 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ctpcon()

 subroutine ctpcon ( character NORM, character UPLO, character DIAG, integer N, complex, dimension( * ) AP, real RCOND, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

CTPCON

Purpose:
``` CTPCON estimates the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] DIAG ``` DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] AP ``` AP is COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.``` [out] RCOND ``` RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [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 128 of file ctpcon.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 DIAG, NORM, UPLO
137 INTEGER INFO, N
138 REAL RCOND
139* ..
140* .. Array Arguments ..
141 REAL RWORK( * )
142 COMPLEX AP( * ), WORK( * )
143* ..
144*
145* =====================================================================
146*
147* .. Parameters ..
148 REAL ONE, ZERO
149 parameter( one = 1.0e+0, zero = 0.0e+0 )
150* ..
151* .. Local Scalars ..
152 LOGICAL NOUNIT, ONENRM, UPPER
153 CHARACTER NORMIN
154 INTEGER IX, KASE, KASE1
155 REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
156 COMPLEX ZDUM
157* ..
158* .. Local Arrays ..
159 INTEGER ISAVE( 3 )
160* ..
161* .. External Functions ..
162 LOGICAL LSAME
163 INTEGER ICAMAX
164 REAL CLANTP, SLAMCH
165 EXTERNAL lsame, icamax, clantp, slamch
166* ..
167* .. External Subroutines ..
168 EXTERNAL clacn2, clatps, csrscl, xerbla
169* ..
170* .. Intrinsic Functions ..
171 INTRINSIC abs, aimag, max, real
172* ..
173* .. Statement Functions ..
174 REAL CABS1
175* ..
176* .. Statement Function definitions ..
177 cabs1( zdum ) = abs( real( zdum ) ) + abs( aimag( zdum ) )
178* ..
179* .. Executable Statements ..
180*
181* Test the input parameters.
182*
183 info = 0
184 upper = lsame( uplo, 'U' )
185 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
186 nounit = lsame( diag, 'N' )
187*
188 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
189 info = -1
190 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
191 info = -2
192 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
193 info = -3
194 ELSE IF( n.LT.0 ) THEN
195 info = -4
196 END IF
197 IF( info.NE.0 ) THEN
198 CALL xerbla( 'CTPCON', -info )
199 RETURN
200 END IF
201*
202* Quick return if possible
203*
204 IF( n.EQ.0 ) THEN
205 rcond = one
206 RETURN
207 END IF
208*
209 rcond = zero
210 smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
211*
212* Compute the norm of the triangular matrix A.
213*
214 anorm = clantp( norm, uplo, diag, n, ap, rwork )
215*
216* Continue only if ANORM > 0.
217*
218 IF( anorm.GT.zero ) THEN
219*
220* Estimate the norm of the inverse of A.
221*
222 ainvnm = zero
223 normin = 'N'
224 IF( onenrm ) THEN
225 kase1 = 1
226 ELSE
227 kase1 = 2
228 END IF
229 kase = 0
230 10 CONTINUE
231 CALL clacn2( n, work( n+1 ), work, ainvnm, kase, isave )
232 IF( kase.NE.0 ) THEN
233 IF( kase.EQ.kase1 ) THEN
234*
235* Multiply by inv(A).
236*
237 CALL clatps( uplo, 'No transpose', diag, normin, n, ap,
238 \$ work, scale, rwork, info )
239 ELSE
240*
241* Multiply by inv(A**H).
242*
243 CALL clatps( uplo, 'Conjugate transpose', diag, normin,
244 \$ n, ap, work, scale, rwork, info )
245 END IF
246 normin = 'Y'
247*
248* Multiply by 1/SCALE if doing so will not cause overflow.
249*
250 IF( scale.NE.one ) THEN
251 ix = icamax( n, work, 1 )
252 xnorm = cabs1( work( ix ) )
253 IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
254 \$ GO TO 20
255 CALL csrscl( n, scale, work, 1 )
256 END IF
257 GO TO 10
258 END IF
259*
260* Compute the estimate of the reciprocal condition number.
261*
262 IF( ainvnm.NE.zero )
263 \$ rcond = ( one / anorm ) / ainvnm
264 END IF
265*
266 20 CONTINUE
267 RETURN
268*
269* End of CTPCON
270*
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 csrscl(N, SA, SX, INCX)
CSRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: csrscl.f:84
subroutine clatps(UPLO, TRANS, DIAG, NORMIN, N, AP, X, SCALE, CNORM, INFO)
CLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition: clatps.f:231
real function clantp(NORM, UPLO, DIAG, N, AP, WORK)
CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clantp.f:125
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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