1: SUBROUTINE DLACON( N, V, X, ISGN, EST, KASE )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER KASE, N
10: DOUBLE PRECISION EST
11: * ..
12: * .. Array Arguments ..
13: INTEGER ISGN( * )
14: DOUBLE PRECISION V( * ), X( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DLACON estimates the 1-norm of a square, real matrix A.
21: * Reverse communication is used for evaluating matrix-vector products.
22: *
23: * Arguments
24: * =========
25: *
26: * N (input) INTEGER
27: * The order of the matrix. N >= 1.
28: *
29: * V (workspace) DOUBLE PRECISION array, dimension (N)
30: * On the final return, V = A*W, where EST = norm(V)/norm(W)
31: * (W is not returned).
32: *
33: * X (input/output) DOUBLE PRECISION array, dimension (N)
34: * On an intermediate return, X should be overwritten by
35: * A * X, if KASE=1,
36: * A**T * X, if KASE=2,
37: * and DLACON must be re-called with all the other parameters
38: * unchanged.
39: *
40: * ISGN (workspace) INTEGER array, dimension (N)
41: *
42: * EST (input/output) DOUBLE PRECISION
43: * On entry with KASE = 1 or 2 and JUMP = 3, EST should be
44: * unchanged from the previous call to DLACON.
45: * On exit, EST is an estimate (a lower bound) for norm(A).
46: *
47: * KASE (input/output) INTEGER
48: * On the initial call to DLACON, KASE should be 0.
49: * On an intermediate return, KASE will be 1 or 2, indicating
50: * whether X should be overwritten by A * X or A**T * X.
51: * On the final return from DLACON, KASE will again be 0.
52: *
53: * Further Details
54: * ======= =======
55: *
56: * Contributed by Nick Higham, University of Manchester.
57: * Originally named SONEST, dated March 16, 1988.
58: *
59: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
60: * a real or complex matrix, with applications to condition estimation",
61: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
62: *
63: * =====================================================================
64: *
65: * .. Parameters ..
66: INTEGER ITMAX
67: PARAMETER ( ITMAX = 5 )
68: DOUBLE PRECISION ZERO, ONE, TWO
69: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
70: * ..
71: * .. Local Scalars ..
72: INTEGER I, ITER, J, JLAST, JUMP
73: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
74: * ..
75: * .. External Functions ..
76: INTEGER IDAMAX
77: DOUBLE PRECISION DASUM
78: EXTERNAL IDAMAX, DASUM
79: * ..
80: * .. External Subroutines ..
81: EXTERNAL DCOPY
82: * ..
83: * .. Intrinsic Functions ..
84: INTRINSIC ABS, DBLE, NINT, SIGN
85: * ..
86: * .. Save statement ..
87: SAVE
88: * ..
89: * .. Executable Statements ..
90: *
91: IF( KASE.EQ.0 ) THEN
92: DO 10 I = 1, N
93: X( I ) = ONE / DBLE( N )
94: 10 CONTINUE
95: KASE = 1
96: JUMP = 1
97: RETURN
98: END IF
99: *
100: GO TO ( 20, 40, 70, 110, 140 )JUMP
101: *
102: * ................ ENTRY (JUMP = 1)
103: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
104: *
105: 20 CONTINUE
106: IF( N.EQ.1 ) THEN
107: V( 1 ) = X( 1 )
108: EST = ABS( V( 1 ) )
109: * ... QUIT
110: GO TO 150
111: END IF
112: EST = DASUM( N, X, 1 )
113: *
114: DO 30 I = 1, N
115: X( I ) = SIGN( ONE, X( I ) )
116: ISGN( I ) = NINT( X( I ) )
117: 30 CONTINUE
118: KASE = 2
119: JUMP = 2
120: RETURN
121: *
122: * ................ ENTRY (JUMP = 2)
123: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
124: *
125: 40 CONTINUE
126: J = IDAMAX( N, X, 1 )
127: ITER = 2
128: *
129: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
130: *
131: 50 CONTINUE
132: DO 60 I = 1, N
133: X( I ) = ZERO
134: 60 CONTINUE
135: X( J ) = ONE
136: KASE = 1
137: JUMP = 3
138: RETURN
139: *
140: * ................ ENTRY (JUMP = 3)
141: * X HAS BEEN OVERWRITTEN BY A*X.
142: *
143: 70 CONTINUE
144: CALL DCOPY( N, X, 1, V, 1 )
145: ESTOLD = EST
146: EST = DASUM( N, V, 1 )
147: DO 80 I = 1, N
148: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
149: $ GO TO 90
150: 80 CONTINUE
151: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
152: GO TO 120
153: *
154: 90 CONTINUE
155: * TEST FOR CYCLING.
156: IF( EST.LE.ESTOLD )
157: $ GO TO 120
158: *
159: DO 100 I = 1, N
160: X( I ) = SIGN( ONE, X( I ) )
161: ISGN( I ) = NINT( X( I ) )
162: 100 CONTINUE
163: KASE = 2
164: JUMP = 4
165: RETURN
166: *
167: * ................ ENTRY (JUMP = 4)
168: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
169: *
170: 110 CONTINUE
171: JLAST = J
172: J = IDAMAX( N, X, 1 )
173: IF( ( X( JLAST ).NE.ABS( X( J ) ) ) .AND. ( ITER.LT.ITMAX ) ) THEN
174: ITER = ITER + 1
175: GO TO 50
176: END IF
177: *
178: * ITERATION COMPLETE. FINAL STAGE.
179: *
180: 120 CONTINUE
181: ALTSGN = ONE
182: DO 130 I = 1, N
183: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
184: ALTSGN = -ALTSGN
185: 130 CONTINUE
186: KASE = 1
187: JUMP = 5
188: RETURN
189: *
190: * ................ ENTRY (JUMP = 5)
191: * X HAS BEEN OVERWRITTEN BY A*X.
192: *
193: 140 CONTINUE
194: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
195: IF( TEMP.GT.EST ) THEN
196: CALL DCOPY( N, X, 1, V, 1 )
197: EST = TEMP
198: END IF
199: *
200: 150 CONTINUE
201: KASE = 0
202: RETURN
203: *
204: * End of DLACON
205: *
206: END
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