Annotation of rpl/lapack/lapack/dgeqp3.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DGEQP3
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEQP3 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqp3.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqp3.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqp3.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, LWORK, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER JPVT( * )
! 28: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DGEQP3 computes a QR factorization with column pivoting of a
! 38: *> matrix A: A*P = Q*R using Level 3 BLAS.
! 39: *> \endverbatim
! 40: *
! 41: * Arguments:
! 42: * ==========
! 43: *
! 44: *> \param[in] M
! 45: *> \verbatim
! 46: *> M is INTEGER
! 47: *> The number of rows of the matrix A. M >= 0.
! 48: *> \endverbatim
! 49: *>
! 50: *> \param[in] N
! 51: *> \verbatim
! 52: *> N is INTEGER
! 53: *> The number of columns of the matrix A. N >= 0.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in,out] A
! 57: *> \verbatim
! 58: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 59: *> On entry, the M-by-N matrix A.
! 60: *> On exit, the upper triangle of the array contains the
! 61: *> min(M,N)-by-N upper trapezoidal matrix R; the elements below
! 62: *> the diagonal, together with the array TAU, represent the
! 63: *> orthogonal matrix Q as a product of min(M,N) elementary
! 64: *> reflectors.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] LDA
! 68: *> \verbatim
! 69: *> LDA is INTEGER
! 70: *> The leading dimension of the array A. LDA >= max(1,M).
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in,out] JPVT
! 74: *> \verbatim
! 75: *> JPVT is INTEGER array, dimension (N)
! 76: *> On entry, if JPVT(J).ne.0, the J-th column of A is permuted
! 77: *> to the front of A*P (a leading column); if JPVT(J)=0,
! 78: *> the J-th column of A is a free column.
! 79: *> On exit, if JPVT(J)=K, then the J-th column of A*P was the
! 80: *> the K-th column of A.
! 81: *> \endverbatim
! 82: *>
! 83: *> \param[out] TAU
! 84: *> \verbatim
! 85: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
! 86: *> The scalar factors of the elementary reflectors.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[out] WORK
! 90: *> \verbatim
! 91: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 92: *> On exit, if INFO=0, WORK(1) returns the optimal LWORK.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] LWORK
! 96: *> \verbatim
! 97: *> LWORK is INTEGER
! 98: *> The dimension of the array WORK. LWORK >= 3*N+1.
! 99: *> For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
! 100: *> is the optimal blocksize.
! 101: *>
! 102: *> If LWORK = -1, then a workspace query is assumed; the routine
! 103: *> only calculates the optimal size of the WORK array, returns
! 104: *> this value as the first entry of the WORK array, and no error
! 105: *> message related to LWORK is issued by XERBLA.
! 106: *> \endverbatim
! 107: *>
! 108: *> \param[out] INFO
! 109: *> \verbatim
! 110: *> INFO is INTEGER
! 111: *> = 0: successful exit.
! 112: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 113: *> \endverbatim
! 114: *
! 115: * Authors:
! 116: * ========
! 117: *
! 118: *> \author Univ. of Tennessee
! 119: *> \author Univ. of California Berkeley
! 120: *> \author Univ. of Colorado Denver
! 121: *> \author NAG Ltd.
! 122: *
! 123: *> \date November 2011
! 124: *
! 125: *> \ingroup doubleGEcomputational
! 126: *
! 127: *> \par Further Details:
! 128: * =====================
! 129: *>
! 130: *> \verbatim
! 131: *>
! 132: *> The matrix Q is represented as a product of elementary reflectors
! 133: *>
! 134: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 135: *>
! 136: *> Each H(i) has the form
! 137: *>
! 138: *> H(i) = I - tau * v * v**T
! 139: *>
! 140: *> where tau is a real/complex scalar, and v is a real/complex vector
! 141: *> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
! 142: *> A(i+1:m,i), and tau in TAU(i).
! 143: *> \endverbatim
! 144: *
! 145: *> \par Contributors:
! 146: * ==================
! 147: *>
! 148: *> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
! 149: *> X. Sun, Computer Science Dept., Duke University, USA
! 150: *>
! 151: * =====================================================================
1.1 bertrand 152: SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
153: *
1.9 ! bertrand 154: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 155: * -- LAPACK is a software package provided by Univ. of Tennessee, --
156: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 157: * November 2011
1.1 bertrand 158: *
159: * .. Scalar Arguments ..
160: INTEGER INFO, LDA, LWORK, M, N
161: * ..
162: * .. Array Arguments ..
163: INTEGER JPVT( * )
164: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
165: * ..
166: *
167: * =====================================================================
168: *
169: * .. Parameters ..
170: INTEGER INB, INBMIN, IXOVER
171: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
172: * ..
173: * .. Local Scalars ..
174: LOGICAL LQUERY
175: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
176: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
177: * ..
178: * .. External Subroutines ..
179: EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA
180: * ..
181: * .. External Functions ..
182: INTEGER ILAENV
183: DOUBLE PRECISION DNRM2
184: EXTERNAL ILAENV, DNRM2
185: * ..
186: * .. Intrinsic Functions ..
187: INTRINSIC INT, MAX, MIN
188: * ..
189: * .. Executable Statements ..
190: *
191: * Test input arguments
1.9 ! bertrand 192: * ====================
1.1 bertrand 193: *
194: INFO = 0
195: LQUERY = ( LWORK.EQ.-1 )
196: IF( M.LT.0 ) THEN
197: INFO = -1
198: ELSE IF( N.LT.0 ) THEN
199: INFO = -2
200: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
201: INFO = -4
202: END IF
203: *
204: IF( INFO.EQ.0 ) THEN
205: MINMN = MIN( M, N )
206: IF( MINMN.EQ.0 ) THEN
207: IWS = 1
208: LWKOPT = 1
209: ELSE
210: IWS = 3*N + 1
211: NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 )
212: LWKOPT = 2*N + ( N + 1 )*NB
213: END IF
214: WORK( 1 ) = LWKOPT
215: *
216: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
217: INFO = -8
218: END IF
219: END IF
220: *
221: IF( INFO.NE.0 ) THEN
222: CALL XERBLA( 'DGEQP3', -INFO )
223: RETURN
224: ELSE IF( LQUERY ) THEN
225: RETURN
226: END IF
227: *
228: * Quick return if possible.
229: *
230: IF( MINMN.EQ.0 ) THEN
231: RETURN
232: END IF
233: *
234: * Move initial columns up front.
235: *
236: NFXD = 1
237: DO 10 J = 1, N
238: IF( JPVT( J ).NE.0 ) THEN
239: IF( J.NE.NFXD ) THEN
240: CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
241: JPVT( J ) = JPVT( NFXD )
242: JPVT( NFXD ) = J
243: ELSE
244: JPVT( J ) = J
245: END IF
246: NFXD = NFXD + 1
247: ELSE
248: JPVT( J ) = J
249: END IF
250: 10 CONTINUE
251: NFXD = NFXD - 1
252: *
253: * Factorize fixed columns
1.9 ! bertrand 254: * =======================
1.1 bertrand 255: *
256: * Compute the QR factorization of fixed columns and update
257: * remaining columns.
258: *
259: IF( NFXD.GT.0 ) THEN
260: NA = MIN( M, NFXD )
261: *CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
262: CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
263: IWS = MAX( IWS, INT( WORK( 1 ) ) )
264: IF( NA.LT.N ) THEN
265: *CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA,
266: *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO )
267: CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU,
268: $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO )
269: IWS = MAX( IWS, INT( WORK( 1 ) ) )
270: END IF
271: END IF
272: *
273: * Factorize free columns
1.9 ! bertrand 274: * ======================
1.1 bertrand 275: *
276: IF( NFXD.LT.MINMN ) THEN
277: *
278: SM = M - NFXD
279: SN = N - NFXD
280: SMINMN = MINMN - NFXD
281: *
282: * Determine the block size.
283: *
284: NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 )
285: NBMIN = 2
286: NX = 0
287: *
288: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
289: *
290: * Determine when to cross over from blocked to unblocked code.
291: *
292: NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1,
293: $ -1 ) )
294: *
295: *
296: IF( NX.LT.SMINMN ) THEN
297: *
298: * Determine if workspace is large enough for blocked code.
299: *
300: MINWS = 2*SN + ( SN+1 )*NB
301: IWS = MAX( IWS, MINWS )
302: IF( LWORK.LT.MINWS ) THEN
303: *
304: * Not enough workspace to use optimal NB: Reduce NB and
305: * determine the minimum value of NB.
306: *
307: NB = ( LWORK-2*SN ) / ( SN+1 )
308: NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN,
309: $ -1, -1 ) )
310: *
311: *
312: END IF
313: END IF
314: END IF
315: *
316: * Initialize partial column norms. The first N elements of work
317: * store the exact column norms.
318: *
319: DO 20 J = NFXD + 1, N
320: WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 )
321: WORK( N+J ) = WORK( J )
322: 20 CONTINUE
323: *
324: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
325: $ ( NX.LT.SMINMN ) ) THEN
326: *
327: * Use blocked code initially.
328: *
329: J = NFXD + 1
330: *
331: * Compute factorization: while loop.
332: *
333: *
334: TOPBMN = MINMN - NX
335: 30 CONTINUE
336: IF( J.LE.TOPBMN ) THEN
337: JB = MIN( NB, TOPBMN-J+1 )
338: *
339: * Factorize JB columns among columns J:N.
340: *
341: CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
342: $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ),
343: $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 )
344: *
345: J = J + FJB
346: GO TO 30
347: END IF
348: ELSE
349: J = NFXD + 1
350: END IF
351: *
352: * Use unblocked code to factor the last or only block.
353: *
354: *
355: IF( J.LE.MINMN )
356: $ CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
357: $ TAU( J ), WORK( J ), WORK( N+J ),
358: $ WORK( 2*N+1 ) )
359: *
360: END IF
361: *
362: WORK( 1 ) = IWS
363: RETURN
364: *
365: * End of DGEQP3
366: *
367: END
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