SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
pdggqrf.f
Go to the documentation of this file.
1 SUBROUTINE pdggqrf( N, M, P, A, IA, JA, DESCA, TAUA, B, IB, JB,
2 $ DESCB, TAUB, WORK, LWORK, 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 1, 1997
8*
9* .. Scalar Arguments ..
10 INTEGER IA, IB, INFO, JA, JB, LWORK, M, N, P
11* ..
12* .. Array Arguments ..
13 INTEGER DESCA( * ), DESCB( * )
14 DOUBLE PRECISION A( * ), B( * ), TAUA( * ), TAUB( * ), WORK( * )
15* ..
16*
17* Purpose
18* =======
19*
20* PDGGQRF computes a generalized QR factorization of
21* an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and
22* an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1):
23*
24* sub( A ) = Q*R, sub( B ) = Q*T*Z,
25*
26* where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal
27* matrix, and R and T assume one of the forms:
28*
29* if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
30* ( 0 ) N-M N M-N
31* M
32*
33* where R11 is upper triangular, and
34*
35* if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
36* P-N N ( T21 ) P
37* P
38*
39* where T12 or T21 is upper triangular.
40*
41* In particular, if sub( B ) is square and nonsingular, the GQR
42* factorization of sub( A ) and sub( B ) implicitly gives the QR
43* factorization of inv( sub( B ) )* sub( A ):
44*
45* inv( sub( B ) )*sub( A )= Z'*(inv(T)*R)
46*
47* where inv( sub( B ) ) denotes the inverse of the matrix sub( B ),
48* and Z' denotes the transpose of matrix Z.
49*
50* Notes
51* =====
52*
53* Each global data object is described by an associated description
54* vector. This vector stores the information required to establish
55* the mapping between an object element and its corresponding process
56* and memory location.
57*
58* Let A be a generic term for any 2D block cyclicly distributed array.
59* Such a global array has an associated description vector DESCA.
60* In the following comments, the character _ should be read as
61* "of the global array".
62*
63* NOTATION STORED IN EXPLANATION
64* --------------- -------------- --------------------------------------
65* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
66* DTYPE_A = 1.
67* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
68* the BLACS process grid A is distribu-
69* ted over. The context itself is glo-
70* bal, but the handle (the integer
71* value) may vary.
72* M_A (global) DESCA( M_ ) The number of rows in the global
73* array A.
74* N_A (global) DESCA( N_ ) The number of columns in the global
75* array A.
76* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
77* the rows of the array.
78* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
79* the columns of the array.
80* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
81* row of the array A is distributed.
82* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
83* first column of the array A is
84* distributed.
85* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
86* array. LLD_A >= MAX(1,LOCr(M_A)).
87*
88* Let K be the number of rows or columns of a distributed matrix,
89* and assume that its process grid has dimension p x q.
90* LOCr( K ) denotes the number of elements of K that a process
91* would receive if K were distributed over the p processes of its
92* process column.
93* Similarly, LOCc( K ) denotes the number of elements of K that a
94* process would receive if K were distributed over the q processes of
95* its process row.
96* The values of LOCr() and LOCc() may be determined via a call to the
97* ScaLAPACK tool function, NUMROC:
98* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
99* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
100* An upper bound for these quantities may be computed by:
101* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
102* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
103*
104* Arguments
105* =========
106*
107* N (global input) INTEGER
108* The number of rows to be operated on i.e the number of rows
109* of the distributed submatrices sub( A ) and sub( B ). N >= 0.
110*
111* M (global input) INTEGER
112* The number of columns to be operated on i.e the number of
113* columns of the distributed submatrix sub( A ). M >= 0.
114*
115* P (global input) INTEGER
116* The number of columns to be operated on i.e the number of
117* columns of the distributed submatrix sub( B ). P >= 0.
118*
119* A (local input/local output) DOUBLE PRECISION pointer into the
120* local memory to an array of dimension (LLD_A, LOCc(JA+M-1)).
121* On entry, the local pieces of the N-by-M distributed matrix
122* sub( A ) which is to be factored. On exit, the elements on
123* and above the diagonal of sub( A ) contain the min(N,M) by M
124* upper trapezoidal matrix R (R is upper triangular if N >= M);
125* the elements below the diagonal, with the array TAUA,
126* represent the orthogonal matrix Q as a product of min(N,M)
127* elementary reflectors (see Further Details).
128*
129* IA (global input) INTEGER
130* The row index in the global array A indicating the first
131* row of sub( A ).
132*
133* JA (global input) INTEGER
134* The column index in the global array A indicating the
135* first column of sub( A ).
136*
137* DESCA (global and local input) INTEGER array of dimension DLEN_.
138* The array descriptor for the distributed matrix A.
139*
140* TAUA (local output) DOUBLE PRECISION array, dimension
141* LOCc(JA+MIN(N,M)-1). This array contains the scalar factors
142* TAUA of the elementary reflectors which represent the
143* orthogonal matrix Q. TAUA is tied to the distributed matrix
144* A. (see Further Details).
145*
146* B (local input/local output) DOUBLE PRECISION pointer into the
147* local memory to an array of dimension (LLD_B, LOCc(JB+P-1)).
148* On entry, the local pieces of the N-by-P distributed matrix
149* sub( B ) which is to be factored. On exit, if N <= P, the
150* upper triangle of B(IB:IB+N-1,JB+P-N:JB+P-1) contains the
151* N by N upper triangular matrix T; if N > P, the elements on
152* and above the (N-P)-th subdiagonal contain the N by P upper
153* trapezoidal matrix T; the remaining elements, with the array
154* TAUB, represent the orthogonal matrix Z as a product of
155* elementary reflectors (see Further Details).
156*
157* IB (global input) INTEGER
158* The row index in the global array B indicating the first
159* row of sub( B ).
160*
161* JB (global input) INTEGER
162* The column index in the global array B indicating the
163* first column of sub( B ).
164*
165* DESCB (global and local input) INTEGER array of dimension DLEN_.
166* The array descriptor for the distributed matrix B.
167*
168* TAUB (local output) DOUBLE PRECISION array, dimension LOCr(IB+N-1)
169* This array contains the scalar factors of the elementary
170* reflectors which represent the orthogonal unitary matrix Z.
171* TAUB is tied to the distributed matrix B (see Further
172* Details).
173*
174* WORK (local workspace/local output) DOUBLE PRECISION array,
175* dimension (LWORK)
176* On exit, WORK(1) returns the minimal and optimal LWORK.
177*
178* LWORK (local or global input) INTEGER
179* The dimension of the array WORK.
180* LWORK is local input and must be at least
181* LWORK >= MAX( NB_A * ( NpA0 + MqA0 + NB_A ),
182* MAX( (NB_A*(NB_A-1))/2, (PqB0 + NpB0)*NB_A ) +
183* NB_A * NB_A,
184* MB_B * ( NpB0 + PqB0 + MB_B ) ), where
185*
186* IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
187* IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
188* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
189* NpA0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ),
190* MqA0 = NUMROC( M+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
191*
192* IROFFB = MOD( IB-1, MB_B ), ICOFFB = MOD( JB-1, NB_B ),
193* IBROW = INDXG2P( IB, MB_B, MYROW, RSRC_B, NPROW ),
194* IBCOL = INDXG2P( JB, NB_B, MYCOL, CSRC_B, NPCOL ),
195* NpB0 = NUMROC( N+IROFFB, MB_B, MYROW, IBROW, NPROW ),
196* PqB0 = NUMROC( P+ICOFFB, NB_B, MYCOL, IBCOL, NPCOL ),
197*
198* and NUMROC, INDXG2P are ScaLAPACK tool functions;
199* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
200* the subroutine BLACS_GRIDINFO.
201*
202* If LWORK = -1, then LWORK is global input and a workspace
203* query is assumed; the routine only calculates the minimum
204* and optimal size for all work arrays. Each of these
205* values is returned in the first entry of the corresponding
206* work array, and no error message is issued by PXERBLA.
207*
208* INFO (global output) INTEGER
209* = 0: successful exit
210* < 0: If the i-th argument is an array and the j-entry had
211* an illegal value, then INFO = -(i*100+j), if the i-th
212* argument is a scalar and had an illegal value, then
213* INFO = -i.
214*
215* Further Details
216* ===============
217*
218* The matrix Q is represented as a product of elementary reflectors
219*
220* Q = H(ja) H(ja+1) . . . H(ja+k-1), where k = min(n,m).
221*
222* Each H(i) has the form
223*
224* H(i) = I - taua * v * v'
225*
226* where taua is a real scalar, and v is a real vector with
227* v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in
228* A(ia+i:ia+n-1,ja+i-1), and taua in TAUA(ja+i-1).
229* To form Q explicitly, use ScaLAPACK subroutine PDORGQR.
230* To use Q to update another matrix, use ScaLAPACK subroutine PDORMQR.
231*
232* The matrix Z is represented as a product of elementary reflectors
233*
234* Z = H(ib) H(ib+1) . . . H(ib+k-1), where k = min(n,p).
235*
236* Each H(i) has the form
237*
238* H(i) = I - taub * v * v'
239*
240* where taub is a real scalar, and v is a real vector with
241* v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
242* B(ib+n-k+i-1,jb:jb+p-k+i-2), and taub in TAUB(ib+n-k+i-1).
243* To form Z explicitly, use ScaLAPACK subroutine PDORGRQ.
244* To use Z to update another matrix, use ScaLAPACK subroutine PDORMRQ.
245*
246* Alignment requirements
247* ======================
248*
249* The distributed submatrices sub( A ) and sub( B ) must verify some
250* alignment properties, namely the following expression should be true:
251*
252* ( MB_A.EQ.MB_B .AND. IROFFA.EQ.IROFFB .AND. IAROW.EQ.IBROW )
253*
254* =====================================================================
255*
256* .. Parameters ..
257 INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
258 $ lld_, mb_, m_, nb_, n_, rsrc_
259 parameter( block_cyclic_2d = 1, dlen_ = 9, dtype_ = 1,
260 $ ctxt_ = 2, m_ = 3, n_ = 4, mb_ = 5, nb_ = 6,
261 $ rsrc_ = 7, csrc_ = 8, lld_ = 9 )
262* ..
263* .. Local Scalars ..
264 LOGICAL LQUERY
265 INTEGER IACOL, IAROW, IBCOL, IBROW, ICOFFA, ICOFFB,
266 $ ictxt, iroffa, iroffb, lwmin, mqa0, mycol,
267 $ myrow, npa0, npb0, npcol, nprow, pqb0
268* ..
269* .. External Subroutines ..
270 EXTERNAL blacs_gridinfo, chk1mat, pchk2mat, pdgeqrf,
272* ..
273* .. Local Arrays ..
274 INTEGER IDUM1( 1 ), IDUM2( 1 )
275* ..
276* .. External Functions ..
277 INTEGER INDXG2P, NUMROC
278 EXTERNAL indxg2p, numroc
279* ..
280* .. Intrinsic Functions ..
281 INTRINSIC dble, int, max, min, mod
282* ..
283* .. Executable Statements ..
284*
285* Get grid parameters
286*
287 ictxt = desca( ctxt_ )
288 CALL blacs_gridinfo( ictxt, nprow, npcol, myrow, mycol )
289*
290* Test the input parameters
291*
292 info = 0
293 IF( nprow.EQ.-1 ) THEN
294 info = -707
295 ELSE
296 CALL chk1mat( n, 1, m, 2, ia, ja, desca, 7, info )
297 CALL chk1mat( n, 1, p, 3, ib, jb, descb, 12, info )
298 IF( info.EQ.0 ) THEN
299 iroffa = mod( ia-1, desca( mb_ ) )
300 icoffa = mod( ja-1, desca( nb_ ) )
301 iroffb = mod( ib-1, descb( mb_ ) )
302 icoffb = mod( jb-1, descb( nb_ ) )
303 iarow = indxg2p( ia, desca( mb_ ), myrow, desca( rsrc_ ),
304 $ nprow )
305 iacol = indxg2p( ja, desca( nb_ ), mycol, desca( csrc_ ),
306 $ npcol )
307 ibrow = indxg2p( ib, descb( mb_ ), myrow, descb( rsrc_ ),
308 $ nprow )
309 ibcol = indxg2p( jb, descb( nb_ ), mycol, descb( csrc_ ),
310 $ npcol )
311 npa0 = numroc( n+iroffa, desca( mb_ ), myrow, iarow, nprow )
312 mqa0 = numroc( m+icoffa, desca( nb_ ), mycol, iacol, npcol )
313 npb0 = numroc( n+iroffb, descb( mb_ ), myrow, ibrow, nprow )
314 pqb0 = numroc( p+icoffb, descb( nb_ ), mycol, ibcol, npcol )
315 lwmin = max( desca( nb_ ) * ( npa0 + mqa0 + desca( nb_ ) ),
316 $ max( max( ( desca( nb_ )*( desca( nb_ ) - 1 ) ) / 2,
317 $ ( pqb0 + npb0 ) * desca( nb_ ) ) +
318 $ desca( nb_ ) * desca( nb_ ),
319 $ descb( mb_ ) * ( npb0 + pqb0 + descb( mb_ ) ) ) )
320*
321 work( 1 ) = dble( lwmin )
322 lquery = ( lwork.EQ.-1 )
323 IF( iarow.NE.ibrow .OR. iroffa.NE.iroffb ) THEN
324 info = -10
325 ELSE IF( desca( mb_ ).NE.descb( mb_ ) ) THEN
326 info = -1203
327 ELSE IF( ictxt.NE.descb( ctxt_ ) ) THEN
328 info = -1207
329 ELSE IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
330 info = -15
331 END IF
332 END IF
333 IF( lquery ) THEN
334 idum1( 1 ) = -1
335 ELSE
336 idum1( 1 ) = 1
337 END IF
338 idum2( 1 ) = 15
339 CALL pchk2mat( n, 1, m, 2, ia, ja, desca, 7, n, 1, p, 3, ib,
340 $ jb, descb, 12, 1, idum1, idum2, info )
341 END IF
342*
343 IF( info.NE.0 ) THEN
344 CALL pxerbla( ictxt, 'PDGGQRF', -info )
345 RETURN
346 ELSE IF( lquery ) THEN
347 RETURN
348 END IF
349*
350* QR factorization of N-by-M matrix sub( A ): sub( A ) = Q*R
351*
352 CALL pdgeqrf( n, m, a, ia, ja, desca, taua, work, lwork, info )
353 lwmin = int( work( 1 ) )
354*
355* Update sub( B ) := Q'*sub( B ).
356*
357 CALL pdormqr( 'Left', 'Transpose', n, p, min( n, m ), a, ia, ja,
358 $ desca, taua, b, ib, jb, descb, work, lwork, info )
359 lwmin = min( lwmin, int( work( 1 ) ) )
360*
361* RQ factorization of N-by-P matrix sub( B ): sub( B ) = T*Z.
362*
363 CALL pdgerqf( n, p, b, ib, jb, descb, taub, work, lwork, info )
364 work( 1 ) = dble( max( lwmin, int( work( 1 ) ) ) )
365*
366 RETURN
367*
368* End of PDGGQRF
369*
370 END
subroutine chk1mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, info)
Definition chk1mat.f:3
#define max(A, B)
Definition pcgemr.c:180
#define min(A, B)
Definition pcgemr.c:181
subroutine pchk2mat(ma, mapos0, na, napos0, ia, ja, desca, descapos0, mb, mbpos0, nb, nbpos0, ib, jb, descb, descbpos0, nextra, ex, expos, info)
Definition pchkxmat.f:175
subroutine pdgeqrf(m, n, a, ia, ja, desca, tau, work, lwork, info)
Definition pdgeqrf.f:3
subroutine pdgerqf(m, n, a, ia, ja, desca, tau, work, lwork, info)
Definition pdgerqf.f:3
subroutine pdggqrf(n, m, p, a, ia, ja, desca, taua, b, ib, jb, descb, taub, work, lwork, info)
Definition pdggqrf.f:3
subroutine pdormqr(side, trans, m, n, k, a, ia, ja, desca, tau, c, ic, jc, descc, work, lwork, info)
Definition pdormqr.f:3
subroutine pxerbla(ictxt, srname, info)
Definition pxerbla.f:2