Annotation of rpl/lapack/lapack/dopgtr.f, revision 1.12
1.8 bertrand 1: *> \brief \b DOPGTR
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DOPGTR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dopgtr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dopgtr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dopgtr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INFO, LDQ, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DOPGTR generates a real orthogonal matrix Q which is defined as the
38: *> product of n-1 elementary reflectors H(i) of order n, as returned by
39: *> DSPTRD 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 DSPTRD;
54: *> = 'L': Lower triangular packed storage used in previous
55: *> call to DSPTRD.
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 DOUBLE PRECISION array, dimension (N*(N+1)/2)
67: *> The vectors which define the elementary reflectors, as
68: *> returned by DSPTRD.
69: *> \endverbatim
70: *>
71: *> \param[in] TAU
72: *> \verbatim
73: *> TAU is DOUBLE PRECISION array, dimension (N-1)
74: *> TAU(i) must contain the scalar factor of the elementary
75: *> reflector H(i), as returned by DSPTRD.
76: *> \endverbatim
77: *>
78: *> \param[out] Q
79: *> \verbatim
80: *> Q is DOUBLE PRECISION array, dimension (LDQ,N)
81: *> The N-by-N orthogonal 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 DOUBLE PRECISION 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: *
105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
109: *
110: *> \date November 2011
111: *
112: *> \ingroup doubleOTHERcomputational
113: *
114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
116: *
1.8 bertrand 117: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 bertrand 120: * November 2011
1.1 bertrand 121: *
122: * .. Scalar Arguments ..
123: CHARACTER UPLO
124: INTEGER INFO, LDQ, N
125: * ..
126: * .. Array Arguments ..
127: DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: DOUBLE PRECISION ZERO, ONE
134: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
135: * ..
136: * .. Local Scalars ..
137: LOGICAL UPPER
138: INTEGER I, IINFO, IJ, J
139: * ..
140: * .. External Functions ..
141: LOGICAL LSAME
142: EXTERNAL LSAME
143: * ..
144: * .. External Subroutines ..
145: EXTERNAL DORG2L, DORG2R, XERBLA
146: * ..
147: * .. Intrinsic Functions ..
148: INTRINSIC MAX
149: * ..
150: * .. Executable Statements ..
151: *
152: * Test the input arguments
153: *
154: INFO = 0
155: UPPER = LSAME( UPLO, 'U' )
156: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
157: INFO = -1
158: ELSE IF( N.LT.0 ) THEN
159: INFO = -2
160: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
161: INFO = -6
162: END IF
163: IF( INFO.NE.0 ) THEN
164: CALL XERBLA( 'DOPGTR', -INFO )
165: RETURN
166: END IF
167: *
168: * Quick return if possible
169: *
170: IF( N.EQ.0 )
171: $ RETURN
172: *
173: IF( UPPER ) THEN
174: *
175: * Q was determined by a call to DSPTRD with UPLO = 'U'
176: *
177: * Unpack the vectors which define the elementary reflectors and
178: * set the last row and column of Q equal to those of the unit
179: * matrix
180: *
181: IJ = 2
182: DO 20 J = 1, N - 1
183: DO 10 I = 1, J - 1
184: Q( I, J ) = AP( IJ )
185: IJ = IJ + 1
186: 10 CONTINUE
187: IJ = IJ + 2
188: Q( N, J ) = ZERO
189: 20 CONTINUE
190: DO 30 I = 1, N - 1
191: Q( I, N ) = ZERO
192: 30 CONTINUE
193: Q( N, N ) = ONE
194: *
195: * Generate Q(1:n-1,1:n-1)
196: *
197: CALL DORG2L( N-1, N-1, N-1, Q, LDQ, TAU, WORK, IINFO )
198: *
199: ELSE
200: *
201: * Q was determined by a call to DSPTRD with UPLO = 'L'.
202: *
203: * Unpack the vectors which define the elementary reflectors and
204: * set the first row and column of Q equal to those of the unit
205: * matrix
206: *
207: Q( 1, 1 ) = ONE
208: DO 40 I = 2, N
209: Q( I, 1 ) = ZERO
210: 40 CONTINUE
211: IJ = 3
212: DO 60 J = 2, N
213: Q( 1, J ) = ZERO
214: DO 50 I = J + 1, N
215: Q( I, J ) = AP( IJ )
216: IJ = IJ + 1
217: 50 CONTINUE
218: IJ = IJ + 2
219: 60 CONTINUE
220: IF( N.GT.1 ) THEN
221: *
222: * Generate Q(2:n,2:n)
223: *
224: CALL DORG2R( N-1, N-1, N-1, Q( 2, 2 ), LDQ, TAU, WORK,
225: $ IINFO )
226: END IF
227: END IF
228: RETURN
229: *
230: * End of DOPGTR
231: *
232: END
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