
244        END IF
245  
246        RETURN
247  
248  *     End of PSLARF
249  
250        END18247