 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dla_porcond()

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

DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

Purpose:
```    DLA_PORCOND 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] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [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 139 of file dla_porcond.f.

142 *
143 * -- LAPACK computational routine --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 *
147 * .. Scalar Arguments ..
148  CHARACTER UPLO
149  INTEGER N, LDA, LDAF, INFO, CMODE
150  DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
151  \$ C( * )
152 * ..
153 * .. Array Arguments ..
154  INTEGER IWORK( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Local Scalars ..
160  INTEGER KASE, I, J
161  DOUBLE PRECISION AINVNM, TMP
162  LOGICAL UP
163 * ..
164 * .. Array Arguments ..
165  INTEGER ISAVE( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  EXTERNAL lsame
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL dlacn2, dpotrs, xerbla
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC abs, max
176 * ..
177 * .. Executable Statements ..
178 *
179  dla_porcond = 0.0d+0
180 *
181  info = 0
182  IF( n.LT.0 ) THEN
183  info = -2
184  END IF
185  IF( info.NE.0 ) THEN
186  CALL xerbla( 'DLA_PORCOND', -info )
187  RETURN
188  END IF
189
190  IF( n.EQ.0 ) THEN
191  dla_porcond = 1.0d+0
192  RETURN
193  END IF
194  up = .false.
195  IF ( lsame( uplo, 'U' ) ) up = .true.
196 *
197 * Compute the equilibration matrix R such that
198 * inv(R)*A*C has unit 1-norm.
199 *
200  IF ( up ) THEN
201  DO i = 1, n
202  tmp = 0.0d+0
203  IF ( cmode .EQ. 1 ) THEN
204  DO j = 1, i
205  tmp = tmp + abs( a( j, i ) * c( j ) )
206  END DO
207  DO j = i+1, n
208  tmp = tmp + abs( a( i, j ) * c( j ) )
209  END DO
210  ELSE IF ( cmode .EQ. 0 ) THEN
211  DO j = 1, i
212  tmp = tmp + abs( a( j, i ) )
213  END DO
214  DO j = i+1, n
215  tmp = tmp + abs( a( i, j ) )
216  END DO
217  ELSE
218  DO j = 1, i
219  tmp = tmp + abs( a( j ,i ) / c( j ) )
220  END DO
221  DO j = i+1, n
222  tmp = tmp + abs( a( i, j ) / c( j ) )
223  END DO
224  END IF
225  work( 2*n+i ) = tmp
226  END DO
227  ELSE
228  DO i = 1, n
229  tmp = 0.0d+0
230  IF ( cmode .EQ. 1 ) THEN
231  DO j = 1, i
232  tmp = tmp + abs( a( i, j ) * c( j ) )
233  END DO
234  DO j = i+1, n
235  tmp = tmp + abs( a( j, i ) * c( j ) )
236  END DO
237  ELSE IF ( cmode .EQ. 0 ) THEN
238  DO j = 1, i
239  tmp = tmp + abs( a( i, j ) )
240  END DO
241  DO j = i+1, n
242  tmp = tmp + abs( a( j, i ) )
243  END DO
244  ELSE
245  DO j = 1, i
246  tmp = tmp + abs( a( i, j ) / c( j ) )
247  END DO
248  DO j = i+1, n
249  tmp = tmp + abs( a( j, i ) / c( j ) )
250  END DO
251  END IF
252  work( 2*n+i ) = tmp
253  END DO
254  ENDIF
255 *
256 * Estimate the norm of inv(op(A)).
257 *
258  ainvnm = 0.0d+0
259
260  kase = 0
261  10 CONTINUE
262  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
263  IF( kase.NE.0 ) THEN
264  IF( kase.EQ.2 ) THEN
265 *
266 * Multiply by R.
267 *
268  DO i = 1, n
269  work( i ) = work( i ) * work( 2*n+i )
270  END DO
271
272  IF (up) THEN
273  CALL dpotrs( 'Upper', n, 1, af, ldaf, work, n, info )
274  ELSE
275  CALL dpotrs( 'Lower', n, 1, af, ldaf, work, n, info )
276  ENDIF
277 *
278 * Multiply by inv(C).
279 *
280  IF ( cmode .EQ. 1 ) THEN
281  DO i = 1, n
282  work( i ) = work( i ) / c( i )
283  END DO
284  ELSE IF ( cmode .EQ. -1 ) THEN
285  DO i = 1, n
286  work( i ) = work( i ) * c( i )
287  END DO
288  END IF
289  ELSE
290 *
291 * Multiply by inv(C**T).
292 *
293  IF ( cmode .EQ. 1 ) THEN
294  DO i = 1, n
295  work( i ) = work( i ) / c( i )
296  END DO
297  ELSE IF ( cmode .EQ. -1 ) THEN
298  DO i = 1, n
299  work( i ) = work( i ) * c( i )
300  END DO
301  END IF
302
303  IF ( up ) THEN
304  CALL dpotrs( 'Upper', n, 1, af, ldaf, work, n, info )
305  ELSE
306  CALL dpotrs( 'Lower', n, 1, af, ldaf, work, n, info )
307  ENDIF
308 *
309 * Multiply by R.
310 *
311  DO i = 1, n
312  work( i ) = work( i ) * work( 2*n+i )
313  END DO
314  END IF
315  GO TO 10
316  END IF
317 *
318 * Compute the estimate of the reciprocal condition number.
319 *
320  IF( ainvnm .NE. 0.0d+0 )
321  \$ dla_porcond = ( 1.0d+0 / ainvnm )
322 *
323  RETURN
324 *
325 * End of DLA_PORCOND
326 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
subroutine dpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOTRS
Definition: dpotrs.f:110
double precision function dla_porcond(UPLO, N, A, LDA, AF, LDAF, CMODE, C, INFO, WORK, IWORK)
DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
Definition: dla_porcond.f:142
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