Steffensen's method: Difference between revisions
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<pre>
Same as C example
</pre>
=={{header|Haxe}}==
{{Trans|ATS|via ALGOL 68}}
<syntaxhighlight lang="haxe">
// Steffensens's method - translated from the ATS sample via Algol 68
class OptionalReal
{
public var v:Float;
public var hasValue:Bool;
public function new( value:Float, notNull:Bool )
{
v = value;
hasValue = notNull;
};
}
class Main {
// Aitken's extrapolation
static function aitken( f:Float->Float // function Float to Float
, p0:Float // initial fixed point estimate
):Float
{
var p1 = f( p0 );
var p2 = f( p1 );
var p1m0 = p1 - p0;
return p0 - ( p1m0 * p1m0 ) / ( p2 - ( 2 * p1 ) + p0 );
};
// finds fixed point p such that f(p) = p
static function steffensenAitken( f:Float->Float // function Float to Float
, pinit:Float // initial estimate
, tol:Float // tolerance
, maxiter:Float // maximum number of iterations
):OptionalReal // return a Float, IF tolerance is met
{
var p0 = pinit;
var p = aitken( f, p0 ); // first iteration
var i = 1;
while( i < ( maxiter - 1 ) && Math.abs( p - p0 ) > tol ) {
p0 = p;
p = aitken( f, p0 );
i += 1;
}
if( Math.abs( p - p0 ) > tol ) {
return new OptionalReal( 0, false );
} else {
return new OptionalReal( p, true );
}
};
static function deCasteljau( c0:Float // control point coordinates (one axis)
, c1:Float
, c2:Float
, t :Float // the indep}ent parameter
) :Float // value of x(t) or y(t)
{
var s = 1 - t;
var c01 = ( s * c0 ) + ( t * c1 );
var c12 = ( s * c1 ) + ( t * c2 );
return ( s * c01 ) + ( t * c12 );
};
static function xConvexLeftParabola( t:Float ):Float { return deCasteljau( 2, -8, 2, t ); }
static function yConvexLeftParabola( t:Float ):Float { return deCasteljau( 1, 2, 3, t ); }
static function implicitEquation( x:Float, y:Float ):Float { return ( 5 * x * x ) + y - 5; }
static function f( t:Float ):Float // find fixed points of this function
{
var x = xConvexLeftParabola( t );
var y = yConvexLeftParabola( t );
return implicitEquation( x, y ) + t;
};
static function main()
{
var t0:Float = 0;
for( i in 1...12 ) {
Sys.print( 't0 = $t0 : ' );
var result = steffensenAitken( f, t0, 0.00000001, 1000 );
if( ! result.hasValue ) {
Sys.println( 'no answer' );
} else {
var x = xConvexLeftParabola( result.v );
var y = yConvexLeftParabola( result.v );
if( Math.abs( implicitEquation( x, y ) ) <= 0.000001 ) {
Sys.println( 'intersection at ($x, $y)' );
} else {
Sys.println( 'spurious solution' );
}
}
t0 += 0.1;
}
}
}
</syntaxhighlight>
{{out}}
<pre>
t0 = 0 : no answer
t0 = 0.1 : intersection at (0.881024967590665, 1.11897503240933)
t0 = 0.2 : no answer
t0 = 0.3 : no answer
t0 = 0.4 : no answer
t0 = 0.5 : no answer
t0 = 0.6 : no answer
t0 = 0.7 : no answer
t0 = 0.8 : no answer
t0 = 0.9 : intersection at (-0.68102496759051, 2.68102496759069)
t0 = 1 : no answer
</pre>
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