Anamorphosis

Anamorphosis

Anamorphosis class.

Allows to transform skew data into standardize data. Transformation is bijective in the interval defined by the data.

Parameters:

Name	Type	Description	Default
data	np.ndarray	Numpy array containing the data.	required
data_min	float	Expected minimum value of the data. None by default and computation are made using the minimum value of the data.	None
data_max	float	Expected maximum value of the data. None by default and computation are made using the maximum value of the data.	None
weights	np.ndarray	numpy array containing the probability weights associated to each interval defined by the order statisticals of the data in order to determine the Gaussian scores. By default None, which implies uniform probability weights (see gauss_score function).	None
gauss_scores	np.ndarray	Option to use the Gaussian scores of the sample as an input directly. By default None. If None, the Gaussian scores will be obtained by this function. If the Gaussian scores are given as an input, they are supposed to be sorted by score. This condition is not verified by this function.	None

Attributes:

Name	Type	Description
data	np.ndarray	Data in real space.
data_min	float	Minimum possible value data. Specified when values can be smaller than observed.
data_max	float	Maximum possible value data. Specified when values can be grater than observed.
weights	np.ndarray	Probability weights of data. Provided if all data have not the same importance.
gauss_scores	np.ndarray	Data in gaussian space.
hermite_coefficients	np.ndarray	Coefficients of hermite polynomials used to transform data from real to gaussian.

data: ndarray property readonly

Return real data.

Returns:

Type	Description
np.ndarray	Array of data.

data_max: float property readonly

Return maximum of real data.

Returns:

Type	Description
float	Maximum value.

data_min: float property readonly

Return minimum of real data.

Returns:

Type	Description
float	Minimum value.

gauss_scores: ndarray property readonly

Return gaussian score of data.

Returns:

Type	Description
np.ndarray	Gaussian scores.

hermite_coefficients: ndarray property readonly

Return coefficients of Hermite Polynomials transform function.

Returns:

Type	Description
np.ndarray	Coefficients of Hermite polynomials.

weights: ndarray property readonly

Return weights of data.

Returns:

Type	Description
np.ndarray	Weights.

compute_hermite_coefficients(self, n, error=False)

Compute coefficients of Hermite polynomials based on a number of polynomials.

Function to obtain the Hermite coefficients of a Gaussian anamorphose model function. The anamorphose used is a continuous piece-wise linear function constructed from the Gaussian scores of the sample data according to weights, together with maximum and minimum optional conditions.

Parameters:

Name	Type	Description	Default
n	int	Order of the Hermite approximation.	required
error	bool	If True, the approximation error (L2 norm with Gaussian weight) will be retourned as a second element of the output list. False by default.	False

Returns:

Type	Description
np.ndarray	Array of n values corresponding to Hermite coefficients.

empirical_inverse_transform(self, x)

Compute the gaussian inverse anamorphosis of the input array using a linear interpolation of the gaussian scores.

Parameters:

Name	Type	Description	Default
x	np.ndarray	Input array containing values in reel space.	required

Returns:

Type	Description
np.ndarray	Transformed array = gaussian values.

empirical_transform(self, x)

Compute the gaussian anamorphosis of the input array using a linear interpolation of the gaussian scores.

Parameters:

Name	Type	Description	Default
x	np.ndarray	Input array containing values in gaussian space.	required

Returns:

Type	Description
np.ndarray	Transformed array = real values.

theoretical_inverse_transform(self, x, r=1.0)

Compute the gaussian inverse anamorphosis of the input array using an interpolation with Hermite polynomials of the gaussian scores. Obtained values are approximates from results of transform gausian values.

Parameters:

Name	Type	Description	Default
x	np.ndarray	Input array containing values in reel space.	required
r	float	Change of support coefficient.	1.0

Returns:

Type	Description
np.ndarray	Transformed array = gaussian values.

theoretical_transform(self, x, r=1.0)

Compute the gaussian anamorphosis of the input array using an interpolation with Hermite polynomials of the gaussian scores.

Parameters:

Name	Type	Description	Default
x	np.ndarray	Input array containing values in gaussian space.	required
r	float	Change of support coefficient.	1.0

Returns:

Type	Description
np.ndarray	Transformed array = real values.

gauss_score(z, weights=None)

Function to obtain the (standard) Gaussian scores of a sample.

Parameters:

Name	Type	Description	Default
z	np.ndarray	numpy array containing the data.	required
weights	np.ndarray	probability weights associated to each interval defined by the order statisticals of the data. Numpy array of size Z.size+1, with non-negative values adding 1 (if not adding 1, they are normalized). weights[j] represent the probability that an anamorphosed standard Gaussian variable according to the empirical cumulative distribution function of Z falls into the interval (Z_(j-1) , Z_(j) ], being Z_(j) the order statistical, j = 1 , ... , N+1, with N the sample size, Z_(0) = -inf, and Z_(N+1) = +inf. If None, a uniform weight vector is used.	None

Returns:

Type	Description
np.ndarray	Returns a numpy array that contains the Gaussian scores.

Exceptions:

Type	Description
ValueError	Weights have not the same size as the data.
ValueError	Some weights are negative.

Warning

Weights are normalized if they do not sum up to 1.