def chi_square_min(self,y,A,N):
'''
- perform chi square minimization
- A is data model
- N are weights of each y_i for fit
- y are dataset
'''
xhat = np.dot( la.inv( np.dot( np.dot(A.T,la.inv(N)), A)), np.dot( np.dot(A.T,la.inv(N)), y) )
self.__dict__.update(ezcreate(['xhat'],locals()))
return xhat
def poly_design_mat(self,Xrange,dim=2,degree=6):
"""
- Create design matrix given discrete values for dependent variables
- dim : number of dependent variables
- degree : degree of polynomial to fit
- Xrange is a list with dim # of arrays, with each array containing
discrete values of the dependent variables that have been unraveled for dim > 1
- Xrange has shape dim x Ndata, where Ndata is the # of discrete data points
- A : Ndata x M design matrix, where M = (dim+degree)!/(dim! * degree!)
- Example of A for dim = 2, degree = 2, Ndata = 3:
A = [ [ 1 x y x^2 y^2 xy ]
[ 1 x y x^2 y^2 xy ]
[ 1 x y x^2 y^2 xy ] ]
"""
# Generate all permutations
perms = itertools.product(range(degree+1),repeat=dim)
perms = np.array(map(list,perms))
# Take the sum of the powers, sort, and eliminate sums > degree
sums = np.array(map(lambda x: reduce(operator.add,x),perms))
argsort = np.argsort(sums)
sums = sums[argsort]
keep = np.where(sums <= degree)[0]
perms = perms[argsort][keep]
# Create design matrix
to_the_power = lambda x,y: np.array(map(lambda z: x**z,y))
dims = []
for i in range(dim):
dims.append(to_the_power(Xrange[i],perms.T[i]).T)
dims = np.array(dims)
A = np.array(map(lambda y: map(lambda x: functools.reduce(operator.mul,x),y),dims.T)).T
# Update Class Namespace
names = ['A','perms']
self.__dict__.update(ezcreate(names,locals()))
return A
