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Examples added
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Ilya Shestakov
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Ilya Shestakov
Ilya Shestakov
parent
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commit
e5bb66c602
@@ -1,22 +1,330 @@
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/// <reference path="mathjs.d.ts" />
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// functions and constants
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math.round(math.e, 3); // 2.718
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math.atan2(3, -3) / math.pi; // 0.75
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math.log(10000, 10); // 4
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math.sqrt(-4); // 2i
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math.pow([[-1, 2], [3, 1]], 2);
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// [[7, 0], [0, 7]]
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// expressions
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math.eval('1.2 * (2 + 4.5)'); // 7.8
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math.eval('5.08 cm to inch'); // 2 inch
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math.eval('sin(45 deg) ^ 2'); // 0.5
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math.eval('9 / 3 + 2i'); // 3 + 2i
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math.eval('det([-1, 2; 3, 1])'); // -7
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/*
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Basic usage examples
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*/
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(function(){
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// functions and constants
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math.round(math.e, 3); // 2.718
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math.atan2(3, -3) / math.pi; // 0.75
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math.log(10000, 10); // 4
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math.sqrt(-4); // 2i
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math.pow([[-1, 2], [3, 1]], 2); // [[7, 0], [0, 7]]
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// expressions
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math.eval('1.2 * (2 + 4.5)'); // 7.8
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math.eval('5.08 cm to inch'); // 2 inch
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math.eval('sin(45 deg) ^ 2'); // 0.5
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math.eval('9 / 3 + 2i'); // 3 + 2i
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math.eval('det([-1, 2; 3, 1])'); // -7
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// chained operations
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var a = math.chain(3)
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.add(4)
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.multiply(2)
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.done(); // 14
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// mixed use of different data types in functions
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console.log('mixed use of data types');
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math.add(4, [5, 6]); // number + Array, [9, 10]
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math.multiply(math.unit('5 mm'), 3); // Unit * number, 15 mm
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math.subtract([2, 3, 4], 5); // Array - number, [-3, -2, -1]
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math.add(math.matrix([2, 3]), [4, 5]); // Matrix + Array, [6, 8]
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}());
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// chaining
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math.chain(3)
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.add(4)
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.multiply(2)
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.done(); // 14
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/*
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Bignumbers examples
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*/
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(function() {
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// configure the default type of numbers as BigNumbers
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math.config({
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number: 'bignumber', // Default type of number:
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// 'number' (default), 'bignumber', or 'fraction'
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precision: 20 // Number of significant digits for BigNumbers
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});
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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 BigNumbers');
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math.add(math.bignumber(0.1), math.bignumber(0.2)); // BigNumber, 0.3
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math.divide(math.bignumber(0.3), math.bignumber(0.2)); // BigNumber, 1.5
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console.log();
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console.log('create BigNumbers from strings when exceeding the range of a number');
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math.bignumber(1.2e+500); // BigNumber, Infinity WRONG
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math.bignumber('1.2e+500'); // BigNumber, 1.2e+500
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console.log();
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// one can work conveniently with BigNumbers using the expression parser.
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// note though that BigNumbers are only supported in arithmetic functions
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console.log('use BigNumbers in the expression parser');
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math.eval('0.1 + 0.2'); // BigNumber, 0.3
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math.eval('0.3 / 0.2'); // BigNumber, 1.5
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console.log();
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}());
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/*
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Chaining examples
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*/
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(function() {
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// create a chained operation using the function `chain(value)`
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// end a chain using done(). Let's calculate (3 + 4) * 2
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var a = math.chain(3)
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.add(4)
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.multiply(2)
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.done(); // 14
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// Another example, calculate square(sin(pi / 4))
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var b = math.chain(math.pi)
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.divide(4)
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.sin()
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.square()
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.done(); // 0.5
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// A chain has a few special methods: done, toString, valueOf, get, and set.
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// these are demonstrated in the following examples
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// toString will return a string representation of the chain's value
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var chain = math.chain(2).divide(3);
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var str = chain.toString(); // "0.6666666666666666"
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// a chain has a function .valueOf(), which returns the value hold by the chain.
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// This allows using it in regular operations. The function valueOf() acts the
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// same as function done().
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chain.valueOf(); // 0.66666666666667
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// the function subset can be used to get or replace sub matrices
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var array = [[1, 2], [3, 4]];
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var v = math.chain(array)
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.subset(math.index(1, 0))
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.done(); // 3
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var m = math.chain(array)
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.subset(math.index(0, 0), 8)
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.multiply(3)
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.done(); // [[24, 6], [9, 12]]
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}());
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/*
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Complex numbers examples
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*/
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(function(){
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var a = math.complex(2, 3); // 2 + 3i
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// read the real and complex parts of the complex number
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a.re; // 2
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a.im; // 3
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// clone a complex value
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var clone = a.clone(); // 2 + 3i
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// adjust the complex value
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a.re = 5; // 5 + 3i
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// create a complex number by providing a string with real and complex parts
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var b = math.complex('3 - 7i'); // 3 - 7i
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console.log();
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// perform operations with complex numbers
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console.log('perform operations');
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math.add(a, b); // 8 - 4i
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math.multiply(a, b); // 36 - 26i
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math.sin(a); // -9.6541254768548 + 2.8416922956064i
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// some operations will return a complex number depending on the arguments
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math.sqrt(4); // 2
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math.sqrt(-4); // 2i
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// create a complex number from polar coordinates
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console.log('create complex numbers with polar coordinates');
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var c = math.complex({r: math.sqrt(2), phi: math.pi / 4}); // 1 + i
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// get polar coordinates of a complex number
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var d = math.complex(3, 4);
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d.toPolar(); // { r: 5, phi: 0.9272952180016122 }
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}());
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/*
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Expressions examples
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*/
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(function() {
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// 1. using the function math.eval
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//
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// Function `eval` accepts a single expression or an array with
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// expressions as first argument, and has an optional second argument
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// containing a scope with variables and functions. The scope is a regular
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// JavaScript Object. The scope will be used to resolve symbols, and to write
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// assigned variables or function.
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console.log('1. USING FUNCTION MATH.EVAL');
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// evaluate expressions
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console.log('\nevaluate expressions');
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math.eval('sqrt(3^2 + 4^2)'); // 5
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math.eval('sqrt(-4)'); // 2i
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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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// evaluate multiple expressions at once
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console.log('\nevaluate multiple expressions at once');
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math.eval([
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'f = 3',
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'g = 4',
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'f * g'
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]); // [3, 4, 12]
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// provide a scope (just a regular JavaScript Object)
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console.log('\nevaluate expressions providing a scope with variables and functions');
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var scope: any = {
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a: 3,
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b: 4
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};
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// variables can be read from the scope
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math.eval('a * b', scope); // 12
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// variable assignments are written to the scope
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math.eval('c = 2.3 + 4.5', scope); // 6.8
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scope.c; // 6.8
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// scope can contain both variables and functions
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scope["hello"] = function (name: string) {
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return 'hello, ' + name + '!';
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};
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math.eval('hello("hero")', scope); // "hello, hero!"
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// define a function as an expression
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var f = math.eval('f(x) = x ^ a', scope);
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f(2); // 8
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scope.f(2); // 8
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// 2. using function math.parse
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//
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// Function `math.parse` parses expressions into a node tree. The syntax is
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// similar to function `math.eval`.
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// Function `parse` accepts a single expression or an array with
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// expressions as first argument. The function returns a node tree, which
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// then can be compiled against math, and then evaluated against an (optional
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// scope. This scope is a regular JavaScript Object. The scope will be used
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// to resolve symbols, and to write assigned variables or function.
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console.log('\n2. USING FUNCTION MATH.PARSE');
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// parse an expression
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console.log('\nparse an expression into a node tree');
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var node1 = math.parse('sqrt(3^2 + 4^2)');
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node1.toString(); // "sqrt((3 ^ 2) + (4 ^ 2))"
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// compile and evaluate the compiled code
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// you could also do this in two steps: node1.compile().eval()
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node1.eval(); // 5
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// provide a scope
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console.log('\nprovide a scope');
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var node2 = math.parse('x^a');
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var code2 = node2.compile();
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node2.toString(); // "x ^ a"
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var scope: any = {
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x: 3,
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a: 2
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};
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code2.eval(scope); // 9
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// change a value in the scope and re-evaluate the node
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scope.a = 3;
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code2.eval(scope); // 27
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// 3. using function math.compile
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//
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// Function `math.compile` compiles expressions into a node tree. The syntax is
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// similar to function `math.eval`.
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// Function `compile` accepts a single expression or an array with
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// expressions as first argument, and returns an object with a function eval
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// to evaluate the compiled expression. On evaluation, an optional scope can
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// be provided. This scope will be used to resolve symbols, and to write
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// assigned variables or function.
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console.log('\n3. USING FUNCTION MATH.COMPILE');
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// parse an expression
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console.log('\ncompile an expression');
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var code3 = math.compile('sqrt(3^2 + 4^2)');
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// evaluate the compiled code
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code3.eval(); // 5
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// provide a scope for the variable assignment
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console.log('\nprovide a scope');
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var code2 = math.compile('a = a + 3');
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var scope: any = {
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a: 7
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};
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code2.eval(scope);
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scope.a; // 10
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// 4. using a parser
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//
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// In addition to the static functions `math.eval` and `math.parse`, math.js
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// contains a parser with functions `eval` and `parse`, which automatically
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// keeps a scope with assigned variables in memory. The parser also contains
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// some convenience methods to get, set, and remove variables from memory.
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console.log('\n4. USING A PARSER');
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var parser = math.parser();
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// evaluate with parser
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console.log('\nevaluate expressions');
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parser.eval('sqrt(3^2 + 4^2)'); // 5
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parser.eval('sqrt(-4)'); // 2i
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parser.eval('2 inch to cm'); // 5.08 cm
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parser.eval('cos(45 deg)'); // 0.70711
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// define variables and functions
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console.log('\ndefine variables and functions');
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parser.eval('x = 7 / 2'); // 3.5
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parser.eval('x + 3'); // 6.5
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parser.eval('f(x, y) = x^y'); // f(x, y)
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parser.eval('f(2, 3)'); // 8
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// manipulate matrices
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// Note that matrix indexes in the expression parser are one-based with the
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// upper-bound included. On a JavaScript level however, math.js uses zero-based
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// indexes with an excluded upper-bound.
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console.log('\nmanipulate matrices');
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parser.eval('k = [1, 2; 3, 4]'); // [[1, 2], [3, 4]]
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parser.eval('l = zeros(2, 2)'); // [[0, 0], [0, 0]]
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parser.eval('l[1, 1:2] = [5, 6]'); // [[5, 6], [0, 0]]
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parser.eval('l[2, :] = [7, 8]'); // [[5, 6], [7, 8]]
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parser.eval('m = k * l'); // [[19, 22], [43, 50]]
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parser.eval('n = m[2, 1]'); // 43
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parser.eval('n = m[:, 1]'); // [[19], [43]]
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// get and set variables and functions
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console.log('\nget and set variables and function in the scope of the parser');
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var x = parser.get('x');
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console.log('x =', x); // x = 7
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var f = parser.get('f');
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console.log('f =', math.format(f)); // f = f(x, y)
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var g = f(3, 3);
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console.log('g =', g); // g = 27
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parser.set('h', 500);
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parser.eval('h / 2'); // 250
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parser.set('hello', function (name: string) {
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return 'hello, ' + name + '!';
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});
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parser.eval('hello("hero")'); // "hello, hero!"
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// clear defined functions and variables
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parser.clear();
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}());
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16
mathjs/mathjs.d.ts
vendored
16
mathjs/mathjs.d.ts
vendored
@@ -16,6 +16,8 @@ declare module mathjs {
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e: number;
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pi: number;
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config(options: any): void;
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/**
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* Solves the linear equation system by forwards substitution. Matrix must be a lower triangular matrix.
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* @param L A N x N matrix or array (L)
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@@ -484,6 +486,7 @@ declare module mathjs {
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complex(complex: Complex): Complex;
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complex(arg: string): Complex;
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complex(array: MathArray): Complex;
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complex(obj: IPolarCoordinates): Complex;
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/**
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* Create a fraction convert a value to a fraction.
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@@ -1278,9 +1281,17 @@ declare module mathjs {
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}
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export interface Complex {
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re: number;
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im: number;
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toPolar(): IPolarCoordinates;
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clone(): Complex;
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}
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export interface IPolarCoordinates {
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r: number;
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phi: number;
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}
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export interface Unit {
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}
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@@ -1290,11 +1301,12 @@ declare module mathjs {
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}
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export interface EvalFunction {
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eval(): any;
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eval(scope?: any): any;
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}
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export interface MathNode {
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compile(): EvalFunction;
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eval(): any;
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}
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export interface Parser {
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