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Ingy döt Net 2023-10-02 18:11:16 -07:00
parent 796d366b97
commit 35bcdeebf8
504 changed files with 7045 additions and 610 deletions
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Task/Steffensens-method/Raku/steffensens-method.raku Normal file
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# 20230928 Raku programming solution
sub aitken($f, $p0) {
my $p2 = $f( my $p1 = $f($p0) );
my $p1m0 = $p1 - $p0;
return $p0 - $p1m0*$p1m0/($p2-2.0*$p1+$p0);
}
sub steffensenAitken($f, $pinit, $tol, $maxiter) {
my ($iter, $p) = 1, aitken($f, my $p0 = $pinit);
while abs($p-$p0) > $tol and $iter < $maxiter {
$p = aitken($f, $p0 = $p);
$iter++
}
return abs($p-$p0) > $tol ?? NaN !! $p
}
sub deCasteljau($c0, $c1, $c2, $t) {
my $s = 1.0 - $t;
return $s*($s*$c0 + $t*$c1) + $t*($s*$c1 + $t*$c2)
}
sub xConvexLeftParabola($t) { return deCasteljau(2.0, -8.0, 2.0, $t) }
sub yConvexRightParabola($t) { return deCasteljau(1.0, 2.0, 3.0, $t) }
sub implicitEquation($x, $y) { return 5.0*$x*$x + $y - 5.0 }
sub f($t) {
implicitEquation(xConvexLeftParabola($t), yConvexRightParabola($t)) + $t
}
my $t0 = 0.0;
for ^11 {
print "t0 = {$t0.fmt: '%0.1f'} : ";
my $t = steffensenAitken(&f, $t0, 0.00000001, 1000);
if $t.isNaN {
say "no answer";
} else {
my ($x, $y) = xConvexLeftParabola($t), yConvexRightParabola($t);
if abs(implicitEquation($x, $y)) <= 0.000001 {
printf "intersection at (%f, %f)\n", $x, $y;
} else {
say "spurious solution";
}
}
$t0 += 0.1;
}