PlasmaCalcs.addons.instability_tools.instability_data_tools.Pwl3FlatendFitter

class PlasmaCalcs.addons.instability_tools.instability_data_tools.Pwl3FlatendFitter(array, dim, *, promote_dims_if_needed=True, pnames=UNSET, pbounds=UNSET, bounds=UNSET, **kw_curve_fit)

Bases: XarrayCurveFitter

CurveFitter with f = pwl3_flatend, for fitting data to piecewise linear with 3 pieces.
When fitting, use bounds:
m0, m1 > 0
1 <= end0 <= len(xdata)-3
2 <= end1add <= len(xdata)-2
# [TODO] It would be good to force end0 + end1add < len(xdata)-1. But I don’t know how to.
pwl3_flatend docs copied below, for convenience:
————————————————
evaluate xx at piecewise linear function with 3 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[floor(end0)] and xx[ceil(end0)].
E.g. end0 = 10.25 –> extend piece 0 to xx[10] + 0.25 * (xx[11] - xx[10])

m1: slope of piece 1 end1add: “index” of end of piece 1, minus end0.

end1 = end0 + end1add. (max=len(xx)-1)
if end1 is not an int, handle similarly to end0 (see above).
b2 is computed based on the other inputs.
This is a decent approx. for ln(val) with linear growth, then damped linear growth, then saturation.
xx <–> time
b0 <–> pre-growth noise level
m0 <–> growth rate of linear growth
end0 <–> “damped index” when linear growth stops.
x0 <–> “damped time” when linear growth stops, where:
x0 = xx[i0] + (end0 - i0) * (xx[i0+1] - xx[i0], where i0 = int(end0).
y0 <–> pre-damped-growth level, where:
y0 = m0 * x0 + b0.
(–> damped growth piece has y-intercept b1 = y0 - m1 * x0.)
m1 <–> growth rate of damped linear growth
end1 <–> “saturation index” when damped growth stops, where:
end1 = end0 + end1add
x1 <–> “saturation time” when damped growth stops, where:
x1 = xx[i1] + (end1 - i1) * (xx[i1+1] - xx[i1], where i1 = int(end1).
y1 <–> “saturation level”; value when saturated, where:
y21= m1 * x1 + b1.
__init__(array, dim, *, promote_dims_if_needed=True, pnames=UNSET, pbounds=UNSET, bounds=UNSET, **kw_curve_fit)

Methods

__init__(array, dim, *[, ...])

eval([xdata, params])

f(xx, b0, m0, end0, m1, end1add)

fit(*[, stddev])

get_x0()

get_x1()

get_y0()

get_y1()

Attributes

fitted

get_xsat

get_ysat

params

pbounds

pnames

xdata

eval(xdata=UNSET, params=UNSET)
evaluate curve fit result (params) at these xdata.

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

xdata: UNSET or 1D xarray.DataArray
x values at which to evaluate the fit.
UNSET –> use self.xdata.
params: UNSET or values of params from a fit.
UNSET –> use self.params
[EFF] note: if self.f is well-vectorized, it is equivalent and faster to do:
self.f(xdata, *params.transpose(‘param’, …))
static f(xx, b0, m0, end0, m1, end1add)
evaluate xx at piecewise linear function with 3 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[floor(end0)] and xx[ceil(end0)].
E.g. end0 = 10.25 –> extend piece 0 to xx[10] + 0.25 * (xx[11] - xx[10])

m1: slope of piece 1 end1add: “index” of end of piece 1, minus end0.

end1 = end0 + end1add. (max=len(xx)-1)
if end1 is not an int, handle similarly to end0 (see above).
b2 is computed based on the other inputs.
This is a decent approx. for ln(val) with linear growth, then damped linear growth, then saturation.
xx <–> time
b0 <–> pre-growth noise level
m0 <–> growth rate of linear growth
end0 <–> “damped index” when linear growth stops.
x0 <–> “damped time” when linear growth stops, where:
x0 = xx[i0] + (end0 - i0) * (xx[i0+1] - xx[i0], where i0 = int(end0).
y0 <–> pre-damped-growth level, where:
y0 = m0 * x0 + b0.
(–> damped growth piece has y-intercept b1 = y0 - m1 * x0.)
m1 <–> growth rate of damped linear growth
end1 <–> “saturation index” when damped growth stops, where:
end1 = end0 + end1add
x1 <–> “saturation time” when damped growth stops, where:
x1 = xx[i1] + (end1 - i1) * (xx[i1+1] - xx[i1], where i1 = int(end1).
y1 <–> “saturation level”; value when saturated, where:
y21= m1 * x1 + b1.
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.
get_x1()
return x1, the x value at the end of piece 1.
(Crashes if run before self.fit())
x1 = xx[i1] + (end1 - i1) * (xx[i1+1] - xx[i1], where i1 = int(end1),
and end1 = end0 + end1add.
[TODO] option to get result +-1 stddev error bounds.
property get_xsat
x value at start of saturation. alias to self.get_x1.
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.
get_y1()
return y1, the y value at the end of piece 1.
(Crashes if run before self.fit())
y1 = m1 * x1 + b1.
[TODO] option to get result +-1 stddev error bounds.
property get_ysat
saturation level (y-value). alias to self.get_y1.
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]