LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zlacn2()

subroutine zlacn2 ( integer n,
complex*16, dimension( * ) v,
complex*16, dimension( * ) x,
double precision est,
integer kase,
integer, dimension( 3 ) isave )

ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Download ZLACN2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> ZLACN2 estimates the 1-norm of a square, complex 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N)
!>         On an intermediate return, X should be overwritten by
!>               A * X,   if KASE=1,
!>               A**H * X,  if KASE=2,
!>         where A**H is the conjugate transpose of A, and ZLACN2 must be
!>         re-called with all the other parameters unchanged.
!>
[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 ZLACN2.
!>         On exit, EST is an estimate (a lower bound) for norm(A).
!>
[in,out]KASE
!>          KASE is INTEGER
!>         On the initial call to ZLACN2, 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**H * X.
!>         On the final return from ZLACN2, KASE will again be 0.
!>
[in,out]ISAVE
!>          ISAVE is INTEGER array, dimension (3)
!>         ISAVE is used to save variables between calls to ZLACN2
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  Originally named CONEST, dated March 16, 1988.
!>
!>  Last modified:  April, 1999
!>
!>  This is a thread safe version of ZLACON, which uses the array ISAVE
!>  in place of a SAVE statement, as follows:
!>
!>     ZLACON     ZLACN2
!>      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 130 of file zlacn2.f.

131*
132* -- LAPACK auxiliary routine --
133* -- LAPACK is a software package provided by Univ. of Tennessee, --
134* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135*
136* .. Scalar Arguments ..
137 INTEGER KASE, N
138 DOUBLE PRECISION EST
139* ..
140* .. Array Arguments ..
141 INTEGER ISAVE( 3 )
142 COMPLEX*16 V( * ), X( * )
143* ..
144*
145* =====================================================================
146*
147* .. Parameters ..
148 INTEGER ITMAX
149 parameter( itmax = 5 )
150 DOUBLE PRECISION ONE, TWO
151 parameter( one = 1.0d0, two = 2.0d0 )
152 COMPLEX*16 CZERO, CONE
153 parameter( czero = ( 0.0d0, 0.0d0 ),
154 $ cone = ( 1.0d0, 0.0d0 ) )
155* ..
156* .. Local Scalars ..
157 INTEGER I, JLAST
158 DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
159* ..
160* .. External Functions ..
161 INTEGER IZMAX1
162 DOUBLE PRECISION DLAMCH, DZSUM1
163 EXTERNAL izmax1, dlamch, dzsum1
164* ..
165* .. External Subroutines ..
166 EXTERNAL zcopy
167* ..
168* .. Intrinsic Functions ..
169 INTRINSIC abs, dble, dcmplx, dimag
170* ..
171* .. Executable Statements ..
172*
173 safmin = dlamch( 'Safe minimum' )
174 IF( kase.EQ.0 ) THEN
175 DO 10 i = 1, n
176 x( i ) = dcmplx( one / dble( n ) )
177 10 CONTINUE
178 kase = 1
179 isave( 1 ) = 1
180 RETURN
181 END IF
182*
183 GO TO ( 20, 40, 70, 90, 120 )isave( 1 )
184*
185* ................ ENTRY (ISAVE( 1 ) = 1)
186* FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
187*
188 20 CONTINUE
189 IF( n.EQ.1 ) THEN
190 v( 1 ) = x( 1 )
191 est = abs( v( 1 ) )
192* ... QUIT
193 GO TO 130
194 END IF
195 est = dzsum1( n, x, 1 )
196*
197 DO 30 i = 1, n
198 absxi = abs( x( i ) )
199 IF( absxi.GT.safmin ) THEN
200 x( i ) = dcmplx( dble( x( i ) ) / absxi,
201 $ dimag( x( i ) ) / absxi )
202 ELSE
203 x( i ) = cone
204 END IF
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 CTRANS(A)*X.
212*
213 40 CONTINUE
214 isave( 2 ) = izmax1( 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 ) = czero
222 60 CONTINUE
223 x( isave( 2 ) ) = cone
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 zcopy( n, x, 1, v, 1 )
233 estold = est
234 est = dzsum1( n, v, 1 )
235*
236* TEST FOR CYCLING.
237 IF( est.LE.estold )
238 $ GO TO 100
239*
240 DO 80 i = 1, n
241 absxi = abs( x( i ) )
242 IF( absxi.GT.safmin ) THEN
243 x( i ) = dcmplx( dble( x( i ) ) / absxi,
244 $ dimag( x( i ) ) / absxi )
245 ELSE
246 x( i ) = cone
247 END IF
248 80 CONTINUE
249 kase = 2
250 isave( 1 ) = 4
251 RETURN
252*
253* ................ ENTRY (ISAVE( 1 ) = 4)
254* X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
255*
256 90 CONTINUE
257 jlast = isave( 2 )
258 isave( 2 ) = izmax1( n, x, 1 )
259 IF( ( abs( x( jlast ) ).NE.abs( x( isave( 2 ) ) ) ) .AND.
260 $ ( isave( 3 ).LT.itmax ) ) THEN
261 isave( 3 ) = isave( 3 ) + 1
262 GO TO 50
263 END IF
264*
265* ITERATION COMPLETE. FINAL STAGE.
266*
267 100 CONTINUE
268 altsgn = one
269 DO 110 i = 1, n
270 x( i ) = dcmplx( altsgn*( one+dble( i-1 ) / dble( n-1 ) ) )
271 altsgn = -altsgn
272 110 CONTINUE
273 kase = 1
274 isave( 1 ) = 5
275 RETURN
276*
277* ................ ENTRY (ISAVE( 1 ) = 5)
278* X HAS BEEN OVERWRITTEN BY A*X.
279*
280 120 CONTINUE
281 temp = two*( dzsum1( n, x, 1 ) / dble( 3*n ) )
282 IF( temp.GT.est ) THEN
283 CALL zcopy( n, x, 1, v, 1 )
284 est = temp
285 END IF
286*
287 130 CONTINUE
288 kase = 0
289 RETURN
290*
291* End of ZLACN2
292*
zcopy
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
Definition zcopy.f:81
izmax1
integer function izmax1(n, zx, incx)
IZMAX1 finds the index of the first vector element of maximum absolute value.
Definition izmax1.f:79
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dzsum1
double precision function dzsum1(n, cx, incx)
DZSUM1 forms the 1-norm of the complex vector using the true absolute value.
Definition dzsum1.f:79
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