LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ zunm2r()

subroutine zunm2r ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( ldc, * )  C,
integer  LDC,
complex*16, dimension( * )  WORK,
integer  INFO 
)

ZUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm).

Download ZUNM2R + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZUNM2R 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 ZGEQRF. 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]A
          A is COMPLEX*16 array, dimension (LDA,K)
          The i-th column must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,...,k, as returned by
          ZGEQRF in the first k columns 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.
          If SIDE = 'L', LDA >= max(1,M);
          if SIDE = 'R', LDA >= max(1,N).
[in]TAU
          TAU is COMPLEX*16 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by ZGEQRF.
[in,out]C
          C is COMPLEX*16 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*16 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.

Definition at line 157 of file zunm2r.f.

159*
160* -- LAPACK computational routine --
161* -- LAPACK is a software package provided by Univ. of Tennessee, --
162* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163*
164* .. Scalar Arguments ..
165 CHARACTER SIDE, TRANS
166 INTEGER INFO, K, LDA, LDC, M, N
167* ..
168* .. Array Arguments ..
169 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170* ..
171*
172* =====================================================================
173*
174* .. Parameters ..
175 COMPLEX*16 ONE
176 parameter( one = ( 1.0d+0, 0.0d+0 ) )
177* ..
178* .. Local Scalars ..
179 LOGICAL LEFT, NOTRAN
180 INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ
181 COMPLEX*16 AII, TAUI
182* ..
183* .. External Functions ..
184 LOGICAL LSAME
185 EXTERNAL lsame
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla, zlarf
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC dconjg, max
192* ..
193* .. Executable Statements ..
194*
195* Test the input arguments
196*
197 info = 0
198 left = lsame( side, 'L' )
199 notran = lsame( trans, 'N' )
200*
201* NQ is the order of Q
202*
203 IF( left ) THEN
204 nq = m
205 ELSE
206 nq = n
207 END IF
208 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
209 info = -1
210 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
211 info = -2
212 ELSE IF( m.LT.0 ) THEN
213 info = -3
214 ELSE IF( n.LT.0 ) THEN
215 info = -4
216 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
217 info = -5
218 ELSE IF( lda.LT.max( 1, nq ) ) THEN
219 info = -7
220 ELSE IF( ldc.LT.max( 1, m ) ) THEN
221 info = -10
222 END IF
223 IF( info.NE.0 ) THEN
224 CALL xerbla( 'ZUNM2R', -info )
225 RETURN
226 END IF
227*
228* Quick return if possible
229*
230 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
231 $ RETURN
232*
233 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
234 i1 = 1
235 i2 = k
236 i3 = 1
237 ELSE
238 i1 = k
239 i2 = 1
240 i3 = -1
241 END IF
242*
243 IF( left ) THEN
244 ni = n
245 jc = 1
246 ELSE
247 mi = m
248 ic = 1
249 END IF
250*
251 DO 10 i = i1, i2, i3
252 IF( left ) THEN
253*
254* H(i) or H(i)**H is applied to C(i:m,1:n)
255*
256 mi = m - i + 1
257 ic = i
258 ELSE
259*
260* H(i) or H(i)**H is applied to C(1:m,i:n)
261*
262 ni = n - i + 1
263 jc = i
264 END IF
265*
266* Apply H(i) or H(i)**H
267*
268 IF( notran ) THEN
269 taui = tau( i )
270 ELSE
271 taui = dconjg( tau( i ) )
272 END IF
273 aii = a( i, i )
274 a( i, i ) = one
275 CALL zlarf( side, mi, ni, a( i, i ), 1, taui, c( ic, jc ), ldc,
276 $ work )
277 a( i, i ) = aii
278 10 CONTINUE
279 RETURN
280*
281* End of ZUNM2R
282*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:128
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