1 SUBROUTINE DORGTR( UPLO, N, 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 UPLO
10 INTEGER INFO, LDA, LWORK, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DORGTR generates a real orthogonal matrix Q which is defined as the
20 * product of n-1 elementary reflectors of order N, as returned by
21 * DSYTRD:
22 *
23 * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
24 *
25 * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
26 *
27 * Arguments
28 * =========
29 *
30 * UPLO (input) CHARACTER*1
31 * = 'U': Upper triangle of A contains elementary reflectors
32 * from DSYTRD;
33 * = 'L': Lower triangle of A contains elementary reflectors
34 * from DSYTRD.
35 *
36 * N (input) INTEGER
37 * The order of the matrix Q. N >= 0.
38 *
39 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the vectors which define the elementary reflectors,
41 * as returned by DSYTRD.
42 * On exit, the N-by-N orthogonal matrix Q.
43 *
44 * LDA (input) INTEGER
45 * The leading dimension of the array A. LDA >= max(1,N).
46 *
47 * TAU (input) DOUBLE PRECISION array, dimension (N-1)
48 * TAU(i) must contain the scalar factor of the elementary
49 * reflector H(i), as returned by DSYTRD.
50 *
51 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
52 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
53 *
54 * LWORK (input) INTEGER
55 * The dimension of the array WORK. LWORK >= max(1,N-1).
56 * For optimum performance LWORK >= (N-1)*NB, where NB is
57 * the optimal blocksize.
58 *
59 * If LWORK = -1, then a workspace query is assumed; the routine
60 * only calculates the optimal size of the WORK array, returns
61 * this value as the first entry of the WORK array, and no error
62 * message related to LWORK is issued by XERBLA.
63 *
64 * INFO (output) INTEGER
65 * = 0: successful exit
66 * < 0: if INFO = -i, the i-th argument had an illegal value
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 DOUBLE PRECISION ZERO, ONE
72 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL LQUERY, UPPER
76 INTEGER I, IINFO, J, LWKOPT, NB
77 * ..
78 * .. External Functions ..
79 LOGICAL LSAME
80 INTEGER ILAENV
81 EXTERNAL LSAME, ILAENV
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DORGQL, DORGQR, XERBLA
85 * ..
86 * .. Intrinsic Functions ..
87 INTRINSIC MAX
88 * ..
89 * .. Executable Statements ..
90 *
91 * Test the input arguments
92 *
93 INFO = 0
94 LQUERY = ( LWORK.EQ.-1 )
95 UPPER = LSAME( UPLO, 'U' )
96 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
97 INFO = -1
98 ELSE IF( N.LT.0 ) THEN
99 INFO = -2
100 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
101 INFO = -4
102 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
103 INFO = -7
104 END IF
105 *
106 IF( INFO.EQ.0 ) THEN
107 IF( UPPER ) THEN
108 NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
109 ELSE
110 NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
111 END IF
112 LWKOPT = MAX( 1, N-1 )*NB
113 WORK( 1 ) = LWKOPT
114 END IF
115 *
116 IF( INFO.NE.0 ) THEN
117 CALL XERBLA( 'DORGTR', -INFO )
118 RETURN
119 ELSE IF( LQUERY ) THEN
120 RETURN
121 END IF
122 *
123 * Quick return if possible
124 *
125 IF( N.EQ.0 ) THEN
126 WORK( 1 ) = 1
127 RETURN
128 END IF
129 *
130 IF( UPPER ) THEN
131 *
132 * Q was determined by a call to DSYTRD with UPLO = 'U'
133 *
134 * Shift the vectors which define the elementary reflectors one
135 * column to the left, and set the last row and column of Q to
136 * those of the unit matrix
137 *
138 DO 20 J = 1, N - 1
139 DO 10 I = 1, J - 1
140 A( I, J ) = A( I, J+1 )
141 10 CONTINUE
142 A( N, J ) = ZERO
143 20 CONTINUE
144 DO 30 I = 1, N - 1
145 A( I, N ) = ZERO
146 30 CONTINUE
147 A( N, N ) = ONE
148 *
149 * Generate Q(1:n-1,1:n-1)
150 *
151 CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
152 *
153 ELSE
154 *
155 * Q was determined by a call to DSYTRD with UPLO = 'L'.
156 *
157 * Shift the vectors which define the elementary reflectors one
158 * column to the right, and set the first row and column of Q to
159 * those of the unit matrix
160 *
161 DO 50 J = N, 2, -1
162 A( 1, J ) = ZERO
163 DO 40 I = J + 1, N
164 A( I, J ) = A( I, J-1 )
165 40 CONTINUE
166 50 CONTINUE
167 A( 1, 1 ) = ONE
168 DO 60 I = 2, N
169 A( I, 1 ) = ZERO
170 60 CONTINUE
171 IF( N.GT.1 ) THEN
172 *
173 * Generate Q(2:n,2:n)
174 *
175 CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
176 $ LWORK, IINFO )
177 END IF
178 END IF
179 WORK( 1 ) = LWKOPT
180 RETURN
181 *
182 * End of DORGTR
183 *
184 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 UPLO
10 INTEGER INFO, LDA, LWORK, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DORGTR generates a real orthogonal matrix Q which is defined as the
20 * product of n-1 elementary reflectors of order N, as returned by
21 * DSYTRD:
22 *
23 * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
24 *
25 * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
26 *
27 * Arguments
28 * =========
29 *
30 * UPLO (input) CHARACTER*1
31 * = 'U': Upper triangle of A contains elementary reflectors
32 * from DSYTRD;
33 * = 'L': Lower triangle of A contains elementary reflectors
34 * from DSYTRD.
35 *
36 * N (input) INTEGER
37 * The order of the matrix Q. N >= 0.
38 *
39 * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40 * On entry, the vectors which define the elementary reflectors,
41 * as returned by DSYTRD.
42 * On exit, the N-by-N orthogonal matrix Q.
43 *
44 * LDA (input) INTEGER
45 * The leading dimension of the array A. LDA >= max(1,N).
46 *
47 * TAU (input) DOUBLE PRECISION array, dimension (N-1)
48 * TAU(i) must contain the scalar factor of the elementary
49 * reflector H(i), as returned by DSYTRD.
50 *
51 * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
52 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
53 *
54 * LWORK (input) INTEGER
55 * The dimension of the array WORK. LWORK >= max(1,N-1).
56 * For optimum performance LWORK >= (N-1)*NB, where NB is
57 * the optimal blocksize.
58 *
59 * If LWORK = -1, then a workspace query is assumed; the routine
60 * only calculates the optimal size of the WORK array, returns
61 * this value as the first entry of the WORK array, and no error
62 * message related to LWORK is issued by XERBLA.
63 *
64 * INFO (output) INTEGER
65 * = 0: successful exit
66 * < 0: if INFO = -i, the i-th argument had an illegal value
67 *
68 * =====================================================================
69 *
70 * .. Parameters ..
71 DOUBLE PRECISION ZERO, ONE
72 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
73 * ..
74 * .. Local Scalars ..
75 LOGICAL LQUERY, UPPER
76 INTEGER I, IINFO, J, LWKOPT, NB
77 * ..
78 * .. External Functions ..
79 LOGICAL LSAME
80 INTEGER ILAENV
81 EXTERNAL LSAME, ILAENV
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DORGQL, DORGQR, XERBLA
85 * ..
86 * .. Intrinsic Functions ..
87 INTRINSIC MAX
88 * ..
89 * .. Executable Statements ..
90 *
91 * Test the input arguments
92 *
93 INFO = 0
94 LQUERY = ( LWORK.EQ.-1 )
95 UPPER = LSAME( UPLO, 'U' )
96 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
97 INFO = -1
98 ELSE IF( N.LT.0 ) THEN
99 INFO = -2
100 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
101 INFO = -4
102 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
103 INFO = -7
104 END IF
105 *
106 IF( INFO.EQ.0 ) THEN
107 IF( UPPER ) THEN
108 NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
109 ELSE
110 NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
111 END IF
112 LWKOPT = MAX( 1, N-1 )*NB
113 WORK( 1 ) = LWKOPT
114 END IF
115 *
116 IF( INFO.NE.0 ) THEN
117 CALL XERBLA( 'DORGTR', -INFO )
118 RETURN
119 ELSE IF( LQUERY ) THEN
120 RETURN
121 END IF
122 *
123 * Quick return if possible
124 *
125 IF( N.EQ.0 ) THEN
126 WORK( 1 ) = 1
127 RETURN
128 END IF
129 *
130 IF( UPPER ) THEN
131 *
132 * Q was determined by a call to DSYTRD with UPLO = 'U'
133 *
134 * Shift the vectors which define the elementary reflectors one
135 * column to the left, and set the last row and column of Q to
136 * those of the unit matrix
137 *
138 DO 20 J = 1, N - 1
139 DO 10 I = 1, J - 1
140 A( I, J ) = A( I, J+1 )
141 10 CONTINUE
142 A( N, J ) = ZERO
143 20 CONTINUE
144 DO 30 I = 1, N - 1
145 A( I, N ) = ZERO
146 30 CONTINUE
147 A( N, N ) = ONE
148 *
149 * Generate Q(1:n-1,1:n-1)
150 *
151 CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
152 *
153 ELSE
154 *
155 * Q was determined by a call to DSYTRD with UPLO = 'L'.
156 *
157 * Shift the vectors which define the elementary reflectors one
158 * column to the right, and set the first row and column of Q to
159 * those of the unit matrix
160 *
161 DO 50 J = N, 2, -1
162 A( 1, J ) = ZERO
163 DO 40 I = J + 1, N
164 A( I, J ) = A( I, J-1 )
165 40 CONTINUE
166 50 CONTINUE
167 A( 1, 1 ) = ONE
168 DO 60 I = 2, N
169 A( I, 1 ) = ZERO
170 60 CONTINUE
171 IF( N.GT.1 ) THEN
172 *
173 * Generate Q(2:n,2:n)
174 *
175 CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
176 $ LWORK, IINFO )
177 END IF
178 END IF
179 WORK( 1 ) = LWKOPT
180 RETURN
181 *
182 * End of DORGTR
183 *
184 END