dmd prediction of initial condition

Nobody has claimed this yet.

My DMD code seems to be working, but it seems to make a large error at the starting time. Shouldn't DMD be able to reproduce the initial condition exactly? Looking at

https://www.librom.net/features.html

I can see the last equation in the DMD section

$$
\mathbf{u}(t) = \mathbf{\Phi\Lambda}^{{t}/{\Delta t}}\mathbf{b}_0
$$

using $\mathbf{b}_0=\mathbf{\Phi}^\dagger\mathbf{u}_0$ we get

$$
\mathbf{u}(t) = \mathbf{\Phi\Lambda}^{{t}/{\Delta t}}\mathbf{\Phi}^\dagger\mathbf{u}_0
$$

At $t=0$ we have $\mathbf{\Lambda}^{{t}/{\Delta t}}=\mathbf{1}$ and hence,

$$
\mathbf{u}(0) = \mathbf{\Phi}\mathbf{\Phi}^\dagger\mathbf{u}_0
$$

Since $\mathbf{\Phi}\mathbf{\Phi}^\dagger=\mathbf{1}$ we get

$$
\mathbf{u}(0)=\mathbf{u}_0
$$

Hence, the initial condition is faithfully reproduced. Is my understanding correct?

Start by reviewing the DMD documentation and equations referenced in the issue, then locate the existing DMD implementation and reproduce the reported initial-condition error. Done would require a clearly defined resolution explaining whether the observed behavior is expected or identifying the implementation change needed.

Written by the indexing model from the issue text.