js-num v1.1.10

JavaScript Numpy

This project aims at providing equivalent of Numpy in JavaScript (A fork of https://github.com/NikhilAshodariya/JavaScript_Numpy) Optimized for generics.js https://www.npmjs.com/package/generics.js

Prerequisites

Node.js, matrix_deep_clone

Installing

First, head over to nodejs.org and install Node.js.

$ npm install @kaustubhbx/jsnumpy

Running the tests

First install the module matrix_deep_clone then type

$ cd node_modules/jsnumpy/

After going inside the library type

$ npm test

Basics

Array Creation

> var nj = require('@kaustubhbx/jsnumpy');

> var a = nj.fillWithNumber([2,3,4],5);
> a
[
  [
    [5, 5, 5, 5],
    [5, 5, 5, 5],
    [5, 5, 5, 5]
  ],
  [
    [5, 5, 5, 5],
    [5, 5, 5, 5],
    [5, 5, 5, 5]
  ]
]

Note: The zeroes will create an array as needed with zeroes.

> var dim = nj.zeroes([3]);
> dim
[0,0,0]

> var dim = nj.zeroes([3,3]);
> dim
[[0,0,0],[0,0,0],[0,0,0]]

Note: The Tanh,sigmoid,sigmoid derivative and tanh derivative activation function has been added.

Example to use:

> var mat = nj.activation.tanh([1,2,2])
> mat
[ 0.7615941559557646, 0.9640275800758169, 0.9640275800758169 ]

Note: The fillWithNumber take two parameter the first parameter is the dimension of the required matrix in the above example the function creates a 3D matrix with three rows and four columns it is similar to Numpy function of Python. The default parameter to fill in array is zero. Here number 5 is used to fill the array.

> var dim = nj.get_Dimensions(a);
> dim
[2,3,4]

NOTE: The function get_Dimensions returns the dimension of the given matrix.

> var dim = [3,3]
> var minRange = 3;
> var maxRange = 25;
> var ans = nj.generateRandomNumbers(dim,minRange,maxRange);
> ans
[
  [22, 10, 20],
  [5, 8, 11],
  [10, 8, 22]
]

NOTE: The function dot returns dot product if it's A 2D matrix then matrix multiplication.

> var A = nj.dot([1,2,3],[4,5,6]);
> ans
32

Note: The function generateRandomNumbers provides a matrix of random numbers depending on the input dimension which is the first parameter of the function the default value for minRange is zero and maxRange is totalNumber. It can also generate an ndArray.

Deep cloning an array

> var a = [[1,2,3],[4,5,6],[7,8,9]];
> var co = nj.copy(a);
> co
[[1,2,3],[4,5,6],[7,8,9]]

> console.log(co===a);
false

Numerical Range

linspace

nj.linspace(start, stop, noOfSample);

NOTE : The default value of noOfSample is ten. If the value of start or stop is not provided then it gives an error.

> var a = nj.linspace(2, 3);
[ 2, 2.111111111111111, 2.2222222222222223, 2.3333333333333335, 2.4444444444444446, 2.555555555555556, 2.666666666666667, 2.777777777777778, 2.8888888888888893, 3.0000000000000004]

NOTE : In the above example since value of noOfSample is not provided so it is taken as ten.

> var a = nj.linspace(6, 7, 4);
[ 6, 6.333333333333333, 6.666666666666666, 7 ];

NOTE : In the above example the value of noOfSample is four so nj.linspace gives four samples which are equally spaced between start and end value.

arange

nj.arange(start, stop, step = 1);

NOTE : The default value of step is one.

> var a = nj.arange(4);
> a
[ 0, 1, 2, 3, 4 ]

NOTE : When only one parameter is passed then it is taken as last value of the array and the start value is then as zero and step is taken as one.

> var a = nj.arange(2,5);
> a
[ 2, 3, 4, 5 ]

NOTE : In the above example the start is two and end is five and the default value of step is one. Since step is not provided therefore it's default value is taken.

> var a = nj.arange(4,9,2);
> a
[ 4, 6, 8 ]

NOTE : In the above example the start is four and the end is nine and step is two.

Matrix Manipulation

> var ans = nj.generateRandomNumbers(16,3,25);
> var res = nj.reshape(ans,[4,2,2]);
> res
[ [ [ 13, 3 ], [ 21, 16 ] ],
  [ [ 25, 4 ], [ 9, 15 ] ],
  [ [ 20, 12 ], [ 17, 14 ] ],
  [ [ 5, 22 ], [ 11, 24 ] ] ]

> ans = nj.flatten(res);
> ans
[ 13, 3, 21, 16, 25, 4, 9, 15, 20, 12, 17, 14, 5, 22, 11, 24 ]

Note : In reshape function the first parameter is the data and the second parameter is the new dimension to which the data needs to be reshaped. The function flatten converts the matrix into a single Array.

Arithmetic Operation

Addition

> var a =  [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var c = [
  [2, 3, 4],
  [5, 32, 2],
  [5, 3, 2]
];

> var ans = nj.add(a,c);
> ans
[
  [5, 8, 6],
  [7, 36, 0],
  [12, 4, 3]
]

The add function provides adds the first row of matrix a i.e. 3, 5, 5 with the corresponding first row of matrix c i.e. 2, 3, 4, second row of matrix a i.e. 2,4,-2 with the corresponding second row of matrix c i.e. 5, 32, 2 and so on.

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var b = [
  [1],
  [2],
  [3]
];

> var ans = nj.add(a,b);
ans
[
  [4, 6, 3],
  [4, 6, 0],
  [10, 4, 4]
]

NOTE: In the above example the add function adds the first row of matrix b i.e. one(1) to the first row of matrix a. It performs the same operation on rest of the rows i.e. it adds two(2) to the second row of the matrix a and so on.

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var b = [1, 2, 3];

> var ans = nj.add(a,b);
ans
[
  [4, 7, 5],
  [3, 6, 1],
  [8, 3, 4]
]

NOTE: In the above example the add function adds matrix b first row of matrix b i.e. 1, 2, 3 to the first row, second row and third row of matrix a.

Subtraction

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];

> var ans = nj.subtract(a,b);
[
  [1, 1, -4],
  [-7, -2, -10],
  [2, -1, -13]
]

NOTE: The subtract function has the same working mechanism like add on ndArray.

Multiply

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];

> var ans = nj.multiply(a,b);
> ans
[
  [6, 20, 12],
  [18, 24, -16],
  [35, 2, 14]
]

Note : The function multiply is not a matrix multiply instead it multiplies element by element an has same working mechanism as add function.

Division

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var b = [
  [2, 3, 4],
  [5, 32, 2],
  [5, 3, 2]
];

> var ans = nj.divide(a,b);
ans
[
  [1.5, 1.6666666666666667, 0.5],
  [0.4, 0.125, -1],
  [1.4, 0.3333333333333333, 0.5]
]

> var c = [1, 2, 3]
> ans = nj.divide(a,c);
ans
[
  [3, 2.5, 0.6666666666666666],
  [2, 2, -0.6666666666666666],
  [7, 0.5, 0.3333333333333333]
]

NOTE: The divide function performs division for any dimension ndArray. It has same working mechanism as add, subtract and multiply functions.

Matrix Multiplication

> var a = [
  [47, 10, 84, 64],
  [33, 19, 98, 25],
];

> var b = [
  [93, 85],
  [66, 91],
  [95, 77],
  [84, 30]
];

> var ans = nj.matrixMultiply(a,b);
ans
[
  [18387, 13293],
  [15733, 12830]
]

The matrixMultiply function multiplies the given matrix according to the matrix multiplication rules.

> var a = [
  [
    [83, 41, 41, 27],
    [66, 63, 51, 15],
    [10, 39, 59, 44],
    [47, 4, 15, 97]
  ],

  [
    [93, 50, 70, 33],
    [32, 22, 27, 67],
    [66, 98, 69, 81],
    [80, 64, 1, 95]
  ]
];

> var b = [
  [67, 52, 43, 68],
  [81, 4, 83, 97],
  [86, 27, 94, 12],
  [85, 81, 17, 61]
];

> var ans = nj.matrixMultiply(a,b);
ans
[
  [
    [14703, 7774, 11285, 11760],
    [15186, 6276, 13116, 12126],
    [12643, 5833, 9961, 7855],
    [13008, 10722, 5412, 9681]
  ],
  [
    [19106, 9599, 15290, 14027],
    [11943, 7908, 6879, 8721],
    [25179, 12248, 18835, 19763],
    [18705, 12138, 10461, 17455]
  ]
]

NOTE: The matrixMultiply function can multiply ndArray with the given matrix of ndArray if the shape of both the matrix are compatible else it generates an error.

Logarithm

The library supports three logarithmic functions first log10, logE, log.

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var ans = nj.log10(a);
> ans
[
  [0, 0.30103, 0.47712125],
  [0.60205999, 0.69897, 0.77815125],
  [0.84509804, 0.90308999, 0.95424251],
  [0.69897, 0.30103, 0]
]

Note : The log10 function finds the log to the base 10 of the given nd-Array or of a Number

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var ans = nj.logE(a);
> ans
[
  [0, 0.69314718, 1.09861229],
  [1.38629436, 1.60943791, 1.79175947],
  [1.94591015, 2.07944154, 2.19722458],
  [1.60943791, 0.69314718, 0]
]

Note : The logE function finds the log to the base e of the given nd-Array or of a Number.

Log to the base n

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];
> var ans = nj.log(a,7);
[
  [0, 0.35620719, 0.56457503],
  [0.71241437, 0.82708748, 0.92078222],
  [1, 1.06862156, 1.12915007],
  [0.82708748, 0.35620719, 0]
]

NOTE: The function declaration is nj.log(exponent, base). In the above example we calculate the log of matrix a with base seven(7).

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var c = [
  [10],
  [20],
  [30],
  [40]
];

> var ans = nj.log(a,c);
ans
[
  [0, 0.30103, 0.47712125],
  [0.46275643, 0.53724357, 0.598104],
  [0.57212503, 0.61138514, 0.64601501],
  [0.43629453, 0.18790182, 0]
]

NOTE: In the above above example log is calculate for matrix a with base c. In the above operation log of first row of matrix a is calculate with base 10 i.e. log10(1), log10(2), log10(3), log of second row of matrix a is calculate with base 20 i.e. log20(4), log20(5), log20(6) and so on.

NOTE: The library is written in such a way that in above example nj.log(a,c) is not equal to nj.log(c,a);

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var c = [
  [10],
  [20],
  [30],
  [40]
];

> var ans = nj.log(c,a);
ans
[
  [Infinity, 3.32192809, 2.09590327],
  [2.16096405, 1.86135312, 1.67195002],
  [1.7478697, 1.6356302, 1.54795164],
  [2.29202967, 5.32192809, Infinity]
]

NOTE: In the above example we have taken nj.log(c,a) that means in the above operation log of first row of matrix c is calculated with bases 1, 2, 3 i.e. the first row of the answer is log1(10), log2(10), log3(10) i.e log of ten with base one, log of ten with base two, and log of ten with base three. For the second row bases are 4, 5, 6 i.e. the second row of the anser is log4(20), log5(20), log6(20) i.e. log of twenty with base four, log of twenty with base five, and log of twenty with base six. For the rest rows the process remains same.

NOTE: The log function provides great flexibility if needed.

Statistics Operation

> var a =   
  [
   [
      [4, 5, -6],
      [8, 0, 4]
   ],
   [
      [10, 15, -70],
      [-30, 70, 40]
   ],
   [
      [12, 3, 10],
      [80, 50, 40]
   ]
 ];

> var ans = nj.negative(a);
> ans
[
  [
    [-4, -5, 6],
    [-8, -0, -4]
  ],
  [
    [-10, -15, 70],
    [30, -70, -40]
  ],
  [
    [-12, -3, -10],
    [-80, -50, -40]
  ]
]

NOTE: The negative function calculates the negative of each element of the given Matrix.

> var res = nj.abs(ans);
> res
[
  [
    [4, 5, 6],
    [8, 0, 4]
  ],
  [
    [10, 15, 70],
    [30, 70, 40]
  ],
  [
    [12, 3, 10],
    [80, 50, 40]
  ]
]

NOTE: The abs function finds the absolute value of the given matrix.

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];
> var ans = nj.mean(a);
> ans
4.416666666666667

The mean function calculates the mean of the matrix provided.

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];
> var ans = nj.mean(b,0);
> ans
[5.333333333333333, 4, 9.333333333333334]

NOTE: mean function takes two parameter the first one is the data and the second parameter is the axis along which we want to find the mean. If value of the axis is not passed then mean of the entire matrix is found.

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];
> var ans = nj.mean(b, 1);
> ans
[ 4, 7.666666666666667, 7 ]

> ans = nj.square(a);
> ans
[
  [1, 4, 9],
  [16, 25, 36],
  [49, 64, 81],
  [25, 4, 1]
]

NOTE: square function calculates the square of each element of the given matrix.

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];

> var ans = nj.squareRoot(b);
ans
[
  [1.4142135623730951, 2, 2.449489742783178],
  [3, 2.449489742783178, 2.8284271247461903],
  [2.23606797749979, 1.4142135623730951, 3.7416573867739413]
]

> ans = nj.cubeRoot(b);
[
  [1.2599210498948732, 1.5874010519681994, 1.8171205928321397],
  [2.080083823051904, 1.8171205928321397, 2],
  [1.7099759466766968, 1.2599210498948732, 2.4101422641752297]
]

The squareRoot, cubeRoot function calculates the squareRoot and cubeRoot of the given ndArray respectively.

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];

> var ans = nj.nThRoot(b,5);
ans
[
  [1.148698354997035, 1.3195079107728942, 1.4309690811052556],
  [1.5518455739153596, 1.4309690811052556, 1.5157165665103982],
  [1.379729661461215, 1.148698354997035, 1.6952182030724354]
]

NOTE: The nThRoot function calculates the nth root of the data. The first parameter of nThRoot function is the data and the second parameter is the value whose nth root is required. nj.nThRoot(b,5) is not equal to nj.nThRoot(5,b).

> var b = [
  [2, 4, 6],
  [9, 6, 8],
  [5, 2, 14]
];

> var ans = nj.nThRoot(5, b);
ans
[
  [2.23606797749979, 1.4953487812212205, 1.3076604860118306],
  [1.195813174500402, 1.3076604860118306, 1.2228445449938519],
  [1.379729661461215, 2.23606797749979, 1.1218283962540023]
]

NOTE: The first row of the ans is five raise to 1/2, five raise to 1/4, five raise to 1/6. The second row of the ans is five raise to 1/9, five raise to 1/6, five raise to 1/8. The rest of the rows are calculated in similar way.

> ans = nj.sum(a);
> ans
53

The sum function returns the sum of all the elements of the matrix.

> ans = nj.totalElements(a);
> ans
12

The totalElements function returns the total number of elements in the given Matrix.

> ans = nj.highestElement(a);
> ans
9

The highestElement function returns the highest value of the matrix provided.

> ans = nj.lowestElement(a);
> ans
1

> ans = nj.range(a);
> ans
8

> var d = [1,2,3,4,5,6,7,8];
> ans = nj.median(d);
> ans
4.5

> ans = nj.frequency(a,1);
> ans
2

Note: In frequency the first parameter is the data and the second parameter is the data whose frequency is required.

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var ans = nj.allFrequency(a);
> ans
{
  '1': 2,
  '2': 2,
  '3': 1,
  '4': 1,
  '5': 2,
  '6': 1,
  '7': 1,
  '8': 1,
  '9': 1
}
> ans = nj.populationStandardDeviation(a);
> ans
2.5967394084804805

> ans = nj.populationVariance(a);
> ans
6.743055555555555

Note: nj.sampleVariance, nj.sampleStandardDeviation is also available

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var ans = nj.mode(a);
> ans
[1,2,5]

> ans = nj.mode([1,2,3,4,5]);
> ans
undefined

> ans = nj.power(a,3);
> ans
[
  [1, 8, 27],
  [64, 125, 216],
  [343, 512, 729],
  [125, 8, 1]
]

> ans = nj.power(3,a);
> ans
[
  [3, 9, 27],
  [81, 243, 729],
  [2187, 6561, 19683],
  [243, 9, 3]
]

NOTE: The power function returns the cube of element of the matrix a. nj.power(3,a) gives a different result it calculates three to the power of first row of matrix a in the above example it calculates 3^1, 3^2, 3^3 for the first row for second row it calculates the three to the power of second row of matrix a in the above example it calculates 3^4, 3^5, 3^6 and so on.

> ans = nj.exp(a);
> ans
[
  [2.71828, 7.3890461584, 20.085496391455553],
  [54.5980031309658, 148.41265995084171, 403.42716529117405],
  [1096.6279948676927, 2980.9419458889515, 8103.034872671019],
  [148.41265995084171, 7.3890461584, 2.71828]
]

NOTE: The exp function calculates e^a i.e it calculates e raise to the power of each element of matrix a.

Matrix Operations

> var a = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9],
  [5, 2, 1]
];

> var ans = nj.transpose(a);
> ans
[
  [1, 4, 7, 5],
  [2, 5, 8, 2],
  [3, 6, 9, 1]
]

NOTE : The transpose function also works for higher dimensions. The transpose function is very much similar to Numpy transpose of Python.

Find Matrix Inverse

> var a = [
  [3, 5, 2],
  [2, 4, -2],
  [7, 1, 1]
];

> var ans = nj.matrixInverse(a);
ans
[
  [-0.05263157894736842, 0.02631578947368421, 0.15789473684210525],
  [0.14035087719298245, 0.09649122807017543, -0.08771929824561403],
  [0.22807017543859648, -0.2807017543859649, -0.017543859649122806]
]

NOTE: The matrixInverse function finds the inverse of the given ndArray. It generates an error if the determinant of the given matrix is zero.

Find Determinant

> var a = [
  [10, 32, 34],
  [54, 50, 26],
  [17, 83, 91]
];
> var ans = nj.determinant(a);
> ans
4304

NOTE: The determinant function finds the Determinant of the given Matrix.

> var b =[
  [34, 59, 51, 63, 69],
  [60, 61, 21, 60, 32],
  [51, 43, 45, 7, 50],
  [42, 90, 46, 86, 9],
  [83, 6, 87, 60, 35]
];

> var ans = nj.determinant(b);
> ans
-979886677

NOTE: The determinant function works for N*N dimension matrix.

> var a = [
  [
    [4, 28],
    [66, 6]
  ],

  [
    [68, 51],
    [64, 5]
  ],

  [
    [76, 96],
    [31, 6]
  ]
];
> var ans = nj.determinant(a);
> ans
[ -1824, -2924, -2520 ]

> var a = [
  [
    [
      [67, 71],
      [22, 75]
    ],

    [
      [97, 77],
      [54, 32]
    ],

    [
      [91, 50],
      [79, 51]
    ]
  ],


  [
    [
      [84, 85],
      [88, 99]
    ],

    [
      [33, 58],
      [51, 50]
    ],

    [
      [30, 8],
      [15, 89]
    ]
  ]
];

> var ans = nj.determinant(a);
> ans
[
  [3463, -1054, 691],
  [836, -1308, 2550]
]

NOTE : determinant function retains the shape of Matrix since the matrix's outer shape was of (2,3) so the ans of determinant is also (2,3).

Generating Identity Matrix

> var dim = [4, 4];
> var ans = nj.generateIdentityMatrix(dim);
ans
[
  [1, 0, 0, 0],
  [0, 1, 0, 0],
  [0, 0, 1, 0],
  [0, 0, 0, 1]
]

NOTE: generateIdentityMatrix function generates an Identity matrix of the given dimension. The function also checks if the dimension given is square. The function can generate an ndArray.

Trigonometric Functions

Note : All the functions like sin, cos, tan allows radian as well as degree.

> var a = [
  [10, 20, 30],
  [40, 50, 60],
  [70, 80, 90],
  [180, 120, 100]
];
> var ans = nj.sin(a);
> ans
[
  [0.174, 0.342, 0.5],
  [0.643, 0.766, 0.866],
  [0.94, 0.985, 1],
  [0, 0.866, 0.985]
]

> ans = nj.sin(a,"radian");
> ans
[
  [-0.544, 0.913, -0.988],
  [0.745, -0.262, -0.305],
  [0.774, -0.994, 0.894],
  [-0.801, 0.581, -0.506]
]

NOTE: nj.sin(a) calculates the sin of the angles provided in matrix a. The angle are assumed to be in degree.

Note: nj.sin(a,"radian") takes matrix a as the matrix of angle in radian. nj.cos, nj.tan also exists.

> var a = [
  [0.1, 0.2, 0.3],
  [0.4, 0.5, 0.6],
  [0.7, 0.8, 0.9],
  [0.75, 0.45, 0.1]
];
> var ans = nj.sinInverse(a);
> ans
[
  [6, 12, 17],
  [24, 30, 37],
  [44, 53, 64],
  [49, 27, 6]
]

Note: The output of sinInverse, cosInverse, tanInverse is in degree.

> var a = [
  [0.1, 0.2, 0.3],
  [0.4, 0.5, 0.6],
  [0.7, 0.8, 0.9],
  [0.75, 0.45, 0.1]
];

> var ans = nj.hyperbolicSine(a);
> ans
[
  [0.10016675001984403, 0.20133600254109402, 0.3045202934471426],
  [0.4107523258028155, 0.5210953054937474, 0.6366535821482412],
  [0.7585837018395334, 0.888105982187623, 1.0265167257081753],
  [0.82231673193583, 0.46534201693419774, 0.10016675001984403]
]

Note: hyperbolicCosine, hyperbolicTangent also exists.

Authors

• Nikhil Ashodariya -(https://github.com/NikhilAshodariya)

License

This project is licensed under the MIT License