node-matrices

node-matrices is a simple, lightweight matrix manipulation library supporting many common matrix operations.

Installation

npm install node-matrices

var Matrix = require('node-matrices');

Documentation

General notes:

• All Matrix objects are immutable.
• All indices are zero-based.

Basic manipulation

.constructor(...rows)

• Each parameter to the constructor should be an array of integers corresponding to a single row of the matrix. All of the rows should have the same length.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
);
// -> Matrix { data: [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ] }

• #numRows() - Returns the number of rows in the matrix.
• #numColumns() - Returns the number of columns in the matrix.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6]
);
m.numRows()
// -> 2
m.numColumns()
// -> 3

• #get(rowIndex, columnIndex) - Returns the value at a specific location. This will return undefined if either index is out of range.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6]
);
m.get(0, 1)
// -> 2
m.get(1, 2)
// -> 6
m.get(500, 0)
// -> undefined

• #getRow(rowIndex) - Returns a new matrix containing only the row at the specified index.
• #getColumn(columnIndex) - Returns a new matrix containing only the column at the specified index.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
);
m.getRow(1)
// -> Matrix { data: [ [ 4, 5, 6 ] ] }
m.getColumn(2)
// -> Matrix { data: [ [ 3 ], [ 6 ], [ 9 ] ] }

• #sliceRows(startIndex[, endIndex])
• #sliceColumns(startIndex[, endIndex])
• #sliceBlock(startRowIndex, endRowIndex, startColumnIndex, endColumnIndex)
• Returns a new matrix containing only the rows between startIndex and endIndex - 1, inclusive. If endIndex is not provided, the rows/columns will be sliced until the end of the matrix.

var m = new Matrix(
  [1, 2, 3, 4],
  [5, 6, 7, 8],
  [9, 10, 11, 12],
  [13, 14, 15, 16]
);
m.sliceRows(1, 3)
// -> Matrix { data: [ [ 5, 6, 7, 8 ], [ 9, 10, 11, 12 ] ] }
m.sliceColumns(0, 2)
// -> Matrix { data: [ [ 1, 2 ], [ 5, 6 ], [ 9, 10 ], [ 13, 14 ] ] }
m.sliceBlock(0, 3, 1, 3)
// -> Matrix { data: [ [ 2, 3 ], [ 6, 7 ], [ 10, 11 ] ] }

• #omitRow(rowIndex)
• #omitColumn(columnIndex)
• Returns a new matrix with the specified row or column omitted.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
);
m.omitRow(0)
// -> Matrix { data: [ [ 4, 5, 6 ], [ 7, 8, 9 ] ] }
m.omitColumn(1)
// -> Matrix { data: [ [ 1, 3 ], [ 4, 6 ], [ 7, 9 ] ] }

• #combineHorizontal(otherMatrix)
• #combineVertical(otherMatrix)
• Combines two matrices as blocks. An error will be thrown if the matrices have a different number of rows (for combineHorizontal) or a different number of columns (for combineVertical).

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
var m2 = new Matrix(
  [5, 6],
  [7, 8]
);
m1.combineHorizontal(m2)
// -> Matrix { data: [ [ 1, 2, 5, 6 ], [ 3, 4, 7, 8 ] ] }
m1.combineVertical(m2)
// -> Matrix { data: [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ], [ 7, 8 ] ] }

• #replace(rowIndex, columnIndex, value)
• Returns a new matrix where the which is exactly the same as the old matrix, except that the value at rowIndex and columnIndex is value.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
);
m.replace(1, 2, Infinity)
// -> Matrix { data: [ [ 1, 2, 3 ], [ 4, 5, Infinity ], [ 7, 8, 9 ] ] }

Matrix operations

• #transpose()
• Returns the transpose of this matrix.

var m = new Matrix(
  [1, 2, 3],
  [4, 5, 6],
);
m.transpose()
// -> Matrix { data: [ [ 1, 4 ], [ 2, 5 ], [ 3, 6 ] ] }

• #determinant()
• Returns the determinant of this matrix. An error will be thrown if this matrix is not square.

var m = new Matrix(
  [1, 2],
  [3, 4]
);
m.determinant()
// -> -2

• #adjugate()
• Returns the adjugate of this matrix. An error will be thrown if this matrix is not square.

var m = new Matrix(
  [1, 2],
  [3, 4]
);
m.adjugate()
// -> Matrix { data: [ [ 4, -2 ], [ -3, 1 ] ] }

• #inverse()
• Returns the inverse of this matrix. An error will be thrown if this matrix is not square, or if this matrix is singular.

var m = new Matrix(
  [1, 2],
  [3, 4]
);
m.inverse()
// -> Matrix { data: [ [ -2, 1 ], [ 1.5, -0.5 ] ] }

• #add(otherMatrix)
• #subtract(otherMatrix)
• Returns the sum or difference of this matrix and another matrix. An error will be thrown if the two matrices have different dimensions.

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
var m2 = new Matrix(
  [5, 5],
  [5, 5]
);
m1.add(m2)
// -> Matrix { data: [ [ 6, 7 ], [ 8, 9 ] ] }
m1.subtract(m2)
// -> Matrix { data: [ [ -4, -3 ], [ -2, -1 ] ] }

• #multiply(otherMatrix)
• Returns the product of this matrix and another matrix. An error will be thrown if the matrices do not have compatible sizes.
• To multiply a matrix by a scalar, use #scale().

var m1 = new Matrix(
  [1, 2, 3],
  [4, 5, 6]
);
var m2 = new Matrix(
  [7, 8],
  [9, 10],
  [11, 12]
);
m1.multiply(m2)
// -> Matrix { data: [ [ 58, 64 ], [ 139, 154 ] ] }
m1.multiply(m1)
// (throws an error)

• #scale(scalar)
• Returns the scalar product of this matrix and scalar.

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
m1.scale(3)
// -> Matrix { data: [ [ 3, 6 ], [ 9, 12 ] ] }

• #pow(exponent)
• Raises this matrix to the exponent power. An error will be thrown if this matrix is not square, or if exponent is not an integer.

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
m1.pow(5)
// -> Matrix { data: [ [ 37, 54 ], [ 81, 118 ] ] }

Value-checking

• #equals(otherMatrix)
• Returns true if this and otherMatrix are equivalent, and false otherwise. Equivalent matrices contain all of the same values in the same locations.

var m1 = new Matrix([1, 2, 3]);
var m2 = new Matrix([1, 2, 3]);
var m3 = new Matrix([1, 2, 4]);
m1.equals(m2)
// -> true
m1.equals(m3)
// -> false

• #isSquare()
• Returns true if this matrix is square (i.e. has the same number of rows and columns), and false otherwise.

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
var m2 = new Matrix(
  [1, 2, 3],
  [4, 5, 6]
);
m1.isSquare()
// -> true
m2.isSquare()
// -> false

• #isSymmetric()
• #isSkewSymmetric()
• Returns true if this matrix is symmetric (for isSymmetric) or skew-symmetric (for isSkewSymmetric). Otherwise, returns false.

var m1 = new Matrix(
  [1, 2],
  [2, 4]
);
var m2 = new Matrix(
  [0, 2],
  [-2, 0]
);
m1.isSymmetric()
// -> true
m1.isSkewSymmetric()
// -> false
m2.isSymmetric()
// -> false
m2.isSkewSymmetric()
// -> true

• #isUpperTriangular()
• #isLowerTriangular()
• #isDiagonal()
• Returns true if this matrix is upper triangular, lower triangular, or diagonal, respectively; otherwise, returns false.

var m1 = new Matrix(
  [1, 2],
  [0, 5]
);
var m2 = new Matrix(
  [1, 0],
  [0, 5]
);
m1.isUpperTriangular()
// -> true
m1.isLowerTriangular()
// -> false
m1.isDiagonal()
// -> false
m2.isUpperTriangular()
// -> true
m2.isLowerTriangular()
// -> true
m2.isDiagonal()
// -> true

• #isIdentity()
• Returns true if this matrix is an identity matrix, otherwise false.

var m1 = new Matrix(
  [1, 0],
  [0, 1]
);
var m2 = new Matrix(
  [1, 1],
  [0, 1]
);
m1.isIdentity()
// -> true
m2.isIdentity()
// -> false

• #isNonZero()
• Returns true if this matrix contains any nonzero values. Otherwise, returns false.

var m1 = new Matrix(
  [0, 0],
  [0, 0]
);
var m2 = new Matrix(
  [0, 1],
  [0, 0]
);
m1.isNonZero()
// -> false
m2.isNonZero()
// -> true

• #isSingular()
• Returns true if this matrix is singular, otherwise false. An error will be thrown if this matrix is not square.

var m1 = new Matrix(
  [1, 2],
  [3, 4]
);
var m2 = new Matrix(
  [1, 2],
  [2, 4]
);
m1.isSingular()
// -> false
m2.isSingular()
// -> true

Static methods

• .identity(size)
• Returns an identity matrix of the specified size.

Matrix.identity(3)
// -> Matrix { data: [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ] }

• .zeros(numRows, numColumns)
• Returns a matrix of the specified dimensions which only contains zeros.

Matrix.zeros(2, 3)
// -> Matrix { data: [ [ 0, 0, 0 ], [ 0, 0, 0 ] ] }