LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgeequ()

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

SGEEQU

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

Purpose:
 SGEEQU 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 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]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 137 of file sgeequ.f.

139 *
140 * -- LAPACK computational routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  INTEGER INFO, LDA, M, N
146  REAL AMAX, COLCND, ROWCND
147 * ..
148 * .. Array Arguments ..
149  REAL A( LDA, * ), C( * ), R( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ONE, ZERO
156  parameter( one = 1.0e+0, zero = 0.0e+0 )
157 * ..
158 * .. Local Scalars ..
159  INTEGER I, J
160  REAL BIGNUM, RCMAX, RCMIN, SMLNUM
161 * ..
162 * .. External Functions ..
163  REAL SLAMCH
164  EXTERNAL slamch
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL xerbla
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC abs, max, min
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176  info = 0
177  IF( m.LT.0 ) THEN
178  info = -1
179  ELSE IF( n.LT.0 ) THEN
180  info = -2
181  ELSE IF( lda.LT.max( 1, m ) ) THEN
182  info = -4
183  END IF
184  IF( info.NE.0 ) THEN
185  CALL xerbla( 'SGEEQU', -info )
186  RETURN
187  END IF
188 *
189 * Quick return if possible
190 *
191  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
192  rowcnd = one
193  colcnd = one
194  amax = zero
195  RETURN
196  END IF
197 *
198 * Get machine constants.
199 *
200  smlnum = slamch( 'S' )
201  bignum = one / smlnum
202 *
203 * Compute row scale factors.
204 *
205  DO 10 i = 1, m
206  r( i ) = zero
207  10 CONTINUE
208 *
209 * Find the maximum element in each row.
210 *
211  DO 30 j = 1, n
212  DO 20 i = 1, m
213  r( i ) = max( r( i ), abs( a( i, j ) ) )
214  20 CONTINUE
215  30 CONTINUE
216 *
217 * Find the maximum and minimum scale factors.
218 *
219  rcmin = bignum
220  rcmax = zero
221  DO 40 i = 1, m
222  rcmax = max( rcmax, r( i ) )
223  rcmin = min( rcmin, r( i ) )
224  40 CONTINUE
225  amax = rcmax
226 *
227  IF( rcmin.EQ.zero ) THEN
228 *
229 * Find the first zero scale factor and return an error code.
230 *
231  DO 50 i = 1, m
232  IF( r( i ).EQ.zero ) THEN
233  info = i
234  RETURN
235  END IF
236  50 CONTINUE
237  ELSE
238 *
239 * Invert the scale factors.
240 *
241  DO 60 i = 1, m
242  r( i ) = one / min( max( r( i ), smlnum ), bignum )
243  60 CONTINUE
244 *
245 * Compute ROWCND = min(R(I)) / max(R(I))
246 *
247  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
248  END IF
249 *
250 * Compute column scale factors
251 *
252  DO 70 j = 1, n
253  c( j ) = zero
254  70 CONTINUE
255 *
256 * Find the maximum element in each column,
257 * assuming the row scaling computed above.
258 *
259  DO 90 j = 1, n
260  DO 80 i = 1, m
261  c( j ) = max( c( j ), abs( a( i, j ) )*r( i ) )
262  80 CONTINUE
263  90 CONTINUE
264 *
265 * Find the maximum and minimum scale factors.
266 *
267  rcmin = bignum
268  rcmax = zero
269  DO 100 j = 1, n
270  rcmin = min( rcmin, c( j ) )
271  rcmax = max( rcmax, c( j ) )
272  100 CONTINUE
273 *
274  IF( rcmin.EQ.zero ) THEN
275 *
276 * Find the first zero scale factor and return an error code.
277 *
278  DO 110 j = 1, n
279  IF( c( j ).EQ.zero ) THEN
280  info = m + j
281  RETURN
282  END IF
283  110 CONTINUE
284  ELSE
285 *
286 * Invert the scale factors.
287 *
288  DO 120 j = 1, n
289  c( j ) = one / min( max( c( j ), smlnum ), bignum )
290  120 CONTINUE
291 *
292 * Compute COLCND = min(C(J)) / max(C(J))
293 *
294  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
295  END IF
296 *
297  RETURN
298 *
299 * End of SGEEQU
300 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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