kNNpy.Auxiliary.Fisher

 1import numpy as np
 2
 3def constructingFishermatrix(data_vectors, covariance_matrix, dtheta, n_params_p_m, n_params_p=0):
 4    """
 5    Constructs the Fisher matrix from data vectors and a covariance matrix.
 6
 7    Parameters:
 8    data_vectors (list of numpy arrays): The data vectors for which the Fisher matrix is to be constructed. The ith element is an array containing two vectors:
 9        - The first vector corresponds to the simulation for parameter p.
10        - The second vector corresponds to the simulation for parameter m OR The second vector corresponds to the simulation for fiducial parameters.
11        Also, if n_params_p!=0, all such parameters, must necessarily come after the parameters with both simulations for p and m.
12    covariance_matrix (numpy array): The covariance matrix associated with the data vectors.
13    n_params_p_m (int): The number of parameters with both simulations for p and m.
14    n_params_p (int): The number of parameters with just simulations for p.
15    dtheta (list of float): The parameter step sizes for the derivatives. Also, if n_params_p!=0, all such parameters, must necessarily come after the parameters
16    with both simulations for p and m.
17    n (int): The number of realizations.
18
19    Returns:
20    numpy array: The constructed Fisher matrix. #Give the expression
21
22    Raises ValueError:
23    -If the length of data_vectors are not of equal length
24    -If the covariance matrix is not square or does not match the length of data_vectors
25    - If length of dtheta and n_params_p_m + n_params_p do not match
26    """
27    # Checking all the input parameters
28    p=len(data_vectors[0][0])
29    for i in range(len(data_vectors)):
30        for j in range(2):
31            if len(data_vectors[i][j]) != p:
32                raise ValueError("All data vectors must be of equal length.")
33    if np.shape(covariance_matrix)[0] != np.shape(covariance_matrix)[1]:
34        raise ValueError("Covariance matrix must be square.")
35    if np.shape(covariance_matrix)[0] != len(data_vectors):
36        raise ValueError("Covariance matrix must match the length of data vectors.")
37    if len(dtheta) != n_params_p_m + n_params_p:
38        raise ValueError("Length of dtheta must match n_params_p_m + n_params_p.")
39    # Constructing the derivatives
40    d = np.zeros([n_params_p_m+n_params_p,len(data_vectors)])
41    for i in range(n_params_p_m):
42
43        d_p = data_vectors[i][0]
44        d_m = data_vectors[i][1]
45        delt = d_p - d_m
46        d[i] = delt/(2*dtheta[i])
47
48    if n_params_p > 0:
49        for j in range(n_params_p_m, n_params_p_m + n_params_p):
50            d_p= data_vectors[i][0]
51            d_0= data_vectors[i][1]
52            delt = d_p - d_0
53            d[j] =  delt/(dtheta[j])
54    
55    # The Fisher matrix
56    c_inv=np.linalg.inv(covariance_matrix)
57    F = np.zeros([n_params_p+n_params_p_m,n_params_p_m+n_params_p])
58    for i in range(0, n_params_p_m + n_params_p):
59        for j in range(0, n_params_p_m + n_params_p):
60            F[i][j] = (np.transpose(d[i])).dot(c_inv).dot(d[j])