Annotation of rpl/lapack/lapack/zungtr.f, revision 1.2
1.1 bertrand 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
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