Simulating Output from an RMFD Model (or obtain residuals)
solve_rmfd_cpp.RdThis RcppArmadillo function calculates for given inputs data_in
of dimension \((n \times nobs)\), where \(nobs\) is the sample size,
the outputs of dimension \(m\).
Note that data matrices are "transposed" in the sense that every column
corresponds to one observation because of memory management.
data_out is thus of dimension \((m x nobs)\).
This function is intended for internal use and thus arguments are not checked.
Arguments
- poly_inv
Matrix of dimension \((n \times n p)\), representing a square matrix polynomial \(c(z)\) with \(c_0\) equal to the identity matrix (and therefore not stored). The coefficients need to be in reverse direction, i.e. \((c_p, ... , c_1)\), where \(p\) denotes the degree of \(c(z)\).
- poly_fwd
Matrix of dimensions \((m \times n(q+1))\), representing a (possibly tall) matrix polynomial \(d(z)\) of dimension \((m \times n)\), where \(m \geq n\). The coefficient are stored "as usual" and including \(d_0\), i.e. \((d_0, d_1, ... , d_{q-1}, d_{q})\), where \(q\) denotes the degree of \(d(z)\).
- data_in
Matrix of dimension \((n \times n_obs)\), i.e. \((u_1, ..., u_T)\). Inputs to the RMFD system.
- data_out
Matrix of dimension \((m \times n_obs)\), i.e. \((y_1, ..., y_T)\). Outputs of the RMFD system. Initially zero and will be overwritten.
- t0
Integer. Time index from which we should start calculating a solution. Usually equal to 1.