LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dgbequb()

subroutine dgbequb ( 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 
)

DGBEQUB

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

Purpose:
 DGBEQUB computes row and column scalings intended to equilibrate an
 M-by-N 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 an absolute value of at most
 the radix.

 R(i) and C(j) are restricted to be a power of the radix 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.

 This routine differs from DGEEQU by restricting the scaling factors
 to a power of the radix.  Barring over- and underflow, scaling by
 these factors introduces no additional rounding errors.  However, the
 scaled entries' magnitudes are no longer approximately 1 but lie
 between sqrt(radix) and 1/sqrt(radix).
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)
          On entry, the matrix A in band storage, 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(N,j+kl)
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array A.  LDAB >= max(1,M).
[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 158 of file dgbequb.f.

160*
161* -- LAPACK computational routine --
162* -- LAPACK is a software package provided by Univ. of Tennessee, --
163* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164*
165* .. Scalar Arguments ..
166 INTEGER INFO, KL, KU, LDAB, M, N
167 DOUBLE PRECISION AMAX, COLCND, ROWCND
168* ..
169* .. Array Arguments ..
170 DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
171* ..
172*
173* =====================================================================
174*
175* .. Parameters ..
176 DOUBLE PRECISION ONE, ZERO
177 parameter( one = 1.0d+0, zero = 0.0d+0 )
178* ..
179* .. Local Scalars ..
180 INTEGER I, J, KD
181 DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM, RADIX, LOGRDX
182* ..
183* .. External Functions ..
184 DOUBLE PRECISION DLAMCH
185 EXTERNAL dlamch
186* ..
187* .. External Subroutines ..
188 EXTERNAL xerbla
189* ..
190* .. Intrinsic Functions ..
191 INTRINSIC abs, max, min, log
192* ..
193* .. Executable Statements ..
194*
195* Test the input parameters.
196*
197 info = 0
198 IF( m.LT.0 ) THEN
199 info = -1
200 ELSE IF( n.LT.0 ) THEN
201 info = -2
202 ELSE IF( kl.LT.0 ) THEN
203 info = -3
204 ELSE IF( ku.LT.0 ) THEN
205 info = -4
206 ELSE IF( ldab.LT.kl+ku+1 ) THEN
207 info = -6
208 END IF
209 IF( info.NE.0 ) THEN
210 CALL xerbla( 'DGBEQUB', -info )
211 RETURN
212 END IF
213*
214* Quick return if possible.
215*
216 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
217 rowcnd = one
218 colcnd = one
219 amax = zero
220 RETURN
221 END IF
222*
223* Get machine constants. Assume SMLNUM is a power of the radix.
224*
225 smlnum = dlamch( 'S' )
226 bignum = one / smlnum
227 radix = dlamch( 'B' )
228 logrdx = log(radix)
229*
230* Compute row scale factors.
231*
232 DO 10 i = 1, m
233 r( i ) = zero
234 10 CONTINUE
235*
236* Find the maximum element in each row.
237*
238 kd = ku + 1
239 DO 30 j = 1, n
240 DO 20 i = max( j-ku, 1 ), min( j+kl, m )
241 r( i ) = max( r( i ), abs( ab( kd+i-j, j ) ) )
242 20 CONTINUE
243 30 CONTINUE
244 DO i = 1, m
245 IF( r( i ).GT.zero ) THEN
246 r( i ) = radix**int( log( r( i ) ) / logrdx )
247 END IF
248 END DO
249*
250* Find the maximum and minimum scale factors.
251*
252 rcmin = bignum
253 rcmax = zero
254 DO 40 i = 1, m
255 rcmax = max( rcmax, r( i ) )
256 rcmin = min( rcmin, r( i ) )
257 40 CONTINUE
258 amax = rcmax
259*
260 IF( rcmin.EQ.zero ) THEN
261*
262* Find the first zero scale factor and return an error code.
263*
264 DO 50 i = 1, m
265 IF( r( i ).EQ.zero ) THEN
266 info = i
267 RETURN
268 END IF
269 50 CONTINUE
270 ELSE
271*
272* Invert the scale factors.
273*
274 DO 60 i = 1, m
275 r( i ) = one / min( max( r( i ), smlnum ), bignum )
276 60 CONTINUE
277*
278* Compute ROWCND = min(R(I)) / max(R(I)).
279*
280 rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
281 END IF
282*
283* Compute column scale factors.
284*
285 DO 70 j = 1, n
286 c( j ) = zero
287 70 CONTINUE
288*
289* Find the maximum element in each column,
290* assuming the row scaling computed above.
291*
292 DO 90 j = 1, n
293 DO 80 i = max( j-ku, 1 ), min( j+kl, m )
294 c( j ) = max( c( j ), abs( ab( kd+i-j, j ) )*r( i ) )
295 80 CONTINUE
296 IF( c( j ).GT.zero ) THEN
297 c( j ) = radix**int( log( c( j ) ) / logrdx )
298 END IF
299 90 CONTINUE
300*
301* Find the maximum and minimum scale factors.
302*
303 rcmin = bignum
304 rcmax = zero
305 DO 100 j = 1, n
306 rcmin = min( rcmin, c( j ) )
307 rcmax = max( rcmax, c( j ) )
308 100 CONTINUE
309*
310 IF( rcmin.EQ.zero ) THEN
311*
312* Find the first zero scale factor and return an error code.
313*
314 DO 110 j = 1, n
315 IF( c( j ).EQ.zero ) THEN
316 info = m + j
317 RETURN
318 END IF
319 110 CONTINUE
320 ELSE
321*
322* Invert the scale factors.
323*
324 DO 120 j = 1, n
325 c( j ) = one / min( max( c( j ), smlnum ), bignum )
326 120 CONTINUE
327*
328* Compute COLCND = min(C(J)) / max(C(J)).
329*
330 colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
331 END IF
332*
333 RETURN
334*
335* End of DGBEQUB
336*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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