Perl AI Deep Learning Tutorial

Find random numbers that follow a normal distribution

Let's find a random number that follows a normal distribution in Perl. Initial value of Xavier and Initial value of He as the initial value of the weight parameter. >, But both are random numbers that follow a normal distribution.

The normal distribution has a high center, and the more you go to the right and left, the lower the distribution. The left and right are targets and smooth graphs. Expressing one normal distribution with (x, y) coordinates is as follows.

(-4, 0.00001)
(-3, 0.001)
(-2, 0.05)
(-1, 0.2)
(0, 0.4)
(1, 0.2)
(2, 0.05)
(3, 0.001)
(4, 0.00001)

The normal distribution is shaped by specifying the mean and standard deviation.

The mean matches the x coordinate at the highest y coordinate. In the case of the above example, it is 0. The smaller the value, called the standard deviation, the sharper the shape.

Random numbers that follow a normal distribution are, as the name implies. The probability that a value near the center will appear is high. Regarding the calculation formula of randn, I do not know the contents of the calculation method well.

use strict;
use warnings;

# Function to find random numbers that follow a normal distribution
# $ave is mean, $sigma is standard deviation,
sub randn {
  my ($ave, $sigma) = @_;
  my ($r1, $r2) = (rand(), rand());
  while ($r1 == 0) {$r1 = rand();}
  return($sigma * sqrt(-2 * log($r1)) * sin(2 * 3.14159265359 * $r2)) + $ave;
}

my $ave = 0;
my $sigma = 1;

# Generate a random number that follows a normal distribution
for (0 .. 100) {
  my $randn = randn ($ave, $sigma);
  print "$randn\n";
}

This is a sample output result.

-0.312900844794695
0.368516508387452
0.588564026974205
-0.832093759572302
-0.373563467435626
0.128322638304041
-0.228427968297216
-0.245046689515676
0.315406051382644
0.658932693772217
0.569456859322423
1.49604255431358
-0.563332708600982
-0.130983698272141
-0.65316083654429
2.21759497277892
-1.13077911035109
0.416355154057237
-0.992338158849582
-0.0415533205367665
-0.139471145014137
-0.555637591105884
0.0610479864678622
-1.83754633603067
-0.355777559590925
-0.733515417984692
-0.586761757878687
-2.56732797838226
-0.0958678885297631
0.610464417758399
-0.400757637198111
2.16917680131624
0.304382226761163
-0.706898412159972
-0.0105635240353556
1.18621562931325
-0.806053955712314
0.0788339133990966
-0.0878677608626948
0.0499876673082178
-0.91469235675378
-0.583570118757101
1.75119496540262
0.717132303416223
-2.33651905151149
0.601256117559849
-0.160805082740475
-1.69726845564479
2.12940182097853
0.165837725238895
-0.255632364287032
-0.163546251052526
-1.33104254345012
0.227482582090221
-0.0967166218513033
-1.32755710603693
0.316919938301281
-0.0212234397436275
0.725093722651192
1.68315876861612
1.74955853858043
0.0842186232602491
-0.145906364613128
1.47917785353059
-0.511611505685728
-0.210334896278017
0.672454440669521
1.64492760302033
1.37283258241519
0.79094523781063
-0.283363372457433
1.18971415501877
0.387045143982198
-0.623982153431303
0.469061730743257
-0.683712125388351
-0.836530854874499
0.638136701054174
0.231606572497369
1.45980005894014
1.06610004144032
0.297129643450955
1.59304995448786
0.979957182081171
1.22931022126118
-0.027647841530499
2.02384036594018
-0.458393546179776
-0.399941978668047
2.01279648101146
1.1528225003866
-1.5332801324075
-1.20378561557291
0.459610546599193
0.570946364435492
0.987438393052072
1.74715213041814
0.0301710690716359
0.456481012707392
-0.713494905933569
-1.10745100942014