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Polynomial regression: Difference between revisions
→{{header|Ada}}: Modified to arbitrary degree
(Ada solution added) |
(→{{header|Ada}}: Modified to arbitrary degree) |
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<ada>
with Ada.Numerics.Real_Arrays; use Ada.Numerics.Real_Arrays;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;▼
procedure Fitting is▼
A : Real_Matrix (0..N, X'Range); -- The plane
▲ function Fit (X, Y : Real_Vector) return Real_Vector is
for I in A
for J in A'Range (1) loop
▲ begin
A (0, I) := 1.0;▼
end loop;
▲ end Fit;
end Fit;
</ada>
The function Fit implements least squares approximation of a function defined in the points as specified by the arrays ''x''<sub>''i''</sub> and ''y''<sub>''i''</sub>. The basis φ<sub>''j''</sub> is
===Example===
<ada>
with Fit;
▲procedure Fitting is
C : constant 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
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end Fitting;
</ada>
▲The function Fit implements least squares approximation of a function defined in the points as specified by the arrays ''x''<sub>''i''</sub> and ''y''<sub>''i''</sub>. The basis φ<sub>''j''</sub> is 1, ''x'', ''x''<sup>2</sup>. The implementation is straightforward. First the plane matrix A is created. A<sub>ji</sub>=φ<sub>''j''</sub>(''x''<sub>''i''</sub>). Then the linear problem AA<sup>''T''</sup>''c''=A''y'' is solved. The result ''c''<sub>''j''</sub> 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>
=={{header|Fortran}}==
{{libheader|LAPACK}}
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