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```#!/usr/bin/env python3

"""
reference:
http://www.geometrictools.com/Documentation/LeastSquaresFitting.pdf
"""

import numpy as np
import numpy.matlib as mat

class _CurveFit() :
def __init__(self, * coef) :
if len(coef) == 1 :
coef = list(coef)
if  len(coef) == len(self.coef) :
self.coef = np.array(coef, dtype=np.float64)
elif len(coef) != 0 :
raise ValueError("Curve is defined by {0} parameters".format(len(self.coef)))

def image(self, * v) :
return (self._order(* v) * self.coef).sum()

def fit(self, * p_list) :
A = mat.zeros((6, 6))
Y = mat.zeros((6, 1))
for x, y, z in p_list :
Q = np.asmatrix(self._order(x, y)).T
A += Q * Q.T
Y += z * Q
self.coef = np.array(np.ravel(A.I * Y))
return self

class Paraboloid(_CurveFit) :
# coef must be defined by default, length must be the same as the return value of self._order()
coef = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0], dtype=np.float64)

def _order(self, x, y) :
return np.array([x**2, x*y, y**2, x, y, 1])

if __name__ == '__main__' :
p = Paraboloid(1, 2, 3, 4, 5, -1)
z = list()
for x in range(-2, 3) :
for y in range(-2, 3) :
z.append((x, y, p.image(x, y)))
q = Paraboloid().fit(* z)
print("original   =", p.coef)
print("estimation =", q.coef)
assert(np.allclose(q.coef, p.coef))

```

#### Diff to Previous Revision

```--- revision 1 2015-10-03 15:27:23
+++ revision 2 2015-10-03 15:32:28
@@ -31,7 +31,7 @@
return self

class Paraboloid(_CurveFit) :
-
+	# coef must be defined by default, length must be the same as the return value of self._order()
coef = np.array([1.0, 1.0, 1.0, 1.0, 1.0, 1.0], dtype=np.float64)

def _order(self, x, y) :
```