mirror of
https://github.com/dlang/phobos.git
synced 2025-04-29 14:40:30 +03:00
85 lines
2.3 KiB
D
85 lines
2.3 KiB
D
// Written in the D programming language.
|
|
|
|
/**
|
|
This module is a port of a growing fragment of the $(D_PARAM numeric)
|
|
header in Alexander Stepanov's $(LINK2 http://sgi.com/tech/stl,
|
|
Standard Template Library), with a few additions.
|
|
|
|
Macros:
|
|
|
|
WIKI = Phobos/StdNumeric
|
|
|
|
Author:
|
|
|
|
Andrei Alexandrescu
|
|
*/
|
|
|
|
/*
|
|
* Copyright (C) 2004-2006 by Digital Mars, www.digitalmars.com
|
|
* Written by Andrei Alexandrescu, www.erdani.org
|
|
*
|
|
* This software is provided 'as-is', without any express or implied
|
|
* warranty. In no event will the authors be held liable for any damages
|
|
* arising from the use of this software.
|
|
*
|
|
* Permission is granted to anyone to use this software for any purpose,
|
|
* including commercial applications, and to alter it and redistribute it
|
|
* freely, subject to the following restrictions:
|
|
*
|
|
* o The origin of this software must not be misrepresented; you must not
|
|
* claim that you wrote the original software. If you use this software
|
|
* in a product, an acknowledgment in the product documentation would be
|
|
* appreciated but is not required.
|
|
* o Altered source versions must be plainly marked as such, and must not
|
|
* be misrepresented as being the original software.
|
|
* o This notice may not be removed or altered from any source
|
|
* distribution.
|
|
*/
|
|
|
|
module std.numeric;
|
|
import std.math;
|
|
import std.stdio;
|
|
|
|
/**
|
|
Implements the $(LINK2 http://tinyurl.com/2zb9yr,secant method) for
|
|
finding a root of the function $(D_PARAM f) starting from points
|
|
[xn_1, x_n] (ideally close to the root). $(D_PARAM Num) may be
|
|
$(D_PARAM float), $(D_PARAM double), or $(D_PARAM real).
|
|
|
|
Example:
|
|
|
|
----
|
|
float f(float x) {
|
|
return cos(x) - x*x*x;
|
|
}
|
|
final x = secantMethod(&f, 0f, 1f);
|
|
assert(approxEqual(x, 0.865474));
|
|
----
|
|
*/
|
|
template secantMethod(alias F)
|
|
{
|
|
Num secantMethod(Num)(Num xn_1, Num xn) {
|
|
auto fxn = F(xn_1), d = xn_1 - xn;
|
|
typeof(fxn) fxn_1;
|
|
xn = xn_1;
|
|
while (!approxEqual(d, 0) && isfinite(d)) {
|
|
xn_1 = xn;
|
|
xn -= d;
|
|
fxn_1 = fxn;
|
|
fxn = F(xn);
|
|
d *= -fxn / (fxn - fxn_1);
|
|
}
|
|
return xn;
|
|
}
|
|
}
|
|
|
|
unittest
|
|
{
|
|
scope(failure) writeln(stderr, "Failure testing secantMethod");
|
|
float f(float x) {
|
|
return cos(x) - x*x*x;
|
|
}
|
|
final x = secantMethod!(f)(0f, 1f);
|
|
assert(approxEqual(x, 0.865474));
|
|
}
|
|
|