Compute definite and improper integrals with Romberg Integration. Easily and accurately integrate JavaScript functions.
- Easily evaluate definite and improper integrals.
- Control the order of accuracy (see "Order of Accuracy").
- Fast computation time (see "Tests").
- Divide-by-zero safeguard.
npm install sm-integral
Below, we demonstrate how to evaluate the following integrals:
const Integral = require('sm-integral');
//definite function to integrate
function f (x) {
return 1 / (x * x);
}
//definite integral
console.log(Integral.integrate(f, 5, 10)); //0.1
//improper integral
console.log(Integral.integrate(f, "-inf", -10)); //0.1The integrate() function has the following parameters.
class Integral {
//...
integrate(f, a, b, e = 18) {
//...
}
}fis the JavaScript function to be integrated.ais the lower bound of the integral (must either be a number or "inf"/"-inf").bis the upper bound of the integral (must either be a number or "inf"/"-inf").eis the order of accuracy (must be a positive even integer - if it is odd, it will be incremented). The default value of 18 is enough to evaluate most integrals to at least +-1e-9 accuracy (see "Tests").
To have an order of accuracy e means that the returnedValue when computing
In the test folder, 8 integrals are tested with the default e=18 parameter. The 8 evaluations were completed within 30ms, each producing results accurate to at least +-1e-9.
describe('sm-integral', () => {
it('Integrating the constant function f(x)=x/x exactly.', () => {
function f (x) {
return x / x; // 1
}
assert.equal(Integral.integrate(f, 0, 10, 18), 10,
'Evaluate constant function f(x)=x/x without error.');
});
it('Integrating the constant function f(x)=x/x exactly, but with a > b.', () => {
function f (x) {
return x / x; // 1
}
assert.equal(Integral.integrate(f, 5, -20, 18), -25,
'Evaluate constant function f(x)=x/x without error where a > b.');
});
it('Integrating the linear function f(x)=0.28*x-127 exactly.', () => {
function f (x) {
return 0.28 * x - 127;
}
assert.equal(Integral.integrate(f, -100, 500, 18), -42600,
'Evaluate linear function f(x)=0.28*x+127 without error.');
});
it('Integrating the quadratic function f(x)=0.56*x*x+0.7*x+17 with order of accuracy of 18.', () => {
function f (x) {
return 0.7 * x * x + 0.56 * x + 17;
}
assert.closeTo(Integral.integrate(f, 5, 13, 18), 659 + 59 / 75, 1e-9,
'Evaluate quadratic function f(x)=0.7*x*x+0.56*x+17 with' +
' order of accuracy 18.');
});
it('Integrating the quadratic function f(x)=1/(x*x).', () => {
function f (x) {
return 1 / (x * x);
}
assert.closeTo(Integral.integrate(f, 5, 10, 18), 0.1, 1e-9,
'Evaluate quadratic function f(x)=1/(x*x)' +
'with order of accuracy 18.');
});
it('Integrating the cubic function f(x)=56.1*x*x*x-2*x+1 with order of accuracy of 18.', () => {
function f (x) {
return 56.1 * x * x * x - 2 * x + 1;
}
assert.closeTo(Integral.integrate(f, -2, 21, 18), 2726957 + 5 / 8, 1e-9,
'Evaluate cubic function f(x)=56.1*x*x*x-2*x+1 with' +
' order of accuracy 18.');
});
it('Integrating the error function with order of accuracy 18.', () => {
function f (x) {
return Math.pow(Math.E, 1 / (x * x));
}
assert.closeTo(Integral.integrate(f, 1, 4, 18), 3.954384577738, 1e-9,
'Evaluate error function with' +
' order of accuracy 18.');
});
it('Testing improper integral on f(x)=1/(x*x)', () => {
function f (x) {
return 1 / (x * x);
}
assert.closeTo(Integral.integrate(f, '-inf', -10, 18), 0.1, 1e-9,
'Evaluate improper integral of' +
' f(x)=1/(x*x) with order of accuracy 18.');
});
});