Apache Commons Math 3.6.1 · org.apache.commons.math3.optim.nonlinear.vector.jacobian.AbstractLeastSquaresOptimizer

Modifier and Type	Field and Description
private double	cost Cost value (square root of the sum of the residuals).
private RealMatrix	weightMatrixSqrt Square-root of the weight matrix.

Access	Constructor and Description
protected	AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> Convergence checker. checker)

Method Summary

Modifier and Type	Method and Description
protected double	Returns: the cost. computeCost(double[] Residuals. residuals) Computes the cost.
public double[][]	Returns: the covariance matrix. computeCovariances(double[] Model parameters. params, double Singularity threshold. threshold) Get the covariance matrix of the optimized parameters.
protected double[]	Returns: the residuals. computeResiduals(double[] Value of the the objective function. This is the value returned from a call to `computeObjectiveValue` (whose array argument contains the model parameters). objectiveValue) Computes the residuals.
public double[]	Returns: an estimate of the standard deviation of the optimized parameters computeSigma(double[] Model parameters. params, double Singularity threshold (see `computeCovariances`). covarianceSingularityThreshold) Computes an estimate of the standard deviation of the parameters.
protected RealMatrix	Returns: the weighted Jacobian: W^1/2 J. computeWeightedJacobian(double[] Model parameters at which to compute the Jacobian. params) Computes the weighted Jacobian matrix.
public double	Returns: chi-square value getChiSquare() Get a Chi-Square-like value assuming the N residuals follow N distinct normal distributions centered on 0 and whose variances are the reciprocal of the weights.
public double	Returns: the RMS value. getRMS() Gets the root-mean-square (RMS) value.
public RealMatrix	Returns: the square-root of the weight matrix. getWeightSquareRoot() Gets the square-root of the weight matrix.
public PointVectorValuePair	Returns: a point/value pair that satisfies the convergence criteria. optimize(OptimizationData... Optimization data. In addition to those documented in `JacobianMultivariateVectorOptimizer`, this method will register the following data: `org.apache.commons.math3.optim.nonlinear.vector.Weight` optData) Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize. Stores data and performs the optimization.
protected void	parseOptimizationData(OptimizationData... Optimization data. The following data will be looked for: `Weight` optData) Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.parseOptimizationData. Scans the list of (required and optional) optimization data that characterize the problem.
protected void	setCost(double Cost value. cost) Sets the cost.
private RealMatrix	Returns: the square-root of the weight matrix. squareRoot(RealMatrix Symmetric, positive-definite (weight) matrix. m) Computes the square-root of the weight matrix.

Inherited from org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer:: computeJacobian

cost	back to summary
private double cost Cost value (square root of the sum of the residuals).

weightMatrixSqrt	back to summary
private RealMatrix weightMatrixSqrt Square-root of the weight matrix.

AbstractLeastSquaresOptimizer	back to summary
protected AbstractLeastSquaresOptimizer(ConvergenceChecker<PointVectorValuePair> checker) Parameters checker:ConvergenceChecker<PointVectorValuePair> Convergence checker.

Method Detail

computeCost back to summary

computeCost	back to summary
protected double computeCost(double[] residuals) Computes the cost. Parameters residuals:double[] Residuals. Returns:double the cost. See Also `computeResiduals(double[])`

protected double computeCost(double[] residuals)

Computes the cost.

Parameters

residuals:double[]: Residuals.

Returns:double

the cost.

See Also

computeResiduals(double[])

computeCovariances back to summary

computeCovariances	back to summary
public double[][] computeCovariances(double[] params, double threshold) Get the covariance matrix of the optimized parameters. Note that this operation involves the inversion of the `J^TJ` matrix, where `J` is the Jacobian matrix. The `threshold` parameter is a way for the caller to specify that the result of this computation should be considered meaningless, and thus trigger an exception. Parameters params:double[] Model parameters. threshold:double Singularity threshold. Returns:double[][] the covariance matrix. Exceptions SingularMatrixException: if the covariance matrix cannot be computed (singular problem).

public double[][] computeCovariances(double[] params, double threshold)

Get the covariance matrix of the optimized parameters.
Note that this operation involves the inversion of the J^TJ matrix, where J is the Jacobian matrix. The threshold parameter is a way for the caller to specify that the result of this computation should be considered meaningless, and thus trigger an exception.

Parameters

params:double[]: Model parameters.
threshold:double: Singularity threshold.

Returns:double[][]

the covariance matrix.

Exceptions

SingularMatrixException:: if the covariance matrix cannot be computed (singular problem).

computeResiduals back to summary

computeResiduals	back to summary
protected double[] computeResiduals(double[] objectiveValue) Computes the residuals. The residual is the difference between the observed (target) values and the model (objective function) value. There is one residual for each element of the vector-valued function. Parameters objectiveValue:double[] Value of the the objective function. This is the value returned from a call to `computeObjectiveValue` (whose array argument contains the model parameters). Returns:double[] the residuals. Exceptions DimensionMismatchException: if `params` has a wrong length.

protected double[] computeResiduals(double[] objectiveValue)

Computes the residuals. The residual is the difference between the observed (target) values and the model (objective function) value. There is one residual for each element of the vector-valued function.

Parameters

objectiveValue:double[]: Value of the the objective function. This is the value returned from a call to computeObjectiveValue (whose array argument contains the model parameters).

Returns:double[]

the residuals.

Exceptions

DimensionMismatchException:: if params has a wrong length.

computeSigma back to summary

computeSigma	back to summary
public double[] computeSigma(double[] params, double covarianceSingularityThreshold) Computes an estimate of the standard deviation of the parameters. The returned values are the square root of the diagonal coefficients of the covariance matrix, `sd(a[i]) ~= sqrt(C[i][i])`, where `a[i]` is the optimized value of the `i`-th parameter, and `C` is the covariance matrix. Parameters params:double[] Model parameters. covarianceSingularityThreshold:double Singularity threshold (see `computeCovariances`). Returns:double[] an estimate of the standard deviation of the optimized parameters Exceptions SingularMatrixException: if the covariance matrix cannot be computed.

public double[] computeSigma(double[] params, double covarianceSingularityThreshold)

Computes an estimate of the standard deviation of the parameters. The returned values are the square root of the diagonal coefficients of the covariance matrix, sd(a[i]) ~= sqrt(C[i][i]), where a[i] is the optimized value of the i-th parameter, and C is the covariance matrix.

Parameters

params:double[]: Model parameters.
covarianceSingularityThreshold:double: Singularity threshold (see computeCovariances).

Returns:double[]

an estimate of the standard deviation of the optimized parameters

Exceptions

SingularMatrixException:: if the covariance matrix cannot be computed.

computeWeightedJacobian	back to summary
protected RealMatrix computeWeightedJacobian(double[] params) Computes the weighted Jacobian matrix. Parameters params:double[] Model parameters at which to compute the Jacobian. Returns:RealMatrix the weighted Jacobian: W^1/2 J. Exceptions DimensionMismatchException: if the Jacobian dimension does not match problem dimension.

computeWeightedJacobian

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protected RealMatrix computeWeightedJacobian(double[] params)

Computes the weighted Jacobian matrix.

Parameters

params:double[]: Model parameters at which to compute the Jacobian.

Returns:RealMatrix

the weighted Jacobian: W^1/2 J.

Exceptions

DimensionMismatchException:: if the Jacobian dimension does not match problem dimension.

getChiSquare	back to summary
public double getChiSquare() Get a Chi-Square-like value assuming the N residuals follow N distinct normal distributions centered on 0 and whose variances are the reciprocal of the weights. Returns:double chi-square value

getChiSquare

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public double getChiSquare()

Get a Chi-Square-like value assuming the N residuals follow N distinct normal distributions centered on 0 and whose variances are the reciprocal of the weights.

Returns:double: chi-square value

getRMS	back to summary
public double getRMS() Gets the root-mean-square (RMS) value. The RMS the root of the arithmetic mean of the square of all weighted residuals. This is related to the criterion that is minimized by the optimizer as follows: If c if the criterion, and n is the number of measurements, then the RMS is sqrt (c/n). Returns:double the RMS value.

getRMS

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public double getRMS()

Gets the root-mean-square (RMS) value. The RMS the root of the arithmetic mean of the square of all weighted residuals. This is related to the criterion that is minimized by the optimizer as follows: If c if the criterion, and n is the number of measurements, then the RMS is sqrt (c/n).

Returns:double: the RMS value.

getWeightSquareRoot	back to summary
public RealMatrix getWeightSquareRoot() Gets the square-root of the weight matrix. Returns:RealMatrix the square-root of the weight matrix.

getWeightSquareRoot

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public RealMatrix getWeightSquareRoot()

Gets the square-root of the weight matrix.

Returns:RealMatrix: the square-root of the weight matrix.

optimize back to summary

optimize	back to summary
public PointVectorValuePair optimize(OptimizationData... optData) throws TooManyEvaluationsException Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize. Doc from org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize. Stores data and performs the optimization. The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations. When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls). Important Note Subclasses must override `parseOptimizationData(OptimizationData[])` if they need to register their own options; but then, they must also call `super.parseOptimizationData(optData)` within that method. Parameters optData:OptimizationData[] Optimization data. In addition to those documented in `JacobianMultivariateVectorOptimizer`, this method will register the following data: `org.apache.commons.math3.optim.nonlinear.vector.Weight` Returns:PointVectorValuePair a point/value pair that satisfies the convergence criteria. Annotations @Override Exceptions TooManyEvaluationsException: if the maximal number of evaluations is exceeded. DimensionMismatchException: if the initial guess, target, and weight arguments have inconsistent dimensions.

public PointVectorValuePair optimize(OptimizationData... optData) throws TooManyEvaluationsException

Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize.

Doc from org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.optimize.

Stores data and performs the optimization.

The list of parameters is open-ended so that sub-classes can extend it with arguments specific to their concrete implementations.

When the method is called multiple times, instance data is overwritten only when actually present in the list of arguments: when not specified, data set in a previous call is retained (and thus is optional in subsequent calls).

Important Note

Subclasses must override parseOptimizationData(OptimizationData[]) if they need to register their own options; but then, they must also call super.parseOptimizationData(optData) within that method.

Parameters

optData:OptimizationData[]

Optimization data. In addition to those documented in JacobianMultivariateVectorOptimizer, this method will register the following data:

org.apache.commons.math3.optim.nonlinear.vector.Weight

Returns:PointVectorValuePair

a point/value pair that satisfies the convergence criteria.

Annotations

@Override

Exceptions

TooManyEvaluationsException:: if the maximal number of evaluations is exceeded.
DimensionMismatchException:: if the initial guess, target, and weight arguments have inconsistent dimensions.

parseOptimizationData back to summary

parseOptimizationData	back to summary
protected void parseOptimizationData(OptimizationData... optData) Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.parseOptimizationData. Scans the list of (required and optional) optimization data that characterize the problem. If the weight matrix is specified, the `weightMatrixSqrt` field is recomputed. Parameters optData:OptimizationData[] Optimization data. The following data will be looked for: `Weight` Annotations @Override

protected void parseOptimizationData(OptimizationData... optData)

Overrides org.apache.commons.math3.optim.nonlinear.vector.JacobianMultivariateVectorOptimizer.parseOptimizationData.

Scans the list of (required and optional) optimization data that characterize the problem. If the weight matrix is specified, the weightMatrixSqrt field is recomputed.

Parameters

optData:OptimizationData[]

Optimization data. The following data will be looked for:

Weight

Annotations

@Override

setCost	back to summary
protected void setCost(double cost) Sets the cost. Parameters cost:double Cost value.

setCost

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protected void setCost(double cost)

Sets the cost.

Parameters

cost:double: Cost value.

squareRoot	back to summary
private RealMatrix squareRoot(RealMatrix m) Computes the square-root of the weight matrix. Parameters m:RealMatrix Symmetric, positive-definite (weight) matrix. Returns:RealMatrix the square-root of the weight matrix.

squareRoot

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private RealMatrix squareRoot(RealMatrix m)

Computes the square-root of the weight matrix.

Parameters

m:RealMatrix: Symmetric, positive-definite (weight) matrix.

Returns:RealMatrix

the square-root of the weight matrix.

public abstract Class AbstractLeastSquaresOptimizer

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