def circle4points(p, tol=1e-1):
A = np.column_stack((2. * p[:, 0], 2. * p[:, 1], [-1, -1, -1]))
b = np.sum(p**2, axis=1)
# Normalizing the vectors
norm = np.sqrt(np.sum(A * A, axis=1))
An = np.transpose(A.T / norm)
bn = b / norm
# Solving the system
M = GaussElimination(An, bn)
M.solve()
sol = M.sol
# Calculating determinant of a 3x3 matrix
det = An[0,0] * An[1,1] * An[2,2] + An[0,1] * An[1,2] * An[2,0] + \
An[0,2] * An[1,0] * An[2,1] - An[0,2] * An[1,1] * An[2,0] - \
An[0,1] * An[1,0] * An[2,2] - An[0,0] * An[1,2] * An[2,1]
r = np.sqrt(sol[0]**2 + sol[1]**2 - sol[2])
eps = np.finfo(float).eps
if np.abs(det) < eps:
print "System does not have a solution (det=0)"
elif np.abs(det) < tol:
print "System is ill conditioned: |det| = {0}".format(np.abs(det))
else:
print "System has a determined solution: det = {0}".format(det)
print "Solution is x = {0:.5f}, y={1:.5f} and r={2:.5f}".format(
sol[0], sol[1], r)
return
def circle4points(p, tol=1e-1):
A = np.column_stack((2. * p[:,0], 2. * p[:,1], [-1,-1,-1]))
b = np.sum(p**2, axis=1)
# Normalizing the vectors
norm = np.sqrt(np.sum(A*A, axis=1))
An = np.transpose(A.T / norm)
bn = b / norm
# Solving the system
M = GaussElimination(An,bn)
M.solve()
sol = M.sol
# Calculating determinant of a 3x3 matrix
det = An[0,0] * An[1,1] * An[2,2] + An[0,1] * An[1,2] * An[2,0] + \
An[0,2] * An[1,0] * An[2,1] - An[0,2] * An[1,1] * An[2,0] - \
An[0,1] * An[1,0] * An[2,2] - An[0,0] * An[1,2] * An[2,1]
r = np.sqrt(sol[0]**2 + sol[1]**2 - sol[2])
eps = np.finfo(float).eps
if np.abs(det) < eps:
print "System does not have a solution (det=0)"
elif np.abs(det) < tol:
print "System is ill conditioned: |det| = {0}".format(np.abs(det))
else:
print "System has a determined solution: det = {0}".format(det)
print "Solution is x = {0:.5f}, y={1:.5f} and r={2:.5f}".format(sol[0],
sol[1],r)
return
class chi2_minimization():
""" Calculate coefficients for linear combination of functions that
minimize the chi^2. """
def __init__(self, x, y, fs):
self.x = x
self.y = y
self.fs = fs
self.dim = len(fs)
self.make_system()
self.M = GaussElimination(self.A, self.b)
self.M.solve()
self.sol = self.M.sol
def make_system(self):
""" Calculate the least square standard system"""
fx = np.zeros((self.dim, len(self.x)))
self.b = np.zeros((self.dim))
for i in range(self.dim):
fx[i] = self.fs[i](self.x)
self.b[i] = np.sum(self.fs[i](self.x) * self.y)
self.A = np.dot(fx, fx.T)
class chi2_minimization():
""" Calculate coefficients for linear combination of functions that
minimize the chi^2. """
def __init__(self, x, y, fs):
self.x = x
self.y = y
self.fs = fs
self.dim = len(fs)
self.make_system()
self.M = GaussElimination(self.A, self.b)
self.M.solve()
self.sol = self.M.sol
def make_system(self):
""" Calculate the least square standard system"""
fx = np.zeros((self.dim, len(self.x)))
self.b = np.zeros((self.dim))
for i in range(self.dim):
fx[i] = self.fs[i](self.x)
self.b[i] = np.sum(self.fs[i](self.x) * self.y)
self.A = np.dot(fx, fx.T)