1: *> \brief \b ZGEQP3
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZGEQP3 + dependencies
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14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqp3.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
22: * INFO )
23: *
24: * .. Scalar Arguments ..
25: * INTEGER INFO, LDA, LWORK, M, N
26: * ..
27: * .. Array Arguments ..
28: * INTEGER JPVT( * )
29: * DOUBLE PRECISION RWORK( * )
30: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZGEQP3 computes a QR factorization with column pivoting of a
40: *> matrix A: A*P = Q*R using Level 3 BLAS.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] M
47: *> \verbatim
48: *> M is INTEGER
49: *> The number of rows of the matrix A. M >= 0.
50: *> \endverbatim
51: *>
52: *> \param[in] N
53: *> \verbatim
54: *> N is INTEGER
55: *> The number of columns of the matrix A. N >= 0.
56: *> \endverbatim
57: *>
58: *> \param[in,out] A
59: *> \verbatim
60: *> A is COMPLEX*16 array, dimension (LDA,N)
61: *> On entry, the M-by-N matrix A.
62: *> On exit, the upper triangle of the array contains the
63: *> min(M,N)-by-N upper trapezoidal matrix R; the elements below
64: *> the diagonal, together with the array TAU, represent the
65: *> unitary matrix Q as a product of min(M,N) elementary
66: *> reflectors.
67: *> \endverbatim
68: *>
69: *> \param[in] LDA
70: *> \verbatim
71: *> LDA is INTEGER
72: *> The leading dimension of the array A. LDA >= max(1,M).
73: *> \endverbatim
74: *>
75: *> \param[in,out] JPVT
76: *> \verbatim
77: *> JPVT is INTEGER array, dimension (N)
78: *> On entry, if JPVT(J).ne.0, the J-th column of A is permuted
79: *> to the front of A*P (a leading column); if JPVT(J)=0,
80: *> the J-th column of A is a free column.
81: *> On exit, if JPVT(J)=K, then the J-th column of A*P was the
82: *> the K-th column of A.
83: *> \endverbatim
84: *>
85: *> \param[out] TAU
86: *> \verbatim
87: *> TAU is COMPLEX*16 array, dimension (min(M,N))
88: *> The scalar factors of the elementary reflectors.
89: *> \endverbatim
90: *>
91: *> \param[out] WORK
92: *> \verbatim
93: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
94: *> On exit, if INFO=0, WORK(1) returns the optimal LWORK.
95: *> \endverbatim
96: *>
97: *> \param[in] LWORK
98: *> \verbatim
99: *> LWORK is INTEGER
100: *> The dimension of the array WORK. LWORK >= N+1.
101: *> For optimal performance LWORK >= ( N+1 )*NB, where NB
102: *> is the optimal blocksize.
103: *>
104: *> If LWORK = -1, then a workspace query is assumed; the routine
105: *> only calculates the optimal size of the WORK array, returns
106: *> this value as the first entry of the WORK array, and no error
107: *> message related to LWORK is issued by XERBLA.
108: *> \endverbatim
109: *>
110: *> \param[out] RWORK
111: *> \verbatim
112: *> RWORK is DOUBLE PRECISION array, dimension (2*N)
113: *> \endverbatim
114: *>
115: *> \param[out] INFO
116: *> \verbatim
117: *> INFO is INTEGER
118: *> = 0: successful exit.
119: *> < 0: if INFO = -i, the i-th argument had an illegal value.
120: *> \endverbatim
121: *
122: * Authors:
123: * ========
124: *
125: *> \author Univ. of Tennessee
126: *> \author Univ. of California Berkeley
127: *> \author Univ. of Colorado Denver
128: *> \author NAG Ltd.
129: *
130: *> \ingroup complex16GEcomputational
131: *
132: *> \par Further Details:
133: * =====================
134: *>
135: *> \verbatim
136: *>
137: *> The matrix Q is represented as a product of elementary reflectors
138: *>
139: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
140: *>
141: *> Each H(i) has the form
142: *>
143: *> H(i) = I - tau * v * v**H
144: *>
145: *> where tau is a complex scalar, and v is a real/complex vector
146: *> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
147: *> A(i+1:m,i), and tau in TAU(i).
148: *> \endverbatim
149: *
150: *> \par Contributors:
151: * ==================
152: *>
153: *> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
154: *> X. Sun, Computer Science Dept., Duke University, USA
155: *>
156: * =====================================================================
157: SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
158: $ INFO )
159: *
160: * -- LAPACK computational routine --
161: * -- LAPACK is a software package provided by Univ. of Tennessee, --
162: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163: *
164: * .. Scalar Arguments ..
165: INTEGER INFO, LDA, LWORK, M, N
166: * ..
167: * .. Array Arguments ..
168: INTEGER JPVT( * )
169: DOUBLE PRECISION RWORK( * )
170: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
171: * ..
172: *
173: * =====================================================================
174: *
175: * .. Parameters ..
176: INTEGER INB, INBMIN, IXOVER
177: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
178: * ..
179: * .. Local Scalars ..
180: LOGICAL LQUERY
181: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
182: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL XERBLA, ZGEQRF, ZLAQP2, ZLAQPS, ZSWAP, ZUNMQR
186: * ..
187: * .. External Functions ..
188: INTEGER ILAENV
189: DOUBLE PRECISION DZNRM2
190: EXTERNAL ILAENV, DZNRM2
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC INT, MAX, MIN
194: * ..
195: * .. Executable Statements ..
196: *
197: * Test input arguments
198: * ====================
199: *
200: INFO = 0
201: LQUERY = ( LWORK.EQ.-1 )
202: IF( M.LT.0 ) THEN
203: INFO = -1
204: ELSE IF( N.LT.0 ) THEN
205: INFO = -2
206: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
207: INFO = -4
208: END IF
209: *
210: IF( INFO.EQ.0 ) THEN
211: MINMN = MIN( M, N )
212: IF( MINMN.EQ.0 ) THEN
213: IWS = 1
214: LWKOPT = 1
215: ELSE
216: IWS = N + 1
217: NB = ILAENV( INB, 'ZGEQRF', ' ', M, N, -1, -1 )
218: LWKOPT = ( N + 1 )*NB
219: END IF
220: WORK( 1 ) = DCMPLX( LWKOPT )
221: *
222: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
223: INFO = -8
224: END IF
225: END IF
226: *
227: IF( INFO.NE.0 ) THEN
228: CALL XERBLA( 'ZGEQP3', -INFO )
229: RETURN
230: ELSE IF( LQUERY ) 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 ZSWAP( 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
254: * =======================
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 ZGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
262: CALL ZGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
263: IWS = MAX( IWS, INT( WORK( 1 ) ) )
264: IF( NA.LT.N ) THEN
265: *CC CALL ZUNM2R( 'Left', 'Conjugate Transpose', M, N-NA,
266: *CC $ NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK,
267: *CC $ INFO )
268: CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, N-NA, NA, A,
269: $ LDA, TAU, A( 1, NA+1 ), LDA, WORK, LWORK,
270: $ INFO )
271: IWS = MAX( IWS, INT( WORK( 1 ) ) )
272: END IF
273: END IF
274: *
275: * Factorize free columns
276: * ======================
277: *
278: IF( NFXD.LT.MINMN ) THEN
279: *
280: SM = M - NFXD
281: SN = N - NFXD
282: SMINMN = MINMN - NFXD
283: *
284: * Determine the block size.
285: *
286: NB = ILAENV( INB, 'ZGEQRF', ' ', SM, SN, -1, -1 )
287: NBMIN = 2
288: NX = 0
289: *
290: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
291: *
292: * Determine when to cross over from blocked to unblocked code.
293: *
294: NX = MAX( 0, ILAENV( IXOVER, 'ZGEQRF', ' ', SM, SN, -1,
295: $ -1 ) )
296: *
297: *
298: IF( NX.LT.SMINMN ) THEN
299: *
300: * Determine if workspace is large enough for blocked code.
301: *
302: MINWS = ( SN+1 )*NB
303: IWS = MAX( IWS, MINWS )
304: IF( LWORK.LT.MINWS ) THEN
305: *
306: * Not enough workspace to use optimal NB: Reduce NB and
307: * determine the minimum value of NB.
308: *
309: NB = LWORK / ( SN+1 )
310: NBMIN = MAX( 2, ILAENV( INBMIN, 'ZGEQRF', ' ', SM, SN,
311: $ -1, -1 ) )
312: *
313: *
314: END IF
315: END IF
316: END IF
317: *
318: * Initialize partial column norms. The first N elements of work
319: * store the exact column norms.
320: *
321: DO 20 J = NFXD + 1, N
322: RWORK( J ) = DZNRM2( SM, A( NFXD+1, J ), 1 )
323: RWORK( N+J ) = RWORK( J )
324: 20 CONTINUE
325: *
326: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
327: $ ( NX.LT.SMINMN ) ) THEN
328: *
329: * Use blocked code initially.
330: *
331: J = NFXD + 1
332: *
333: * Compute factorization: while loop.
334: *
335: *
336: TOPBMN = MINMN - NX
337: 30 CONTINUE
338: IF( J.LE.TOPBMN ) THEN
339: JB = MIN( NB, TOPBMN-J+1 )
340: *
341: * Factorize JB columns among columns J:N.
342: *
343: CALL ZLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
344: $ JPVT( J ), TAU( J ), RWORK( J ),
345: $ RWORK( N+J ), WORK( 1 ), WORK( JB+1 ),
346: $ N-J+1 )
347: *
348: J = J + FJB
349: GO TO 30
350: END IF
351: ELSE
352: J = NFXD + 1
353: END IF
354: *
355: * Use unblocked code to factor the last or only block.
356: *
357: *
358: IF( J.LE.MINMN )
359: $ CALL ZLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
360: $ TAU( J ), RWORK( J ), RWORK( N+J ), WORK( 1 ) )
361: *
362: END IF
363: *
364: WORK( 1 ) = DCMPLX( LWKOPT )
365: RETURN
366: *
367: * End of ZGEQP3
368: *
369: END
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