LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ slarf()

subroutine slarf ( character  SIDE,
integer  M,
integer  N,
real, dimension( * )  V,
integer  INCV,
real  TAU,
real, dimension( ldc, * )  C,
integer  LDC,
real, dimension( * )  WORK 
)

SLARF applies an elementary reflector to a general rectangular matrix.

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Purpose:
 SLARF applies a real elementary reflector H to a real m by n matrix
 C, from either the left or the right. H is represented in the form

       H = I - tau * v * v**T

 where tau is a real scalar and v is a real vector.

 If tau = 0, then H is taken to be the unit matrix.
Parameters
[in]SIDE
          SIDE is CHARACTER*1
          = 'L': form  H * C
          = 'R': form  C * H
[in]M
          M is INTEGER
          The number of rows of the matrix C.
[in]N
          N is INTEGER
          The number of columns of the matrix C.
[in]V
          V is REAL array, dimension
                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
          The vector v in the representation of H. V is not used if
          TAU = 0.
[in]INCV
          INCV is INTEGER
          The increment between elements of v. INCV <> 0.
[in]TAU
          TAU is REAL
          The value tau in the representation of H.
[in,out]C
          C is REAL array, dimension (LDC,N)
          On entry, the m by n matrix C.
          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
          or C * H if SIDE = 'R'.
[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'
                      or (M) if SIDE = 'R'
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 123 of file slarf.f.

124 *
125 * -- LAPACK auxiliary routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER SIDE
131  INTEGER INCV, LDC, M, N
132  REAL TAU
133 * ..
134 * .. Array Arguments ..
135  REAL C( LDC, * ), V( * ), WORK( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  REAL ONE, ZERO
142  parameter( one = 1.0e+0, zero = 0.0e+0 )
143 * ..
144 * .. Local Scalars ..
145  LOGICAL APPLYLEFT
146  INTEGER I, LASTV, LASTC
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL sgemv, sger
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME
153  INTEGER ILASLR, ILASLC
154  EXTERNAL lsame, ilaslr, ilaslc
155 * ..
156 * .. Executable Statements ..
157 *
158  applyleft = lsame( side, 'L' )
159  lastv = 0
160  lastc = 0
161  IF( tau.NE.zero ) THEN
162 ! Set up variables for scanning V. LASTV begins pointing to the end
163 ! of V.
164  IF( applyleft ) THEN
165  lastv = m
166  ELSE
167  lastv = n
168  END IF
169  IF( incv.GT.0 ) THEN
170  i = 1 + (lastv-1) * incv
171  ELSE
172  i = 1
173  END IF
174 ! Look for the last non-zero row in V.
175  DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
176  lastv = lastv - 1
177  i = i - incv
178  END DO
179  IF( applyleft ) THEN
180 ! Scan for the last non-zero column in C(1:lastv,:).
181  lastc = ilaslc(lastv, n, c, ldc)
182  ELSE
183 ! Scan for the last non-zero row in C(:,1:lastv).
184  lastc = ilaslr(m, lastv, c, ldc)
185  END IF
186  END IF
187 ! Note that lastc.eq.0 renders the BLAS operations null; no special
188 ! case is needed at this level.
189  IF( applyleft ) THEN
190 *
191 * Form H * C
192 *
193  IF( lastv.GT.0 ) THEN
194 *
195 * w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
196 *
197  CALL sgemv( 'Transpose', lastv, lastc, one, c, ldc, v, incv,
198  $ zero, work, 1 )
199 *
200 * C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
201 *
202  CALL sger( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
203  END IF
204  ELSE
205 *
206 * Form C * H
207 *
208  IF( lastv.GT.0 ) THEN
209 *
210 * w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
211 *
212  CALL sgemv( 'No transpose', lastc, lastv, one, c, ldc,
213  $ v, incv, zero, work, 1 )
214 *
215 * C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
216 *
217  CALL sger( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
218  END IF
219  END IF
220  RETURN
221 *
222 * End of SLARF
223 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
integer function ilaslr(M, N, A, LDA)
ILASLR scans a matrix for its last non-zero row.
Definition: ilaslr.f:78
integer function ilaslc(M, N, A, LDA)
ILASLC scans a matrix for its last non-zero column.
Definition: ilaslc.f:78
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:130
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:156
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