-
Notifications
You must be signed in to change notification settings - Fork 59
/
bisection_integer.html
187 lines (154 loc) · 5.19 KB
/
bisection_integer.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
<html>
<head>
<title>
BISECTION_INTEGER - Seek Integer Roots for F(X)=0
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BISECTION_INTEGER <br> Seek Integer Roots for F(X)=0
</h1>
<hr>
<p>
<b>BISECTION_INTEGER</b>
is a FORTRAN90 library which
seeks an integer solution to the equation F(X)=0,
using bisection within a user-supplied change of sign interval [A,B].
</p>
<p>
A function F(X) confined to integer arguments is given, with an
interval [A,B] over which F changes sign. An integer C is sought
such that A ≤ C ≤ B and F(C) = 0.
</p>
<p>
Because we are restricted to integer arguments, it may the case that
there is no such C.
</p>
<p>
This routine proceeds by a form of bisection, in which the enclosing
interval is restricted to be defined by integer values.
</p>
<p>
If the user has given a true change of sign interval [A,B], and if,
in the interval, there is a single integer value C for which F(C) = 0,
with the additional restrictions that F(C-1) and F(C+1) are of opposite
signs, then this procedure should locate and return C.
</p>
<p>
In particular, if the function F is monotone, and there is an integer
solution C in the interval, then this procedure will find it.
</p>
<p>
However, in general, even if there is an integer C in the interval,
such that F(C) = 0, this procedure may be unable to find it, particularly
if there are also nonintegral solutions within the same interval.
</p>
<p>
While any integer function can be used with this program, the bisection
approach is most useful if the integer function is monotone, or
varies slowly, or can be regarded as the restriction to integer arguments
of a continuous (and smoothly varying) function of a real argument.
In such cases, knowing that F is negative at A and positive at B
suggests that F generally increases from A to B, and might attain
the value 0 at some intermediate argument C.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>BISECTION_INTEGER</b> is available in
<a href = "../../c_src/bisection_integer/bisection_integer.html">a C version</a> and
<a href = "../../cpp_src/bisection_integer/bisection_integer.html">a C++ version</a> and
<a href = "../../f77_src/bisection_integer/bisection_integer.html">a FORTRAN77 version</a> and
<a href = "../../f_src/bisection_integer/bisection_integer.html">a FORTRAN90 version</a> and
<a href = "../../m_src/bisection_integer/bisection_integer.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/brent/brent.html">
BRENT</a>,
a FORTRAN90 library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
</p>
<p>
<a href = "../../f_src/test_zero/test_zero.html">
TEST_ZERO</a>,
a FORTRAN90 library which
defines functions which can be used to test zero finders.
</p>
<p>
<a href = "../../f_src/zoomin/zoomin.html">
ZOOMIN</a>,
a FORTRAN90 library which
includes various zero finder routines.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bisection_integer.f90">bisection_integer.f90</a>, the source code.
</li>
<li>
<a href = "bisection_integer.sh">bisection_integer.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "bisection_integer_prb.f90">bisection_integer_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "bisection_integer_prb.sh">bisection_integer_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "bisection_integer_prb_output.txt">bisection_integer_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BISECTION_INTEGER</b> seeks an integer root using bisection.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 26 May 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>