 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dla_gercond()

 double precision function dla_gercond ( character TRANS, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldaf, * ) AF, integer LDAF, integer, dimension( * ) IPIV, integer CMODE, double precision, dimension( * ) C, integer INFO, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK )

DLA_GERCOND estimates the Skeel condition number for a general matrix.

Purpose:
```    DLA_GERCOND estimates the Skeel condition number of op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)
The Skeel condition number cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate Transpose = Transpose)``` [in] N ``` N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the N-by-N matrix A.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] AF ``` AF is DOUBLE PRECISION array, dimension (LDAF,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices from the factorization A = P*L*U as computed by DGETRF; row i of the matrix was interchanged with row IPIV(i).``` [in] CMODE ``` CMODE is INTEGER Determines op2(C) in the formula op(A) * op2(C) as follows: CMODE = 1 op2(C) = C CMODE = 0 op2(C) = I CMODE = -1 op2(C) = inv(C)``` [in] C ``` C is DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * op2(C).``` [out] INFO ``` INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.``` [out] WORK ``` WORK is DOUBLE PRECISION array, dimension (3*N). Workspace.``` [out] IWORK ``` IWORK is INTEGER array, dimension (N). Workspace.```

Definition at line 149 of file dla_gercond.f.

152*
153* -- LAPACK computational routine --
154* -- LAPACK is a software package provided by Univ. of Tennessee, --
155* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157* .. Scalar Arguments ..
158 CHARACTER TRANS
159 INTEGER N, LDA, LDAF, INFO, CMODE
160* ..
161* .. Array Arguments ..
162 INTEGER IPIV( * ), IWORK( * )
163 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
164 \$ C( * )
165* ..
166*
167* =====================================================================
168*
169* .. Local Scalars ..
170 LOGICAL NOTRANS
171 INTEGER KASE, I, J
172 DOUBLE PRECISION AINVNM, TMP
173* ..
174* .. Local Arrays ..
175 INTEGER ISAVE( 3 )
176* ..
177* .. External Functions ..
178 LOGICAL LSAME
179 EXTERNAL lsame
180* ..
181* .. External Subroutines ..
182 EXTERNAL dlacn2, dgetrs, xerbla
183* ..
184* .. Intrinsic Functions ..
185 INTRINSIC abs, max
186* ..
187* .. Executable Statements ..
188*
189 dla_gercond = 0.0d+0
190*
191 info = 0
192 notrans = lsame( trans, 'N' )
193 IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T')
194 \$ .AND. .NOT. lsame(trans, 'C') ) THEN
195 info = -1
196 ELSE IF( n.LT.0 ) THEN
197 info = -2
198 ELSE IF( lda.LT.max( 1, n ) ) THEN
199 info = -4
200 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
201 info = -6
202 END IF
203 IF( info.NE.0 ) THEN
204 CALL xerbla( 'DLA_GERCOND', -info )
205 RETURN
206 END IF
207 IF( n.EQ.0 ) THEN
208 dla_gercond = 1.0d+0
209 RETURN
210 END IF
211*
212* Compute the equilibration matrix R such that
213* inv(R)*A*C has unit 1-norm.
214*
215 IF (notrans) THEN
216 DO i = 1, n
217 tmp = 0.0d+0
218 IF ( cmode .EQ. 1 ) THEN
219 DO j = 1, n
220 tmp = tmp + abs( a( i, j ) * c( j ) )
221 END DO
222 ELSE IF ( cmode .EQ. 0 ) THEN
223 DO j = 1, n
224 tmp = tmp + abs( a( i, j ) )
225 END DO
226 ELSE
227 DO j = 1, n
228 tmp = tmp + abs( a( i, j ) / c( j ) )
229 END DO
230 END IF
231 work( 2*n+i ) = tmp
232 END DO
233 ELSE
234 DO i = 1, n
235 tmp = 0.0d+0
236 IF ( cmode .EQ. 1 ) THEN
237 DO j = 1, n
238 tmp = tmp + abs( a( j, i ) * c( j ) )
239 END DO
240 ELSE IF ( cmode .EQ. 0 ) THEN
241 DO j = 1, n
242 tmp = tmp + abs( a( j, i ) )
243 END DO
244 ELSE
245 DO j = 1, n
246 tmp = tmp + abs( a( j, i ) / c( j ) )
247 END DO
248 END IF
249 work( 2*n+i ) = tmp
250 END DO
251 END IF
252*
253* Estimate the norm of inv(op(A)).
254*
255 ainvnm = 0.0d+0
256
257 kase = 0
258 10 CONTINUE
259 CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
260 IF( kase.NE.0 ) THEN
261 IF( kase.EQ.2 ) THEN
262*
263* Multiply by R.
264*
265 DO i = 1, n
266 work(i) = work(i) * work(2*n+i)
267 END DO
268
269 IF (notrans) THEN
270 CALL dgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
271 \$ work, n, info )
272 ELSE
273 CALL dgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
274 \$ work, n, info )
275 END IF
276*
277* Multiply by inv(C).
278*
279 IF ( cmode .EQ. 1 ) THEN
280 DO i = 1, n
281 work( i ) = work( i ) / c( i )
282 END DO
283 ELSE IF ( cmode .EQ. -1 ) THEN
284 DO i = 1, n
285 work( i ) = work( i ) * c( i )
286 END DO
287 END IF
288 ELSE
289*
290* Multiply by inv(C**T).
291*
292 IF ( cmode .EQ. 1 ) THEN
293 DO i = 1, n
294 work( i ) = work( i ) / c( i )
295 END DO
296 ELSE IF ( cmode .EQ. -1 ) THEN
297 DO i = 1, n
298 work( i ) = work( i ) * c( i )
299 END DO
300 END IF
301
302 IF (notrans) THEN
303 CALL dgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
304 \$ work, n, info )
305 ELSE
306 CALL dgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
307 \$ work, n, info )
308 END IF
309*
310* Multiply by R.
311*
312 DO i = 1, n
313 work( i ) = work( i ) * work( 2*n+i )
314 END DO
315 END IF
316 GO TO 10
317 END IF
318*
319* Compute the estimate of the reciprocal condition number.
320*
321 IF( ainvnm .NE. 0.0d+0 )
322 \$ dla_gercond = ( 1.0d+0 / ainvnm )
323*
324 RETURN
325*
326* End of DLA_GERCOND
327*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function dla_gercond(TRANS, N, A, LDA, AF, LDAF, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_GERCOND estimates the Skeel condition number for a general matrix.
Definition: dla_gercond.f:152
subroutine dgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DGETRS
Definition: dgetrs.f:121
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
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