leastsq2.py

Functions
	leastsq2.LeastSqModelData.buildModel (self)
	adding the variables and constraints to the model
	leastsq2.LeastSqModelData.evaluateNonlinearTerm (self, x, rowno, ignerr, thread)
	callback method for evaluating the nonlinear terms in a given row
	leastsq2.LeastSqModelData.evaluateNonlinearJacobian (self, x, rowno, jacnum, ignerr, thread)
	callback method for evaluating the jacobian for the nonlinear terms in a given row
	leastsq2.LeastSqModelData.evaluateSDLagrangian (self, x, u, hessianrow, hessiancol)
	Computes and returns the numerical values of the Lagrangian of the Hessian.

Detailed Description

This model is similar to leastsq. The key difference is that we supply a callback routine that can compute 2nd derivatives of the model. However, we only include part of the 2nd derivatives corresponding to the direct objective terms, res(i)**2. The terms from b(i,j)*x(j)**2 are ignored in the 2nd derivatives. CONOPT will not notice the incorrect derivatives but it may converge more slowly.

We solve the following nonlinear least squares model:

\[ \min \sum_i res_{i}^2 \!! \sum_j ( a_{ij}x_j + b_{ij}x_j^2 ) + res_i = obs_i \]

where \(a\), \(b\), and \(obs\) are known data, and \(res\) and \(x\) are the variables of the model.

For more information about the individual callbacks, please have a look at the source code.

Function Documentation

buildModel()

leastsq2.LeastSqModelData.buildModel

(

self

)

adding the variables and constraints to the model

Definition at line 67 of file leastsq2.py.

evaluateNonlinearTerm()

leastsq2.LeastSqModelData.evaluateNonlinearTerm	(		self,
			x,
			rowno,
			ignerr,
			thread )

callback method for evaluating the nonlinear terms in a given row

Parameters

x	the solution vector that needs to be evaluated.
rowno	the number for the row in which the nonlinear term exists.
ignerr	a boolean to indicate whether the current point is safe or unsafe.
thread	the index of the thread from which this method is being called from.

Returns

the value of the nonlinear terms.

Notes: an error in the evaluation is reported by calling errorInEvaluation()

Definition at line 134 of file leastsq2.py.

evaluateNonlinearJacobian()

leastsq2.LeastSqModelData.evaluateNonlinearJacobian	(		self,
			x,
			rowno,
			jacnum,
			ignerr,
			thread )

callback method for evaluating the jacobian for the nonlinear terms in a given row

Parameters

x	the solution vector that needs to be evaluated.
rowno	the number for the row in which the nonlinear term exists.
jacnum	vector with a list of column numbers for the nonlinear nonzero Jacobian elements in the row.
ignerr	a boolean to indicate whether the current point is safe or unsafe.
thread	the index of the thread from which this method is being called from.

Returns

a vector the length of jacnum that contains the jacobian values for the referenced elements.

Notes: an error in the evaluation is reported by calling errorInEvaluation()

Definition at line 158 of file leastsq2.py.

evaluateSDLagrangian()

leastsq2.LeastSqModelData.evaluateSDLagrangian	(		self,
			x,
			u,
			hessianrow,
			hessiancol )

Computes and returns the numerical values of the Lagrangian of the Hessian.

Parameters

x	the solution vector that needs to be evaluated.
u	the vector of weights on the individual constraints.
hessianrow	vector of row numbers of the lower triangular part of the hessian.
hessiancol	vector of column numbers of the lower triangular part of the hessian.

returns a vector for the values of the Lagrangian of the Hessian. The length of the vector is of size numHessianNonzeros().

Notes: an error in the evaluation is reported by calling errorInEvaluation()

Definition at line 177 of file leastsq2.py.