LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
sorgtr.f
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1 *> \brief \b SORGTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER UPLO
25 * INTEGER INFO, LDA, LWORK, N
26 * ..
27 * .. Array Arguments ..
28 * REAL A( LDA, * ), TAU( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SORGTR generates a real orthogonal matrix Q which is defined as the
38 *> product of n-1 elementary reflectors of order N, as returned by
39 *> SSYTRD:
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 triangle of A contains elementary reflectors
53 *> from SSYTRD;
54 *> = 'L': Lower triangle of A contains elementary reflectors
55 *> from SSYTRD.
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,out] A
65 *> \verbatim
66 *> A is REAL array, dimension (LDA,N)
67 *> On entry, the vectors which define the elementary reflectors,
68 *> as returned by SSYTRD.
69 *> On exit, the N-by-N orthogonal matrix Q.
70 *> \endverbatim
71 *>
72 *> \param[in] LDA
73 *> \verbatim
74 *> LDA is INTEGER
75 *> The leading dimension of the array A. LDA >= max(1,N).
76 *> \endverbatim
77 *>
78 *> \param[in] TAU
79 *> \verbatim
80 *> TAU is REAL array, dimension (N-1)
81 *> TAU(i) must contain the scalar factor of the elementary
82 *> reflector H(i), as returned by SSYTRD.
83 *> \endverbatim
84 *>
85 *> \param[out] WORK
86 *> \verbatim
87 *> WORK is REAL array, dimension (MAX(1,LWORK))
88 *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
89 *> \endverbatim
90 *>
91 *> \param[in] LWORK
92 *> \verbatim
93 *> LWORK is INTEGER
94 *> The dimension of the array WORK. LWORK >= max(1,N-1).
95 *> For optimum performance LWORK >= (N-1)*NB, where NB is
96 *> the optimal blocksize.
97 *>
98 *> If LWORK = -1, then a workspace query is assumed; the routine
99 *> only calculates the optimal size of the WORK array, returns
100 *> this value as the first entry of the WORK array, and no error
101 *> message related to LWORK is issued by XERBLA.
102 *> \endverbatim
103 *>
104 *> \param[out] INFO
105 *> \verbatim
106 *> INFO is INTEGER
107 *> = 0: successful exit
108 *> < 0: if INFO = -i, the i-th argument had an illegal value
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \date December 2016
120 *
121 *> \ingroup realOTHERcomputational
122 *
123 * =====================================================================
124  SUBROUTINE sorgtr( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
125 *
126 * -- LAPACK computational routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER UPLO
133  INTEGER INFO, LDA, LWORK, N
134 * ..
135 * .. Array Arguments ..
136  REAL A( lda, * ), TAU( * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL ZERO, ONE
143  parameter( zero = 0.0e+0, one = 1.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL LQUERY, UPPER
147  INTEGER I, IINFO, J, LWKOPT, NB
148 * ..
149 * .. External Functions ..
150  LOGICAL LSAME
151  INTEGER ILAENV
152  EXTERNAL ilaenv, lsame
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL sorgql, sorgqr, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Test the input arguments
163 *
164  info = 0
165  lquery = ( lwork.EQ.-1 )
166  upper = lsame( uplo, 'U' )
167  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
168  info = -1
169  ELSE IF( n.LT.0 ) THEN
170  info = -2
171  ELSE IF( lda.LT.max( 1, n ) ) THEN
172  info = -4
173  ELSE IF( lwork.LT.max( 1, n-1 ) .AND. .NOT.lquery ) THEN
174  info = -7
175  END IF
176 *
177  IF( info.EQ.0 ) THEN
178  IF ( upper ) THEN
179  nb = ilaenv( 1, 'SORGQL', ' ', n-1, n-1, n-1, -1 )
180  ELSE
181  nb = ilaenv( 1, 'SORGQR', ' ', n-1, n-1, n-1, -1 )
182  END IF
183  lwkopt = max( 1, n-1 )*nb
184  work( 1 ) = lwkopt
185  END IF
186 *
187  IF( info.NE.0 ) THEN
188  CALL xerbla( 'SORGTR', -info )
189  RETURN
190  ELSE IF( lquery ) THEN
191  RETURN
192  END IF
193 *
194 * Quick return if possible
195 *
196  IF( n.EQ.0 ) THEN
197  work( 1 ) = 1
198  RETURN
199  END IF
200 *
201  IF( upper ) THEN
202 *
203 * Q was determined by a call to SSYTRD with UPLO = 'U'
204 *
205 * Shift the vectors which define the elementary reflectors one
206 * column to the left, and set the last row and column of Q to
207 * those of the unit matrix
208 *
209  DO 20 j = 1, n - 1
210  DO 10 i = 1, j - 1
211  a( i, j ) = a( i, j+1 )
212  10 CONTINUE
213  a( n, j ) = zero
214  20 CONTINUE
215  DO 30 i = 1, n - 1
216  a( i, n ) = zero
217  30 CONTINUE
218  a( n, n ) = one
219 *
220 * Generate Q(1:n-1,1:n-1)
221 *
222  CALL sorgql( n-1, n-1, n-1, a, lda, tau, work, lwork, iinfo )
223 *
224  ELSE
225 *
226 * Q was determined by a call to SSYTRD with UPLO = 'L'.
227 *
228 * Shift the vectors which define the elementary reflectors one
229 * column to the right, and set the first row and column of Q to
230 * those of the unit matrix
231 *
232  DO 50 j = n, 2, -1
233  a( 1, j ) = zero
234  DO 40 i = j + 1, n
235  a( i, j ) = a( i, j-1 )
236  40 CONTINUE
237  50 CONTINUE
238  a( 1, 1 ) = one
239  DO 60 i = 2, n
240  a( i, 1 ) = zero
241  60 CONTINUE
242  IF( n.GT.1 ) THEN
243 *
244 * Generate Q(2:n,2:n)
245 *
246  CALL sorgqr( n-1, n-1, n-1, a( 2, 2 ), lda, tau, work,
247  $ lwork, iinfo )
248  END IF
249  END IF
250  work( 1 ) = lwkopt
251  RETURN
252 *
253 * End of SORGTR
254 *
255  END
subroutine sorgql(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQL
Definition: sorgql.f:130
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sorgqr(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
SORGQR
Definition: sorgqr.f:130
subroutine sorgtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
SORGTR
Definition: sorgtr.f:125