 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dgecon()

 subroutine dgecon ( character NORM, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision ANORM, double precision RCOND, double precision, dimension( * ) WORK, integer, dimension( * ) IWORK, integer INFO )

DGECON

Purpose:
``` DGECON 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 DGETRF.

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 DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] ANORM ``` ANORM is DOUBLE PRECISION 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 DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).``` [out] WORK ` WORK is DOUBLE PRECISION 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```

Definition at line 122 of file dgecon.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  DOUBLE PRECISION ANORM, RCOND
133 * ..
134 * .. Array Arguments ..
135  INTEGER IWORK( * )
136  DOUBLE PRECISION A( LDA, * ), WORK( * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  DOUBLE PRECISION ONE, ZERO
143  parameter( one = 1.0d+0, zero = 0.0d+0 )
144 * ..
145 * .. Local Scalars ..
146  LOGICAL ONENRM
147  CHARACTER NORMIN
148  INTEGER IX, KASE, KASE1
149  DOUBLE PRECISION AINVNM, SCALE, SL, SMLNUM, SU
150 * ..
151 * .. Local Arrays ..
152  INTEGER ISAVE( 3 )
153 * ..
154 * .. External Functions ..
155  LOGICAL LSAME
156  INTEGER IDAMAX
157  DOUBLE PRECISION DLAMCH
158  EXTERNAL lsame, idamax, dlamch
159 * ..
160 * .. External Subroutines ..
161  EXTERNAL dlacn2, dlatrs, drscl, 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( 'DGECON', -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 = dlamch( '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 dlacn2( 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 dlatrs( '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 dlatrs( '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 dlatrs( '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 dlatrs( '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 = idamax( n, work, 1 )
241  IF( scale.LT.abs( work( ix ) )*smlnum .OR. scale.EQ.zero )
242  \$ GO TO 20
243  CALL drscl( 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 DGECON
257 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine drscl(N, SA, SX, INCX)
DRSCL multiplies a vector by the reciprocal of a real scalar.
Definition: drscl.f:84
subroutine dlacn2(N, V, X, ISGN, EST, KASE, ISAVE)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vec...
Definition: dlacn2.f:136
subroutine dlatrs(UPLO, TRANS, DIAG, NORMIN, N, A, LDA, X, SCALE, CNORM, INFO)
DLATRS solves a triangular system of equations with the scale factor set to prevent overflow.
Definition: dlatrs.f:238
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