1      SUBROUTINE PDORGL2( M, N, K, A, IA, JA, DESCA, TAU, WORK, LWORK,
2     $                    INFO )
3*
4*  -- ScaLAPACK routine (version 1.7) --
5*     University of Tennessee, Knoxville, Oak Ridge National Laboratory,
6*     and University of California, Berkeley.
7*     May 25, 2001
8*
9*     .. Scalar Arguments ..
10      INTEGER            IA, INFO, JA, K, LWORK, M, N
11*     ..
12*     .. Array Arguments ..
13      INTEGER            DESCA( * )
14      DOUBLE PRECISION   A( * ), TAU( * ), WORK( * )
15*     ..
16*
17*  Purpose
18*  =======
19*
20*  PDORGL2 generates an M-by-N real distributed matrix Q denoting
21*  A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as
22*  the first M rows of a product of K elementary reflectors of order N
23*
24*        Q  =  H(k) . . . H(2) H(1)
25*
26*  as returned by PDGELQF.
27*
28*  Notes
29*  =====
30*
31*  Each global data object is described by an associated description
32*  vector.  This vector stores the information required to establish
33*  the mapping between an object element and its corresponding process
34*  and memory location.
35*
36*  Let A be a generic term for any 2D block cyclicly distributed array.
37*  Such a global array has an associated description vector DESCA.
38*  In the following comments, the character _ should be read as
39*  "of the global array".
40*
41*  NOTATION        STORED IN      EXPLANATION
42*  --------------- -------------- --------------------------------------
43*  DTYPE_A(global) DESCA( DTYPE_ )The descriptor type.  In this case,
44*                                 DTYPE_A = 1.
45*  CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
46*                                 the BLACS process grid A is distribu-
47*                                 ted over. The context itself is glo-
48*                                 bal, but the handle (the integer
49*                                 value) may vary.
50*  M_A    (global) DESCA( M_ )    The number of rows in the global
51*                                 array A.
52*  N_A    (global) DESCA( N_ )    The number of columns in the global
53*                                 array A.
54*  MB_A   (global) DESCA( MB_ )   The blocking factor used to distribute
55*                                 the rows of the array.
56*  NB_A   (global) DESCA( NB_ )   The blocking factor used to distribute
57*                                 the columns of the array.
58*  RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
59*                                 row of the array A is distributed.
60*  CSRC_A (global) DESCA( CSRC_ ) The process column over which the
61*                                 first column of the array A is
62*                                 distributed.
63*  LLD_A  (local)  DESCA( LLD_ )  The leading dimension of the local
64*                                 array.  LLD_A >= MAX(1,LOCr(M_A)).
65*
66*  Let K be the number of rows or columns of a distributed matrix,
67*  and assume that its process grid has dimension p x q.
68*  LOCr( K ) denotes the number of elements of K that a process
69*  would receive if K were distributed over the p processes of its
70*  process column.
71*  Similarly, LOCc( K ) denotes the number of elements of K that a
72*  process would receive if K were distributed over the q processes of
73*  its process row.
74*  The values of LOCr() and LOCc() may be determined via a call to the
75*  ScaLAPACK tool function, NUMROC:
76*          LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
77*          LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
78*  An upper bound for these quantities may be computed by:
79*          LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
80*          LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
81*
82*  Arguments
83*  =========
84*
85*  M       (global input) INTEGER
86*          The number of rows to be operated on i.e the number of rows
87*          of the distributed submatrix Q. M >= 0.
88*
89*  N       (global input) INTEGER
90*          The number of columns to be operated on i.e the number of
91*          columns of the distributed submatrix Q. N >= M >= 0.
92*
93*  K       (global input) INTEGER
94*          The number of elementary reflectors whose product defines the
95*          matrix Q. M >= K >= 0.
96*
97*  A       (local input/local output) DOUBLE PRECISION pointer into the
98*          local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
99*          On entry, the i-th row must contain the vector which defines
100*          the elementary reflector H(i), IA <= i <= IA+K-1, as
101*          returned by PDGELQF in the K rows of its distributed matrix
102*          argument A(IA:IA+K-1,JA:*). On exit, this array contains the
103*          local pieces of the M-by-N distributed matrix Q.
104*
105*  IA      (global input) INTEGER
106*          The row index in the global array A indicating the first
107*          row of sub( A ).
108*
109*  JA      (global input) INTEGER
110*          The column index in the global array A indicating the
111*          first column of sub( A ).
112*
113*  DESCA   (global and local input) INTEGER array of dimension DLEN_.
114*          The array descriptor for the distributed matrix A.
115*
116*  TAU     (local input) DOUBLE PRECISION array, dimension LOCr(IA+K-1).
117*          This array contains the scalar factors TAU(i) of the
118*          elementary reflectors H(i) as returned by PDGELQF.
119*          TAU is tied to the distributed matrix A.
120*
121*  WORK    (local workspace/local output) DOUBLE PRECISION array,
122*                                                      dimension (LWORK)
123*          On exit, WORK(1) returns the minimal and optimal LWORK.
124*
125*  LWORK   (local or global input) INTEGER
126*          The dimension of the array WORK.
127*          LWORK is local input and must be at least
128*          LWORK >= NqA0 + MAX( 1, MpA0 ), where
129*
130*          IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
131*          IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
132*          IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
133*          MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
134*          NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
135*
136*          INDXG2P and NUMROC are ScaLAPACK tool functions;
137*          MYROW, MYCOL, NPROW and NPCOL can be determined by calling
138*          the subroutine BLACS_GRIDINFO.
139*
140*          If LWORK = -1, then LWORK is global input and a workspace
141*          query is assumed; the routine only calculates the minimum
142*          and optimal size for all work arrays. Each of these
143*          values is returned in the first entry of the corresponding
144*          work array, and no error message is issued by PXERBLA.
145*
146*
147*  INFO    (local output) INTEGER
148*          = 0:  successful exit
149*          < 0:  If the i-th argument is an array and the j-entry had
150*                an illegal value, then INFO = -(i*100+j), if the i-th
151*                argument is a scalar and had an illegal value, then
152*                INFO = -i.
153*
154*  =====================================================================
155*
156*     .. Parameters ..
157      INTEGER            BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
158     $                   LLD_, MB_, M_, NB_, N_, RSRC_
159      PARAMETER          ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
160     $                     CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
161     $                     RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
162      DOUBLE PRECISION   ONE, ZERO
163      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
164*     ..
165*     .. Local Scalars ..
166      LOGICAL            LQUERY
167      CHARACTER          COLBTOP, ROWBTOP
168      INTEGER            IACOL, IAROW, I, ICTXT, II, J, KP, LWMIN, MPA0,
169     $                   MYCOL, MYROW, NPCOL, NPROW, NQA0
170      DOUBLE PRECISION   TAUI
171*     ..
172*     .. External Subroutines ..
173      EXTERNAL           BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT, PDELSET,
174     $                   PDLARF, PDLASET, PDSCAL, PB_TOPGET,
175     $                   PB_TOPSET, PXERBLA
176*     ..
177*     .. External Functions ..
178      INTEGER            INDXG2L, INDXG2P, NUMROC
179      EXTERNAL           INDXG2L, INDXG2P, NUMROC
180*     ..
181*     .. Intrinsic Functions ..
182      INTRINSIC          DBLE, MAX, MIN, MOD
183*     ..
184*     .. Executable Statements ..
185*
186*     Get grid parameters
187*
188      ICTXT = DESCA( CTXT_ )
189      CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
190*
191*     Test the input parameters
192*
193      INFO = 0
194      IF( NPROW.EQ.-1 ) THEN
195         INFO = -(700+CTXT_)
196      ELSE
197         CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO )
198         IF( INFO.EQ.0 ) THEN
199            IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
200     $                       NPROW )
201            IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
202     $                       NPCOL )
203            MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
204     $                     MYROW, IAROW, NPROW )
205            NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
206     $                     MYCOL, IACOL, NPCOL )
207            LWMIN = NQA0 + MAX( 1, MPA0 )
208*
209            WORK( 1 ) = DBLE( LWMIN )
210            LQUERY = ( LWORK.EQ.-1 )
211            IF( N.LT.M ) THEN
212               INFO = -2
213            ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
214               INFO = -3
215            ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
216               INFO = -10
217            END IF
218         END IF
219      END IF
220      IF( INFO.NE.0 ) THEN
221         CALL PXERBLA( ICTXT, 'PDORGL2', -INFO )
222         CALL BLACS_ABORT( ICTXT, 1 )
223         RETURN
224      ELSE IF( LQUERY ) THEN
225         RETURN
226      END IF
227*
228*     Quick return if possible
229*
230      IF( M.LE.0 )
231     $   RETURN
232*
233      CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
234      CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
235      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' )
236      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' )
237*
238      IF( K.LT.M ) THEN
239*
240*        Initialise rows ia+k:ia+m-1 to rows of the unit matrix
241*
242         CALL PDLASET( 'All', M-K, K, ZERO, ZERO, A, IA+K, JA, DESCA )
243         CALL PDLASET( 'All', M-K, N-K, ZERO, ONE, A, IA+K, JA+K,
244     $                 DESCA )
245*
246      END IF
247*
248      TAUI = ZERO
249      KP = NUMROC( IA+K-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW )
250*
251      DO 10 I = IA+K-1, IA, -1
252*
253*        Apply H(i) to A(i:ia+m-1,ja+i-ia:ja+n-1) from the right
254*
255         J = JA + I - IA
256         II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW )
257         IAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
258     $                    NPROW )
259         IF( MYROW.EQ.IAROW )
260     $      TAUI = TAU( MIN( II, KP ) )
261         IF( J.LT.JA+N-1 ) THEN
262            IF( I.LT.IA+M-1 ) THEN
263               CALL PDELSET( A, I, J, DESCA, ONE )
264               CALL PDLARF( 'Right', M-I+IA-1, N-J+JA, A, I, J, DESCA,
265     $                      DESCA( M_ ), TAU, A, I+1, J, DESCA, WORK )
266            END IF
267            CALL PDSCAL( N-J+JA-1, -TAUI, A, I, J+1, DESCA,
268     $                        DESCA( M_ ) )
269         END IF
270         CALL PDELSET( A, I, J, DESCA, ONE-TAUI )
271*
272*        Set A(i,ja:j-1) to zero
273*
274         CALL PDLASET( 'All', 1, J-JA, ZERO, ZERO, A, I, JA, DESCA )
275*
276   10 CONTINUE
277*
278      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
279      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
280*
281      WORK( 1 ) = DBLE( LWMIN )
282*
283      RETURN
284*
285*     End of PDORGL2
286*
287      END
288