 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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.

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.
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 *
integer function idamax(N, DX, INCX)
IDAMAX
Definition: idamax.f:71
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
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