mathjs/types/index.ts

import {
  create,
  factory,
  all,
  MathJsFunctionName,
  fractionDependencies,
  addDependencies,
  divideDependencies,
  formatDependencies,
} from 'mathjs';

/*
Basic usage examples
*/
{
  const math = create(all);

  // functions and constants
  math.round(math.e, 3);
  math.round(100.123, 3);
  math.atan2(3, -3) / math.pi;
  math.log(10000, 10);
  math.sqrt(-4);
  math.pow([[-1, 2], [3, 1]], 2);
  const angle = 0.2;
  math.add(math.pow(math.sin(angle), 2), math.pow(math.cos(angle), 2));

  // expressions
  math.evaluate('1.2 * (2 + 4.5)');

  // chained operations
  const a = math.chain(3).add(4).multiply(2).done(); // 14

  // mixed use of different data types in functions
  math.add(4, [5, 6]); // number + Array, [9, 10]
  math.multiply(math.unit('5 mm'), 3); // Unit * number,  15 mm
  math.subtract([2, 3, 4], 5); // Array - number, [-3, -2, -1]
  math.add(math.matrix([2, 3]), [4, 5]); // Matrix + Array, [6, 8]
}

/*
Bignumbers examples
*/
{
  // configure the default type of numbers as BigNumbers
  const math = create(all, {
    number: 'BigNumber',
    precision: 20,
  });

  {
    math.add(math.bignumber(0.1), math.bignumber(0.2)); // BigNumber, 0.3
    math.divide(math.bignumber(0.3), math.bignumber(0.2)); // BigNumber, 1.5
  }
}

/*
Chaining examples
*/
{
  const math = create(all, {});
  const a = math.chain(3).add(4).multiply(2).done(); // 14

  // Another example, calculate square(sin(pi / 4))
  const b = math.chain(math.pi).divide(4).sin().square().done();

  // toString will return a string representation of the chain's value
  const chain = math.chain(2).divide(3);
  const str: string = chain.toString(); // "0.6666666666666666"

  chain.valueOf();

  // the function subset can be used to get or replace sub matrices
  const array = [
    [1, 2],
    [3, 4],
  ];
  const v = math.chain(array).subset(math.index(1, 0)).done(); // 3

  const m = math.chain(array).subset(math.index(0, 0), 8).multiply(3).done();

  // filtering
  math
    .chain([-1, 0, 1.1, 2, 3, 1000])
    .filter(math.isPositive)
    .filter(math.isInteger)
    .filter((n) => n !== 1000)
    .done(); // [2, 3]
}

/*
Simplify examples
*/
{
  const math = create(all);

  math.simplify("2 * 1 * x ^ (2 - 1)");
  math.simplify("2 * 3 * x", { x: 4 });

  const f = math.parse("2 * 1 * x ^ (2 - 1)");
  math.simplify(f);

  math.simplify("0.4 * x", {}, { exactFractions: true });
  math.simplify("0.4 * x", {}, { exactFractions: false });
}

/*
Complex numbers examples
*/
{
  const math = create(all, {});
  const a = math.complex(2, 3);
  // create a complex number by providing a string with real and complex parts
  const b = math.complex('3 - 7i');

  // read the real and complex parts of the complex number
  {
    const x: number = a.re;
    const y: number = a.im;

    // adjust the complex value
    a.re = 5;
  }

  // clone a complex value
  {
    const clone = a.clone();
  }

  // perform operations with complex numbers
  {
    math.add(a, b);
    math.multiply(a, b);
    math.sin(a);
  }

  // create a complex number from polar coordinates
  {
    const p: math.PolarCoordinates = { r: math.sqrt(2), phi: math.pi / 4 };
    const c: math.Complex = math.complex(p);
  }

  // get polar coordinates of a complex number
  {
    const p: math.PolarCoordinates = math.complex(3, 4).toPolar();
  }
}

/*
Expressions examples
*/
{
  const math = create(all, {});
  // evaluate expressions
  {
    math.evaluate('sqrt(3^2 + 4^2)');
  }

  // evaluate multiple expressions at once
  {
    math.evaluate(['f = 3', 'g = 4', 'f * g']);
  }

  // get content of a parenthesis node
  {
    const node = math.parse('(1)');
    const innerNode = node.content;
  }

  // scope can contain both variables and functions
  {
    const scope = { hello: (name: string) => `hello, ${name}!` };
    math.evaluate('hello("hero")', scope); // "hello, hero!"
  }

  // define a function as an expression
  {
    const scope: any = {
      a: 3,
      b: 4,
    };
    const f = math.evaluate('f(x) = x ^ a', scope);
    f(2);
    scope.f(2);
  }

  {
    const node2 = math.parse('x^a');
    const code2: math.EvalFunction = node2.compile();
    node2.toString();
  }

  // 3. using function math.compile
  // parse an expression
  {
    // provide a scope for the variable assignment
    const code2 = math.compile('a = a + 3');
    const scope = { a: 7 };
    code2.evaluate(scope);
  }
  // 4. using a parser
  const parser = math.parser();

  // get and set variables and functions
  {
    parser.evaluate('x = 7 / 2'); // 3.5
    parser.evaluate('x + 3'); // 6.5
    parser.evaluate('f(x, y) = x^y'); // f(x, y)
    parser.evaluate('f(2, 3)'); // 8

    const x = parser.get('x');
    const f = parser.get('f');
    const y = parser.getAll();
    const g = f(3, 3);

    parser.set('h', 500);
    parser.set('hello', (name: string) => `hello, ${name}!`);
  }

  // clear defined functions and variables
  parser.clear();
}

/*
Fractions examples
*/
{
  // configure the default type of numbers as Fractions
  const math = create(all, {
    number: 'Fraction',
  });

  const x = math.fraction(0.125);
  const y = math.fraction('1/3');
  math.fraction(2, 3);

  math.add(x, y);
  math.divide(x, y);

  // output formatting
  const a = math.fraction('2/3');
}

/*
Matrices examples
*/
{
  const math = create(all, {});

  // create matrices and arrays. a matrix is just a wrapper around an Array,
  // providing some handy utilities.
  const a: math.Matrix = math.matrix([1, 4, 9, 16, 25]);
  const b: math.Matrix = math.matrix(math.ones([2, 3]));
  b.size();

  // the Array data of a Matrix can be retrieved using valueOf()
  const array = a.valueOf();

  // Matrices can be cloned
  const clone: math.Matrix = a.clone();

  // perform operations with matrices
  math.sqrt(a);
  math.factorial(a);

  // create and manipulate matrices. Arrays and Matrices can be used mixed.
  {
    const a = [
      [1, 2],
      [3, 4],
    ];
    const b: math.Matrix = math.matrix([
      [5, 6],
      [1, 1],
    ]);

    b.subset(math.index(1, [0, 1]), [[7, 8]]);
    const c = math.multiply(a, b);
    const f: math.Matrix = math.matrix([1, 0]);
    const d: math.Matrix = f.subset(math.index(1, 0));
  }

  // get a sub matrix
  {
    const a: math.Matrix = math.diag(math.range(1, 4));
    a.subset(math.index([1, 2], [1, 2]));
    const b: math.Matrix = math.range(1, 6);
    b.subset(math.index(math.range(1, 4)));
  }

  // resize a multi dimensional matrix
  {
    const a = math.matrix();
    a.resize([2, 2, 2], 0);
    a.size();
    a.resize([2, 2]);
    a.size();
  }

  // can set a subset of a matrix to uninitialized
  {
    const m = math.matrix();
    m.subset(math.index(2), 6, math.uninitialized);
  }

  // create ranges
  {
    math.range(1, 6);
    math.range(0, 18, 3);
    math.range('2:-1:-3');
    math.factorial(math.range('1:6'));
  }

  // map matrix
  {
    math.map([1, 2, 3], function (value) {
      return value * value;
    }); // returns [1, 4, 9]
  }

  // filter matrix
  {
    math.filter([6, -2, -1, 4, 3], function (x) {
      return x > 0;
    }); // returns [6, 4, 3]
    math.filter(['23', 'foo', '100', '55', 'bar'], /[0-9]+/); // returns ["23", "100", "55"]
  }

  // concat matrix
  {
    math.concat([[0, 1, 2]], [[1, 2, 3]]); // returns [[ 0, 1, 2, 1, 2, 3 ]]
    math.concat([[0, 1, 2]], [[1, 2, 3]], 0); // returns [[ 0, 1, 2 ], [ 1, 2, 3 ]]
  }
}

/*
Sparse matrices examples
*/
{
  const math = create(all, {});

  // create a sparse matrix
  const a = math.identity(1000, 1000, 'sparse');

  // do operations with a sparse matrix
  const b = math.multiply(a, a);
  const c = math.multiply(b, math.complex(2, 2));
  const d = math.matrix([0, 1]);
  const e = math.transpose(d);
  const f = math.multiply(e, a);
}

/*
Units examples
*/
{
  const math = create(all, {});

  // units can be created by providing a value and unit name, or by providing
  // a string with a valued unit.
  const a = math.unit(45, 'cm'); // 450 mm
  const b = math.unit('0.1m'); // 100 mm

  // creating units
  math.createUnit('foo');
  math.createUnit('furlong', '220 yards');
  math.createUnit('furlong', '220 yards', { override: true });
  math.createUnit('testunit', { definition: '0.555556 kelvin', offset: 459.67 });
  math.createUnit('testunit', { definition: '0.555556 kelvin', offset: 459.67 }, { override: true });
  math.createUnit('knot', { definition: '0.514444 m/s', aliases: ['knots', 'kt', 'kts'] });
  math.createUnit('knot', { definition: '0.514444 m/s', aliases: ['knots', 'kt', 'kts'] }, { override: true });
  math.createUnit(
    'knot',
    {
      definition: '0.514444 m/s',
      aliases: ['knots', 'kt', 'kts'],
      prefixes: 'long',
    },
    { override: true }
  );
  math.createUnit(
    {
      foo_2: {
        prefixes: 'long',
      },
      bar: '40 foo',
      baz: {
        definition: '1 bar/hour',
        prefixes: 'long',
      },
    },
    {
      override: true,
    }
  );
  // use Unit as definition
  math.createUnit('c', { definition: b });
  math.createUnit('c', { definition: b }, { override: true });

  // units can be added, subtracted, and multiplied or divided by numbers and by other units
  math.add(a, b);
  math.multiply(b, 2);
  math.divide(math.unit('1 m'), math.unit('1 s'));
  math.pow(math.unit('12 in'), 3);

  // units can be converted to a specific type, or to a number
  b.to('cm');
  math.to(b, 'inch');
  b.toNumber('cm');
  math.number(b, 'cm');

  // the expression parser supports units too
  math.evaluate('2 inch to cm');

  // units can be converted to SI
  math.unit('1 inch').toSI();

  // units can be split into other units
  math.unit('1 m').splitUnit(['ft', 'in']);
}

/*
Expression tree examples
*/
{
  const math = create(all, {});

  // Filter an expression tree
  const node: math.MathNode = math.parse('x^2 + x/4 + 3*y');
  const filtered: math.MathNode[] = node.filter((node: math.MathNode) => node.isSymbolNode && node.name === 'x');

  const arr: string[] = filtered.map((node: math.MathNode) => node.toString());

  // Traverse an expression tree
  const node1: math.MathNode = math.parse('3 * x + 2');
  node1.traverse((node: math.MathNode, path: string, parent: math.MathNode) => {
    switch (node.type) {
      case 'OperatorNode':
        return node.type === 'OperatorNode';
      case 'ConstantNode':
        return node.type === 'ConstantNode';
      case 'SymbolNode':
        return node.type === 'SymbolNode';
      default:
        return node.type === 'any string at all';
    }
  });
}

/*
Function floor examples
*/
{
  const math = create(all, {});

  // number input
  math.floor(3.2); // returns number 3
  math.floor(-4.2); // returns number -5

  // number input
  // roundoff result to 2 decimals
  math.floor(3.212, 2); // returns number 3.21
  math.floor(-4.212, 2); // returns number -4.22

  // Complex input
  const c = math.complex(3.24, -2.71); // returns Complex 3 - 3i
  math.floor(c); // returns Complex 3 - 3i
  math.floor(c, 1); // returns Complex 3.2 - 2.8i

  //array input
  math.floor([3.2, 3.8, -4.7]); // returns Array [3, 3, -5]
  math.floor([3.21, 3.82, -4.71], 1); // returns Array [3.2, 3.8, -4.8]
}


/*
JSON serialization/deserialization
*/
{
  const math = create(all, {});

  const data = {
    bigNumber: math.bignumber('1.5'),
  };
  const stringified = JSON.stringify(data);
  const parsed = JSON.parse(stringified, math.json.reviver);
  parsed.bigNumber === math.bignumber('1.5'); // true
}

/*
Extend functionality with import
 */

declare module 'mathjs' {
  interface MathJsStatic {
    testFun(): number;
    value: number;
  }
}

{
  const math = create(all, {});
  const testFun = () => 5;

  math.import(
    {
      testFun,
      value: 10,
    },
    {}
  );

  math.testFun();

  const a = math.value * 2;
}

/*
Renamed functions from v5 => v6
 */
{
  const math = create(all, {});
  math.typeOf(1);
  math.variance([1, 2, 3, 4]);
  math.evaluate('1 + 2');

  // chained operations
  math.chain(3).typeOf().done();
  math.chain([1, 2, 3]).variance().done();
  math.chain('1 + 2').evaluate().done();
}

/*
Factory Test
 */
{
  // create a factory function
  const name = 'negativeSquare';
  const dependencies: MathJsFunctionName[] = ['multiply', 'unaryMinus'];
  const createNegativeSquare = factory(name, dependencies, (injected) => {
    const { multiply, unaryMinus } = injected;
    return function negativeSquare(x: number): number {
      return unaryMinus(multiply(x, x));
    };
  });

  // create an instance of the function yourself:
  const multiply = (a: number, b: number) => a * b;
  const unaryMinus = (a: number) => -a;
  const negativeSquare = createNegativeSquare({ multiply, unaryMinus });
  negativeSquare(3);
}

/**
 * Dependency map typing test from mathjs official document:
 * https://mathjs.org/docs/custom_bundling.html#using-just-a-few-functions
 */
{
  const config = {
    // optionally, you can specify configuration
  };

  // Create just the functions we need
  const { fraction, add, divide, format } = create(
    {
      fractionDependencies,
      addDependencies,
      divideDependencies,
      formatDependencies,
    },
    config
  );

  // Use the created functions
  const a = fraction(1, 3);
  const b = fraction(3, 7);
  const c = add(a, b);
  const d = divide(a, b);
  console.log('c =', format(c)); // outputs "c = 16/21"
  console.log('d =', format(d)); // outputs "d = 7/9"
}

/**
 * Custom parsing functions
 * https://mathjs.org/docs/expressions/customization.html#customize-supported-characters
 */
{
  const math = create(all, {});
  const isAlphaOriginal = math.parse.isAlpha;
  math.parse.isAlpha = (c, cPrev, cNext) => {
    return isAlphaOriginal(c, cPrev, cNext) || c === "\u260E";
  };

  // now we can use the \u260E (phone) character in expressions
  const result = math.evaluate("\u260Efoo", { "\u260Efoo": 42 }); // returns 42
  console.log(result);
}

/**
 * Util functions
 * https://mathjs.org/docs/reference/functions.html#utils-functions
 */
{
  const math = create(all, {});

  // hasNumericValue function
  math.hasNumericValue(2);                     // returns true
  math.hasNumericValue('2');                   // returns true
  math.isNumeric('2');                         // returns false
  math.hasNumericValue(0);                     // returns true
  math.hasNumericValue(math.bignumber(500));   // returns true
  math.hasNumericValue([2.3, 'foo', false]);   // returns [true, false, true]
  math.hasNumericValue(math.fraction(4));      // returns true
  math.hasNumericValue(math.complex('2-4i'));  // returns false
}