 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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.

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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.``` [in] WORK ``` WORK is DOUBLE PRECISION array, dimension (3*N). Workspace.``` [in] IWORK ``` IWORK is INTEGER array, dimension (N). Workspace.```
Date
September 2012

Definition at line 144 of file dla_porcond.f.

144 *
145 * -- LAPACK computational routine (version 3.4.2) --
146 * -- LAPACK is a software package provided by Univ. of Tennessee, --
147 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148 * September 2012
149 *
150 * .. Scalar Arguments ..
151  CHARACTER uplo
152  INTEGER n, lda, ldaf, info, cmode
153  DOUBLE PRECISION a( lda, * ), af( ldaf, * ), work( * ),
154  \$ c( * )
155 * ..
156 * .. Array Arguments ..
157  INTEGER iwork( * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Local Scalars ..
163  INTEGER kase, i, j
164  DOUBLE PRECISION ainvnm, tmp
165  LOGICAL up
166 * ..
167 * .. Array Arguments ..
168  INTEGER isave( 3 )
169 * ..
170 * .. External Functions ..
171  LOGICAL lsame
172  INTEGER idamax
173  EXTERNAL lsame, idamax
174 * ..
175 * .. External Subroutines ..
176  EXTERNAL dlacn2, dpotrs, xerbla
177 * ..
178 * .. Intrinsic Functions ..
179  INTRINSIC abs, max
180 * ..
181 * .. Executable Statements ..
182 *
183  dla_porcond = 0.0d+0
184 *
185  info = 0
186  IF( n.LT.0 ) THEN
187  info = -2
188  END IF
189  IF( info.NE.0 ) THEN
190  CALL xerbla( 'DLA_PORCOND', -info )
191  RETURN
192  END IF
193
194  IF( n.EQ.0 ) THEN
195  dla_porcond = 1.0d+0
196  RETURN
197  END IF
198  up = .false.
199  IF ( lsame( uplo, 'U' ) ) up = .true.
200 *
201 * Compute the equilibration matrix R such that
202 * inv(R)*A*C has unit 1-norm.
203 *
204  IF ( up ) THEN
205  DO i = 1, n
206  tmp = 0.0d+0
207  IF ( cmode .EQ. 1 ) THEN
208  DO j = 1, i
209  tmp = tmp + abs( a( j, i ) * c( j ) )
210  END DO
211  DO j = i+1, n
212  tmp = tmp + abs( a( i, j ) * c( j ) )
213  END DO
214  ELSE IF ( cmode .EQ. 0 ) THEN
215  DO j = 1, i
216  tmp = tmp + abs( a( j, i ) )
217  END DO
218  DO j = i+1, n
219  tmp = tmp + abs( a( i, j ) )
220  END DO
221  ELSE
222  DO j = 1, i
223  tmp = tmp + abs( a( j ,i ) / c( j ) )
224  END DO
225  DO j = i+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 = 0.0d+0
234  IF ( cmode .EQ. 1 ) THEN
235  DO j = 1, i
236  tmp = tmp + abs( a( i, j ) * c( j ) )
237  END DO
238  DO j = i+1, n
239  tmp = tmp + abs( a( j, i ) * c( j ) )
240  END DO
241  ELSE IF ( cmode .EQ. 0 ) THEN
242  DO j = 1, i
243  tmp = tmp + abs( a( i, j ) )
244  END DO
245  DO j = i+1, n
246  tmp = tmp + abs( a( j, i ) )
247  END DO
248  ELSE
249  DO j = 1, i
250  tmp = tmp + abs( a( i, j ) / c( j ) )
251  END DO
252  DO j = i+1, n
253  tmp = tmp + abs( a( j, i ) / c( j ) )
254  END DO
255  END IF
256  work( 2*n+i ) = tmp
257  END DO
258  ENDIF
259 *
260 * Estimate the norm of inv(op(A)).
261 *
262  ainvnm = 0.0d+0
263
264  kase = 0
265  10 CONTINUE
266  CALL dlacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
267  IF( kase.NE.0 ) THEN
268  IF( kase.EQ.2 ) THEN
269 *
270 * Multiply by R.
271 *
272  DO i = 1, n
273  work( i ) = work( i ) * work( 2*n+i )
274  END DO
275
276  IF (up) THEN
277  CALL dpotrs( 'Upper', n, 1, af, ldaf, work, n, info )
278  ELSE
279  CALL dpotrs( 'Lower', n, 1, af, ldaf, work, n, info )
280  ENDIF
281 *
282 * Multiply by inv(C).
283 *
284  IF ( cmode .EQ. 1 ) THEN
285  DO i = 1, n
286  work( i ) = work( i ) / c( i )
287  END DO
288  ELSE IF ( cmode .EQ. -1 ) THEN
289  DO i = 1, n
290  work( i ) = work( i ) * c( i )
291  END DO
292  END IF
293  ELSE
294 *
295 * Multiply by inv(C**T).
296 *
297  IF ( cmode .EQ. 1 ) THEN
298  DO i = 1, n
299  work( i ) = work( i ) / c( i )
300  END DO
301  ELSE IF ( cmode .EQ. -1 ) THEN
302  DO i = 1, n
303  work( i ) = work( i ) * c( i )
304  END DO
305  END IF
306
307  IF ( up ) THEN
308  CALL dpotrs( 'Upper', n, 1, af, ldaf, work, n, info )
309  ELSE
310  CALL dpotrs( 'Lower', n, 1, af, ldaf, work, n, info )
311  ENDIF
312 *
313 * Multiply by R.
314 *
315  DO i = 1, n
316  work( i ) = work( i ) * work( 2*n+i )
317  END DO
318  END IF
319  GO TO 10
320  END IF
321 *
322 * Compute the estimate of the reciprocal condition number.
323 *
324  IF( ainvnm .NE. 0.0d+0 )
325  \$ dla_porcond = ( 1.0d+0 / ainvnm )
326 *
327  RETURN
328 *
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:144
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:53
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
DPOTRS
Definition: dpotrs.f:112
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:138

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