notebooks/cplx/digest.md

+# fit_sequence_v1
+
+> `fit_sequence_v1`
+
+Version 1 smart fitter in IIRrational library. Uses SVD method with high order over fitting, then switches to nonlinear fits with heuristics to remove poles and zeros down to a reasonable system order.
+
+
+## `1` initial
+
+### `1.1` initial_poles
+
+> `fit_poles_mod_zeros`
+
+Performs the SVD for a rough initial guess
+
+
+![Fitttt](plot-1-1.png)
+
+### `1.2` initial_zeros
+
+> `fit_poles_mod_zeros`
+
+Performs the SVD for a rough initial guess
+
+
+![Fitttt](plot-1-2.png)
+
+### `1.3` choose poles
+
+> `if`
+
+Chose the Poles SVD fitter as it had the smaller residual of 1.91e+02 vs. 1.93e+04 for the zeros
+
+
+### `1.4` seq_iter_1
+
+> `IIRrational.fit_poles, IIRrational.fit_zeros`
+
+First iterations, enforcing mindelay and stabilized poles residual of 6.33e+03
+
+
+![Fitttt](plot-1-4.png)
+
+### `1.5` seq_iter_2
+
+> `IIRrational.fit_poles, IIRrational.fit_zeros`
+
+First iterations, enforcing stabilized poles residual of 1.51e+04
+
+
+![Fitttt](plot-1-5.png)
+
+### `1.6` seq_iter_3
+
+> `IIRrational.fit_poles, IIRrational.fit_zeros`
+
+First iterations, enforcing stabilized poles residual of 1.19e+02
+
+
+![Fitttt](plot-1-6.png)
+
+### `1.7` seq_iter_4
+
+> `IIRrational.fit_poles, IIRrational.fit_zeros`
+
+First iterations, enforcing stabilized poles residual of 8.89e+01
+
+
+![Fitttt](plot-1-7.png)
+
+### `1.8` nyquist_move
+
+> `IIRrational.nyquist_move`
+
+Moves to intended nyquist, clipping negative real poles/zeros likely caused by phase defects of low nyquist
+
+
+![Fitttt](plot-1-8.png)
+
+### `1.9` Final
+
+> `SVD_method`
+
+Uses SVD to create initial guess of fit for data, followed by several iterative fits
+(see reference ???).
+   * It is a linear method, finding global optimum (nonlocal). This makes it get stuck if systematics are bad. To prevent this,
+it requires gratuitous overfitting to reliably get good fits.
+   * It requires a nyquist frequency that is very low, near the last data point. This can cause artifacts due to phasing discontinuity near the nyquist.
+   * The provided nyquist frequency is shifted up at the end, removing the real poles/zeros that are typically due to phasing discontinuity
+
+
+![Fitttt](plot-1-9.png)
+
+## `2` optimize nonlinear
+
+> `MultiReprFilter.optimize`
+
+Optimizes using nonlinear parameterizations,
+TODO: describe as used
+
+
+![Fitttt](plot-2.png)
+
+## `3` order_reduce 1
+
+### `3.1` duals_ID_1
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+
+![Fitttt](plot-3-1.png)
+
+### `3.2` seq_order_reduce_opt_1
+
+> `MultiReprFilter.optimize`
+
+Optimize again after order reduction
+
+
+![Fitttt](plot-3-2.png)
+
+### `3.3` duals_ID_2
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+
+![Fitttt](plot-3-3.png)
+
+### `3.4` seq_order_reduce_opt_2
+
+> `MultiReprFilter.optimize`
+
+Optimize again after order reduction
+
+
+![Fitttt](plot-3-4.png)
+
+### `3.5` duals_ID_3
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+
+![Fitttt](plot-3-5.png)
+
+## `4` flip mindelay
+
+## `5` order_reduce 2
+
+### `5.1` duals_ID_1
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+
+![Fitttt](plot-5-1.png)
+