1 SUBROUTINE ZUNGTR( 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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZUNGTR generates a complex unitary matrix Q which is defined as the
20 * product of n-1 elementary reflectors of order N, as returned by
21 * ZHETRD:
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 ZHETRD;
33 * = 'L': Lower triangle of A contains elementary reflectors
34 * from ZHETRD.
35 *
36 * N (input) INTEGER
37 * The order of the matrix Q. N >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the vectors which define the elementary reflectors,
41 * as returned by ZHETRD.
42 * On exit, the N-by-N unitary matrix Q.
43 *
44 * LDA (input) INTEGER
45 * The leading dimension of the array A. LDA >= N.
46 *
47 * TAU (input) COMPLEX*16 array, dimension (N-1)
48 * TAU(i) must contain the scalar factor of the elementary
49 * reflector H(i), as returned by ZHETRD.
50 *
51 * WORK (workspace/output) COMPLEX*16 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 >= 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 COMPLEX*16 ZERO, ONE
72 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
73 $ ONE = ( 1.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL LQUERY, UPPER
77 INTEGER I, IINFO, J, LWKOPT, NB
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 INTEGER ILAENV
82 EXTERNAL LSAME, ILAENV
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL XERBLA, ZUNGQL, ZUNGQR
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC MAX
89 * ..
90 * .. Executable Statements ..
91 *
92 * Test the input arguments
93 *
94 INFO = 0
95 LQUERY = ( LWORK.EQ.-1 )
96 UPPER = LSAME( UPLO, 'U' )
97 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
98 INFO = -1
99 ELSE IF( N.LT.0 ) THEN
100 INFO = -2
101 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
102 INFO = -4
103 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
104 INFO = -7
105 END IF
106 *
107 IF( INFO.EQ.0 ) THEN
108 IF( UPPER ) THEN
109 NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
110 ELSE
111 NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
112 END IF
113 LWKOPT = MAX( 1, N-1 )*NB
114 WORK( 1 ) = LWKOPT
115 END IF
116 *
117 IF( INFO.NE.0 ) THEN
118 CALL XERBLA( 'ZUNGTR', -INFO )
119 RETURN
120 ELSE IF( LQUERY ) THEN
121 RETURN
122 END IF
123 *
124 * Quick return if possible
125 *
126 IF( N.EQ.0 ) THEN
127 WORK( 1 ) = 1
128 RETURN
129 END IF
130 *
131 IF( UPPER ) THEN
132 *
133 * Q was determined by a call to ZHETRD with UPLO = 'U'
134 *
135 * Shift the vectors which define the elementary reflectors one
136 * column to the left, and set the last row and column of Q to
137 * those of the unit matrix
138 *
139 DO 20 J = 1, N - 1
140 DO 10 I = 1, J - 1
141 A( I, J ) = A( I, J+1 )
142 10 CONTINUE
143 A( N, J ) = ZERO
144 20 CONTINUE
145 DO 30 I = 1, N - 1
146 A( I, N ) = ZERO
147 30 CONTINUE
148 A( N, N ) = ONE
149 *
150 * Generate Q(1:n-1,1:n-1)
151 *
152 CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
153 *
154 ELSE
155 *
156 * Q was determined by a call to ZHETRD with UPLO = 'L'.
157 *
158 * Shift the vectors which define the elementary reflectors one
159 * column to the right, and set the first row and column of Q to
160 * those of the unit matrix
161 *
162 DO 50 J = N, 2, -1
163 A( 1, J ) = ZERO
164 DO 40 I = J + 1, N
165 A( I, J ) = A( I, J-1 )
166 40 CONTINUE
167 50 CONTINUE
168 A( 1, 1 ) = ONE
169 DO 60 I = 2, N
170 A( I, 1 ) = ZERO
171 60 CONTINUE
172 IF( N.GT.1 ) THEN
173 *
174 * Generate Q(2:n,2:n)
175 *
176 CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
177 $ LWORK, IINFO )
178 END IF
179 END IF
180 WORK( 1 ) = LWKOPT
181 RETURN
182 *
183 * End of ZUNGTR
184 *
185 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 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZUNGTR generates a complex unitary matrix Q which is defined as the
20 * product of n-1 elementary reflectors of order N, as returned by
21 * ZHETRD:
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 ZHETRD;
33 * = 'L': Lower triangle of A contains elementary reflectors
34 * from ZHETRD.
35 *
36 * N (input) INTEGER
37 * The order of the matrix Q. N >= 0.
38 *
39 * A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 * On entry, the vectors which define the elementary reflectors,
41 * as returned by ZHETRD.
42 * On exit, the N-by-N unitary matrix Q.
43 *
44 * LDA (input) INTEGER
45 * The leading dimension of the array A. LDA >= N.
46 *
47 * TAU (input) COMPLEX*16 array, dimension (N-1)
48 * TAU(i) must contain the scalar factor of the elementary
49 * reflector H(i), as returned by ZHETRD.
50 *
51 * WORK (workspace/output) COMPLEX*16 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 >= 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 COMPLEX*16 ZERO, ONE
72 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
73 $ ONE = ( 1.0D+0, 0.0D+0 ) )
74 * ..
75 * .. Local Scalars ..
76 LOGICAL LQUERY, UPPER
77 INTEGER I, IINFO, J, LWKOPT, NB
78 * ..
79 * .. External Functions ..
80 LOGICAL LSAME
81 INTEGER ILAENV
82 EXTERNAL LSAME, ILAENV
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL XERBLA, ZUNGQL, ZUNGQR
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC MAX
89 * ..
90 * .. Executable Statements ..
91 *
92 * Test the input arguments
93 *
94 INFO = 0
95 LQUERY = ( LWORK.EQ.-1 )
96 UPPER = LSAME( UPLO, 'U' )
97 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
98 INFO = -1
99 ELSE IF( N.LT.0 ) THEN
100 INFO = -2
101 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
102 INFO = -4
103 ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
104 INFO = -7
105 END IF
106 *
107 IF( INFO.EQ.0 ) THEN
108 IF( UPPER ) THEN
109 NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
110 ELSE
111 NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
112 END IF
113 LWKOPT = MAX( 1, N-1 )*NB
114 WORK( 1 ) = LWKOPT
115 END IF
116 *
117 IF( INFO.NE.0 ) THEN
118 CALL XERBLA( 'ZUNGTR', -INFO )
119 RETURN
120 ELSE IF( LQUERY ) THEN
121 RETURN
122 END IF
123 *
124 * Quick return if possible
125 *
126 IF( N.EQ.0 ) THEN
127 WORK( 1 ) = 1
128 RETURN
129 END IF
130 *
131 IF( UPPER ) THEN
132 *
133 * Q was determined by a call to ZHETRD with UPLO = 'U'
134 *
135 * Shift the vectors which define the elementary reflectors one
136 * column to the left, and set the last row and column of Q to
137 * those of the unit matrix
138 *
139 DO 20 J = 1, N - 1
140 DO 10 I = 1, J - 1
141 A( I, J ) = A( I, J+1 )
142 10 CONTINUE
143 A( N, J ) = ZERO
144 20 CONTINUE
145 DO 30 I = 1, N - 1
146 A( I, N ) = ZERO
147 30 CONTINUE
148 A( N, N ) = ONE
149 *
150 * Generate Q(1:n-1,1:n-1)
151 *
152 CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
153 *
154 ELSE
155 *
156 * Q was determined by a call to ZHETRD with UPLO = 'L'.
157 *
158 * Shift the vectors which define the elementary reflectors one
159 * column to the right, and set the first row and column of Q to
160 * those of the unit matrix
161 *
162 DO 50 J = N, 2, -1
163 A( 1, J ) = ZERO
164 DO 40 I = J + 1, N
165 A( I, J ) = A( I, J-1 )
166 40 CONTINUE
167 50 CONTINUE
168 A( 1, 1 ) = ONE
169 DO 60 I = 2, N
170 A( I, 1 ) = ZERO
171 60 CONTINUE
172 IF( N.GT.1 ) THEN
173 *
174 * Generate Q(2:n,2:n)
175 *
176 CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
177 $ LWORK, IINFO )
178 END IF
179 END IF
180 WORK( 1 ) = LWKOPT
181 RETURN
182 *
183 * End of ZUNGTR
184 *
185 END