1      SUBROUTINE PZUNG2L( 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      COMPLEX*16         A( * ), TAU( * ), WORK( * )
15*     ..
16*
17*  Purpose
18*  =======
19*
20*  PZUNG2L generates an M-by-N complex distributed matrix Q denoting
21*  A(IA:IA+M-1,JA:JA+N-1) with orthonormal columns, which is defined as
22*  the last N columns of a product of K elementary reflectors of order M
23*
24*        Q  =  H(k) . . . H(2) H(1)
25*
26*  as returned by PZGEQLF.
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. M >= N >= 0.
92*
93*  K       (global input) INTEGER
94*          The number of elementary reflectors whose product defines the
95*          matrix Q. N >= K >= 0.
96*
97*  A       (local input/local output) COMPLEX*16 pointer into the
98*          local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
99*          On entry, the j-th column must contain the vector which
100*          defines the elementary reflector H(j), JA+N-K <= j <= JA+N-1,
101*          as returned by PZGEQLF in the K columns of its distributed
102*          matrix argument A(IA:*,JA+N-K:JA+N-1). On exit, this array
103*          contains the 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) COMPLEX*16, array, dimension LOCc(JA+N-1)
117*          This array contains the scalar factors TAU(j) of the
118*          elementary reflectors H(j) as returned by PZGEQLF.
119*          TAU is tied to the distributed matrix A.
120*
121*  WORK    (local workspace/local output) COMPLEX*16 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 >= MpA0 + MAX( 1, NqA0 ), 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      COMPLEX*16         ONE, ZERO
163      PARAMETER          ( ONE  = ( 1.0D+0, 0.0D+0 ),
164     $                     ZERO = ( 0.0D+0, 0.0D+0 ) )
165*     ..
166*     .. Local Scalars ..
167      LOGICAL            LQUERY
168      CHARACTER          COLBTOP, ROWBTOP
169      INTEGER            IACOL, IAROW, ICTXT, J, JJ, LWMIN, MPA0, MYCOL,
170     $                   MYROW, NPCOL, NPROW, NQA0
171      COMPLEX*16         TAUJ
172*     ..
173*     .. External Subroutines ..
174      EXTERNAL           BLACS_ABORT, BLACS_GRIDINFO, CHK1MAT,
175     $                   PB_TOPGET, PB_TOPSET, PXERBLA, PZELSET, PZLARF,
176     $                   PZLASET, PZSCAL
177*     ..
178*     .. External Functions ..
179      INTEGER            INDXG2L, INDXG2P, NUMROC
180      EXTERNAL           INDXG2L, INDXG2P, NUMROC
181*     ..
182*     .. Intrinsic Functions ..
183      INTRINSIC          DBLE, DCMPLX, MAX, MIN, MOD
184*     ..
185*     .. Executable Statements ..
186*
187*     Get grid parameters
188*
189      ICTXT = DESCA( CTXT_ )
190      CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
191*
192*     Test the input parameters
193*
194      INFO = 0
195      IF( NPROW.EQ.-1 ) THEN
196         INFO = -(700+CTXT_)
197      ELSE
198         CALL CHK1MAT( M, 1, N, 2, IA, JA, DESCA, 7, INFO )
199         IF( INFO.EQ.0 ) THEN
200            IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),
201     $                       NPROW )
202            IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
203     $                       NPCOL )
204            MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),
205     $                     MYROW, IAROW, NPROW )
206            NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),
207     $                     MYCOL, IACOL, NPCOL )
208            LWMIN = MPA0 + MAX( 1, NQA0 )
209*
210            WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
211            LQUERY = ( LWORK.EQ.-1 )
212            IF( N.GT.M ) THEN
213               INFO = -2
214            ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
215               INFO = -3
216            ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
217               INFO = -10
218            END IF
219         END IF
220      END IF
221      IF( INFO.NE.0 ) THEN
222         CALL PXERBLA( ICTXT, 'PZUNG2L', -INFO )
223         CALL BLACS_ABORT( ICTXT, 1 )
224         RETURN
225      ELSE IF( LQUERY ) THEN
226         RETURN
227      END IF
228*
229*     Quick return if possible
230*
231      IF( N.LE.0 )
232     $   RETURN
233*
234      CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
235      CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
236      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'I-ring' )
237      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' )
238*
239*     Initialise columns ja:ja+n-k-1 to columns of the unit matrix
240*
241      CALL PZLASET( 'All', M-N, N-K, ZERO, ZERO, A, IA, JA, DESCA )
242      CALL PZLASET( 'All', N, N-K, ZERO, ONE, A, IA+M-N, JA, DESCA )
243*
244      TAUJ = ZERO
245      NQA0 = MAX( 1, NUMROC( JA+N-1, DESCA( NB_ ), MYCOL,
246     $                       DESCA( CSRC_ ), NPCOL ) )
247      DO 10 J = JA+N-K, JA+N-1
248*
249*        Apply H(j) to A(ia:ia+m-n+j-ja,ja:j) from the left
250*
251         CALL PZELSET( A, IA+M-N+J-JA, J, DESCA, ONE )
252         CALL PZLARF( 'Left', M-N+J-JA+1, J-JA, A, IA, J, DESCA, 1, TAU,
253     $                A, IA, JA, DESCA, WORK )
254*
255         JJ = INDXG2L( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL )
256         IACOL = INDXG2P( J, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
257     $                    NPCOL )
258         IF( MYCOL.EQ.IACOL )
259     $      TAUJ = TAU( MIN( JJ, NQA0 ) )
260         CALL PZSCAL( M-N+J-JA, -TAUJ, A, IA, J, DESCA, 1 )
261         CALL PZELSET( A, IA+M-N+J-JA, J, DESCA, ONE-TAUJ )
262*
263*        Set A(ia+m-n+j-ja+1:ia+m-1,j) to zero
264*
265         CALL PZLASET( 'All', JA+N-1-J, 1, ZERO, ZERO, A, IA+M-N+J-JA+1,
266     $                 J, DESCA )
267*
268   10 CONTINUE
269*
270      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP )
271      CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP )
272*
273      WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
274*
275      RETURN
276*
277*     End of PZUNG2L
278*
279      END
280