// matrices

// load math.js (using node.js)
var math = require('../index');


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

// the Array data of a Matrix can be retrieved using valueOf()
var array = a.valueOf();
print(array);                               // [1, 4, 9, 16, 25]

// Matrices can be cloned
var clone = a.clone();
print(clone);                               // [1, 4, 9, 16, 25]
console.log();

// perform operations with matrices
console.log('perform operations');
print(math.sqrt(a));                       // [1, 2, 3, 4, 5]
var c = [1, 2, 3, 4, 5];
print(math.factorial(c));                  // [1, 2, 6, 24, 120]
console.log();

// create and manipulate matrices. Arrays and Matrices can be used mixed.
console.log('manipulate matrices');
var d = [[1, 2], [3, 4]];
print(d);                                   // [[1, 2], [3, 4]]
var e = math.matrix([[5, 6], [1, 1]]);
print(e);                                   // [[5, 6], [1, 1]]

// set a submatrix.
// Matrix indexes are zero-based.
e.subset(math.index(1, [0, 1]), [[7, 8]]);
print(e);                                   // [[5, 6], [7, 8]]
var f = math.multiply(d, e);
print(f);                                   // [[19, 22], [43, 50]]
var g = f.subset(math.index(1, 0));
print(g);                                   // 43
console.log();

// get a sub matrix
// Matrix indexes are zero-based.
console.log('get a sub matrix');
var h = math.diag(math.range(1,4));
print(h);                                     // [[1, 0, 0], [0, 2, 0], [0, 0, 3]]
print(h.subset( math.index([1, 2], [1, 2]))); // [[2, 0], [0, 3]]
var i = math.range(1,6);
print(i);                                     // [1, 2, 3, 4, 5]
print(i.subset(math.index(math.range(1,4)))); // [2, 3, 4]
console.log();


// resize a multi dimensional matrix
console.log('resizing a matrix');
var j = math.matrix();
var defaultValue = 0;
j.resize([2, 2, 2], defaultValue);
print(j);                                   // [[[0, 0], [0, 0]], [[0, 0], [0, 0]]]
print(j.size());                            // [2, 2, 2]
j.resize([2, 2]);
print(j);                                   // [[0, 0], [0, 0]]
print(j.size());                            // [2, 2]
console.log();

// setting a value outside the matrices range will resize the matrix.
// new elements will be initialized with zero.
console.log('set a value outside a matrices range');
var k = math.matrix();
k.subset(math.index(2), 6);
print(k);                                   // [0, 0, 6]
console.log();

console.log('set a value outside a matrices range, leaving new entries uninitialized');
var m = math.matrix();
defaultValue = math.uninitialized;
m.subset(math.index(2), 6, defaultValue);
print(m);                                   // [undefined, undefined, 6]
console.log();

// create ranges
console.log('create ranges');
print(math.range(1, 6));                    // [1, 2, 3, 4, 5]
print(math.range(0, 18, 3));                // [0, 3, 6, 9, 12, 15]
print(math.range('2:-1:-3'));               // [2, 1, 0, -1, -2]
print(math.factorial(math.range('1:6')));   // [1, 2, 6, 24, 120]
console.log();


/**
 * Helper function to output a value in the console. Value will be formatted.
 * @param {*} value
 */
function print (value) {
  var precision = 14;
  console.log(math.format(value, precision));
}