summaryrefslogtreecommitdiff
path: root/static/src/assets/viz/2/goog/math/math.js
blob: b8dbfb0215500edfbddf4c86a5e3748685462023 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
// Copyright 2006 The Closure Library Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS-IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

/**
 * @fileoverview Additional mathematical functions.
 */

goog.provide('goog.math');

goog.require('goog.array');
goog.require('goog.asserts');


/**
 * Returns a random integer greater than or equal to 0 and less than {@code a}.
 * @param {number} a  The upper bound for the random integer (exclusive).
 * @return {number} A random integer N such that 0 <= N < a.
 */
goog.math.randomInt = function(a) {
  return Math.floor(Math.random() * a);
};


/**
 * Returns a random number greater than or equal to {@code a} and less than
 * {@code b}.
 * @param {number} a  The lower bound for the random number (inclusive).
 * @param {number} b  The upper bound for the random number (exclusive).
 * @return {number} A random number N such that a <= N < b.
 */
goog.math.uniformRandom = function(a, b) {
  return a + Math.random() * (b - a);
};


/**
 * Takes a number and clamps it to within the provided bounds.
 * @param {number} value The input number.
 * @param {number} min The minimum value to return.
 * @param {number} max The maximum value to return.
 * @return {number} The input number if it is within bounds, or the nearest
 *     number within the bounds.
 */
goog.math.clamp = function(value, min, max) {
  return Math.min(Math.max(value, min), max);
};


/**
 * The % operator in JavaScript returns the remainder of a / b, but differs from
 * some other languages in that the result will have the same sign as the
 * dividend. For example, -1 % 8 == -1, whereas in some other languages
 * (such as Python) the result would be 7. This function emulates the more
 * correct modulo behavior, which is useful for certain applications such as
 * calculating an offset index in a circular list.
 *
 * @param {number} a The dividend.
 * @param {number} b The divisor.
 * @return {number} a % b where the result is between 0 and b (either 0 <= x < b
 *     or b < x <= 0, depending on the sign of b).
 */
goog.math.modulo = function(a, b) {
  var r = a % b;
  // If r and b differ in sign, add b to wrap the result to the correct sign.
  return (r * b < 0) ? r + b : r;
};


/**
 * Performs linear interpolation between values a and b. Returns the value
 * between a and b proportional to x (when x is between 0 and 1. When x is
 * outside this range, the return value is a linear extrapolation).
 * @param {number} a A number.
 * @param {number} b A number.
 * @param {number} x The proportion between a and b.
 * @return {number} The interpolated value between a and b.
 */
goog.math.lerp = function(a, b, x) {
  return a + x * (b - a);
};


/**
 * Tests whether the two values are equal to each other, within a certain
 * tolerance to adjust for floating point errors.
 * @param {number} a A number.
 * @param {number} b A number.
 * @param {number=} opt_tolerance Optional tolerance range. Defaults
 *     to 0.000001. If specified, should be greater than 0.
 * @return {boolean} Whether {@code a} and {@code b} are nearly equal.
 */
goog.math.nearlyEquals = function(a, b, opt_tolerance) {
  return Math.abs(a - b) <= (opt_tolerance || 0.000001);
};


// TODO(user): Rename to normalizeAngle, retaining old name as deprecated
// alias.
/**
 * Normalizes an angle to be in range [0-360). Angles outside this range will
 * be normalized to be the equivalent angle with that range.
 * @param {number} angle Angle in degrees.
 * @return {number} Standardized angle.
 */
goog.math.standardAngle = function(angle) {
  return goog.math.modulo(angle, 360);
};


/**
 * Normalizes an angle to be in range [0-2*PI). Angles outside this range will
 * be normalized to be the equivalent angle with that range.
 * @param {number} angle Angle in radians.
 * @return {number} Standardized angle.
 */
goog.math.standardAngleInRadians = function(angle) {
  return goog.math.modulo(angle, 2 * Math.PI);
};


/**
 * Converts degrees to radians.
 * @param {number} angleDegrees Angle in degrees.
 * @return {number} Angle in radians.
 */
goog.math.toRadians = function(angleDegrees) {
  return angleDegrees * Math.PI / 180;
};


/**
 * Converts radians to degrees.
 * @param {number} angleRadians Angle in radians.
 * @return {number} Angle in degrees.
 */
goog.math.toDegrees = function(angleRadians) {
  return angleRadians * 180 / Math.PI;
};


/**
 * For a given angle and radius, finds the X portion of the offset.
 * @param {number} degrees Angle in degrees (zero points in +X direction).
 * @param {number} radius Radius.
 * @return {number} The x-distance for the angle and radius.
 */
goog.math.angleDx = function(degrees, radius) {
  return radius * Math.cos(goog.math.toRadians(degrees));
};


/**
 * For a given angle and radius, finds the Y portion of the offset.
 * @param {number} degrees Angle in degrees (zero points in +X direction).
 * @param {number} radius Radius.
 * @return {number} The y-distance for the angle and radius.
 */
goog.math.angleDy = function(degrees, radius) {
  return radius * Math.sin(goog.math.toRadians(degrees));
};


/**
 * Computes the angle between two points (x1,y1) and (x2,y2).
 * Angle zero points in the +X direction, 90 degrees points in the +Y
 * direction (down) and from there we grow clockwise towards 360 degrees.
 * @param {number} x1 x of first point.
 * @param {number} y1 y of first point.
 * @param {number} x2 x of second point.
 * @param {number} y2 y of second point.
 * @return {number} Standardized angle in degrees of the vector from
 *     x1,y1 to x2,y2.
 */
goog.math.angle = function(x1, y1, x2, y2) {
  return goog.math.standardAngle(
      goog.math.toDegrees(Math.atan2(y2 - y1, x2 - x1)));
};


/**
 * Computes the difference between startAngle and endAngle (angles in degrees).
 * @param {number} startAngle  Start angle in degrees.
 * @param {number} endAngle  End angle in degrees.
 * @return {number} The number of degrees that when added to
 *     startAngle will result in endAngle. Positive numbers mean that the
 *     direction is clockwise. Negative numbers indicate a counter-clockwise
 *     direction.
 *     The shortest route (clockwise vs counter-clockwise) between the angles
 *     is used.
 *     When the difference is 180 degrees, the function returns 180 (not -180)
 *     angleDifference(30, 40) is 10, and angleDifference(40, 30) is -10.
 *     angleDifference(350, 10) is 20, and angleDifference(10, 350) is -20.
 */
goog.math.angleDifference = function(startAngle, endAngle) {
  var d =
      goog.math.standardAngle(endAngle) - goog.math.standardAngle(startAngle);
  if (d > 180) {
    d = d - 360;
  } else if (d <= -180) {
    d = 360 + d;
  }
  return d;
};


/**
 * Returns the sign of a number as per the "sign" or "signum" function.
 * @param {number} x The number to take the sign of.
 * @return {number} -1 when negative, 1 when positive, 0 when 0. Preserves
 *     signed zeros and NaN.
 */
goog.math.sign = function(x) {
  if (x > 0) {
    return 1;
  }
  if (x < 0) {
    return -1;
  }
  return x;  // Preserves signed zeros and NaN.
};


/**
 * JavaScript implementation of Longest Common Subsequence problem.
 * http://en.wikipedia.org/wiki/Longest_common_subsequence
 *
 * Returns the longest possible array that is subarray of both of given arrays.
 *
 * @param {IArrayLike<S>} array1 First array of objects.
 * @param {IArrayLike<T>} array2 Second array of objects.
 * @param {Function=} opt_compareFn Function that acts as a custom comparator
 *     for the array ojects. Function should return true if objects are equal,
 *     otherwise false.
 * @param {Function=} opt_collectorFn Function used to decide what to return
 *     as a result subsequence. It accepts 2 arguments: index of common element
 *     in the first array and index in the second. The default function returns
 *     element from the first array.
 * @return {!Array<S|T>} A list of objects that are common to both arrays
 *     such that there is no common subsequence with size greater than the
 *     length of the list.
 * @template S,T
 */
goog.math.longestCommonSubsequence = function(
    array1, array2, opt_compareFn, opt_collectorFn) {

  var compare = opt_compareFn || function(a, b) { return a == b; };

  var collect = opt_collectorFn || function(i1, i2) { return array1[i1]; };

  var length1 = array1.length;
  var length2 = array2.length;

  var arr = [];
  for (var i = 0; i < length1 + 1; i++) {
    arr[i] = [];
    arr[i][0] = 0;
  }

  for (var j = 0; j < length2 + 1; j++) {
    arr[0][j] = 0;
  }

  for (i = 1; i <= length1; i++) {
    for (j = 1; j <= length2; j++) {
      if (compare(array1[i - 1], array2[j - 1])) {
        arr[i][j] = arr[i - 1][j - 1] + 1;
      } else {
        arr[i][j] = Math.max(arr[i - 1][j], arr[i][j - 1]);
      }
    }
  }

  // Backtracking
  var result = [];
  var i = length1, j = length2;
  while (i > 0 && j > 0) {
    if (compare(array1[i - 1], array2[j - 1])) {
      result.unshift(collect(i - 1, j - 1));
      i--;
      j--;
    } else {
      if (arr[i - 1][j] > arr[i][j - 1]) {
        i--;
      } else {
        j--;
      }
    }
  }

  return result;
};


/**
 * Returns the sum of the arguments.
 * @param {...number} var_args Numbers to add.
 * @return {number} The sum of the arguments (0 if no arguments were provided,
 *     {@code NaN} if any of the arguments is not a valid number).
 */
goog.math.sum = function(var_args) {
  return /** @type {number} */ (
      goog.array.reduce(
          arguments, function(sum, value) { return sum + value; }, 0));
};


/**
 * Returns the arithmetic mean of the arguments.
 * @param {...number} var_args Numbers to average.
 * @return {number} The average of the arguments ({@code NaN} if no arguments
 *     were provided or any of the arguments is not a valid number).
 */
goog.math.average = function(var_args) {
  return goog.math.sum.apply(null, arguments) / arguments.length;
};


/**
 * Returns the unbiased sample variance of the arguments. For a definition,
 * see e.g. http://en.wikipedia.org/wiki/Variance
 * @param {...number} var_args Number samples to analyze.
 * @return {number} The unbiased sample variance of the arguments (0 if fewer
 *     than two samples were provided, or {@code NaN} if any of the samples is
 *     not a valid number).
 */
goog.math.sampleVariance = function(var_args) {
  var sampleSize = arguments.length;
  if (sampleSize < 2) {
    return 0;
  }

  var mean = goog.math.average.apply(null, arguments);
  var variance =
      goog.math.sum.apply(null, goog.array.map(arguments, function(val) {
        return Math.pow(val - mean, 2);
      })) / (sampleSize - 1);

  return variance;
};


/**
 * Returns the sample standard deviation of the arguments.  For a definition of
 * sample standard deviation, see e.g.
 * http://en.wikipedia.org/wiki/Standard_deviation
 * @param {...number} var_args Number samples to analyze.
 * @return {number} The sample standard deviation of the arguments (0 if fewer
 *     than two samples were provided, or {@code NaN} if any of the samples is
 *     not a valid number).
 */
goog.math.standardDeviation = function(var_args) {
  return Math.sqrt(goog.math.sampleVariance.apply(null, arguments));
};


/**
 * Returns whether the supplied number represents an integer, i.e. that is has
 * no fractional component.  No range-checking is performed on the number.
 * @param {number} num The number to test.
 * @return {boolean} Whether {@code num} is an integer.
 */
goog.math.isInt = function(num) {
  return isFinite(num) && num % 1 == 0;
};


/**
 * Returns whether the supplied number is finite and not NaN.
 * @param {number} num The number to test.
 * @return {boolean} Whether {@code num} is a finite number.
 * @deprecated Use {@link isFinite} instead.
 */
goog.math.isFiniteNumber = function(num) {
  return isFinite(num);
};


/**
 * @param {number} num The number to test.
 * @return {boolean} Whether it is negative zero.
 */
goog.math.isNegativeZero = function(num) {
  return num == 0 && 1 / num < 0;
};


/**
 * Returns the precise value of floor(log10(num)).
 * Simpler implementations didn't work because of floating point rounding
 * errors. For example
 * <ul>
 * <li>Math.floor(Math.log(num) / Math.LN10) is off by one for num == 1e+3.
 * <li>Math.floor(Math.log(num) * Math.LOG10E) is off by one for num == 1e+15.
 * <li>Math.floor(Math.log10(num)) is off by one for num == 1e+15 - 1.
 * </ul>
 * @param {number} num A floating point number.
 * @return {number} Its logarithm to base 10 rounded down to the nearest
 *     integer if num > 0. -Infinity if num == 0. NaN if num < 0.
 */
goog.math.log10Floor = function(num) {
  if (num > 0) {
    var x = Math.round(Math.log(num) * Math.LOG10E);
    return x - (parseFloat('1e' + x) > num ? 1 : 0);
  }
  return num == 0 ? -Infinity : NaN;
};


/**
 * A tweaked variant of {@code Math.floor} which tolerates if the passed number
 * is infinitesimally smaller than the closest integer. It often happens with
 * the results of floating point calculations because of the finite precision
 * of the intermediate results. For example {@code Math.floor(Math.log(1000) /
 * Math.LN10) == 2}, not 3 as one would expect.
 * @param {number} num A number.
 * @param {number=} opt_epsilon An infinitesimally small positive number, the
 *     rounding error to tolerate.
 * @return {number} The largest integer less than or equal to {@code num}.
 */
goog.math.safeFloor = function(num, opt_epsilon) {
  goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);
  return Math.floor(num + (opt_epsilon || 2e-15));
};


/**
 * A tweaked variant of {@code Math.ceil}. See {@code goog.math.safeFloor} for
 * details.
 * @param {number} num A number.
 * @param {number=} opt_epsilon An infinitesimally small positive number, the
 *     rounding error to tolerate.
 * @return {number} The smallest integer greater than or equal to {@code num}.
 */
goog.math.safeCeil = function(num, opt_epsilon) {
  goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);
  return Math.ceil(num - (opt_epsilon || 2e-15));
};