1 SUBROUTINE DLARZT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
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 CHARACTER DIRECT, STOREV
10 INTEGER K, LDT, LDV, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLARZT forms the triangular factor T of a real block reflector
20 * H of order > n, which is defined as a product of k elementary
21 * reflectors.
22 *
23 * If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
24 *
25 * If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
26 *
27 * If STOREV = 'C', the vector which defines the elementary reflector
28 * H(i) is stored in the i-th column of the array V, and
29 *
30 * H = I - V * T * V**T
31 *
32 * If STOREV = 'R', the vector which defines the elementary reflector
33 * H(i) is stored in the i-th row of the array V, and
34 *
35 * H = I - V**T * T * V
36 *
37 * Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
38 *
39 * Arguments
40 * =========
41 *
42 * DIRECT (input) CHARACTER*1
43 * Specifies the order in which the elementary reflectors are
44 * multiplied to form the block reflector:
45 * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
46 * = 'B': H = H(k) . . . H(2) H(1) (Backward)
47 *
48 * STOREV (input) CHARACTER*1
49 * Specifies how the vectors which define the elementary
50 * reflectors are stored (see also Further Details):
51 * = 'C': columnwise (not supported yet)
52 * = 'R': rowwise
53 *
54 * N (input) INTEGER
55 * The order of the block reflector H. N >= 0.
56 *
57 * K (input) INTEGER
58 * The order of the triangular factor T (= the number of
59 * elementary reflectors). K >= 1.
60 *
61 * V (input/output) DOUBLE PRECISION array, dimension
62 * (LDV,K) if STOREV = 'C'
63 * (LDV,N) if STOREV = 'R'
64 * The matrix V. See further details.
65 *
66 * LDV (input) INTEGER
67 * The leading dimension of the array V.
68 * If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
69 *
70 * TAU (input) DOUBLE PRECISION array, dimension (K)
71 * TAU(i) must contain the scalar factor of the elementary
72 * reflector H(i).
73 *
74 * T (output) DOUBLE PRECISION array, dimension (LDT,K)
75 * The k by k triangular factor T of the block reflector.
76 * If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
77 * lower triangular. The rest of the array is not used.
78 *
79 * LDT (input) INTEGER
80 * The leading dimension of the array T. LDT >= K.
81 *
82 * Further Details
83 * ===============
84 *
85 * Based on contributions by
86 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
87 *
88 * The shape of the matrix V and the storage of the vectors which define
89 * the H(i) is best illustrated by the following example with n = 5 and
90 * k = 3. The elements equal to 1 are not stored; the corresponding
91 * array elements are modified but restored on exit. The rest of the
92 * array is not used.
93 *
94 * DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
95 *
96 * ______V_____
97 * ( v1 v2 v3 ) / \
98 * ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
99 * V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
100 * ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
101 * ( v1 v2 v3 )
102 * . . .
103 * . . .
104 * 1 . .
105 * 1 .
106 * 1
107 *
108 * DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
109 *
110 * ______V_____
111 * 1 / \
112 * . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
113 * . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
114 * . . . ( . . 1 . . v3 v3 v3 v3 v3 )
115 * . . .
116 * ( v1 v2 v3 )
117 * ( v1 v2 v3 )
118 * V = ( v1 v2 v3 )
119 * ( v1 v2 v3 )
120 * ( v1 v2 v3 )
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125 DOUBLE PRECISION ZERO
126 PARAMETER ( ZERO = 0.0D+0 )
127 * ..
128 * .. Local Scalars ..
129 INTEGER I, INFO, J
130 * ..
131 * .. External Subroutines ..
132 EXTERNAL DGEMV, DTRMV, XERBLA
133 * ..
134 * .. External Functions ..
135 LOGICAL LSAME
136 EXTERNAL LSAME
137 * ..
138 * .. Executable Statements ..
139 *
140 * Check for currently supported options
141 *
142 INFO = 0
143 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
144 INFO = -1
145 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
146 INFO = -2
147 END IF
148 IF( INFO.NE.0 ) THEN
149 CALL XERBLA( 'DLARZT', -INFO )
150 RETURN
151 END IF
152 *
153 DO 20 I = K, 1, -1
154 IF( TAU( I ).EQ.ZERO ) THEN
155 *
156 * H(i) = I
157 *
158 DO 10 J = I, K
159 T( J, I ) = ZERO
160 10 CONTINUE
161 ELSE
162 *
163 * general case
164 *
165 IF( I.LT.K ) THEN
166 *
167 * T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
168 *
169 CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
170 $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
171 $ T( I+1, I ), 1 )
172 *
173 * T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
174 *
175 CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
176 $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
177 END IF
178 T( I, I ) = TAU( I )
179 END IF
180 20 CONTINUE
181 RETURN
182 *
183 * End of DLARZT
184 *
185 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 CHARACTER DIRECT, STOREV
10 INTEGER K, LDT, LDV, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION T( LDT, * ), TAU( * ), V( LDV, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLARZT forms the triangular factor T of a real block reflector
20 * H of order > n, which is defined as a product of k elementary
21 * reflectors.
22 *
23 * If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
24 *
25 * If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
26 *
27 * If STOREV = 'C', the vector which defines the elementary reflector
28 * H(i) is stored in the i-th column of the array V, and
29 *
30 * H = I - V * T * V**T
31 *
32 * If STOREV = 'R', the vector which defines the elementary reflector
33 * H(i) is stored in the i-th row of the array V, and
34 *
35 * H = I - V**T * T * V
36 *
37 * Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
38 *
39 * Arguments
40 * =========
41 *
42 * DIRECT (input) CHARACTER*1
43 * Specifies the order in which the elementary reflectors are
44 * multiplied to form the block reflector:
45 * = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
46 * = 'B': H = H(k) . . . H(2) H(1) (Backward)
47 *
48 * STOREV (input) CHARACTER*1
49 * Specifies how the vectors which define the elementary
50 * reflectors are stored (see also Further Details):
51 * = 'C': columnwise (not supported yet)
52 * = 'R': rowwise
53 *
54 * N (input) INTEGER
55 * The order of the block reflector H. N >= 0.
56 *
57 * K (input) INTEGER
58 * The order of the triangular factor T (= the number of
59 * elementary reflectors). K >= 1.
60 *
61 * V (input/output) DOUBLE PRECISION array, dimension
62 * (LDV,K) if STOREV = 'C'
63 * (LDV,N) if STOREV = 'R'
64 * The matrix V. See further details.
65 *
66 * LDV (input) INTEGER
67 * The leading dimension of the array V.
68 * If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
69 *
70 * TAU (input) DOUBLE PRECISION array, dimension (K)
71 * TAU(i) must contain the scalar factor of the elementary
72 * reflector H(i).
73 *
74 * T (output) DOUBLE PRECISION array, dimension (LDT,K)
75 * The k by k triangular factor T of the block reflector.
76 * If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
77 * lower triangular. The rest of the array is not used.
78 *
79 * LDT (input) INTEGER
80 * The leading dimension of the array T. LDT >= K.
81 *
82 * Further Details
83 * ===============
84 *
85 * Based on contributions by
86 * A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
87 *
88 * The shape of the matrix V and the storage of the vectors which define
89 * the H(i) is best illustrated by the following example with n = 5 and
90 * k = 3. The elements equal to 1 are not stored; the corresponding
91 * array elements are modified but restored on exit. The rest of the
92 * array is not used.
93 *
94 * DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
95 *
96 * ______V_____
97 * ( v1 v2 v3 ) / \
98 * ( v1 v2 v3 ) ( v1 v1 v1 v1 v1 . . . . 1 )
99 * V = ( v1 v2 v3 ) ( v2 v2 v2 v2 v2 . . . 1 )
100 * ( v1 v2 v3 ) ( v3 v3 v3 v3 v3 . . 1 )
101 * ( v1 v2 v3 )
102 * . . .
103 * . . .
104 * 1 . .
105 * 1 .
106 * 1
107 *
108 * DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
109 *
110 * ______V_____
111 * 1 / \
112 * . 1 ( 1 . . . . v1 v1 v1 v1 v1 )
113 * . . 1 ( . 1 . . . v2 v2 v2 v2 v2 )
114 * . . . ( . . 1 . . v3 v3 v3 v3 v3 )
115 * . . .
116 * ( v1 v2 v3 )
117 * ( v1 v2 v3 )
118 * V = ( v1 v2 v3 )
119 * ( v1 v2 v3 )
120 * ( v1 v2 v3 )
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125 DOUBLE PRECISION ZERO
126 PARAMETER ( ZERO = 0.0D+0 )
127 * ..
128 * .. Local Scalars ..
129 INTEGER I, INFO, J
130 * ..
131 * .. External Subroutines ..
132 EXTERNAL DGEMV, DTRMV, XERBLA
133 * ..
134 * .. External Functions ..
135 LOGICAL LSAME
136 EXTERNAL LSAME
137 * ..
138 * .. Executable Statements ..
139 *
140 * Check for currently supported options
141 *
142 INFO = 0
143 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
144 INFO = -1
145 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
146 INFO = -2
147 END IF
148 IF( INFO.NE.0 ) THEN
149 CALL XERBLA( 'DLARZT', -INFO )
150 RETURN
151 END IF
152 *
153 DO 20 I = K, 1, -1
154 IF( TAU( I ).EQ.ZERO ) THEN
155 *
156 * H(i) = I
157 *
158 DO 10 J = I, K
159 T( J, I ) = ZERO
160 10 CONTINUE
161 ELSE
162 *
163 * general case
164 *
165 IF( I.LT.K ) THEN
166 *
167 * T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
168 *
169 CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
170 $ V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
171 $ T( I+1, I ), 1 )
172 *
173 * T(i+1:k,i) = T(i+1:k,i+1:k) * T(i+1:k,i)
174 *
175 CALL DTRMV( 'Lower', 'No transpose', 'Non-unit', K-I,
176 $ T( I+1, I+1 ), LDT, T( I+1, I ), 1 )
177 END IF
178 T( I, I ) = TAU( I )
179 END IF
180 20 CONTINUE
181 RETURN
182 *
183 * End of DLARZT
184 *
185 END