Pwl2FlatendFitter

class PlasmaCalcs.addons.instability_tools.instability_data_tools.Pwl2FlatendFitter(array, dim, *, promote_dims_if_needed=True, pnames=UNSET, pbounds=UNSET, bounds=UNSET, **kw_curve_fit)

Bases: XarrayCurveFitter

CurveFitter with f = pwl2_flatend, for fitting data to piecewise linear with 2 pieces.

When fitting, use bounds:

m0 > 0.

1 <= end0 <= len(xdata)-2

pwl2_flatend docs copied below, for convenience:

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evaluate xx at piecewise linear function with 2 pieces, with final piece slope=0.

xx: 1D array. Assumed to be monotonically increasing. b0: y-intercept of piece 0 m0: slope of piece 0 end0: “index” of end of piece 0

if end0 is not an int, does weighted averaging of xx[int(end0)] and xx[int(end0)+1].

E.g. end0 = 10.25 –> extend piece 0 to xx[10] + 0.25 * (xx[11] - xx[10])

b1 is computed based on the other inputs.

This is a decent approx. for ln(val) with linear growth then saturation.

xx <–> time

b0 <–> pre-growth noise level

m0 <–> growth rate

end0 <–> “saturation index” when linear growth stops.

x0 <–> “saturation time” when linear growth stops, where:

x0 = xx[i0] + (end0 - i0) * (xx[i0+1] - xx[i0], where i0 = int(end0).

y0 <–> “saturation level”; value when saturated, where:

y0 = m0 * x0 + b0.

Methods

eval([xdata, params, stddev])	evaluate curve fit result (params) at these xdata.
f(xx, b0, m0, end0)	evaluate xx at piecewise linear function with 2 pieces, with final piece slope=0.
fit(*[, stddev])	curve_fit to ydata = self.array, xdata = self.array[self.dim].
get_x0()	return x0, the x value at the end of piece 0.
get_y0()	return y0, the y value at the end of piece 0.

Attributes

fitted	result of latest call to self.fit().
get_xsat	x value at start of saturation.
get_ysat	saturation level (y-value).
params	alias to self.fitted['params'], the params from latest call to self.fit.
pbounds
pnames
xdata	alias to self.array[self.dim]

eval(xdata=UNSET, params=UNSET, stddev=False)

evaluate curve fit result (params) at these xdata.

Equivalent: xarray_curve_eval(params, self.f, xdata)

xdata: UNSET, 1D xarray.DataArray, or other 1D array-like

x values at which to evaluate the fit.

UNSET –> use self.xdata.

non-xarray 1D array-like –> convert to 1D DataArray via xr1d(xdata, self.dim)

params: UNSET or values of params from a fit.

UNSET –> use self.fitted

stddev: bool

whether to instead return Dataset with data_vars ‘eval+std’, ‘eval’, and ‘eval-std’,

telling f(xdata, *(params+std)), f(xdata, *params), and f(xdata, *(params-std)).

Fails if params is not a Dataset with ‘stddev’ data_var.

[EFF] note: if self.f is well-vectorized, it is equivalent (when stddev=False) and faster to do:

self.f(xdata, *params.transpose(‘param’, …))

static f(xx, b0, m0, end0)

evaluate xx at piecewise linear function with 2 pieces, with final piece slope=0.

xx: 1D array. Assumed to be monotonically increasing. b0: y-intercept of piece 0 m0: slope of piece 0 end0: “index” of end of piece 0

if end0 is not an int, does weighted averaging of xx[int(end0)] and xx[int(end0)+1].

E.g. end0 = 10.25 –> extend piece 0 to xx[10] + 0.25 * (xx[11] - xx[10])

b1 is computed based on the other inputs.

This is a decent approx. for ln(val) with linear growth then saturation.

xx <–> time

b0 <–> pre-growth noise level

m0 <–> growth rate

end0 <–> “saturation index” when linear growth stops.

x0 <–> “saturation time” when linear growth stops, where:

x0 = xx[i0] + (end0 - i0) * (xx[i0+1] - xx[i0], where i0 = int(end0).

y0 <–> “saturation level”; value when saturated, where:

y0 = m0 * x0 + b0.

fit(*, stddev=UNSET)

curve_fit to ydata = self.array, xdata = self.array[self.dim].

Remembers result in self.fitted. Returns self.fitted.

stddev: UNSET or bool

whether to include data_var ‘stddev’ telling standard deviation of the fit.

UNSET –> use value from self.kw_curve_fit, else default of xarray_curve_fit.

property fitted

result of latest call to self.fit().

None if never called self.fit(), or if crashed before finishing self.fit().

get_x0()

return x0, the x value at the end of piece 0.

(Crashes if run before self.fit())

x0 = xx[i0] + (end0 - i0) * (xx[i0+1] - xx[i0], where i0 = int(end0).

[TODO] option to get result +-1 stddev error bounds.

property get_xsat

x value at start of saturation. alias to self.get_x0.

get_y0()

return y0, the y value at the end of piece 0.

(Crashes if run before self.fit())

y0 = m0 * x0 + b0.

[TODO] option to get result +-1 stddev error bounds.

property get_ysat

saturation level (y-value). alias to self.get_y0.

property params

alias to self.fitted[‘params’], the params from latest call to self.fit.

crash with helpful message if self.fitted doesn’t exist.

property xdata

alias to self.array[self.dim]