 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 real function sla_porcond ( character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, real, dimension( ldaf, * ) AF, integer LDAF, integer CMODE, real, dimension( * ) C, integer INFO, real, dimension( * ) WORK, integer, dimension( * ) IWORK )

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

Purpose:
```    SLA_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 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 triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.``` [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 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.``` [in] WORK ``` WORK is REAL array, dimension (3*N). Workspace.``` [in] IWORK ``` IWORK is INTEGER array, dimension (N). Workspace.```
Date
September 2012

Definition at line 142 of file sla_porcond.f.

142 *
143 * -- LAPACK computational routine (version 3.4.2) --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 * September 2012
147 *
148 * .. Scalar Arguments ..
149  CHARACTER uplo
150  INTEGER n, lda, ldaf, info, cmode
151  REAL a( lda, * ), af( ldaf, * ), work( * ),
152  \$ c( * )
153 * ..
154 * .. Array Arguments ..
155  INTEGER iwork( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Local Scalars ..
161  INTEGER kase, i, j
162  REAL ainvnm, tmp
163  LOGICAL up
164 * ..
165 * .. Array Arguments ..
166  INTEGER isave( 3 )
167 * ..
168 * .. External Functions ..
169  LOGICAL lsame
170  INTEGER isamax
171  EXTERNAL lsame, isamax
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL slacn2, spotrs, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max
178 * ..
179 * .. Executable Statements ..
180 *
181  sla_porcond = 0.0
182 *
183  info = 0
184  IF( n.LT.0 ) THEN
185  info = -2
186  END IF
187  IF( info.NE.0 ) THEN
188  CALL xerbla( 'SLA_PORCOND', -info )
189  RETURN
190  END IF
191
192  IF( n.EQ.0 ) THEN
193  sla_porcond = 1.0
194  RETURN
195  END IF
196  up = .false.
197  IF ( lsame( uplo, 'U' ) ) up = .true.
198 *
199 * Compute the equilibration matrix R such that
200 * inv(R)*A*C has unit 1-norm.
201 *
202  IF ( up ) THEN
203  DO i = 1, n
204  tmp = 0.0
205  IF ( cmode .EQ. 1 ) THEN
206  DO j = 1, i
207  tmp = tmp + abs( a( j, i ) * c( j ) )
208  END DO
209  DO j = i+1, n
210  tmp = tmp + abs( a( i, j ) * c( j ) )
211  END DO
212  ELSE IF ( cmode .EQ. 0 ) THEN
213  DO j = 1, i
214  tmp = tmp + abs( a( j, i ) )
215  END DO
216  DO j = i+1, n
217  tmp = tmp + abs( a( i, j ) )
218  END DO
219  ELSE
220  DO j = 1, i
221  tmp = tmp + abs( a( j ,i ) / c( j ) )
222  END DO
223  DO j = i+1, n
224  tmp = tmp + abs( a( i, j ) / c( j ) )
225  END DO
226  END IF
227  work( 2*n+i ) = tmp
228  END DO
229  ELSE
230  DO i = 1, n
231  tmp = 0.0
232  IF ( cmode .EQ. 1 ) THEN
233  DO j = 1, i
234  tmp = tmp + abs( a( i, j ) * c( j ) )
235  END DO
236  DO j = i+1, n
237  tmp = tmp + abs( a( j, i ) * c( j ) )
238  END DO
239  ELSE IF ( cmode .EQ. 0 ) THEN
240  DO j = 1, i
241  tmp = tmp + abs( a( i, j ) )
242  END DO
243  DO j = i+1, n
244  tmp = tmp + abs( a( j, i ) )
245  END DO
246  ELSE
247  DO j = 1, i
248  tmp = tmp + abs( a( i, j ) / c( j ) )
249  END DO
250  DO j = i+1, n
251  tmp = tmp + abs( a( j, i ) / c( j ) )
252  END DO
253  END IF
254  work( 2*n+i ) = tmp
255  END DO
256  ENDIF
257 *
258 * Estimate the norm of inv(op(A)).
259 *
260  ainvnm = 0.0
261
262  kase = 0
263  10 CONTINUE
264  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
265  IF( kase.NE.0 ) THEN
266  IF( kase.EQ.2 ) THEN
267 *
268 * Multiply by R.
269 *
270  DO i = 1, n
271  work( i ) = work( i ) * work( 2*n+i )
272  END DO
273
274  IF (up) THEN
275  CALL spotrs( 'Upper', n, 1, af, ldaf, work, n, info )
276  ELSE
277  CALL spotrs( 'Lower', n, 1, af, ldaf, work, n, info )
278  ENDIF
279 *
280 * Multiply by inv(C).
281 *
282  IF ( cmode .EQ. 1 ) THEN
283  DO i = 1, n
284  work( i ) = work( i ) / c( i )
285  END DO
286  ELSE IF ( cmode .EQ. -1 ) THEN
287  DO i = 1, n
288  work( i ) = work( i ) * c( i )
289  END DO
290  END IF
291  ELSE
292 *
293 * Multiply by inv(C**T).
294 *
295  IF ( cmode .EQ. 1 ) THEN
296  DO i = 1, n
297  work( i ) = work( i ) / c( i )
298  END DO
299  ELSE IF ( cmode .EQ. -1 ) THEN
300  DO i = 1, n
301  work( i ) = work( i ) * c( i )
302  END DO
303  END IF
304
305  IF ( up ) THEN
306  CALL spotrs( 'Upper', n, 1, af, ldaf, work, n, info )
307  ELSE
308  CALL spotrs( 'Lower', n, 1, af, ldaf, work, n, info )
309  ENDIF
310 *
311 * Multiply by R.
312 *
313  DO i = 1, n
314  work( i ) = work( i ) * work( 2*n+i )
315  END DO
316  END IF
317  GO TO 10
318  END IF
319 *
320 * Compute the estimate of the reciprocal condition number.
321 *
322  IF( ainvnm .NE. 0.0 )
323  \$ sla_porcond = ( 1.0 / ainvnm )
324 *
325  RETURN
326 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:53
real function sla_porcond(UPLO, N, A, LDA, AF, LDAF, CMODE, C, INFO, WORK, IWORK)
SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix...
Definition: sla_porcond.f:142
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:138
subroutine spotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
SPOTRS
Definition: spotrs.f:112
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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