loss_h_gradient: Gradient of loss function for registration step
In julia-wrobel/registr: Curve Registration for Exponential Family Functional Data

Description Usage Arguments Value Author(s)

Gradient of loss function for registration step

loss_h_gradient(
  Y,
  Theta_h,
  mean_coefs,
  knots,
  beta.inner,
  family = "gaussian",
  incompleteness = NULL,
  lambda_inc = NULL,
  t_min,
  t_max,
  t_min_curve,
  t_max_curve,
  Kt = 8,
  periodic = FALSE,
  warping = "nonparametric"
)

`Y`	vector of observed points.
`Theta_h`	B-spline basis for inverse warping functions.
`mean_coefs`	spline coefficient vector for mean curve.
`knots`	knot locations for B-spline basis used to estimate mean and FPC basis function.
`beta.inner`	spline coefficient vector to be estimated for warping function h.
`family`	One of `c("gaussian","binomial")`. Defaults to `"gaussian"`.
`incompleteness`	Optional specification of incompleteness structure. One of `c("leading","trailing","full")`, specifying that incompleteness is present only in the initial measurements, only in the trailing measurements, or in both, respectively. For details see the accompanying vignette. Defaults to NULL, i.e. no incompleteness structure. Can only be set when `warping = "nonparametric"`.
`lambda_inc`	Penalization parameter to control the amount of overall dilation of the domain. The higher this lambda, the more the registered domains are forced to have the same length as the observed domains. Only used if `incompleteness` is not NULL.
`t_min`	minimum and maximum value to be evaluated on the time domain.
`t_max`	minimum and maximum value to be evaluated on the time domain.
`t_min_curve`	minimum and maximum value of the observed time domain of the (potentially incomplete) curve.
`t_max_curve`	minimum and maximum value of the observed time domain of the (potentially incomplete) curve.
`Kt`	Number of B-spline basis functions used to estimate mean functions. Default is 8.
`periodic`	If `TRUE`, uses periodic b-spline basis functions. Default is `FALSE`. `loss_h_gradient()` is currently only available for `periodic = FALSE`.
`warping`	If `nonparametric` (default), inverse warping functions are estimated nonparametrically. If `piecewise_linear2` they follow a piecewise linear function with 2 knots. `loss_h_gradient()` is currently only available for `warping = "nonparametric"`.