LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
dopgtr.f
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1 *> \brief \b DOPGTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
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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 *> \ingroup doubleOTHERcomputational
111 *
112 * =====================================================================
113  SUBROUTINE dopgtr( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
114 *
115 * -- LAPACK computational routine --
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  DOUBLE PRECISION AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  DOUBLE PRECISION ZERO, ONE
131  parameter( zero = 0.0d+0, one = 1.0d+0 )
132 * ..
133 * .. Local Scalars ..
134  LOGICAL UPPER
135  INTEGER I, IINFO, IJ, J
136 * ..
137 * .. External Functions ..
138  LOGICAL LSAME
139  EXTERNAL lsame
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL dorg2l, dorg2r, xerbla
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input arguments
150 *
151  info = 0
152  upper = lsame( uplo, 'U' )
153  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
154  info = -1
155  ELSE IF( n.LT.0 ) THEN
156  info = -2
157  ELSE IF( ldq.LT.max( 1, n ) ) THEN
158  info = -6
159  END IF
160  IF( info.NE.0 ) THEN
161  CALL xerbla( 'DOPGTR', -info )
162  RETURN
163  END IF
164 *
165 * Quick return if possible
166 *
167  IF( n.EQ.0 )
168  \$ RETURN
169 *
170  IF( upper ) THEN
171 *
172 * Q was determined by a call to DSPTRD with UPLO = 'U'
173 *
174 * Unpack the vectors which define the elementary reflectors and
175 * set the last row and column of Q equal to those of the unit
176 * matrix
177 *
178  ij = 2
179  DO 20 j = 1, n - 1
180  DO 10 i = 1, j - 1
181  q( i, j ) = ap( ij )
182  ij = ij + 1
183  10 CONTINUE
184  ij = ij + 2
185  q( n, j ) = zero
186  20 CONTINUE
187  DO 30 i = 1, n - 1
188  q( i, n ) = zero
189  30 CONTINUE
190  q( n, n ) = one
191 *
192 * Generate Q(1:n-1,1:n-1)
193 *
194  CALL dorg2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
195 *
196  ELSE
197 *
198 * Q was determined by a call to DSPTRD with UPLO = 'L'.
199 *
200 * Unpack the vectors which define the elementary reflectors and
201 * set the first row and column of Q equal to those of the unit
202 * matrix
203 *
204  q( 1, 1 ) = one
205  DO 40 i = 2, n
206  q( i, 1 ) = zero
207  40 CONTINUE
208  ij = 3
209  DO 60 j = 2, n
210  q( 1, j ) = zero
211  DO 50 i = j + 1, n
212  q( i, j ) = ap( ij )
213  ij = ij + 1
214  50 CONTINUE
215  ij = ij + 2
216  60 CONTINUE
217  IF( n.GT.1 ) THEN
218 *
219 * Generate Q(2:n,2:n)
220 *
221  CALL dorg2r( n-1, n-1, n-1, q( 2, 2 ), ldq, tau, work,
222  \$ iinfo )
223  END IF
224  END IF
225  RETURN
226 *
227 * End of DOPGTR
228 *
229  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dorg2r(M, N, K, A, LDA, TAU, WORK, INFO)
DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
Definition: dorg2r.f:114
subroutine dopgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
DOPGTR
Definition: dopgtr.f:114
subroutine dorg2l(M, N, K, A, LDA, TAU, WORK, INFO)
DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf ...
Definition: dorg2l.f:114