Annotation of rpl/lapack/lapack/dgeqrfp.f, revision 1.15
1.6 bertrand 1: *> \brief \b DGEQRFP
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.6 bertrand 7: *
8: *> \htmlonly
1.13 bertrand 9: *> Download DGEQRFP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqrfp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqrfp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqrfp.f">
1.6 bertrand 15: *> [TXT]</a>
1.13 bertrand 16: *> \endhtmlonly
1.6 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
1.13 bertrand 22: *
1.6 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, LWORK, M, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
1.13 bertrand 29: *
1.6 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DGEQRFP computes a QR factorization of a real M-by-N matrix A:
1.11 bertrand 37: *> A = Q * R. The diagonal entries of R are nonnegative.
1.6 bertrand 38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] M
44: *> \verbatim
45: *> M is INTEGER
46: *> The number of rows of the matrix A. M >= 0.
47: *> \endverbatim
48: *>
49: *> \param[in] N
50: *> \verbatim
51: *> N is INTEGER
52: *> The number of columns of the matrix A. N >= 0.
53: *> \endverbatim
54: *>
55: *> \param[in,out] A
56: *> \verbatim
57: *> A is DOUBLE PRECISION array, dimension (LDA,N)
58: *> On entry, the M-by-N matrix A.
59: *> On exit, the elements on and above the diagonal of the array
60: *> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
1.11 bertrand 61: *> upper triangular if m >= n). The diagonal entries of R
62: *> are nonnegative; the elements below the diagonal,
1.6 bertrand 63: *> with the array TAU, represent the orthogonal matrix Q as a
64: *> product of min(m,n) elementary reflectors (see Further
65: *> Details).
66: *> \endverbatim
67: *>
68: *> \param[in] LDA
69: *> \verbatim
70: *> LDA is INTEGER
71: *> The leading dimension of the array A. LDA >= max(1,M).
72: *> \endverbatim
73: *>
74: *> \param[out] TAU
75: *> \verbatim
76: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
77: *> The scalar factors of the elementary reflectors (see Further
78: *> Details).
79: *> \endverbatim
80: *>
81: *> \param[out] WORK
82: *> \verbatim
83: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
84: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
85: *> \endverbatim
86: *>
87: *> \param[in] LWORK
88: *> \verbatim
89: *> LWORK is INTEGER
90: *> The dimension of the array WORK. LWORK >= max(1,N).
91: *> For optimum performance LWORK >= N*NB, where NB is
92: *> the optimal blocksize.
93: *>
94: *> If LWORK = -1, then a workspace query is assumed; the routine
95: *> only calculates the optimal size of the WORK array, returns
96: *> this value as the first entry of the WORK array, and no error
97: *> message related to LWORK is issued by XERBLA.
98: *> \endverbatim
99: *>
100: *> \param[out] INFO
101: *> \verbatim
102: *> INFO is INTEGER
103: *> = 0: successful exit
104: *> < 0: if INFO = -i, the i-th argument had an illegal value
105: *> \endverbatim
106: *
107: * Authors:
108: * ========
109: *
1.13 bertrand 110: *> \author Univ. of Tennessee
111: *> \author Univ. of California Berkeley
112: *> \author Univ. of Colorado Denver
113: *> \author NAG Ltd.
1.6 bertrand 114: *
1.13 bertrand 115: *> \date December 2016
1.6 bertrand 116: *
117: *> \ingroup doubleGEcomputational
118: *
119: *> \par Further Details:
120: * =====================
121: *>
122: *> \verbatim
123: *>
124: *> The matrix Q is represented as a product of elementary reflectors
125: *>
126: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
127: *>
128: *> Each H(i) has the form
129: *>
130: *> H(i) = I - tau * v * v**T
131: *>
132: *> where tau is a real scalar, and v is a real vector with
133: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
134: *> and tau in TAU(i).
1.11 bertrand 135: *>
136: *> See Lapack Working Note 203 for details
1.6 bertrand 137: *> \endverbatim
138: *>
139: * =====================================================================
1.1 bertrand 140: SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
141: *
1.13 bertrand 142: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 143: * -- LAPACK is a software package provided by Univ. of Tennessee, --
144: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.13 bertrand 145: * December 2016
1.1 bertrand 146: *
147: * .. Scalar Arguments ..
148: INTEGER INFO, LDA, LWORK, M, N
149: * ..
150: * .. Array Arguments ..
151: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
152: * ..
153: *
154: * =====================================================================
155: *
156: * .. Local Scalars ..
157: LOGICAL LQUERY
158: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
159: $ NBMIN, NX
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL DGEQR2P, DLARFB, DLARFT, XERBLA
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC MAX, MIN
166: * ..
167: * .. External Functions ..
168: INTEGER ILAENV
169: EXTERNAL ILAENV
170: * ..
171: * .. Executable Statements ..
172: *
173: * Test the input arguments
174: *
175: INFO = 0
176: NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
177: LWKOPT = N*NB
178: WORK( 1 ) = LWKOPT
179: LQUERY = ( LWORK.EQ.-1 )
180: IF( M.LT.0 ) THEN
181: INFO = -1
182: ELSE IF( N.LT.0 ) THEN
183: INFO = -2
184: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
185: INFO = -4
186: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
187: INFO = -7
188: END IF
189: IF( INFO.NE.0 ) THEN
190: CALL XERBLA( 'DGEQRFP', -INFO )
191: RETURN
192: ELSE IF( LQUERY ) THEN
193: RETURN
194: END IF
195: *
196: * Quick return if possible
197: *
198: K = MIN( M, N )
199: IF( K.EQ.0 ) THEN
200: WORK( 1 ) = 1
201: RETURN
202: END IF
203: *
204: NBMIN = 2
205: NX = 0
206: IWS = N
207: IF( NB.GT.1 .AND. NB.LT.K ) THEN
208: *
209: * Determine when to cross over from blocked to unblocked code.
210: *
211: NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) )
212: IF( NX.LT.K ) THEN
213: *
214: * Determine if workspace is large enough for blocked code.
215: *
216: LDWORK = N
217: IWS = LDWORK*NB
218: IF( LWORK.LT.IWS ) THEN
219: *
220: * Not enough workspace to use optimal NB: reduce NB and
221: * determine the minimum value of NB.
222: *
223: NB = LWORK / LDWORK
224: NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1,
225: $ -1 ) )
226: END IF
227: END IF
228: END IF
229: *
230: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
231: *
232: * Use blocked code initially
233: *
234: DO 10 I = 1, K - NX, NB
235: IB = MIN( K-I+1, NB )
236: *
237: * Compute the QR factorization of the current block
238: * A(i:m,i:i+ib-1)
239: *
240: CALL DGEQR2P( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
241: $ IINFO )
242: IF( I+IB.LE.N ) THEN
243: *
244: * Form the triangular factor of the block reflector
245: * H = H(i) H(i+1) . . . H(i+ib-1)
246: *
247: CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
248: $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
249: *
1.5 bertrand 250: * Apply H**T to A(i:m,i+ib:n) from the left
1.1 bertrand 251: *
252: CALL DLARFB( 'Left', 'Transpose', 'Forward',
253: $ 'Columnwise', M-I+1, N-I-IB+1, IB,
254: $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
255: $ LDA, WORK( IB+1 ), LDWORK )
256: END IF
257: 10 CONTINUE
258: ELSE
259: I = 1
260: END IF
261: *
262: * Use unblocked code to factor the last or only block.
263: *
264: IF( I.LE.K )
265: $ CALL DGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
266: $ IINFO )
267: *
268: WORK( 1 ) = IWS
269: RETURN
270: *
271: * End of DGEQRFP
272: *
273: END
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