1: SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
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( * ), ISAVE( 3 )
14: DOUBLE PRECISION V( * ), X( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DLACN2 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' * X, if KASE=2,
37: * and DLACN2 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 ISAVE(1) = 3, EST should be
44: * unchanged from the previous call to DLACN2.
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 DLACN2, 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' * X.
51: * On the final return from DLACN2, KASE will again be 0.
52: *
53: * ISAVE (input/output) INTEGER array, dimension (3)
54: * ISAVE is used to save variables between calls to DLACN2
55: *
56: * Further Details
57: * ======= =======
58: *
59: * Contributed by Nick Higham, University of Manchester.
60: * Originally named SONEST, dated March 16, 1988.
61: *
62: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
63: * a real or complex matrix, with applications to condition estimation",
64: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
65: *
66: * This is a thread safe version of DLACON, which uses the array ISAVE
67: * in place of a SAVE statement, as follows:
68: *
69: * DLACON DLACN2
70: * JUMP ISAVE(1)
71: * J ISAVE(2)
72: * ITER ISAVE(3)
73: *
74: * =====================================================================
75: *
76: * .. Parameters ..
77: INTEGER ITMAX
78: PARAMETER ( ITMAX = 5 )
79: DOUBLE PRECISION ZERO, ONE, TWO
80: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TWO = 2.0D+0 )
81: * ..
82: * .. Local Scalars ..
83: INTEGER I, JLAST
84: DOUBLE PRECISION ALTSGN, ESTOLD, TEMP
85: * ..
86: * .. External Functions ..
87: INTEGER IDAMAX
88: DOUBLE PRECISION DASUM
89: EXTERNAL IDAMAX, DASUM
90: * ..
91: * .. External Subroutines ..
92: EXTERNAL DCOPY
93: * ..
94: * .. Intrinsic Functions ..
95: INTRINSIC ABS, DBLE, NINT, SIGN
96: * ..
97: * .. Executable Statements ..
98: *
99: IF( KASE.EQ.0 ) THEN
100: DO 10 I = 1, N
101: X( I ) = ONE / DBLE( N )
102: 10 CONTINUE
103: KASE = 1
104: ISAVE( 1 ) = 1
105: RETURN
106: END IF
107: *
108: GO TO ( 20, 40, 70, 110, 140 )ISAVE( 1 )
109: *
110: * ................ ENTRY (ISAVE( 1 ) = 1)
111: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
112: *
113: 20 CONTINUE
114: IF( N.EQ.1 ) THEN
115: V( 1 ) = X( 1 )
116: EST = ABS( V( 1 ) )
117: * ... QUIT
118: GO TO 150
119: END IF
120: EST = DASUM( N, X, 1 )
121: *
122: DO 30 I = 1, N
123: X( I ) = SIGN( ONE, X( I ) )
124: ISGN( I ) = NINT( X( I ) )
125: 30 CONTINUE
126: KASE = 2
127: ISAVE( 1 ) = 2
128: RETURN
129: *
130: * ................ ENTRY (ISAVE( 1 ) = 2)
131: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
132: *
133: 40 CONTINUE
134: ISAVE( 2 ) = IDAMAX( N, X, 1 )
135: ISAVE( 3 ) = 2
136: *
137: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
138: *
139: 50 CONTINUE
140: DO 60 I = 1, N
141: X( I ) = ZERO
142: 60 CONTINUE
143: X( ISAVE( 2 ) ) = ONE
144: KASE = 1
145: ISAVE( 1 ) = 3
146: RETURN
147: *
148: * ................ ENTRY (ISAVE( 1 ) = 3)
149: * X HAS BEEN OVERWRITTEN BY A*X.
150: *
151: 70 CONTINUE
152: CALL DCOPY( N, X, 1, V, 1 )
153: ESTOLD = EST
154: EST = DASUM( N, V, 1 )
155: DO 80 I = 1, N
156: IF( NINT( SIGN( ONE, X( I ) ) ).NE.ISGN( I ) )
157: $ GO TO 90
158: 80 CONTINUE
159: * REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED.
160: GO TO 120
161: *
162: 90 CONTINUE
163: * TEST FOR CYCLING.
164: IF( EST.LE.ESTOLD )
165: $ GO TO 120
166: *
167: DO 100 I = 1, N
168: X( I ) = SIGN( ONE, X( I ) )
169: ISGN( I ) = NINT( X( I ) )
170: 100 CONTINUE
171: KASE = 2
172: ISAVE( 1 ) = 4
173: RETURN
174: *
175: * ................ ENTRY (ISAVE( 1 ) = 4)
176: * X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X.
177: *
178: 110 CONTINUE
179: JLAST = ISAVE( 2 )
180: ISAVE( 2 ) = IDAMAX( N, X, 1 )
181: IF( ( X( JLAST ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
182: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
183: ISAVE( 3 ) = ISAVE( 3 ) + 1
184: GO TO 50
185: END IF
186: *
187: * ITERATION COMPLETE. FINAL STAGE.
188: *
189: 120 CONTINUE
190: ALTSGN = ONE
191: DO 130 I = 1, N
192: X( I ) = ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) )
193: ALTSGN = -ALTSGN
194: 130 CONTINUE
195: KASE = 1
196: ISAVE( 1 ) = 5
197: RETURN
198: *
199: * ................ ENTRY (ISAVE( 1 ) = 5)
200: * X HAS BEEN OVERWRITTEN BY A*X.
201: *
202: 140 CONTINUE
203: TEMP = TWO*( DASUM( N, X, 1 ) / DBLE( 3*N ) )
204: IF( TEMP.GT.EST ) THEN
205: CALL DCOPY( N, X, 1, V, 1 )
206: EST = TEMP
207: END IF
208: *
209: 150 CONTINUE
210: KASE = 0
211: RETURN
212: *
213: * End of DLACN2
214: *
215: END
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