LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dorm2l()

 subroutine dorm2l ( 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 )

DORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:
``` DORM2L 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(k) . . . H(2) H(1)

as returned by DGEQLF. 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 DGEQLF 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 DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF.``` [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```

Definition at line 157 of file dorm2l.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, 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( 'DORM2L', -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. notran ) .OR. ( .NOT.left .AND. .NOT.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 ELSE
247 mi = m
248 END IF
249*
250 DO 10 i = i1, i2, i3
251 IF( left ) THEN
252*
253* H(i) is applied to C(1:m-k+i,1:n)
254*
255 mi = m - k + i
256 ELSE
257*
258* H(i) is applied to C(1:m,1:n-k+i)
259*
260 ni = n - k + i
261 END IF
262*
263* Apply H(i)
264*
265 aii = a( nq-k+i, i )
266 a( nq-k+i, i ) = one
267 CALL dlarf( side, mi, ni, a( 1, i ), 1, tau( i ), c, ldc,
268 \$ work )
269 a( nq-k+i, i ) = aii
270 10 CONTINUE
271 RETURN
272*
273* End of DORM2L
274*
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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