LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
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