Beispiel #1
0
 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
Beispiel #2
0
    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