LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ stbcon()

subroutine stbcon ( character  NORM,
character  UPLO,
character  DIAG,
integer  N,
integer  KD,
real, dimension( ldab, * )  AB,
integer  LDAB,
real  RCOND,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

STBCON

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Purpose:
 STBCON estimates the reciprocal of the condition number of a
 triangular band 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]KD
          KD is INTEGER
          The number of superdiagonals or subdiagonals of the
          triangular band matrix A.  KD >= 0.
[in]AB
          AB is REAL array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first kd+1 rows of the array. The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
          If DIAG = 'U', the diagonal elements of A are not referenced
          and are assumed to be 1.
[in]LDAB
          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= KD+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 141 of file stbcon.f.

143 *
144 * -- LAPACK computational routine --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 *
148 * .. Scalar Arguments ..
149  CHARACTER DIAG, NORM, UPLO
150  INTEGER INFO, KD, LDAB, N
151  REAL RCOND
152 * ..
153 * .. Array Arguments ..
154  INTEGER IWORK( * )
155  REAL AB( LDAB, * ), WORK( * )
156 * ..
157 *
158 * =====================================================================
159 *
160 * .. Parameters ..
161  REAL ONE, ZERO
162  parameter( one = 1.0e+0, zero = 0.0e+0 )
163 * ..
164 * .. Local Scalars ..
165  LOGICAL NOUNIT, ONENRM, UPPER
166  CHARACTER NORMIN
167  INTEGER IX, KASE, KASE1
168  REAL AINVNM, ANORM, SCALE, SMLNUM, XNORM
169 * ..
170 * .. Local Arrays ..
171  INTEGER ISAVE( 3 )
172 * ..
173 * .. External Functions ..
174  LOGICAL LSAME
175  INTEGER ISAMAX
176  REAL SLAMCH, SLANTB
177  EXTERNAL lsame, isamax, slamch, slantb
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL slacn2, slatbs, srscl, xerbla
181 * ..
182 * .. Intrinsic Functions ..
183  INTRINSIC abs, max, real
184 * ..
185 * .. Executable Statements ..
186 *
187 * Test the input parameters.
188 *
189  info = 0
190  upper = lsame( uplo, 'U' )
191  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
192  nounit = lsame( diag, 'N' )
193 *
194  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
195  info = -1
196  ELSE IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
197  info = -2
198  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
199  info = -3
200  ELSE IF( n.LT.0 ) THEN
201  info = -4
202  ELSE IF( kd.LT.0 ) THEN
203  info = -5
204  ELSE IF( ldab.LT.kd+1 ) THEN
205  info = -7
206  END IF
207  IF( info.NE.0 ) THEN
208  CALL xerbla( 'STBCON', -info )
209  RETURN
210  END IF
211 *
212 * Quick return if possible
213 *
214  IF( n.EQ.0 ) THEN
215  rcond = one
216  RETURN
217  END IF
218 *
219  rcond = zero
220  smlnum = slamch( 'Safe minimum' )*real( max( 1, n ) )
221 *
222 * Compute the norm of the triangular matrix A.
223 *
224  anorm = slantb( norm, uplo, diag, n, kd, ab, ldab, work )
225 *
226 * Continue only if ANORM > 0.
227 *
228  IF( anorm.GT.zero ) THEN
229 *
230 * Estimate the norm of the inverse of A.
231 *
232  ainvnm = zero
233  normin = 'N'
234  IF( onenrm ) THEN
235  kase1 = 1
236  ELSE
237  kase1 = 2
238  END IF
239  kase = 0
240  10 CONTINUE
241  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
242  IF( kase.NE.0 ) THEN
243  IF( kase.EQ.kase1 ) THEN
244 *
245 * Multiply by inv(A).
246 *
247  CALL slatbs( uplo, 'No transpose', diag, normin, n, kd,
248  $ ab, ldab, work, scale, work( 2*n+1 ), info )
249  ELSE
250 *
251 * Multiply by inv(A**T).
252 *
253  CALL slatbs( uplo, 'Transpose', diag, normin, n, kd, ab,
254  $ ldab, work, scale, work( 2*n+1 ), info )
255  END IF
256  normin = 'Y'
257 *
258 * Multiply by 1/SCALE if doing so will not cause overflow.
259 *
260  IF( scale.NE.one ) THEN
261  ix = isamax( n, work, 1 )
262  xnorm = abs( work( ix ) )
263  IF( scale.LT.xnorm*smlnum .OR. scale.EQ.zero )
264  $ GO TO 20
265  CALL srscl( n, scale, work, 1 )
266  END IF
267  GO TO 10
268  END IF
269 *
270 * Compute the estimate of the reciprocal condition number.
271 *
272  IF( ainvnm.NE.zero )
273  $ rcond = ( one / anorm ) / ainvnm
274  END IF
275 *
276  20 CONTINUE
277  RETURN
278 *
279 * End of STBCON
280 *
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
subroutine slatbs(UPLO, TRANS, DIAG, NORMIN, N, KD, AB, LDAB, X, SCALE, CNORM, INFO)
SLATBS solves a triangular banded system of equations.
Definition: slatbs.f:242
real function slantb(NORM, UPLO, DIAG, N, K, AB, LDAB, WORK)
SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantb.f:140
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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