CholeskyMethod

class CholeskyMethod(*args)

Least squares solver using Cholesky decomposition.

Available constructors:

CholeskyMethod(proxy, weight, indices)

CholeskyMethod(proxy, indices)

Parameters:

proxy : DesignProxy

Input sample

weight : sequence of float

Output weights

indices : sequence of int

Indices allowed in the basis

Methods

buildCurrentBasis() Build the current basis.
computeWeightedDesign([whole]) Build the design matrix.
getBasis() Accessor to the basis.
getClassName() Accessor to the object’s name.
getCurrentIndices() Current indices accessor.
getGramInverse() Get the inverse Gram matrix of input sample.
getGramInverseDiag() Get the diagonal of the inverse Gram matrix.
getGramInverseTrace() Get the trace of the inverse Gram matrix.
getH() Get the projection matrix H.
getHDiag() Get the diagonal of the projection matrix H.
getId() Accessor to the object’s id.
getInitialIndices() Initial indices accessor.
getInputSample() Input sample accessor.
getName() Accessor to the object’s name.
getShadowedId() Accessor to the object’s shadowed id.
getVisibility() Accessor to the object’s visibility state.
getWeight() Accessor to the weights.
hasName() Test if the object is named.
hasVisibleName() Test if the object has a distinguishable name.
setName(name) Accessor to the object’s name.
setShadowedId(id) Accessor to the object’s shadowed id.
setVisibility(visible) Accessor to the object’s visibility state.
solve(rhs) Solve the least-squares problem.
solveNormal(rhs) Solve the least-squares problem using normal equation.
trashDecomposition() Drop the current decomposition.
update(addedIndices, conservedIndices, …) Update the current decomposition.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

buildCurrentBasis()

Build the current basis.

Returns:

phi : Basis

The basis according to current indices.

computeWeightedDesign(whole=False)

Build the design matrix.

Parameters:

whole : bool, defaults to False

Whether to use the initial indices instead of the current indices

Returns:

psiAk : Matrix

The design matrix

getBasis()

Accessor to the basis.

Returns:

basis : getBasis

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.

getGramInverse()

Get the inverse Gram matrix of input sample.

G^{-1} = (X^T * X)^{-1}

Returns:

c : CovarianceMatrix

The inverse Gram matrix.

getGramInverseDiag()

Get the diagonal of the inverse Gram matrix.

diag(G^{-1}) = diag((X^T * X)^{-1})

Returns:

d : Point

The diagonal of the inverse Gram matrix.

getGramInverseTrace()

Get the trace of the inverse Gram matrix.

Tr(G^{-1}) = Tr(x^T * x)^{-1}

Returns:

x : Scalar

The trace of inverse Gram matrix.

getH()

Get the projection matrix H.

H = X * (X^T * X)^{-1} * X^T

Returns:

h : SymmetricMatrix

The projection matrix H.

getHDiag()

Get the diagonal of the projection matrix H.

H = X * (X^T * X)^{-1} * X^T

Returns:

d : Point

The diagonal of H.

getId()

Accessor to the object’s id.

Returns:

id : int

Internal unique identifier.

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.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:

id : int

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns:

visible : bool

Visibility flag.

getWeight()

Accessor to the weights.

Returns:

weight : Point

Weights.

hasName()

Test if the object is named.

Returns:

hasName : bool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:

hasVisibleName : bool

True if the name is not empty and not the default one.

setName(name)

Accessor to the object’s name.

Parameters:

name : str

The name of the object.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:

id : int

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:

visible : bool

Visibility flag.

solve(rhs)

Solve the least-squares problem.

\vect{a} = \argmin_{\vect{x} \in \Rset^P} ||M\vect{x}-\vect{b}||^2

Parameters:

b : sequence of float

Second term of the equation

Returns:

a : Point

The solution.

solveNormal(rhs)

Solve the least-squares problem using normal equation.

M^T*M*x=M^T*b

Parameters:

b : sequence of float

Second term of the equation

Returns:

x : Point

The solution.

trashDecomposition()

Drop the current decomposition.

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.