notebooks/docs/random/digest.md

+# fit_sequence version 1
+
+> `v1.fit_sequence`
+
+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_direct
+
+> `fit_poles, fit_zeros`
+
+initial guess without SVD technique
+
+![](plot-1-1.png)
+
+### `1.2` initial_poles
+
+> `fit_poles_mod_zeros`
+
+Performs the SVD for a rough initial guess
+
+![](plot-1-2.png)
+
+### `1.3` initial_zeros
+
+> `fit_poles_mod_zeros`
+
+Performs the SVD for a rough initial guess
+
+![](plot-1-3.png)
+
+### `1.4` choose zeros
+
+> `if`
+
+Chose the zeros SVD fitter as it had the smaller residual of 4.04e+00 vs. 4.46e+00 for the poles
+
+### `1.5` seq_iter_3
+
+> `RationalDiscFilter.fit_poles, RationalDiscFilter.fit_zeros`
+
+First iterations, enforcing stabilized poles residual of 3.95e+00
+
+![](plot-1-5.png)
+
+### `1.6` seq_iter_4
+
+> `RationalDiscFilter.fit_poles, RationalDiscFilter.fit_zeros`
+
+First iterations, enforcing stabilized poles residual of 3.95e+00
+
+![](plot-1-6.png)
+
+### `1.7` Final
+
+> `SVD_method`
+
+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
+
+![](plot-1-7.png)
+
+## `2` nonlinear pre-reduce and optimize
+
+> `MultiReprFilter.optimize`
+
+initial conservative order reduction (for speed), followed by a nonlinear optimization.
+
+![](plot-2.png)
+
+## `3` optimize nonlinear after bandwidth limiting
+
+> `MultiReprFilter.optimize`
+
+ths limited in the nonlinear representation to half of the local average the frequency spacing.
+Nonlinear optimization then applied.
+
+![](plot-3.png)
+
+## `4` order_reduce 1
+
+### `4.1` duals_ID_1
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+![](plot-4-1.png)
+
+### `4.2` duals_ID_2
+
+> `MultiReprFilter.optimize`
+
+ID Pairs for order reduction
+
+![](plot-4-2.png)
+
+## `5` remove_negroots
+
+## `6` remove_weakroots
+
+## `7` remove_negroots
+
+## `8` remove_negroots
+
+## `9` flip mindelay
+
+## `10` final
+
+> `MultiReprFilter.optimize`
+
+ing nonlinear parameterizations,
+TODO: describe as used
+
+![](plot-10.png)
+