Nth Permutation Mathematics
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rlab

0.5.1 • 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

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);
log("x=", x.str());
log("x.sort()=", x.sort().str());
 
var t1=R.ttest({x:x, mu:0});
R.report(t1);

run :

$ node testEx.js
x= [-0.1405,0.0495,-0.1850,0.0824,0.0687,-0.0854,-0.1049,-0.1171,0.0947,-0.1592]

x.sort()= [-0.0854,-0.1049,-0.1171,-0.1405,-0.1592,-0.1850,0.0495,0.0687,0.0824,
0.0947]
=========== report ==========
name    : ttest(X)
h       : H0:mu=0
alpha   : 0.0500
op      : =
pvalue  : 0.0003
ci      : [-0.2599,-0.1101]
df      : 9.0000
mean    : -0.1850
sd      : 0.1047

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

IDE

There is a webIDE for rlab , you may start it by open rlab.html

Author

Author: ccckmit

Email : ccckmit@gmail.com

Install

npm i [email protected]

Version

0.5.1

License

MIT

Last publish

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