 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zla_porcond_c()

 double precision function zla_porcond_c ( character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldaf, * ) AF, integer LDAF, double precision, dimension( * ) C, logical CAPPLY, integer INFO, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK )

ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.

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

Purpose:
```    ZLA_PORCOND_C Computes the infinity norm condition number of
op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector```
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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDAF,N) The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.``` [in] LDAF ``` LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).``` [in] C ``` C is DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * inv(diag(C)).``` [in] CAPPLY ``` CAPPLY is LOGICAL If .TRUE. then access the vector C in the formula above.``` [out] INFO ``` INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.``` [out] WORK ``` WORK is COMPLEX*16 array, dimension (2*N). Workspace.``` [out] RWORK ``` RWORK is DOUBLE PRECISION array, dimension (N). Workspace.```

Definition at line 129 of file zla_porcond_c.f.

132 *
133 * -- LAPACK computational routine --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 *
137 * .. Scalar Arguments ..
138  CHARACTER UPLO
139  LOGICAL CAPPLY
140  INTEGER N, LDA, LDAF, INFO
141 * ..
142 * .. Array Arguments ..
143  COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
144  DOUBLE PRECISION C( * ), RWORK( * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Local Scalars ..
150  INTEGER KASE
151  DOUBLE PRECISION AINVNM, ANORM, TMP
152  INTEGER I, J
153  LOGICAL UP, UPPER
154  COMPLEX*16 ZDUM
155 * ..
156 * .. Local Arrays ..
157  INTEGER ISAVE( 3 )
158 * ..
159 * .. External Functions ..
160  LOGICAL LSAME
161  EXTERNAL lsame
162 * ..
163 * .. External Subroutines ..
164  EXTERNAL zlacn2, zpotrs, xerbla
165 * ..
166 * .. Intrinsic Functions ..
167  INTRINSIC abs, max, real, dimag
168 * ..
169 * .. Statement Functions ..
170  DOUBLE PRECISION CABS1
171 * ..
172 * .. Statement Function Definitions ..
173  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
174 * ..
175 * .. Executable Statements ..
176 *
177  zla_porcond_c = 0.0d+0
178 *
179  info = 0
180  upper = lsame( uplo, 'U' )
181  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
182  info = -1
183  ELSE IF( n.LT.0 ) THEN
184  info = -2
185  ELSE IF( lda.LT.max( 1, n ) ) THEN
186  info = -4
187  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
188  info = -6
189  END IF
190  IF( info.NE.0 ) THEN
191  CALL xerbla( 'ZLA_PORCOND_C', -info )
192  RETURN
193  END IF
194  up = .false.
195  IF ( lsame( uplo, 'U' ) ) up = .true.
196 *
197 * Compute norm of op(A)*op2(C).
198 *
199  anorm = 0.0d+0
200  IF ( up ) THEN
201  DO i = 1, n
202  tmp = 0.0d+0
203  IF ( capply ) THEN
204  DO j = 1, i
205  tmp = tmp + cabs1( a( j, i ) ) / c( j )
206  END DO
207  DO j = i+1, n
208  tmp = tmp + cabs1( a( i, j ) ) / c( j )
209  END DO
210  ELSE
211  DO j = 1, i
212  tmp = tmp + cabs1( a( j, i ) )
213  END DO
214  DO j = i+1, n
215  tmp = tmp + cabs1( a( i, j ) )
216  END DO
217  END IF
218  rwork( i ) = tmp
219  anorm = max( anorm, tmp )
220  END DO
221  ELSE
222  DO i = 1, n
223  tmp = 0.0d+0
224  IF ( capply ) THEN
225  DO j = 1, i
226  tmp = tmp + cabs1( a( i, j ) ) / c( j )
227  END DO
228  DO j = i+1, n
229  tmp = tmp + cabs1( a( j, i ) ) / c( j )
230  END DO
231  ELSE
232  DO j = 1, i
233  tmp = tmp + cabs1( a( i, j ) )
234  END DO
235  DO j = i+1, n
236  tmp = tmp + cabs1( a( j, i ) )
237  END DO
238  END IF
239  rwork( i ) = tmp
240  anorm = max( anorm, tmp )
241  END DO
242  END IF
243 *
244 * Quick return if possible.
245 *
246  IF( n.EQ.0 ) THEN
247  zla_porcond_c = 1.0d+0
248  RETURN
249  ELSE IF( anorm .EQ. 0.0d+0 ) THEN
250  RETURN
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 zlacn2( n, work( n+1 ), work, 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 ) * rwork( i )
267  END DO
268 *
269  IF ( up ) THEN
270  CALL zpotrs( 'U', n, 1, af, ldaf,
271  \$ work, n, info )
272  ELSE
273  CALL zpotrs( 'L', n, 1, af, ldaf,
274  \$ work, n, info )
275  ENDIF
276 *
277 * Multiply by inv(C).
278 *
279  IF ( capply ) THEN
280  DO i = 1, n
281  work( i ) = work( i ) * c( i )
282  END DO
283  END IF
284  ELSE
285 *
286 * Multiply by inv(C**H).
287 *
288  IF ( capply ) THEN
289  DO i = 1, n
290  work( i ) = work( i ) * c( i )
291  END DO
292  END IF
293 *
294  IF ( up ) THEN
295  CALL zpotrs( 'U', n, 1, af, ldaf,
296  \$ work, n, info )
297  ELSE
298  CALL zpotrs( 'L', n, 1, af, ldaf,
299  \$ work, n, info )
300  END IF
301 *
302 * Multiply by R.
303 *
304  DO i = 1, n
305  work( i ) = work( i ) * rwork( i )
306  END DO
307  END IF
308  GO TO 10
309  END IF
310 *
311 * Compute the estimate of the reciprocal condition number.
312 *
313  IF( ainvnm .NE. 0.0d+0 )
314  \$ zla_porcond_c = 1.0d+0 / ainvnm
315 *
316  RETURN
317 *
318 * End of ZLA_PORCOND_C
319 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zlacn2(N, V, X, EST, KASE, ISAVE)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: zlacn2.f:133
double precision function zla_porcond_c(UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, INFO, WORK, RWORK)
ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
subroutine zpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
ZPOTRS
Definition: zpotrs.f:110
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