module

la

Linear algebra module.

Example

// import la module
var la = require('qminer').la;
// create a random matrix
var mat = new la.Matrix({ rows: 10, cols: 5, random: true });
// create a vector
var vec = new la.Vector([1, 2, 3, 0, -1]);
// multiply the matrix and vector
var vec2 = mat.multiply(vec);
// calculate the svd decomposition of the matrix
var svd = la.svd(mat, 3);

Child classes

BoolVector([arg])
IntVector([arg])
Matrix([arg])

SparseMatrix([arg][, rows])
SparseVector([arg][, dim])
StrVector([arg])

Vector([arg])

Methods

cat(nestedArrMat)
conjgrad(A, b[, x][, verbose])
copyVecToArray(vec)
eye(dim)
findMaxIdx(X)
inverseSVD(mat)
ones(dim)

pdist2(X1, X2)
randi(num[, len])
randn([arg1][, arg2])
randPerm(k)
randVariation(n, k)
rangeVec(min, max)
sparse(rows[, cols])

speye(dim)
square(x)
zeros(rows[, cols])
qr(mat[, tol])
svd(mat, k[, json][, callback])

Abstract types

boolVectorCompareCb(arg1, arg2)
intVectorCompareCb(arg1, arg2)

matrixArg
strVectorCompareCb(arg1, arg2)

vectorCompareCb(arg1, arg2)

Classes

BoolVector

IntVector

Matrix

SparseMatrix

SparseVector

StrVector

Vector

Methods

static

cat(nestedArrMat) → module:la.Matrix

Constructs a matrix by concatenating a double-nested array of matrices.

Example

// import la module
var la = require('qminer').la;
// create four matrices and concatenate (2 block columns, 2 block rows)
var la = require('qminer').la;
var A = new la.Matrix([[1,2], [3,4]]);
var B = new la.Matrix([[5,6], [7,8]]);
var C = new la.Matrix([[9,10], [11,12]]);
var D = new la.Matrix([[13,14], [15,16]]);
// create a nested matrix
// returns the matrix:
// 1  2  5  6
// 3  4  7  8
// 9  10 13 14
// 11 12 15 16
var mat = la.cat([[A,B], [C,D]]);

Parameter

Name	Type	Optional	Description
nestedArrMat	Array of Array of module:la.Matrix		An array of block rows, where each block row is an array of matrices. For example: `[[m_11, m_12], [m_21, m_22]]` is used to construct a matrix where the (i,j)-th block submatrix is `m_ij`.

Returns: module:la.MatrixB Concatenated matrix.

static

conjgrad(A, b[, x][, verbose]) → module:la.Vector

Solves the PSD symmetric system: A x = b, where A is a positive-definite symmetric matrix.

Example

// import la module
var la = require('qminer').la;
// create a positive-definite symmetric matrix
var vecTemp = new la.Vector([1, 2, 3]);
var mat = vecTemp.diag();
// create the right-hand side vector 
var vec = new la.Vector([0.5, 3, -2]);
// solve the PSD symmetric system
var x = la.conjgrad(mat, vec);

Parameters

Name	Type	Optional	Description
A	(module:la.Matrix or module:la.SparseMatrix)		The matrix on the left-hand side of the system.
b	module:la.Vector		The vector on the right-hand side of the system.
x	module:la.Vector	Yes	Current solution. Default is a vector of zeros.
verbose	boolean	Yes	If true, console logs the residuum value. Defaults to `false`.

Returns: module:la.VectorB Solution to the system.

static

copyVecToArray(vec) → Array of number

Copies the vector into a JavaScript array of numbers.

Example

// import la module
var la = require('qminer').la;
// create a new vector
var vec = new la.Vector([1, 2, 3]);
// create a JavaScript array out of vec
var arr = la.copyVecToArray(vec); // returns an array [1, 2, 3]

Parameter

Name	Type	Optional	Description
vec	module:la.Vector		Copied vector.

Returns: Array of numberB A JavaScript array of numbers.

static

eye(dim) → module:la.Matrix

Returns an dense identity matrix.

Example

// import la module
var la = require('qminer').la;
// generate a dense identity matrix of dimension 5
var id = la.eye(5);

Parameter

Name	Type	Optional	Description
dim	number		The dimension of the identity matrix. Must be a positive integer.

Returns: module:la.MatrixB A dim-by-dim identity matrix.

static

findMaxIdx(X) → Array of number

Returns a JS array of indices idxArray that correspond to the max elements in each column of dense matrix. The resulting array has one element for vector input.

Example

// import la module
var la = require('qminer').la;
// create a dense matrix
var mat = new la.Matrix([[1, 2], [2, 0]]);
// get the indices of the maximum elements in each column of mat
// returns the array:
// [1, 0]
la.findMaxIdx(mat);

Parameter

Name	Type	Optional	Description
X	(module:la.Matrix or module:la.Vector)		The matrix or vector.

Returns: Array of numberB Array of indexes where maximum is found, one for each column.

static

inverseSVD(mat) → module:la.Matrix

Calculates the inverse matrix with SVD.

Example

// import la module
var la = require('qminer').la;
// create a random matrix
var mat = new la.Matrix({ rows: 5, cols: 5, random: true });
// get the inverse of mat
var inv = la.inverseSVD(mat);

Parameter

Name	Type	Optional	Description
mat	module:la.Matrix		The matrix we want to inverse.

Returns: module:la.MatrixB The inverse matrix of mat.

static

ones(dim) → module:la.Vector

Returns a vector with all entries set to 1.0.

Example

// import la module
var la = require('qminer').la;
// create a 3-dimensional vector with all entries set to 1.0
var vec = la.ones(3);

Parameter

Name	Type	Optional	Description
dim	number		Dimension of the vector.

Returns: module:la.VectorB A dim-dimensional vector whose entries are set to 1.0.

static

pdist2(X1, X2) → module:la.Matrix

Computes and returns the pairwise squared euclidean distances between columns of X1 and X2 (mat3[i,j] = ||mat(:,i) - mat2(:,j)||^2).

Example

// import la module
var la = require('qminer').la;
// construct two input matrices
var X1 = new la.Matrix([[1,2], [2,0]]);
var X2 = new la.Matrix([[1,0.5,0],[0,-0.5,-1]]);
// get the pairwise squared distance between the matrices
// returns the matrix:
// 4 6.5 10
// 1 2.5 5
la.pdist2(X1, X2);

Parameters

Name	Type	Optional	Description
X1	module:la.Matrix		First matrix.
X2	module:la.Matrix		Second matrix.

Returns: module:la.MatrixB Matrix with X1.cols rows and X2.cols columns containing squared euclidean distances.

static

randi(num[, len]) → (number or la.IntVector)

Returns a randomly selected integer(s) from an array.

Example

// import la module
var la = require('qminer').la;
// generate a random integer between 0 and 10
var number = la.randi(10);
// generate an integer vector containing 5 random integers between 0 and 10
var vec = la.randi(10, 5);

Parameters

Name	Type	Optional	Description
num	number		The upper bound of the array. Must be an integer.
len	number	Yes	The number of selected integers. Must be an integer.

Returns: (number or la.IntVector)B
1. Randomly selected integer from the array [0,...,num-1], if no parameters are given.
2. module:la.IntVector, if parameter len is given. The vector contains random integers from the array [0,...,num-1] (with repetition).

static

randn([arg1][, arg2]) → (number, module:la.Vector, or module:la.Matrix)

Returns an object with random numbers.

Example

// import la module
var la = require('qminer').la;
// generate a random number
var number = la.randn();
// generate a random vector of length 7
var vector = la.randn(7);
// generate a random matrix with 7 rows and 10 columns
var mat = la.randn(7, 10);

Parameters

Name	Type	Optional	Description
arg1	number	Yes	Represents dimension of vector or number of rows in matrix. Must be an integer.
arg2	number	Yes	Represents number of columns in matrix. Must be an integer.

Returns: (number, module:la.Vector, or module:la.Matrix)B
1. Number, if no parameters are given.
2. module:la.Vector, if parameter arg1 is given.
3. module:la.Matrix, if parameters arg1 and arg2 are given.

static

randPerm(k) → Array of number

Returns a permutation of elements.

Example

// import la module
var la = require('qminer').la;
// create an array/permutation of 5 elements
var perm = la.randPerm(5);

Parameter

Name	Type	Optional	Description
k	number		Number of elements to permutate.

Returns: Array of numberB A JavaScript array of integers. Represents a permutation of k elements.

static

randVariation(n, k) → Array of number

Returns a JavaScript array, which is a sample of integers from an array.

Example

// import la module
var la = require('qminer').la;
// create an array containing 5 integers between 0 and 15
var arr = la.randVariation(15, 5);

Parameters

Name	Type	Optional	Description
n	number		The upper bound of the generated array `[0,...,n-1]`. Must be an integer.
k	number		Length of the sample. Must be smaller or equal to `n`.

Returns: Array of numberB The sample of k numbers from [0,...,n-1], sampled without replacement.

static

rangeVec(min, max) → module:la.IntVector

Generates an integer vector given range.

Example

// import la module
var la = require('qminer').la;
// create a range vector containing 1, 2, 3
var vec = la.rangeVec(1, 3);

Parameters

Name	Type	Optional	Description
min	number		Start value. Should be an integer.
max	number		End value. Should be an integer.

Returns: module:la.IntVectorB Integer range vector.

static

sparse(rows[, cols]) → module:la.SparseMatrix

Returns a sparse zero matrix.

Example

// import la module
var la = require('qminer').la;
// create a sparse zero matrix with 5 rows and columns
var spMat = la.sparse(5);

Parameters

Name Type Optional Description

Name	Type	Optional	Description
rows	number		Number of rows of the sparse matrix.
cols	number	Yes	Number of columns of the sparse matrix. Defaults to `rows`.

rows

number

Number of rows of the sparse matrix.

cols

number

Yes

Number of columns of the sparse matrix.

Defaults to rows.

Returns: module:la.SparseMatrixB A rows-by-cols sparse zero matrix.

static

speye(dim) → module:la.SparseMatrix

Returns a sparse identity matrix

Example

// import la module
var la = require('qminer').la;
// generate a sparse identity matrix of dimension 5
var spId = la.speye(5);

Parameter

Name	Type	Optional	Description
dim	number		The dimension of the identity matrix. Must be a positive integer.

Returns: module:la.SparseMatrixB A dim-by-dim identity matrix.

static

square(x) → (number or module:la.Vector)

Squares the values in vector.

Example

// import la module
var la = require('qminer').la;
// create a vector
var vec = new la.Vector([1, 2, 3]);
// square the values of the vector
// returns the vector containing  the values 1, 4, 9
var sqr = la.square(vec);

Parameter

Name	Type	Optional	Description
x	(number or module:la.Vector)		The value/vector.

Returns: (number or module:la.Vector)B
1. If x is a number, returns square of x.
2. If x is a module:la.Vector, returns a module:la.Vector, where the i-th value of the vector is the square of x[i].

static

zeros(rows[, cols]) → module:la.Matrix

Returns a dense zero matrix.

Example

// import la module
var la = require('qminer').la;
// create a sparse zero matrix with 5 rows and 3 columns
var mat = la.zeros(5, 3);

Parameters

Name Type Optional Description

Name	Type	Optional	Description
rows	number		Number of rows of the matrix.
cols	number	Yes	Number of columns of the matrix. Defaults to `rows`.

rows

number

Number of rows of the matrix.

cols

number

Yes

Number of columns of the matrix.

Defaults to rows.

Returns: module:la.MatrixB A rows-by-cols dense zero matrix.

qr(mat[, tol]) → Object

Computes the QR decomposition.

Example

// import la module
var la = require('qminer').la;
// create a random matrix
var mat = new la.Matrix({ rows: 10, cols: 5, random: true });
// calculate the QR decomposition of mat
var qrRes = la.qr(mat);

Parameters

Name Type Optional Description

Name	Type	Optional	Description
mat	module:la.Matrix		The matrix.
tol	number	Yes	The tolerance number. Defaults to `1e-6`.

mat

module:la.Matrix

The matrix.

tol

number

Yes

The tolerance number.

Defaults to 1e-6.

Returns: ObjectB A JSON object qrRes which contains the decomposition matrices:
qrRes.Q - The orthogonal matrix Q of the QR decomposition. Type module:la.Matrix.
qrRes.R - The upper triangular matrix R of the QR decomposition. Type module:la.Matrix.

svd(mat, k[, json][, callback]) → Object

Computes the truncated SVD decomposition.

Examples

Asynchronous function

// import the modules
var la = require('qminer').la;
// create a random matrix
var A = new la.Matrix({ rows: 10, cols: 5, random: true });
// set the parameters for the calculation
var k = 2; // number of singular vectors
var param = { iter: 1000, tol: 1e-4 };
// calculate the svd
la.svd(A, k, param, function (err, result) {
   if (err) { console.log(err); }
   // successful calculation
   var U = result.U;
   var V = result.V;
   var s = result.s;
});

Synchronous function

// import the modules
var la = require('qminer').la;
// create a random matrix
var A = new la.Matrix({ rows: 10, cols: 5, random: true });
// set the parameters for the calculation
var k = 2; // number of singular vectors
var param = { iter: 1000, tol: 1e-4 };
// calculate the svd
var result = la.svd(A, k, param);
// successful calculation
var U = result.U;
var V = result.V;
var s = result.s;

Parameters

Name Type Optional Description

mat

(module:la.Matrix or module:la.SparseMatrix)

The matrix.

number

The number of singular vectors to be computed.

json

Object

Yes

The JSON object.

Values in json have the following properties:

Name Type Optional Description

iter

number

Yes

The number of iterations used for the algorithm.

Defaults to 100.

tol

number

Yes

The tolerance number.

Defaults to 1e-6.

callback

function()

Yes

The callback function, that takes the error parameters (err) and the result parameter (res). Only for the asynchronous function.

Returns: ObjectB The JSON object svdRes which contains the SVD decomposition USV^T matrices:
svdRes.U - The dense matrix of the decomposition. Type module:la.Matrix.
svdRes.V - The dense matrix of the decomposition. Type module:la.Matrix.
svdRes.s - The vector containing the singular values of the decomposition. Type module:la.Vector.

Abstract types

inner

boolVectorCompareCb(arg1, arg2) → (number or boolean)

Vector sort comparator callback.

Parameters

Name	Type	Optional	Description
arg1	boolean		First argument.
arg2	boolean		Second argument.

Returns: (number or boolean)B If boolVectorCompareCb(arg1, arg2) is less than 0 or false, sort arg1 to a lower index than arg2, i.e. arg1 comes first.

inner

intVectorCompareCb(arg1, arg2) → (number or boolean)

Vector sort comparator callback.

Parameters

Name	Type	Optional	Description
arg1	number		First argument.
arg2	number		Second argument.

Returns: (number or boolean)B If intVectorCompareCb(arg1, arg2) is less than 0 or false, sort arg1 to a lower index than arg2, i.e. arg1 comes first.

inner

matrixArg Object

Matrix constructor parameter object.

Properties

Name Type Optional Description

Name	Type	Optional	Description
rows	number		Number of rows.
cols	number		Number of columns.
random	boolean	Yes	Generate a random matrix with entries sampled from a uniform [0,1] distribution. If set to false, a zero matrix is created. Defaults to `false`.

rows

number

Number of rows.

cols

number

Number of columns.

random

boolean

Yes

Generate a random matrix with entries sampled from a uniform [0,1] distribution. If set to false, a zero matrix is created.

Defaults to false.

inner

strVectorCompareCb(arg1, arg2) → (number or boolean)

Vector sort comparator callback.

Parameters

Name	Type	Optional	Description
arg1	string		First argument.
arg2	string		Second argument.

Returns: (number or boolean)B If strVectorCompareCb(arg1, arg2) is less than 0 or false, sort arg1 to a lower index than arg2, i.e. arg1 comes first.

inner

vectorCompareCb(arg1, arg2) → (number or boolean)

Vector sort comparator callback.

Parameters

Name	Type	Optional	Description
arg1	number		First argument.
arg2	number		Second argument.

Returns: (number or boolean)B If vectorCompareCb(arg1, arg2) is less than 0 or false, sort arg1 to a lower index than arg2, i.e. arg1 comes first.