1: *> \brief \b DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLACON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlacon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlacon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlacon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER KASE, N
25: * DOUBLE PRECISION EST
26: * ..
27: * .. Array Arguments ..
28: * INTEGER ISGN( * )
29: * DOUBLE PRECISION V( * ), X( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLACON estimates the 1-norm of a square, real matrix A.
39: *> Reverse communication is used for evaluating matrix-vector products.
40: *> \endverbatim
41: *
42: * Arguments:
43: * ==========
44: *
45: *> \param[in] N
46: *> \verbatim
47: *> N is INTEGER
48: *> The order of the matrix. N >= 1.
49: *> \endverbatim
50: *>
51: *> \param[out] V
52: *> \verbatim
53: *> V is DOUBLE PRECISION array, dimension (N)
54: *> On the final return, V = A*W, where EST = norm(V)/norm(W)
55: *> (W is not returned).
56: *> \endverbatim
57: *>
58: *> \param[in,out] X
59: *> \verbatim
60: *> X is DOUBLE PRECISION array, dimension (N)
61: *> On an intermediate return, X should be overwritten by
62: *> A * X, if KASE=1,
63: *> A**T * X, if KASE=2,
64: *> and DLACON must be re-called with all the other parameters
65: *> unchanged.
66: *> \endverbatim
67: *>
68: *> \param[out] ISGN
69: *> \verbatim
70: *> ISGN is INTEGER array, dimension (N)
71: *> \endverbatim
72: *>
73: *> \param[in,out] EST
74: *> \verbatim
75: *> EST is DOUBLE PRECISION
76: *> On entry with KASE = 1 or 2 and JUMP = 3, EST should be
77: *> unchanged from the previous call to DLACON.
78: *> On exit, EST is an estimate (a lower bound) for norm(A).
79: *> \endverbatim
80: *>
81: *> \param[in,out] KASE
82: *> \verbatim
83: *> KASE is INTEGER
84: *> On the initial call to DLACON, KASE should be 0.
85: *> On an intermediate return, KASE will be 1 or 2, indicating
86: *> whether X should be overwritten by A * X or A**T * X.
87: *> On the final return from DLACON, KASE will again be 0.
88: *> \endverbatim
89: *
90: * Authors:
91: * ========
92: *
93: *> \author Univ. of Tennessee
94: *> \author Univ. of California Berkeley
95: *> \author Univ. of Colorado Denver
96: *> \author NAG Ltd.
97: *
98: *> \date September 2012
99: *
100: *> \ingroup doubleOTHERauxiliary
101: *
102: *> \par Contributors:
103: * ==================
104: *>
105: *> Nick Higham, University of Manchester. \n
106: *> Originally named SONEST, dated March 16, 1988.
107: *
108: *> \par References:
109: * ================
110: *>
111: *> N.J. Higham, "FORTRAN codes for estimating the one-norm of
112: *> a real or complex matrix, with applications to condition estimation",
113: *> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
114: *>
115: * =====================================================================
116: SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
117: *
118: * -- LAPACK auxiliary routine (version 3.4.2) --
119: * -- LAPACK is a software package provided by Univ. of Tennessee, --
120: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121: * September 2012
122: *
123: * .. Scalar Arguments ..
124: INTEGER KASE, N
125: DOUBLE PRECISION EST
126: * ..
127: * .. Array Arguments ..
128: INTEGER ISGN( * )
129: DOUBLE PRECISION V( * ), X( * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: INTEGER ITMAX
136: PARAMETER ( ITMAX = 5 )
137: DOUBLE PRECISION ZERO, ONE, TWO
138: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
139: * ..
140: * .. Local Scalars ..
141: INTEGER I, ITER, J, JLAST, JUMP
142: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
143: * ..
144: * .. External Functions ..
145: INTEGER IDAMAX
146: DOUBLE PRECISION DASUM
147: EXTERNAL IDAMAX, DASUM
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL DCOPY
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC ABS, DBLE, NINT, SIGN
154: * ..
155: * .. Save statement ..
156: SAVE
157: * ..
158: * .. Executable Statements ..
159: *
160: IF( KASE.EQ.0 ) THEN
161: DO 10 I = 1, N
162: X( I ) = ONE / DBLE( N )
163: 10 CONTINUE
164: KASE = 1
165: JUMP = 1
166: RETURN
167: END IF
168: *
169: GO TO ( 20, 40, 70, 110, 140 )JUMP
170: *
171: * ................ ENTRY (JUMP = 1)
172: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
173: *
174: 20 CONTINUE
175: IF( N.EQ.1 ) THEN
176: V( 1 ) = X( 1 )
177: EST = ABS( V( 1 ) )
178: * ... QUIT
179: GO TO 150
180: END IF
181: EST = DASUM( N, X, 1 )
182: *
183: DO 30 I = 1, N
184: X( I ) = SIGN( ONE, X( I ) )
185: ISGN( I ) = NINT( X( I ) )
186: 30 CONTINUE
187: KASE = 2
188: JUMP = 2
189: RETURN
190: *
191: * ................ ENTRY (JUMP = 2)
192: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
193: *
194: 40 CONTINUE
195: J = IDAMAX( N, X, 1 )
196: ITER = 2
197: *
198: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
199: *
200: 50 CONTINUE
201: DO 60 I = 1, N
202: X( I ) = ZERO
203: 60 CONTINUE
204: X( J ) = ONE
205: KASE = 1
206: JUMP = 3
207: RETURN
208: *
209: * ................ ENTRY (JUMP = 3)
210: * X HAS BEEN OVERWRITTEN BY A*X.
211: *
212: 70 CONTINUE
213: CALL DCOPY( N, X, 1, V, 1 )
214: ESTOLD = EST
215: EST = DASUM( N, V, 1 )
216: DO 80 I = 1, N
217: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
218: $ GO TO 90
219: 80 CONTINUE
220: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
221: GO TO 120
222: *
223: 90 CONTINUE
224: * TEST FOR CYCLING.
225: IF( EST.LE.ESTOLD )
226: $ GO TO 120
227: *
228: DO 100 I = 1, N
229: X( I ) = SIGN( ONE, X( I ) )
230: ISGN( I ) = NINT( X( I ) )
231: 100 CONTINUE
232: KASE = 2
233: JUMP = 4
234: RETURN
235: *
236: * ................ ENTRY (JUMP = 4)
237: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
238: *
239: 110 CONTINUE
240: JLAST = J
241: J = IDAMAX( N, X, 1 )
242: IF( ( X( JLAST ).NE.ABS( X( J ) ) ) .AND. ( ITER.LT.ITMAX ) ) THEN
243: ITER = ITER + 1
244: GO TO 50
245: END IF
246: *
247: * ITERATION COMPLETE. FINAL STAGE.
248: *
249: 120 CONTINUE
250: ALTSGN = ONE
251: DO 130 I = 1, N
252: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
253: ALTSGN = -ALTSGN
254: 130 CONTINUE
255: KASE = 1
256: JUMP = 5
257: RETURN
258: *
259: * ................ ENTRY (JUMP = 5)
260: * X HAS BEEN OVERWRITTEN BY A*X.
261: *
262: 140 CONTINUE
263: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
264: IF( TEMP.GT.EST ) THEN
265: CALL DCOPY( N, X, 1, V, 1 )
266: EST = TEMP
267: END IF
268: *
269: 150 CONTINUE
270: KASE = 0
271: RETURN
272: *
273: * End of DLACON
274: *
275: END
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