LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zgeequ()

 subroutine zgeequ ( integer M, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, integer INFO )

ZGEEQU

Purpose:
``` ZGEEQU 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 COMPLEX*16 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 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```

Definition at line 138 of file zgeequ.f.

140 *
141 * -- LAPACK computational routine --
142 * -- LAPACK is a software package provided by Univ. of Tennessee, --
143 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144 *
145 * .. Scalar Arguments ..
146  INTEGER INFO, LDA, M, N
147  DOUBLE PRECISION AMAX, COLCND, ROWCND
148 * ..
149 * .. Array Arguments ..
150  DOUBLE PRECISION C( * ), R( * )
151  COMPLEX*16 A( LDA, * )
152 * ..
153 *
154 * =====================================================================
155 *
156 * .. Parameters ..
157  DOUBLE PRECISION ONE, ZERO
158  parameter( one = 1.0d+0, zero = 0.0d+0 )
159 * ..
160 * .. Local Scalars ..
161  INTEGER I, J
162  DOUBLE PRECISION BIGNUM, RCMAX, RCMIN, SMLNUM
163  COMPLEX*16 ZDUM
164 * ..
165 * .. External Functions ..
166  DOUBLE PRECISION DLAMCH
167  EXTERNAL dlamch
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC abs, dble, dimag, max, min
174 * ..
175 * .. Statement Functions ..
176  DOUBLE PRECISION CABS1
177 * ..
178 * .. Statement Function definitions ..
179  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
180 * ..
181 * .. Executable Statements ..
182 *
183 * Test the input parameters.
184 *
185  info = 0
186  IF( m.LT.0 ) THEN
187  info = -1
188  ELSE IF( n.LT.0 ) THEN
189  info = -2
190  ELSE IF( lda.LT.max( 1, m ) ) THEN
191  info = -4
192  END IF
193  IF( info.NE.0 ) THEN
194  CALL xerbla( 'ZGEEQU', -info )
195  RETURN
196  END IF
197 *
198 * Quick return if possible
199 *
200  IF( m.EQ.0 .OR. n.EQ.0 ) THEN
201  rowcnd = one
202  colcnd = one
203  amax = zero
204  RETURN
205  END IF
206 *
207 * Get machine constants.
208 *
209  smlnum = dlamch( 'S' )
210  bignum = one / smlnum
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 ), cabs1( a( i, j ) ) )
223  20 CONTINUE
224  30 CONTINUE
225 *
226 * Find the maximum and minimum scale factors.
227 *
228  rcmin = bignum
229  rcmax = zero
230  DO 40 i = 1, m
231  rcmax = max( rcmax, r( i ) )
232  rcmin = min( rcmin, r( i ) )
233  40 CONTINUE
234  amax = rcmax
235 *
236  IF( rcmin.EQ.zero ) THEN
237 *
238 * Find the first zero scale factor and return an error code.
239 *
240  DO 50 i = 1, m
241  IF( r( i ).EQ.zero ) THEN
242  info = i
243  RETURN
244  END IF
245  50 CONTINUE
246  ELSE
247 *
248 * Invert the scale factors.
249 *
250  DO 60 i = 1, m
251  r( i ) = one / min( max( r( i ), smlnum ), bignum )
252  60 CONTINUE
253 *
254 * Compute ROWCND = min(R(I)) / max(R(I))
255 *
256  rowcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
257  END IF
258 *
259 * Compute column scale factors
260 *
261  DO 70 j = 1, n
262  c( j ) = zero
263  70 CONTINUE
264 *
265 * Find the maximum element in each column,
266 * assuming the row scaling computed above.
267 *
268  DO 90 j = 1, n
269  DO 80 i = 1, m
270  c( j ) = max( c( j ), cabs1( a( i, j ) )*r( i ) )
271  80 CONTINUE
272  90 CONTINUE
273 *
274 * Find the maximum and minimum scale factors.
275 *
276  rcmin = bignum
277  rcmax = zero
278  DO 100 j = 1, n
279  rcmin = min( rcmin, c( j ) )
280  rcmax = max( rcmax, c( j ) )
281  100 CONTINUE
282 *
283  IF( rcmin.EQ.zero ) THEN
284 *
285 * Find the first zero scale factor and return an error code.
286 *
287  DO 110 j = 1, n
288  IF( c( j ).EQ.zero ) THEN
289  info = m + j
290  RETURN
291  END IF
292  110 CONTINUE
293  ELSE
294 *
295 * Invert the scale factors.
296 *
297  DO 120 j = 1, n
298  c( j ) = one / min( max( c( j ), smlnum ), bignum )
299  120 CONTINUE
300 *
301 * Compute COLCND = min(C(J)) / max(C(J))
302 *
303  colcnd = max( rcmin, smlnum ) / min( rcmax, bignum )
304  END IF
305 *
306  RETURN
307 *
308 * End of ZGEEQU
309 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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