LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dlacn2()

subroutine dlacn2 ( integer  n,
double precision, dimension( * )  v,
double precision, dimension( * )  x,
integer, dimension( * )  isgn,
double precision  est,
integer  kase,
integer, dimension( 3 )  isave 
)

DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Download DLACN2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLACN2 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 DLACN2 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 ISAVE(1) = 3, EST should be
         unchanged from the previous call to DLACN2.
         On exit, EST is an estimate (a lower bound) for norm(A).
[in,out]KASE
          KASE is INTEGER
         On the initial call to DLACN2, 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 DLACN2, KASE will again be 0.
[in,out]ISAVE
          ISAVE is INTEGER array, dimension (3)
         ISAVE is used to save variables between calls to DLACN2
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  Originally named SONEST, dated March 16, 1988.

  This is a thread safe version of DLACON, which uses the array ISAVE
  in place of a SAVE statement, as follows:

     DLACON     DLACN2
      JUMP     ISAVE(1)
      J        ISAVE(2)
      ITER     ISAVE(3)
Contributors:
Nick Higham, University of Manchester
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 135 of file dlacn2.f.

136*
137* -- LAPACK auxiliary routine --
138* -- LAPACK is a software package provided by Univ. of Tennessee, --
139* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140*
141* .. Scalar Arguments ..
142 INTEGER KASE, N
143 DOUBLE PRECISION EST
144* ..
145* .. Array Arguments ..
146 INTEGER ISGN( * ), ISAVE( 3 )
147 DOUBLE PRECISION V( * ), X( * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 INTEGER ITMAX
154 parameter( itmax = 5 )
155 DOUBLE PRECISION ZERO, ONE, TWO
156 parameter( zero = 0.0d+0, one = 1.0d+0, two = 2.0d+0 )
157* ..
158* .. Local Scalars ..
159 INTEGER I, JLAST
160 DOUBLE PRECISION ALTSGN, ESTOLD, TEMP, XS
161* ..
162* .. External Functions ..
163 INTEGER IDAMAX
164 DOUBLE PRECISION DASUM
165 EXTERNAL idamax, dasum
166* ..
167* .. External Subroutines ..
168 EXTERNAL dcopy
169* ..
170* .. Intrinsic Functions ..
171 INTRINSIC abs, dble, nint
172* ..
173* .. Executable Statements ..
174*
175 IF( kase.EQ.0 ) THEN
176 DO 10 i = 1, n
177 x( i ) = one / dble( n )
178 10 CONTINUE
179 kase = 1
180 isave( 1 ) = 1
181 RETURN
182 END IF
183*
184 GO TO ( 20, 40, 70, 110, 140 )isave( 1 )
185*
186* ................ ENTRY (ISAVE( 1 ) = 1)
187* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
188*
189 20 CONTINUE
190 IF( n.EQ.1 ) THEN
191 v( 1 ) = x( 1 )
192 est = abs( v( 1 ) )
193* ... QUIT
194 GO TO 150
195 END IF
196 est = dasum( n, x, 1 )
197*
198 DO 30 i = 1, n
199 IF( x(i).GE.zero ) THEN
200 x(i) = one
201 ELSE
202 x(i) = -one
203 END IF
204 isgn( i ) = nint( x( i ) )
205 30 CONTINUE
206 kase = 2
207 isave( 1 ) = 2
208 RETURN
209*
210* ................ ENTRY (ISAVE( 1 ) = 2)
211* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
212*
213 40 CONTINUE
214 isave( 2 ) = idamax( n, x, 1 )
215 isave( 3 ) = 2
216*
217* MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
218*
219 50 CONTINUE
220 DO 60 i = 1, n
221 x( i ) = zero
222 60 CONTINUE
223 x( isave( 2 ) ) = one
224 kase = 1
225 isave( 1 ) = 3
226 RETURN
227*
228* ................ ENTRY (ISAVE( 1 ) = 3)
229* X HAS BEEN OVERWRITTEN BY A*X.
230*
231 70 CONTINUE
232 CALL dcopy( n, x, 1, v, 1 )
233 estold = est
234 est = dasum( n, v, 1 )
235 DO 80 i = 1, n
236 IF( x(i).GE.zero ) THEN
237 xs = one
238 ELSE
239 xs = -one
240 END IF
241 IF( nint( xs ).NE.isgn( i ) )
242 $ GO TO 90
243 80 CONTINUE
244* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
245 GO TO 120
246*
247 90 CONTINUE
248* TEST FOR CYCLING.
249 IF( est.LE.estold )
250 $ GO TO 120
251*
252 DO 100 i = 1, n
253 IF( x(i).GE.zero ) THEN
254 x(i) = one
255 ELSE
256 x(i) = -one
257 END IF
258 isgn( i ) = nint( x( i ) )
259 100 CONTINUE
260 kase = 2
261 isave( 1 ) = 4
262 RETURN
263*
264* ................ ENTRY (ISAVE( 1 ) = 4)
265* X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
266*
267 110 CONTINUE
268 jlast = isave( 2 )
269 isave( 2 ) = idamax( n, x, 1 )
270 IF( ( x( jlast ).NE.abs( x( isave( 2 ) ) ) ) .AND.
271 $ ( isave( 3 ).LT.itmax ) ) THEN
272 isave( 3 ) = isave( 3 ) + 1
273 GO TO 50
274 END IF
275*
276* ITERATION COMPLETE. FINAL STAGE.
277*
278 120 CONTINUE
279 altsgn = one
280 DO 130 i = 1, n
281 x( i ) = altsgn*( one+dble( i-1 ) / dble( n-1 ) )
282 altsgn = -altsgn
283 130 CONTINUE
284 kase = 1
285 isave( 1 ) = 5
286 RETURN
287*
288* ................ ENTRY (ISAVE( 1 ) = 5)
289* X HAS BEEN OVERWRITTEN BY A*X.
290*
291 140 CONTINUE
292 temp = two*( dasum( n, x, 1 ) / dble( 3*n ) )
293 IF( temp.GT.est ) THEN
294 CALL dcopy( n, x, 1, v, 1 )
295 est = temp
296 END IF
297*
298 150 CONTINUE
299 kase = 0
300 RETURN
301*
302* End of DLACN2
303*
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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