LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sormr3()

 subroutine sormr3 ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO )

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:
SORMR3 overwrites the general real m by n matrix C with

Q * C  if SIDE = 'L' and TRANS = 'N', or

Q**T* C  if SIDE = 'L' and TRANS = 'C', or

C * Q  if SIDE = 'R' and TRANS = 'N', or

C * Q**T if SIDE = 'R' and TRANS = 'C',

where Q is a real orthogonal matrix defined as the product of k
elementary reflectors

Q = H(1) H(2) . . . H(k)

as returned by STZRZF. Q is of order m if SIDE = 'L' and of order n
if SIDE = 'R'.
Parameters
 [in] SIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left = 'R': apply Q or Q**T from the Right [in] TRANS TRANS is CHARACTER*1 = 'N': apply Q (No transpose) = 'T': apply Q**T (Transpose) [in] M M is INTEGER The number of rows of the matrix C. M >= 0. [in] N N is INTEGER The number of columns of the matrix C. N >= 0. [in] K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. [in] L L is INTEGER The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. [in] A A is REAL array, dimension (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit. [in] LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,K). [in] TAU TAU is REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF. [in,out] C C is REAL array, dimension (LDC,N) On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. [in] LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). [out] WORK WORK is REAL array, dimension (N) if SIDE = 'L', (M) if SIDE = 'R' [out] INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:

Definition at line 176 of file sormr3.f.

178*
179* -- LAPACK computational routine --
180* -- LAPACK is a software package provided by Univ. of Tennessee, --
181* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182*
183* .. Scalar Arguments ..
184 CHARACTER SIDE, TRANS
185 INTEGER INFO, K, L, LDA, LDC, M, N
186* ..
187* .. Array Arguments ..
188 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
189* ..
190*
191* =====================================================================
192*
193* .. Local Scalars ..
194 LOGICAL LEFT, NOTRAN
195 INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
196* ..
197* .. External Functions ..
198 LOGICAL LSAME
199 EXTERNAL lsame
200* ..
201* .. External Subroutines ..
202 EXTERNAL slarz, xerbla
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC max
206* ..
207* .. Executable Statements ..
208*
209* Test the input arguments
210*
211 info = 0
212 left = lsame( side, 'L' )
213 notran = lsame( trans, 'N' )
214*
215* NQ is the order of Q
216*
217 IF( left ) THEN
218 nq = m
219 ELSE
220 nq = n
221 END IF
222 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223 info = -1
224 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225 info = -2
226 ELSE IF( m.LT.0 ) THEN
227 info = -3
228 ELSE IF( n.LT.0 ) THEN
229 info = -4
230 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231 info = -5
232 ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
233 \$ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
234 info = -6
235 ELSE IF( lda.LT.max( 1, k ) ) THEN
236 info = -8
237 ELSE IF( ldc.LT.max( 1, m ) ) THEN
238 info = -11
239 END IF
240 IF( info.NE.0 ) THEN
241 CALL xerbla( 'SORMR3', -info )
242 RETURN
243 END IF
244*
245* Quick return if possible
246*
247 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
248 \$ RETURN
249*
250 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
251 i1 = 1
252 i2 = k
253 i3 = 1
254 ELSE
255 i1 = k
256 i2 = 1
257 i3 = -1
258 END IF
259*
260 IF( left ) THEN
261 ni = n
262 ja = m - l + 1
263 jc = 1
264 ELSE
265 mi = m
266 ja = n - l + 1
267 ic = 1
268 END IF
269*
270 DO 10 i = i1, i2, i3
271 IF( left ) THEN
272*
273* H(i) or H(i)**T is applied to C(i:m,1:n)
274*
275 mi = m - i + 1
276 ic = i
277 ELSE
278*
279* H(i) or H(i)**T is applied to C(1:m,i:n)
280*
281 ni = n - i + 1
282 jc = i
283 END IF
284*
285* Apply H(i) or H(i)**T
286*
287 CALL slarz( side, mi, ni, l, a( i, ja ), lda, tau( i ),
288 \$ c( ic, jc ), ldc, work )
289*
290 10 CONTINUE
291*
292 RETURN
293*
294* End of SORMR3
295*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: slarz.f:145
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