def iter_over_coordinates(input_coordinates_part, C, COV, structure, k):
"""
input: input_coordinates_part numpy array, coordinates for model creation
C numpy array kxd, matrix of k d-dimensional cluster centres
COV numpy array kxdxd, matrix of covariance matrices
structure list(int, list(floats), list(floats)),
number of non-hypertime dimensions, list of hypertime
radii nad list of wavelengths
k positive integer, number of clusters
output: grid_densities_part numpy array kx1, number of part of cells
belonging to the clusters
uses: dio.create_X(), np.shape(), gc.collect(), np.tile(),
np.sum(), np.dot(), np.array(),
cl.partition_matrix()
objective: to find out the number of cells (part of them) belonging to
the clusters
"""
X = dio.create_X(input_coordinates_part, structure)
n, d = np.shape(X)
gc.collect()
D = []
for cluster in range(k):
C_cluster = np.tile(C[cluster, :], (n, 1))
XC = dio.hypertime_substraction(X, C_cluster, structure)
#XC = X - C_cluster
VI = COV[cluster]#COV[cluster, :, :]
D.append(np.sum(np.dot(XC, VI) * XC, axis=1))
gc.collect()
D = np.array(D)
gc.collect()
U = cl.partition_matrix(D, version='model')
#U = U ** 2 #!!!
gc.collect()
grid_densities_part = np.sum(U, axis=1, keepdims=True)
return grid_densities_part
def covariance_matrices(X, C, U, structure):
"""
input: X numpy array nxd, matrix of n d-dimensional observations
C numpy array kxd, matrix of k d-dimensional cluster centres
U numpy array kxn, matrix of weights
structure list(int, list(floats), list(floats)),
number of non-hypertime dimensions, list of hypertime
radii nad list of wavelengths
output: COV numpy array kxdxd, matrix of covariance matrices
uses: cl.distance_matrix(), cl.partition_matrix()
np.shape(), np.tile(), np.cov(), np.linalg.inv(), np.array()
objective: to calculate covariance matrices for model
"""
k, n = np.shape(U)
D = cl.distance_matrix(X, C, U, structure)
## not pure fuzzy W :)
#W = cl.partition_matrix(D, version='fuzzy')
## W with binary memberships from U
#W = W * U
COV = []
for cluster in range(k):
C_cluster = np.tile(C[cluster, :], (n, 1))
XC = dio.hypertime_substraction(X, C_cluster, structure)
#XC = X - C_cluster
#V = np.cov(XC, aweights=W[cluster, :], ddof=0, rowvar=False)
#V = np.cov(XC, ddof=0, rowvar=False) # puvodni, melo by byt stejne
V = np.cov(XC, bias=True, rowvar=False)
if len(np.shape(V)) == 2:
Vinv = np.linalg.inv(V)
else:
#print('V: ' + str(V))
Vinv = np.array([[1 / V]])
COV.append(Vinv)
COV = np.array(COV)
return COV
def one_freq(one_input_coordinate, C, COV, structure, k,
density_integrals):
"""
input: one_input_coordinate numpy array, coordinates for model creation
C numpy array kxd, matrix of k d-dimensional cluster centres
COV numpy array kxdxd, matrix of covariance matrices
structure list(int, list(floats), list(floats)),
number of non-hypertime dimensions, list of hypertime
radii nad list of wavelengths
k positive integer, number of clusters
density_integrals numpy array kx1, matrix of ratios between
measurements and grid cells
belonging to the clusters
output: freq array len(input_coordinates_part)x1,
frequencies(stat) obtained
from model in positions of part
of input_coordinates
uses: dio.create_X(), np.shape(), gc.collect(), np.tile(),
np.sum(), np.dot(), np.array(),
cl.partition_matrix()
objective: to create grid of frequencies(stat) over a part time-space
(histogram)
"""
X = dio.create_X(one_input_coordinate, structure)
n, d = np.shape(X)
D = []
for cluster in range(k):
# C_cluster = np.tile(C[cluster, :], (n, 1))
XC = dio.hypertime_substraction(X, C[cluster:cluster+1], structure)
#XC = X - C[cluster]
VI = COV[cluster]#COV[cluster, :, :]
D.append(np.sum(np.dot(XC, VI) * XC, axis=1))
# gc.collect()
D = np.array(D)
# gc.collect()
U = cl.partition_matrix(D, version='model')
#U = (U ** 2) * density_integrals
U = U * density_integrals
# gc.collect()
freq = np.sum(U, axis=0)
return freq
def distance_matrix(X, C, U, structure):
"""
input: X numpy array nxd, matrix of n d-dimensional observations
C numpy array kxd, matrix of k d-dimensional cluster centres
U numpy array kxn, matrix of weights
output: D numpy array kxn, matrix of distances between every observation
and every center
uses: np.shape(), np.tile(), np.array(), np.abs()
objective: to find difference between every observation and every
center in every dimension
"""
k, n = np.shape(U)
D = []
for cluster in range(k):
C_cluster = np.tile(C[cluster, :], (n, 1))
XC = dio.hypertime_substraction(X, C_cluster, structure)
#XC = X - C_cluster
# PROC ????
## L1 metrics
#D.append(np.sum(np.abs(XC), axis=1))
D.append(np.sqrt(np.sum(XC**2, axis=1)))
D = np.array(D)
return D
