LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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sormhr.f
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1*> \brief \b SORMHR
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download SORMHR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormhr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormhr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormhr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
22* LDC, WORK, LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N
27* ..
28* .. Array Arguments ..
29* REAL A( LDA, * ), C( LDC, * ), TAU( * ),
30* $ WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> SORMHR overwrites the general real M-by-N matrix C with
40*>
41*> SIDE = 'L' SIDE = 'R'
42*> TRANS = 'N': Q * C C * Q
43*> TRANS = 'T': Q**T * C C * Q**T
44*>
45*> where Q is a real orthogonal matrix of order nq, with nq = m if
46*> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
47*> IHI-ILO elementary reflectors, as returned by SGEHRD:
48*>
49*> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
50*> \endverbatim
51*
52* Arguments:
53* ==========
54*
55*> \param[in] SIDE
56*> \verbatim
57*> SIDE is CHARACTER*1
58*> = 'L': apply Q or Q**T from the Left;
59*> = 'R': apply Q or Q**T from the Right.
60*> \endverbatim
61*>
62*> \param[in] TRANS
63*> \verbatim
64*> TRANS is CHARACTER*1
65*> = 'N': No transpose, apply Q;
66*> = 'T': Transpose, apply Q**T.
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*> M is INTEGER
72*> The number of rows of the matrix C. M >= 0.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The number of columns of the matrix C. N >= 0.
79*> \endverbatim
80*>
81*> \param[in] ILO
82*> \verbatim
83*> ILO is INTEGER
84*> \endverbatim
85*>
86*> \param[in] IHI
87*> \verbatim
88*> IHI is INTEGER
89*>
90*> ILO and IHI must have the same values as in the previous call
91*> of SGEHRD. Q is equal to the unit matrix except in the
92*> submatrix Q(ilo+1:ihi,ilo+1:ihi).
93*> If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
94*> ILO = 1 and IHI = 0, if M = 0;
95*> if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
96*> ILO = 1 and IHI = 0, if N = 0.
97*> \endverbatim
98*>
99*> \param[in] A
100*> \verbatim
101*> A is REAL array, dimension
102*> (LDA,M) if SIDE = 'L'
103*> (LDA,N) if SIDE = 'R'
104*> The vectors which define the elementary reflectors, as
105*> returned by SGEHRD.
106*> \endverbatim
107*>
108*> \param[in] LDA
109*> \verbatim
110*> LDA is INTEGER
111*> The leading dimension of the array A.
112*> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
113*> \endverbatim
114*>
115*> \param[in] TAU
116*> \verbatim
117*> TAU is REAL array, dimension
118*> (M-1) if SIDE = 'L'
119*> (N-1) if SIDE = 'R'
120*> TAU(i) must contain the scalar factor of the elementary
121*> reflector H(i), as returned by SGEHRD.
122*> \endverbatim
123*>
124*> \param[in,out] C
125*> \verbatim
126*> C is REAL array, dimension (LDC,N)
127*> On entry, the M-by-N matrix C.
128*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
129*> \endverbatim
130*>
131*> \param[in] LDC
132*> \verbatim
133*> LDC is INTEGER
134*> The leading dimension of the array C. LDC >= max(1,M).
135*> \endverbatim
136*>
137*> \param[out] WORK
138*> \verbatim
139*> WORK is REAL array, dimension (MAX(1,LWORK))
140*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
141*> \endverbatim
142*>
143*> \param[in] LWORK
144*> \verbatim
145*> LWORK is INTEGER
146*> The dimension of the array WORK.
147*> If SIDE = 'L', LWORK >= max(1,N);
148*> if SIDE = 'R', LWORK >= max(1,M).
149*> For optimum performance LWORK >= N*NB if SIDE = 'L', and
150*> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
151*> blocksize.
152*>
153*> If LWORK = -1, then a workspace query is assumed; the routine
154*> only calculates the optimal size of the WORK array, returns
155*> this value as the first entry of the WORK array, and no error
156*> message related to LWORK is issued by XERBLA.
157*> \endverbatim
158*>
159*> \param[out] INFO
160*> \verbatim
161*> INFO is INTEGER
162*> = 0: successful exit
163*> < 0: if INFO = -i, the i-th argument had an illegal value
164*> \endverbatim
165*
166* Authors:
167* ========
168*
169*> \author Univ. of Tennessee
170*> \author Univ. of California Berkeley
171*> \author Univ. of Colorado Denver
172*> \author NAG Ltd.
173*
174*> \ingroup realOTHERcomputational
175*
176* =====================================================================
177 SUBROUTINE sormhr( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
178 $ LDC, WORK, LWORK, INFO )
179*
180* -- LAPACK computational routine --
181* -- LAPACK is a software package provided by Univ. of Tennessee, --
182* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183*
184* .. Scalar Arguments ..
185 CHARACTER SIDE, TRANS
186 INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N
187* ..
188* .. Array Arguments ..
189 REAL A( LDA, * ), C( LDC, * ), TAU( * ),
190 $ work( * )
191* ..
192*
193* =====================================================================
194*
195* .. Local Scalars ..
196 LOGICAL LEFT, LQUERY
197 INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
198* ..
199* .. External Functions ..
200 LOGICAL LSAME
201 INTEGER ILAENV
202 EXTERNAL ilaenv, lsame
203* ..
204* .. External Subroutines ..
205 EXTERNAL sormqr, xerbla
206* ..
207* .. Intrinsic Functions ..
208 INTRINSIC max, min
209* ..
210* .. Executable Statements ..
211*
212* Test the input arguments
213*
214 info = 0
215 nh = ihi - ilo
216 left = lsame( side, 'L' )
217 lquery = ( lwork.EQ.-1 )
218*
219* NQ is the order of Q and NW is the minimum dimension of WORK
220*
221 IF( left ) THEN
222 nq = m
223 nw = max( 1, n )
224 ELSE
225 nq = n
226 nw = max( 1, m )
227 END IF
228 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
229 info = -1
230 ELSE IF( .NOT.lsame( trans, 'N' ) .AND. .NOT.lsame( trans, 'T' ) )
231 $ THEN
232 info = -2
233 ELSE IF( m.LT.0 ) THEN
234 info = -3
235 ELSE IF( n.LT.0 ) THEN
236 info = -4
237 ELSE IF( ilo.LT.1 .OR. ilo.GT.max( 1, nq ) ) THEN
238 info = -5
239 ELSE IF( ihi.LT.min( ilo, nq ) .OR. ihi.GT.nq ) THEN
240 info = -6
241 ELSE IF( lda.LT.max( 1, nq ) ) THEN
242 info = -8
243 ELSE IF( ldc.LT.max( 1, m ) ) THEN
244 info = -11
245 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
246 info = -13
247 END IF
248*
249 IF( info.EQ.0 ) THEN
250 IF( left ) THEN
251 nb = ilaenv( 1, 'SORMQR', side // trans, nh, n, nh, -1 )
252 ELSE
253 nb = ilaenv( 1, 'SORMQR', side // trans, m, nh, nh, -1 )
254 END IF
255 lwkopt = nw*nb
256 work( 1 ) = lwkopt
257 END IF
258*
259 IF( info.NE.0 ) THEN
260 CALL xerbla( 'SORMHR', -info )
261 RETURN
262 ELSE IF( lquery ) THEN
263 RETURN
264 END IF
265*
266* Quick return if possible
267*
268 IF( m.EQ.0 .OR. n.EQ.0 .OR. nh.EQ.0 ) THEN
269 work( 1 ) = 1
270 RETURN
271 END IF
272*
273 IF( left ) THEN
274 mi = nh
275 ni = n
276 i1 = ilo + 1
277 i2 = 1
278 ELSE
279 mi = m
280 ni = nh
281 i1 = 1
282 i2 = ilo + 1
283 END IF
284*
285 CALL sormqr( side, trans, mi, ni, nh, a( ilo+1, ilo ), lda,
286 $ tau( ilo ), c( i1, i2 ), ldc, work, lwork, iinfo )
287*
288 work( 1 ) = lwkopt
289 RETURN
290*
291* End of SORMHR
292*
293 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sormhr(SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMHR
Definition: sormhr.f:179
subroutine sormqr(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMQR
Definition: sormqr.f:168