get_init

pygom.loss.get_init.cost_grad_interpolant(ode, spline_list, t, theta)

Returns the cost (sum of squared residuals) and the gradient between the first derivative of the interpolant and the function of the ode

Parameters:	ode: :class:`.DeterministicOde` an ode object spline_list: list list of `scipy.interpolate.UnivariateSpline` t: array like time theta: array list parameter value
Returns:	cost: double sum of squared residuals g: gradient of the squared residuals

pygom.loss.get_init.cost_interpolant(ode, spline_list, t, theta, vec=True, aggregate=True)

Returns the cost (sum of squared residuals) between the first derivative of the interpolant and the function of the ode

Parameters:	ode: :class:`.DeterministicOde` an ode object spline_list: list list of `scipy.interpolate.UnivariateSpline` t: array like time theta: array list paramter value vec: bool, optional if the matrix should be flattened to be a vector aggregate: bool, optional sum the vector/matrix
Returns:	cost: double sum of squared residuals

pygom.loss.get_init.cost_sample(ode, fxApprox, xApprox, t, theta, vec=True, aggregate=True)

Returns the cost (sum of squared residuals) between the first derivative of the interpolant and the function of the ode using samples at time points t.

Parameters:

ode: :class:`.DeterministicOde`: an ode object
fxApprox: list: list of approximated values for the first derivative
xApprox: list: list of approximated values for the states
t: array like: time
theta: array list: parameter value
vec: bool, optional: if the matrix should be flattened to be a vector.
aggregate: bool/str, optional: sum the vector/matrix. If this is equals to ‘int’ then the Simpsons rule is applied to the samples. Also changes the behaviour of vec, where True outputs a vector where the elements contain the values of the integrand on each of the dimensions of the ode. False returns the sum of this vector, a scalar.

Returns:

r: array list: the cost or the residuals if vec is True

See also

residual_sample()

pygom.loss.get_init.get_init(y, t, ode, theta=None, full_output=False)

Get an initial guess of theta given the observations y and the corresponding time points t.

Parameters:	y: :array like observed values t: array like time ode: :class:`.DeterministicOde` an ode object theta: array like parameter value full_output: bool, optional True if the optimization result should be returned. Defaults to False.
Returns:	theta: array like a guess of the parameters

pygom.loss.get_init.grad_sample(ode, fxApprox, xApprox, t, theta, vec=False, output_residual=False)

Returns the gradient of the objective value using the state values of the interpolant given samples at time points t. Note that the parameters taken here is chosen to be same as cost_sample() for convenience.

Parameters:

ode: :class:`.DeterministicOde`: an ode object
fxApprox: list: list of approximated values for the first derivative
xApprox: list: list of approximated values for the states
t: array like: time
theta: array list: parameter value
vec: bool, optional: if the matrix should be flattened to be a vector
output_residual: bool, optional: if True, then the residuals will be returned as an additional argument

Returns:

g: numpy.ndarray: gradient of the objective function

See also

jac_sample()

pygom.loss.get_init.interpolate(solution, t, s=0)

Interpolate the solution of the ode given the time points and a suitable smoothing vector using univariate spline

Parameters:	solution: :class:`numpy.ndarray` f(t) of the ode with the rows correspond to time t: array like time s: smoothing scalar, optional greater or equal to zero
Returns:	splineList: list of `scipy.interpolate.UnivariateSpline`

pygom.loss.get_init.jac_sample(ode, fxApprox, xApprox, t, theta, vec=True)

Returns the Jacobian of the objective value using the state values of the interpolant given samples at time points t. Note that the parameters taken here is chosen to be same as cost_sample() for convenience.

Parameters:	ode: :class:`.DeterministicOde` an ode object fxApprox: list list of approximated values for the first derivative xApprox: list list of approximated values for the states t: array like time theta: array list parameter value vec: bool, optional if the matrix should be flattened to be a vector
Returns:	r: array list the residuals

See also

cost_sample()

pygom.loss.get_init.residual_interpolant(ode, spline_list, t, theta, vec=True)

Returns the residuals between the first derivative of the interpolant and the function of the ode

Parameters:	ode: :class:`.DeterministicOde` an ode object spline_list: list list of `scipy.interpolate.UnivariateSpline` t: array like time theta: array list parameter value vec: bool, optional if the matrix should be flattened to be a vector aggregate: bool, optional sum the vector/matrix
Returns:	r: array list the residuals

pygom.loss.get_init.residual_sample(ode, fxApprox, xApprox, t, theta, vec=True)

Returns the residuals between the first derivative of the interpolant and the function of the ode using samples at time points t.

Parameters:	ode: :class:`.DeterministicOde` an ode object fxApprox: list list of approximated values for the first derivative xApprox: list list of approximated values for the states t: array like time theta: array list parameter value vec: bool, optional if the matrix should be flattened to be a vector
Returns:	r: array list the residuals

See also

cost_sample()