Polynomial regression: Difference between revisions

=={{header|Ada}}==

<ada>

with Ada.Numerics.Real_Arrays; use Ada.Numerics.Real_Arrays;

with Ada.Float_Text_IO; use Ada.Float_Text_IO;

procedure Fitting is

function Fit (X, Y : Real_Vector) return Real_Vector is

A : Real_Matrix (0..2, X'Range); -- The plane

begin

for I in A'Range (2) loop

A (0, I) := 1.0;

A (1, I) := X (I);

A (2, I) := X (I)**2;

end loop;

return Solve (A * Transpose (A), A * Y);

end Fit;

C : Real_Vector :=

Fit

( (0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0),

(1.0, 6.0, 17.0, 34.0, 57.0, 86.0, 121.0, 162.0, 209.0, 262.0, 321.0)

);

begin

Put (C (0), Aft => 3, Exp => 0);

Put (C (1), Aft => 3, Exp => 0);

Put (C (2), Aft => 3, Exp => 0);

end Fitting;

</ada>

The function Fit implements least squares approximation of a function defined in the points as specified by the arrays ''x''_''i'' and ''y''_''i''. The basis &phi;_''j'' is 1, ''x'', ''x''². The implementation is straightforward. First the plane matrix A is created. A_ji=&phi;_''j''(''x''_''i''). Then the linear problem AA^''T''''c''=A''y'' is solved. The result ''c''_''j'' are the coefficients. Constraint_Error is propagated when dimensions of X and Y differ or else when the problem is ill-defined.

Sample output:

<pre>

1.000 2.000 3.000

</pre>