1 SUBROUTINE ZUNGBR( 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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZUNGBR generates one of the complex unitary matrices Q or P**H
20 * determined by ZGEBRD when reducing a complex matrix A to bidiagonal
21 * form: A = Q * B * P**H. Q and P**H 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 ZUNGBR 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 ZUNGBR 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**H
32 * is of order N:
33 * if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
34 * rows of P**H, where n >= m >= k;
35 * if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H 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**H is
43 * required, as defined in the transformation applied by ZGEBRD:
44 * = 'Q': generate Q;
45 * = 'P': generate P**H.
46 *
47 * M (input) INTEGER
48 * The number of rows of the matrix Q or P**H to be returned.
49 * M >= 0.
50 *
51 * N (input) INTEGER
52 * The number of columns of the matrix Q or P**H 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 ZGEBRD.
60 * If VECT = 'P', the number of rows in the original K-by-N
61 * matrix reduced by ZGEBRD.
62 * K >= 0.
63 *
64 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
65 * On entry, the vectors which define the elementary reflectors,
66 * as returned by ZGEBRD.
67 * On exit, the M-by-N matrix Q or P**H.
68 *
69 * LDA (input) INTEGER
70 * The leading dimension of the array A. LDA >= M.
71 *
72 * TAU (input) COMPLEX*16 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**H, as
77 * returned by ZGEBRD in its array argument TAUQ or TAUP.
78 *
79 * WORK (workspace/output) COMPLEX*16 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 COMPLEX*16 ZERO, ONE
100 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
101 $ ONE = ( 1.0D+0, 0.0D+0 ) )
102 * ..
103 * .. Local Scalars ..
104 LOGICAL LQUERY, WANTQ
105 INTEGER I, IINFO, J, LWKOPT, MN, NB
106 * ..
107 * .. External Functions ..
108 LOGICAL LSAME
109 INTEGER ILAENV
110 EXTERNAL LSAME, ILAENV
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL XERBLA, ZUNGLQ, ZUNGQR
114 * ..
115 * .. Intrinsic Functions ..
116 INTRINSIC MAX, MIN
117 * ..
118 * .. Executable Statements ..
119 *
120 * Test the input arguments
121 *
122 INFO = 0
123 WANTQ = LSAME( VECT, 'Q' )
124 MN = MIN( M, N )
125 LQUERY = ( LWORK.EQ.-1 )
126 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
127 INFO = -1
128 ELSE IF( M.LT.0 ) THEN
129 INFO = -2
130 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
131 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
132 $ MIN( N, K ) ) ) ) THEN
133 INFO = -3
134 ELSE IF( K.LT.0 ) THEN
135 INFO = -4
136 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
137 INFO = -6
138 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
139 INFO = -9
140 END IF
141 *
142 IF( INFO.EQ.0 ) THEN
143 IF( WANTQ ) THEN
144 NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 )
145 ELSE
146 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
147 END IF
148 LWKOPT = MAX( 1, MN )*NB
149 WORK( 1 ) = LWKOPT
150 END IF
151 *
152 IF( INFO.NE.0 ) THEN
153 CALL XERBLA( 'ZUNGBR', -INFO )
154 RETURN
155 ELSE IF( LQUERY ) THEN
156 RETURN
157 END IF
158 *
159 * Quick return if possible
160 *
161 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
162 WORK( 1 ) = 1
163 RETURN
164 END IF
165 *
166 IF( WANTQ ) THEN
167 *
168 * Form Q, determined by a call to ZGEBRD to reduce an m-by-k
169 * matrix
170 *
171 IF( M.GE.K ) THEN
172 *
173 * If m >= k, assume m >= n >= k
174 *
175 CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
176 *
177 ELSE
178 *
179 * If m < k, assume m = n
180 *
181 * Shift the vectors which define the elementary reflectors one
182 * column to the right, and set the first row and column of Q
183 * to those of the unit matrix
184 *
185 DO 20 J = M, 2, -1
186 A( 1, J ) = ZERO
187 DO 10 I = J + 1, M
188 A( I, J ) = A( I, J-1 )
189 10 CONTINUE
190 20 CONTINUE
191 A( 1, 1 ) = ONE
192 DO 30 I = 2, M
193 A( I, 1 ) = ZERO
194 30 CONTINUE
195 IF( M.GT.1 ) THEN
196 *
197 * Form Q(2:m,2:m)
198 *
199 CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
200 $ LWORK, IINFO )
201 END IF
202 END IF
203 ELSE
204 *
205 * Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
206 * matrix
207 *
208 IF( K.LT.N ) THEN
209 *
210 * If k < n, assume k <= m <= n
211 *
212 CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
213 *
214 ELSE
215 *
216 * If k >= n, assume m = n
217 *
218 * Shift the vectors which define the elementary reflectors one
219 * row downward, and set the first row and column of P**H to
220 * those of the unit matrix
221 *
222 A( 1, 1 ) = ONE
223 DO 40 I = 2, N
224 A( I, 1 ) = ZERO
225 40 CONTINUE
226 DO 60 J = 2, N
227 DO 50 I = J - 1, 2, -1
228 A( I, J ) = A( I-1, J )
229 50 CONTINUE
230 A( 1, J ) = ZERO
231 60 CONTINUE
232 IF( N.GT.1 ) THEN
233 *
234 * Form P**H(2:n,2:n)
235 *
236 CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
237 $ LWORK, IINFO )
238 END IF
239 END IF
240 END IF
241 WORK( 1 ) = LWKOPT
242 RETURN
243 *
244 * End of ZUNGBR
245 *
246 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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZUNGBR generates one of the complex unitary matrices Q or P**H
20 * determined by ZGEBRD when reducing a complex matrix A to bidiagonal
21 * form: A = Q * B * P**H. Q and P**H 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 ZUNGBR 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 ZUNGBR 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**H
32 * is of order N:
33 * if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
34 * rows of P**H, where n >= m >= k;
35 * if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H 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**H is
43 * required, as defined in the transformation applied by ZGEBRD:
44 * = 'Q': generate Q;
45 * = 'P': generate P**H.
46 *
47 * M (input) INTEGER
48 * The number of rows of the matrix Q or P**H to be returned.
49 * M >= 0.
50 *
51 * N (input) INTEGER
52 * The number of columns of the matrix Q or P**H 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 ZGEBRD.
60 * If VECT = 'P', the number of rows in the original K-by-N
61 * matrix reduced by ZGEBRD.
62 * K >= 0.
63 *
64 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
65 * On entry, the vectors which define the elementary reflectors,
66 * as returned by ZGEBRD.
67 * On exit, the M-by-N matrix Q or P**H.
68 *
69 * LDA (input) INTEGER
70 * The leading dimension of the array A. LDA >= M.
71 *
72 * TAU (input) COMPLEX*16 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**H, as
77 * returned by ZGEBRD in its array argument TAUQ or TAUP.
78 *
79 * WORK (workspace/output) COMPLEX*16 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 COMPLEX*16 ZERO, ONE
100 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
101 $ ONE = ( 1.0D+0, 0.0D+0 ) )
102 * ..
103 * .. Local Scalars ..
104 LOGICAL LQUERY, WANTQ
105 INTEGER I, IINFO, J, LWKOPT, MN, NB
106 * ..
107 * .. External Functions ..
108 LOGICAL LSAME
109 INTEGER ILAENV
110 EXTERNAL LSAME, ILAENV
111 * ..
112 * .. External Subroutines ..
113 EXTERNAL XERBLA, ZUNGLQ, ZUNGQR
114 * ..
115 * .. Intrinsic Functions ..
116 INTRINSIC MAX, MIN
117 * ..
118 * .. Executable Statements ..
119 *
120 * Test the input arguments
121 *
122 INFO = 0
123 WANTQ = LSAME( VECT, 'Q' )
124 MN = MIN( M, N )
125 LQUERY = ( LWORK.EQ.-1 )
126 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
127 INFO = -1
128 ELSE IF( M.LT.0 ) THEN
129 INFO = -2
130 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
131 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
132 $ MIN( N, K ) ) ) ) THEN
133 INFO = -3
134 ELSE IF( K.LT.0 ) THEN
135 INFO = -4
136 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
137 INFO = -6
138 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
139 INFO = -9
140 END IF
141 *
142 IF( INFO.EQ.0 ) THEN
143 IF( WANTQ ) THEN
144 NB = ILAENV( 1, 'ZUNGQR', ' ', M, N, K, -1 )
145 ELSE
146 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
147 END IF
148 LWKOPT = MAX( 1, MN )*NB
149 WORK( 1 ) = LWKOPT
150 END IF
151 *
152 IF( INFO.NE.0 ) THEN
153 CALL XERBLA( 'ZUNGBR', -INFO )
154 RETURN
155 ELSE IF( LQUERY ) THEN
156 RETURN
157 END IF
158 *
159 * Quick return if possible
160 *
161 IF( M.EQ.0 .OR. N.EQ.0 ) THEN
162 WORK( 1 ) = 1
163 RETURN
164 END IF
165 *
166 IF( WANTQ ) THEN
167 *
168 * Form Q, determined by a call to ZGEBRD to reduce an m-by-k
169 * matrix
170 *
171 IF( M.GE.K ) THEN
172 *
173 * If m >= k, assume m >= n >= k
174 *
175 CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
176 *
177 ELSE
178 *
179 * If m < k, assume m = n
180 *
181 * Shift the vectors which define the elementary reflectors one
182 * column to the right, and set the first row and column of Q
183 * to those of the unit matrix
184 *
185 DO 20 J = M, 2, -1
186 A( 1, J ) = ZERO
187 DO 10 I = J + 1, M
188 A( I, J ) = A( I, J-1 )
189 10 CONTINUE
190 20 CONTINUE
191 A( 1, 1 ) = ONE
192 DO 30 I = 2, M
193 A( I, 1 ) = ZERO
194 30 CONTINUE
195 IF( M.GT.1 ) THEN
196 *
197 * Form Q(2:m,2:m)
198 *
199 CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
200 $ LWORK, IINFO )
201 END IF
202 END IF
203 ELSE
204 *
205 * Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
206 * matrix
207 *
208 IF( K.LT.N ) THEN
209 *
210 * If k < n, assume k <= m <= n
211 *
212 CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
213 *
214 ELSE
215 *
216 * If k >= n, assume m = n
217 *
218 * Shift the vectors which define the elementary reflectors one
219 * row downward, and set the first row and column of P**H to
220 * those of the unit matrix
221 *
222 A( 1, 1 ) = ONE
223 DO 40 I = 2, N
224 A( I, 1 ) = ZERO
225 40 CONTINUE
226 DO 60 J = 2, N
227 DO 50 I = J - 1, 2, -1
228 A( I, J ) = A( I-1, J )
229 50 CONTINUE
230 A( 1, J ) = ZERO
231 60 CONTINUE
232 IF( N.GT.1 ) THEN
233 *
234 * Form P**H(2:n,2:n)
235 *
236 CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
237 $ LWORK, IINFO )
238 END IF
239 END IF
240 END IF
241 WORK( 1 ) = LWKOPT
242 RETURN
243 *
244 * End of ZUNGBR
245 *
246 END