rlab Release 0.1.2

Javascript scientific library like R

Keywords
R, Matlab, Scientific Computing, Statistics, Probability, Matrix
MIT
Install
``` npm install rlab@0.1.2 ```

Documentation

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 = Eλ.E, λ=Eλ.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',
'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 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.

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