ModeBasis¶

class hcipy.mode_basis.ModeBasis(transformation_matrix, grid=None)¶

Bases: object

A list of modes.

Parameters

transformation_matrixarray_like or list of array_like: The transformation matrix of the mode basis or a list of modes.
gridGrid or None: The grid on which the modes are defined.

Attributes Summary

`is_dense`	If the mode basis is dense.
`is_sparse`	If the mode basis is sparse.
`orthogonalized`	Get an orthogonalized version of this ModeBasis.
`transformation_matrix`	The transformation matrix of this mode basis.

Methods Summary

`append`(self, mode)	Append mode to this mode basis.
`coefficients_for`(self, b[, dampening_factor])	Calculate the coefficients on this mode basis in a least squares fashion.
`extend`(self, modes)	Extend the mode basis with modes.
`linear_combination`(self, coefficients)	Calculate a linear combination using this mode basis.
`to_dense`(self[, copy])	Convert the mode basis to a dense mode basis.
`to_sparse`(self[, copy])	Convert the mode basis to a sparse mode basis.

Attributes Documentation

is_dense¶: If the mode basis is dense.

is_sparse¶: If the mode basis is sparse.

orthogonalized¶

Get an orthogonalized version of this ModeBasis.

The resulting ModeBasis spans the same vector space, but each mode is orthogonal to all others. In general the resulting ModeBasis is dense, so no distinction is made between sparse and dense mode bases in this function. This function will always return a dense mode basis.

Returns

ModeBasis: A mode basis with orthogonalized modes.

Raises

NotImplementedError: If the mode basis is a mode basis containing non-scalar fields.

transformation_matrix¶: The transformation matrix of this mode basis.

Methods Documentation

append(self, mode)¶

Append mode to this mode basis.

Parameters

modearray_like or Field: The mode to add to the ModeBasis

coefficients_for(self, b, dampening_factor=0)¶

Calculate the coefficients on this mode basis in a least squares fashion.

The vector b is projection onto the mode basis in a least squares fashion. This means that the const function

\[J(c) = |b - A x|^2_2 + |\lambda x|^2_2\]

is minimized, where \(x\) are the coefficients, and \(\lambda\) is the dampening factor.

If this projection needs to be done repeatedly, you may be better off calculating the inverse of the transformation matrix directly and left-multiplying that with your vector, rather than using a least squares estimation every time.

Parameters

barray_like or Field: The vector for which to calculate the coefficients.
dampening_factorscalar: The Tikhonov dampening factor used for the least squares procedure.

Returns

array_like: The coefficients that correspond to the vector b.

extend(self, modes)¶

Extend the mode basis with modes.

Parameters

modeslist or array_like or ModeBasis: The modes to add to the ModeBasis.

linear_combination(self, coefficients)¶

Calculate a linear combination using this mode basis.

Parameters

coefficientsarray_like or list: The coefficients of the linear combinations.

Returns

array_like or Field: The calculated linear combination.

to_dense(self, copy=False)¶

Convert the mode basis to a dense mode basis.

Parameters

copyboolean: Whether to force a copy or not. A copy is always made if the current ModeBasis is not dense.

Returns

ModeBasis: The densified ModeBasis.

to_sparse(self, copy=False)¶

Convert the mode basis to a sparse mode basis.

Parameters

copyboolean: Whether to force a copy or not. A copy is always made if the current ModeBasis is not sparse.

Returns

ModeBasis: The sparsified ModeBasis.

Raises

TypeError: If this ModeBasis cannot be sparsified.