1: *> \brief \b DLACN2 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 DLACN2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlacn2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlacn2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlacn2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER KASE, N
25: * DOUBLE PRECISION EST
26: * ..
27: * .. Array Arguments ..
28: * INTEGER ISGN( * ), ISAVE( 3 )
29: * DOUBLE PRECISION V( * ), X( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLACN2 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 DLACN2 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 ISAVE(1) = 3, EST should be
77: *> unchanged from the previous call to DLACN2.
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 DLACN2, 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 DLACN2, KASE will again be 0.
88: *> \endverbatim
89: *>
90: *> \param[in,out] ISAVE
91: *> \verbatim
92: *> ISAVE is INTEGER array, dimension (3)
93: *> ISAVE is used to save variables between calls to DLACN2
94: *> \endverbatim
95: *
96: * Authors:
97: * ========
98: *
99: *> \author Univ. of Tennessee
100: *> \author Univ. of California Berkeley
101: *> \author Univ. of Colorado Denver
102: *> \author NAG Ltd.
103: *
104: *> \date September 2012
105: *
106: *> \ingroup doubleOTHERauxiliary
107: *
108: *> \par Further Details:
109: * =====================
110: *>
111: *> \verbatim
112: *>
113: *> Originally named SONEST, dated March 16, 1988.
114: *>
115: *> This is a thread safe version of DLACON, which uses the array ISAVE
116: *> in place of a SAVE statement, as follows:
117: *>
118: *> DLACON DLACN2
119: *> JUMP ISAVE(1)
120: *> J ISAVE(2)
121: *> ITER ISAVE(3)
122: *> \endverbatim
123: *
124: *> \par Contributors:
125: * ==================
126: *>
127: *> Nick Higham, University of Manchester
128: *
129: *> \par References:
130: * ================
131: *>
132: *> N.J. Higham, "FORTRAN codes for estimating the one-norm of
133: *> a real or complex matrix, with applications to condition estimation",
134: *> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
135: *>
136: * =====================================================================
137: SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
138: *
139: * -- LAPACK auxiliary routine (version 3.4.2) --
140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142: * September 2012
143: *
144: * .. Scalar Arguments ..
145: INTEGER KASE, N
146: DOUBLE PRECISION EST
147: * ..
148: * .. Array Arguments ..
149: INTEGER ISGN( * ), ISAVE( 3 )
150: DOUBLE PRECISION V( * ), X( * )
151: * ..
152: *
153: * =====================================================================
154: *
155: * .. Parameters ..
156: INTEGER ITMAX
157: PARAMETER ( ITMAX = 5 )
158: DOUBLE PRECISION ZERO, ONE, TWO
159: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
160: * ..
161: * .. Local Scalars ..
162: INTEGER I, JLAST
163: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
164: * ..
165: * .. External Functions ..
166: INTEGER IDAMAX
167: DOUBLE PRECISION DASUM
168: EXTERNAL IDAMAX, DASUM
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL DCOPY
172: * ..
173: * .. Intrinsic Functions ..
174: INTRINSIC ABS, DBLE, NINT, SIGN
175: * ..
176: * .. Executable Statements ..
177: *
178: IF( KASE.EQ.0 ) THEN
179: DO 10 I = 1, N
180: X( I ) = ONE / DBLE( N )
181: 10 CONTINUE
182: KASE = 1
183: ISAVE( 1 ) = 1
184: RETURN
185: END IF
186: *
187: GO TO ( 20, 40, 70, 110, 140 )ISAVE( 1 )
188: *
189: * ................ ENTRY (ISAVE( 1 ) = 1)
190: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
191: *
192: 20 CONTINUE
193: IF( N.EQ.1 ) THEN
194: V( 1 ) = X( 1 )
195: EST = ABS( V( 1 ) )
196: * ... QUIT
197: GO TO 150
198: END IF
199: EST = DASUM( N, X, 1 )
200: *
201: DO 30 I = 1, N
202: X( I ) = SIGN( ONE, X( I ) )
203: ISGN( I ) = NINT( X( I ) )
204: 30 CONTINUE
205: KASE = 2
206: ISAVE( 1 ) = 2
207: RETURN
208: *
209: * ................ ENTRY (ISAVE( 1 ) = 2)
210: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
211: *
212: 40 CONTINUE
213: ISAVE( 2 ) = IDAMAX( N, X, 1 )
214: ISAVE( 3 ) = 2
215: *
216: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
217: *
218: 50 CONTINUE
219: DO 60 I = 1, N
220: X( I ) = ZERO
221: 60 CONTINUE
222: X( ISAVE( 2 ) ) = ONE
223: KASE = 1
224: ISAVE( 1 ) = 3
225: RETURN
226: *
227: * ................ ENTRY (ISAVE( 1 ) = 3)
228: * X HAS BEEN OVERWRITTEN BY A*X.
229: *
230: 70 CONTINUE
231: CALL DCOPY( N, X, 1, V, 1 )
232: ESTOLD = EST
233: EST = DASUM( N, V, 1 )
234: DO 80 I = 1, N
235: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
236: $ GO TO 90
237: 80 CONTINUE
238: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
239: GO TO 120
240: *
241: 90 CONTINUE
242: * TEST FOR CYCLING.
243: IF( EST.LE.ESTOLD )
244: $ GO TO 120
245: *
246: DO 100 I = 1, N
247: X( I ) = SIGN( ONE, X( I ) )
248: ISGN( I ) = NINT( X( I ) )
249: 100 CONTINUE
250: KASE = 2
251: ISAVE( 1 ) = 4
252: RETURN
253: *
254: * ................ ENTRY (ISAVE( 1 ) = 4)
255: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
256: *
257: 110 CONTINUE
258: JLAST = ISAVE( 2 )
259: ISAVE( 2 ) = IDAMAX( N, X, 1 )
260: IF( ( X( JLAST ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
261: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
262: ISAVE( 3 ) = ISAVE( 3 ) + 1
263: GO TO 50
264: END IF
265: *
266: * ITERATION COMPLETE. FINAL STAGE.
267: *
268: 120 CONTINUE
269: ALTSGN = ONE
270: DO 130 I = 1, N
271: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
272: ALTSGN = -ALTSGN
273: 130 CONTINUE
274: KASE = 1
275: ISAVE( 1 ) = 5
276: RETURN
277: *
278: * ................ ENTRY (ISAVE( 1 ) = 5)
279: * X HAS BEEN OVERWRITTEN BY A*X.
280: *
281: 140 CONTINUE
282: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
283: IF( TEMP.GT.EST ) THEN
284: CALL DCOPY( N, X, 1, V, 1 )
285: EST = TEMP
286: END IF
287: *
288: 150 CONTINUE
289: KASE = 0
290: RETURN
291: *
292: * End of DLACN2
293: *
294: END
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