The functions module

A module which contains various reference functions which are useful for frequency combination functions.

functions.identity(vec)

Apply the identity function to the input value (x).

We recall that the identify function is expressed as follows: \(f(x) = x\)

Parameters:vec (float array like) – the input vector

Warning

No verifications are carried out within the function so the user must make sure the input vector only has one component, as implicitely assumed.

functions.identity_gradient(vec)

Apply the gradient of the identity function to the input value (x).

We recall that the gradient of the identify function is expressed as follows: \(\vec{\Delta} f(x) = 1\)

Parameters:vec (float array like) – the input vector

Warning

No verifications are carried out within the function so the user must make sure the input vector only has one component, as implicitely assumed.

functions.norm(vec)

Return the norm of an input vector.

We recall that the norm is expressed as follows: \(\|(\vec{v})\| = \sqrt{\sum_i v_i^2}\)

Parameters:vec (float array like) – the input vector

functions.norm_gradient(vec)

Return the gradient of the norm function for an input vector.

We recall that the gradient of the norm function takes on the following expression: \(\vec{\Delta}\|(\vec{v})\| = \frac{\vec{v}}{\|\vec{v}\|}\)

Parameters:vec (float array like) – the input vector

functions.ratio(vec)

Return the ratio for input values (x,y).

We recall that the ratio function is expressed as follows: \(f(x,y) = \frac{x}{y}\)

Parameters:vec (float array like) – the input vector

Warning

No verifications are carried out within the function so the user must make sure the input vector only has two components, as implicitely assumed.

functions.ratio_gradient(vec)

Return the gradient of the ratio function for input values (x,y).

We recall that gradient of the ratio function is expressed as follows: \(\vec{\Delta} f(x,y) = \left(\frac{1}{y},-\frac{x}{y^2}\right)\)

Parameters:vec (float array like) – the input vector

Warning

No verifications are carried out within the function so the user must make sure the input vector only has two components, as implicitely assumed.