1: SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER VECT
10: INTEGER INFO, K, LDA, LWORK, M, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DORGBR generates one of the real orthogonal matrices Q or P**T
20: * determined by DGEBRD when reducing a real matrix A to bidiagonal
21: * form: A = Q * B * P**T. Q and P**T are defined as products of
22: * elementary reflectors H(i) or G(i) respectively.
23: *
24: * If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
25: * is of order M:
26: * if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
27: * columns of Q, where m >= n >= k;
28: * if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
29: * M-by-M matrix.
30: *
31: * If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
32: * is of order N:
33: * if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
34: * rows of P**T, where n >= m >= k;
35: * if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
36: * an N-by-N matrix.
37: *
38: * Arguments
39: * =========
40: *
41: * VECT (input) CHARACTER*1
42: * Specifies whether the matrix Q or the matrix P**T is
43: * required, as defined in the transformation applied by DGEBRD:
44: * = 'Q': generate Q;
45: * = 'P': generate P**T.
46: *
47: * M (input) INTEGER
48: * The number of rows of the matrix Q or P**T to be returned.
49: * M >= 0.
50: *
51: * N (input) INTEGER
52: * The number of columns of the matrix Q or P**T to be returned.
53: * N >= 0.
54: * If VECT = 'Q', M >= N >= min(M,K);
55: * if VECT = 'P', N >= M >= min(N,K).
56: *
57: * K (input) INTEGER
58: * If VECT = 'Q', the number of columns in the original M-by-K
59: * matrix reduced by DGEBRD.
60: * If VECT = 'P', the number of rows in the original K-by-N
61: * matrix reduced by DGEBRD.
62: * K >= 0.
63: *
64: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
65: * On entry, the vectors which define the elementary reflectors,
66: * as returned by DGEBRD.
67: * On exit, the M-by-N matrix Q or P**T.
68: *
69: * LDA (input) INTEGER
70: * The leading dimension of the array A. LDA >= max(1,M).
71: *
72: * TAU (input) DOUBLE PRECISION array, dimension
73: * (min(M,K)) if VECT = 'Q'
74: * (min(N,K)) if VECT = 'P'
75: * TAU(i) must contain the scalar factor of the elementary
76: * reflector H(i) or G(i), which determines Q or P**T, as
77: * returned by DGEBRD in its array argument TAUQ or TAUP.
78: *
79: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
80: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
81: *
82: * LWORK (input) INTEGER
83: * The dimension of the array WORK. LWORK >= max(1,min(M,N)).
84: * For optimum performance LWORK >= min(M,N)*NB, where NB
85: * is the optimal blocksize.
86: *
87: * If LWORK = -1, then a workspace query is assumed; the routine
88: * only calculates the optimal size of the WORK array, returns
89: * this value as the first entry of the WORK array, and no error
90: * message related to LWORK is issued by XERBLA.
91: *
92: * INFO (output) INTEGER
93: * = 0: successful exit
94: * < 0: if INFO = -i, the i-th argument had an illegal value
95: *
96: * =====================================================================
97: *
98: * .. Parameters ..
99: DOUBLE PRECISION ZERO, ONE
100: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
101: * ..
102: * .. Local Scalars ..
103: LOGICAL LQUERY, WANTQ
104: INTEGER I, IINFO, J, LWKOPT, MN, NB
105: * ..
106: * .. External Functions ..
107: LOGICAL LSAME
108: INTEGER ILAENV
109: EXTERNAL LSAME, ILAENV
110: * ..
111: * .. External Subroutines ..
112: EXTERNAL DORGLQ, DORGQR, XERBLA
113: * ..
114: * .. Intrinsic Functions ..
115: INTRINSIC MAX, MIN
116: * ..
117: * .. Executable Statements ..
118: *
119: * Test the input arguments
120: *
121: INFO = 0
122: WANTQ = LSAME( VECT, 'Q' )
123: MN = MIN( M, N )
124: LQUERY = ( LWORK.EQ.-1 )
125: IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
126: INFO = -1
127: ELSE IF( M.LT.0 ) THEN
128: INFO = -2
129: ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
130: $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
131: $ MIN( N, K ) ) ) ) THEN
132: INFO = -3
133: ELSE IF( K.LT.0 ) THEN
134: INFO = -4
135: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
136: INFO = -6
137: ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
138: INFO = -9
139: END IF
140: *
141: IF( INFO.EQ.0 ) THEN
142: IF( WANTQ ) THEN
143: NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
144: ELSE
145: NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )
146: END IF
147: LWKOPT = MAX( 1, MN )*NB
148: WORK( 1 ) = LWKOPT
149: END IF
150: *
151: IF( INFO.NE.0 ) THEN
152: CALL XERBLA( 'DORGBR', -INFO )
153: RETURN
154: ELSE IF( LQUERY ) THEN
155: RETURN
156: END IF
157: *
158: * Quick return if possible
159: *
160: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
161: WORK( 1 ) = 1
162: RETURN
163: END IF
164: *
165: IF( WANTQ ) THEN
166: *
167: * Form Q, determined by a call to DGEBRD to reduce an m-by-k
168: * matrix
169: *
170: IF( M.GE.K ) THEN
171: *
172: * If m >= k, assume m >= n >= k
173: *
174: CALL DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
175: *
176: ELSE
177: *
178: * If m < k, assume m = n
179: *
180: * Shift the vectors which define the elementary reflectors one
181: * column to the right, and set the first row and column of Q
182: * to those of the unit matrix
183: *
184: DO 20 J = M, 2, -1
185: A( 1, J ) = ZERO
186: DO 10 I = J + 1, M
187: A( I, J ) = A( I, J-1 )
188: 10 CONTINUE
189: 20 CONTINUE
190: A( 1, 1 ) = ONE
191: DO 30 I = 2, M
192: A( I, 1 ) = ZERO
193: 30 CONTINUE
194: IF( M.GT.1 ) THEN
195: *
196: * Form Q(2:m,2:m)
197: *
198: CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
199: $ LWORK, IINFO )
200: END IF
201: END IF
202: ELSE
203: *
204: * Form P', determined by a call to DGEBRD to reduce a k-by-n
205: * matrix
206: *
207: IF( K.LT.N ) THEN
208: *
209: * If k < n, assume k <= m <= n
210: *
211: CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
212: *
213: ELSE
214: *
215: * If k >= n, assume m = n
216: *
217: * Shift the vectors which define the elementary reflectors one
218: * row downward, and set the first row and column of P' to
219: * those of the unit matrix
220: *
221: A( 1, 1 ) = ONE
222: DO 40 I = 2, N
223: A( I, 1 ) = ZERO
224: 40 CONTINUE
225: DO 60 J = 2, N
226: DO 50 I = J - 1, 2, -1
227: A( I, J ) = A( I-1, J )
228: 50 CONTINUE
229: A( 1, J ) = ZERO
230: 60 CONTINUE
231: IF( N.GT.1 ) THEN
232: *
233: * Form P'(2:n,2:n)
234: *
235: CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
236: $ LWORK, IINFO )
237: END IF
238: END IF
239: END IF
240: WORK( 1 ) = LWKOPT
241: RETURN
242: *
243: * End of DORGBR
244: *
245: END
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