LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zgbequ()

subroutine zgbequ ( integer  m,
integer  n,
integer  kl,
integer  ku,
complex*16, dimension( ldab, * )  ab,
integer  ldab,
double precision, dimension( * )  r,
double precision, dimension( * )  c,
double precision  rowcnd,
double precision  colcnd,
double precision  amax,
integer  info 
)

ZGBEQU

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

Purpose:
 ZGBEQU 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 COMPLEX*16 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 152 of file zgbequ.f.

154*
155* -- LAPACK computational routine --
156* -- LAPACK is a software package provided by Univ. of Tennessee, --
157* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158*
159* .. Scalar Arguments ..
160 INTEGER INFO, KL, KU, LDAB, M, N
161 DOUBLE PRECISION AMAX, COLCND, ROWCND
162* ..
163* .. Array Arguments ..
164 DOUBLE PRECISION C( * ), R( * )
165 COMPLEX*16 AB( LDAB, * )
166* ..
167*
168* =====================================================================
169*
170* .. Parameters ..
171 DOUBLE PRECISION ONE, ZERO
172 parameter( one = 1.0d+0, zero = 0.0d+0 )
173* ..
174* .. Local Scalars ..
175 INTEGER I, J, KD
176 DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
177 COMPLEX*16 ZDUM
178* ..
179* .. External Functions ..
180 DOUBLE PRECISION DLAMCH
181 EXTERNAL dlamch
182* ..
183* .. External Subroutines ..
184 EXTERNAL xerbla
185* ..
186* .. Intrinsic Functions ..
187 INTRINSIC abs, dble, dimag, max, min
188* ..
189* .. Statement Functions ..
190 DOUBLE PRECISION CABS1
191* ..
192* .. Statement Function definitions ..
193 cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
194* ..
195* .. Executable Statements ..
196*
197* Test the input parameters
198*
199 info = 0
200 IF( m.LT.0 ) THEN
201 info = -1
202 ELSE IF( n.LT.0 ) THEN
203 info = -2
204 ELSE IF( kl.LT.0 ) THEN
205 info = -3
206 ELSE IF( ku.LT.0 ) THEN
207 info = -4
208 ELSE IF( ldab.LT.kl+ku+1 ) THEN
209 info = -6
210 END IF
211 IF( info.NE.0 ) THEN
212 CALL xerbla( 'ZGBEQU', -info )
213 RETURN
214 END IF
215*
216* Quick return if possible
217*
218 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
219 rowcnd = one
220 colcnd = one
221 amax = zero
222 RETURN
223 END IF
224*
225* Get machine constants.
226*
227 smlnum = dlamch( 'S' )
228 bignum = one / smlnum
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 ), cabs1( ab( kd+i-j, j ) ) )
242 20 CONTINUE
243 30 CONTINUE
244*
245* Find the maximum and minimum scale factors.
246*
247 rcmin = bignum
248 rcmax = zero
249 DO 40 i = 1, m
250 rcmax = max( rcmax, r( i ) )
251 rcmin = min( rcmin, r( i ) )
252 40 CONTINUE
253 amax = rcmax
254*
255 IF( rcmin.EQ.zero ) THEN
256*
257* Find the first zero scale factor and return an error code.
258*
259 DO 50 i = 1, m
260 IF( r( i ).EQ.zero ) THEN
261 info = i
262 RETURN
263 END IF
264 50 CONTINUE
265 ELSE
266*
267* Invert the scale factors.
268*
269 DO 60 i = 1, m
270 r( i ) = one / min( max( r( i ), smlnum ), bignum )
271 60 CONTINUE
272*
273* Compute ROWCND = min(R(I)) / max(R(I))
274*
275 rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
276 END IF
277*
278* Compute column scale factors
279*
280 DO 70 j = 1, n
281 c( j ) = zero
282 70 CONTINUE
283*
284* Find the maximum element in each column,
285* assuming the row scaling computed above.
286*
287 kd = ku + 1
288 DO 90 j = 1, n
289 DO 80 i = max( j-ku, 1 ), min( j+kl, m )
290 c( j ) = max( c( j ), cabs1( ab( kd+i-j, j ) )*r( i ) )
291 80 CONTINUE
292 90 CONTINUE
293*
294* Find the maximum and minimum scale factors.
295*
296 rcmin = bignum
297 rcmax = zero
298 DO 100 j = 1, n
299 rcmin = min( rcmin, c( j ) )
300 rcmax = max( rcmax, c( j ) )
301 100 CONTINUE
302*
303 IF( rcmin.EQ.zero ) THEN
304*
305* Find the first zero scale factor and return an error code.
306*
307 DO 110 j = 1, n
308 IF( c( j ).EQ.zero ) THEN
309 info = m + j
310 RETURN
311 END IF
312 110 CONTINUE
313 ELSE
314*
315* Invert the scale factors.
316*
317 DO 120 j = 1, n
318 c( j ) = one / min( max( c( j ), smlnum ), bignum )
319 120 CONTINUE
320*
321* Compute COLCND = min(C(J)) / max(C(J))
322*
323 colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
324 END IF
325*
326 RETURN
327*
328* End of ZGBEQU
329*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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