Novelty Polygonal Mathematics

    rlab

    1.0.0 • Public • Published

    rlab -- A JavaScript Scientific Library like R

    Introduction

    The rlab is a A JavaScript Scientific Library like R.

    It's based on lodash.js , jStat.js and numeric.js

    Install

    npm install rlab
    

    Use rlab in console mode

    file : probabilityEx.js

    var R = require("rlab");
    var dice = R.steps(1,6);
    log("sample(1:6, 10)", R.samples(dice, 10));
    log("runif(10,0,1)=", R.runif(10, 0, 1).str());
    log("rnorm(10,5,1)=", R.rnorm(10, 5, 1).str());
    log("dnorm(5,5,1)=", R.dnorm(5, 5, 1));
    log("pnorm(5,5,1)=", R.pnorm(5, 5, 1));
    log("qnorm(0.5,5,1)=", R.qnorm(0.5, 5, 1));
    log("rbinom(10, 5, 0.5)=", R.rbinom(10,5,0.5));
    log("dbinom(4, 5, 0.5)=", R.dbinom(4,5,0.5));
    log("dbinom(5, 5, 0.5)=", R.dbinom(5,5,0.5));
    log("pbinom(4, 5, 0.5)=", R.pbinom(4,5,0.5));
    log("qbinom(0.9, 5, 0.5)=", R.qbinom(0.9,5,0.5));
     

    run :

    $ node probabilityEx.js
    sample(1:6, 10) [ 3, 5, 3, 2, 3, 3, 1, 2, 4, 3 ]
    runif(10,0,1)= [0.9119,0.5899,0.6839,0.1350,0.6894,0.9512,0.8186,0.5826,0.4279,0
    .5125]
    rnorm(10,5,1)= [5.8961,5.4312,6.0002,5.3623,5.5281,4.4413,6.2144,5.7173,5.3111,1
    .3146]
    dnorm(5,5,1)= 0.3989422804014327
    pnorm(5,5,1)= 0.5
    qnorm(0.5,5,1)= 5
    rbinom(10, 5, 0.5)= [ 2, 1, 2, 2, 4, 4, 1, 4, 3, 2 ]
    dbinom(4, 5, 0.5)= 0.15625
    dbinom(5, 5, 0.5)= 0.03125
    pbinom(4, 5, 0.5)= 0.96875
    qbinom(0.9, 5, 0.5)= 4
    

    file : statisticsEx.js

    var R = require("rlab");
    var v = [1,3,5];
    log("v.max()=", v.max());
    log("v.min()=", v.min());
    log("v.sum()=", v.sum());
    log("v.normalize()=", v.normalize());
    log("v.normalize().sum()=", v.normalize().sum());
    log("v.product()=", v.product());
    log("v.mean()=", v.mean());
    log("v.range()=", v.range());
    log("v.median()=", v.median());
    log("v.variance()=", v.variance());
    log("v.sd()=", v.sd(), " sd^2=", v.sd()*v.sd());
    log("v.cov(v)=", v.cov(v), "v.cor(v)=", v.cor(v));
    log("factorial(5)=", R.factorial(5));

    run :

    $ node statisticsEx.js
    v.max()= 5
    v.min()= 1
    v.sum()= 9
    v.normalize()= [ 0.1111111111111111, 0.3333333333333333, 0.5555555555555556 ]
    v.normalize().sum()= 1
    v.product()= 15
    v.mean()= 1
    v.range()= 4
    v.median()= 3
    v.variance()= 2.6666666666666665
    v.sd()= 1.632993161855452  sd^2= 2.6666666666666665
    v.cov(v)= 4 v.cor(v)= 1
    factorial(5)= 120
    

    file : testEx.js

    var R = require("../rlab");
    var v = [1,3,5];
     
    var x = R.rnorm(10, 0, 0.1);
    print("x=", x.str());
     
    var t1=R.ttest({x:x, mu:0});
    R.report(t1);

    run :

    $ node testEx.js
    x= [-0.1117,-0.1211,0.0382,-0.1902,0.0124,0.0949,0.2326,0.1315,-0.0261,0.0874]
    
    =========== report ==========
    name    : ttest(X)
    h       : H0:mu=0
    alpha   : 0.0500
    op      : =
    pvalue  : 0.7129
    ci      : [-0.0733,0.1028]
    df      : 9.0000
    mean    : 0.0148
    sd      : 0.1231
    

    file : matrixEx.js

    var M = require("rlab").M;
    var v = [1,2,3];
    log("v.sin()=", v.sin());
    log("v.norm2()=", v.norm2());
    log("v.norm2Squared()=", v.norm2Squared());
     
    var A = [[1,2,3],[4,5,6],[7,3,9]];
    var AiA = A.inv().dot(A);
    log("AiA=\n", AiA.strM());
    log("AiA.tr()=\n", AiA.tr().strM());
    log("A=\n", A.str());
    log("A.mul(0.1)=\n", A.mul(0.1).strM());
    log("A.row(1)=", A.row(1));
    log("A.col(1)=", A.col(1));
    log("A.sumM()=", A.sumM());
    log("A.rowSum()=", A.rowSum());
    log("A.colSum()=", A.colSum());
    log("A.mean(row)=", A.rowMean().str());
    log("A.mean(col)=", A.colMean().str());
     
    var D = M.diag(v);
    log("D=", D);
     
    var Eλ = M.eigR(A);
    var E = .E, λ=.lambda;
    log("E*[λ]*E-1=", E.dot(λ.diag()).dot(E.inv()).strM());

    run :

    $ node matrixEx.js
    v.sin()= [ 0.8414709848078965, 0.9092974268256817, 0.1411200080598672 ]
    v.norm2()= 3.7416573867739413
    v.norm2Squared()= 14
    AiA=
     [[          1,   1.11e-16,  -1.11e-16],
     [          0,          1,  4.441e-16],
     [ -3.331e-16, -3.331e-16,          1]]
    AiA.tr()=
     [[          1,          0, -3.331e-16],
     [   1.11e-16,          1, -3.331e-16],
     [  -1.11e-16,  4.441e-16,          1]]
    A=
     [[1.0000,2.0000,3.0000],[4.0000,5.0000,6.0000],[7.0000,3.0000,9.0000]]
    A.mul(0.1)=
     [[        0.1,        0.2,        0.3],
     [        0.4,        0.5,        0.6],
     [        0.7,        0.3,        0.9]]
    A.row(1)= [ 4, 5, 6 ]
    A.col(1)= [ 2, 5, 3 ]
    A.sumM()= 40
    A.rowSum(2)= [ 6, 15, 19 ]
    A.colSum(2)= [ 12, 10, 18 ]
    A.mean(row)= [2.0000,5.0000,6.3333]
    A.mean(col)= [4.0000,3.3333,6.0000]
    D= [ [ 1, 0, 0 ], [ 0, 2, 0 ], [ 0, 0, 3 ] ]
    E*[λ]*E-1= [[          1,          2,          3],
     [          4,          5,          6],
     [          7,          3,          9]]
    

    file : differentialEx.js

    var R = require("rlab");
     
    var d = R.D.d, i=R.D.i, sin=R.sin, PI = R.PI, x2=(x)=>x*x;
     
    log('d(x^2,2)=', d(x2, 2));
    log('d(sin(x/4),pi/4)=', d(sin, PI/4));
    log('i(x^2,0,1)=', i(x2,0,1));
    log('i(sin(x),0,pi/2)=', i(sin,0,PI/2));
     

    run :

    D:\Dropbox\github\rlab\example>node differentialEx.js
    d(x^2,2)= 4.000999999999699
    d(sin(x/4),pi/4)= 0.7067531099743674
    i(x^2,0,1)= 0.33283350000000095
    i(sin(x),0,pi/2)= 0.9997035898637557
    

    file: symbolEx.js

    var R = require("../rlab");
    var S = R.Symbol;
     
    print('x+x=', S.run('x + x')) // => 2 x"
     
    print('10!=', S.factor('10!').toString()); // => "2^8 3^4 5^2 7"
     
    print('integral(x^2)=', S.eval('integral(x^2)').toString()); // => "1/3 x^3"
     
    // composing...
    print('integral(x)=', S.integral(S.eval('x')).toString()); // => "1/2 x^2"
     
    var questions=[
    '13579/99999 + 13580/100000',
    'numerator(1/a+1/b)',
    'denominator(1/(x-1)/(x-2))',
    'rationalize(a/b+b/a)',
    'A=1+i;B=sqrt(2)*exp(i*pi/4);A-B',
    'simplify(cos(x)^2 + sin(x)^2)',
    'simplify(a*b+a*c)',
    'simplify(n!/(n+1)!)',
    '(x-1)(x-2)^3',
    'subst( u, exp(x), 2*exp(x) )',
    'roots(3 x + 12 + y = 24)',
    'roots(a*x^2+b*x+c)',
    'roots(x^4 + x^3 + x^2 + x + 1)',
    'roots(m*x^9 + n)',
    'roots((x^4+x^3)*(x^4*x^2))',
    'nroots(x^4+1)',
    'velocity=17000*"mile"/"hr";time=8*"min"/(60*"min"/"hr");velocity/time',
    'A=((a,b),(c,d));inv(A);adj(A);det(A);inv(A)-adj(A)/det(A)',
    'd(x^2);r=sqrt(x^2+y^2);d(r,(x,y))',
    'F=(x+2y,3x+4y);d(F,(x,y))',
    'integral(x^2)',
    'integral(x*y,x,y)',
    // 'defint(x^2,y,0,sqrt(1-x^2),x,-1,1)', // very slow, why ?
    // 'f=sin(t)^4-2*cos(t/2)^3*sin(t);f=circexp(f);defint(f,t,0,2*pi)', // very slow, why ?
    ];
     
    print("=========== Q&A =============");
     
    for (var i in questions) {
        var q = questions[i];
        print(q, "=", S.run(q.replace(/;/g, '\n')));
    }

    run :

    D:\js\rlab\example>node symbolEx.js
    x+x= 2 x
    10!= 2^8 3^4 5^2 7
    integral(x^2)= 1/3 x^3
    integral(x)= 1/2 x^2
    =========== Q&A =============
    13579/99999 + 13580/100000 = 135794321/499995000
    numerator(1/a+1/b) = a + b
    denominator(1/(x-1)/(x-2)) = x^2 - 3 x + 2
    rationalize(a/b+b/a) = (a^2 + b^2) / (a b)
    A=1+i;B=sqrt(2)*exp(i*pi/4);A-B = 1 + i - 2^(1/2) exp(1/4 i pi)
    simplify(cos(x)^2 + sin(x)^2) = 1
    simplify(a*b+a*c) = a (b + c)
    simplify(n!/(n+1)!) = 1 / (1 + n)
    (x-1)(x-2)^3 = x^4 - 7 x^3 + 18 x^2 - 20 x + 8
    subst( u, exp(x), 2*exp(x) ) = 2 u
    roots(3 x + 12 + y = 24) = -1/3 y + 4
    roots(a*x^2+b*x+c) = (-b / (2 a) - (-4 a c + b^2)^(1/2) / (2 a),-b / (2 a) + (-4
     a c + b^2)^(1/2) / (2 a))
    roots(x^4 + x^3 + x^2 + x + 1) = Stop: roots: the polynomial is not factorable,
    try nroots
    roots(m*x^9 + n) = Stop: roots: the polynomial is not factorable, try nroots
    roots((x^4+x^3)*(x^4*x^2)) = (-1,0)
    nroots(x^4+1) = (-0.707107 - 0.707107 i,-0.707107 + 0.707107 i,0.707107 + 0.7071
    07 i,0.707107 - 0.707107 i)
    velocity=17000*"mile"/"hr";time=8*"min"/(60*"min"/"hr");velocity/time = 127500 "
    mile" / ("hr"^2)
    A=((a,b),(c,d));inv(A);adj(A);det(A);inv(A)-adj(A)/det(A) = ((d / (a d - b c),-b
     / (a d - b c)),(-c / (a d - b c),a / (a d - b c)))
    ((d,-b),(-c,a))
    a d - b c
    ((0,0),(0,0))
    d(x^2);r=sqrt(x^2+y^2);d(r,(x,y)) = 2 x
    (x / ((x^2 + y^2)^(1/2)),y / ((x^2 + y^2)^(1/2)))
    F=(x+2y,3x+4y);d(F,(x,y)) = ((1,2),(3,4))
    integral(x^2) = 1/3 x^3
    integral(x*y,x,y) = 1/4 x^2 y^2
    

    Run rlab on Web

    Fdbserver is a used in the server.js of rlab. You have to install fdbserver before start the server.js

    $ git clone https://github.com/ccckmit/rlab
    ...
    $ cd rlab
    ...
    $ npm install fdbserver
    rlab@0.7.1 D:\Dropbox\github\rlab
    +-- chai@3.5.0  extraneous
    +-- express@4.13.4  extraneous
    `-- fdbserver@1.6.6  extraneous
    
    $ node server.js
    

    A demo for rlab is on my web site http://ccc.nqu.edu.tw/rlab/rlab.html .

    The following figure is Screen Shot for Rlab GUI.

    Run rlab on Web

    If you visit the site in https protocol, there will be a Button for 'Save File', and menus for 'Login' and 'Logout'. These function can only be used in the https mode, not in the http mode.

    You have to login to save code. The default code path is in 'file/' directory with the file name you choose to upload.

    Rebuild Web Version

    You have to wrap rlab for web by browserify in the following command.

    $npm run-script build-web
    
    > rlab@0.5.4 build-web D:\Dropbox\github\rlab
    > browserify web/_rlab.js -o web/rlab.js
    

    When you modify the rlab source, make sure to wrap it again.

    Author

    Author: ccckmit

    Email : ccckmit@gmail.com

    License

    The rlab project is licensed in MIT license.

    Copyright (c) 2013 rlab

    Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

    Install

    npm i rlab

    DownloadsWeekly Downloads

    200

    Version

    1.0.0

    License

    MIT

    Last publish

    Collaborators

    • ccckmit