chris-taylor

classdef Dual
% DUAL Dual numbers class for automatic differentiation.
%
% To do automatic differentiation we introduce a number d such that d^2 == 0.
% Then by a simple application of Taylor's theorem we have
%
%     f(x + d) = f(x) + f'(x) d
%
% with all higher-order terms vanishing. Therefore applying a function to a dual
% number x + d generates both the value f(x) *and* the derivative f'(x).

chris-taylor

function b = isdual(a)
%ISDUAL Return true if a is of class Dual, else return false
    b = strcmp(class(a),'Dual');
end

chris-taylor

function SetDefault(argname,value)
%SETDEFAULT Provide a default value of VALUE for the argument ARGNAME.
%
%USAGE
%   SetDefault('x',1)
%   If no variable 'x' exists in the calling function, or if the variable exists
%   but it is empty, then this call assigns the value 1 to 'x'. If the variable
%   'x' already exists, and is non-empty, then no action is taken.
%

chris-taylor

import Control.Monad.ST
import Data.STRef

-- Primitive actions

getSignal wire = wire GetSignal

setSignal wire x = wire (SetSignal x)

addAction wire proc = wire (AddAction proc)

chris-taylor

import random
import time

N = 200
binsize = 8000;
xs = [100 * random.randint(1,40) for i in range(N)]

print '\nObjects to be packed:\n'
print xs

chris-taylor

data NewFloat a = F a deriving (Eq,Ord,Show)

instance RealFloat a => Num (NewFloat a) where
    F x + F y = F (x + y)
    F x - F y = F (x - y)
    F x * F y = F (x * y)
    fromInteger n = F (fromInteger n)
    abs = newAbs
    signum = newSignum

chris-taylor

-- A semi-fast isPrime algorithm

noDivs factors n = foldr (\f r -> f*f > n || (rem n f /= 0 && r))
                         True factors

primesTD = 2 : 3 : filter (noDivs $ tail primesTD) [5,7..]

isPrime n = n > 1 && noDivs primesTD n

divides a b = b `mod` a == 0

chris-taylor

{-# LANGUAGE MultiParamTypeClasses #-}

import Data.Maybe
import Data.List as List

-- Group stuff

class Group g where
    eye :: g
    (%) :: g -> g -> g

chris-taylor

/**********************************************************************
 *
 *   Customize the values given below to suit your needs.
 *   You can make additional copies of this file with
 *   different customizated settings if you need to load
 *   jsMath with different parameters.
 *   
 *   Load this page via:
 *   
 *   <SCRIPT SRC="path-to-jsMath/easy/load.js"></SCRIPT>

chris-taylor

function [T Y] = relent(Tspan)

    %% Configuration

    leg = {'Species 1','Species 2'};

    opts = odeset();
    opts.AbsTol = 1e-8;
    opts.RelTol = 1e-4;