com.opengamma.strata.math.impl.statistics.leastsquare

Class NonLinearLeastSquareWithPenalty

java.lang.Object

com.opengamma.strata.math.impl.statistics.leastsquare.NonLinearLeastSquareWithPenalty

public class NonLinearLeastSquareWithPenalty
extends Object

Modification to NonLinearLeastSquare to use a penalty function add to the normal chi^2 term of the form $a^TPa$ where $a$ is the vector of model parameters sort and P is some matrix. The idea is to extend the p-spline concept to non-linear models of the form $\hat{y}_j = H\left(\sum_{i=0}^{M-1} w_i b_i (x_j)\right)$ where $H(\cdot)$ is some non-linear function, $b_i(\cdot)$ are a set of basis functions and $w_i$ are the weights (to be found). As with (linear) p-splines, smoothness of the function is obtained by having a penalty on the nth order difference of the weights. The modified chi-squared is written as $\chi^2 = \sum_{i=0}^{N-1} \left(\frac{y_i-H\left(\sum_{k=0}^{M-1} w_k b_k (x_i)\right)}{\sigma_i} \right)^2 + \sum_{i,j=0}^{M-1}P_{i,j}x_ix_j$

Field Summary

Fields

Modifier and Type	Field and Description
static Function<DoubleArray,Boolean>	UNCONSTRAINED Unconstrained allowed function - always returns true

Constructor Summary

Constructors

Constructor and Description
NonLinearLeastSquareWithPenalty() Default constructor.
NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition) Constructor allowing matrix decomposition to be set.
NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition, double eps) Constructor allowing matrix decomposition and convergence tolerance to be set.
NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition, MatrixAlgebra algebra, double eps) General constructor.
NonLinearLeastSquareWithPenalty(double eps) Constructor allowing convergence tolerance to be set.

Method Summary

Modifier and Type	Method and Description
LeastSquareWithPenaltyResults	solve(DoubleArray observedValues, DoubleArray sigma, Function<DoubleArray,DoubleArray> func, DoubleArray startPos, DoubleMatrix penalty) Use this when the model is given as a function of its parameters only (i.e.
LeastSquareWithPenaltyResults	solve(DoubleArray observedValues, DoubleArray sigma, Function<DoubleArray,DoubleArray> func, DoubleArray startPos, DoubleMatrix penalty, Function<DoubleArray,Boolean> allowedValue) Use this when the model is given as a function of its parameters only (i.e.
LeastSquareWithPenaltyResults	solve(DoubleArray observedValues, DoubleArray sigma, Function<DoubleArray,DoubleArray> func, Function<DoubleArray,DoubleMatrix> jac, DoubleArray startPos, DoubleMatrix penalty) Use this when the model is given as a function of its parameters only (i.e.
LeastSquareWithPenaltyResults	solve(DoubleArray observedValues, DoubleArray sigma, Function<DoubleArray,DoubleArray> func, Function<DoubleArray,DoubleMatrix> jac, DoubleArray startPos, DoubleMatrix penalty, Function<DoubleArray,Boolean> allowedValue) Use this when the model is given as a function of its parameters only (i.e.
LeastSquareWithPenaltyResults	solve(DoubleArray observedValues, Function<DoubleArray,DoubleArray> func, DoubleArray startPos, DoubleMatrix penalty) Use this when the model is given as a function of its parameters only (i.e.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

UNCONSTRAINED

public static final Function<DoubleArray,Boolean> UNCONSTRAINED

Unconstrained allowed function - always returns true

Constructor Detail

NonLinearLeastSquareWithPenalty

public NonLinearLeastSquareWithPenalty()

Default constructor. This uses SVD, OGMatrixAlgebra and a convergence tolerance of 1e-8

NonLinearLeastSquareWithPenalty

public NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition)

Constructor allowing matrix decomposition to be set. This uses OGMatrixAlgebra and a convergence tolerance of 1e-8.

Parameters:

decomposition - Matrix decomposition (see DecompositionFactory for list)

NonLinearLeastSquareWithPenalty

public NonLinearLeastSquareWithPenalty(double eps)

Constructor allowing convergence tolerance to be set. This uses SVD and OGMatrixAlgebra.

Parameters:

eps - Convergence tolerance

NonLinearLeastSquareWithPenalty

public NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition,
                                       double eps)

Constructor allowing matrix decomposition and convergence tolerance to be set. This uses OGMatrixAlgebra.

Parameters:

decomposition - Matrix decomposition (see DecompositionFactory for list)

eps - Convergence tolerance

NonLinearLeastSquareWithPenalty

public NonLinearLeastSquareWithPenalty(Decomposition<?> decomposition,
                                       MatrixAlgebra algebra,
                                       double eps)

General constructor.

Parameters:

decomposition - Matrix decomposition (see DecompositionFactory for list)

algebra - The matrix algebra (see MatrixAlgebraFactory for list)

eps - Convergence tolerance

Method Detail

solve

public LeastSquareWithPenaltyResults solve(DoubleArray observedValues,
                                           Function<DoubleArray,DoubleArray> func,
                                           DoubleArray startPos,
                                           DoubleMatrix penalty)

Use this when the model is given as a function of its parameters only (i.e. a function that takes a set of parameters and return a set of model values, so the measurement points are already known to the function), and analytic parameter sensitivity is not available.

Parameters:

observedValues - Set of measurement values

func - The model as a function of its parameters only

startPos - Initial value of the parameters

penalty - Penalty matrix

Returns:

value of the fitted parameters

solve

public LeastSquareWithPenaltyResults solve(DoubleArray observedValues,
                                           DoubleArray sigma,
                                           Function<DoubleArray,DoubleArray> func,
                                           DoubleArray startPos,
                                           DoubleMatrix penalty)

Use this when the model is given as a function of its parameters only (i.e. a function that takes a set of parameters and return a set of model values, so the measurement points are already known to the function), and analytic parameter sensitivity is not available

Parameters:

observedValues - Set of measurement values

sigma - Set of measurement errors

func - The model as a function of its parameters only

startPos - Initial value of the parameters

penalty - Penalty matrix

Returns:

value of the fitted parameters

solve

public LeastSquareWithPenaltyResults solve(DoubleArray observedValues,
                                           DoubleArray sigma,
                                           Function<DoubleArray,DoubleArray> func,
                                           DoubleArray startPos,
                                           DoubleMatrix penalty,
                                           Function<DoubleArray,Boolean> allowedValue)

Use this when the model is given as a function of its parameters only (i.e. a function that takes a set of parameters and return a set of model values, so the measurement points are already known to the function), and analytic parameter sensitivity is not available

Parameters:

observedValues - Set of measurement values

sigma - Set of measurement errors

func - The model as a function of its parameters only

startPos - Initial value of the parameters

penalty - Penalty matrix

allowedValue - a function which returned true if the new trial position is allowed by the model. An example would be to enforce positive parameters without resorting to a non-linear parameter transform. In some circumstances this approach will lead to slow convergence.

Returns:

value of the fitted parameters

solve

public LeastSquareWithPenaltyResults solve(DoubleArray observedValues,
                                           DoubleArray sigma,
                                           Function<DoubleArray,DoubleArray> func,
                                           Function<DoubleArray,DoubleMatrix> jac,
                                           DoubleArray startPos,
                                           DoubleMatrix penalty)

Use this when the model is given as a function of its parameters only (i.e. a function that takes a set of parameters and return a set of model values, so the measurement points are already known to the function), and analytic parameter sensitivity is available

Parameters:

observedValues - Set of measurement values

sigma - Set of measurement errors

func - The model as a function of its parameters only

jac - The model sensitivity to its parameters (i.e. the Jacobian matrix) as a function of its parameters only

startPos - Initial value of the parameters

penalty - Penalty matrix

Returns:

the least-square results

solve

public LeastSquareWithPenaltyResults solve(DoubleArray observedValues,
                                           DoubleArray sigma,
                                           Function<DoubleArray,DoubleArray> func,
                                           Function<DoubleArray,DoubleMatrix> jac,
                                           DoubleArray startPos,
                                           DoubleMatrix penalty,
                                           Function<DoubleArray,Boolean> allowedValue)

Use this when the model is given as a function of its parameters only (i.e. a function that takes a set of parameters and return a set of model values, so the measurement points are already known to the function), and analytic parameter sensitivity is available

Parameters:

observedValues - Set of measurement values

sigma - Set of measurement errors

func - The model as a function of its parameters only

jac - The model sensitivity to its parameters (i.e. the Jacobian matrix) as a function of its parameters only

startPos - Initial value of the parameters

penalty - Penalty matrix (must be positive semi-definite)

allowedValue - a function which returned true if the new trial position is allowed by the model. An example would be to enforce positive parameters without resorting to a non-linear parameter transform. In some circumstances this approach will lead to slow convergence.

Returns:

the least-square results