 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cpocon()

 subroutine cpocon ( character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real ANORM, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CPOCON

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Purpose:
``` CPOCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite matrix using the
Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).```
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 order of the matrix A. N >= 0.``` [in] A ``` A is COMPLEX array, dimension (LDA,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] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] ANORM ``` ANORM is REAL The 1-norm (or infinity-norm) of the Hermitian matrix A.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.``` [out] WORK ` WORK is COMPLEX array, dimension (2*N)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```

Definition at line 119 of file cpocon.f.

121 *
122 * -- LAPACK computational routine --
123 * -- LAPACK is a software package provided by Univ. of Tennessee, --
124 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
125 *
126 * .. Scalar Arguments ..
127  CHARACTER UPLO
128  INTEGER INFO, LDA, N
129  REAL ANORM, RCOND
130 * ..
131 * .. Array Arguments ..
132  REAL RWORK( * )
133  COMPLEX A( LDA, * ), WORK( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  REAL ONE, ZERO
140  parameter( one = 1.0e+0, zero = 0.0e+0 )
141 * ..
142 * .. Local Scalars ..
143  LOGICAL UPPER
144  CHARACTER NORMIN
145  INTEGER IX, KASE
146  REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
147  COMPLEX ZDUM
148 * ..
149 * .. Local Arrays ..
150  INTEGER ISAVE( 3 )
151 * ..
152 * .. External Functions ..
153  LOGICAL LSAME
154  INTEGER ICAMAX
155  REAL SLAMCH
156  EXTERNAL lsame, icamax, slamch
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL clacn2, clatrs, csrscl, xerbla
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC abs, aimag, max, real
163 * ..
164 * .. Statement Functions ..
165  REAL CABS1
166 * ..
167 * .. Statement Function definitions ..
168  cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
169 * ..
170 * .. Executable Statements ..
171 *
172 * Test the input parameters.
173 *
174  info = 0
175  upper = lsame( uplo, 'U' )
176  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
177  info = -1
178  ELSE IF( n.LT.0 ) THEN
179  info = -2
180  ELSE IF( lda.LT.max( 1, n ) ) THEN
181  info = -4
182  ELSE IF( anorm.LT.zero ) THEN
183  info = -5
184  END IF
185  IF( info.NE.0 ) THEN
186  CALL xerbla( 'CPOCON', -info )
187  RETURN
188  END IF
189 *
190 * Quick return if possible
191 *
192  rcond = zero
193  IF( n.EQ.0 ) THEN
194  rcond = one
195  RETURN
196  ELSE IF( anorm.EQ.zero ) THEN
197  RETURN
198  END IF
199 *
200  smlnum = slamch( 'Safe minimum' )
201 *
202 * Estimate the 1-norm of inv(A).
203 *
204  kase = 0
205  normin = 'N'
206  10 CONTINUE
207  CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
208  IF( kase.NE.0 ) THEN
209  IF( upper ) THEN
210 *
211 * Multiply by inv(U**H).
212 *
213  CALL clatrs( 'Upper', 'Conjugate transpose', 'Non-unit',
214  \$ normin, n, a, lda, work, scalel, rwork, info )
215  normin = 'Y'
216 *
217 * Multiply by inv(U).
218 *
219  CALL clatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
220  \$ a, lda, work, scaleu, rwork, info )
221  ELSE
222 *
223 * Multiply by inv(L).
224 *
225  CALL clatrs( 'Lower', 'No transpose', 'Non-unit', normin, n,
226  \$ a, lda, work, scalel, rwork, info )
227  normin = 'Y'
228 *
229 * Multiply by inv(L**H).
230 *
231  CALL clatrs( 'Lower', 'Conjugate transpose', 'Non-unit',
232  \$ normin, n, a, lda, work, scaleu, rwork, info )
233  END IF
234 *
235 * Multiply by 1/SCALE if doing so will not cause overflow.
236 *
237  scale = scalel*scaleu
238  IF( scale.NE.one ) THEN
239  ix = icamax( n, work, 1 )
240  IF( scale.LT.cabs1( work( ix ) )*smlnum .OR. scale.EQ.zero )
241  \$ GO TO 20
242  CALL csrscl( n, scale, work, 1 )
243  END IF
244  GO TO 10
245  END IF
246 *
247 * Compute the estimate of the reciprocal condition number.
248 *
249  IF( ainvnm.NE.zero )
250  \$ rcond = ( one / ainvnm ) / anorm
251 *
252  20 CONTINUE
253  RETURN
254 *
255 * End of CPOCON
256 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
integer function icamax(N, CX, INCX)
ICAMAX
Definition: icamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine clatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
CLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: clatrs.f:239
subroutine csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
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 slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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