1: *> \brief \b ZLACON 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 ZLACON + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlacon.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlacon.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlacon.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLACON( N, V, X, EST, KASE )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER KASE, N
25: * DOUBLE PRECISION EST
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 V( N ), X( N )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZLACON estimates the 1-norm of a square, complex matrix A.
38: *> Reverse communication is used for evaluating matrix-vector products.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] N
45: *> \verbatim
46: *> N is INTEGER
47: *> The order of the matrix. N >= 1.
48: *> \endverbatim
49: *>
50: *> \param[out] V
51: *> \verbatim
52: *> V is COMPLEX*16 array, dimension (N)
53: *> On the final return, V = A*W, where EST = norm(V)/norm(W)
54: *> (W is not returned).
55: *> \endverbatim
56: *>
57: *> \param[in,out] X
58: *> \verbatim
59: *> X is COMPLEX*16 array, dimension (N)
60: *> On an intermediate return, X should be overwritten by
61: *> A * X, if KASE=1,
62: *> A**H * X, if KASE=2,
63: *> where A**H is the conjugate transpose of A, and ZLACON must be
64: *> re-called with all the other parameters unchanged.
65: *> \endverbatim
66: *>
67: *> \param[in,out] EST
68: *> \verbatim
69: *> EST is DOUBLE PRECISION
70: *> On entry with KASE = 1 or 2 and JUMP = 3, EST should be
71: *> unchanged from the previous call to ZLACON.
72: *> On exit, EST is an estimate (a lower bound) for norm(A).
73: *> \endverbatim
74: *>
75: *> \param[in,out] KASE
76: *> \verbatim
77: *> KASE is INTEGER
78: *> On the initial call to ZLACON, KASE should be 0.
79: *> On an intermediate return, KASE will be 1 or 2, indicating
80: *> whether X should be overwritten by A * X or A**H * X.
81: *> On the final return from ZLACON, KASE will again be 0.
82: *> \endverbatim
83: *
84: * Authors:
85: * ========
86: *
87: *> \author Univ. of Tennessee
88: *> \author Univ. of California Berkeley
89: *> \author Univ. of Colorado Denver
90: *> \author NAG Ltd.
91: *
92: *> \ingroup complex16OTHERauxiliary
93: *
94: *> \par Further Details:
95: * =====================
96: *>
97: *> Originally named CONEST, dated March 16, 1988. \n
98: *> Last modified: April, 1999
99: *
100: *> \par Contributors:
101: * ==================
102: *>
103: *> Nick Higham, University of Manchester
104: *
105: *> \par References:
106: * ================
107: *>
108: *> N.J. Higham, "FORTRAN codes for estimating the one-norm of
109: *> a real or complex matrix, with applications to condition estimation",
110: *> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
111: *>
112: * =====================================================================
113: SUBROUTINE ZLACON( N, V, X, EST, KASE )
114: *
115: * -- LAPACK auxiliary routine --
116: * -- LAPACK is a software package provided by Univ. of Tennessee, --
117: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118: *
119: * .. Scalar Arguments ..
120: INTEGER KASE, N
121: DOUBLE PRECISION EST
122: * ..
123: * .. Array Arguments ..
124: COMPLEX*16 V( N ), X( N )
125: * ..
126: *
127: * =====================================================================
128: *
129: * .. Parameters ..
130: INTEGER ITMAX
131: PARAMETER ( ITMAX = 5 )
132: DOUBLE PRECISION ONE, TWO
133: PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
134: COMPLEX*16 CZERO, CONE
135: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
136: $ CONE = ( 1.0D0, 0.0D0 ) )
137: * ..
138: * .. Local Scalars ..
139: INTEGER I, ITER, J, JLAST, JUMP
140: DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
141: * ..
142: * .. External Functions ..
143: INTEGER IZMAX1
144: DOUBLE PRECISION DLAMCH, DZSUM1
145: EXTERNAL IZMAX1, DLAMCH, DZSUM1
146: * ..
147: * .. External Subroutines ..
148: EXTERNAL ZCOPY
149: * ..
150: * .. Intrinsic Functions ..
151: INTRINSIC ABS, DBLE, DCMPLX, DIMAG
152: * ..
153: * .. Save statement ..
154: SAVE
155: * ..
156: * .. Executable Statements ..
157: *
158: SAFMIN = DLAMCH( 'Safe minimum' )
159: IF( KASE.EQ.0 ) THEN
160: DO 10 I = 1, N
161: X( I ) = DCMPLX( ONE / DBLE( N ) )
162: 10 CONTINUE
163: KASE = 1
164: JUMP = 1
165: RETURN
166: END IF
167: *
168: GO TO ( 20, 40, 70, 90, 120 )JUMP
169: *
170: * ................ ENTRY (JUMP = 1)
171: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
172: *
173: 20 CONTINUE
174: IF( N.EQ.1 ) THEN
175: V( 1 ) = X( 1 )
176: EST = ABS( V( 1 ) )
177: * ... QUIT
178: GO TO 130
179: END IF
180: EST = DZSUM1( N, X, 1 )
181: *
182: DO 30 I = 1, N
183: ABSXI = ABS( X( I ) )
184: IF( ABSXI.GT.SAFMIN ) THEN
185: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
186: $ DIMAG( X( I ) ) / ABSXI )
187: ELSE
188: X( I ) = CONE
189: END IF
190: 30 CONTINUE
191: KASE = 2
192: JUMP = 2
193: RETURN
194: *
195: * ................ ENTRY (JUMP = 2)
196: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
197: *
198: 40 CONTINUE
199: J = IZMAX1( N, X, 1 )
200: ITER = 2
201: *
202: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
203: *
204: 50 CONTINUE
205: DO 60 I = 1, N
206: X( I ) = CZERO
207: 60 CONTINUE
208: X( J ) = CONE
209: KASE = 1
210: JUMP = 3
211: RETURN
212: *
213: * ................ ENTRY (JUMP = 3)
214: * X HAS BEEN OVERWRITTEN BY A*X.
215: *
216: 70 CONTINUE
217: CALL ZCOPY( N, X, 1, V, 1 )
218: ESTOLD = EST
219: EST = DZSUM1( N, V, 1 )
220: *
221: * TEST FOR CYCLING.
222: IF( EST.LE.ESTOLD )
223: $ GO TO 100
224: *
225: DO 80 I = 1, N
226: ABSXI = ABS( X( I ) )
227: IF( ABSXI.GT.SAFMIN ) THEN
228: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
229: $ DIMAG( X( I ) ) / ABSXI )
230: ELSE
231: X( I ) = CONE
232: END IF
233: 80 CONTINUE
234: KASE = 2
235: JUMP = 4
236: RETURN
237: *
238: * ................ ENTRY (JUMP = 4)
239: * X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
240: *
241: 90 CONTINUE
242: JLAST = J
243: J = IZMAX1( N, X, 1 )
244: IF( ( ABS( X( JLAST ) ).NE.ABS( X( J ) ) ) .AND.
245: $ ( ITER.LT.ITMAX ) ) THEN
246: ITER = ITER + 1
247: GO TO 50
248: END IF
249: *
250: * ITERATION COMPLETE. FINAL STAGE.
251: *
252: 100 CONTINUE
253: ALTSGN = ONE
254: DO 110 I = 1, N
255: X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
256: ALTSGN = -ALTSGN
257: 110 CONTINUE
258: KASE = 1
259: JUMP = 5
260: RETURN
261: *
262: * ................ ENTRY (JUMP = 5)
263: * X HAS BEEN OVERWRITTEN BY A*X.
264: *
265: 120 CONTINUE
266: TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
267: IF( TEMP.GT.EST ) THEN
268: CALL ZCOPY( N, X, 1, V, 1 )
269: EST = TEMP
270: END IF
271: *
272: 130 CONTINUE
273: KASE = 0
274: RETURN
275: *
276: * End of ZLACON
277: *
278: END
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