LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dorm2r()

subroutine dorm2r ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  WORK,
integer  INFO 
)

DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).

Download DORM2R + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DORM2R 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 = 'T', or

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

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

 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 DGEQRF. 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]A
          A is DOUBLE PRECISION 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
          DGEQRF 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 DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGEQRF.
[in,out]C
          C is DOUBLE PRECISION 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 DOUBLE PRECISION 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 dorm2r.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  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION ONE
176  parameter( one = 1.0d+0 )
177 * ..
178 * .. Local Scalars ..
179  LOGICAL LEFT, NOTRAN
180  INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ
181  DOUBLE PRECISION AII
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL dlarf, xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC 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, 'T' ) ) 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( 'DORM2R', -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 ) )
234  $ THEN
235  i1 = 1
236  i2 = k
237  i3 = 1
238  ELSE
239  i1 = k
240  i2 = 1
241  i3 = -1
242  END IF
243 *
244  IF( left ) THEN
245  ni = n
246  jc = 1
247  ELSE
248  mi = m
249  ic = 1
250  END IF
251 *
252  DO 10 i = i1, i2, i3
253  IF( left ) THEN
254 *
255 * H(i) is applied to C(i:m,1:n)
256 *
257  mi = m - i + 1
258  ic = i
259  ELSE
260 *
261 * H(i) is applied to C(1:m,i:n)
262 *
263  ni = n - i + 1
264  jc = i
265  END IF
266 *
267 * Apply H(i)
268 *
269  aii = a( i, i )
270  a( i, i ) = one
271  CALL dlarf( side, mi, ni, a( i, i ), 1, tau( i ), c( ic, jc ),
272  $ ldc, work )
273  a( i, i ) = aii
274  10 CONTINUE
275  RETURN
276 *
277 * End of DORM2R
278 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:124
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