# LeastSquaresMethod¶

class LeastSquaresMethod(*args)

Base class for least square solvers.

Available constructors:

LeastSquaresMethod(proxy, weight, indices)

LeastSquaresMethod(proxy, indices)

Parameters: proxy : DesignProxy Input sample weight : sequence of float Output weights indices : sequence of int Indices allowed in the basis

Notes

Solve the least-squares problem:

Methods

 Build(*args) Instanciate a decomposition method from its name. computeWeightedDesign([whole]) Build the design matrix. getBasis() Accessor to the basis. getClassName() Accessor to the object’s name. getCurrentIndices() Current indices accessor. getGramInverseDiag() Get the diagonal of the inverse Gram matrix. getGramInverseTrace() Get the trace of the inverse Gram matrix. getHDiag() Get the diagonal of the projection matrix H. getId() Accessor to the object’s id. getImplementation(*args) Accessor to the underlying implementation. getInitialIndices() Initial indices accessor. getInputSample() Input sample accessor. getName() Accessor to the object’s name. getWeight() Accessor to the weights. setName(name) Accessor to the object’s name. solve(rhs) Solve the least-squares problem. solveNormal(rhs) Solve the least-squares problem using normal equation. update(addedIndices, conservedIndices, …) Update the current decomposition.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

static Build(*args)

Instanciate a decomposition method from its name.

Parameters: proxy : DesignProxy Input sample weight : sequence of float, optional Output weights indices : sequence of int Indices allowed in the basis method : LeastSquaresMethod The built method
computeWeightedDesign(whole=False)

Build the design matrix.

Parameters: whole : bool, defaults to False Whether to use the initial indices instead of the current indices psiAk : Matrix The design matrix
getBasis()

Accessor to the basis.

Returns: basis : collection of Function Basis.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getCurrentIndices()

Current indices accessor.

Returns: indices : Indices Indices of the current decomposition in the global basis.
getGramInverseDiag()

Get the diagonal of the inverse Gram matrix.

Returns: d : Point The diagonal of the inverse Gram matrix.
getGramInverseTrace()

Get the trace of the inverse Gram matrix.

Returns: x : Scalar The trace of inverse Gram matrix.
getHDiag()

Get the diagonal of the projection matrix H.

Returns: d : Point The diagonal of H.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getImplementation(*args)

Accessor to the underlying implementation.

Returns: impl : Implementation The implementation class.
getInitialIndices()

Initial indices accessor.

Returns: indices : Indices Initial indices of the terms in the global basis.
getInputSample()

Input sample accessor.

Returns: inputSample : Sample Input sample.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getWeight()

Accessor to the weights.

Returns: weight : Point Weights.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
solve(rhs)

Solve the least-squares problem.

Parameters: b : sequence of float Second term of the equation a : Point The solution.
solveNormal(rhs)

Solve the least-squares problem using normal equation.

Parameters: b : sequence of float Second term of the equation x : Point The solution.
update(addedIndices, conservedIndices, removedIndices, row=False)

Update the current decomposition.

Parameters: addedIndices : sequence of int Indices of added basis terms. conservedIndices : sequence of int Indices of conserved basis terms. removedIndices : sequence of int Indices of removed basis terms.