LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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

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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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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 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
subroutine srscl(N, SA, SX, INCX)
SRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: srscl.f:84
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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