LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ sorml2()

 subroutine sorml2 ( character SIDE, character TRANS, integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK, integer INFO )

SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

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Purpose:
``` SORML2 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 SGELQF. 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 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 SGELQF in the first 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 SGELQF.``` [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```

Definition at line 157 of file sorml2.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  REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  REAL ONE
176  parameter( one = 1.0e+0 )
177 * ..
178 * .. Local Scalars ..
179  LOGICAL LEFT, NOTRAN
180  INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ
181  REAL AII
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL slarf, 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, k ) ) 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( 'SORML2', -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  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 slarf( side, mi, ni, a( i, i ), lda, tau( i ),
272  \$ c( ic, jc ), ldc, work )
273  a( i, i ) = aii
274  10 CONTINUE
275  RETURN
276 *
277 * End of SORML2
278 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:124
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