QRMethod¶

class QRMethod(*args)¶

Least squares solver using the QR decomposition.

Available constructors:

QRMethod(proxy, weight, indices)

QRMethod(proxy, indices)

QRMethod(design)

Parameters:

proxyDesignProxy: Input sample
weightsequence of float: Output weights
indicessequence of int: Indices allowed in the basis
design2-d sequence of float: A priori known design matrix

See also

LeastSquaresMethod, CholeskyMethod, SVDMethod

Examples

Solves a linear least squares problem with SVD method:

>>> import openturns as ot
>>> A = ot.Matrix([[1,1],[1,2],[1,3],[1,4]])
>>> y = [6, 5, 7, 10]
>>> method = ot.QRMethod(A)
>>> x = method.solve(y)
>>> print(x)
[3.5,1.4]

Methods

`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)¶

computeWeightedDesign(whole=False)¶

Build the design matrix.

Parameters:

wholebool, defaults to False: Whether to use the initial indices instead of the current indices

Returns:

psiAkMatrix: The design matrix

getBasis()¶

Accessor to the basis.

Returns:

basiscollection of Function: Basis.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getCurrentIndices()¶

Current indices accessor.

Returns:

indicesIndices: 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:

cCovarianceMatrix: The inverse Gram matrix.

getGramInverseDiag()¶

Get the diagonal of the inverse Gram matrix.

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

Returns:

dPoint: 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:

xScalar: The trace of inverse Gram matrix.

getH()¶

Get the projection matrix H.

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

Returns:

hSymmetricMatrix: The projection matrix H.

getHDiag()¶

Get the diagonal of the projection matrix H.

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

Returns:

dPoint: The diagonal of H.

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getInitialIndices()¶

Initial indices accessor.

Returns:

indicesIndices: Initial indices of the terms in the global basis.

getInputSample()¶

Input sample accessor.

Returns:

inputSampleSample: Input sample.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

getWeight()¶

Accessor to the weights.

Returns:

weightPoint: Weights.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

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

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

solve(rhs)¶

Solve the least-squares problem.

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

Parameters:

bsequence of float: Second term of the equation

Returns:

aPoint: The solution.

solveNormal(rhs)¶

Solve the least-squares problem using normal equation.

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

Parameters:

bsequence of float: Second term of the equation

Returns:

xPoint: The solution.

trashDecomposition()¶: Drop the current decomposition.

update(addedIndices, conservedIndices, removedIndices, row=False)¶

Update the current decomposition.

Parameters:

addedIndicessequence of int: Indices of added basis terms.
conservedIndicessequence of int: Indices of conserved basis terms.
removedIndicessequence of int: Indices of removed basis terms.

Examples using the class¶

Compute leave-one-out error of a polynomial chaos expansion

Compute confidence intervals of a regression model from data

Compute confidence intervals of a univariate noisy function

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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QRMethod¶

Examples using the class¶