1: *> \brief \b DORGBR
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGBR + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgbr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER VECT
25: * INTEGER INFO, K, LDA, LWORK, M, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DORGBR generates one of the real orthogonal matrices Q or P**T
38: *> determined by DGEBRD when reducing a real matrix A to bidiagonal
39: *> form: A = Q * B * P**T. Q and P**T are defined as products of
40: *> elementary reflectors H(i) or G(i) respectively.
41: *>
42: *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
43: *> is of order M:
44: *> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
45: *> columns of Q, where m >= n >= k;
46: *> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
47: *> M-by-M matrix.
48: *>
49: *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
50: *> is of order N:
51: *> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
52: *> rows of P**T, where n >= m >= k;
53: *> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
54: *> an N-by-N matrix.
55: *> \endverbatim
56: *
57: * Arguments:
58: * ==========
59: *
60: *> \param[in] VECT
61: *> \verbatim
62: *> VECT is CHARACTER*1
63: *> Specifies whether the matrix Q or the matrix P**T is
64: *> required, as defined in the transformation applied by DGEBRD:
65: *> = 'Q': generate Q;
66: *> = 'P': generate P**T.
67: *> \endverbatim
68: *>
69: *> \param[in] M
70: *> \verbatim
71: *> M is INTEGER
72: *> The number of rows of the matrix Q or P**T to be returned.
73: *> M >= 0.
74: *> \endverbatim
75: *>
76: *> \param[in] N
77: *> \verbatim
78: *> N is INTEGER
79: *> The number of columns of the matrix Q or P**T to be returned.
80: *> N >= 0.
81: *> If VECT = 'Q', M >= N >= min(M,K);
82: *> if VECT = 'P', N >= M >= min(N,K).
83: *> \endverbatim
84: *>
85: *> \param[in] K
86: *> \verbatim
87: *> K is INTEGER
88: *> If VECT = 'Q', the number of columns in the original M-by-K
89: *> matrix reduced by DGEBRD.
90: *> If VECT = 'P', the number of rows in the original K-by-N
91: *> matrix reduced by DGEBRD.
92: *> K >= 0.
93: *> \endverbatim
94: *>
95: *> \param[in,out] A
96: *> \verbatim
97: *> A is DOUBLE PRECISION array, dimension (LDA,N)
98: *> On entry, the vectors which define the elementary reflectors,
99: *> as returned by DGEBRD.
100: *> On exit, the M-by-N matrix Q or P**T.
101: *> \endverbatim
102: *>
103: *> \param[in] LDA
104: *> \verbatim
105: *> LDA is INTEGER
106: *> The leading dimension of the array A. LDA >= max(1,M).
107: *> \endverbatim
108: *>
109: *> \param[in] TAU
110: *> \verbatim
111: *> TAU is DOUBLE PRECISION array, dimension
112: *> (min(M,K)) if VECT = 'Q'
113: *> (min(N,K)) if VECT = 'P'
114: *> TAU(i) must contain the scalar factor of the elementary
115: *> reflector H(i) or G(i), which determines Q or P**T, as
116: *> returned by DGEBRD in its array argument TAUQ or TAUP.
117: *> \endverbatim
118: *>
119: *> \param[out] WORK
120: *> \verbatim
121: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
122: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
123: *> \endverbatim
124: *>
125: *> \param[in] LWORK
126: *> \verbatim
127: *> LWORK is INTEGER
128: *> The dimension of the array WORK. LWORK >= max(1,min(M,N)).
129: *> For optimum performance LWORK >= min(M,N)*NB, where NB
130: *> is the optimal blocksize.
131: *>
132: *> If LWORK = -1, then a workspace query is assumed; the routine
133: *> only calculates the optimal size of the WORK array, returns
134: *> this value as the first entry of the WORK array, and no error
135: *> message related to LWORK is issued by XERBLA.
136: *> \endverbatim
137: *>
138: *> \param[out] INFO
139: *> \verbatim
140: *> INFO is INTEGER
141: *> = 0: successful exit
142: *> < 0: if INFO = -i, the i-th argument had an illegal value
143: *> \endverbatim
144: *
145: * Authors:
146: * ========
147: *
148: *> \author Univ. of Tennessee
149: *> \author Univ. of California Berkeley
150: *> \author Univ. of Colorado Denver
151: *> \author NAG Ltd.
152: *
153: *> \ingroup doubleGBcomputational
154: *
155: * =====================================================================
156: SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
157: *
158: * -- LAPACK computational routine --
159: * -- LAPACK is a software package provided by Univ. of Tennessee, --
160: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161: *
162: * .. Scalar Arguments ..
163: CHARACTER VECT
164: INTEGER INFO, K, LDA, LWORK, M, N
165: * ..
166: * .. Array Arguments ..
167: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
168: * ..
169: *
170: * =====================================================================
171: *
172: * .. Parameters ..
173: DOUBLE PRECISION ZERO, ONE
174: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
175: * ..
176: * .. Local Scalars ..
177: LOGICAL LQUERY, WANTQ
178: INTEGER I, IINFO, J, LWKOPT, MN
179: * ..
180: * .. External Functions ..
181: LOGICAL LSAME
182: EXTERNAL LSAME
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL DORGLQ, DORGQR, XERBLA
186: * ..
187: * .. Intrinsic Functions ..
188: INTRINSIC MAX, MIN
189: * ..
190: * .. Executable Statements ..
191: *
192: * Test the input arguments
193: *
194: INFO = 0
195: WANTQ = LSAME( VECT, 'Q' )
196: MN = MIN( M, N )
197: LQUERY = ( LWORK.EQ.-1 )
198: IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
199: INFO = -1
200: ELSE IF( M.LT.0 ) THEN
201: INFO = -2
202: ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
203: $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
204: $ MIN( N, K ) ) ) ) THEN
205: INFO = -3
206: ELSE IF( K.LT.0 ) THEN
207: INFO = -4
208: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
209: INFO = -6
210: ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
211: INFO = -9
212: END IF
213: *
214: IF( INFO.EQ.0 ) THEN
215: WORK( 1 ) = 1
216: IF( WANTQ ) THEN
217: IF( M.GE.K ) THEN
218: CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
219: ELSE
220: IF( M.GT.1 ) THEN
221: CALL DORGQR( M-1, M-1, M-1, A, LDA, TAU, WORK, -1,
222: $ IINFO )
223: END IF
224: END IF
225: ELSE
226: IF( K.LT.N ) THEN
227: CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
228: ELSE
229: IF( N.GT.1 ) THEN
230: CALL DORGLQ( N-1, N-1, N-1, A, LDA, TAU, WORK, -1,
231: $ IINFO )
232: END IF
233: END IF
234: END IF
235: LWKOPT = INT( WORK( 1 ) )
236: LWKOPT = MAX (LWKOPT, MN)
237: END IF
238: *
239: IF( INFO.NE.0 ) THEN
240: CALL XERBLA( 'DORGBR', -INFO )
241: RETURN
242: ELSE IF( LQUERY ) THEN
243: WORK( 1 ) = LWKOPT
244: RETURN
245: END IF
246: *
247: * Quick return if possible
248: *
249: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
250: WORK( 1 ) = 1
251: RETURN
252: END IF
253: *
254: IF( WANTQ ) THEN
255: *
256: * Form Q, determined by a call to DGEBRD to reduce an m-by-k
257: * matrix
258: *
259: IF( M.GE.K ) THEN
260: *
261: * If m >= k, assume m >= n >= k
262: *
263: CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
264: *
265: ELSE
266: *
267: * If m < k, assume m = n
268: *
269: * Shift the vectors which define the elementary reflectors one
270: * column to the right, and set the first row and column of Q
271: * to those of the unit matrix
272: *
273: DO 20 J = M, 2, -1
274: A( 1, J ) = ZERO
275: DO 10 I = J + 1, M
276: A( I, J ) = A( I, J-1 )
277: 10 CONTINUE
278: 20 CONTINUE
279: A( 1, 1 ) = ONE
280: DO 30 I = 2, M
281: A( I, 1 ) = ZERO
282: 30 CONTINUE
283: IF( M.GT.1 ) THEN
284: *
285: * Form Q(2:m,2:m)
286: *
287: CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
288: $ LWORK, IINFO )
289: END IF
290: END IF
291: ELSE
292: *
293: * Form P**T, determined by a call to DGEBRD to reduce a k-by-n
294: * matrix
295: *
296: IF( K.LT.N ) THEN
297: *
298: * If k < n, assume k <= m <= n
299: *
300: CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
301: *
302: ELSE
303: *
304: * If k >= n, assume m = n
305: *
306: * Shift the vectors which define the elementary reflectors one
307: * row downward, and set the first row and column of P**T to
308: * those of the unit matrix
309: *
310: A( 1, 1 ) = ONE
311: DO 40 I = 2, N
312: A( I, 1 ) = ZERO
313: 40 CONTINUE
314: DO 60 J = 2, N
315: DO 50 I = J - 1, 2, -1
316: A( I, J ) = A( I-1, J )
317: 50 CONTINUE
318: A( 1, J ) = ZERO
319: 60 CONTINUE
320: IF( N.GT.1 ) THEN
321: *
322: * Form P**T(2:n,2:n)
323: *
324: CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
325: $ LWORK, IINFO )
326: END IF
327: END IF
328: END IF
329: WORK( 1 ) = LWKOPT
330: RETURN
331: *
332: * End of DORGBR
333: *
334: END
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