Annotation of rpl/lapack/lapack/zlacn2.f, revision 1.8
1.1 bertrand 1: SUBROUTINE ZLACN2( N, V, X, 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 ISAVE( 3 )
14: COMPLEX*16 V( * ), X( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZLACN2 estimates the 1-norm of a square, complex 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) COMPLEX*16 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) COMPLEX*16 array, dimension (N)
34: * On an intermediate return, X should be overwritten by
35: * A * X, if KASE=1,
1.8 ! bertrand 36: * A**H * X, if KASE=2,
! 37: * where A**H is the conjugate transpose of A, and ZLACN2 must be
1.1 bertrand 38: * re-called with all the other parameters unchanged.
39: *
40: * EST (input/output) DOUBLE PRECISION
41: * On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
42: * unchanged from the previous call to ZLACN2.
43: * On exit, EST is an estimate (a lower bound) for norm(A).
44: *
45: * KASE (input/output) INTEGER
46: * On the initial call to ZLACN2, KASE should be 0.
47: * On an intermediate return, KASE will be 1 or 2, indicating
1.8 ! bertrand 48: * whether X should be overwritten by A * X or A**H * X.
1.1 bertrand 49: * On the final return from ZLACN2, KASE will again be 0.
50: *
51: * ISAVE (input/output) INTEGER array, dimension (3)
52: * ISAVE is used to save variables between calls to ZLACN2
53: *
54: * Further Details
55: * ======= =======
56: *
57: * Contributed by Nick Higham, University of Manchester.
58: * Originally named CONEST, dated March 16, 1988.
59: *
60: * Reference: N.J. Higham, "FORTRAN codes for estimating the one-norm of
61: * a real or complex matrix, with applications to condition estimation",
62: * ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
63: *
64: * Last modified: April, 1999
65: *
66: * This is a thread safe version of ZLACON, which uses the array ISAVE
67: * in place of a SAVE statement, as follows:
68: *
69: * ZLACON ZLACN2
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 ONE, TWO
80: PARAMETER ( ONE = 1.0D0, TWO = 2.0D0 )
81: COMPLEX*16 CZERO, CONE
82: PARAMETER ( CZERO = ( 0.0D0, 0.0D0 ),
83: $ CONE = ( 1.0D0, 0.0D0 ) )
84: * ..
85: * .. Local Scalars ..
86: INTEGER I, JLAST
87: DOUBLE PRECISION ABSXI, ALTSGN, ESTOLD, SAFMIN, TEMP
88: * ..
89: * .. External Functions ..
90: INTEGER IZMAX1
91: DOUBLE PRECISION DLAMCH, DZSUM1
92: EXTERNAL IZMAX1, DLAMCH, DZSUM1
93: * ..
94: * .. External Subroutines ..
95: EXTERNAL ZCOPY
96: * ..
97: * .. Intrinsic Functions ..
98: INTRINSIC ABS, DBLE, DCMPLX, DIMAG
99: * ..
100: * .. Executable Statements ..
101: *
102: SAFMIN = DLAMCH( 'Safe minimum' )
103: IF( KASE.EQ.0 ) THEN
104: DO 10 I = 1, N
105: X( I ) = DCMPLX( ONE / DBLE( N ) )
106: 10 CONTINUE
107: KASE = 1
108: ISAVE( 1 ) = 1
109: RETURN
110: END IF
111: *
112: GO TO ( 20, 40, 70, 90, 120 )ISAVE( 1 )
113: *
114: * ................ ENTRY (ISAVE( 1 ) = 1)
115: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X.
116: *
117: 20 CONTINUE
118: IF( N.EQ.1 ) THEN
119: V( 1 ) = X( 1 )
120: EST = ABS( V( 1 ) )
121: * ... QUIT
122: GO TO 130
123: END IF
124: EST = DZSUM1( N, X, 1 )
125: *
126: DO 30 I = 1, N
127: ABSXI = ABS( X( I ) )
128: IF( ABSXI.GT.SAFMIN ) THEN
129: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
130: $ DIMAG( X( I ) ) / ABSXI )
131: ELSE
132: X( I ) = CONE
133: END IF
134: 30 CONTINUE
135: KASE = 2
136: ISAVE( 1 ) = 2
137: RETURN
138: *
139: * ................ ENTRY (ISAVE( 1 ) = 2)
140: * FIRST ITERATION. X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
141: *
142: 40 CONTINUE
143: ISAVE( 2 ) = IZMAX1( N, X, 1 )
144: ISAVE( 3 ) = 2
145: *
146: * MAIN LOOP - ITERATIONS 2,3,...,ITMAX.
147: *
148: 50 CONTINUE
149: DO 60 I = 1, N
150: X( I ) = CZERO
151: 60 CONTINUE
152: X( ISAVE( 2 ) ) = CONE
153: KASE = 1
154: ISAVE( 1 ) = 3
155: RETURN
156: *
157: * ................ ENTRY (ISAVE( 1 ) = 3)
158: * X HAS BEEN OVERWRITTEN BY A*X.
159: *
160: 70 CONTINUE
161: CALL ZCOPY( N, X, 1, V, 1 )
162: ESTOLD = EST
163: EST = DZSUM1( N, V, 1 )
164: *
165: * TEST FOR CYCLING.
166: IF( EST.LE.ESTOLD )
167: $ GO TO 100
168: *
169: DO 80 I = 1, N
170: ABSXI = ABS( X( I ) )
171: IF( ABSXI.GT.SAFMIN ) THEN
172: X( I ) = DCMPLX( DBLE( X( I ) ) / ABSXI,
173: $ DIMAG( X( I ) ) / ABSXI )
174: ELSE
175: X( I ) = CONE
176: END IF
177: 80 CONTINUE
178: KASE = 2
179: ISAVE( 1 ) = 4
180: RETURN
181: *
182: * ................ ENTRY (ISAVE( 1 ) = 4)
183: * X HAS BEEN OVERWRITTEN BY CTRANS(A)*X.
184: *
185: 90 CONTINUE
186: JLAST = ISAVE( 2 )
187: ISAVE( 2 ) = IZMAX1( N, X, 1 )
188: IF( ( ABS( X( JLAST ) ).NE.ABS( X( ISAVE( 2 ) ) ) ) .AND.
189: $ ( ISAVE( 3 ).LT.ITMAX ) ) THEN
190: ISAVE( 3 ) = ISAVE( 3 ) + 1
191: GO TO 50
192: END IF
193: *
194: * ITERATION COMPLETE. FINAL STAGE.
195: *
196: 100 CONTINUE
197: ALTSGN = ONE
198: DO 110 I = 1, N
199: X( I ) = DCMPLX( ALTSGN*( ONE+DBLE( I-1 ) / DBLE( N-1 ) ) )
200: ALTSGN = -ALTSGN
201: 110 CONTINUE
202: KASE = 1
203: ISAVE( 1 ) = 5
204: RETURN
205: *
206: * ................ ENTRY (ISAVE( 1 ) = 5)
207: * X HAS BEEN OVERWRITTEN BY A*X.
208: *
209: 120 CONTINUE
210: TEMP = TWO*( DZSUM1( N, X, 1 ) / DBLE( 3*N ) )
211: IF( TEMP.GT.EST ) THEN
212: CALL ZCOPY( N, X, 1, V, 1 )
213: EST = TEMP
214: END IF
215: *
216: 130 CONTINUE
217: KASE = 0
218: RETURN
219: *
220: * End of ZLACN2
221: *
222: END
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