Class Model

expts  A sequence of Experiments to be fit to.
calcs  A sequence of calculation objects referred to by the 
       Experiments.

Get the initial conditions currently present in a model
for dynamic variables that are not assigned variables.

Outputs:
  KeyedList with keys (calcName,varName) --> initialValue

Sets the initial conditions into the model. Uses the input
format defined by 'getICs'.

Inputs:
 ics -- Initial conditions to set in KeyedList form:
          keys: (calcName, varName) --> intialValue

Outputs:
 None

Return chi-squared divided by the number of degrees of freedom

Question: Are priors to be included in the N data points?
          How do scale factors change the number of d.o.f.?

Force(parameters, epsilon factor) -> list

Returns a list containing the numerical gradient of the cost with
respect to each parameter (in the parameter order of the
CalculationCollection). Each element of the gradient is:
    cost(param + eps) - cost(param - eps)/(2 * eps).
If relativeScale is False then epsf is the stepsize used (it should
already be multiplied by typicalValues before Jacobian is called)
If relativeScale is True then epsf is multiplied by params.
The two previous statements hold for both scalar and vector valued
epsf.

Return the gradient of the cost, d_cost/d_param as a KeyedList.

This method uses sensitivity integration, so it only applies to
ReactionNetworks.

Return the gradient of the cost wrt log parameters, d_cost/d_log_param
as a KeyedList.

This method uses sensitivity integration, so it only applies to
ReactionNetworks.

Gets a dictionary of measured independent variables indexed by 
calculation from the ExperimentCollection and passes it to the
CalculationCollection. The returned dictionary is of the form:
 dictionary[experiment][calculation][dependent variable]
           [independent variabled] -> calculated value.

Returns:

dictionary

Gets a dictionary of measured independent variables indexed by
calculation from the ExperimentCollection and passes it to the
CalculationCollection. The returned dictionary is of the form:
 dictionary[experiment][calculation][dependent variable]
           [independent variabled][parameter] -> sensitivity.

Returns:

dictionary

Compute the scale factors for the current parameters and return a dict.

The dictionary is of the form dict[exptId][varId] = scale_factor

Returns the scale factor derivatives w.r.t. parameters
appropriate for each chemical in each
experiment, given the current parameters. The returned dictionary
is of the form: internalVarsDerivs['scaleFactors']                 = dict[experiment][chemical][parametername] -> derivative.

Returns:

dictionary

Return a KeyedList of the derivatives of the model residuals w.r.t.
the lograithms of the parameters parameters.

The method uses the sensitivity integration. As such, it will only
work with ReactionNetworks.

The KeyedList is of the form:
    kl.get(resId) = [dres/dlogp1, dres/dlogp2...]

Return a KeyedList of the derivatives of the model residuals w.r.t.
parameters.

The method uses the sensitivity integration. As such, it will only
work with ReactionNetworks.

The KeyedList is of the form:
    kl[resId] = [dres/dp1, dres/dp2...]

Return a KeyedList of the derivatives of the model residuals w.r.t.
parameters.

The method uses finite differences.

Inputs:
 params -- Parameters about which to calculate the jacobian
 eps -- Step size to take, may be vector or scalar.
 relativeScale -- If true, the eps is taken to be the fractional
                  change in parameter to use in finite differences.
 stepSizeCutoff -- Minimum step size to take.

Gets a dictionary of the sensitivities at the time points of
the independent variables for the measured dependent variables
for each calculation and experiment.
Form:
dictionary[(experiment,calculation,dependent variable,
independent variable)] -> result

result is a vector of length number of parameters containing
the sensitivity at that time point, in the order of the ordered
parameters

Returns:

dictionary

Finite difference the residual dictionary to get a dictionary
for the Jacobian. It will be indexed the same as the residuals.
Note: epsf is either a scalar or an array.
If relativeScale is False then epsf is the stepsize used (it should
already be multiplied by typicalValues before Jacobian is called)
If relativeScale is True then epsf is multiplied by params.
The two previous statements hold for both scalar and vector valued
epsf.

Return the second partial derivative for func w.r.t. parameters i and j

f0: The value of the function at params
eps: Sets the stepsize to try
relativeScale: If True, step i is of size p[i] * eps, otherwise it is
               eps
stepSizeCutoff: The minimum stepsize to take

Returns the hessian of the model.

epsf: Sets the stepsize to try
relativeScale: If True, step i is of size p[i] * eps, otherwise it is
               eps
stepSizeCutoff: The minimum stepsize to take
jacobian: If the jacobian is passed, it will be used to estimate
          the step size to take.
vebose: If True, a message will be printed with each hessian element
        calculated

Returns the hessian of the model in log parameters.

eps: Sets the stepsize to try
relativeScale: If True, step i is of size p[i] * eps, otherwise it is
               eps
stepSizeCutoff: The minimum stepsize to take
vebose: If True, a message will be printed with each hessian element
        calculated

Finite difference the residual dictionary to get a dictionary
for the Hessian. It will be indexed the same as the residuals.
Note: epsf is either a scalar or an array.
If relativeScale is False then epsf is the stepsize used (it should
already be multiplied by typicalValues before Jacobian is called)
If relativeScale is True then epsf is multiplied by params.
The two previous statements hold for both scalar and vector valued
epsf.

Calculate the Residual Response array. This array represents the change
in a residual obtained by a finite change in a data value.

Inputs:
(self, j, h)
j -- jacobian matrix to use
h -- hessian matrix to use

Outputs:
response -- The response array

Calculate the parameter response to residual array. This array
represents the change in parameter resulting from a change in data
(residual).

Inputs:
(self, j, h)
j -- jacobian matrix to use
h -- hessian matrix to use

Outputs:
response -- The response array