LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dormr3()

subroutine dormr3 ( character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
integer  L,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  WORK,
integer  INFO 
)

DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Download DORMR3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DORMR3 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 = 'C', or

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

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

 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 DTZRZF. 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]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 DOUBLE PRECISION 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
          DTZRZF 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 DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DTZRZF.
[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.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
 

Definition at line 176 of file dormr3.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 DOUBLE PRECISION 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* ..
197* .. External Functions ..
198 LOGICAL LSAME
199 EXTERNAL lsame
200* ..
201* .. External Subroutines ..
202 EXTERNAL dlarz, xerbla
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC max
206* ..
207* .. Executable Statements ..
208*
209* Test the input arguments
210*
211 info = 0
212 left = lsame( side, 'L' )
213 notran = lsame( trans, 'N' )
214*
215* NQ is the order of Q
216*
217 IF( left ) THEN
218 nq = m
219 ELSE
220 nq = n
221 END IF
222 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223 info = -1
224 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225 info = -2
226 ELSE IF( m.LT.0 ) THEN
227 info = -3
228 ELSE IF( n.LT.0 ) THEN
229 info = -4
230 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231 info = -5
232 ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
233 $ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
234 info = -6
235 ELSE IF( lda.LT.max( 1, k ) ) THEN
236 info = -8
237 ELSE IF( ldc.LT.max( 1, m ) ) THEN
238 info = -11
239 END IF
240 IF( info.NE.0 ) THEN
241 CALL xerbla( 'DORMR3', -info )
242 RETURN
243 END IF
244*
245* Quick return if possible
246*
247 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
248 $ RETURN
249*
250 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
251 i1 = 1
252 i2 = k
253 i3 = 1
254 ELSE
255 i1 = k
256 i2 = 1
257 i3 = -1
258 END IF
259*
260 IF( left ) THEN
261 ni = n
262 ja = m - l + 1
263 jc = 1
264 ELSE
265 mi = m
266 ja = n - l + 1
267 ic = 1
268 END IF
269*
270 DO 10 i = i1, i2, i3
271 IF( left ) THEN
272*
273* H(i) or H(i)**T is applied to C(i:m,1:n)
274*
275 mi = m - i + 1
276 ic = i
277 ELSE
278*
279* H(i) or H(i)**T is applied to C(1:m,i:n)
280*
281 ni = n - i + 1
282 jc = i
283 END IF
284*
285* Apply H(i) or H(i)**T
286*
287 CALL dlarz( side, mi, ni, l, a( i, ja ), lda, tau( i ),
288 $ c( ic, jc ), ldc, work )
289*
290 10 CONTINUE
291*
292 RETURN
293*
294* End of DORMR3
295*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dlarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
DLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: dlarz.f:145
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