LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dgbequ()

subroutine dgbequ ( integer  M,
integer  N,
integer  KL,
integer  KU,
double precision, dimension( ldab, * )  AB,
integer  LDAB,
double precision, dimension( * )  R,
double precision, dimension( * )  C,
double precision  ROWCND,
double precision  COLCND,
double precision  AMAX,
integer  INFO 
)

DGBEQU

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

Purpose:
 DGBEQU computes row and column scalings intended to equilibrate an
 M-by-N band matrix A and reduce its condition number.  R returns the
 row scale factors and C the column scale factors, chosen to try to
 make the largest element in each row and column of the matrix B with
 elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.

 R(i) and C(j) are restricted to be between SMLNUM = smallest safe
 number and BIGNUM = largest safe number.  Use of these scaling
 factors is not guaranteed to reduce the condition number of A but
 works well in practice.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in]KL
          KL is INTEGER
          The number of subdiagonals within the band of A.  KL >= 0.
[in]KU
          KU is INTEGER
          The number of superdiagonals within the band of A.  KU >= 0.
[in]AB
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The band matrix A, stored in rows 1 to KL+KU+1.  The j-th
          column of A is stored in the j-th column of the array AB as
          follows:
          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl).
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KL+KU+1.
[out]R
          R is DOUBLE PRECISION array, dimension (M)
          If INFO = 0, or INFO > M, R contains the row scale factors
          for A.
[out]C
          C is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, C contains the column scale factors for A.
[out]ROWCND
          ROWCND is DOUBLE PRECISION
          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
          AMAX is neither too large nor too small, it is not worth
          scaling by R.
[out]COLCND
          COLCND is DOUBLE PRECISION
          If INFO = 0, COLCND contains the ratio of the smallest
          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
          worth scaling by C.
[out]AMAX
          AMAX is DOUBLE PRECISION
          Absolute value of largest matrix element.  If AMAX is very
          close to overflow or very close to underflow, the matrix
          should be scaled.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, and i is
                <= M:  the i-th row of A is exactly zero
                >  M:  the (i-M)-th column of A is exactly zero
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 151 of file dgbequ.f.

153 *
154 * -- LAPACK computational routine --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 *
158 * .. Scalar Arguments ..
159  INTEGER INFO, KL, KU, LDAB, M, N
160  DOUBLE PRECISION AMAX, COLCND, ROWCND
161 * ..
162 * .. Array Arguments ..
163  DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  DOUBLE PRECISION ONE, ZERO
170  parameter( one = 1.0d+0, zero = 0.0d+0 )
171 * ..
172 * .. Local Scalars ..
173  INTEGER I, J, KD
174  DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
175 * ..
176 * .. External Functions ..
177  DOUBLE PRECISION DLAMCH
178  EXTERNAL dlamch
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL xerbla
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC abs, max, min
185 * ..
186 * .. Executable Statements ..
187 *
188 * Test the input parameters
189 *
190  info = 0
191  IF( m.LT.0 ) THEN
192  info = -1
193  ELSE IF( n.LT.0 ) THEN
194  info = -2
195  ELSE IF( kl.LT.0 ) THEN
196  info = -3
197  ELSE IF( ku.LT.0 ) THEN
198  info = -4
199  ELSE IF( ldab.LT.kl+ku+1 ) THEN
200  info = -6
201  END IF
202  IF( info.NE.0 ) THEN
203  CALL xerbla( 'DGBEQU', -info )
204  RETURN
205  END IF
206 *
207 * Quick return if possible
208 *
209  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
210  rowcnd = one
211  colcnd = one
212  amax = zero
213  RETURN
214  END IF
215 *
216 * Get machine constants.
217 *
218  smlnum = dlamch( 'S' )
219  bignum = one / smlnum
220 *
221 * Compute row scale factors.
222 *
223  DO 10 i = 1, m
224  r( i ) = zero
225  10 CONTINUE
226 *
227 * Find the maximum element in each row.
228 *
229  kd = ku + 1
230  DO 30 j = 1, n
231  DO 20 i = max( j-ku, 1 ), min( j+kl, m )
232  r( i ) = max( r( i ), abs( ab( kd+i-j, j ) ) )
233  20 CONTINUE
234  30 CONTINUE
235 *
236 * Find the maximum and minimum scale factors.
237 *
238  rcmin = bignum
239  rcmax = zero
240  DO 40 i = 1, m
241  rcmax = max( rcmax, r( i ) )
242  rcmin = min( rcmin, r( i ) )
243  40 CONTINUE
244  amax = rcmax
245 *
246  IF( rcmin.EQ.zero ) THEN
247 *
248 * Find the first zero scale factor and return an error code.
249 *
250  DO 50 i = 1, m
251  IF( r( i ).EQ.zero ) THEN
252  info = i
253  RETURN
254  END IF
255  50 CONTINUE
256  ELSE
257 *
258 * Invert the scale factors.
259 *
260  DO 60 i = 1, m
261  r( i ) = one / min( max( r( i ), smlnum ), bignum )
262  60 CONTINUE
263 *
264 * Compute ROWCND = min(R(I)) / max(R(I))
265 *
266  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
267  END IF
268 *
269 * Compute column scale factors
270 *
271  DO 70 j = 1, n
272  c( j ) = zero
273  70 CONTINUE
274 *
275 * Find the maximum element in each column,
276 * assuming the row scaling computed above.
277 *
278  kd = ku + 1
279  DO 90 j = 1, n
280  DO 80 i = max( j-ku, 1 ), min( j+kl, m )
281  c( j ) = max( c( j ), abs( ab( kd+i-j, j ) )*r( i ) )
282  80 CONTINUE
283  90 CONTINUE
284 *
285 * Find the maximum and minimum scale factors.
286 *
287  rcmin = bignum
288  rcmax = zero
289  DO 100 j = 1, n
290  rcmin = min( rcmin, c( j ) )
291  rcmax = max( rcmax, c( j ) )
292  100 CONTINUE
293 *
294  IF( rcmin.EQ.zero ) THEN
295 *
296 * Find the first zero scale factor and return an error code.
297 *
298  DO 110 j = 1, n
299  IF( c( j ).EQ.zero ) THEN
300  info = m + j
301  RETURN
302  END IF
303  110 CONTINUE
304  ELSE
305 *
306 * Invert the scale factors.
307 *
308  DO 120 j = 1, n
309  c( j ) = one / min( max( c( j ), smlnum ), bignum )
310  120 CONTINUE
311 *
312 * Compute COLCND = min(C(J)) / max(C(J))
313 *
314  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
315  END IF
316 *
317  RETURN
318 *
319 * End of DGBEQU
320 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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