LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ slacon()

subroutine slacon ( integer  N,
real, dimension( * )  V,
real, dimension( * )  X,
integer, dimension( * )  ISGN,
real  EST,
integer  KASE 
)

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

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Purpose:
 SLACON 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 REAL 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 REAL array, dimension (N)
         On an intermediate return, X should be overwritten by
               A * X,   if KASE=1,
               A**T * X,  if KASE=2,
         and SLACON must be re-called with all the other parameters
         unchanged.
[out]ISGN
          ISGN is INTEGER array, dimension (N)
[in,out]EST
          EST is REAL
         On entry with KASE = 1 or 2 and JUMP = 3, EST should be
         unchanged from the previous call to SLACON.
         On exit, EST is an estimate (a lower bound) for norm(A).
[in,out]KASE
          KASE is INTEGER
         On the initial call to SLACON, 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 SLACON, 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 slacon.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  REAL EST
123 * ..
124 * .. Array Arguments ..
125  INTEGER ISGN( * )
126  REAL V( * ), X( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  INTEGER ITMAX
133  parameter( itmax = 5 )
134  REAL ZERO, ONE, TWO
135  parameter( zero = 0.0e+0, one = 1.0e+0, two = 2.0e+0 )
136 * ..
137 * .. Local Scalars ..
138  INTEGER I, ITER, J, JLAST, JUMP
139  REAL ALTSGN, ESTOLD, TEMP
140 * ..
141 * .. External Functions ..
142  INTEGER ISAMAX
143  REAL SASUM
144  EXTERNAL isamax, sasum
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL scopy
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC abs, nint, real, 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 / real( 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 = sasum( 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 = isamax( 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 scopy( n, x, 1, v, 1 )
211  estold = est
212  est = sasum( 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 = isamax( 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+real( i-1 ) / real( 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*( sasum( n, x, 1 ) / real( 3*n ) )
261  IF( temp.GT.est ) THEN
262  CALL scopy( n, x, 1, v, 1 )
263  est = temp
264  END IF
265 *
266  150 CONTINUE
267  kase = 0
268  RETURN
269 *
270 * End of SLACON
271 *
integer function isamax(N, SX, INCX)
ISAMAX
Definition: isamax.f:71
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
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