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326 lines
13 KiB
JavaScript
326 lines
13 KiB
JavaScript
// test data type Complex
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var assert = require('assert');
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var math = require('../../index');
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var Unit = math.type.Unit;
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var Complex = math.type.Complex;
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describe('Complex', function () {
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assertComplex = function(complex, re, im) {
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assert(complex instanceof Complex);
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assert.strictEqual(complex.re, re);
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assert.strictEqual(complex.im, im);
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};
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describe('constructor', function() {
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it('should create a complex number correctly', function () {
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var complex1 = new Complex(3, -4);
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assertComplex(complex1, 3, -4);
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var complex2 = new Complex();
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assertComplex(complex2, 0, 0);
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});
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it('should throw an error if called with wrong number of arguments', function() {
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assert.throws(function () { new Complex(3, -4, 5); });
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assert.throws(function () { new Complex(1); });
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});
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it('should throw an error if called with wrong type of arguments', function() {
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assert.throws(function () { new Complex(1, true); });
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assert.throws(function () { new Complex(true, 2); });
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});
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it('should throw an error if called with wrong type of arguments', function() {
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assert.throws(function () { new Complex(1, true); });
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assert.throws(function () { new Complex({}); }, /Object with the re and im or r and phi properties expected/);
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});
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it('should throw an error if called without new operator', function() {
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assert.throws(function () { Complex(3, -4); });
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});
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it('should accept an object with im and re as keys', function() {
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assertComplex(new Complex({re: 1, im: 2}), 1, 2);
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});
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it('should accept an object with polar coordinates like fromPolar', function() {
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assert.deepEqual(new Complex({r: 3, phi: 4}), Complex.fromPolar(3, 4));
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});
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});
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describe('toString', function() {
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it('stringify a complex number', function() {
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assert.equal(new Complex(3, -4).toString(), '3 - 4i');
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assert.equal(new Complex().toString(), '0');
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assert.equal(new Complex(2, 3).toString(), '2 + 3i');
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assert.equal(new Complex(2, 0).toString(), '2');
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assert.equal(new Complex(0, 3).toString(), '3i');
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assert.equal(new Complex().toString(), '0');
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assert.equal(new Complex(0, 2).toString(), '2i');
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assert.equal(new Complex(0, 1).toString(), 'i');
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assert.equal(new Complex(1, 1).toString(), '1 + i');
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assert.equal(new Complex(1, 2).toString(), '1 + 2i');
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assert.equal(new Complex(1, -1).toString(), '1 - i');
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assert.equal(new Complex(1, -2).toString(), '1 - 2i');
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assert.equal(new Complex(1, 0).toString(), '1');
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assert.equal(new Complex(-1, 2).toString(), '-1 + 2i');
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assert.equal(new Complex(-1, 1).toString(), '-1 + i');
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});
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it('should not round off digits', function() {
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assert.equal(new Complex(1/3, 1/3).toString(), '0.3333333333333333 + 0.3333333333333333i');
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});
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});
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describe('valueOf', function() {
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it('should return string representation when calling valueOf', function() {
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assert.strictEqual(new Complex(3, -4).valueOf(), '3 - 4i');
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assert.strictEqual(new Complex().valueOf(), '0');
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assert.strictEqual(new Complex(2, 3).valueOf(), '2 + 3i');
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});
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});
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describe('format', function() {
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it('should format a complex number', function() {
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assert.equal(new Complex(2, 3).format(), '2 + 3i');
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assert.equal(new Complex(2, -3).format(), '2 - 3i');
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assert.equal(new Complex(-2, 3).format(), '-2 + 3i');
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assert.equal(new Complex(-2, -3).format(), '-2 - 3i');
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assert.equal(new Complex(2, 1).format(), '2 + i');
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assert.equal(new Complex(2, -1).format(), '2 - i');
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assert.equal(new Complex(2, 0).format(), '2');
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assert.equal(new Complex(0, 2).format(), '2i');
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});
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it('should format a complex number with custom precision', function() {
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assert.equal(new Complex(1/3, 1/3).format(3), '0.333 + 0.333i');
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assert.equal(new Complex(1/3, 1/3).format(4), '0.3333 + 0.3333i');
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assert.equal(new Complex(1/3, 1/3).format(), '0.3333333333333333 + 0.3333333333333333i');
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});
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it('should round im to zero if very small compared to re', function() {
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assert.equal(new Complex(-1, 1.22e-16).format(), '-1 + 1.22e-16i');
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assert.equal(new Complex(-1, 1.22e-16).format(15), '-1');
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assert.equal(new Complex(-1, -1.22e-16).format(15), '-1');
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assert.equal(new Complex(1, -1.22e-16).format(15), '1');
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assert.equal(new Complex(1, 1.22e-16).format(15), '1');
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assert.equal(new Complex(-1, 1e-7).format(5), '-1');
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});
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it('should round re to zero if very small compared to im', function() {
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assert.equal(new Complex(1.22e-16, -1).format(), '1.22e-16 - i');
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assert.equal(new Complex(1.22e-16, -1).format(15), '-i');
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assert.equal(new Complex(-1.22e-16, -1).format(15), '-i');
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assert.equal(new Complex(-1.22e-16, 1).format(15), 'i');
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assert.equal(new Complex(1.22e-16, 1).format(15), 'i');
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assert.equal(new Complex(1e-7, -1).format(5), '-i');
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});
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});
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describe('parse', function() {
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it('should parse rightly', function () {
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assertComplex(Complex.parse('2 + 3i'), 2, 3);
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assertComplex(Complex.parse('2 +3i'), 2, 3);
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assertComplex(Complex.parse('2+3i'), 2, 3);
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assertComplex(Complex.parse(' 2+3i '), 2, 3);
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assertComplex(Complex.parse('2-3i'), 2, -3);
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assertComplex(Complex.parse('2 + i'), 2, 1);
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assertComplex(Complex.parse('-2-3i'), -2, - 3);
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assertComplex(Complex.parse('-2+3i'), -2, 3);
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assertComplex(Complex.parse('-2+-3i'), -2, -3);
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assertComplex(Complex.parse('-2-+3i'), -2, -3);
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assertComplex(Complex.parse('+2-+3i'), 2, -3);
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assertComplex(Complex.parse('+2-+3i'), 2, -3);
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assertComplex(Complex.parse('2 + 3i'), 2, 3);
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assertComplex(Complex.parse('2 - -3i'), 2, 3);
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assertComplex(Complex.parse(' 2 + 3i '), 2, 3);
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assertComplex(Complex.parse('2 + i'), 2, 1);
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assertComplex(Complex.parse('2 - i'), 2, -1);
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assertComplex(Complex.parse('2 + -i'), 2, -1);
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assertComplex(Complex.parse('-2+3e-1i'), -2, 0.3);
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assertComplex(Complex.parse('-2+3e+1i'), -2, 30);
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assertComplex(Complex.parse('2+3e2i'), 2, 300);
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assertComplex(Complex.parse('2.2e-1-3.2e-1i'), 0.22, -0.32);
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assertComplex(Complex.parse('2.2e-1-+3.2e-1i'), 0.22, -0.32);
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assertComplex(Complex.parse('2'), 2, 0);
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assertComplex(Complex.parse('i'), 0, 1);
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assertComplex(Complex.parse(' i '), 0, 1);
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assertComplex(Complex.parse('-i'), 0, -1);
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assertComplex(Complex.parse(' -i '), 0, -1);
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assertComplex(Complex.parse('+i'), 0, 1);
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assertComplex(Complex.parse(' +i '), 0, 1);
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assertComplex(Complex.parse('-2'), -2, 0);
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assertComplex(Complex.parse('3I'), 0, 3);
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assertComplex(Complex.parse('-3i'), 0, -3);
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assertComplex(Complex.parse('.2i'), 0, 0.2);
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assertComplex(Complex.parse('.2'), 0.2, 0);
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assertComplex(Complex.parse('2.i'), 0, 2);
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assertComplex(Complex.parse('2.'), 2, 0);
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});
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it('should return null if called with an invalid string', function() {
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assert.strictEqual(Complex.parse('str', 2), null);
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assert.strictEqual(Complex.parse(''), null);
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assert.strictEqual(Complex.parse('2r'), null);
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assert.strictEqual(Complex.parse('str'), null);
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assert.strictEqual(Complex.parse('2i+3i'), null);
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assert.strictEqual(Complex.parse('2ia'), null);
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assert.strictEqual(Complex.parse('3+4'), null);
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assert.strictEqual(Complex.parse('3i+4'), null);
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assert.strictEqual(Complex.parse('3e + 4i'), null);
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assert.strictEqual(Complex.parse('3 + 4i bla'), null);
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assert.strictEqual(Complex.parse('3e1.2 + 4i'), null);
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assert.strictEqual(Complex.parse('3e1.2i'), null);
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assert.strictEqual(Complex.parse('3e1.2i'), null);
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assert.strictEqual(Complex.parse('- i'), null);
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assert.strictEqual(Complex.parse('+ i'), null);
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assert.strictEqual(Complex.parse('.'), null);
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assert.strictEqual(Complex.parse('2 + .i'), null);
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assert.strictEqual(Complex.parse('4i bla'), null);
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assert.strictEqual(Complex.parse('i bla'), null);
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assert.strictEqual(Complex.parse(2), null);
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});
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});
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describe('clone', function() {
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it('should clone the complex properly', function () {
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var complex1 = new Complex(3, -4);
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var clone = complex1.clone();
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clone.re = 100;
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clone.im = 200;
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assert.notEqual(complex1, clone);
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assert.equal(complex1.re, 3);
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assert.equal(complex1.im, -4);
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assert.equal(clone.re, 100);
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assert.equal(clone.im, 200);
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});
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});
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describe('equals', function() {
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it('should test equality of two complex numbers', function () {
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assert.equal(new Complex(2, 4).equals(new Complex(2, 4)), true);
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assert.equal(new Complex(2, 3).equals(new Complex(2, 4)), false);
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assert.equal(new Complex(2, 4).equals(new Complex(1, 4)), false);
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assert.equal(new Complex(2, 4).equals(new Complex(1, 3)), false);
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assert.equal(new Complex(2, 4).equals(new Complex(2, 0)), false);
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assert.equal(new Complex(2, 4).equals(new Complex(0, 4)), false);
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assert.equal(new Complex(0, 0).equals(new Complex()), true);
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});
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});
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describe('fromPolar', function() {
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it('should save polar coordinates input correctly', function() {
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var complex1 = Complex.fromPolar({r: 0, phi: 4});
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var complex2 = Complex.fromPolar({r: 5, phi: 0});
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var complex3 = Complex.fromPolar({r: 1, phi: Math.PI});
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var complex4 = Complex.fromPolar({r: 3, phi: Math.PI / 2});
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var complex5 = Complex.fromPolar({r: 3, phi: -Math.PI / 2});
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assertComplex(complex1, 0, 0);
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assertComplex(complex2, 5, 0);
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assert.equal(complex3.re, -1);
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assert.equal(complex4.im, 3);
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assert.equal(complex5.im, -3);
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});
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it('should have the same value for the different import ways', function() {
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var way1 = Complex.fromPolar(1, 1);
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var way2 = Complex.fromPolar({r: 1, phi: 1});
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assert(way1.equals(way2));
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});
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it('should accept angle units for phi properly', function() {
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var fromDeg = Complex.fromPolar(1, new Unit(90, 'deg')),
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fromRad = Complex.fromPolar(1, new Unit(0, 'rad')),
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fromGrad = Complex.fromPolar(1, new Unit(100, 'grad'));
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assert.equal(fromDeg.im, 1);
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assert.equal(fromGrad.im, 1);
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assert.equal(fromRad.im, 0);
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});
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it('should only accept an object with r and phi keys for 1 argument', function() {
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assert.throws(function() { Complex.fromPolar({}) }, TypeError);
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assert.throws(function() { Complex.fromPolar({r: 1}) }, TypeError);
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assert.throws(function() { Complex.fromPolar({phi: 1}) }, TypeError);
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assert.throws(function() { Complex.fromPolar("") }, TypeError);
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});
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it('should only accept a number as r', function() {
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assert.throws(function() { Complex.fromPolar("1", 0); });
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assert.throws(function() { Complex.fromPolar(true, 0); });
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assert.throws(function() { Complex.fromPolar({}, 0); });
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});
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it('should only accept units and numbers as phi', function() {
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assert.throws(function() { Complex.fromPolar(1, "1")});
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assert.throws(function() { Complex.fromPolar(1, true)});
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assert.throws(function() { Complex.fromPolar(1, {})});
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});
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it('should throw an error in case of wrong number of arguments', function() {
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assert.throws(function() { Complex.fromPolar(1,2,3)}, /Wrong number of arguments/);
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assert.throws(function() { Complex.fromPolar()}, /Wrong number of arguments/);
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});
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});
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describe('toPolar', function() {
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it('should return polar coordinates properly', function() {
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var polar0 = (new Complex(0, 0)).toPolar();
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var polar1 = (new Complex(3, 4)).toPolar();
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var polar2 = (new Complex(-3, 4)).toPolar();
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var polar3 = (new Complex(3, -4)).toPolar();
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var polar4 = (new Complex(-3, -4)).toPolar();
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var polar5 = (new Complex(0, -1)).toPolar();
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assert.equal(polar0.r, 0);
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assert.equal(polar1.r, 5);
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assert.equal(polar2.r, 5);
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assert.equal(polar3.r, 5);
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assert.equal(polar4.r, 5);
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assert.equal(polar5.r, 1);
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assert.equal(polar0.phi, 0);
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assert.equal(polar1.phi, 0.9272952180016122);
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assert.equal(polar2.phi, 2.214297435588181);
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assert.equal(polar3.phi, -0.9272952180016122);
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assert.equal(polar4.phi, -2.214297435588181);
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assert.equal(polar5.phi, -1.5707963267948966);
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});
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});
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it('toJSON', function () {
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assert.deepEqual(new Complex(2, 4).toJSON(), {'mathjs': 'Complex', re: 2, im: 4});
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assert.deepEqual(new Complex(3, 0).toJSON(), {'mathjs': 'Complex', re: 3, im: 0});
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});
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it('fromJSON', function () {
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var c1 = Complex.fromJSON({re: 2, im: 4});
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assert.ok(c1 instanceof Complex);
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assert.strictEqual(c1.re, 2);
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assert.strictEqual(c1.im, 4);
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var c2 = Complex.fromJSON({re: 3, im: 0});
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assert.ok(c2 instanceof Complex);
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assert.strictEqual(c2.re, 3);
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assert.strictEqual(c2.im, 0);
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});
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});
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