Annotation of rpl/lapack/lapack/dlaqp2.f, revision 1.20
1.13 bertrand 1: *> \brief \b DLAQP2 computes a QR factorization with column pivoting of the matrix block.
1.10 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.18 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.10 bertrand 7: *
8: *> \htmlonly
1.18 bertrand 9: *> Download DLAQP2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqp2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqp2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqp2.f">
1.10 bertrand 15: *> [TXT]</a>
1.18 bertrand 16: *> \endhtmlonly
1.10 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
22: * WORK )
1.18 bertrand 23: *
1.10 bertrand 24: * .. Scalar Arguments ..
25: * INTEGER LDA, M, N, OFFSET
26: * ..
27: * .. Array Arguments ..
28: * INTEGER JPVT( * )
29: * DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ),
30: * $ WORK( * )
31: * ..
1.18 bertrand 32: *
1.10 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DLAQP2 computes a QR factorization with column pivoting of
40: *> the block A(OFFSET+1:M,1:N).
41: *> The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] M
48: *> \verbatim
49: *> M is INTEGER
50: *> The number of rows of the matrix A. M >= 0.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> The number of columns of the matrix A. N >= 0.
57: *> \endverbatim
58: *>
59: *> \param[in] OFFSET
60: *> \verbatim
61: *> OFFSET is INTEGER
62: *> The number of rows of the matrix A that must be pivoted
63: *> but no factorized. OFFSET >= 0.
64: *> \endverbatim
65: *>
66: *> \param[in,out] A
67: *> \verbatim
68: *> A is DOUBLE PRECISION array, dimension (LDA,N)
69: *> On entry, the M-by-N matrix A.
1.18 bertrand 70: *> On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
1.10 bertrand 71: *> the triangular factor obtained; the elements in block
72: *> A(OFFSET+1:M,1:N) below the diagonal, together with the
73: *> array TAU, represent the orthogonal matrix Q as a product of
74: *> elementary reflectors. Block A(1:OFFSET,1:N) has been
75: *> accordingly pivoted, but no factorized.
76: *> \endverbatim
77: *>
78: *> \param[in] LDA
79: *> \verbatim
80: *> LDA is INTEGER
81: *> The leading dimension of the array A. LDA >= max(1,M).
82: *> \endverbatim
83: *>
84: *> \param[in,out] JPVT
85: *> \verbatim
86: *> JPVT is INTEGER array, dimension (N)
87: *> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
88: *> to the front of A*P (a leading column); if JPVT(i) = 0,
89: *> the i-th column of A is a free column.
90: *> On exit, if JPVT(i) = k, then the i-th column of A*P
91: *> was the k-th column of A.
92: *> \endverbatim
93: *>
94: *> \param[out] TAU
95: *> \verbatim
96: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
97: *> The scalar factors of the elementary reflectors.
98: *> \endverbatim
99: *>
100: *> \param[in,out] VN1
101: *> \verbatim
102: *> VN1 is DOUBLE PRECISION array, dimension (N)
103: *> The vector with the partial column norms.
104: *> \endverbatim
105: *>
106: *> \param[in,out] VN2
107: *> \verbatim
108: *> VN2 is DOUBLE PRECISION array, dimension (N)
109: *> The vector with the exact column norms.
110: *> \endverbatim
111: *>
112: *> \param[out] WORK
113: *> \verbatim
114: *> WORK is DOUBLE PRECISION array, dimension (N)
115: *> \endverbatim
116: *
117: * Authors:
118: * ========
119: *
1.18 bertrand 120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
1.10 bertrand 124: *
1.18 bertrand 125: *> \date December 2016
1.10 bertrand 126: *
127: *> \ingroup doubleOTHERauxiliary
128: *
129: *> \par Contributors:
130: * ==================
131: *>
132: *> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
133: *> X. Sun, Computer Science Dept., Duke University, USA
134: *> \n
135: *> Partial column norm updating strategy modified on April 2011
136: *> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
137: *> University of Zagreb, Croatia.
138: *
139: *> \par References:
140: * ================
141: *>
142: *> LAPACK Working Note 176
143: *
144: *> \htmlonly
1.18 bertrand 145: *> <a href="http://www.netlib.org/lapack/lawnspdf/lawn176.pdf">[PDF]</a>
146: *> \endhtmlonly
1.10 bertrand 147: *
148: * =====================================================================
1.1 bertrand 149: SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
150: $ WORK )
151: *
1.18 bertrand 152: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 153: * -- LAPACK is a software package provided by Univ. of Tennessee, --
154: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.18 bertrand 155: * December 2016
1.1 bertrand 156: *
157: * .. Scalar Arguments ..
158: INTEGER LDA, M, N, OFFSET
159: * ..
160: * .. Array Arguments ..
161: INTEGER JPVT( * )
162: DOUBLE PRECISION A( LDA, * ), TAU( * ), VN1( * ), VN2( * ),
163: $ WORK( * )
164: * ..
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ZERO, ONE
170: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
171: * ..
172: * .. Local Scalars ..
173: INTEGER I, ITEMP, J, MN, OFFPI, PVT
174: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
175: * ..
176: * .. External Subroutines ..
1.5 bertrand 177: EXTERNAL DLARF, DLARFG, DSWAP
1.1 bertrand 178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC ABS, MAX, MIN, SQRT
181: * ..
182: * .. External Functions ..
183: INTEGER IDAMAX
184: DOUBLE PRECISION DLAMCH, DNRM2
185: EXTERNAL IDAMAX, DLAMCH, DNRM2
186: * ..
187: * .. Executable Statements ..
188: *
189: MN = MIN( M-OFFSET, N )
190: TOL3Z = SQRT(DLAMCH('Epsilon'))
191: *
192: * Compute factorization.
193: *
194: DO 20 I = 1, MN
195: *
196: OFFPI = OFFSET + I
197: *
198: * Determine ith pivot column and swap if necessary.
199: *
200: PVT = ( I-1 ) + IDAMAX( N-I+1, VN1( I ), 1 )
201: *
202: IF( PVT.NE.I ) THEN
203: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
204: ITEMP = JPVT( PVT )
205: JPVT( PVT ) = JPVT( I )
206: JPVT( I ) = ITEMP
207: VN1( PVT ) = VN1( I )
208: VN2( PVT ) = VN2( I )
209: END IF
210: *
211: * Generate elementary reflector H(i).
212: *
213: IF( OFFPI.LT.M ) THEN
1.5 bertrand 214: CALL DLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1,
1.1 bertrand 215: $ TAU( I ) )
216: ELSE
1.5 bertrand 217: CALL DLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) )
1.1 bertrand 218: END IF
219: *
1.15 bertrand 220: IF( I.LT.N ) THEN
1.1 bertrand 221: *
1.9 bertrand 222: * Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
1.1 bertrand 223: *
224: AII = A( OFFPI, I )
225: A( OFFPI, I ) = ONE
226: CALL DLARF( 'Left', M-OFFPI+1, N-I, A( OFFPI, I ), 1,
227: $ TAU( I ), A( OFFPI, I+1 ), LDA, WORK( 1 ) )
228: A( OFFPI, I ) = AII
229: END IF
230: *
231: * Update partial column norms.
232: *
233: DO 10 J = I + 1, N
234: IF( VN1( J ).NE.ZERO ) THEN
235: *
236: * NOTE: The following 4 lines follow from the analysis in
237: * Lapack Working Note 176.
238: *
239: TEMP = ONE - ( ABS( A( OFFPI, J ) ) / VN1( J ) )**2
240: TEMP = MAX( TEMP, ZERO )
241: TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2
242: IF( TEMP2 .LE. TOL3Z ) THEN
243: IF( OFFPI.LT.M ) THEN
244: VN1( J ) = DNRM2( M-OFFPI, A( OFFPI+1, J ), 1 )
245: VN2( J ) = VN1( J )
246: ELSE
247: VN1( J ) = ZERO
248: VN2( J ) = ZERO
249: END IF
250: ELSE
251: VN1( J ) = VN1( J )*SQRT( TEMP )
252: END IF
253: END IF
254: 10 CONTINUE
255: *
256: 20 CONTINUE
257: *
258: RETURN
259: *
260: * End of DLAQP2
261: *
262: END
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