LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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dlarot.f
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1*> \brief \b DLAROT
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8* Definition:
9* ===========
10*
11* SUBROUTINE DLAROT( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
12* XRIGHT )
13*
14* .. Scalar Arguments ..
15* LOGICAL LLEFT, LRIGHT, LROWS
16* INTEGER LDA, NL
17* DOUBLE PRECISION C, S, XLEFT, XRIGHT
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION A( * )
21* ..
22*
23*
24*> \par Purpose:
25* =============
26*>
27*> \verbatim
28*>
29*> DLAROT applies a (Givens) rotation to two adjacent rows or
30*> columns, where one element of the first and/or last column/row
31*> for use on matrices stored in some format other than GE, so
32*> that elements of the matrix may be used or modified for which
33*> no array element is provided.
34*>
35*> One example is a symmetric matrix in SB format (bandwidth=4), for
36*> which UPLO='L': Two adjacent rows will have the format:
37*>
38*> row j: C> C> C> C> C> . . . .
39*> row j+1: C> C> C> C> C> . . . .
40*>
41*> '*' indicates elements for which storage is provided,
42*> '.' indicates elements for which no storage is provided, but
43*> are not necessarily zero; their values are determined by
44*> symmetry. ' ' indicates elements which are necessarily zero,
45*> and have no storage provided.
46*>
47*> Those columns which have two '*'s can be handled by DROT.
48*> Those columns which have no '*'s can be ignored, since as long
49*> as the Givens rotations are carefully applied to preserve
50*> symmetry, their values are determined.
51*> Those columns which have one '*' have to be handled separately,
52*> by using separate variables "p" and "q":
53*>
54*> row j: C> C> C> C> C> p . . .
55*> row j+1: q C> C> C> C> C> . . . .
56*>
57*> The element p would have to be set correctly, then that column
58*> is rotated, setting p to its new value. The next call to
59*> DLAROT would rotate columns j and j+1, using p, and restore
60*> symmetry. The element q would start out being zero, and be
61*> made non-zero by the rotation. Later, rotations would presumably
62*> be chosen to zero q out.
63*>
64*> Typical Calling Sequences: rotating the i-th and (i+1)-st rows.
65*> ------- ------- ---------
66*>
67*> General dense matrix:
68*>
69*> CALL DLAROT(.TRUE.,.FALSE.,.FALSE., N, C,S,
70*> A(i,1),LDA, DUMMY, DUMMY)
71*>
72*> General banded matrix in GB format:
73*>
74*> j = MAX(1, i-KL )
75*> NL = MIN( N, i+KU+1 ) + 1-j
76*> CALL DLAROT( .TRUE., i-KL.GE.1, i+KU.LT.N, NL, C,S,
77*> A(KU+i+1-j,j),LDA-1, XLEFT, XRIGHT )
78*>
79*> [ note that i+1-j is just MIN(i,KL+1) ]
80*>
81*> Symmetric banded matrix in SY format, bandwidth K,
82*> lower triangle only:
83*>
84*> j = MAX(1, i-K )
85*> NL = MIN( K+1, i ) + 1
86*> CALL DLAROT( .TRUE., i-K.GE.1, .TRUE., NL, C,S,
87*> A(i,j), LDA, XLEFT, XRIGHT )
88*>
89*> Same, but upper triangle only:
90*>
91*> NL = MIN( K+1, N-i ) + 1
92*> CALL DLAROT( .TRUE., .TRUE., i+K.LT.N, NL, C,S,
93*> A(i,i), LDA, XLEFT, XRIGHT )
94*>
95*> Symmetric banded matrix in SB format, bandwidth K,
96*> lower triangle only:
97*>
98*> [ same as for SY, except:]
99*> . . . .
100*> A(i+1-j,j), LDA-1, XLEFT, XRIGHT )
101*>
102*> [ note that i+1-j is just MIN(i,K+1) ]
103*>
104*> Same, but upper triangle only:
105*> . . .
106*> A(K+1,i), LDA-1, XLEFT, XRIGHT )
107*>
108*> Rotating columns is just the transpose of rotating rows, except
109*> for GB and SB: (rotating columns i and i+1)
110*>
111*> GB:
112*> j = MAX(1, i-KU )
113*> NL = MIN( N, i+KL+1 ) + 1-j
114*> CALL DLAROT( .TRUE., i-KU.GE.1, i+KL.LT.N, NL, C,S,
115*> A(KU+j+1-i,i),LDA-1, XTOP, XBOTTM )
116*>
117*> [note that KU+j+1-i is just MAX(1,KU+2-i)]
118*>
119*> SB: (upper triangle)
120*>
121*> . . . . . .
122*> A(K+j+1-i,i),LDA-1, XTOP, XBOTTM )
123*>
124*> SB: (lower triangle)
125*>
126*> . . . . . .
127*> A(1,i),LDA-1, XTOP, XBOTTM )
128*> \endverbatim
129*
130* Arguments:
131* ==========
132*
133*> \verbatim
134*> LROWS - LOGICAL
135*> If .TRUE., then DLAROT will rotate two rows. If .FALSE.,
136*> then it will rotate two columns.
137*> Not modified.
138*>
139*> LLEFT - LOGICAL
140*> If .TRUE., then XLEFT will be used instead of the
141*> corresponding element of A for the first element in the
142*> second row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.)
143*> If .FALSE., then the corresponding element of A will be
144*> used.
145*> Not modified.
146*>
147*> LRIGHT - LOGICAL
148*> If .TRUE., then XRIGHT will be used instead of the
149*> corresponding element of A for the last element in the
150*> first row (if LROWS=.FALSE.) or column (if LROWS=.TRUE.) If
151*> .FALSE., then the corresponding element of A will be used.
152*> Not modified.
153*>
154*> NL - INTEGER
155*> The length of the rows (if LROWS=.TRUE.) or columns (if
156*> LROWS=.FALSE.) to be rotated. If XLEFT and/or XRIGHT are
157*> used, the columns/rows they are in should be included in
158*> NL, e.g., if LLEFT = LRIGHT = .TRUE., then NL must be at
159*> least 2. The number of rows/columns to be rotated
160*> exclusive of those involving XLEFT and/or XRIGHT may
161*> not be negative, i.e., NL minus how many of LLEFT and
162*> LRIGHT are .TRUE. must be at least zero; if not, XERBLA
163*> will be called.
164*> Not modified.
165*>
166*> C, S - DOUBLE PRECISION
167*> Specify the Givens rotation to be applied. If LROWS is
168*> true, then the matrix ( c s )
169*> (-s c ) is applied from the left;
170*> if false, then the transpose thereof is applied from the
171*> right. For a Givens rotation, C**2 + S**2 should be 1,
172*> but this is not checked.
173*> Not modified.
174*>
175*> A - DOUBLE PRECISION array.
176*> The array containing the rows/columns to be rotated. The
177*> first element of A should be the upper left element to
178*> be rotated.
179*> Read and modified.
180*>
181*> LDA - INTEGER
182*> The "effective" leading dimension of A. If A contains
183*> a matrix stored in GE or SY format, then this is just
184*> the leading dimension of A as dimensioned in the calling
185*> routine. If A contains a matrix stored in band (GB or SB)
186*> format, then this should be *one less* than the leading
187*> dimension used in the calling routine. Thus, if
188*> A were dimensioned A(LDA,*) in DLAROT, then A(1,j) would
189*> be the j-th element in the first of the two rows
190*> to be rotated, and A(2,j) would be the j-th in the second,
191*> regardless of how the array may be stored in the calling
192*> routine. [A cannot, however, actually be dimensioned thus,
193*> since for band format, the row number may exceed LDA, which
194*> is not legal FORTRAN.]
195*> If LROWS=.TRUE., then LDA must be at least 1, otherwise
196*> it must be at least NL minus the number of .TRUE. values
197*> in XLEFT and XRIGHT.
198*> Not modified.
199*>
200*> XLEFT - DOUBLE PRECISION
201*> If LLEFT is .TRUE., then XLEFT will be used and modified
202*> instead of A(2,1) (if LROWS=.TRUE.) or A(1,2)
203*> (if LROWS=.FALSE.).
204*> Read and modified.
205*>
206*> XRIGHT - DOUBLE PRECISION
207*> If LRIGHT is .TRUE., then XRIGHT will be used and modified
208*> instead of A(1,NL) (if LROWS=.TRUE.) or A(NL,1)
209*> (if LROWS=.FALSE.).
210*> Read and modified.
211*> \endverbatim
212*
213* Authors:
214* ========
215*
216*> \author Univ. of Tennessee
217*> \author Univ. of California Berkeley
218*> \author Univ. of Colorado Denver
219*> \author NAG Ltd.
220*
221*> \ingroup double_matgen
222*
223* =====================================================================
224 SUBROUTINE dlarot( LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT,
225 $ XRIGHT )
226*
227* -- LAPACK auxiliary routine --
228* -- LAPACK is a software package provided by Univ. of Tennessee, --
229* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
230*
231* .. Scalar Arguments ..
232 LOGICAL LLEFT, LRIGHT, LROWS
233 INTEGER LDA, NL
234 DOUBLE PRECISION C, S, XLEFT, XRIGHT
235* ..
236* .. Array Arguments ..
237 DOUBLE PRECISION A( * )
238* ..
239*
240* =====================================================================
241*
242* .. Local Scalars ..
243 INTEGER IINC, INEXT, IX, IY, IYT, NT
244* ..
245* .. Local Arrays ..
246 DOUBLE PRECISION XT( 2 ), YT( 2 )
247* ..
248* .. External Subroutines ..
249 EXTERNAL drot, xerbla
250* ..
251* .. Executable Statements ..
252*
253* Set up indices, arrays for ends
254*
255 IF( lrows ) THEN
256 iinc = lda
257 inext = 1
258 ELSE
259 iinc = 1
260 inext = lda
261 END IF
262*
263 IF( lleft ) THEN
264 nt = 1
265 ix = 1 + iinc
266 iy = 2 + lda
267 xt( 1 ) = a( 1 )
268 yt( 1 ) = xleft
269 ELSE
270 nt = 0
271 ix = 1
272 iy = 1 + inext
273 END IF
274*
275 IF( lright ) THEN
276 iyt = 1 + inext + ( nl-1 )*iinc
277 nt = nt + 1
278 xt( nt ) = xright
279 yt( nt ) = a( iyt )
280 END IF
281*
282* Check for errors
283*
284 IF( nl.LT.nt ) THEN
285 CALL xerbla( 'DLAROT', 4 )
286 RETURN
287 END IF
288 IF( lda.LE.0 .OR. ( .NOT.lrows .AND. lda.LT.nl-nt ) ) THEN
289 CALL xerbla( 'DLAROT', 8 )
290 RETURN
291 END IF
292*
293* Rotate
294*
295 CALL drot( nl-nt, a( ix ), iinc, a( iy ), iinc, c, s )
296 CALL drot( nt, xt, 1, yt, 1, c, s )
297*
298* Stuff values back into XLEFT, XRIGHT, etc.
299*
300 IF( lleft ) THEN
301 a( 1 ) = xt( 1 )
302 xleft = yt( 1 )
303 END IF
304*
305 IF( lright ) THEN
306 xright = xt( nt )
307 a( iyt ) = yt( nt )
308 END IF
309*
310 RETURN
311*
312* End of DLAROT
313*
314 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine drot(N, DX, INCX, DY, INCY, C, S)
DROT
Definition: drot.f:92
subroutine dlarot(LROWS, LLEFT, LRIGHT, NL, C, S, A, LDA, XLEFT, XRIGHT)
DLAROT
Definition: dlarot.f:226