1: SUBROUTINE DGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO )
2: *
3: * -- LAPACK routine (version 3.3.1) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * -- April 2011 --
7: *
8: * .. Scalar Arguments ..
9: INTEGER INFO, LDA, LWORK, M, N
10: * ..
11: * .. Array Arguments ..
12: INTEGER JPVT( * )
13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DGEQP3 computes a QR factorization with column pivoting of a
20: * matrix A: A*P = Q*R using Level 3 BLAS.
21: *
22: * Arguments
23: * =========
24: *
25: * M (input) INTEGER
26: * The number of rows of the matrix A. M >= 0.
27: *
28: * N (input) INTEGER
29: * The number of columns of the matrix A. N >= 0.
30: *
31: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
32: * On entry, the M-by-N matrix A.
33: * On exit, the upper triangle of the array contains the
34: * min(M,N)-by-N upper trapezoidal matrix R; the elements below
35: * the diagonal, together with the array TAU, represent the
36: * orthogonal matrix Q as a product of min(M,N) elementary
37: * reflectors.
38: *
39: * LDA (input) INTEGER
40: * The leading dimension of the array A. LDA >= max(1,M).
41: *
42: * JPVT (input/output) INTEGER array, dimension (N)
43: * On entry, if JPVT(J).ne.0, the J-th column of A is permuted
44: * to the front of A*P (a leading column); if JPVT(J)=0,
45: * the J-th column of A is a free column.
46: * On exit, if JPVT(J)=K, then the J-th column of A*P was the
47: * the K-th column of A.
48: *
49: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
50: * The scalar factors of the elementary reflectors.
51: *
52: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
53: * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
54: *
55: * LWORK (input) INTEGER
56: * The dimension of the array WORK. LWORK >= 3*N+1.
57: * For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
58: * is the optimal blocksize.
59: *
60: * If LWORK = -1, then a workspace query is assumed; the routine
61: * only calculates the optimal size of the WORK array, returns
62: * this value as the first entry of the WORK array, and no error
63: * message related to LWORK is issued by XERBLA.
64: *
65: * INFO (output) INTEGER
66: * = 0: successful exit.
67: * < 0: if INFO = -i, the i-th argument had an illegal value.
68: *
69: * Further Details
70: * ===============
71: *
72: * The matrix Q is represented as a product of elementary reflectors
73: *
74: * Q = H(1) H(2) . . . H(k), where k = min(m,n).
75: *
76: * Each H(i) has the form
77: *
78: * H(i) = I - tau * v * v**T
79: *
80: * where tau is a real/complex scalar, and v is a real/complex vector
81: * with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
82: * A(i+1:m,i), and tau in TAU(i).
83: *
84: * Based on contributions by
85: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
86: * X. Sun, Computer Science Dept., Duke University, USA
87: *
88: * =====================================================================
89: *
90: * .. Parameters ..
91: INTEGER INB, INBMIN, IXOVER
92: PARAMETER ( INB = 1, INBMIN = 2, IXOVER = 3 )
93: * ..
94: * .. Local Scalars ..
95: LOGICAL LQUERY
96: INTEGER FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
97: $ NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
98: * ..
99: * .. External Subroutines ..
100: EXTERNAL DGEQRF, DLAQP2, DLAQPS, DORMQR, DSWAP, XERBLA
101: * ..
102: * .. External Functions ..
103: INTEGER ILAENV
104: DOUBLE PRECISION DNRM2
105: EXTERNAL ILAENV, DNRM2
106: * ..
107: * .. Intrinsic Functions ..
108: INTRINSIC INT, MAX, MIN
109: * ..
110: * .. Executable Statements ..
111: *
112: * Test input arguments
113: * ====================
114: *
115: INFO = 0
116: LQUERY = ( LWORK.EQ.-1 )
117: IF( M.LT.0 ) THEN
118: INFO = -1
119: ELSE IF( N.LT.0 ) THEN
120: INFO = -2
121: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
122: INFO = -4
123: END IF
124: *
125: IF( INFO.EQ.0 ) THEN
126: MINMN = MIN( M, N )
127: IF( MINMN.EQ.0 ) THEN
128: IWS = 1
129: LWKOPT = 1
130: ELSE
131: IWS = 3*N + 1
132: NB = ILAENV( INB, 'DGEQRF', ' ', M, N, -1, -1 )
133: LWKOPT = 2*N + ( N + 1 )*NB
134: END IF
135: WORK( 1 ) = LWKOPT
136: *
137: IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
138: INFO = -8
139: END IF
140: END IF
141: *
142: IF( INFO.NE.0 ) THEN
143: CALL XERBLA( 'DGEQP3', -INFO )
144: RETURN
145: ELSE IF( LQUERY ) THEN
146: RETURN
147: END IF
148: *
149: * Quick return if possible.
150: *
151: IF( MINMN.EQ.0 ) THEN
152: RETURN
153: END IF
154: *
155: * Move initial columns up front.
156: *
157: NFXD = 1
158: DO 10 J = 1, N
159: IF( JPVT( J ).NE.0 ) THEN
160: IF( J.NE.NFXD ) THEN
161: CALL DSWAP( M, A( 1, J ), 1, A( 1, NFXD ), 1 )
162: JPVT( J ) = JPVT( NFXD )
163: JPVT( NFXD ) = J
164: ELSE
165: JPVT( J ) = J
166: END IF
167: NFXD = NFXD + 1
168: ELSE
169: JPVT( J ) = J
170: END IF
171: 10 CONTINUE
172: NFXD = NFXD - 1
173: *
174: * Factorize fixed columns
175: * =======================
176: *
177: * Compute the QR factorization of fixed columns and update
178: * remaining columns.
179: *
180: IF( NFXD.GT.0 ) THEN
181: NA = MIN( M, NFXD )
182: *CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO )
183: CALL DGEQRF( M, NA, A, LDA, TAU, WORK, LWORK, INFO )
184: IWS = MAX( IWS, INT( WORK( 1 ) ) )
185: IF( NA.LT.N ) THEN
186: *CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA,
187: *CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO )
188: CALL DORMQR( 'Left', 'Transpose', M, N-NA, NA, A, LDA, TAU,
189: $ A( 1, NA+1 ), LDA, WORK, LWORK, INFO )
190: IWS = MAX( IWS, INT( WORK( 1 ) ) )
191: END IF
192: END IF
193: *
194: * Factorize free columns
195: * ======================
196: *
197: IF( NFXD.LT.MINMN ) THEN
198: *
199: SM = M - NFXD
200: SN = N - NFXD
201: SMINMN = MINMN - NFXD
202: *
203: * Determine the block size.
204: *
205: NB = ILAENV( INB, 'DGEQRF', ' ', SM, SN, -1, -1 )
206: NBMIN = 2
207: NX = 0
208: *
209: IF( ( NB.GT.1 ) .AND. ( NB.LT.SMINMN ) ) THEN
210: *
211: * Determine when to cross over from blocked to unblocked code.
212: *
213: NX = MAX( 0, ILAENV( IXOVER, 'DGEQRF', ' ', SM, SN, -1,
214: $ -1 ) )
215: *
216: *
217: IF( NX.LT.SMINMN ) THEN
218: *
219: * Determine if workspace is large enough for blocked code.
220: *
221: MINWS = 2*SN + ( SN+1 )*NB
222: IWS = MAX( IWS, MINWS )
223: IF( LWORK.LT.MINWS ) THEN
224: *
225: * Not enough workspace to use optimal NB: Reduce NB and
226: * determine the minimum value of NB.
227: *
228: NB = ( LWORK-2*SN ) / ( SN+1 )
229: NBMIN = MAX( 2, ILAENV( INBMIN, 'DGEQRF', ' ', SM, SN,
230: $ -1, -1 ) )
231: *
232: *
233: END IF
234: END IF
235: END IF
236: *
237: * Initialize partial column norms. The first N elements of work
238: * store the exact column norms.
239: *
240: DO 20 J = NFXD + 1, N
241: WORK( J ) = DNRM2( SM, A( NFXD+1, J ), 1 )
242: WORK( N+J ) = WORK( J )
243: 20 CONTINUE
244: *
245: IF( ( NB.GE.NBMIN ) .AND. ( NB.LT.SMINMN ) .AND.
246: $ ( NX.LT.SMINMN ) ) THEN
247: *
248: * Use blocked code initially.
249: *
250: J = NFXD + 1
251: *
252: * Compute factorization: while loop.
253: *
254: *
255: TOPBMN = MINMN - NX
256: 30 CONTINUE
257: IF( J.LE.TOPBMN ) THEN
258: JB = MIN( NB, TOPBMN-J+1 )
259: *
260: * Factorize JB columns among columns J:N.
261: *
262: CALL DLAQPS( M, N-J+1, J-1, JB, FJB, A( 1, J ), LDA,
263: $ JPVT( J ), TAU( J ), WORK( J ), WORK( N+J ),
264: $ WORK( 2*N+1 ), WORK( 2*N+JB+1 ), N-J+1 )
265: *
266: J = J + FJB
267: GO TO 30
268: END IF
269: ELSE
270: J = NFXD + 1
271: END IF
272: *
273: * Use unblocked code to factor the last or only block.
274: *
275: *
276: IF( J.LE.MINMN )
277: $ CALL DLAQP2( M, N-J+1, J-1, A( 1, J ), LDA, JPVT( J ),
278: $ TAU( J ), WORK( J ), WORK( N+J ),
279: $ WORK( 2*N+1 ) )
280: *
281: END IF
282: *
283: WORK( 1 ) = IWS
284: RETURN
285: *
286: * End of DGEQP3
287: *
288: END
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