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Min and max

Min and Max return the smallest or largest sampled value of the response over the supplied time window. They are purely time-domain extrema: useful for bounds, peak clipping checks, and asymmetric signals.

For each mode \(i\),

\[ A_i^{\min} = \min_{k=1,\dots,N} x_i(t_k) \]

and the maximum response is defined as

\[ A_i^{\max} = \max_{k=1,\dots,N} x_i(t_k) \]

where \(x_i(t_k)\) is the modal displacement at sample \(t_k\).

If \(\text{modal_contributions} = (\phi_1, \dots, \phi_{n_{\mathrm{modes}}})\) is provided, the total signal is reconstructed as

\[ x_{\mathrm{total}}(t_k) = \sum_{i=1}^{n_{\mathrm{modes}}} \phi_i \, x_i(t_k) \]

and the extrema are then

\[ A_{\mathrm{total}}^{\min} = \min_{k=1,\dots,N} x_{\mathrm{total}}(t_k) \]
\[ A_{\mathrm{total}}^{\max} = \max_{k=1,\dots,N} x_{\mathrm{total}}(t_k) \]

If modal_contributions is omitted, unit weights are used. When those weights come from a mode shape at a measurement point, the total entry becomes the physical minimum or maximum displacement at that point.