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**T, 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**T 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**T(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
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**T, 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**T 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**T(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