1 SUBROUTINE DORGQR( 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 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DORGQR generates an M-by-N real matrix Q with orthonormal columns,
19 * which is defined as the first N columns of a product of K elementary
20 * reflectors of order M
21 *
22 * Q = H(1) H(2) . . . H(k)
23 *
24 * as returned by DGEQRF.
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. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the i-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by DGEQRF in the first k columns of its array
43 * argument A.
44 * On exit, the M-by-N matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGEQRF.
52 *
53 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
54 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
55 *
56 * LWORK (input) INTEGER
57 * The dimension of the array WORK. LWORK >= max(1,N).
58 * For optimum performance LWORK >= N*NB, where NB is the
59 * optimal blocksize.
60 *
61 * If LWORK = -1, then a workspace query is assumed; the routine
62 * only calculates the optimal size of the WORK array, returns
63 * this value as the first entry of the WORK array, and no error
64 * message related to LWORK is issued by XERBLA.
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument has an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ZERO
74 PARAMETER ( ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL LQUERY
78 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
79 $ LWKOPT, NB, NBMIN, NX
80 * ..
81 * .. External Subroutines ..
82 EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA
83 * ..
84 * .. Intrinsic Functions ..
85 INTRINSIC MAX, MIN
86 * ..
87 * .. External Functions ..
88 INTEGER ILAENV
89 EXTERNAL ILAENV
90 * ..
91 * .. Executable Statements ..
92 *
93 * Test the input arguments
94 *
95 INFO = 0
96 NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
97 LWKOPT = MAX( 1, N )*NB
98 WORK( 1 ) = LWKOPT
99 LQUERY = ( LWORK.EQ.-1 )
100 IF( M.LT.0 ) THEN
101 INFO = -1
102 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
103 INFO = -2
104 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
105 INFO = -3
106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
107 INFO = -5
108 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
109 INFO = -8
110 END IF
111 IF( INFO.NE.0 ) THEN
112 CALL XERBLA( 'DORGQR', -INFO )
113 RETURN
114 ELSE IF( LQUERY ) THEN
115 RETURN
116 END IF
117 *
118 * Quick return if possible
119 *
120 IF( N.LE.0 ) THEN
121 WORK( 1 ) = 1
122 RETURN
123 END IF
124 *
125 NBMIN = 2
126 NX = 0
127 IWS = N
128 IF( NB.GT.1 .AND. NB.LT.K ) THEN
129 *
130 * Determine when to cross over from blocked to unblocked code.
131 *
132 NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) )
133 IF( NX.LT.K ) THEN
134 *
135 * Determine if workspace is large enough for blocked code.
136 *
137 LDWORK = N
138 IWS = LDWORK*NB
139 IF( LWORK.LT.IWS ) THEN
140 *
141 * Not enough workspace to use optimal NB: reduce NB and
142 * determine the minimum value of NB.
143 *
144 NB = LWORK / LDWORK
145 NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) )
146 END IF
147 END IF
148 END IF
149 *
150 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
151 *
152 * Use blocked code after the last block.
153 * The first kk columns are handled by the block method.
154 *
155 KI = ( ( K-NX-1 ) / NB )*NB
156 KK = MIN( K, KI+NB )
157 *
158 * Set A(1:kk,kk+1:n) to zero.
159 *
160 DO 20 J = KK + 1, N
161 DO 10 I = 1, KK
162 A( I, J ) = ZERO
163 10 CONTINUE
164 20 CONTINUE
165 ELSE
166 KK = 0
167 END IF
168 *
169 * Use unblocked code for the last or only block.
170 *
171 IF( KK.LT.N )
172 $ CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
173 $ TAU( KK+1 ), WORK, IINFO )
174 *
175 IF( KK.GT.0 ) THEN
176 *
177 * Use blocked code
178 *
179 DO 50 I = KI + 1, 1, -NB
180 IB = MIN( NB, K-I+1 )
181 IF( I+IB.LE.N ) THEN
182 *
183 * Form the triangular factor of the block reflector
184 * H = H(i) H(i+1) . . . H(i+ib-1)
185 *
186 CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
187 $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
188 *
189 * Apply H to A(i:m,i+ib:n) from the left
190 *
191 CALL DLARFB( 'Left', 'No transpose', 'Forward',
192 $ 'Columnwise', M-I+1, N-I-IB+1, IB,
193 $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
194 $ LDA, WORK( IB+1 ), LDWORK )
195 END IF
196 *
197 * Apply H to rows i:m of current block
198 *
199 CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
200 $ IINFO )
201 *
202 * Set rows 1:i-1 of current block to zero
203 *
204 DO 40 J = I, I + IB - 1
205 DO 30 L = 1, I - 1
206 A( L, J ) = ZERO
207 30 CONTINUE
208 40 CONTINUE
209 50 CONTINUE
210 END IF
211 *
212 WORK( 1 ) = IWS
213 RETURN
214 *
215 * End of DORGQR
216 *
217 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 INTEGER INFO, K, LDA, LWORK, M, N
10 * ..
11 * .. Array Arguments ..
12 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * DORGQR generates an M-by-N real matrix Q with orthonormal columns,
19 * which is defined as the first N columns of a product of K elementary
20 * reflectors of order M
21 *
22 * Q = H(1) H(2) . . . H(k)
23 *
24 * as returned by DGEQRF.
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. M >= N >= 0.
34 *
35 * K (input) INTEGER
36 * The number of elementary reflectors whose product defines the
37 * matrix Q. N >= K >= 0.
38 *
39 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the i-th column must contain the vector which
41 * defines the elementary reflector H(i), for i = 1,2,...,k, as
42 * returned by DGEQRF in the first k columns of its array
43 * argument A.
44 * On exit, the M-by-N matrix Q.
45 *
46 * LDA (input) INTEGER
47 * The first dimension of the array A. LDA >= max(1,M).
48 *
49 * TAU (input) DOUBLE PRECISION array, dimension (K)
50 * TAU(i) must contain the scalar factor of the elementary
51 * reflector H(i), as returned by DGEQRF.
52 *
53 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
54 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
55 *
56 * LWORK (input) INTEGER
57 * The dimension of the array WORK. LWORK >= max(1,N).
58 * For optimum performance LWORK >= N*NB, where NB is the
59 * optimal blocksize.
60 *
61 * If LWORK = -1, then a workspace query is assumed; the routine
62 * only calculates the optimal size of the WORK array, returns
63 * this value as the first entry of the WORK array, and no error
64 * message related to LWORK is issued by XERBLA.
65 *
66 * INFO (output) INTEGER
67 * = 0: successful exit
68 * < 0: if INFO = -i, the i-th argument has an illegal value
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ZERO
74 PARAMETER ( ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 LOGICAL LQUERY
78 INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
79 $ LWKOPT, NB, NBMIN, NX
80 * ..
81 * .. External Subroutines ..
82 EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA
83 * ..
84 * .. Intrinsic Functions ..
85 INTRINSIC MAX, MIN
86 * ..
87 * .. External Functions ..
88 INTEGER ILAENV
89 EXTERNAL ILAENV
90 * ..
91 * .. Executable Statements ..
92 *
93 * Test the input arguments
94 *
95 INFO = 0
96 NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
97 LWKOPT = MAX( 1, N )*NB
98 WORK( 1 ) = LWKOPT
99 LQUERY = ( LWORK.EQ.-1 )
100 IF( M.LT.0 ) THEN
101 INFO = -1
102 ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
103 INFO = -2
104 ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
105 INFO = -3
106 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
107 INFO = -5
108 ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
109 INFO = -8
110 END IF
111 IF( INFO.NE.0 ) THEN
112 CALL XERBLA( 'DORGQR', -INFO )
113 RETURN
114 ELSE IF( LQUERY ) THEN
115 RETURN
116 END IF
117 *
118 * Quick return if possible
119 *
120 IF( N.LE.0 ) THEN
121 WORK( 1 ) = 1
122 RETURN
123 END IF
124 *
125 NBMIN = 2
126 NX = 0
127 IWS = N
128 IF( NB.GT.1 .AND. NB.LT.K ) THEN
129 *
130 * Determine when to cross over from blocked to unblocked code.
131 *
132 NX = MAX( 0, ILAENV( 3, 'DORGQR', ' ', M, N, K, -1 ) )
133 IF( NX.LT.K ) THEN
134 *
135 * Determine if workspace is large enough for blocked code.
136 *
137 LDWORK = N
138 IWS = LDWORK*NB
139 IF( LWORK.LT.IWS ) THEN
140 *
141 * Not enough workspace to use optimal NB: reduce NB and
142 * determine the minimum value of NB.
143 *
144 NB = LWORK / LDWORK
145 NBMIN = MAX( 2, ILAENV( 2, 'DORGQR', ' ', M, N, K, -1 ) )
146 END IF
147 END IF
148 END IF
149 *
150 IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
151 *
152 * Use blocked code after the last block.
153 * The first kk columns are handled by the block method.
154 *
155 KI = ( ( K-NX-1 ) / NB )*NB
156 KK = MIN( K, KI+NB )
157 *
158 * Set A(1:kk,kk+1:n) to zero.
159 *
160 DO 20 J = KK + 1, N
161 DO 10 I = 1, KK
162 A( I, J ) = ZERO
163 10 CONTINUE
164 20 CONTINUE
165 ELSE
166 KK = 0
167 END IF
168 *
169 * Use unblocked code for the last or only block.
170 *
171 IF( KK.LT.N )
172 $ CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
173 $ TAU( KK+1 ), WORK, IINFO )
174 *
175 IF( KK.GT.0 ) THEN
176 *
177 * Use blocked code
178 *
179 DO 50 I = KI + 1, 1, -NB
180 IB = MIN( NB, K-I+1 )
181 IF( I+IB.LE.N ) THEN
182 *
183 * Form the triangular factor of the block reflector
184 * H = H(i) H(i+1) . . . H(i+ib-1)
185 *
186 CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
187 $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
188 *
189 * Apply H to A(i:m,i+ib:n) from the left
190 *
191 CALL DLARFB( 'Left', 'No transpose', 'Forward',
192 $ 'Columnwise', M-I+1, N-I-IB+1, IB,
193 $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
194 $ LDA, WORK( IB+1 ), LDWORK )
195 END IF
196 *
197 * Apply H to rows i:m of current block
198 *
199 CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
200 $ IINFO )
201 *
202 * Set rows 1:i-1 of current block to zero
203 *
204 DO 40 J = I, I + IB - 1
205 DO 30 L = 1, I - 1
206 A( L, J ) = ZERO
207 30 CONTINUE
208 40 CONTINUE
209 50 CONTINUE
210 END IF
211 *
212 WORK( 1 ) = IWS
213 RETURN
214 *
215 * End of DORGQR
216 *
217 END