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29f3cc23f7
std.contracts: added functions pointsTo() std.numeric: minor unittest fixes. std.bitmanip: fixed code bloat issue, reintroduced FloatRep and DoubleRep. std.conv: minor simplification of implementation. std.regexp: added reference to ECMA standard in the documentation. std.getopt: changed return type from bool to void, error is signaled by use of exceptions. std.functional: added unaryFun, binaryFun, adjoin. std.string: updated documentation, changed code to compile with warnings enabled. std.traits: changed FieldTypeTuple; added RepresentationTypeTuple, hasAliasing; fixed bug 1826; added call to flush() from within write; fixed unlisted bug in lines(). std.algorithm: added map, reduce, filter, inPlace, move, swap, overwriteAdjacent, find, findRange, findBoyerMoore, findAdjacent, findAmong, findAmongSorted, canFind, canFindAmong, canFindAmongSorted, count, equal, overlap, min, max, mismatch, EditOp, none, substitute, insert, remove, levenshteinDistance, levenshteinDistanceAndPath, copy, copyIf, iterSwap, swapRanges, reverse, rotate, SwapStrategy, Unstable, Semistable, Stable, eliminate, partition, nthElement, sort, schwartzSort, partialSort, isSorted, makeIndex, schwartzMakeIndex, lowerBound, upperBound, equalRange, canFindSorted. std.thread: fixed so it compiles with warnings enabled. std.file: made getSize() faster under Linux. std.random: fixed so it compiles with warnings enabled; improved function uniform so it deduces type generated from its arguments. std.format: added fixes to make formatting work with const data. std.path: minor documentation changes.
85 lines
2.4 KiB
D
85 lines
2.4 KiB
D
// Written in the D programming language.
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/**
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This module is a port of a growing fragment of the $(D_PARAM numeric)
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header in Alexander Stepanov's $(LINK2 http://sgi.com/tech/stl,
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Standard Template Library), with a few additions.
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Macros:
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WIKI = Phobos/StdNumeric
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Author:
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$(WEB erdani.org, Andrei Alexandrescu)
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*/
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/*
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* Copyright (C) 2004-2006 by Digital Mars, www.digitalmars.com
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* Written by Andrei Alexandrescu, www.erdani.org
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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*
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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*
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* o The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* o Altered source versions must be plainly marked as such, and must not
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* be misrepresented as being the original software.
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* o This notice may not be removed or altered from any source
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* distribution.
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*/
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module std.numeric;
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import std.math;
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import std.stdio;
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/**
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Implements the $(LINK2 http://tinyurl.com/2zb9yr,secant method) for
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finding a root of the function $(D_PARAM f) starting from points
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[xn_1, x_n] (ideally close to the root). $(D_PARAM Num) may be
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$(D_PARAM float), $(D_PARAM double), or $(D_PARAM real).
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Example:
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----
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float f(float x) {
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return cos(x) - x*x*x;
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}
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auto x = secantMethod(&f, 0f, 1f);
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assert(approxEqual(x, 0.865474));
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----
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*/
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template secantMethod(alias F)
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{
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Num secantMethod(Num)(Num xn_1, Num xn) {
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auto fxn = F(xn_1), d = xn_1 - xn;
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typeof(fxn) fxn_1;
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xn = xn_1;
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while (!approxEqual(d, 0) && isfinite(d)) {
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xn_1 = xn;
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xn -= d;
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fxn_1 = fxn;
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fxn = F(xn);
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d *= -fxn / (fxn - fxn_1);
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}
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return xn;
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}
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}
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unittest
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{
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scope(failure) writeln(stderr, "Failure testing secantMethod");
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float f(float x) {
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return cos(x) - x*x*x;
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}
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invariant x = secantMethod!(f)(0f, 1f);
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assert(approxEqual(x, 0.865474));
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}
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