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).

Download CUNMR3 + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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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