1 SUBROUTINE DORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
2 $ WORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER SIDE, TRANS
11 INTEGER INFO, K, LDA, LDC, M, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DORM2L overwrites the general real m by n matrix C with
21 *
22 * Q * C if SIDE = 'L' and TRANS = 'N', or
23 *
24 * Q**T * C if SIDE = 'L' and TRANS = 'T', or
25 *
26 * C * Q if SIDE = 'R' and TRANS = 'N', or
27 *
28 * C * Q**T if SIDE = 'R' and TRANS = 'T',
29 *
30 * where Q is a real orthogonal matrix defined as the product of k
31 * elementary reflectors
32 *
33 * Q = H(k) . . . H(2) H(1)
34 *
35 * as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n
36 * if SIDE = 'R'.
37 *
38 * Arguments
39 * =========
40 *
41 * SIDE (input) CHARACTER*1
42 * = 'L': apply Q or Q**T from the Left
43 * = 'R': apply Q or Q**T from the Right
44 *
45 * TRANS (input) CHARACTER*1
46 * = 'N': apply Q (No transpose)
47 * = 'T': apply Q**T (Transpose)
48 *
49 * M (input) INTEGER
50 * The number of rows of the matrix C. M >= 0.
51 *
52 * N (input) INTEGER
53 * The number of columns of the matrix C. N >= 0.
54 *
55 * K (input) INTEGER
56 * The number of elementary reflectors whose product defines
57 * the matrix Q.
58 * If SIDE = 'L', M >= K >= 0;
59 * if SIDE = 'R', N >= K >= 0.
60 *
61 * A (input) DOUBLE PRECISION array, dimension (LDA,K)
62 * The i-th column must contain the vector which defines the
63 * elementary reflector H(i), for i = 1,2,...,k, as returned by
64 * DGEQLF in the last k columns of its array argument A.
65 * A is modified by the routine but restored on exit.
66 *
67 * LDA (input) INTEGER
68 * The leading dimension of the array A.
69 * If SIDE = 'L', LDA >= max(1,M);
70 * if SIDE = 'R', LDA >= max(1,N).
71 *
72 * TAU (input) DOUBLE PRECISION array, dimension (K)
73 * TAU(i) must contain the scalar factor of the elementary
74 * reflector H(i), as returned by DGEQLF.
75 *
76 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
77 * On entry, the m by n matrix C.
78 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
79 *
80 * LDC (input) INTEGER
81 * The leading dimension of the array C. LDC >= max(1,M).
82 *
83 * WORK (workspace) DOUBLE PRECISION array, dimension
84 * (N) if SIDE = 'L',
85 * (M) if SIDE = 'R'
86 *
87 * INFO (output) INTEGER
88 * = 0: successful exit
89 * < 0: if INFO = -i, the i-th argument had an illegal value
90 *
91 * =====================================================================
92 *
93 * .. Parameters ..
94 DOUBLE PRECISION ONE
95 PARAMETER ( ONE = 1.0D+0 )
96 * ..
97 * .. Local Scalars ..
98 LOGICAL LEFT, NOTRAN
99 INTEGER I, I1, I2, I3, MI, NI, NQ
100 DOUBLE PRECISION AII
101 * ..
102 * .. External Functions ..
103 LOGICAL LSAME
104 EXTERNAL LSAME
105 * ..
106 * .. External Subroutines ..
107 EXTERNAL DLARF, XERBLA
108 * ..
109 * .. Intrinsic Functions ..
110 INTRINSIC MAX
111 * ..
112 * .. Executable Statements ..
113 *
114 * Test the input arguments
115 *
116 INFO = 0
117 LEFT = LSAME( SIDE, 'L' )
118 NOTRAN = LSAME( TRANS, 'N' )
119 *
120 * NQ is the order of Q
121 *
122 IF( LEFT ) THEN
123 NQ = M
124 ELSE
125 NQ = N
126 END IF
127 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
128 INFO = -1
129 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
130 INFO = -2
131 ELSE IF( M.LT.0 ) THEN
132 INFO = -3
133 ELSE IF( N.LT.0 ) THEN
134 INFO = -4
135 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
136 INFO = -5
137 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
138 INFO = -7
139 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
140 INFO = -10
141 END IF
142 IF( INFO.NE.0 ) THEN
143 CALL XERBLA( 'DORM2L', -INFO )
144 RETURN
145 END IF
146 *
147 * Quick return if possible
148 *
149 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
150 $ RETURN
151 *
152 IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
153 $ THEN
154 I1 = 1
155 I2 = K
156 I3 = 1
157 ELSE
158 I1 = K
159 I2 = 1
160 I3 = -1
161 END IF
162 *
163 IF( LEFT ) THEN
164 NI = N
165 ELSE
166 MI = M
167 END IF
168 *
169 DO 10 I = I1, I2, I3
170 IF( LEFT ) THEN
171 *
172 * H(i) is applied to C(1:m-k+i,1:n)
173 *
174 MI = M - K + I
175 ELSE
176 *
177 * H(i) is applied to C(1:m,1:n-k+i)
178 *
179 NI = N - K + I
180 END IF
181 *
182 * Apply H(i)
183 *
184 AII = A( NQ-K+I, I )
185 A( NQ-K+I, I ) = ONE
186 CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC,
187 $ WORK )
188 A( NQ-K+I, I ) = AII
189 10 CONTINUE
190 RETURN
191 *
192 * End of DORM2L
193 *
194 END
2 $ WORK, INFO )
3 *
4 * -- LAPACK routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER SIDE, TRANS
11 INTEGER INFO, K, LDA, LDC, M, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DORM2L overwrites the general real m by n matrix C with
21 *
22 * Q * C if SIDE = 'L' and TRANS = 'N', or
23 *
24 * Q**T * C if SIDE = 'L' and TRANS = 'T', or
25 *
26 * C * Q if SIDE = 'R' and TRANS = 'N', or
27 *
28 * C * Q**T if SIDE = 'R' and TRANS = 'T',
29 *
30 * where Q is a real orthogonal matrix defined as the product of k
31 * elementary reflectors
32 *
33 * Q = H(k) . . . H(2) H(1)
34 *
35 * as returned by DGEQLF. Q is of order m if SIDE = 'L' and of order n
36 * if SIDE = 'R'.
37 *
38 * Arguments
39 * =========
40 *
41 * SIDE (input) CHARACTER*1
42 * = 'L': apply Q or Q**T from the Left
43 * = 'R': apply Q or Q**T from the Right
44 *
45 * TRANS (input) CHARACTER*1
46 * = 'N': apply Q (No transpose)
47 * = 'T': apply Q**T (Transpose)
48 *
49 * M (input) INTEGER
50 * The number of rows of the matrix C. M >= 0.
51 *
52 * N (input) INTEGER
53 * The number of columns of the matrix C. N >= 0.
54 *
55 * K (input) INTEGER
56 * The number of elementary reflectors whose product defines
57 * the matrix Q.
58 * If SIDE = 'L', M >= K >= 0;
59 * if SIDE = 'R', N >= K >= 0.
60 *
61 * A (input) DOUBLE PRECISION array, dimension (LDA,K)
62 * The i-th column must contain the vector which defines the
63 * elementary reflector H(i), for i = 1,2,...,k, as returned by
64 * DGEQLF in the last k columns of its array argument A.
65 * A is modified by the routine but restored on exit.
66 *
67 * LDA (input) INTEGER
68 * The leading dimension of the array A.
69 * If SIDE = 'L', LDA >= max(1,M);
70 * if SIDE = 'R', LDA >= max(1,N).
71 *
72 * TAU (input) DOUBLE PRECISION array, dimension (K)
73 * TAU(i) must contain the scalar factor of the elementary
74 * reflector H(i), as returned by DGEQLF.
75 *
76 * C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
77 * On entry, the m by n matrix C.
78 * On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
79 *
80 * LDC (input) INTEGER
81 * The leading dimension of the array C. LDC >= max(1,M).
82 *
83 * WORK (workspace) DOUBLE PRECISION array, dimension
84 * (N) if SIDE = 'L',
85 * (M) if SIDE = 'R'
86 *
87 * INFO (output) INTEGER
88 * = 0: successful exit
89 * < 0: if INFO = -i, the i-th argument had an illegal value
90 *
91 * =====================================================================
92 *
93 * .. Parameters ..
94 DOUBLE PRECISION ONE
95 PARAMETER ( ONE = 1.0D+0 )
96 * ..
97 * .. Local Scalars ..
98 LOGICAL LEFT, NOTRAN
99 INTEGER I, I1, I2, I3, MI, NI, NQ
100 DOUBLE PRECISION AII
101 * ..
102 * .. External Functions ..
103 LOGICAL LSAME
104 EXTERNAL LSAME
105 * ..
106 * .. External Subroutines ..
107 EXTERNAL DLARF, XERBLA
108 * ..
109 * .. Intrinsic Functions ..
110 INTRINSIC MAX
111 * ..
112 * .. Executable Statements ..
113 *
114 * Test the input arguments
115 *
116 INFO = 0
117 LEFT = LSAME( SIDE, 'L' )
118 NOTRAN = LSAME( TRANS, 'N' )
119 *
120 * NQ is the order of Q
121 *
122 IF( LEFT ) THEN
123 NQ = M
124 ELSE
125 NQ = N
126 END IF
127 IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
128 INFO = -1
129 ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
130 INFO = -2
131 ELSE IF( M.LT.0 ) THEN
132 INFO = -3
133 ELSE IF( N.LT.0 ) THEN
134 INFO = -4
135 ELSE IF( K.LT.0 .OR. K.GT.NQ ) THEN
136 INFO = -5
137 ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
138 INFO = -7
139 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
140 INFO = -10
141 END IF
142 IF( INFO.NE.0 ) THEN
143 CALL XERBLA( 'DORM2L', -INFO )
144 RETURN
145 END IF
146 *
147 * Quick return if possible
148 *
149 IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 )
150 $ RETURN
151 *
152 IF( ( LEFT .AND. NOTRAN ) .OR. ( .NOT.LEFT .AND. .NOT.NOTRAN ) )
153 $ THEN
154 I1 = 1
155 I2 = K
156 I3 = 1
157 ELSE
158 I1 = K
159 I2 = 1
160 I3 = -1
161 END IF
162 *
163 IF( LEFT ) THEN
164 NI = N
165 ELSE
166 MI = M
167 END IF
168 *
169 DO 10 I = I1, I2, I3
170 IF( LEFT ) THEN
171 *
172 * H(i) is applied to C(1:m-k+i,1:n)
173 *
174 MI = M - K + I
175 ELSE
176 *
177 * H(i) is applied to C(1:m,1:n-k+i)
178 *
179 NI = N - K + I
180 END IF
181 *
182 * Apply H(i)
183 *
184 AII = A( NQ-K+I, I )
185 A( NQ-K+I, I ) = ONE
186 CALL DLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC,
187 $ WORK )
188 A( NQ-K+I, I ) = AII
189 10 CONTINUE
190 RETURN
191 *
192 * End of DORM2L
193 *
194 END