LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
sopgtr.f
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1 *> \brief \b SOPGTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SOPGTR( 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 * REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SOPGTR 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 *> SSPTRD 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 SSPTRD;
54 *> = 'L': Lower triangular packed storage used in previous
55 *> call to SSPTRD.
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 REAL array, dimension (N*(N+1)/2)
67 *> The vectors which define the elementary reflectors, as
68 *> returned by SSPTRD.
69 *> \endverbatim
70 *>
71 *> \param[in] TAU
72 *> \verbatim
73 *> TAU is REAL array, dimension (N-1)
74 *> TAU(i) must contain the scalar factor of the elementary
75 *> reflector H(i), as returned by SSPTRD.
76 *> \endverbatim
77 *>
78 *> \param[out] Q
79 *> \verbatim
80 *> Q is REAL 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 REAL 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 December 2016
111 *
112 *> \ingroup realOTHERcomputational
113 *
114 * =====================================================================
115  SUBROUTINE sopgtr( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )
116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  CHARACTER UPLO
124  INTEGER INFO, LDQ, N
125 * ..
126 * .. Array Arguments ..
127  REAL AP( * ), Q( LDQ, * ), TAU( * ), WORK( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  REAL ZERO, ONE
134  parameter( zero = 0.0e+0, one = 1.0e+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 sorg2l, sorg2r, 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( 'SOPGTR', -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 SSPTRD 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 sorg2l( n-1, n-1, n-1, q, ldq, tau, work, iinfo )
198 *
199  ELSE
200 *
201 * Q was determined by a call to SSPTRD 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 sorg2r( 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 SOPGTR
231 *
232  END
sopgtr
subroutine sopgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
SOPGTR
Definition: sopgtr.f:116
sorg2l
subroutine sorg2l(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf ...
Definition: sorg2l.f:116
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
sorg2r
subroutine sorg2r(M, N, K, A, LDA, TAU, WORK, INFO)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf ...
Definition: sorg2r.f:116