 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ cla_porcond_x()

 real function cla_porcond_x ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldaf, * ) AF, integer LDAF, complex, dimension( * ) X, integer INFO, complex, dimension( * ) WORK, real, dimension( * ) RWORK )

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

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Purpose:
```    CLA_PORCOND_X Computes the infinity norm condition number of
op(A) * diag(X) where X is a COMPLEX 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] X ``` X is COMPLEX array, dimension (N) The vector X in the formula op(A) * diag(X).``` [out] INFO ``` INFO is INTEGER = 0: Successful exit. i > 0: The ith argument is invalid.``` [in] WORK ``` WORK is COMPLEX array, dimension (2*N). Workspace.``` [in] RWORK ``` RWORK is REAL array, dimension (N). Workspace.```
Date
December 2016

Definition at line 125 of file cla_porcond_x.f.

125 *
126 * -- LAPACK computational routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER uplo
133  INTEGER n, lda, ldaf, info
134 * ..
135 * .. Array Arguments ..
136  COMPLEX a( lda, * ), af( ldaf, * ), work( * ), x( * )
137  REAL rwork( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Local Scalars ..
143  INTEGER kase, i, j
144  REAL ainvnm, anorm, tmp
145  LOGICAL up, upper
146  COMPLEX zdum
147 * ..
148 * .. Local Arrays ..
149  INTEGER isave( 3 )
150 * ..
151 * .. External Functions ..
152  LOGICAL lsame
153  EXTERNAL lsame
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL clacn2, cpotrs, xerbla
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, max, REAL, aimag
160 * ..
161 * .. Statement Functions ..
162  REAL cabs1
163 * ..
164 * .. Statement Function Definitions ..
165  cabs1( zdum ) = abs( REAL( ZDUM ) ) + abs( aimag( zdum ) )
166 * ..
167 * .. Executable Statements ..
168 *
169  cla_porcond_x = 0.0e+0
170 *
171  info = 0
172  upper = lsame( uplo, 'U' )
173  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
174  info = -1
175  ELSE IF ( n.LT.0 ) THEN
176  info = -2
177  ELSE IF( lda.LT.max( 1, n ) ) THEN
178  info = -4
179  ELSE IF( ldaf.LT.max( 1, n ) ) THEN
180  info = -6
181  END IF
182  IF( info.NE.0 ) THEN
183  CALL xerbla( 'CLA_PORCOND_X', -info )
184  RETURN
185  END IF
186  up = .false.
187  IF ( lsame( uplo, 'U' ) ) up = .true.
188 *
189 * Compute norm of op(A)*op2(C).
190 *
191  anorm = 0.0
192  IF ( up ) THEN
193  DO i = 1, n
194  tmp = 0.0e+0
195  DO j = 1, i
196  tmp = tmp + cabs1( a( j, i ) * x( j ) )
197  END DO
198  DO j = i+1, n
199  tmp = tmp + cabs1( a( i, j ) * x( j ) )
200  END DO
201  rwork( i ) = tmp
202  anorm = max( anorm, tmp )
203  END DO
204  ELSE
205  DO i = 1, n
206  tmp = 0.0e+0
207  DO j = 1, i
208  tmp = tmp + cabs1( a( i, j ) * x( j ) )
209  END DO
210  DO j = i+1, n
211  tmp = tmp + cabs1( a( j, i ) * x( j ) )
212  END DO
213  rwork( i ) = tmp
214  anorm = max( anorm, tmp )
215  END DO
216  END IF
217 *
218 * Quick return if possible.
219 *
220  IF( n.EQ.0 ) THEN
221  cla_porcond_x = 1.0e+0
222  RETURN
223  ELSE IF( anorm .EQ. 0.0e+0 ) THEN
224  RETURN
225  END IF
226 *
227 * Estimate the norm of inv(op(A)).
228 *
229  ainvnm = 0.0e+0
230 *
231  kase = 0
232  10 CONTINUE
233  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
234  IF( kase.NE.0 ) THEN
235  IF( kase.EQ.2 ) THEN
236 *
237 * Multiply by R.
238 *
239  DO i = 1, n
240  work( i ) = work( i ) * rwork( i )
241  END DO
242 *
243  IF ( up ) THEN
244  CALL cpotrs( 'U', n, 1, af, ldaf,
245  \$ work, n, info )
246  ELSE
247  CALL cpotrs( 'L', n, 1, af, ldaf,
248  \$ work, n, info )
249  ENDIF
250 *
251 * Multiply by inv(X).
252 *
253  DO i = 1, n
254  work( i ) = work( i ) / x( i )
255  END DO
256  ELSE
257 *
258 * Multiply by inv(X**H).
259 *
260  DO i = 1, n
261  work( i ) = work( i ) / x( i )
262  END DO
263 *
264  IF ( up ) THEN
265  CALL cpotrs( 'U', n, 1, af, ldaf,
266  \$ work, n, info )
267  ELSE
268  CALL cpotrs( 'L', n, 1, af, ldaf,
269  \$ work, n, info )
270  END IF
271 *
272 * Multiply by R.
273 *
274  DO i = 1, n
275  work( i ) = work( i ) * rwork( i )
276  END DO
277  END IF
278  GO TO 10
279  END IF
280 *
281 * Compute the estimate of the reciprocal condition number.
282 *
283  IF( ainvnm .NE. 0.0e+0 )
284  \$ cla_porcond_x = 1.0e+0 / ainvnm
285 *
286  RETURN
287 *
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:135
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function cla_porcond_x(UPLO, N, A, LDA, AF, LDAF, X, INFO, WORK, RWORK)
CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-def...
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine cpotrs(UPLO, N, NRHS, A, LDA, B, LDB, INFO)
CPOTRS
Definition: cpotrs.f:112
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