LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ strcon()

subroutine strcon ( character  NORM,
character  UPLO,
character  DIAG,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real  RCOND,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

STRCON

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Purpose:
 STRCON estimates the reciprocal of the condition number of a
 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]A
          A is REAL array, dimension (LDA,N)
          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[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 135 of file strcon.f.

137 *
138 * -- LAPACK computational routine --
139 * -- LAPACK is a software package provided by Univ. of Tennessee, --
140 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141 *
142 * .. Scalar Arguments ..
143  CHARACTER DIAG, NORM, UPLO
144  INTEGER INFO, LDA, N
145  REAL RCOND
146 * ..
147 * .. Array Arguments ..
148  INTEGER IWORK( * )
149  REAL A( LDA, * ), WORK( * )
150 * ..
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155  REAL ONE, ZERO
156  parameter( one = 1.0e+0, zero = 0.0e+0 )
157 * ..
158 * .. Local Scalars ..
159  LOGICAL NOUNIT, ONENRM, UPPER
160  CHARACTER NORMIN
161  INTEGER IX, KASE, KASE1
162  REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
163 * ..
164 * .. Local Arrays ..
165  INTEGER ISAVE( 3 )
166 * ..
167 * .. External Functions ..
168  LOGICAL LSAME
169  INTEGER ISAMAX
170  REAL SLAMCH, SLANTR
171  EXTERNAL lsame, isamax, slamch, slantr
172 * ..
173 * .. External Subroutines ..
174  EXTERNAL slacn2, slatrs, srscl, xerbla
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max, real
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  ELSE IF( lda.LT.max( 1, n ) ) THEN
197  info = -6
198  END IF
199  IF( info.NE.0 ) THEN
200  CALL xerbla( 'STRCON', -info )
201  RETURN
202  END IF
203 *
204 * Quick return if possible
205 *
206  IF( n.EQ.0 ) THEN
207  rcond = one
208  RETURN
209  END IF
210 *
211  rcond = zero
212  smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
213 *
214 * Compute the norm of the triangular matrix A.
215 *
216  anorm = slantr( norm, uplo, diag, n, n, a, lda, work )
217 *
218 * Continue only if ANORM > 0.
219 *
220  IF( anorm.GT.zero ) THEN
221 *
222 * Estimate the norm of the inverse of A.
223 *
224  ainvnm = zero
225  normin = 'N'
226  IF( onenrm ) THEN
227  kase1 = 1
228  ELSE
229  kase1 = 2
230  END IF
231  kase = 0
232  10 CONTINUE
233  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
234  IF( kase.NE.0 ) THEN
235  IF( kase.EQ.kase1 ) THEN
236 *
237 * Multiply by inv(A).
238 *
239  CALL slatrs( uplo, 'No transpose', diag, normin, n, a,
240  $ lda, work, scale, work( 2*n+1 ), info )
241  ELSE
242 *
243 * Multiply by inv(A**T).
244 *
245  CALL slatrs( uplo, 'Transpose', diag, normin, n, a, lda,
246  $ work, scale, work( 2*n+1 ), info )
247  END IF
248  normin = 'Y'
249 *
250 * Multiply by 1/SCALE if doing so will not cause overflow.
251 *
252  IF( scale.NE.one ) THEN
253  ix = isamax( n, work, 1 )
254  xnorm = abs( work( ix ) )
255  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
256  $ GO TO 20
257  CALL srscl( n, scale, work, 1 )
258  END IF
259  GO TO 10
260  END IF
261 *
262 * Compute the estimate of the reciprocal condition number.
263 *
264  IF( ainvnm.NE.zero )
265  $ rcond = ( one / anorm ) / ainvnm
266  END IF
267 *
268  20 CONTINUE
269  RETURN
270 *
271 * End of STRCON
272 *
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 slatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
SLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: slatrs.f:238
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 slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantr.f:141
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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