LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ sla_gercond()

real function sla_gercond ( character  trans,
integer  n,
real, dimension( lda, * )  a,
integer  lda,
real, dimension( ldaf, * )  af,
integer  ldaf,
integer, dimension( * )  ipiv,
integer  cmode,
real, dimension( * )  c,
integer  info,
real, dimension( * )  work,
integer, dimension( * )  iwork 
)

SLA_GERCOND estimates the Skeel condition number for a general matrix.

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

Purpose:
    SLA_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 REAL 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 REAL array, dimension (LDAF,N)
     The factors L and U from the factorization
     A = P*L*U as computed by SGETRF.
[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 SGETRF; 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 REAL 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 REAL array, dimension (3*N).
     Workspace.
[out]IWORK
          IWORK is INTEGER array, dimension (N).
     Workspace.2
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 148 of file sla_gercond.f.

150*
151* -- LAPACK computational routine --
152* -- LAPACK is a software package provided by Univ. of Tennessee, --
153* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154*
155* .. Scalar Arguments ..
156 CHARACTER TRANS
157 INTEGER N, LDA, LDAF, INFO, CMODE
158* ..
159* .. Array Arguments ..
160 INTEGER IPIV( * ), IWORK( * )
161 REAL A( LDA, * ), AF( LDAF, * ), WORK( * ),
162 $ C( * )
163* ..
164*
165* =====================================================================
166*
167* .. Local Scalars ..
168 LOGICAL NOTRANS
169 INTEGER KASE, I, J
170 REAL AINVNM, TMP
171* ..
172* .. Local Arrays ..
173 INTEGER ISAVE( 3 )
174* ..
175* .. External Functions ..
176 LOGICAL LSAME
177 EXTERNAL lsame
178* ..
179* .. External Subroutines ..
180 EXTERNAL slacn2, sgetrs, xerbla
181* ..
182* .. Intrinsic Functions ..
183 INTRINSIC abs, max
184* ..
185* .. Executable Statements ..
186*
187 sla_gercond = 0.0
188*
189 info = 0
190 notrans = lsame( trans, 'N' )
191 IF ( .NOT. notrans .AND. .NOT. lsame(trans, 'T')
192 $ .AND. .NOT. lsame(trans, 'C') ) THEN
193 info = -1
194 ELSE IF( n.LT.0 ) THEN
195 info = -2
196 ELSE IF( lda.LT.max( 1, n ) ) THEN
197 info = -4
198 ELSE IF( ldaf.LT.max( 1, n ) ) THEN
199 info = -6
200 END IF
201 IF( info.NE.0 ) THEN
202 CALL xerbla( 'SLA_GERCOND', -info )
203 RETURN
204 END IF
205 IF( n.EQ.0 ) THEN
206 sla_gercond = 1.0
207 RETURN
208 END IF
209*
210* Compute the equilibration matrix R such that
211* inv(R)*A*C has unit 1-norm.
212*
213 IF (notrans) THEN
214 DO i = 1, n
215 tmp = 0.0
216 IF ( cmode .EQ. 1 ) THEN
217 DO j = 1, n
218 tmp = tmp + abs( a( i, j ) * c( j ) )
219 END DO
220 ELSE IF ( cmode .EQ. 0 ) THEN
221 DO j = 1, n
222 tmp = tmp + abs( a( i, j ) )
223 END DO
224 ELSE
225 DO j = 1, n
226 tmp = tmp + abs( a( i, j ) / c( j ) )
227 END DO
228 END IF
229 work( 2*n+i ) = tmp
230 END DO
231 ELSE
232 DO i = 1, n
233 tmp = 0.0
234 IF ( cmode .EQ. 1 ) THEN
235 DO j = 1, n
236 tmp = tmp + abs( a( j, i ) * c( j ) )
237 END DO
238 ELSE IF ( cmode .EQ. 0 ) THEN
239 DO j = 1, n
240 tmp = tmp + abs( a( j, i ) )
241 END DO
242 ELSE
243 DO j = 1, n
244 tmp = tmp + abs( a( j, i ) / c( j ) )
245 END DO
246 END IF
247 work( 2*n+i ) = tmp
248 END DO
249 END IF
250*
251* Estimate the norm of inv(op(A)).
252*
253 ainvnm = 0.0
254
255 kase = 0
256 10 CONTINUE
257 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
258 IF( kase.NE.0 ) THEN
259 IF( kase.EQ.2 ) THEN
260*
261* Multiply by R.
262*
263 DO i = 1, n
264 work(i) = work(i) * work(2*n+i)
265 END DO
266
267 IF (notrans) THEN
268 CALL sgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
269 $ work, n, info )
270 ELSE
271 CALL sgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
272 $ work, n, info )
273 END IF
274*
275* Multiply by inv(C).
276*
277 IF ( cmode .EQ. 1 ) THEN
278 DO i = 1, n
279 work( i ) = work( i ) / c( i )
280 END DO
281 ELSE IF ( cmode .EQ. -1 ) THEN
282 DO i = 1, n
283 work( i ) = work( i ) * c( i )
284 END DO
285 END IF
286 ELSE
287*
288* Multiply by inv(C**T).
289*
290 IF ( cmode .EQ. 1 ) THEN
291 DO i = 1, n
292 work( i ) = work( i ) / c( i )
293 END DO
294 ELSE IF ( cmode .EQ. -1 ) THEN
295 DO i = 1, n
296 work( i ) = work( i ) * c( i )
297 END DO
298 END IF
299
300 IF (notrans) THEN
301 CALL sgetrs( 'Transpose', n, 1, af, ldaf, ipiv,
302 $ work, n, info )
303 ELSE
304 CALL sgetrs( 'No transpose', n, 1, af, ldaf, ipiv,
305 $ work, n, info )
306 END IF
307*
308* Multiply by R.
309*
310 DO i = 1, n
311 work( i ) = work( i ) * work( 2*n+i )
312 END DO
313 END IF
314 GO TO 10
315 END IF
316*
317* Compute the estimate of the reciprocal condition number.
318*
319 IF( ainvnm .NE. 0.0 )
320 $ sla_gercond = ( 1.0 / ainvnm )
321*
322 RETURN
323*
324* End of SLA_GERCOND
325*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
sgetrs
subroutine sgetrs(trans, n, nrhs, a, lda, ipiv, b, ldb, info)
SGETRS
Definition sgetrs.f:121
sla_gercond
real function sla_gercond(trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)
SLA_GERCOND estimates the Skeel condition number for a general matrix.
Definition sla_gercond.f:150
slacn2
subroutine slacn2(n, v, x, isgn, est, kase, isave)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition slacn2.f:136
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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