LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ cla_porcond_c()

real function cla_porcond_c ( character  UPLO,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldaf, * )  AF,
integer  LDAF,
real, dimension( * )  C,
logical  CAPPLY,
integer  INFO,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK 
)

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

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Purpose:
    CLA_PORCOND_C Computes the infinity norm condition number of
    op(A) * inv(diag(C)) where C is a REAL 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 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 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 CPOTRF.
[in]LDAF
          LDAF is INTEGER
     The leading dimension of the array AF.  LDAF >= max(1,N).
[in]C
          C is REAL 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 array, dimension (2*N).
     Workspace.
[out]RWORK
          RWORK is REAL array, dimension (N).
     Workspace.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 128 of file cla_porcond_c.f.

130 *
131 * -- LAPACK computational routine --
132 * -- LAPACK is a software package provided by Univ. of Tennessee, --
133 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134 *
135 * .. Scalar Arguments ..
136  CHARACTER UPLO
137  LOGICAL CAPPLY
138  INTEGER N, LDA, LDAF, INFO
139 * ..
140 * .. Array Arguments ..
141  COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * )
142  REAL C( * ), RWORK( * )
143 * ..
144 *
145 * =====================================================================
146 *
147 * .. Local Scalars ..
148  INTEGER KASE
149  REAL AINVNM, ANORM, TMP
150  INTEGER I, J
151  LOGICAL UP, UPPER
152  COMPLEX ZDUM
153 * ..
154 * .. Local Arrays ..
155  INTEGER ISAVE( 3 )
156 * ..
157 * .. External Functions ..
158  LOGICAL LSAME
159  EXTERNAL lsame
160 * ..
161 * .. External Subroutines ..
162  EXTERNAL clacn2, cpotrs, xerbla
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC abs, max, real, aimag
166 * ..
167 * .. Statement Functions ..
168  REAL CABS1
169 * ..
170 * .. Statement Function Definitions ..
171  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
172 * ..
173 * .. Executable Statements ..
174 *
175  cla_porcond_c = 0.0e+0
176 *
177  info = 0
178  upper = lsame( uplo, 'U' )
179  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
180  info = -1
181  ELSE IF( n.LT.0 ) THEN
182  info = -2
183  ELSE IF( lda.LT.max( 1, n ) ) THEN
184  info = -4
185  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
186  info = -6
187  END IF
188  IF( info.NE.0 ) THEN
189  CALL xerbla( 'CLA_PORCOND_C', -info )
190  RETURN
191  END IF
192  up = .false.
193  IF ( lsame( uplo, 'U' ) ) up = .true.
194 *
195 * Compute norm of op(A)*op2(C).
196 *
197  anorm = 0.0e+0
198  IF ( up ) THEN
199  DO i = 1, n
200  tmp = 0.0e+0
201  IF ( capply ) THEN
202  DO j = 1, i
203  tmp = tmp + cabs1( a( j, i ) ) / c( j )
204  END DO
205  DO j = i+1, n
206  tmp = tmp + cabs1( a( i, j ) ) / c( j )
207  END DO
208  ELSE
209  DO j = 1, i
210  tmp = tmp + cabs1( a( j, i ) )
211  END DO
212  DO j = i+1, n
213  tmp = tmp + cabs1( a( i, j ) )
214  END DO
215  END IF
216  rwork( i ) = tmp
217  anorm = max( anorm, tmp )
218  END DO
219  ELSE
220  DO i = 1, n
221  tmp = 0.0e+0
222  IF ( capply ) THEN
223  DO j = 1, i
224  tmp = tmp + cabs1( a( i, j ) ) / c( j )
225  END DO
226  DO j = i+1, n
227  tmp = tmp + cabs1( a( j, i ) ) / c( j )
228  END DO
229  ELSE
230  DO j = 1, i
231  tmp = tmp + cabs1( a( i, j ) )
232  END DO
233  DO j = i+1, n
234  tmp = tmp + cabs1( a( j, i ) )
235  END DO
236  END IF
237  rwork( i ) = tmp
238  anorm = max( anorm, tmp )
239  END DO
240  END IF
241 *
242 * Quick return if possible.
243 *
244  IF( n.EQ.0 ) THEN
245  cla_porcond_c = 1.0e+0
246  RETURN
247  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
248  RETURN
249  END IF
250 *
251 * Estimate the norm of inv(op(A)).
252 *
253  ainvnm = 0.0e+0
254 *
255  kase = 0
256  10 CONTINUE
257  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
258  IF( kase.NE.0 ) THEN
259  IF( kase.EQ.2 ) THEN
260 *
261 * Multiply by R.
262 *
263  DO i = 1, n
264  work( i ) = work( i ) * rwork( i )
265  END DO
266 *
267  IF ( up ) THEN
268  CALL cpotrs( 'U', n, 1, af, ldaf,
269  $ work, n, info )
270  ELSE
271  CALL cpotrs( 'L', n, 1, af, ldaf,
272  $ work, n, info )
273  ENDIF
274 *
275 * Multiply by inv(C).
276 *
277  IF ( capply ) THEN
278  DO i = 1, n
279  work( i ) = work( i ) * c( i )
280  END DO
281  END IF
282  ELSE
283 *
284 * Multiply by inv(C**H).
285 *
286  IF ( capply ) THEN
287  DO i = 1, n
288  work( i ) = work( i ) * c( i )
289  END DO
290  END IF
291 *
292  IF ( up ) THEN
293  CALL cpotrs( 'U', n, 1, af, ldaf,
294  $ work, n, info )
295  ELSE
296  CALL cpotrs( 'L', n, 1, af, ldaf,
297  $ work, n, info )
298  END IF
299 *
300 * Multiply by R.
301 *
302  DO i = 1, n
303  work( i ) = work( i ) * rwork( i )
304  END DO
305  END IF
306  GO TO 10
307  END IF
308 *
309 * Compute the estimate of the reciprocal condition number.
310 *
311  IF( ainvnm .NE. 0.0e+0 )
312  $ cla_porcond_c = 1.0e+0 / ainvnm
313 *
314  RETURN
315 *
316 * End of CLA_PORCOND_C
317 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clacn2(N, V, X, EST, KASE, ISAVE)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: clacn2.f:133
real function cla_porcond_c(UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, INFO, WORK, RWORK)
CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positiv...
subroutine cpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
CPOTRS
Definition: cpotrs.f:110
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