sparse.DDE: Sparsity selection for the lags of delay.

In gpDDE: General Profiling Method for Delay Differential Equation

Description

This function carry out one step sparsity selection for the lags of delay given the profiled optimization result.

Usage

sparse.DDE(fn, data, times, basisvals = NULL, lambda, fd.obj = NULL,
  more = NULL, weights = NULL, quadrature = NULL, in.meth = "nlminb",
  out.meth = "nls", control.in = list(), control.out = list(),
  eps = 1e-06, active = NULL, posproc = FALSE, poslik = FALSE,
  names = NULL, sparse = FALSE, discrete = FALSE, basisvals0 = NULL,
  coefs0 = NULL, nbeta, ndelay, tau, nnls.res)

Arguments

fn	A named list of functions giving the righthand side of a delay differential equation. The functions should have arguments times he times at which the righthand side is being evaluated. x The state values at those times. p Parameters to be entered in the system. more A list object containing additional inputs to fn, The distributed delay state are passed into derivative calculation as more$y. The list of functions should contain the elements: fn Function to calculate the right hand sid. dfdx Function to calculate the derivative of each right-hand function with respect to the states. dfdp calculates the derivative of therighthand side function with respect to parameters. d2fdx2 Function to calculate the second derivatives with respect to states. d2fdxdp Function to calculate the cross derivatives of each right-hand function with respect to state and parameters. dfdx.d Function to calculate the the derivative of each righthand function with respect to the delayed states. d2fdx.ddp Function to calculate the cross derivatives of each righthand function with respect to the delayed states and parameters. d2fdxdx.d Function to calculate the cross derivatives of each right-hand function with respect to the state and the delayed states. d2fdx.d2 Function to calculate the second derivatives of the right-hand function with respect to the delayed states.
data	Matrix of observed data values.
times	Vector observation times for the data.
basisvals	Values of the collocation basis to be used. This should be a basis object from the fda package.
lambda	Penalty value trading off fidelity to data with fidelity to dif- ferential equations.
fd.obj	A functional data object; if this is non-null, coefs and basisvals is extracted from here.
more	An object specifying additional arguments to fn.
weights	Weights for weighted estimation.
quadrature	Quadrature points, should contain two elements (if not NULL) qpts sQuadrature points; defaults to midpoints between knots qwts Quadrature weights; defaults to normalizing by the length of qpts.
in.meth	Inner optimization function currently one of 'nlminb', 'optim', or 'trustOptim'.
out.meth	Outer optimization selection function to be used, depending on the type of method. "penalized" Uses LASSO method from penalized package. "addaptive" Positive addaptive lasso using lars algorithm. "lars" Positive lasso using lars algorithm.
control.in	Control object for inner optimization function.
control.out	Control object for outer optimization function.
eps	Finite differencing step size, if needed.
active	Incides indicating which parameters of pars should be estimated; defaults to all of them.
posproc	Should the state vector be constrained to be positive? If this is the case, the state is represented by an exponentiated basis expansion in the proc object.
poslik	Should the state be exponentiated before being compared to the data? When the state is represented on the log scale (posproc=TRUE), this is an alternative to taking the log of the data.
names	The names of the state variables if not given by the column names of coefs.
sparse	Should sparse matrices be used for basis values? This option can save memory when using 'trust' optimization method.
discrete	Is it a discrete process?
basisvals0	Values of the collocation basis to be used for the history part of the data. This should be a basis object from the fda package.
coefs0	Vector giving the estimate of the coefficients in the spline for the history part of the data.
nbeta	The number of lags for the delay.
ndelay	A vector inidicating which state process has a delay term.
tau	A list of delay lags.
nnls.res	res item returned from Profile.LS.DDE

Value

A list with elements

data

The matrix for the observed data.

res

The inner optimization result.

select

A list containing the result after selection, the parameter, delay contribution and coefficients after the selection.

Author(s)

Ziqian Zhou

See Also

Profile.LS.DDE

gpDDE documentation built on May 2, 2019, 1:09 p.m.