LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgeequb()

subroutine sgeequb ( integer  M,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real, dimension( * )  R,
real, dimension( * )  C,
real  ROWCND,
real  COLCND,
real  AMAX,
integer  INFO 
)

SGEEQUB

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

Purpose:
 SGEEQUB 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 SGEEQU 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]A
          A is REAL array, dimension (LDA,N)
          The M-by-N matrix whose equilibration factors are
          to be computed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]R
          R is REAL array, dimension (M)
          If INFO = 0 or INFO > M, R contains the row scale factors
          for A.
[out]C
          C is REAL array, dimension (N)
          If INFO = 0,  C contains the column scale factors for A.
[out]ROWCND
          ROWCND is REAL
          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 REAL
          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 REAL
          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 144 of file sgeequb.f.

146 *
147 * -- LAPACK computational routine --
148 * -- LAPACK is a software package provided by Univ. of Tennessee, --
149 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150 *
151 * .. Scalar Arguments ..
152  INTEGER INFO, LDA, M, N
153  REAL AMAX, COLCND, ROWCND
154 * ..
155 * .. Array Arguments ..
156  REAL A( LDA, * ), C( * ), R( * )
157 * ..
158 *
159 * =====================================================================
160 *
161 * .. Parameters ..
162  REAL ONE, ZERO
163  parameter( one = 1.0e+0, zero = 0.0e+0 )
164 * ..
165 * .. Local Scalars ..
166  INTEGER I, J
167  REAL BIGNUM, RCMAX, RCMIN, SMLNUM, RADIX, LOGRDX
168 * ..
169 * .. External Functions ..
170  REAL SLAMCH
171  EXTERNAL slamch
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max, min, log
178 * ..
179 * .. Executable Statements ..
180 *
181 * Test the input parameters.
182 *
183  info = 0
184  IF( m.LT.0 ) THEN
185  info = -1
186  ELSE IF( n.LT.0 ) THEN
187  info = -2
188  ELSE IF( lda.LT.max( 1, m ) ) THEN
189  info = -4
190  END IF
191  IF( info.NE.0 ) THEN
192  CALL xerbla( 'SGEEQUB', -info )
193  RETURN
194  END IF
195 *
196 * Quick return if possible.
197 *
198  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
199  rowcnd = one
200  colcnd = one
201  amax = zero
202  RETURN
203  END IF
204 *
205 * Get machine constants. Assume SMLNUM is a power of the radix.
206 *
207  smlnum = slamch( 'S' )
208  bignum = one / smlnum
209  radix = slamch( 'B' )
210  logrdx = log( radix )
211 *
212 * Compute row scale factors.
213 *
214  DO 10 i = 1, m
215  r( i ) = zero
216  10 CONTINUE
217 *
218 * Find the maximum element in each row.
219 *
220  DO 30 j = 1, n
221  DO 20 i = 1, m
222  r( i ) = max( r( i ), abs( a( i, j ) ) )
223  20 CONTINUE
224  30 CONTINUE
225  DO i = 1, m
226  IF( r( i ).GT.zero ) THEN
227  r( i ) = radix**int( log( r( i ) ) / logrdx )
228  END IF
229  END DO
230 *
231 * Find the maximum and minimum scale factors.
232 *
233  rcmin = bignum
234  rcmax = zero
235  DO 40 i = 1, m
236  rcmax = max( rcmax, r( i ) )
237  rcmin = min( rcmin, r( i ) )
238  40 CONTINUE
239  amax = rcmax
240 *
241  IF( rcmin.EQ.zero ) THEN
242 *
243 * Find the first zero scale factor and return an error code.
244 *
245  DO 50 i = 1, m
246  IF( r( i ).EQ.zero ) THEN
247  info = i
248  RETURN
249  END IF
250  50 CONTINUE
251  ELSE
252 *
253 * Invert the scale factors.
254 *
255  DO 60 i = 1, m
256  r( i ) = one / min( max( r( i ), smlnum ), bignum )
257  60 CONTINUE
258 *
259 * Compute ROWCND = min(R(I)) / max(R(I)).
260 *
261  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
262  END IF
263 *
264 * Compute column scale factors
265 *
266  DO 70 j = 1, n
267  c( j ) = zero
268  70 CONTINUE
269 *
270 * Find the maximum element in each column,
271 * assuming the row scaling computed above.
272 *
273  DO 90 j = 1, n
274  DO 80 i = 1, m
275  c( j ) = max( c( j ), abs( a( i, j ) )*r( i ) )
276  80 CONTINUE
277  IF( c( j ).GT.zero ) THEN
278  c( j ) = radix**int( log( c( j ) ) / logrdx )
279  END IF
280  90 CONTINUE
281 *
282 * Find the maximum and minimum scale factors.
283 *
284  rcmin = bignum
285  rcmax = zero
286  DO 100 j = 1, n
287  rcmin = min( rcmin, c( j ) )
288  rcmax = max( rcmax, c( j ) )
289  100 CONTINUE
290 *
291  IF( rcmin.EQ.zero ) THEN
292 *
293 * Find the first zero scale factor and return an error code.
294 *
295  DO 110 j = 1, n
296  IF( c( j ).EQ.zero ) THEN
297  info = m + j
298  RETURN
299  END IF
300  110 CONTINUE
301  ELSE
302 *
303 * Invert the scale factors.
304 *
305  DO 120 j = 1, n
306  c( j ) = one / min( max( c( j ), smlnum ), bignum )
307  120 CONTINUE
308 *
309 * Compute COLCND = min(C(J)) / max(C(J)).
310 *
311  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
312  END IF
313 *
314  RETURN
315 *
316 * End of SGEEQUB
317 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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