LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlacon()

subroutine dlacon ( integer  n,
double precision, dimension( * )  v,
double precision, dimension( * )  x,
integer, dimension( * )  isgn,
double precision  est,
integer  kase 
)

DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

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

Purpose:
 DLACON estimates the 1-norm of a square, real matrix A.
 Reverse communication is used for evaluating matrix-vector products.
Parameters
[in]N
          N is INTEGER
         The order of the matrix.  N >= 1.
[out]V
          V is DOUBLE PRECISION array, dimension (N)
         On the final return, V = A*W,  where  EST = norm(V)/norm(W)
         (W is not returned).
[in,out]X
          X is DOUBLE PRECISION array, dimension (N)
         On an intermediate return, X should be overwritten by
               A * X,   if KASE=1,
               A**T * X,  if KASE=2,
         and DLACON must be re-called with all the other parameters
         unchanged.
[out]ISGN
          ISGN is INTEGER array, dimension (N)
[in,out]EST
          EST is DOUBLE PRECISION
         On entry with KASE = 1 or 2 and JUMP = 3, EST should be
         unchanged from the previous call to DLACON.
         On exit, EST is an estimate (a lower bound) for norm(A).
[in,out]KASE
          KASE is INTEGER
         On the initial call to DLACON, KASE should be 0.
         On an intermediate return, KASE will be 1 or 2, indicating
         whether X should be overwritten by A * X  or A**T * X.
         On the final return from DLACON, KASE will again be 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Nick Higham, University of Manchester.
Originally named SONEST, dated March 16, 1988.
References:
N.J. Higham, "FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 114 of file dlacon.f.

115*
116* -- LAPACK auxiliary routine --
117* -- LAPACK is a software package provided by Univ. of Tennessee, --
118* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119*
120* .. Scalar Arguments ..
121 INTEGER KASE, N
122 DOUBLE PRECISION EST
123* ..
124* .. Array Arguments ..
125 INTEGER ISGN( * )
126 DOUBLE PRECISION V( * ), X( * )
127* ..
128*
129* =====================================================================
130*
131* .. Parameters ..
132 INTEGER ITMAX
133 parameter( itmax = 5 )
134 DOUBLE PRECISION ZERO, ONE, TWO
135 parameter( zero = 0.0d+0, one = 1.0d+0, two = 2.0d+0 )
136* ..
137* .. Local Scalars ..
138 INTEGER I, ITER, J, JLAST, JUMP
139 DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
140* ..
141* .. External Functions ..
142 INTEGER IDAMAX
143 DOUBLE PRECISION DASUM
144 EXTERNAL idamax, dasum
145* ..
146* .. External Subroutines ..
147 EXTERNAL dcopy
148* ..
149* .. Intrinsic Functions ..
150 INTRINSIC abs, dble, nint, sign
151* ..
152* .. Save statement ..
153 SAVE
154* ..
155* .. Executable Statements ..
156*
157 IF( kase.EQ.0 ) THEN
158 DO 10 i = 1, n
159 x( i ) = one / dble( n )
160 10 CONTINUE
161 kase = 1
162 jump = 1
163 RETURN
164 END IF
165*
166 GO TO ( 20, 40, 70, 110, 140 )jump
167*
168* ................ ENTRY (JUMP = 1)
169* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
170*
171 20 CONTINUE
172 IF( n.EQ.1 ) THEN
173 v( 1 ) = x( 1 )
174 est = abs( v( 1 ) )
175* ... QUIT
176 GO TO 150
177 END IF
178 est = dasum( n, x, 1 )
179*
180 DO 30 i = 1, n
181 x( i ) = sign( one, x( i ) )
182 isgn( i ) = nint( x( i ) )
183 30 CONTINUE
184 kase = 2
185 jump = 2
186 RETURN
187*
188* ................ ENTRY (JUMP = 2)
189* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
190*
191 40 CONTINUE
192 j = idamax( n, x, 1 )
193 iter = 2
194*
195* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
196*
197 50 CONTINUE
198 DO 60 i = 1, n
199 x( i ) = zero
200 60 CONTINUE
201 x( j ) = one
202 kase = 1
203 jump = 3
204 RETURN
205*
206* ................ ENTRY (JUMP = 3)
207* X HAS BEEN OVERWRITTEN BY A*X.
208*
209 70 CONTINUE
210 CALL dcopy( n, x, 1, v, 1 )
211 estold = est
212 est = dasum( n, v, 1 )
213 DO 80 i = 1, n
214 IF( nint( sign( one, x( i ) ) ).NE.isgn( i ) )
215 $ GO TO 90
216 80 CONTINUE
217* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
218 GO TO 120
219*
220 90 CONTINUE
221* TEST FOR CYCLING.
222 IF( est.LE.estold )
223 $ GO TO 120
224*
225 DO 100 i = 1, n
226 x( i ) = sign( one, x( i ) )
227 isgn( i ) = nint( x( i ) )
228 100 CONTINUE
229 kase = 2
230 jump = 4
231 RETURN
232*
233* ................ ENTRY (JUMP = 4)
234* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
235*
236 110 CONTINUE
237 jlast = j
238 j = idamax( n, x, 1 )
239 IF( ( x( jlast ).NE.abs( x( j ) ) ) .AND. ( iter.LT.itmax ) ) THEN
240 iter = iter + 1
241 GO TO 50
242 END IF
243*
244* ITERATION COMPLETE. FINAL STAGE.
245*
246 120 CONTINUE
247 altsgn = one
248 DO 130 i = 1, n
249 x( i ) = altsgn*( one+dble( i-1 ) / dble( n-1 ) )
250 altsgn = -altsgn
251 130 CONTINUE
252 kase = 1
253 jump = 5
254 RETURN
255*
256* ................ ENTRY (JUMP = 5)
257* X HAS BEEN OVERWRITTEN BY A*X.
258*
259 140 CONTINUE
260 temp = two*( dasum( n, x, 1 ) / dble( 3*n ) )
261 IF( temp.GT.est ) THEN
262 CALL dcopy( n, x, 1, v, 1 )
263 est = temp
264 END IF
265*
266 150 CONTINUE
267 kase = 0
268 RETURN
269*
270* End of DLACON
271*
dasum
double precision function dasum(n, dx, incx)
DASUM
Definition dasum.f:71
dcopy
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
idamax
integer function idamax(n, dx, incx)
IDAMAX
Definition idamax.f:71
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