LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cunm2l()

subroutine cunm2l ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( ldc, * )  C,
integer  LDC,
complex, dimension( * )  WORK,
integer  INFO 
)

CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf (unblocked algorithm).

Download CUNM2L + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CUNM2L 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(k) . . . H(2) H(1)

 as returned by CGEQLF. 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 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
          CGEQLF in the last 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 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CGEQLF.
[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.
Date
December 2016

Definition at line 161 of file cunm2l.f.

161 *
162 * -- LAPACK computational routine (version 3.7.0) --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * December 2016
166 *
167 * .. Scalar Arguments ..
168  CHARACTER side, trans
169  INTEGER info, k, lda, ldc, m, n
170 * ..
171 * .. Array Arguments ..
172  COMPLEX a( lda, * ), c( ldc, * ), tau( * ), work( * )
173 * ..
174 *
175 * =====================================================================
176 *
177 * .. Parameters ..
178  COMPLEX one
179  parameter( one = ( 1.0e+0, 0.0e+0 ) )
180 * ..
181 * .. Local Scalars ..
182  LOGICAL left, notran
183  INTEGER i, i1, i2, i3, mi, ni, nq
184  COMPLEX aii, taui
185 * ..
186 * .. External Functions ..
187  LOGICAL lsame
188  EXTERNAL lsame
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL clarf, xerbla
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC conjg, max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input arguments
199 *
200  info = 0
201  left = lsame( side, 'L' )
202  notran = lsame( trans, 'N' )
203 *
204 * NQ is the order of Q
205 *
206  IF( left ) THEN
207  nq = m
208  ELSE
209  nq = n
210  END IF
211  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
212  info = -1
213  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
214  info = -2
215  ELSE IF( m.LT.0 ) THEN
216  info = -3
217  ELSE IF( n.LT.0 ) THEN
218  info = -4
219  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
220  info = -5
221  ELSE IF( lda.LT.max( 1, nq ) ) THEN
222  info = -7
223  ELSE IF( ldc.LT.max( 1, m ) ) THEN
224  info = -10
225  END IF
226  IF( info.NE.0 ) THEN
227  CALL xerbla( 'CUNM2L', -info )
228  RETURN
229  END IF
230 *
231 * Quick return if possible
232 *
233  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
234  $ RETURN
235 *
236  IF( ( left .AND. notran .OR. .NOT.left .AND. .NOT.notran ) ) THEN
237  i1 = 1
238  i2 = k
239  i3 = 1
240  ELSE
241  i1 = k
242  i2 = 1
243  i3 = -1
244  END IF
245 *
246  IF( left ) THEN
247  ni = n
248  ELSE
249  mi = m
250  END IF
251 *
252  DO 10 i = i1, i2, i3
253  IF( left ) THEN
254 *
255 * H(i) or H(i)**H is applied to C(1:m-k+i,1:n)
256 *
257  mi = m - k + i
258  ELSE
259 *
260 * H(i) or H(i)**H is applied to C(1:m,1:n-k+i)
261 *
262  ni = n - k + i
263  END IF
264 *
265 * Apply H(i) or H(i)**H
266 *
267  IF( notran ) THEN
268  taui = tau( i )
269  ELSE
270  taui = conjg( tau( i ) )
271  END IF
272  aii = a( nq-k+i, i )
273  a( nq-k+i, i ) = one
274  CALL clarf( side, mi, ni, a( 1, i ), 1, taui, c, ldc, work )
275  a( nq-k+i, i ) = aii
276  10 CONTINUE
277  RETURN
278 *
279 * End of CUNM2L
280 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:130
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