LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sormr3()

 subroutine sormr3 ( character SIDE, character TRANS, integer M, integer N, integer K, integer L, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO )

SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).

Purpose:
``` SORMR3 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 STZRZF. 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 REAL 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 STZRZF 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 REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.``` [in,out] C ``` C is REAL 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 REAL 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```
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
` `

Definition at line 176 of file sormr3.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  REAL 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 slarz, 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( 'SORMR3', -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 slarz( 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 SORMR3
295 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: slarz.f:145
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