Annotation of rpl/lapack/lapack/zupgtr.f, revision 1.17
1.8 bertrand 1: *> \brief \b ZUPGTR
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download ZUPGTR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zupgtr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zupgtr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zupgtr.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
1.14 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDQ, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
29: * ..
1.14 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZUPGTR generates a complex unitary matrix Q which is defined as the
38: *> product of n-1 elementary reflectors H(i) of order n, as returned by
39: *> ZHPTRD using packed storage:
40: *>
41: *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
42: *>
43: *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] UPLO
50: *> \verbatim
51: *> UPLO is CHARACTER*1
52: *> = 'U': Upper triangular packed storage used in previous
53: *> call to ZHPTRD;
54: *> = 'L': Lower triangular packed storage used in previous
55: *> call to ZHPTRD.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix Q. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] AP
65: *> \verbatim
66: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
67: *> The vectors which define the elementary reflectors, as
68: *> returned by ZHPTRD.
69: *> \endverbatim
70: *>
71: *> \param[in] TAU
72: *> \verbatim
73: *> TAU is COMPLEX*16 array, dimension (N-1)
74: *> TAU(i) must contain the scalar factor of the elementary
75: *> reflector H(i), as returned by ZHPTRD.
76: *> \endverbatim
77: *>
78: *> \param[out] Q
79: *> \verbatim
80: *> Q is COMPLEX*16 array, dimension (LDQ,N)
81: *> The N-by-N unitary matrix Q.
82: *> \endverbatim
83: *>
84: *> \param[in] LDQ
85: *> \verbatim
86: *> LDQ is INTEGER
87: *> The leading dimension of the array Q. LDQ >= max(1,N).
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is COMPLEX*16 array, dimension (N-1)
93: *> \endverbatim
94: *>
95: *> \param[out] INFO
96: *> \verbatim
97: *> INFO is INTEGER
98: *> = 0: successful exit
99: *> < 0: if INFO = -i, the i-th argument had an illegal value
100: *> \endverbatim
101: *
102: * Authors:
103: * ========
104: *
1.14 bertrand 105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
1.8 bertrand 109: *
110: *> \ingroup complex16OTHERcomputational
111: *
112: * =====================================================================
1.1 bertrand 113: SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
114: *
1.17 ! bertrand 115: * -- LAPACK computational routine --
1.1 bertrand 116: * -- LAPACK is a software package provided by Univ. of Tennessee, --
117: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118: *
119: * .. Scalar Arguments ..
120: CHARACTER UPLO
121: INTEGER INFO, LDQ, N
122: * ..
123: * .. Array Arguments ..
124: COMPLEX*16 AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125: * ..
126: *
127: * =====================================================================
128: *
129: * .. Parameters ..
130: COMPLEX*16 CZERO, CONE
131: PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
132: $ CONE = ( 1.0D+0, 0.0D+0 ) )
133: * ..
134: * .. Local Scalars ..
135: LOGICAL UPPER
136: INTEGER I, IINFO, IJ, J
137: * ..
138: * .. External Functions ..
139: LOGICAL LSAME
140: EXTERNAL LSAME
141: * ..
142: * .. External Subroutines ..
143: EXTERNAL XERBLA, ZUNG2L, ZUNG2R
144: * ..
145: * .. Intrinsic Functions ..
146: INTRINSIC MAX
147: * ..
148: * .. Executable Statements ..
149: *
150: * Test the input arguments
151: *
152: INFO = 0
153: UPPER = LSAME( UPLO, 'U' )
154: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
155: INFO = -1
156: ELSE IF( N.LT.0 ) THEN
157: INFO = -2
158: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
159: INFO = -6
160: END IF
161: IF( INFO.NE.0 ) THEN
162: CALL XERBLA( 'ZUPGTR', -INFO )
163: RETURN
164: END IF
165: *
166: * Quick return if possible
167: *
168: IF( N.EQ.0 )
169: $ RETURN
170: *
171: IF( UPPER ) THEN
172: *
173: * Q was determined by a call to ZHPTRD with UPLO = 'U'
174: *
175: * Unpack the vectors which define the elementary reflectors and
176: * set the last row and column of Q equal to those of the unit
177: * matrix
178: *
179: IJ = 2
180: DO 20 J = 1, N - 1
181: DO 10 I = 1, J - 1
182: Q( I, J ) = AP( IJ )
183: IJ = IJ + 1
184: 10 CONTINUE
185: IJ = IJ + 2
186: Q( N, J ) = CZERO
187: 20 CONTINUE
188: DO 30 I = 1, N - 1
189: Q( I, N ) = CZERO
190: 30 CONTINUE
191: Q( N, N ) = CONE
192: *
193: * Generate Q(1:n-1,1:n-1)
194: *
195: CALL ZUNG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
196: *
197: ELSE
198: *
199: * Q was determined by a call to ZHPTRD with UPLO = 'L'.
200: *
201: * Unpack the vectors which define the elementary reflectors and
202: * set the first row and column of Q equal to those of the unit
203: * matrix
204: *
205: Q( 1, 1 ) = CONE
206: DO 40 I = 2, N
207: Q( I, 1 ) = CZERO
208: 40 CONTINUE
209: IJ = 3
210: DO 60 J = 2, N
211: Q( 1, J ) = CZERO
212: DO 50 I = J + 1, N
213: Q( I, J ) = AP( IJ )
214: IJ = IJ + 1
215: 50 CONTINUE
216: IJ = IJ + 2
217: 60 CONTINUE
218: IF( N.GT.1 ) THEN
219: *
220: * Generate Q(2:n,2:n)
221: *
222: CALL ZUNG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
223: $ IINFO )
224: END IF
225: END IF
226: RETURN
227: *
228: * End of ZUPGTR
229: *
230: END
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