wecopttool.time_mat

time_mat(f1, nfreq, nsubsteps=1, zero_freq=True)

Assemble the time matrix that converts the state to a time-series.

For a state $x$ consisting of the mean (DC) component followed by the real and imaginary components of the Fourier coefficients (excluding the imaginary component of the 2-point wave) as $x=[X0,Re(X1),Im(X1),...,Re(Xn)]$, the response vector in the time-domain ($x(t)$) is given as $Mx$, where $M$ is the time matrix.

The time matrix has size (nfreq*2, nfreq*2).

If zero_freq = False (not default), the mean (DC) component X0 is excluded, and the matrix/vector length is reduced by 1.

Parameters:

• f1 (float) – Fundamental frequency f1 [$Hz$].

• nfreq (int) – Number of frequencies.

• nsubsteps (int | None) – Number of steps between the default (implied) time steps. A value of 1 corresponds to the default step length.

• zero_freq (bool | None) – Whether the first frequency should be zero.

Return type:

ndarray