LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sopmtr.f
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1 *> \brief \b SOPMTR
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 SOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS, UPLO
26 * INTEGER INFO, LDC, M, N
27 * ..
28 * .. Array Arguments ..
29 * REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SOPMTR overwrites the general real M-by-N matrix C with
39 *>
40 *> SIDE = 'L' SIDE = 'R'
41 *> TRANS = 'N': Q * C C * Q
42 *> TRANS = 'T': Q**T * C C * Q**T
43 *>
44 *> where Q is a real orthogonal matrix of order nq, with nq = m if
45 *> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
46 *> nq-1 elementary reflectors, as returned by SSPTRD using packed
47 *> storage:
48 *>
49 *> if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
50 *>
51 *> if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
52 *> \endverbatim
53 *
54 * Arguments:
55 * ==========
56 *
57 *> \param[in] SIDE
58 *> \verbatim
59 *> SIDE is CHARACTER*1
60 *> = 'L': apply Q or Q**T from the Left;
61 *> = 'R': apply Q or Q**T from the Right.
62 *> \endverbatim
63 *>
64 *> \param[in] UPLO
65 *> \verbatim
66 *> UPLO is CHARACTER*1
67 *> = 'U': Upper triangular packed storage used in previous
68 *> call to SSPTRD;
69 *> = 'L': Lower triangular packed storage used in previous
70 *> call to SSPTRD.
71 *> \endverbatim
72 *>
73 *> \param[in] TRANS
74 *> \verbatim
75 *> TRANS is CHARACTER*1
76 *> = 'N': No transpose, apply Q;
77 *> = 'T': Transpose, apply Q**T.
78 *> \endverbatim
79 *>
80 *> \param[in] M
81 *> \verbatim
82 *> M is INTEGER
83 *> The number of rows of the matrix C. M >= 0.
84 *> \endverbatim
85 *>
86 *> \param[in] N
87 *> \verbatim
88 *> N is INTEGER
89 *> The number of columns of the matrix C. N >= 0.
90 *> \endverbatim
91 *>
92 *> \param[in] AP
93 *> \verbatim
94 *> AP is REAL array, dimension
95 *> (M*(M+1)/2) if SIDE = 'L'
96 *> (N*(N+1)/2) if SIDE = 'R'
97 *> The vectors which define the elementary reflectors, as
98 *> returned by SSPTRD. AP is modified by the routine but
99 *> restored on exit.
100 *> \endverbatim
101 *>
102 *> \param[in] TAU
103 *> \verbatim
104 *> TAU is REAL array, dimension (M-1) if SIDE = 'L'
105 *> or (N-1) if SIDE = 'R'
106 *> TAU(i) must contain the scalar factor of the elementary
107 *> reflector H(i), as returned by SSPTRD.
108 *> \endverbatim
109 *>
110 *> \param[in,out] C
111 *> \verbatim
112 *> C is REAL array, dimension (LDC,N)
113 *> On entry, the M-by-N matrix C.
114 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
115 *> \endverbatim
116 *>
117 *> \param[in] LDC
118 *> \verbatim
119 *> LDC is INTEGER
120 *> The leading dimension of the array C. LDC >= max(1,M).
121 *> \endverbatim
122 *>
123 *> \param[out] WORK
124 *> \verbatim
125 *> WORK is REAL array, dimension
126 *> (N) if SIDE = 'L'
127 *> (M) if SIDE = 'R'
128 *> \endverbatim
129 *>
130 *> \param[out] INFO
131 *> \verbatim
132 *> INFO is INTEGER
133 *> = 0: successful exit
134 *> < 0: if INFO = -i, the i-th argument had an illegal value
135 *> \endverbatim
136 *
137 * Authors:
138 * ========
139 *
140 *> \author Univ. of Tennessee
141 *> \author Univ. of California Berkeley
142 *> \author Univ. of Colorado Denver
143 *> \author NAG Ltd.
144 *
145 *> \ingroup realOTHERcomputational
146 *
147 * =====================================================================
148  SUBROUTINE sopmtr( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK,
149  $ INFO )
150 *
151 * -- LAPACK computational routine --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 *
155 * .. Scalar Arguments ..
156  CHARACTER SIDE, TRANS, UPLO
157  INTEGER INFO, LDC, M, N
158 * ..
159 * .. Array Arguments ..
160  REAL AP( * ), C( LDC, * ), TAU( * ), WORK( * )
161 * ..
162 *
163 * =====================================================================
164 *
165 * .. Parameters ..
166  REAL ONE
167  parameter( one = 1.0e+0 )
168 * ..
169 * .. Local Scalars ..
170  LOGICAL FORWRD, LEFT, NOTRAN, UPPER
171  INTEGER I, I1, I2, I3, IC, II, JC, MI, NI, NQ
172  REAL AII
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL slarf, xerbla
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC max
183 * ..
184 * .. Executable Statements ..
185 *
186 * Test the input arguments
187 *
188  info = 0
189  left = lsame( side, 'L' )
190  notran = lsame( trans, 'N' )
191  upper = lsame( uplo, 'U' )
192 *
193 * NQ is the order of Q
194 *
195  IF( left ) THEN
196  nq = m
197  ELSE
198  nq = n
199  END IF
200  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
201  info = -1
202  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
203  info = -2
204  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
205  info = -3
206  ELSE IF( m.LT.0 ) THEN
207  info = -4
208  ELSE IF( n.LT.0 ) THEN
209  info = -5
210  ELSE IF( ldc.LT.max( 1, m ) ) THEN
211  info = -9
212  END IF
213  IF( info.NE.0 ) THEN
214  CALL xerbla( 'SOPMTR', -info )
215  RETURN
216  END IF
217 *
218 * Quick return if possible
219 *
220  IF( m.EQ.0 .OR. n.EQ.0 )
221  $ RETURN
222 *
223  IF( upper ) THEN
224 *
225 * Q was determined by a call to SSPTRD with UPLO = 'U'
226 *
227  forwrd = ( left .AND. notran ) .OR.
228  $ ( .NOT.left .AND. .NOT.notran )
229 *
230  IF( forwrd ) THEN
231  i1 = 1
232  i2 = nq - 1
233  i3 = 1
234  ii = 2
235  ELSE
236  i1 = nq - 1
237  i2 = 1
238  i3 = -1
239  ii = nq*( nq+1 ) / 2 - 1
240  END IF
241 *
242  IF( left ) THEN
243  ni = n
244  ELSE
245  mi = m
246  END IF
247 *
248  DO 10 i = i1, i2, i3
249  IF( left ) THEN
250 *
251 * H(i) is applied to C(1:i,1:n)
252 *
253  mi = i
254  ELSE
255 *
256 * H(i) is applied to C(1:m,1:i)
257 *
258  ni = i
259  END IF
260 *
261 * Apply H(i)
262 *
263  aii = ap( ii )
264  ap( ii ) = one
265  CALL slarf( side, mi, ni, ap( ii-i+1 ), 1, tau( i ), c, ldc,
266  $ work )
267  ap( ii ) = aii
268 *
269  IF( forwrd ) THEN
270  ii = ii + i + 2
271  ELSE
272  ii = ii - i - 1
273  END IF
274  10 CONTINUE
275  ELSE
276 *
277 * Q was determined by a call to SSPTRD with UPLO = 'L'.
278 *
279  forwrd = ( left .AND. .NOT.notran ) .OR.
280  $ ( .NOT.left .AND. notran )
281 *
282  IF( forwrd ) THEN
283  i1 = 1
284  i2 = nq - 1
285  i3 = 1
286  ii = 2
287  ELSE
288  i1 = nq - 1
289  i2 = 1
290  i3 = -1
291  ii = nq*( nq+1 ) / 2 - 1
292  END IF
293 *
294  IF( left ) THEN
295  ni = n
296  jc = 1
297  ELSE
298  mi = m
299  ic = 1
300  END IF
301 *
302  DO 20 i = i1, i2, i3
303  aii = ap( ii )
304  ap( ii ) = one
305  IF( left ) THEN
306 *
307 * H(i) is applied to C(i+1:m,1:n)
308 *
309  mi = m - i
310  ic = i + 1
311  ELSE
312 *
313 * H(i) is applied to C(1:m,i+1:n)
314 *
315  ni = n - i
316  jc = i + 1
317  END IF
318 *
319 * Apply H(i)
320 *
321  CALL slarf( side, mi, ni, ap( ii ), 1, tau( i ),
322  $ c( ic, jc ), ldc, work )
323  ap( ii ) = aii
324 *
325  IF( forwrd ) THEN
326  ii = ii + nq - i + 1
327  ELSE
328  ii = ii - nq + i - 2
329  END IF
330  20 CONTINUE
331  END IF
332  RETURN
333 *
334 * End of SOPMTR
335 *
336  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
subroutine sopmtr(SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO)
SOPMTR
Definition: sopmtr.f:150