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Added examples
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Ilya Shestakov
@@ -327,4 +327,255 @@ Expressions examples
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// clear defined functions and variables
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parser.clear();
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}());
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/*
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Fractions examples
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*/
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(function(){
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// configure the default type of numbers as Fractions
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math.config({
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number: 'fraction' // Default type of number:
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// 'number' (default), 'bignumber', or 'fraction'
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});
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console.log('basic usage');
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math.fraction(0.125); // Fraction, 1/8
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math.fraction(0.32); // Fraction, 8/25
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math.fraction('1/3'); // Fraction, 1/3
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math.fraction('0.(3)'); // Fraction, 1/3
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math.fraction(2, 3); // Fraction, 2/3
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math.fraction('0.(285714)'); // Fraction, 2/7
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console.log();
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console.log('round-off errors with numbers');
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math.add(0.1, 0.2); // number, 0.30000000000000004
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math.divide(0.3, 0.2); // number, 1.4999999999999998
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console.log();
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console.log('no round-off errors with fractions :)');
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math.add(math.fraction(0.1), math.fraction(0.2)); // Fraction, 3/10
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math.divide(math.fraction(0.3), math.fraction(0.2)); // Fraction, 3/2
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console.log();
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console.log('represent an infinite number of repeating digits');
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math.fraction('1/3'); // Fraction, 0.(3)
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math.fraction('2/7'); // Fraction, 0.(285714)
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math.fraction('23/11'); // Fraction, 2.(09)
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console.log();
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// one can work conveniently with fractions using the expression parser.
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// note though that Fractions are only supported by basic arithmetic functions
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console.log('use fractions in the expression parser');
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math.eval('0.1 + 0.2'); // Fraction, 3/10
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math.eval('0.3 / 0.2'); // Fraction, 3/2
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math.eval('23 / 11'); // Fraction, 23/11
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console.log();
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// output formatting
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console.log('output formatting of fractions');
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var a = math.fraction('2/3');
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console.log(math.format(a)); // Fraction, 2/3
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console.log(math.format(a, {fraction: 'ratio'})); // Fraction, 2/3
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console.log(math.format(a, {fraction: 'decimal'})); // Fraction, 0.(6)
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console.log(a.toString()); // Fraction, 0.(6)
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console.log();
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}());
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/*
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Matrices examples
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*/
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(function() {
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// create matrices and arrays. a matrix is just a wrapper around an Array,
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// providing some handy utilities.
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console.log('create a matrix');
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var a = math.matrix([1, 4, 9, 16, 25]); // [1, 4, 9, 16, 25]
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var b = math.matrix(math.ones([2, 3])); // [[1, 1, 1], [1, 1, 1]]
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b.size(); // [2, 3]
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// the Array data of a Matrix can be retrieved using valueOf()
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var array = a.valueOf(); // [1, 4, 9, 16, 25]
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// Matrices can be cloned
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var clone = a.clone(); // [1, 4, 9, 16, 25]
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console.log();
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// perform operations with matrices
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console.log('perform operations');
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math.sqrt(a); // [1, 2, 3, 4, 5]
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var c = [1, 2, 3, 4, 5];
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math.factorial(c); // [1, 2, 6, 24, 120]
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console.log();
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// create and manipulate matrices. Arrays and Matrices can be used mixed.
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console.log('manipulate matrices');
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var d = [[1, 2], [3, 4]]; // [[1, 2], [3, 4]]
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var e = math.matrix([[5, 6], [1, 1]]); // [[5, 6], [1, 1]]
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// set a submatrix.
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// Matrix indexes are zero-based.
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e.subset(math.index(1, [0, 1]), [[7, 8]]); // [[5, 6], [7, 8]]
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var f = math.multiply(d, e); // [[19, 22], [43, 50]]
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var g = f.subset(math.index(1, 0)); // 43
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console.log();
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// get a sub matrix
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// Matrix indexes are zero-based.
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console.log('get a sub matrix');
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var h = math.diag(math.range(1,4)); // [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
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h.subset( math.index([1, 2], [1, 2])); // [[2, 0], [0, 3]]
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var i = math.range(1,6); // [1, 2, 3, 4, 5]
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i.subset(math.index(math.range(1,4))); // [2, 3, 4]
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console.log();
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// resize a multi dimensional matrix
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console.log('resizing a matrix');
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var j = math.matrix();
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var defaultValue = 0;
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j.resize([2, 2, 2], defaultValue); // [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
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j.size(); // [2, 2, 2]
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j.resize([2, 2]); // [[0, 0], [0, 0]]
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j.size(); // [2, 2]
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console.log();
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// setting a value outside the matrices range will resize the matrix.
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// new elements will be initialized with zero.
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console.log('set a value outside a matrices range');
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var k = math.matrix();
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k.subset(math.index(2), 6); // [0, 0, 6]
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console.log();
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console.log('set a value outside a matrices range, leaving new entries uninitialized');
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var m = math.matrix();
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defaultValue = math.uninitialized;
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m.subset(math.index(2), 6, defaultValue); // [undefined, undefined, 6]
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console.log();
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// create ranges
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console.log('create ranges');
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math.range(1, 6); // [1, 2, 3, 4, 5]
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math.range(0, 18, 3); // [0, 3, 6, 9, 12, 15]
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math.range('2:-1:-3'); // [2, 1, 0, -1, -2]
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math.factorial(math.range('1:6')); // [1, 2, 6, 24, 120]
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console.log();
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}());
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/*
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Sparse matrices examples
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*/
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(function() {
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// create a sparse matrix
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console.log('creating a 1000x1000 sparse matrix...');
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var a = math.eye(1000, 1000, 'sparse');
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// do operations with a sparse matrix
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console.log('doing some operations on the sparse matrix...');
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var b = math.multiply(a, a);
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var c = math.multiply(b, math.complex(2, 2));
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var d = math.transpose(c);
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var e = math.multiply(d, a);
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// we will not print the output, but doing the same operations
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// with a dense matrix are very slow, try it for yourself.
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console.log('already done');
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console.log('now try this with a dense matrix :)');
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}());
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/*
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Units examples
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*/
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(function() {
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// units can be created by providing a value and unit name, or by providing
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// a string with a valued unit.
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console.log('create units');
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var a = math.unit(45, 'cm'); // 450 mm
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var b = math.unit('0.1m'); // 100 mm
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console.log();
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// units can be added, subtracted, and multiplied or divided by numbers and by other units
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console.log('perform operations');
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math.add(a, b); // 0.55 m
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math.multiply(b, 2); // 200 mm
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math.divide(math.unit('1 m'), math.unit('1 s')); // 1 m / s
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math.pow(math.unit('12 in'), 3); // 1728 in^3
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console.log();
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// units can be converted to a specific type, or to a number
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console.log('convert to another type or to a number');
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b.to('cm'); // 10 cm Alternatively: math.to(b, 'cm')
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math.to(b, 'inch'); // 3.9370... inch
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b.toNumber('cm'); // 10
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math.number(b, 'cm'); // 10
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console.log();
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// the expression parser supports units too
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console.log('parse expressions');
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math.eval('2 inch to cm'); // 5.08 cm
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math.eval('cos(45 deg)'); // 0.70711...
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math.eval('90 km/h to m/s'); // 25 m / s
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console.log();
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// convert a unit to a number
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// A second parameter with the unit for the exported number must be provided
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math.eval('number(5 cm, mm)'); // number, 50
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console.log();
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// simplify units
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console.log('simplify units');
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math.eval('100000 N / m^2'); // 100 kPa
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math.eval('9.81 m/s^2 * 100 kg * 40 m'); // 39.24 kJ
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console.log();
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// example engineering calculations
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console.log('compute molar volume of ideal gas at 65 Fahrenheit, 14.7 psi in L/mol');
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var Rg = math.unit('8.314 N m / (mol K)');
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var T = math.unit('65 degF');
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var P = math.unit('14.7 psi');
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var v = math.divide(math.multiply(Rg, T), P);
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console.log('gas constant (Rg) = ', format(Rg));
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console.log('P = ' + format(P));
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console.log('T = ' + format(T));
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console.log('v = Rg * T / P = ' + format(math.to(v, 'L/mol'))); // 23.910... L / mol
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console.log();
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console.log('compute speed of fluid flowing out of hole in a container');
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var g = math.unit('9.81 m / s^2');
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var h = math.unit('1 m');
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var v2 = math.pow(math.multiply(2, math.multiply(g, h)), 0.5); // Can also use math.sqrt
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console.log('g = ' + format(g));
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console.log('h = ' + format(h));
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console.log('v = (2 g h) ^ 0.5 = ' + format(v2)); // 4.429... m / s
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console.log();
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console.log('electrical power consumption:');
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var expr = '460 V * 20 A * 30 days to kWh';
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console.log(expr + ' = ' + math.eval(expr)); // 6624 kWh
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console.log();
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console.log('circuit design:');
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var expr = '24 V / (6 mA)';
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console.log(expr + ' = ' + math.eval(expr)); // 4 kohm
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console.log();
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console.log('operations on arrays:');
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var B = math.eval('[1, 0, 0] T');
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var v3 = math.eval('[0, 1, 0] m/s');
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var q = math.eval('1 C');
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var F = math.multiply(q, math.cross(v3, B));
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console.log('B (magnetic field strength) = ' + format(B)); // [1 T, 0 T, 0 T]
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console.log('v (particle velocity) = ' + format(v3)); // [0 m / s, 1 m / s, 0 m / s]
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console.log('q (particle charge) = ' + format(q)); // 1 C
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console.log('F (force) = q (v cross B) = ' + format(F)); // [0 N, 0 N, -1 N]
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/**
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* Helper function to format an output a value.
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* @param {*} value
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* @return {string} Returns the formatted value
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*/
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function format (value: any): string {
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var precision = 14;
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return math.format(value, precision);
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}
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}());
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