 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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```
Date
November 2011

Definition at line 132 of file stpcon.f.

132 *
133 * -- LAPACK computational routine (version 3.4.0) --
134 * -- LAPACK is a software package provided by Univ. of Tennessee, --
135 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136 * November 2011
137 *
138 * .. Scalar Arguments ..
139  CHARACTER diag, norm, uplo
140  INTEGER info, n
141  REAL rcond
142 * ..
143 * .. Array Arguments ..
144  INTEGER iwork( * )
145  REAL ap( * ), work( * )
146 * ..
147 *
148 * =====================================================================
149 *
150 * .. Parameters ..
151  REAL one, zero
152  parameter ( one = 1.0e+0, zero = 0.0e+0 )
153 * ..
154 * .. Local Scalars ..
155  LOGICAL nounit, onenrm, upper
156  CHARACTER normin
157  INTEGER ix, kase, kase1
158  REAL ainvnm, anorm, scale, smlnum, xnorm
159 * ..
160 * .. Local Arrays ..
161  INTEGER isave( 3 )
162 * ..
163 * .. External Functions ..
164  LOGICAL lsame
165  INTEGER isamax
166  REAL slamch, slantp
167  EXTERNAL lsame, isamax, slamch, slantp
168 * ..
169 * .. External Subroutines ..
170  EXTERNAL slacn2, slatps, srscl, xerbla
171 * ..
172 * .. Intrinsic Functions ..
173  INTRINSIC abs, max, real
174 * ..
175 * .. Executable Statements ..
176 *
177 * Test the input parameters.
178 *
179  info = 0
180  upper = lsame( uplo, 'U' )
181  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
182  nounit = lsame( diag, 'N' )
183 *
184  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
185  info = -1
186  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
187  info = -2
188  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
189  info = -3
190  ELSE IF( n.LT.0 ) THEN
191  info = -4
192  END IF
193  IF( info.NE.0 ) THEN
194  CALL xerbla( 'STPCON', -info )
195  RETURN
196  END IF
197 *
198 * Quick return if possible
199 *
200  IF( n.EQ.0 ) THEN
201  rcond = one
202  RETURN
203  END IF
204 *
205  rcond = zero
206  smlnum = slamch( 'Safe minimum' )*REAL( MAX( 1, N ) )
207 *
208 * Compute the norm of the triangular matrix A.
209 *
210  anorm = slantp( norm, uplo, diag, n, ap, work )
211 *
212 * Continue only if ANORM > 0.
213 *
214  IF( anorm.GT.zero ) THEN
215 *
216 * Estimate the norm of the inverse of A.
217 *
218  ainvnm = zero
219  normin = 'N'
220  IF( onenrm ) THEN
221  kase1 = 1
222  ELSE
223  kase1 = 2
224  END IF
225  kase = 0
226  10 CONTINUE
227  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
228  IF( kase.NE.0 ) THEN
229  IF( kase.EQ.kase1 ) THEN
230 *
231 * Multiply by inv(A).
232 *
233  CALL slatps( uplo, 'No transpose', diag, normin, n, ap,
234  \$ work, scale, work( 2*n+1 ), info )
235  ELSE
236 *
237 * Multiply by inv(A**T).
238 *
239  CALL slatps( uplo, 'Transpose', diag, normin, n, ap,
240  \$ work, scale, work( 2*n+1 ), info )
241  END IF
242  normin = 'Y'
243 *
244 * Multiply by 1/SCALE if doing so will not cause overflow.
245 *
246  IF( scale.NE.one ) THEN
247  ix = isamax( n, work, 1 )
248  xnorm = abs( work( ix ) )
249  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
250  \$ GO TO 20
251  CALL srscl( n, scale, work, 1 )
252  END IF
253  GO TO 10
254  END IF
255 *
256 * Compute the estimate of the reciprocal condition number.
257 *
258  IF( ainvnm.NE.zero )
259  \$ rcond = ( one / anorm ) / ainvnm
260  END IF
261 *
262  20 CONTINUE
263  RETURN
264 *
265 * End of STPCON
266 *
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:86
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:231
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:53
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:138
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, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: slantp.f:126
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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