LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ sgecon()

subroutine sgecon ( character  NORM,
integer  N,
real, dimension( lda, * )  A,
integer  LDA,
real  ANORM,
real  RCOND,
real, dimension( * )  WORK,
integer, dimension( * )  IWORK,
integer  INFO 
)

SGECON

Download SGECON + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 SGECON estimates the reciprocal of the condition number of a general
 real matrix A, in either the 1-norm or the infinity-norm, using
 the LU factorization computed by SGETRF.

 An estimate is obtained for norm(inv(A)), and 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]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]A
          A is REAL array, dimension (LDA,N)
          The factors L and U from the factorization A = P*L*U
          as computed by SGETRF.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in]ANORM
          ANORM is REAL
          If NORM = '1' or 'O', the 1-norm of the original matrix A.
          If NORM = 'I', the infinity-norm of the original matrix A.
[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 (4*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 122 of file sgecon.f.

124 *
125 * -- LAPACK computational routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER NORM
131  INTEGER INFO, LDA, N
132  REAL ANORM, RCOND
133 * ..
134 * .. Array Arguments ..
135  INTEGER IWORK( * )
136  REAL A( LDA, * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL ONE, ZERO
143  parameter( one = 1.0e+0, zero = 0.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL ONENRM
147  CHARACTER NORMIN
148  INTEGER IX, KASE, KASE1
149  REAL AINVNM, SCALE, SL, SMLNUM, SU
150 * ..
151 * .. Local Arrays ..
152  INTEGER ISAVE( 3 )
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME
156  INTEGER ISAMAX
157  REAL SLAMCH
158  EXTERNAL lsame, isamax, slamch
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL slacn2, slatrs, srscl, xerbla
162 * ..
163 * .. Intrinsic Functions ..
164  INTRINSIC abs, max
165 * ..
166 * .. Executable Statements ..
167 *
168 * Test the input parameters.
169 *
170  info = 0
171  onenrm = norm.EQ.'1' .OR. lsame( norm, 'O' )
172  IF( .NOT.onenrm .AND. .NOT.lsame( norm, 'I' ) ) THEN
173  info = -1
174  ELSE IF( n.LT.0 ) THEN
175  info = -2
176  ELSE IF( lda.LT.max( 1, n ) ) THEN
177  info = -4
178  ELSE IF( anorm.LT.zero ) THEN
179  info = -5
180  END IF
181  IF( info.NE.0 ) THEN
182  CALL xerbla( 'SGECON', -info )
183  RETURN
184  END IF
185 *
186 * Quick return if possible
187 *
188  rcond = zero
189  IF( n.EQ.0 ) THEN
190  rcond = one
191  RETURN
192  ELSE IF( anorm.EQ.zero ) THEN
193  RETURN
194  END IF
195 *
196  smlnum = slamch( 'Safe minimum' )
197 *
198 * Estimate the norm of inv(A).
199 *
200  ainvnm = zero
201  normin = 'N'
202  IF( onenrm ) THEN
203  kase1 = 1
204  ELSE
205  kase1 = 2
206  END IF
207  kase = 0
208  10 CONTINUE
209  CALL slacn2( n, work( n+1 ), work, iwork, ainvnm, kase, isave )
210  IF( kase.NE.0 ) THEN
211  IF( kase.EQ.kase1 ) THEN
212 *
213 * Multiply by inv(L).
214 *
215  CALL slatrs( 'Lower', 'No transpose', 'Unit', normin, n, a,
216  $ lda, work, sl, work( 2*n+1 ), info )
217 *
218 * Multiply by inv(U).
219 *
220  CALL slatrs( 'Upper', 'No transpose', 'Non-unit', normin, n,
221  $ a, lda, work, su, work( 3*n+1 ), info )
222  ELSE
223 *
224 * Multiply by inv(U**T).
225 *
226  CALL slatrs( 'Upper', 'Transpose', 'Non-unit', normin, n, a,
227  $ lda, work, su, work( 3*n+1 ), info )
228 *
229 * Multiply by inv(L**T).
230 *
231  CALL slatrs( 'Lower', 'Transpose', 'Unit', normin, n, a,
232  $ lda, work, sl, work( 2*n+1 ), info )
233  END IF
234 *
235 * Divide X by 1/(SL*SU) if doing so will not cause overflow.
236 *
237  scale = sl*su
238  normin = 'Y'
239  IF( scale.NE.one ) THEN
240  ix = isamax( n, work, 1 )
241  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
242  $ GO TO 20
243  CALL srscl( n, scale, work, 1 )
244  END IF
245  GO TO 10
246  END IF
247 *
248 * Compute the estimate of the reciprocal condition number.
249 *
250  IF( ainvnm.NE.zero )
251  $ rcond = ( one / ainvnm ) / anorm
252 *
253  20 CONTINUE
254  RETURN
255 *
256 * End of SGECON
257 *
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
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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