 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ cunmr3()

 subroutine cunmr3 ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( * ) WORK, integer INFO )

CUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).

Purpose:
``` CUNMR3 overwrites the general complex m by n matrix C with

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

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

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

C * Q**H if SIDE = 'R' and TRANS = 'C',

where Q is a complex unitary matrix defined as the product of k
elementary reflectors

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

as returned by CTZRZF. 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**H from the Left = 'R': apply Q or Q**H from the Right``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': apply Q (No transpose) = 'C': apply Q**H (Conjugate 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 COMPLEX 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 CTZRZF 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 COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CTZRZF.``` [in,out] C ``` C is COMPLEX array, dimension (LDC,N) On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ``` WORK is COMPLEX 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 cunmr3.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 COMPLEX 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 COMPLEX TAUI
197* ..
198* .. External Functions ..
199 LOGICAL LSAME
200 EXTERNAL lsame
201* ..
202* .. External Subroutines ..
203 EXTERNAL clarz, xerbla
204* ..
205* .. Intrinsic Functions ..
206 INTRINSIC conjg, max
207* ..
208* .. Executable Statements ..
209*
210* Test the input arguments
211*
212 info = 0
213 left = lsame( side, 'L' )
214 notran = lsame( trans, 'N' )
215*
216* NQ is the order of Q
217*
218 IF( left ) THEN
219 nq = m
220 ELSE
221 nq = n
222 END IF
223 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
224 info = -1
225 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
226 info = -2
227 ELSE IF( m.LT.0 ) THEN
228 info = -3
229 ELSE IF( n.LT.0 ) THEN
230 info = -4
231 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
232 info = -5
233 ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
234 \$ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
235 info = -6
236 ELSE IF( lda.LT.max( 1, k ) ) THEN
237 info = -8
238 ELSE IF( ldc.LT.max( 1, m ) ) THEN
239 info = -11
240 END IF
241 IF( info.NE.0 ) THEN
242 CALL xerbla( 'CUNMR3', -info )
243 RETURN
244 END IF
245*
246* Quick return if possible
247*
248 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
249 \$ RETURN
250*
251 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
252 i1 = 1
253 i2 = k
254 i3 = 1
255 ELSE
256 i1 = k
257 i2 = 1
258 i3 = -1
259 END IF
260*
261 IF( left ) THEN
262 ni = n
263 ja = m - l + 1
264 jc = 1
265 ELSE
266 mi = m
267 ja = n - l + 1
268 ic = 1
269 END IF
270*
271 DO 10 i = i1, i2, i3
272 IF( left ) THEN
273*
274* H(i) or H(i)**H is applied to C(i:m,1:n)
275*
276 mi = m - i + 1
277 ic = i
278 ELSE
279*
280* H(i) or H(i)**H is applied to C(1:m,i:n)
281*
282 ni = n - i + 1
283 jc = i
284 END IF
285*
286* Apply H(i) or H(i)**H
287*
288 IF( notran ) THEN
289 taui = tau( i )
290 ELSE
291 taui = conjg( tau( i ) )
292 END IF
293 CALL clarz( side, mi, ni, l, a( i, ja ), lda, taui,
294 \$ c( ic, jc ), ldc, work )
295*
296 10 CONTINUE
297*
298 RETURN
299*
300* End of CUNMR3
301*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: clarz.f:147
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