topic fit special polynomial - how to input coefficients? in Discussions

fit special polynomial - how to input coefficients?

Jumble — Thu, 08 Jun 2023 16:36:19 GMT

Hi.

Im plotting data using Fit Y by X.

I would like to plot a pre-known quadratic as a reference line (rather than fitting one to the data shown). I can see how this would be done for a linear fit using Fit Special, linear, then constrain the intercept and slope to what ever values, but when selecting quadratic (or higher orders) from the drop down box it doesnt give you somewhere to input the extra coefficients to constrain.

Can I do it via script instead and if so what would the format be?

Many thanks

Re: fit special polynomial - how to input coefficients?

Thierry_S — Mon, 13 Feb 2023 19:04:19 GMT

Hi,

A possible low-tech solution would be to compute your reference curve in a separate column in your data table and then plot it with the rest of the data.

Best,

Re: fit special polynomial - how to input coefficients?

brady_brady — Mon, 13 Feb 2023 20:35:45 GMT

Hi,

Right-clicking on the graph, select "Customize" from the context menu, click the "+" icon. From here you can add a script using the Y function ( ) function, which takes 2 arguments: an expression (the function) and the domain variable (here, x).

Click OK and you're done.

This is also easy to do via scripting with the Y function ( ) function. Here, y = 2x^2 + 3x -5, corresponding to coefficients [2, 3, -5] is plotted. I've used Horner's rule here, as it makes things easier in the next illustration.

dt = astable(J(40,2,randominteger(-20,20)));

gb = dt << Graph Builder( Variables( X( :Col2 ), Y( :Col1 ) ), Elements( Points( X, Y, Legend( 3 ) ) ) );

report(gb)[framebox(1)] << add graphics script ( Y Function( (2 * x + 3) * x - 5, x ) );

One issue is that the coefficients might be determined at runtime, might not be integers, and the degree of the polynomial might be unknown. In this case something like the following will work:

dt = astable(J(40,2,randominteger(-20,20)));

gb = dt << Graph Builder(
	Variables( X( :Col2 ), Y( :Col1 ) ),
	Elements( Points( X, Y, Legend( 3 ) ) ),
);

// get random uniform coefficient matrix 
coef = J(5, 1, randomuniform());

// build an expression using Horner's rule:
for each ( {v, i }, coef,// i = 1; v = coef[i];
	if (i  > 1, 
		fctExp = insert ( insert ( expr ( multiply ( ) ), nameExpr ( fctExp ) ), expr ( x ) );
	,
		fctExp = expr ( 0 );
	);
	fctExp = insert ( insert ( expr( add ( ) ), nameexpr( fctExp ) ), v );	
);

// substitute into a graph script expressison and evaluate
graphAdd = expr (
	report(gb)[framebox(1)] << add graphics script ( Y Function( _EXPRESSION_ , x ) )
);

eval ( substitute ( nameexpr(graphAdd), expr( _EXPRESSION_ ), nameexpr ( fctExp ) ) );

//show the expression in the log
show ( fctExp )

Re: fit special polynomial - how to input coefficients?

Jumble — Wed, 15 Feb 2023 10:40:27 GMT

Your initial suggestion of adding a script via the customize function worked. Thank you!