Gradient descent: Difference between revisions

Line 202:

use v6.d;

sub steepestDescent(@x, $alpha is copy, $~~tolerance~~) {

sub steepestDescent(@x, $alpha is copy, $h is copy) {

my \N = +@x ; my $h = $tolerance ;

my $g0 = g(@x) ; # ~~Initial estimate~~ of ~~result~~.

my ~~@fi~~ = ~~gradG~~(@x~~, $h~~) ; # ~~Calculate~~ ~~initial~~ ~~gradient~~

my $g0 = g(@x) ; # Initial estimate of result.

# Calculate initial ~~norm.~~

my @fi = gradG(@x, $h, $g0) ; # Calculate initial gradient

my $b = $alpha / (my $delG = (map {~~@fi[~~$_]²}, ^N)~~.sum~~ )~~.sqrt~~;

# Calculate initial norm.

while ( $delG > $tolerance ) { # Iterate until value is <= tolerance.

my $b = $alpha / sqrt(my $delG = sum(map {$_²}, @fi));

# Calculate ~~next~~ ~~value~~.

for ^N { @x[$_] -= $b * @fi[$_] }

$h /= 2;

~~@fi = gradG(@x,~~ $h); # ~~Calculate~~ ~~next~~ ~~gradient~~.

while ( $delG > $h ) { # Iterate until value is <= tolerance.

# Calculate next ~~norm~~.

for @fi.kv -> $i, $j { @x[$i] -= $b * $j } # Calculate next value.

$b = $alpha / ($delG = (map {@fi[$_]²}, ^N).sum ).sqrt;

my $g1 = g(@x); # Calculate next ~~value~~.

@fi = gradG(@x, $h /= 2, g(@x)); # Calculate next gradient.

$g1 > $g0 ?? ( $~~alpha~~ /= ~~2 ) !!~~ ( $g0 ~~= $g1~~ ) # ~~Adjust~~ ~~parameter~~.

$b = $alpha / sqrt($delG = sum(map {$_²}, @fi) ); # Calculate next norm.

}

my $g1 = g(@x); # Calculate next value.

$g1 > $g0 ?? ( $alpha /= 2 ) !! ( $g0 = $g1 ) # Adjust parameter.

}

sub gradG(@x, $h) { # ~~Provides~~ a rough calculation of gradient g(x).

sub gradG(@x is copy, $h, $g0) { # gives a rough calculation of gradient g(x).

my \N = +@x ; ~~my @y =~~ @x ~~; my~~ $g0 = g(@x~~) ;~~

return map { $_ += $h ; (g(@x) - $g0) / $h }, @x

return map { @y[$_] += $h ; (g(@y) - $g0) / $h }, ^N

}

# Function for which minimum is to be found.

sub g(\x) { (x[0]-1)² * (-x[1]²)~~.exp~~ + x[1]*(x[1]+2) * (-2*x[0]²)~~.exp~~ }

sub g(\x) { (x[0]-1)² * exp(-x[1]²) + x[1]*(x[1]+2) * exp(-2*x[0]²) }