LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ stpcon()

 subroutine stpcon ( character norm, character uplo, character diag, integer n, real, dimension( * ) ap, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info )

STPCON

Purpose:
``` STPCON 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 REAL 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 REAL array, dimension (3*N)` [out] IWORK ` IWORK is INTEGER 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 stpcon.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 INTEGER IWORK( * )
142 REAL 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* ..
157* .. Local Arrays ..
158 INTEGER ISAVE( 3 )
159* ..
160* .. External Functions ..
161 LOGICAL LSAME
162 INTEGER ISAMAX
163 REAL SLAMCH, SLANTP
164 EXTERNAL lsame, isamax, slamch, slantp
165* ..
166* .. External Subroutines ..
167 EXTERNAL slacn2, slatps, srscl, xerbla
168* ..
169* .. Intrinsic Functions ..
170 INTRINSIC abs, max, real
171* ..
172* .. Executable Statements ..
173*
174* Test the input parameters.
175*
176 info = 0
177 upper = lsame( uplo, 'U' )
178 onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
179 nounit = lsame( diag, 'N' )
180*
181 IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
182 info = -1
183 ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
184 info = -2
185 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
186 info = -3
187 ELSE IF( n.LT.0 ) THEN
188 info = -4
189 END IF
190 IF( info.NE.0 ) THEN
191 CALL xerbla( 'STPCON', -info )
192 RETURN
193 END IF
194*
195* Quick return if possible
196*
197 IF( n.EQ.0 ) THEN
198 rcond = one
199 RETURN
200 END IF
201*
202 rcond = zero
203 smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
204*
205* Compute the norm of the triangular matrix A.
206*
207 anorm = slantp( norm, uplo, diag, n, ap, work )
208*
209* Continue only if ANORM > 0.
210*
211 IF( anorm.GT.zero ) THEN
212*
213* Estimate the norm of the inverse of A.
214*
215 ainvnm = zero
216 normin = 'N'
217 IF( onenrm ) THEN
218 kase1 = 1
219 ELSE
220 kase1 = 2
221 END IF
222 kase = 0
223 10 CONTINUE
224 CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
225 IF( kase.NE.0 ) THEN
226 IF( kase.EQ.kase1 ) THEN
227*
228* Multiply by inv(A).
229*
230 CALL slatps( uplo, 'No transpose', diag, normin, n, ap,
231 \$ work, scale, work( 2*n+1 ), info )
232 ELSE
233*
234* Multiply by inv(A**T).
235*
236 CALL slatps( uplo, 'Transpose', diag, normin, n, ap,
237 \$ work, scale, work( 2*n+1 ), info )
238 END IF
239 normin = 'Y'
240*
241* Multiply by 1/SCALE if doing so will not cause overflow.
242*
243 IF( scale.NE.one ) THEN
244 ix = isamax( n, work, 1 )
245 xnorm = abs( work( ix ) )
246 IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
247 \$ GO TO 20
248 CALL srscl( n, scale, work, 1 )
249 END IF
250 GO TO 10
251 END IF
252*
253* Compute the estimate of the reciprocal condition number.
254*
255 IF( ainvnm.NE.zero )
256 \$ rcond = ( one / anorm ) / ainvnm
257 END IF
258*
259 20 CONTINUE
260 RETURN
261*
262* End of STPCON
263*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function isamax(n, sx, incx)
ISAMAX
Definition isamax.f:71
subroutine slacn2(n, v, x, isgn, est, kase, isave)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition slacn2.f:136
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slantp(norm, uplo, diag, n, ap, work)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slantp.f:124
subroutine slatps(uplo, trans, diag, normin, n, ap, x, scale, cnorm, info)
SLATPS solves a triangular system of equations with the matrix held in packed storage.
Definition slatps.f:229
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine srscl(n, sa, sx, incx)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition srscl.f:84
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