 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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.

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
Further Details:
Originally named CONEST, dated March 16, 1988.

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 132 of file zlacn2.f.

133 *
134 * -- LAPACK auxiliary routine --
135 * -- LAPACK is a software package provided by Univ. of Tennessee, --
136 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
137 *
138 * .. Scalar Arguments ..
139  INTEGER KASE, N
140  DOUBLE PRECISION EST
141 * ..
142 * .. Array Arguments ..
143  INTEGER ISAVE( 3 )
144  COMPLEX*16 V( * ), X( * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Parameters ..
150  INTEGER ITMAX
151  parameter( itmax = 5 )
152  DOUBLE PRECISION ONE, TWO
153  parameter( one = 1.0d0, two = 2.0d0 )
154  COMPLEX*16 CZERO, CONE
155  parameter( czero = ( 0.0d0, 0.0d0 ),
156  \$ cone = ( 1.0d0, 0.0d0 ) )
157 * ..
158 * .. Local Scalars ..
159  INTEGER I, JLAST
160  DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
161 * ..
162 * .. External Functions ..
163  INTEGER IZMAX1
164  DOUBLE PRECISION DLAMCH, DZSUM1
165  EXTERNAL izmax1, dlamch, dzsum1
166 * ..
167 * .. External Subroutines ..
168  EXTERNAL zcopy
169 * ..
170 * .. Intrinsic Functions ..
171  INTRINSIC abs, dble, dcmplx, dimag
172 * ..
173 * .. Executable Statements ..
174 *
175  safmin = dlamch( 'Safe minimum' )
176  IF( kase.EQ.0 ) THEN
177  DO 10 i = 1, n
178  x( i ) = dcmplx( one / dble( n ) )
179  10 CONTINUE
180  kase = 1
181  isave( 1 ) = 1
182  RETURN
183  END IF
184 *
185  GO TO ( 20, 40, 70, 90, 120 )isave( 1 )
186 *
187 * ................ ENTRY (ISAVE( 1 ) = 1)
188 * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
189 *
190  20 CONTINUE
191  IF( n.EQ.1 ) THEN
192  v( 1 ) = x( 1 )
193  est = abs( v( 1 ) )
194 * ... QUIT
195  GO TO 130
196  END IF
197  est = dzsum1( n, x, 1 )
198 *
199  DO 30 i = 1, n
200  absxi = abs( x( i ) )
201  IF( absxi.GT.safmin ) THEN
202  x( i ) = dcmplx( dble( x( i ) ) / absxi,
203  \$ dimag( x( i ) ) / absxi )
204  ELSE
205  x( i ) = cone
206  END IF
207  30 CONTINUE
208  kase = 2
209  isave( 1 ) = 2
210  RETURN
211 *
212 * ................ ENTRY (ISAVE( 1 ) = 2)
213 * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
214 *
215  40 CONTINUE
216  isave( 2 ) = izmax1( n, x, 1 )
217  isave( 3 ) = 2
218 *
219 * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
220 *
221  50 CONTINUE
222  DO 60 i = 1, n
223  x( i ) = czero
224  60 CONTINUE
225  x( isave( 2 ) ) = cone
226  kase = 1
227  isave( 1 ) = 3
228  RETURN
229 *
230 * ................ ENTRY (ISAVE( 1 ) = 3)
231 * X HAS BEEN OVERWRITTEN BY A*X.
232 *
233  70 CONTINUE
234  CALL zcopy( n, x, 1, v, 1 )
235  estold = est
236  est = dzsum1( n, v, 1 )
237 *
238 * TEST FOR CYCLING.
239  IF( est.LE.estold )
240  \$ GO TO 100
241 *
242  DO 80 i = 1, n
243  absxi = abs( x( i ) )
244  IF( absxi.GT.safmin ) THEN
245  x( i ) = dcmplx( dble( x( i ) ) / absxi,
246  \$ dimag( x( i ) ) / absxi )
247  ELSE
248  x( i ) = cone
249  END IF
250  80 CONTINUE
251  kase = 2
252  isave( 1 ) = 4
253  RETURN
254 *
255 * ................ ENTRY (ISAVE( 1 ) = 4)
256 * X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
257 *
258  90 CONTINUE
259  jlast = isave( 2 )
260  isave( 2 ) = izmax1( n, x, 1 )
261  IF( ( abs( x( jlast ) ).NE.abs( x( isave( 2 ) ) ) ) .AND.
262  \$ ( isave( 3 ).LT.itmax ) ) THEN
263  isave( 3 ) = isave( 3 ) + 1
264  GO TO 50
265  END IF
266 *
267 * ITERATION COMPLETE. FINAL STAGE.
268 *
269  100 CONTINUE
270  altsgn = one
271  DO 110 i = 1, n
272  x( i ) = dcmplx( altsgn*( one+dble( i-1 ) / dble( n-1 ) ) )
273  altsgn = -altsgn
274  110 CONTINUE
275  kase = 1
276  isave( 1 ) = 5
277  RETURN
278 *
279 * ................ ENTRY (ISAVE( 1 ) = 5)
280 * X HAS BEEN OVERWRITTEN BY A*X.
281 *
282  120 CONTINUE
283  temp = two*( dzsum1( n, x, 1 ) / dble( 3*n ) )
284  IF( temp.GT.est ) THEN
285  CALL zcopy( n, x, 1, v, 1 )
286  est = temp
287  END IF
288 *
289  130 CONTINUE
290  kase = 0
291  RETURN
292 *
293 * End of ZLACN2
294 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
double precision function dzsum1(N, CX, INCX)
DZSUM1 forms the 1-norm of the complex vector using the true absolute value.
Definition: dzsum1.f:81
integer function izmax1(N, ZX, INCX)
IZMAX1 finds the index of the first vector element of maximum absolute value.
Definition: izmax1.f:81
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