Polynomial regression: Difference between revisions

 

=={{header|Ada}}==

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

 

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

end Fit;

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 φ_''j'' is ''x''^''j'', ''j''=0,1,..,''N''. The implementation is straightforward. First the plane matrix A is created. A_ji=φ_''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.

===Example===

with Fit;

with Ada.Float_Text_IO; use Ada.Float_Text_IO;

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

end Fitting;

Sample output:

<pre>

=={{header|Fortran}}==

{{libheader|LAPACK}}

module fitting

contains

end module

 

===Example===

program PolynomalFitting

use fitting

 

end program

 

Output (lower powers first, so this seems the opposite of the Python output):

 

{{libheader|numpy}}

>>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

>>> y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]

>>> coeffs

array([ 3., 2., 1.])

Substitute back received coefficients.

>>> yf = numpy.polyval(numpy.poly1d(coeffs), x)

>>> yf

array([ 1., 6., 17., 34., 57., 86., 121., 162., 209., 262., 321.])

Find max absolute error.

>>> '%.1g' % max(y-yf)

'1e-013'

 

===Example===

For input arrays `x' and `y':

>>> x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> y = [2.7, 2.8, 31.4, 38.1, 58.0, 76.2, 100.5, 130.0, 149.3, 180.0]

 

>>> p = numpy.poly1d(numpy.polyfit(x, y, deg=2), variable='N')

>>> print p

2

1.085 N + 10.36 N - 0.6164

Thus we confirm once more that for already sorted sequences the considered quick sort implementation has quadratic dependence on sequence length (see [[Query Performance|'''Example''' section for Python language on ''Query Performance'' page]]).