@rayyamhk/matrix
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A professional, comprehensive and high-performance library for you to manipulate matrices.
npm install --save @rayyamhk/matrix
const Matrix = require('@rayyamhk/matrix');
const A = new Matrix([
[1, 2],
[3, 4],
]);
const B = new Matrix([
[2, 3],
[4, 5],
]);
const Sum = Matrix.add(A, B);
const [Q, R] = Matrix.QR(Sum);
const det = Sum.det();
const eigenvalues = Sum.eigenvalues();
npm install
npm run build
It creates a production version in /lib
npm install
npm run test
It runs all tests in /src/tests
@param { Array } A - Two dimensional array where A[i][j] represents the i-th row and j-th column of a matrix
@return { Matrix } - Returns instance of Matrix
new Matrix([]); // 0x0 matrix
new Matrix([
[1, 2, 3, 4],
]); // 1x4 matrix
new Matrix([
[1],
[2],
[3],
]); // 3x1 matrix
new Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
]); // 3x3 matrix
@param { Matrix } A - Any matrix
@param { Boolean } optimized - Returns [P, LU] if it is true, [P, L, U] if it is false
@return { Array } - Returns the LUP decomposition of matrix
Find the LUP decomposition of a matrix, where L is lower triangular matrix which diagonal entries are always 1, U is upper triangular matrix, and P is permutation matrix. It is implemented using Gaussian Elimination with Partial Pivoting. The reason of using Partial Pivoting is to reduce the error caused by floating-point arithmetic. If you choose the optimized algorithm, both L and U are merged into one matrix in order to improve performance.
const A = new Matrix([
[4, 3],
[6, 3],
]);
const [P, L, U] = Matrix.LU(A, false);
// P is [[0, 1], [1, 0]], L is [[1, 0], [2/3, 1]], U is [[6, 3], [0, 1]] and A = PLU.
const [P, LU] = Matrix.LU(A, true);
// P is [ 1, 0 ], LU = [[6, 3], [2/3, 1]]
// Note: P is an permutation array, L and U can be extracted from LU.
@param { Matrix } A - Any matrix
@return { Array } - Returns [Q, R], which is the QR decomposition of A
Find the QR decomposition of a matrix, where Q is orthogonal matrix, R is upper triangular matrix. The algorithm is implemented using Householder Transform instead of Gram–Schmidt process because the Householder Transform is more numerically stable.
const A = new Matrix([
[12, -51, 4],
[6, 167, -68],
[-4, 24, -41],
]);
const [Q, R] = Matrix.QR(A);
// Q is [[-0.8571, 0.3943, 0.3314], [-0.4286, -0.9029, -0.0343], [0.2857, -0.1714, 0.9429]],
// R is [[-14, -21, 14], [0, -175, 70], [0, 0, -35]],
// and A = QR
@param { Matrix } U - n x n upper triangular matrix
@param { Matrix } y - n x 1 matrix
@return { Matrix } - Returns n x 1 matrix which is the solution of Ux = y
Solve system of linear equations Ux = y using backward substitution, where U is an upper triangular matrix. If there is no unique solutions, an error is thrown.
const A = new Matrix([
[1, 2],
[0, 3],
]);
const y = new Matrix([
[1],
[3],
]);
try {
const x = Matrix.backward(A, y); // [[-1], [1]]
} catch (e) {
console.log(e.message);
}
@param { Matrix } L - n x n lower triangular matrix
@param { Matrix } y - n x 1 matrix
@return { Matrix } - Returns n x 1 matrix which is the solution of Lx = y
Solve system of linear equations Lx = y using forward substitution, where L is a lower triangular matrix. If there is no unique solutions, an error is thrown.
const A = new Matrix([
[1, 0],
[2, 3],
]);
const y = new Matrix([
[1],
[8],
]);
try {
const x = Matrix.forward(A, y); // [[1], [2]]
} catch (e) {
console.log(e.message);
}
@param { Matrix } A - n x n square matrix
@param { Matrix } y - n x 1 matrix
@return { Matrix } - Returns n x 1 matrix which is the solution of Ax = y
Solve system of linear equations Ax = y using LU decomposition. If there is no unique solutions, an error is thrown.
const A = new Matrix([
[1, 2],
[3, 4],
]);
const y = new Matrix([
[5],
[11],
]);
try {
const x = Matrix.solve(A, y); // [[1], [2]]
} catch (e) {
console.log(e.message);
}
@param { Matrix } A - Any matrix
@param { Matrix } B - Any matrix that has same size with A
@return { Matrix } - Returns sum of two matrices
const A = new Matrix([
[1, 2],
[3, 4],
]);
const B = new Matrix([
[5, 6],
[7, 8],
]);
const Sum = Matrix.add(A, B); // [[6, 8], [10, 12]]
@param { Matrix } A - Any non-singular matrix
@return { Matrix } - Returns the inverse of A
Find the inverse of non-singular matrix using Elementary Row Operations. If the matrix is singular, an error is thrown.
const A = new Matrix([
[1, 2],
[3, 4],
]);
try {
const inv = Matrix.inverse(A); // [[-2, 1], [1.5, -0.5]]
} catch (e) {
console.log(e.message);
}
@param { Matrix } A - Any matrix
@param { Matrix } B - Any matrix that is size-compatible with A
@return { Matrix } - Returns the product of two matrices
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
]);
const B = new Matrix([
[-1, -2],
[3, 4],
[-5, -6],
]);
const Product = Matrix.multiply(A, B); // [[-10, -12], [-19, -24]]
@param { Matrix } A - Any square matrix
@param { Number } exponent - Any Non-negative integer
@return { Matrix } - Returns the power of A
The algorithm is implemented recursively.
const A = new Matrix([
[2, 0],
[0, 2],
]);
const Result = Matrix.pow(A, 10); // [[1024, 0], [0, 1024]]
@param { Matrix } A - Any matrix
@param { Matrix } B - Any matrix that has same size with A
@return { Matrix } - Returns difference of two matrices
const A = new Matrix([
[1, 2],
[3, 4],
]);
const B = new Matrix([
[4, 3],
[2, 1],
]);
const Diff = Matrix.subtract(A, B); // [[-3, -1], [1, 3]]
@param { Matrix } A - Any matrix
@return { Matrix } - Returns transpose of A
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
]);
const T = Matrix.transpose(A); // [[1, 4], [2, 5], [3, 6]]
@param { Number | String } p - Type of matrix norm, it can be 1, 2, Infinity or 'F'
@return { Number } - Returns the condition number of matrix
Find the condition number of square matrix with respect to different matrix norm. If the matrix is singular, returns Infinity. The condition number is not cached.
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
[1, 2, 7],
]);
A.cond(1); // 64
A.cond(2); // 32.844126527227147
A.cond(Infinity); // 42.4999,
A.cond('F'); // 34.117851306578174
@return { Number } - Returns the determinant of square matrirx
Find the determinant of square matrirx. The determinant is cached.
const A = new Matrix([
[1, 3, 5, 9],
[1, 3, 1, 7],
[4, 3, 9, 7],
[5, 2, 0, 9],
]);
A.det(); // -376
@return { Array } - Returns array of eigenvalues
Find the eigenvalues of any square matrix using QR Algorithm with single shift. The eigenvalues can be either real number or complex number. Note that all eigenvalues are instance of Complex, for more details please visit Complex.js. The eigenvalues are cached.
const A = new Matrix([
[13, -12, 6, -9],
[1, -11, -13, 0],
[-6, -2, 15, -6],
[14, -8, 1, 11],
]);
const eigenvalues = A.eigenvalues();
eigenvalues.forEach((eigenvalue) => {
console.log(eigenvalue.toString()); // Instance method of Complex
});
// Result: '10.7046681565572', '-12.9152701010176', '15.1053009722302 + 14.3131819845827i', '15.1053009722302 - 14.3131819845827i'
@param { Number | String } p - The choice of matrix norm, it can be 1, 2, Infinity or 'F'
@return { Number } - Returns p-norm of the matrix.
Find the matrix norm of any matrix with respect to the choice of norm. The norms are not cached. 1-norm: maximum absolute column sum of the matrix 2-norm: the largest singular value of matrix Infinity-norm: maximum absolute row sum of the matrix Frobenius norm: Euclidean norm invloving all entries
const A = new Matrix([
[1, 7, -5, 2, -7],
[-8, 0, 2, 9, 4],
[3, 4, 9, 6, 5],
]);
A.norm(1); // 17
A.norm(2); // 15.849881886952135
A.norm(Infinity); // 27
A.norm('F'); // 21.447610589527216
@return { Number } - Returns the nullity of the matrix
Find the nullity of any matrix, which is the dimension of the nullspace. The nullity is cached.
const A = new Matrix([
[0, 1, 2],
[1, 2, 1],
[2, 7, 8],
]);
A.nullity(); // 1
@return { Number } - Returns the rank of the matrix
Find the rank of any matrix, which is the dimension of the row space. The rank is cached.
const A = new Matrix([
[0, 1, 2],
[1, 2, 1],
[2, 7, 8],
]);
A.rank(); // 2
@return { Array } - Returns the number of rows and columns of a matrix.
Find the size of any matrix, which is in the form of [row, column]. The size of matrix is cached.
const A = new Matrix([
[0, 1, 2, 3],
[4, 5, 6, 7],
]);
const [row, col] = A.size(); // 2, 4
@return { Number } - Returns the trace of the square matrix.
Find the trace of any square matrix, which is the sum of all entries on the main diagonal. The trace is cached.
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
]);
A.trace(); // 15
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the matrix is diagonal matrix
Diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. Note that the term diagonal refers to rectangular diagonal. The result is cached.
const A = new Matrix([
[1, 0, 0],
[0, 5, 0],
[0, 0, -3],
]);
const B = new Matrix([
[1, 0, 0.1],
[0, 5, 0],
[0, 0, -3],
]);
A.isDiagonal(); // true
B.isDiagonal(); // false
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the matrix is lower triangular
Lower triangular matrix is a matrix in which all the entries above the main diagonal are zero. Note that it can be applied to any non-square matrix. The result is cached.
const A = new Matrix([
[6, 0, 0, 0],
[1, -5, 0, 0],
[2, 30, 1, 0],
]);
A.isLowerTriangular(); // true
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the square matrix is orthogonal
Orthogonal matrix is a matrix in which all rows and columns are orthonormal vectors. The result is cached.
const Reflection = new Matrix([
[1, 0],
[0, -1],
]);
Reflection.isOrthongonal(); // true
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the square matrix is skew symmetric
Skew symmetric matrix is a square matrix whose transpose equals its negative. The result is cached.
const A = new Matrix([
[1, 2, 3, 4],
[-2, 2, -4, 5],
[-3, 4, 100, 10],
[-4, -5, -10, 5],
]);
A.isSkewSymmetric(); // true
@return { Boolean } - Returns true if the matrix is square
Square matrix is a matrix with same number of rows and columns. The result is cached.
const A = new Matrix([
[1, 2],
[3, 4],
]);
A.isSquare(); // true
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the square matrix is symmetric
symmetric matrix is a square matrix that is equal to its transpose. The result is cached.
const A = new Matrix([
[1, 4, 3],
[4, 5, 4],
[3, 4, 5],
]);
A.isSymmetric(); // true
@param { Number } digit - Number of significant digits
@return { Boolean } - Returns true if the matrix is upper triangular
Upper triangular matrix is a matrix in which all the entries below the main diagonal are zero. Note that it can be applied to any non-square matrix. The result is cached
const A = new Matrix([
[6, 0, 1, 5],
[0, -5, 4, 7],
[0, 0, 1, 2],
]);
A.isUpperTriangular(); // true
@param { Matrix } A - Any matrix
@return { Matrix } - Returns a copy of A
Create a copy of matrix. Note that it resets the cached data.
const A = new Matrix([
[1, 2],
[3, 4],
]);
Matrix.clone(A); // [[1, 2], [3, 4]]
@param { Matrix } A - Any matrix
@param { Integer } index - Any valid column index
@return { Matrix } - Returns column of A
const A = new Matrix([
[1, 2],
[3, 4],
[5, 6],
]);
Matrix.column(A, 0); // [[1], [3], [5]]
Matrix.column(A, 1); // [[2], [4], [6]]
@param { Array } values - Array of numbers or matrices
@return { Array } - Returns a block diagonal matrix
Generate diagonal matrix if the argument is an array of numbers, generate block diagonal matrix if the argument is an array of matrices.
Matrix.diag([1, 2, 3]); // [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
const values = [
new Matrix([
[1, 2],
[3, 4],
]),
new Matrix([
[5, 6],
[7, 8],
])
];
Matrix.diag(values); // [[1, 2, 0, 0], [3, 4, 0, 0], [0, 0, 5, 6], [0, 0, 7, 8]]
@param { Matrix } A - Any matrix
@param { Function } cb - Callback function which applies on each entry of A
@return { Matrix } - Returns a copy of new matrix
Apply a function over each entry of a matrix and return a new copy of the new matrix.
Matrix.elementwise(A, (entry) => entry * 2); // element-wise multiplication
Matrix.elementwise(A, (entry) => entry ** 2); // element-wise power
Matrix.elementwise(A, (entry) => entry - 10); // element-wise subtraction
@param { Integer } row - Any valid row index
@param { Integer } col - Any valid column index
@return { Number } - Returns entry of the matrix
const A = new Matrix([
[1, 2],
[3, 4],
]);
A.entry(0, 0); // 1
A.entry(0, 1); // 2
A.entry(1, 0); // 3
A.entry(1, 1); // 4
@param { Integer } row - Number of rows of matrix
@param { Integer } col - Number of columns of matrix
@param { Function } cb - Callback function which takes row and column as arguments and generate the corresponding entry
Generate a matrix which entries are the returned value of callback function.
Matrix.generate(3, 3, () => 0); // 3 x 3 zero matrix
Matrix.generate(3, 3, (i, j) => 1 / (i + j + 1)); // 3 x 3 Hilbert matrix
Matrix.generate(3, 3, (i, j) => i >= j ? 1 : 0); // 3 x 3 lower triangular matrix
@param { Matrix } A - Any matrix
@return { Array } - Returns entries of A on the main diagonal
const A = new Matrix([
[1, 2, 3, 4],
[5, 6, 7, 8],
]);
Matrix.getDiag(A); // [1, 6]
@param { Integer } row - Number of rows of a matrix
@param { Integer } col - Number of columns of a matrix
@param { Number } min - Lower bound of each entry
@param { Number } max - Upper bound of each entry
@param { Integer } toFixed - Number of decimal places
@return { Matrix } - Returns random matrix
Matrix.getRandomMatrix(3, 4, -10, 10, 2); // 3 x 4 matrix which entries are bounded by -10 and 10 and has 2 decimal places
@param { Integer } size - The size of matrix
@return { Matrix } - Returns identity matrix
Generate identity matrix with given size.
Matrix.identity(2); // 2 x 2 identity matrix
Matrix.identity(10); // 10 x 10 identity matrix
@param { Matirx } A - Any Matrix
@param { Matirx } B - Any Matrix
@param { Integer } digit - Number of significant digits
@return { Boolean } - Returns true if two matrices are considered as same
Determine whether two matrices are considered as equal.
const A = new Matrix([
[1, 2],
[3, 4],
]);
const B = new Matrix([
[1, 2],
[3, 4 + 10e-10],
]);
Matrix.isEqual(A, B); // true
const C = new Matrix([
[1, 2],
[3, 4 + 10e-2],
]);
Matrix.isEqual(A, C); // false
@param { Matrix } A - Any matrix
@param { Integer } index - Any valid row index
@return { Matrix } - Returns row of A
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
]);
Matrix.row(A, 0); // [[1, 2, 3]]
Matrix.row(A, 1); // [[4, 5, 6]]
@param { Matrix } A - Any matrix
@param { String | Number } rowsExp - Rows expression
@param { String | Number } colsExp - Columns expression
@return { Matrix } - Returns submatrix of A
Generate a submatrix of a matrix. Note that both rows and columns expression can be either string or nunmber.
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
]);
Matrix.submatrix(A, 0, 1); // [[2]], row 0 & column 1
Matrix.submatrix(A, '0:1', 1); [[1], [4]], row 0 + row 1 & column 1
Matrix.submatrix(A, '0:1', '0:1'); [[1, 2], [4, 5]], row 0 + row 1 & column 0 + column 1
Matrix.submatrix(A, ':', '1:2'); [[2, 3], [5, 6], [8,9]], all rows && column 1 + column 2
Matrix.submatrix(A, ':', ':'); same with A
@return { Boolean } - Returns the stringified matrix
const A = new Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
]);
A.toString(); // '1 2 3\n4 5 6\n7 8 9'
// 1 2 3
// 4 5 6
// 7 8 9
@param { Integer } row - Number of rows of the matrix
@param { Integer } col - Number of columns of the matrix
@return { Matrix } - Returns zero matrix
Generate a zero matrix
Matrix.zero(3, 4); // 3 x 4 zero matrix
Matrix.zero(10, 1); // 10 x 1 zero matrix
You are welcome to contribute by:
Copyright (C) 2020 Ray Yam
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
FAQs
A professional, comprehensive and high-performance library for you to manipulate matrices.
The npm package @rayyamhk/matrix receives a total of 419 weekly downloads. As such, @rayyamhk/matrix popularity was classified as not popular.
We found that @rayyamhk/matrix demonstrated a not healthy version release cadence and project activity because the last version was released a year ago. It has 1 open source maintainer collaborating on the project.
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