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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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: *> \date December 2016
131: *
132: *> \ingroup complex16GEcomputational
133: *
134: *> \par Further Details:
135: * =====================
136: *>
137: *> \verbatim
138: *>
139: *> The matrix Q is represented as a product of elementary reflectors
140: *>
141: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
142: *>
143: *> Each H(i) has the form
144: *>
145: *> H(i) = I - tau * v * v**H
146: *>
147: *> where tau is a complex scalar, and v is a real/complex vector
148: *> with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
149: *> A(i+1:m,i), and tau in TAU(i).
150: *> \endverbatim
151: *
152: *> \par Contributors:
153: * ==================
154: *>
155: *> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
156: *> X. Sun, Computer Science Dept., Duke University, USA
157: *>
158: * =====================================================================
159: SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, RWORK,
160: $ INFO )
161: *
162: * -- LAPACK computational routine (version 3.7.0) --
163: * -- LAPACK is a software package provided by Univ. of Tennessee, --
164: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165: * December 2016
166: *
167: * .. Scalar Arguments ..
168: INTEGER INFO, LDA, LWORK, M, N
169: * ..
170: * .. Array Arguments ..
171: INTEGER JPVT( * )
172: DOUBLE PRECISION RWORK( * )
173: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
174: * ..
175: *
176: * =====================================================================
177: *
178: * .. Parameters ..
179: INTEGER INB, INBMIN, IXOVER
180: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
181: * ..
182: * .. Local Scalars ..
183: LOGICAL LQUERY
184: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
185: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
186: * ..
187: * .. External Subroutines ..
188: EXTERNAL XERBLA, ZGEQRF, ZLAQP2, ZLAQPS, ZSWAP, ZUNMQR
189: * ..
190: * .. External Functions ..
191: INTEGER ILAENV
192: DOUBLE PRECISION DZNRM2
193: EXTERNAL ILAENV, DZNRM2
194: * ..
195: * .. Intrinsic Functions ..
196: INTRINSIC INT, MAX, MIN
197: * ..
198: * .. Executable Statements ..
199: *
200: * Test input arguments
201: * ====================
202: *
203: INFO = 0
204: LQUERY = ( LWORK.EQ.-1 )
205: IF( M.LT.0 ) THEN
206: INFO = -1
207: ELSE IF( N.LT.0 ) THEN
208: INFO = -2
209: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
210: INFO = -4
211: END IF
212: *
213: IF( INFO.EQ.0 ) THEN
214: MINMN = MIN( M, N )
215: IF( MINMN.EQ.0 ) THEN
216: IWS = 1
217: LWKOPT = 1
218: ELSE
219: IWS = N + 1
220: NB = ILAENV( INB, 'ZGEQRF', ' ', M, N, -1, -1 )
221: LWKOPT = ( N + 1 )*NB
222: END IF
223: WORK( 1 ) = DCMPLX( LWKOPT )
224: *
225: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
226: INFO = -8
227: END IF
228: END IF
229: *
230: IF( INFO.NE.0 ) THEN
231: CALL XERBLA( 'ZGEQP3', -INFO )
232: RETURN
233: ELSE IF( LQUERY ) THEN
234: RETURN
235: END IF
236: *
237: * Move initial columns up front.
238: *
239: NFXD = 1
240: DO 10 J = 1, N
241: IF( JPVT( J ).NE.0 ) THEN
242: IF( J.NE.NFXD ) THEN
243: CALL ZSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
244: JPVT( J ) = JPVT( NFXD )
245: JPVT( NFXD ) = J
246: ELSE
247: JPVT( J ) = J
248: END IF
249: NFXD = NFXD + 1
250: ELSE
251: JPVT( J ) = J
252: END IF
253: 10 CONTINUE
254: NFXD = NFXD - 1
255: *
256: * Factorize fixed columns
257: * =======================
258: *
259: * Compute the QR factorization of fixed columns and update
260: * remaining columns.
261: *
262: IF( NFXD.GT.0 ) THEN
263: NA = MIN( M, NFXD )
264: *CC CALL ZGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
265: CALL ZGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
266: IWS = MAX( IWS, INT( WORK( 1 ) ) )
267: IF( NA.LT.N ) THEN
268: *CC CALL ZUNM2R( 'Left', 'Conjugate Transpose', M, N-NA,
269: *CC $ NA, A, LDA, TAU, A( 1, NA+1 ), LDA, WORK,
270: *CC $ INFO )
271: CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, N-NA, NA, A,
272: $ LDA, TAU, A( 1, NA+1 ), LDA, WORK, LWORK,
273: $ INFO )
274: IWS = MAX( IWS, INT( WORK( 1 ) ) )
275: END IF
276: END IF
277: *
278: * Factorize free columns
279: * ======================
280: *
281: IF( NFXD.LT.MINMN ) THEN
282: *
283: SM = M - NFXD
284: SN = N - NFXD
285: SMINMN = MINMN - NFXD
286: *
287: * Determine the block size.
288: *
289: NB = ILAENV( INB, 'ZGEQRF', ' ', SM, SN, -1, -1 )
290: NBMIN = 2
291: NX = 0
292: *
293: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
294: *
295: * Determine when to cross over from blocked to unblocked code.
296: *
297: NX = MAX( 0, ILAENV( IXOVER, 'ZGEQRF', ' ', SM, SN, -1,
298: $ -1 ) )
299: *
300: *
301: IF( NX.LT.SMINMN ) THEN
302: *
303: * Determine if workspace is large enough for blocked code.
304: *
305: MINWS = ( SN+1 )*NB
306: IWS = MAX( IWS, MINWS )
307: IF( LWORK.LT.MINWS ) THEN
308: *
309: * Not enough workspace to use optimal NB: Reduce NB and
310: * determine the minimum value of NB.
311: *
312: NB = LWORK / ( SN+1 )
313: NBMIN = MAX( 2, ILAENV( INBMIN, 'ZGEQRF', ' ', SM, SN,
314: $ -1, -1 ) )
315: *
316: *
317: END IF
318: END IF
319: END IF
320: *
321: * Initialize partial column norms. The first N elements of work
322: * store the exact column norms.
323: *
324: DO 20 J = NFXD + 1, N
325: RWORK( J ) = DZNRM2( SM, A( NFXD+1, J ), 1 )
326: RWORK( N+J ) = RWORK( J )
327: 20 CONTINUE
328: *
329: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
330: $ ( NX.LT.SMINMN ) ) THEN
331: *
332: * Use blocked code initially.
333: *
334: J = NFXD + 1
335: *
336: * Compute factorization: while loop.
337: *
338: *
339: TOPBMN = MINMN - NX
340: 30 CONTINUE
341: IF( J.LE.TOPBMN ) THEN
342: JB = MIN( NB, TOPBMN-J+1 )
343: *
344: * Factorize JB columns among columns J:N.
345: *
346: CALL ZLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
347: $ JPVT( J ), TAU( J ), RWORK( J ),
348: $ RWORK( N+J ), WORK( 1 ), WORK( JB+1 ),
349: $ N-J+1 )
350: *
351: J = J + FJB
352: GO TO 30
353: END IF
354: ELSE
355: J = NFXD + 1
356: END IF
357: *
358: * Use unblocked code to factor the last or only block.
359: *
360: *
361: IF( J.LE.MINMN )
362: $ CALL ZLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
363: $ TAU( J ), RWORK( J ), RWORK( N+J ), WORK( 1 ) )
364: *
365: END IF
366: *
367: WORK( 1 ) = DCMPLX( LWKOPT )
368: RETURN
369: *
370: * End of ZGEQP3
371: *
372: END
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