Annotation of rpl/lapack/lapack/zlacn2.f, revision 1.17
1.12 bertrand 1: *> \brief \b ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
1.9 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 9: *> Download ZLACN2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlacn2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlacn2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlacn2.f">
1.9 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
1.16 bertrand 22: *
1.9 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER KASE, N
25: * DOUBLE PRECISION EST
26: * ..
27: * .. Array Arguments ..
28: * INTEGER ISAVE( 3 )
29: * COMPLEX*16 V( * ), X( * )
30: * ..
1.16 bertrand 31: *
1.9 bertrand 32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLACN2 estimates the 1-norm of a square, complex 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N)
61: *> On an intermediate return, X should be overwritten by
62: *> A * X, if KASE=1,
63: *> A**H * X, if KASE=2,
64: *> where A**H is the conjugate transpose of A, and ZLACN2 must be
65: *> re-called with all the other parameters unchanged.
66: *> \endverbatim
67: *>
68: *> \param[in,out] EST
69: *> \verbatim
70: *> EST is DOUBLE PRECISION
71: *> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
72: *> unchanged from the previous call to ZLACN2.
1.16 bertrand 73: *> On exit, EST is an estimate (a lower bound) for norm(A).
1.9 bertrand 74: *> \endverbatim
75: *>
76: *> \param[in,out] KASE
77: *> \verbatim
78: *> KASE is INTEGER
79: *> On the initial call to ZLACN2, KASE should be 0.
80: *> On an intermediate return, KASE will be 1 or 2, indicating
81: *> whether X should be overwritten by A * X or A**H * X.
82: *> On the final return from ZLACN2, KASE will again be 0.
83: *> \endverbatim
84: *>
85: *> \param[in,out] ISAVE
86: *> \verbatim
87: *> ISAVE is INTEGER array, dimension (3)
88: *> ISAVE is used to save variables between calls to ZLACN2
89: *> \endverbatim
90: *
91: * Authors:
92: * ========
93: *
1.16 bertrand 94: *> \author Univ. of Tennessee
95: *> \author Univ. of California Berkeley
96: *> \author Univ. of Colorado Denver
97: *> \author NAG Ltd.
1.9 bertrand 98: *
1.16 bertrand 99: *> \date December 2016
1.9 bertrand 100: *
101: *> \ingroup complex16OTHERauxiliary
102: *
103: *> \par Further Details:
104: * =====================
105: *>
106: *> \verbatim
107: *>
108: *> Originally named CONEST, dated March 16, 1988.
109: *>
110: *> Last modified: April, 1999
111: *>
112: *> This is a thread safe version of ZLACON, which uses the array ISAVE
113: *> in place of a SAVE statement, as follows:
114: *>
115: *> ZLACON ZLACN2
116: *> JUMP ISAVE(1)
117: *> J ISAVE(2)
118: *> ITER ISAVE(3)
119: *> \endverbatim
120: *
121: *> \par Contributors:
122: * ==================
123: *>
124: *> Nick Higham, University of Manchester
125: *
126: *> \par References:
127: * ================
128: *>
129: *> N.J. Higham, "FORTRAN codes for estimating the one-norm of
130: *> a real or complex matrix, with applications to condition estimation",
131: *> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
132: *>
133: * =====================================================================
1.1 bertrand 134: SUBROUTINE ZLACN2( N, V, X, EST, KASE, ISAVE )
135: *
1.16 bertrand 136: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 137: * -- LAPACK is a software package provided by Univ. of Tennessee, --
138: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.16 bertrand 139: * December 2016
1.1 bertrand 140: *
141: * .. Scalar Arguments ..
142: INTEGER KASE, N
143: DOUBLE PRECISION EST
144: * ..
145: * .. Array Arguments ..
146: INTEGER ISAVE( 3 )
147: COMPLEX*16 V( * ), X( * )
148: * ..
149: *
150: * =====================================================================
151: *
152: * .. Parameters ..
153: INTEGER ITMAX
154: PARAMETER ( ITMAX = 5 )
155: DOUBLE PRECISION ONE, TWO
156: PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
157: COMPLEX*16 CZERO, CONE
158: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
159: $ CONE = ( 1.0D0, 0.0D0 ) )
160: * ..
161: * .. Local Scalars ..
162: INTEGER I, JLAST
163: DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
164: * ..
165: * .. External Functions ..
166: INTEGER IZMAX1
167: DOUBLE PRECISION DLAMCH, DZSUM1
168: EXTERNAL IZMAX1, DLAMCH, DZSUM1
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL ZCOPY
172: * ..
173: * .. Intrinsic Functions ..
174: INTRINSIC ABS, DBLE, DCMPLX, DIMAG
175: * ..
176: * .. Executable Statements ..
177: *
178: SAFMIN = DLAMCH( 'Safe minimum' )
179: IF( KASE.EQ.0 ) THEN
180: DO 10 I = 1, N
181: X( I ) = DCMPLX( ONE / DBLE( N ) )
182: 10 CONTINUE
183: KASE = 1
184: ISAVE( 1 ) = 1
185: RETURN
186: END IF
187: *
188: GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 )
189: *
190: * ................ ENTRY (ISAVE( 1 ) = 1)
191: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
192: *
193: 20 CONTINUE
194: IF( N.EQ.1 ) THEN
195: V( 1 ) = X( 1 )
196: EST = ABS( V( 1 ) )
197: * ... QUIT
198: GO TO 130
199: END IF
200: EST = DZSUM1( N, X, 1 )
201: *
202: DO 30 I = 1, N
203: ABSXI = ABS( X( I ) )
204: IF( ABSXI.GT.SAFMIN ) THEN
205: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
206: $ DIMAG( X( I ) ) / ABSXI )
207: ELSE
208: X( I ) = CONE
209: END IF
210: 30 CONTINUE
211: KASE = 2
212: ISAVE( 1 ) = 2
213: RETURN
214: *
215: * ................ ENTRY (ISAVE( 1 ) = 2)
216: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
217: *
218: 40 CONTINUE
219: ISAVE( 2 ) = IZMAX1( N, X, 1 )
220: ISAVE( 3 ) = 2
221: *
222: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
223: *
224: 50 CONTINUE
225: DO 60 I = 1, N
226: X( I ) = CZERO
227: 60 CONTINUE
228: X( ISAVE( 2 ) ) = CONE
229: KASE = 1
230: ISAVE( 1 ) = 3
231: RETURN
232: *
233: * ................ ENTRY (ISAVE( 1 ) = 3)
234: * X HAS BEEN OVERWRITTEN BY A*X.
235: *
236: 70 CONTINUE
237: CALL ZCOPY( N, X, 1, V, 1 )
238: ESTOLD = EST
239: EST = DZSUM1( N, V, 1 )
240: *
241: * TEST FOR CYCLING.
242: IF( EST.LE.ESTOLD )
243: $ GO TO 100
244: *
245: DO 80 I = 1, N
246: ABSXI = ABS( X( I ) )
247: IF( ABSXI.GT.SAFMIN ) THEN
248: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
249: $ DIMAG( X( I ) ) / ABSXI )
250: ELSE
251: X( I ) = CONE
252: END IF
253: 80 CONTINUE
254: KASE = 2
255: ISAVE( 1 ) = 4
256: RETURN
257: *
258: * ................ ENTRY (ISAVE( 1 ) = 4)
259: * X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
260: *
261: 90 CONTINUE
262: JLAST = ISAVE( 2 )
263: ISAVE( 2 ) = IZMAX1( N, X, 1 )
264: IF( ( ABS( X( JLAST ) ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
265: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
266: ISAVE( 3 ) = ISAVE( 3 ) + 1
267: GO TO 50
268: END IF
269: *
270: * ITERATION COMPLETE. FINAL STAGE.
271: *
272: 100 CONTINUE
273: ALTSGN = ONE
274: DO 110 I = 1, N
275: X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
276: ALTSGN = -ALTSGN
277: 110 CONTINUE
278: KASE = 1
279: ISAVE( 1 ) = 5
280: RETURN
281: *
282: * ................ ENTRY (ISAVE( 1 ) = 5)
283: * X HAS BEEN OVERWRITTEN BY A*X.
284: *
285: 120 CONTINUE
286: TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
287: IF( TEMP.GT.EST ) THEN
288: CALL ZCOPY( N, X, 1, V, 1 )
289: EST = TEMP
290: END IF
291: *
292: 130 CONTINUE
293: KASE = 0
294: RETURN
295: *
296: * End of ZLACN2
297: *
298: END
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