1 SUBROUTINE ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
19 * which is defined as the first M rows of a product of K elementary
20 * reflectors of order N
21 *
22 * Q = H(k)**H . . . H(2)**H H(1)**H
23 *
24 * as returned by ZGELQF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. N >= M.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. M >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by ZGELQF in the first k rows of its array argument A.
43 * On exit, the M-by-N matrix Q.
44 *
45 * LDA (input) INTEGER
46 * The first dimension of the array A. LDA >= max(1,M).
47 *
48 * TAU (input) COMPLEX*16 array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by ZGELQF.
51 *
52 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
53 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
54 *
55 * LWORK (input) INTEGER
56 * The dimension of the array WORK. LWORK >= max(1,M).
57 * For optimum performance LWORK >= M*NB, where NB is
58 * the optimal blocksize.
59 *
60 * If LWORK = -1, then a workspace query is assumed; the routine
61 * only calculates the optimal size of the WORK array, returns
62 * this value as the first entry of the WORK array, and no error
63 * message related to LWORK is issued by XERBLA.
64 *
65 * INFO (output) INTEGER
66 * = 0: successful exit;
67 * < 0: if INFO = -i, the i-th argument has an illegal value
68 *
69 * =====================================================================
70 *
71 * .. Parameters ..
72 COMPLEX*16 ZERO
73 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL LQUERY
77 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
78 $ LWKOPT, NB, NBMIN, NX
79 * ..
80 * .. External Subroutines ..
81 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGL2
82 * ..
83 * .. Intrinsic Functions ..
84 INTRINSIC MAX, MIN
85 * ..
86 * .. External Functions ..
87 INTEGER ILAENV
88 EXTERNAL ILAENV
89 * ..
90 * .. Executable Statements ..
91 *
92 * Test the input arguments
93 *
94 INFO = 0
95 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
96 LWKOPT = MAX( 1, M )*NB
97 WORK( 1 ) = LWKOPT
98 LQUERY = ( LWORK.EQ.-1 )
99 IF( M.LT.0 ) THEN
100 INFO = -1
101 ELSE IF( N.LT.M ) THEN
102 INFO = -2
103 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
104 INFO = -3
105 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
106 INFO = -5
107 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
108 INFO = -8
109 END IF
110 IF( INFO.NE.0 ) THEN
111 CALL XERBLA( 'ZUNGLQ', -INFO )
112 RETURN
113 ELSE IF( LQUERY ) THEN
114 RETURN
115 END IF
116 *
117 * Quick return if possible
118 *
119 IF( M.LE.0 ) THEN
120 WORK( 1 ) = 1
121 RETURN
122 END IF
123 *
124 NBMIN = 2
125 NX = 0
126 IWS = M
127 IF( NB.GT.1 .AND. NB.LT.K ) THEN
128 *
129 * Determine when to cross over from blocked to unblocked code.
130 *
131 NX = MAX( 0, ILAENV( 3, 'ZUNGLQ', ' ', M, N, K, -1 ) )
132 IF( NX.LT.K ) THEN
133 *
134 * Determine if workspace is large enough for blocked code.
135 *
136 LDWORK = M
137 IWS = LDWORK*NB
138 IF( LWORK.LT.IWS ) THEN
139 *
140 * Not enough workspace to use optimal NB: reduce NB and
141 * determine the minimum value of NB.
142 *
143 NB = LWORK / LDWORK
144 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGLQ', ' ', M, N, K, -1 ) )
145 END IF
146 END IF
147 END IF
148 *
149 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
150 *
151 * Use blocked code after the last block.
152 * The first kk rows are handled by the block method.
153 *
154 KI = ( ( K-NX-1 ) / NB )*NB
155 KK = MIN( K, KI+NB )
156 *
157 * Set A(kk+1:m,1:kk) to zero.
158 *
159 DO 20 J = 1, KK
160 DO 10 I = KK + 1, M
161 A( I, J ) = ZERO
162 10 CONTINUE
163 20 CONTINUE
164 ELSE
165 KK = 0
166 END IF
167 *
168 * Use unblocked code for the last or only block.
169 *
170 IF( KK.LT.M )
171 $ CALL ZUNGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
172 $ TAU( KK+1 ), WORK, IINFO )
173 *
174 IF( KK.GT.0 ) THEN
175 *
176 * Use blocked code
177 *
178 DO 50 I = KI + 1, 1, -NB
179 IB = MIN( NB, K-I+1 )
180 IF( I+IB.LE.M ) THEN
181 *
182 * Form the triangular factor of the block reflector
183 * H = H(i) H(i+1) . . . H(i+ib-1)
184 *
185 CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
186 $ LDA, TAU( I ), WORK, LDWORK )
187 *
188 * Apply H**H to A(i+ib:m,i:n) from the right
189 *
190 CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward',
191 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
192 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
193 $ WORK( IB+1 ), LDWORK )
194 END IF
195 *
196 * Apply H**H to columns i:n of current block
197 *
198 CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
199 $ IINFO )
200 *
201 * Set columns 1:i-1 of current block to zero
202 *
203 DO 40 J = 1, I - 1
204 DO 30 L = I, I + IB - 1
205 A( L, J ) = ZERO
206 30 CONTINUE
207 40 CONTINUE
208 50 CONTINUE
209 END IF
210 *
211 WORK( 1 ) = IWS
212 RETURN
213 *
214 * End of ZUNGLQ
215 *
216 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
7 *
8 * .. Scalar Arguments ..
9 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * ZUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
19 * which is defined as the first M rows of a product of K elementary
20 * reflectors of order N
21 *
22 * Q = H(k)**H . . . H(2)**H H(1)**H
23 *
24 * as returned by ZGELQF.
25 *
26 * Arguments
27 * =========
28 *
29 * M (input) INTEGER
30 * The number of rows of the matrix Q. M >= 0.
31 *
32 * N (input) INTEGER
33 * The number of columns of the matrix Q. N >= M.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. M >= K >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the i-th row must contain the vector which defines
41 * the elementary reflector H(i), for i = 1,2,...,k, as returned
42 * by ZGELQF in the first k rows of its array argument A.
43 * On exit, the M-by-N matrix Q.
44 *
45 * LDA (input) INTEGER
46 * The first dimension of the array A. LDA >= max(1,M).
47 *
48 * TAU (input) COMPLEX*16 array, dimension (K)
49 * TAU(i) must contain the scalar factor of the elementary
50 * reflector H(i), as returned by ZGELQF.
51 *
52 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
53 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
54 *
55 * LWORK (input) INTEGER
56 * The dimension of the array WORK. LWORK >= max(1,M).
57 * For optimum performance LWORK >= M*NB, where NB is
58 * the optimal blocksize.
59 *
60 * If LWORK = -1, then a workspace query is assumed; the routine
61 * only calculates the optimal size of the WORK array, returns
62 * this value as the first entry of the WORK array, and no error
63 * message related to LWORK is issued by XERBLA.
64 *
65 * INFO (output) INTEGER
66 * = 0: successful exit;
67 * < 0: if INFO = -i, the i-th argument has an illegal value
68 *
69 * =====================================================================
70 *
71 * .. Parameters ..
72 COMPLEX*16 ZERO
73 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL LQUERY
77 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
78 $ LWKOPT, NB, NBMIN, NX
79 * ..
80 * .. External Subroutines ..
81 EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGL2
82 * ..
83 * .. Intrinsic Functions ..
84 INTRINSIC MAX, MIN
85 * ..
86 * .. External Functions ..
87 INTEGER ILAENV
88 EXTERNAL ILAENV
89 * ..
90 * .. Executable Statements ..
91 *
92 * Test the input arguments
93 *
94 INFO = 0
95 NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
96 LWKOPT = MAX( 1, M )*NB
97 WORK( 1 ) = LWKOPT
98 LQUERY = ( LWORK.EQ.-1 )
99 IF( M.LT.0 ) THEN
100 INFO = -1
101 ELSE IF( N.LT.M ) THEN
102 INFO = -2
103 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
104 INFO = -3
105 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
106 INFO = -5
107 ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
108 INFO = -8
109 END IF
110 IF( INFO.NE.0 ) THEN
111 CALL XERBLA( 'ZUNGLQ', -INFO )
112 RETURN
113 ELSE IF( LQUERY ) THEN
114 RETURN
115 END IF
116 *
117 * Quick return if possible
118 *
119 IF( M.LE.0 ) THEN
120 WORK( 1 ) = 1
121 RETURN
122 END IF
123 *
124 NBMIN = 2
125 NX = 0
126 IWS = M
127 IF( NB.GT.1 .AND. NB.LT.K ) THEN
128 *
129 * Determine when to cross over from blocked to unblocked code.
130 *
131 NX = MAX( 0, ILAENV( 3, 'ZUNGLQ', ' ', M, N, K, -1 ) )
132 IF( NX.LT.K ) THEN
133 *
134 * Determine if workspace is large enough for blocked code.
135 *
136 LDWORK = M
137 IWS = LDWORK*NB
138 IF( LWORK.LT.IWS ) THEN
139 *
140 * Not enough workspace to use optimal NB: reduce NB and
141 * determine the minimum value of NB.
142 *
143 NB = LWORK / LDWORK
144 NBMIN = MAX( 2, ILAENV( 2, 'ZUNGLQ', ' ', M, N, K, -1 ) )
145 END IF
146 END IF
147 END IF
148 *
149 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
150 *
151 * Use blocked code after the last block.
152 * The first kk rows are handled by the block method.
153 *
154 KI = ( ( K-NX-1 ) / NB )*NB
155 KK = MIN( K, KI+NB )
156 *
157 * Set A(kk+1:m,1:kk) to zero.
158 *
159 DO 20 J = 1, KK
160 DO 10 I = KK + 1, M
161 A( I, J ) = ZERO
162 10 CONTINUE
163 20 CONTINUE
164 ELSE
165 KK = 0
166 END IF
167 *
168 * Use unblocked code for the last or only block.
169 *
170 IF( KK.LT.M )
171 $ CALL ZUNGL2( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
172 $ TAU( KK+1 ), WORK, IINFO )
173 *
174 IF( KK.GT.0 ) THEN
175 *
176 * Use blocked code
177 *
178 DO 50 I = KI + 1, 1, -NB
179 IB = MIN( NB, K-I+1 )
180 IF( I+IB.LE.M ) THEN
181 *
182 * Form the triangular factor of the block reflector
183 * H = H(i) H(i+1) . . . H(i+ib-1)
184 *
185 CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
186 $ LDA, TAU( I ), WORK, LDWORK )
187 *
188 * Apply H**H to A(i+ib:m,i:n) from the right
189 *
190 CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward',
191 $ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
192 $ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
193 $ WORK( IB+1 ), LDWORK )
194 END IF
195 *
196 * Apply H**H to columns i:n of current block
197 *
198 CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
199 $ IINFO )
200 *
201 * Set columns 1:i-1 of current block to zero
202 *
203 DO 40 J = 1, I - 1
204 DO 30 L = I, I + IB - 1
205 A( L, J ) = ZERO
206 30 CONTINUE
207 40 CONTINUE
208 50 CONTINUE
209 END IF
210 *
211 WORK( 1 ) = IWS
212 RETURN
213 *
214 * End of ZUNGLQ
215 *
216 END