regressioninc.linear.models module#

This module implements estimators for linear complex problems

These are built on scipy as scipy.linalg.lstsq does allow and support complex-valued inputs. However, it does not output residuals for complex-valued variables, therefore these are calculated out explicitly.

regressioninc.linear.models.add_intercept(X: ndarray) → ndarray[source]#

Add an intercept to the regressors

Parameters:: X (np.ndarray) – The regressors
Returns:: The regressors with an extra column of ones to represent to allow solving for the intercept term
Return type:: np.ndarray

Examples

>>> import numpy as np
>>> from regressioninc.linear.models import add_intercept
>>> X = np.array([[2,3], [4,5]])
>>> X
array([[2, 3],
       [4, 5]])

Now add the intercept

>>> X = add_intercept(X)
>>> X
array([[2, 3, 1],
       [4, 5, 1]])

regressioninc.linear.models.complex_to_real(X: ndarray, y: ndarray) → tuple[numpy.ndarray, numpy.ndarray][source]#

Convert complex-valued linear problem to a real-valued linear regression

Parameters:

X (np.ndarray) – The regressors
y (np.ndarray) – The observations

Returns:

X, y converted to real-valued generalised linear regression

Return type:

tuple[np.ndarray, np.ndarray]

Examples

>>> from regressioninc.linear.models import add_intercept, complex_to_real
>>> X = np.array([3 + 4j, 2 + 8j, 6 + 4j]).reshape(3,1)
>>> X = add_intercept(X)
>>> y = np.array([-2 - 4j, -1 - 3j, 5 + 6j])
>>> X_real, y_real = complex_to_real(X, y)
>>> X_real
array([[ 3., -4.,  1., -0.],
       [ 4.,  3.,  0.,  1.],
       [ 2., -8.,  1., -0.],
       [ 8.,  2.,  0.,  1.],
       [ 6., -4.,  1., -0.],
       [ 4.,  6.,  0.,  1.]])
>>> y_real
array([-2., -4., -1., -3.,  5.,  6.])

regressioninc.linear.models.real_params_to_complex(params: ndarray) → ndarray[source]#

Convert real-valued parameters to complex-valued ones for problems that were transformed from complex-valued to real-valued.

Parameters:: params (np.ndarray) – Real-valued parameters array
Returns:: The complex-valued parameters
Return type:: np.ndarray

Examples

Let’s generate a complex-valued linear problem, pose it as a real-valued linear problem and then convert the returned parameters back to complex.

Generate the linear problem and add an intercept column to the regressors

>>> import numpy as np
>>> np.set_printoptions(precision=3, suppress=True)
>>> from regressioninc.testing.complex import ComplexGrid, generate_linear_grid
>>> from regressioninc.linear.models import add_intercept, OLS
>>> from regressioninc.linear.models import complex_to_real, real_params_to_complex
>>> params = np.array([3 + 2j])
>>> grid = ComplexGrid(r1=-1, r2=1, nr=3, i1=4, i2=6, ni=3)
>>> X, y = generate_linear_grid(params, [grid], intercept=10)
>>> X = add_intercept(X)

Convert the complex-valued problem to a real-valued problem

>>> X_real, y_real = complex_to_real(X, y)

Solve the real-valued linear problem

>>> model = OLS()
>>> model.fit(X_real, y_real)
OLS...

Look at the real-valued coefficients

>>> model.estimate.params
array([ 3.,  2., 10.,  0.])

Convert the coefficients back to the complex domain

>>> real_params_to_complex(model.estimate.params)
array([ 3.+2.j, 10.+0.j])

regressioninc.linear.models.apply_weights(X: ndarray, y: ndarray, weights: ndarray) → tuple[numpy.ndarray, numpy.ndarray][source]#

Transform X and y using the weights to perform a weighted least squares

\[\sqrt{weights} y = \sqrt{weights} X coef ,\]

is equivalent to,

\[X^H weights y = X^H weights X coef ,\]

where \(X^H\) is the hermitian transpose of X.

In this method, both the observations y and the predictors X are multipled by the square root of the weights and then returned.

Parameters:

X (np.ndarray) – The regressors
y (np.ndarray) – The regressands
weights (np.ndarray) – The weights

Returns:

The weighted regressors and the weights regrassands

Return type:

tuple[np.ndarray, np.ndarray]

Examples

>>> import numpy as np
>>> X = [5, 3]
>>> y = [2, 8]
>>> weights = []

pydantic model regressioninc.linear.models.LinearEstimate[source]#

Bases: Estimate

A linear estimate

Fields:

rank (int)
residues (float | numpy.ndarray)
singular_values (None | numpy.ndarray)

field residues: float | ndarray [Required]#

field rank: int [Required]#

field singular_values: None | ndarray [Required]#

pydantic model regressioninc.linear.models.LinearEstimator[source]#

Bases: Estimator

Base class for a linear estimator

Fields:

predict(X: ndarray) → ndarray[source]#

Predict regrassands given regressors using the estimated parameters

Parameters:: X (np.ndarray) – The regressors
Returns:: The regressands
Return type:: np.ndarray
Raises:: EstimatorError – If no estimate exists

regressioninc.linear.models.lstsq(X: ndarray, y: ndarray, weights: ndarray | None = None, cond=None, overwrite_a=False, overwrite_b=False, check_finite=True, lapack_driver=None)[source]#: OLS from scipy wrapped here in case support for complex is dropped