LAPACK  3.9.1
LAPACK: Linear Algebra PACKage

◆ 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.

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

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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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 *
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
dla_gercond
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
dgetrs
subroutine dgetrs(TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO)
DGETRS
Definition: dgetrs.f:121
dlacn2
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
Here is the call graph for this function:
Here is the caller graph for this function: