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[M]:
Mathjs Deep Dive: A Comprehensive Guide
Math.js is a powerful mathematics library for JavaScript that provides advanced mathematical capabilities beyond the native Math object. In this comprehensive guide, we'll explore the advanced features of math.js including matrix manipulations, symbolic computing, numerical methods, and practical applications.
Whether you're working on scientific computing, engineering calculations, or data analysis, this deep dive will help you leverage the full power of math.js in your projects.
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// Install math.js
!npm install mathjs
$ npm install mathjs up to date in 295ms 30 packages are looking for funding run `npm fund` for details
[26]:
// Import the library
const math = require('mathjs');
console.log('Math.js version:', math.version, '\n');
console.log('Library loaded successfully\n');
Math.js version: 14.3.1 Library loaded successfully
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1. Advanced Matrix Operations
Math.js provides powerful matrix operations that are essential for linear algebra, data analysis, and scientific computing. Let's explore some advanced matrix capabilities.
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// Creating matrices
console.log('Creating different types of matrices:\n');
// From array of arrays
const matrix1 = math.matrix([[1, 2], [3, 4]]);
console.log('Matrix from arrays:\n', matrix1.toString(), '\n');
// Using range and reshape
const matrix2 = math.reshape(math.range(1, 10), [3, 3]);
console.log('Matrix from range and reshape:\n', matrix2.toString(), '\n');
// Using eye for identity matrix
const identity = math.identity(3);
console.log('3x3 identity matrix:\n', identity.toString(), '\n');
// Creating a zeros or ones matrix
const zeros = math.zeros(2, 3);
const ones = math.ones(2, 3);
console.log('Zeros matrix:\n', zeros.toString(), '\n');
console.log('Ones matrix:\n', ones.toString(), '\n');
Creating different types of matrices: Matrix from arrays: [[1, 2], [3, 4]] Matrix from range and reshape: [[1, 2, 3], [4, 5, 6], [7, 8, 9]] 3x3 identity matrix: [[1, 0, 0], [0, 1, 0], [0, 0, 1]] Zeros matrix: [[0, 0, 0], [0, 0, 0]] Ones matrix: [[1, 1, 1], [1, 1, 1]]
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// Matrix operations
console.log('Basic matrix operations:\n');
const A = math.matrix([[1, 2], [3, 4]]);
const B = math.matrix([[5, 6], [7, 8]]);
// Addition and subtraction
console.log('A + B:\n', math.add(A, B).toString(), '\n');
console.log('A - B:\n', math.subtract(A, B).toString(), '\n');
// Matrix multiplication
console.log('A * B (matrix product):\n', math.multiply(A, B).toString(), '\n');
// Element-wise multiplication
console.log('A .* B (element-wise):\n', math.dotMultiply(A, B).toString(), '\n');
// Matrix power
console.log('A^2:\n', math.pow(A, 2).toString(), '\n');
// Transpose
console.log('A transpose:\n', math.transpose(A).toString(), '\n');
Basic matrix operations: A + B: [[6, 8], [10, 12]] A - B: [[-4, -4], [-4, -4]] A * B (matrix product): [[19, 22], [43, 50]] A .* B (element-wise): [[5, 12], [21, 32]] A^2: [[7, 10], [15, 22]] A transpose: [[1, 3], [2, 4]]
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// Matrix decompositions and advanced operations
console.log('Advanced matrix operations:\n');
// Create a square matrix for demonstrations
const M = math.matrix([[9, 3, 2], [3, 8, 4], [2, 4, 7]]);
console.log('Matrix M:\n', M.toString(), '\n');
// Determinant
const det = math.det(M);
console.log(`Determinant of M: ${det}\n`);
// Inverse matrix
const inv = math.inv(M);
console.log('Inverse of M:\n', inv.toString(), '\n');
// Verify inverse: M * M^-1 should be identity
const MTimesInv = math.multiply(M, inv);
console.log('M * M^-1 (should be identity):\n', MTimesInv.toString(), '\n');
// Eigenvalues and eigenvectors
const eigs = math.eigs(M);
console.log('Eigenvalues:\n', eigs.values.toString(), '\n');
Advanced matrix operations: Matrix M: [[9, 3, 2], [3, 8, 4], [2, 4, 7]] Determinant of M: 313 Inverse of M: [[0.12779552715654952, -0.04153354632587859, -0.012779552715654952], [-0.04153354632587859, 0.18849840255591055, -0.09584664536741215], [-0.012779552715654952, -0.09584664536741214, 0.2012779552715655]] M * M^-1 (should be identity): [[0.9999999999999999, 5.551115123125783e-17, 0], [0, 1, 0], [0, 1.1102230246251565e-16, 1]] Eigenvalues: [3.41007767316509, 6.526744108201979, 14.06317821863293]
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2. Symbolic Mathematics
One of math.js's powerful features is symbolic mathematics - working with expressions and equations algebraically rather than just numerically.
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// Creating and manipulating expressions
console.log('Working with symbolic expressions:\n');
// Create a symbolic expression
const expr1 = math.parse('x^2 + 2*x + 3');
console.log(`Expression: ${expr1.toString()}\n`);
// Evaluate with specific values
const result = expr1.evaluate({ x: 4 });
console.log(`Expression evaluated at x=4: ${result}\n`);
// Simplify expressions
const expr2 = math.parse('x*y + x*z');
const simplified = math.simplify(expr2);
console.log(`Original: ${expr2.toString()}\n`);
console.log(`Simplified: ${simplified.toString()}\n`);
// More complex simplification
const expr3 = math.parse('sin(x)^2 + cos(x)^2');
const simplified2 = math.simplify(expr3);
console.log(`Original: ${expr3.toString()}\n`);
console.log(`Simplified: ${simplified2.toString()}\n`);
Working with symbolic expressions: Expression: x ^ 2 + 2 * x + 3 Expression evaluated at x=4: 27 Original: x * y + x * z Simplified: x * (y + z) Original: sin(x) ^ 2 + cos(x) ^ 2 Simplified: sin(x) ^ 2 + cos(x) ^ 2
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// Symbolic differentiation
console.log('Symbolic differentiation:\n');
// Differentiate expressions
const expr = math.parse('x^3 + 2*x^2 - 5*x + 3');
const derivative = math.derivative(expr, 'x');
console.log(`Original expression: ${expr.toString()}\n`);
console.log(`Derivative: ${derivative.toString()}\n`);
// Evaluate the derivative
console.log(`Derivative at x=2: ${derivative.evaluate({x: 2})}\n`);
// Partial derivatives
const multiExpr = math.parse('x^2 * y + 3*x*y^2');
const dfdx = math.derivative(multiExpr, 'x');
const dfdy = math.derivative(multiExpr, 'y');
console.log(`Expression: ${multiExpr.toString()}\n`);
console.log(`∂f/∂x: ${dfdx.toString()}\n`);
console.log(`∂f/∂y: ${dfdy.toString()}\n`);
// Second derivatives
const d2fdx2 = math.derivative(dfdx, 'x');
console.log(`∂²f/∂x²: ${d2fdx2.toString()}\n`);
Symbolic differentiation: Original expression: x ^ 3 + 2 * x ^ 2 - 5 * x + 3 Derivative: 3 * x ^ 2 + 4 * x - 5 Derivative at x=2: 15 Expression: x ^ 2 * y + 3 * x * y ^ 2 ∂f/∂x: 2 * y * x + 3 * y ^ 2 ∂f/∂y: x ^ 2 + 6 * x * y ∂²f/∂x²: 2 * y
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3. Complex Analysis and Advanced Number Systems
Math.js supports complex numbers, advanced operations, and different number formats for precise calculations.
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// Advanced complex number operations
console.log('Advanced complex number operations:\n');
// Define complex numbers
const z1 = math.complex(3, 4); // 3 + 4i
const z2 = math.complex(1, -2); // 1 - 2i
console.log(`z1 = ${z1.toString()}\n`);
console.log(`z2 = ${z2.toString()}\n`);
// Basic operations
console.log(`z1 + z2 = ${math.add(z1, z2).toString()}\n`);
console.log(`z1 * z2 = ${math.multiply(z1, z2).toString()}\n`);
console.log(`z1 / z2 = ${math.divide(z1, z2).toString()}\n`);
// Polar form and exponential form
console.log(`|z1| (magnitude): ${math.abs(z1)}\n`);
console.log(`arg(z1) (phase in radians): ${math.arg(z1)}\n`);
console.log(`arg(z1) (phase in degrees): ${math.arg(z1) * 180 / Math.PI}°\n`);
// Convert between forms
const polarForm = { r: math.abs(z1), phi: math.arg(z1) };
console.log(`Polar form of z1: ${polarForm.r} ∠ ${polarForm.phi} rad\n`);
// Create complex from polar coordinates
const fromPolar = math.complex({ r: 5, phi: Math.PI/4 });
console.log(`Complex from polar (5 ∠ π/4): ${fromPolar.toString()}\n`);
// Complex exponential and logarithm
console.log(`e^(i*π) = ${math.evaluate('e^(i*pi)').toString()}\n`); // Should be close to -1
console.log(`ln(z1) = ${math.log(z1).toString()}\n`);
Advanced complex number operations: z1 = 3 + 4i z2 = 1 - 2i z1 + z2 = 4 + 2i z1 * z2 = 11 - 2i z1 / z2 = -1 + 2i |z1| (magnitude): 5 arg(z1) (phase in radians): 0.9272952180016122 arg(z1) (phase in degrees): 53.13010235415598° Polar form of z1: 5 ∠ 0.9272952180016122 rad Complex from polar (5 ∠ π/4): 3.5355339059327378 + 3.5355339059327373i e^(i*π) = -1 ln(z1) = 1.6094379124341003 + 0.9272952180016122i
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// Complex analysis functions
console.log('Complex analysis functions:\n');
// Evaluating functions with complex arguments
console.log(`sin(z1) = ${math.sin(z1).toString()}\n`);
console.log(`cos(z1) = ${math.cos(z1).toString()}\n`);
console.log(`tan(z1) = ${math.tan(z1).toString()}\n`);
// Complex roots and powers
console.log(`z1^2 = ${math.pow(z1, 2).toString()}\n`);
console.log(`sqrt(z1) = ${math.sqrt(z1).toString()}\n`);
// Complex functions from expression strings
const complexExpr = math.evaluate('(2+3i)^(1+i)');
console.log(`(2+3i)^(1+i) = ${complexExpr.toString()}\n`);
// Complex matrix operations
const complexMatrix = math.matrix([
[math.complex(1, 1), math.complex(2, -1)],
[math.complex(0, 2), math.complex(3, 0)]
]);
console.log('Complex matrix:\n', complexMatrix.toString(), '\n');
console.log('Determinant of complex matrix:\n', math.det(complexMatrix).toString(), '\n');
console.log('Inverse of complex matrix:\n', math.inv(complexMatrix).toString(), '\n');
Complex analysis functions: sin(z1) = 3.853738037919377 - 27.016813258003932i cos(z1) = -27.034945603074224 - 3.851153334811777i tan(z1) = -0.00018734620462947842 + 0.9993559873814732i z1^2 = -6.999999999999997 + 24i sqrt(z1) = 2 + i (2+3i)^(1+i) = -0.8636068988831277 + 1.0368893969147763i Complex matrix: [[1 + i, 2 - i], [2i, 3]] Determinant of complex matrix: 1 - i Inverse of complex matrix: [[1.5 + 1.5i, -1.5 - 0.5i], [1 - i, i]]
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4. Numerical Methods and Optimization
Math.js provides various numerical methods for solving equations and optimization problems.
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// Solving equations numerically
console.log('Solving equations numerically:\n');
// Define a function to find its roots
const f = (x) => math.evaluate('x^3 - 6*x^2 + 11*x - 6', { x: x });
// Find roots using a numerical solver
// Math.js doesn't have a built-in root finder, so we'll implement a simple one
function findRoot(f, start, end, tolerance = 1e-10, maxIterations = 100) {
// Bisection method
let a = start;
let b = end;
let fa = f(a);
let fb = f(b);
if (fa * fb > 0) {
return null; // No guaranteed root in this interval
}
for (let i = 0; i < maxIterations; i++) {
let c = (a + b) / 2;
let fc = f(c);
if (Math.abs(fc) < tolerance) {
return c; // Root found
}
if (fa * fc < 0) {
b = c;
fb = fc;
} else {
a = c;
fa = fc;
}
}
Solving equations numerically: Equation: x^3 - 6x^2 + 11x - 6 = 0 Root 1: 1 (f(root1) = 0) Root 2: 2.999999999970896 (f(root2) = -5.820766091346741e-11) Root 3: 4 (f(root3) = 6) Factored form check: (x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x - 6
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// Numerical Integration
console.log('Numerical Integration:\n');
// Implementing numerical integration (Simpson's rule)
function simpsonsRule(f, a, b, n = 100) {
const h = (b - a) / n;
let sum = f(a) + f(b);
// Add 4 * f(a + h), 2 * f(a + 2h), 4 * f(a + 3h), ...
for (let i = 1; i < n; i++) {
const x = a + i * h;
sum += (i % 2 === 0 ? 2 : 4) * f(x);
}
return (h / 3) * sum;
}
// Example: integrate sin(x) from 0 to Pi
const integrand1 = (x) => math.sin(x);
const result1 = simpsonsRule(integrand1, 0, math.pi, 1000);
console.log(`∫ sin(x) dx from 0 to π ≈ ${result1} (exact: 2.0)\n`);
// Example: integrate x^2 from 0 to 1
const integrand2 = (x) => x * x;
const result2 = simpsonsRule(integrand2, 0, 1, 1000);
console.log(`∫ x^2 dx from 0 to 1 ≈ ${result2} (exact: 1/3 ≈ 0.3333)\n`);
// Example: integrate e^(-x^2) from -2 to 2 (related to error function)
const integrand3 = (x) => math.exp(-x * x);
const result3 = simpsonsRule(integrand3, -2, 2, 1000);
console.log(`∫ e^(-x^2) dx from -2 to 2 ≈ ${result3}\n`);
Numerical Integration: ∫ sin(x) dx from 0 to π ≈ 2.0000000000010805 (exact: 2.0) ∫ x^2 dx from 0 to 1 ≈ 0.33333333333333315 (exact: 1/3 ≈ 0.3333) ∫ e^(-x^2) dx from -2 to 2 ≈ 1.7641627815227583
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// Solving systems of linear equations
console.log('Solving systems of linear equations:\n');
// Define system: 2x + y = 5, 3x - 2y = 4
const A = math.matrix([[2, 1], [3, -2]]);
const b = math.matrix([5, 4]);
console.log('System of equations:\n');
console.log('2x + y = 5\n3x - 2y = 4\n');
// Solve using matrix methods (A * x = b => x = A^-1 * b)
const solution = math.multiply(math.inv(A), b);
console.log('Solution (using inverse):\n', solution.toString(), '\n');
// Alternatively, use math.js lusolve (more efficient and stable)
const solution2 = math.lusolve(A, b);
console.log('Solution (using LU decomposition):\n', solution2.toString(), '\n');
// Verify solution
const verification = math.multiply(A, solution);
console.log('Verification (A * x = b):\n', verification.toString(), '\n');
// Solving an underdetermined system
console.log('Underdetermined system (more variables than equations):\n');
const A2 = math.matrix([[1, 2, 3], [4, 5, 6]]);
const b2 = math.matrix([7, 8]);
console.log('Equations:\n');
console.log('x + 2y + 3z = 7\n4x + 5y + 6z = 8\n');
// Use pseudoinverse for underdetermined system
// This requires SVD which might not be available in all versions
try {
const solution3 = math.pinv ? math.multiply(math.pinv(A2), b2) : "SVD not available";
console.log('Particular solution (using pseudoinverse):\n', solution3.toString(), '\n');
} catch (e) {
console.log('Pseudoinverse calculation not available in this version.\n');
Solving systems of linear equations: System of equations: 2x + y = 5 3x - 2y = 4 Solution (using inverse): [1.9999999999999998, 1] Solution (using LU decomposition): [[2], [1.0000000000000002]] Verification (A * x = b): [5, 3.999999999999999] Underdetermined system (more variables than equations): Equations: x + 2y + 3z = 7 4x + 5y + 6z = 8 Particular solution (using pseudoinverse): [-3.0555555555555642, 0.11111111111110683, 3.2777777777777772]
[M]:
5. Custom Functions and Extensions
Math.js allows you to extend its functionality with custom functions and transformations.
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// Creating custom functions
console.log('Creating custom functions:\n');
// Create a new math.js instance to avoid modifying the global one
const myMath = math.create(math.all);
// Add a custom function to calculate the nth triangular number
myMath.import({
triangular: function(n) {
if (!Number.isInteger(n) || n < 0) {
throw new Error('Triangular number requires non-negative integer');
}
return (n * (n + 1)) / 2;
}
});
// Use the custom function
console.log(`Triangular(5) = ${myMath.triangular(5)}\n`); // Should be 15
console.log(`Triangular(10) = ${myMath.triangular(10)}\n`); // Should be 55
// Add a factorial function that works with big numbers
myMath.import({
factorial: function(n) {
if (!Number.isInteger(n) || n < 0) {
throw new Error('Factorial requires non-negative integer');
}
if (n === 0 || n === 1) {
return myMath.bignumber(1);
}
let result = myMath.bignumber(1);
for (let i = 2; i <= n; i++) {
result = myMath.multiply(result, i);
}
Error during execution: Cannot import "factorial": already existsCreating custom functions:
Triangular(5) = 15
Triangular(10) = 55
[M]:
6. Practical Applications
Let's explore some practical applications of math.js in real-world problems.
[40]:
// Application: Linear Regression
console.log('Application: Linear Regression\n');
// Sample data
const x = [1, 2, 3, 4, 5];
const y = [2, 3.5, 4.8, 6.3, 8.1];
// Function to perform linear regression
function linearRegression(x, y) {
const n = x.length;
// Calculate means
const xMean = math.mean(x);
const yMean = math.mean(y);
// Calculate slope
let numerator = 0;
let denominator = 0;
for (let i = 0; i < n; i++) {
numerator += (x[i] - xMean) * (y[i] - yMean);
denominator += (x[i] - xMean) * (x[i] - xMean);
}
const m = numerator / denominator;
const b = yMean - m * xMean;
// Calculate R-squared
let ssTotal = 0;
let ssResidual = 0;
for (let i = 0; i < n; i++) {
const yPred = m * x[i] + b;
ssTotal += Math.pow(y[i] - yMean, 2);
ssResidual += Math.pow(y[i] - yPred, 2);
}
Application: Linear Regression Slope (m): 1.4999999999999998 Intercept (b): 0.4400000000000013 R-squared: 0.9968102073365231 Predictions for new x values: x = 2.5, predicted y = 4.190000000000001 x = 6, predicted y = 9.44
[41]:
// Application: Optimization problem
console.log('Application: Finding minimum of a function\n');
// Define the function: f(x) = x^2 - 4x + 4
const f = math.parse('x^2 - 4*x + 4');
const fCompiled = f.compile();
// Calculate function values for a range of x
const xValues = math.range(-2, 8, 0.5).toArray();
const fValues = xValues.map(x => fCompiled.evaluate({x: x}));
// Print some values
console.log('Function f(x) = x^2 - 4x + 4\n');
console.log('x\tf(x)\n');
for (let i = 0; i < 5; i++) {
console.log(`${xValues[i]}\t${fValues[i]}\n`);
}
// Find the minimum using simple numerical approach
const minIndex = fValues.indexOf(math.min(fValues));
console.log(`\nApproximate minimum: f(${xValues[minIndex]}) = ${fValues[minIndex]}\n`);
// Find symbolic derivative to find exact minimum
const df = math.derivative(f, 'x');
console.log(`Derivative: ${df.toString()}\n`);
// Solve df/dx = 0
const equation = math.parse(`${df.toString()} = 0`);
console.log(`Solving: ${equation.toString()}\n`);
// We can solve this simple equation analytically
// 2x - 4 = 0 => x = 2
const criticalPoint = 2;
const exactMinimum = fCompiled.evaluate({x: criticalPoint});
console.log(`Critical point at x = ${criticalPoint}\n`);
console.log(`Exact minimum: f(${criticalPoint}) = ${exactMinimum}\n`);
Error during execution: Invalid left hand side of assignment operator = (char 11)Application: Finding minimum of a function
Function f(x) = x^2 - 4x + 4
x f(x)
-2 16
-1.5 12.25
-1 9
-0.5 6.25
0 4
Approximate minimum: f(2) = 0
Derivative: 2 * x - 4
[42]:
// Application: Statistical analysis
console.log('Application: Statistical analysis\n');
// Generate some random data with normal distribution
const sampleSize = 1000;
const mean = 50;
const stdDev = 10;
// Generate random normal numbers
function generateNormalSample(mu, sigma, size) {
const data = [];
for (let i = 0; i < size; i++) {
// Box-Muller transform
const u1 = math.random();
const u2 = math.random();
const z = math.sqrt(-2 * math.log(u1)) * math.cos(2 * math.pi * u2);
data.push(mu + sigma * z);
}
return data;
}
const sample = generateNormalSample(mean, stdDev, sampleSize);
// Calculate statistics
const sampleMean = math.mean(sample);
const sampleMedian = math.median(sample);
const sampleStdDev = math.std(sample);
const sampleMin = math.min(sample);
const sampleMax = math.max(sample);
console.log(`Sample statistics (n=${sampleSize}):\n`);
console.log(`Mean: ${sampleMean}\n`);
console.log(`Median: ${sampleMedian}\n`);
console.log(`Standard Deviation: ${sampleStdDev}\n`);
console.log(`Range: [${sampleMin}, ${sampleMax}]\n`);
Application: Statistical analysis Sample statistics (n=1000): Mean: 49.848103126421364 Median: 49.92090757521336 Standard Deviation: 9.579327666021364 Range: [16.081342666086776, 79.81270439924904] Percentiles: 25th percentile: 43.47979603687525 50th percentile: 49.92090757521336 75th percentile: 56.1182468610788 90th percentile: 62.220846622312045 95th percentile: 65.42574749322438
[M]:
7. Performance Optimization and Advanced Configurations
When working with math.js in production or with large datasets, performance optimization becomes important.
[43]:
// Creating a custom math.js instance with only needed functions
console.log('Performance optimization with custom configuration:\n');
// Create minimal math.js instance
const minimalMath = math.create();
// Import only the functions we need
minimalMath.import({
add: math.add,
subtract: math.subtract,
multiply: math.multiply,
divide: math.divide,
sqrt: math.sqrt,
evaluate: math.evaluate
});
console.log('Created minimal math instance with only basic functions\n');
console.log(`Result of 2+3: ${minimalMath.add(2, 3)}\n`);
// Benchmark comparison
console.log('Benchmark: Full vs. minimal library for simple operations:\n');
function benchmark(fn, iterations) {
const start = process.hrtime.bigint();
for (let i = 0; i < iterations; i++) {
fn();
}
const end = process.hrtime.bigint();
// Convert nanoseconds to milliseconds
return Number(end - start) / 1000000;
}
const iterations = 100000;
const fullLibTime = benchmark(() => {
math.evaluate('2 + 3 * 4');
Performance optimization with custom configuration: Created minimal math instance with only basic functions Result of 2+3: 5 Benchmark: Full vs. minimal library for simple operations: Full library: 315.68 ms for 100000 iterations Minimal library: 246.87 ms for 100000 iterations Performance ratio: 1.28x
[44]:
// Performance optimization: Compiled expressions
console.log('Using compiled expressions for better performance:\n');
// Create a complex expression
const complexExpr = 'sin(x)^2 + cos(x)^2 + tan(y) * log(z, 10)';
// Compare regular evaluate vs compiled
const regularTime = benchmark(() => {
math.evaluate(complexExpr, { x: 1, y: 0.5, z: 100 });
}, 10000);
// Pre-compile the expression
const compiledExpr = math.compile(complexExpr);
const compiledTime = benchmark(() => {
compiledExpr.evaluate({ x: 1, y: 0.5, z: 100 });
}, 10000);
console.log(`Regular evaluation: ${regularTime.toFixed(2)} ms\n`);
console.log(`Compiled evaluation: ${compiledTime.toFixed(2)} ms\n`);
console.log(`Speedup: ${(regularTime / compiledTime).toFixed(2)}x\n`);
// When to use which approach
console.log('Recommendations:\n');
console.log('- Use compile() when evaluating the same expression multiple times\n');
console.log('- Use evaluate() for one-time expressions\n');
console.log('- Create custom math.js instances for specific applications\n');
console.log('- Consider native JavaScript for very simple operations\n');
Using compiled expressions for better performance: Regular evaluation: 158.79 ms Compiled evaluation: 13.94 ms Speedup: 11.39x Recommendations: - Use compile() when evaluating the same expression multiple times - Use evaluate() for one-time expressions - Create custom math.js instances for specific applications - Consider native JavaScript for very simple operations
[M]:
8. Best Practices and Common Pitfalls
Let's review some best practices and common issues when working with math.js.
[M]:
Best Practices
-
Use the right number type for your application:
- Regular JavaScript numbers for basic calculations and performance
- BigNumber for precise decimal arithmetic
- Fractions for exact rational arithmetic
- Complex numbers for calculations involving imaginary numbers
-
Optimize for performance:
- Use compiled expressions for repeated evaluations
- Create specialized math.js instances with only needed functions
- Use typed arrays for large numerical datasets
- Consider alternative libraries for specialized use cases (e.g., NumJs for NDArray operations)
-
Error handling:
- Always wrap evaluations in try-catch blocks for user-provided expressions
- Provide helpful error messages for parsing and evaluation issues
- Validate inputs before complex calculations
-
Memory management:
- Watch out for large matrices and repeated calculations
- Release references to large objects when no longer needed
- For large datasets, process in chunks where possible
Common Pitfalls
-
Mixing number types: Calculations involving different types (like BigNumber and regular numbers) can give unexpected results
-
Equality checks: Math.js objects often need special equality functions rather than
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Performance expectations: Some operations (like symbolic computation) can be much slower than numerical equivalents
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Matrix indexing: Math.js uses 0-based indexing, which can differ from mathematical conventions
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Operator precedence: Math.js follows standard precedence rules which might differ from some other systems
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// Example of a common pitfall: Mixing number types
console.log('Example of a common pitfall: Mixing number types\n');
const regularNum = 0.1;
const bigNum = math.bignumber(0.1);
const fractionNum = math.fraction(1, 10);
console.log('Different representations of 0.1:\n');
console.log(`Regular JavaScript: ${regularNum}\n`);
console.log(`BigNumber: ${bigNum.toString()}\n`);
console.log(`Fraction: ${fractionNum.toString()}\n`);
// Adding different types
try {
const sum = math.add(regularNum, bigNum);
console.log(`Direct addition: ${sum}\n`);
} catch (e) {
console.log(`Error: ${e.message}\n`);
console.log('Solution: Convert to the same type first\n');
const sum1 = math.add(math.bignumber(regularNum), bigNum);
const sum2 = math.add(regularNum, Number(bigNum));
console.log(`Adding as BigNumbers: ${sum1.toString()}\n`);
console.log(`Adding as regular numbers: ${sum2}\n`);
}
Example of a common pitfall: Mixing number types Different representations of 0.1: Regular JavaScript: 0.1 BigNumber: 0.1 Fraction: 0.1 Direct addition: 0.2
[M]:
Summary
In this deep dive, we've explored the advanced capabilities of math.js including:
- Advanced matrix operations and decompositions
- Working with different number types (BigNumber, fractions, complex numbers)
- Symbolic math and expression parsing
- Solving equations numerically and symbolically
- Creating custom functions and transformations
- Real-world applications including regression, optimization, and statistics
- Performance optimization techniques
- Best practices and common pitfalls
Math.js provides a comprehensive mathematical toolkit for JavaScript developers, enabling sophisticated numerical and symbolic computation directly in JavaScript environments. Whether you're building scientific applications, data analysis tools, or financial calculators, math.js offers the advanced mathematical capabilities you need.
For more information, check out the official math.js documentation and GitHub repository.
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