ModSimPy/code/modsim.py at master · gitMilan/ModSimPy · GitHub

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"""

Code from Modeling and Simulation in Python.

License: https://creativecommons.org/licenses/by/4.0)

"""

import logging

logger = logging.getLogger(name='modsim.py')

#TODO: Make this Python 3.7 when conda is ready

# make sure we have Python 3.6 or better

import sys

if sys.version_info < (3, 6):

logger.warning('modsim.py depends on Python 3.6 features.')

import inspect

import matplotlib.pyplot as plt

import numpy as np

import pandas as pd

import scipy

import sympy

import seaborn as sns

sns.set(style='white', font_scale=1.2)

import pint

UNITS = pint.UnitRegistry()

Quantity = UNITS.Quantity

# expose some names so we can use them without dot notation

from copy import copy

from numpy import sqrt, log, exp, pi

from pandas import DataFrame, Series

from time import sleep

from scipy.interpolate import interp1d

from scipy.interpolate import InterpolatedUnivariateSpline

from scipy.integrate import odeint

from scipy.integrate import solve_ivp

from scipy.optimize import leastsq

from scipy.optimize import minimize_scalar

import scipy.optimize

def flip(p=0.5):

"""Flips a coin with the given probability.

p: float 0-1

returns: boolean (True or False)

"""

return np.random.random() < p

# For all the built-in Python functions that do math,

# let's use the NumPy version instead.

abs = np.abs

min = np.min

max = np.max

pow = np.power

sum = np.sum

round = np.round

def cart2pol(x, y, z=None):

"""Convert Cartesian coordinates to polar.

x: number or sequence

y: number or sequence

z: number or sequence (optional)

returns: theta, rho OR theta, rho, z

"""

x = np.asarray(x)

y = np.asarray(y)

# TODO: use hypot?

rho = np.sqrt(x**2 + y**2)

theta = np.arctan2(y, x)

if z is None:

return theta, rho

else:

return theta, rho, z

def pol2cart(theta, rho, z=None):

"""Convert polar coordinates to Cartesian.

theta: number or sequence

rho: number or sequence

z: number or sequence (optional)

returns: x, y OR x, y, z

"""

if hasattr(theta, 'units'):

if theta.units == UNITS.degree:

theta = theta.to(UNITS.radian)

if theta.units != UNITS.radian:

msg = """In pol2cart, theta must be either a number or

a Quantity in degrees or radians."""

raise ValueError(msg)

x = rho * np.cos(theta)

y = rho * np.sin(theta)

if z is None:

return x, y

else:

return x, y, z

def linspace(start, stop, num=50, **options):

"""Returns an array of evenly-spaced values in the interval [start, stop].

start: first value

stop: last value

num: number of values

Also accepts the same keyword arguments as np.linspace. See

https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html

returns: array or Quantity

"""

underride(options, dtype=np.float64)

# see if either of the arguments has units

units = getattr(start, 'units', None)

units = getattr(stop, 'units', units)

array = np.linspace(start, stop, num, **options)

if units:

array = array * units

return array

def linrange(start=0, stop=None, step=1, **options):

"""Returns an array of evenly-spaced values in the interval [start, stop].

This function works best if the space between start and stop

is divisible by step; otherwise the results might be surprising.

By default, the last value in the array is `stop-step`

(at least approximately).

If you provide the keyword argument `endpoint=True`,

the last value in the array is `stop`.

start: first value

stop: last value

step: space between values

returns: array or Quantity

"""

if stop is None:

stop = start

start = 0

# TODO: what breaks if we don't make the dtype float?

#underride(options, endpoint=True, dtype=np.float64)

underride(options, endpoint=False)

# see if any of the arguments has units

units = getattr(start, 'units', None)

units = getattr(stop, 'units', units)

units = getattr(step, 'units', units)

n = np.round((stop - start) / step)

if options['endpoint']:

n += 1

array = np.full(int(n), magnitude(step))

array[0] = magnitude(start)

array = np.cumsum(array)

if units:

array = array * units

return array

def magnitude(x):

"""Returns the magnitude of a Quantity or number.

x: Quantity or number

returns: number

"""

return x.magnitude if isinstance(x, Quantity) else x

def magnitudes(x):

"""Returns the magnitude of a Quantity or number, or sequence.

x: Quantity or number, or sequence

returns: number

"""

try:

return [magnitude(elt) for elt in x]

except TypeError: # not iterable

return magnitude(x)

def units(x):

"""Returns the units of a Quantity or number.

x: Quantity or number

returns: Unit object or 1

"""

return x.units if isinstance(x, Quantity) else 1

def remove_units(series):

"""Removes units from the values in a Series.

Only removes units from top-level values;

does not traverse nested values.

returns: new Series object

"""

res = copy(series)

print(type(res))

for label, value in res.iteritems():

res[label] = magnitude(value)

return res

def require_units(x, units):

"""Apply units to `x`, if necessary.

x: Quantity or number

units: Pint Units object

returns: Quantity

"""

if isinstance(x, Quantity):

return x.to(units)

else:

return Quantity(x, units)

def fit_leastsq(error_func, params, *args, **options):

"""Find the parameters that yield the best fit for the data.

`params` can be a sequence, array, or Series

Whatever arguments are provided are passed along to `error_func`

error_func: function that computes a sequence of errors

params: initial guess for the best parameters

data: the data to be fit; will be passed to min_fun

options: any other arguments are passed to leastsq

"""

# if any of the params are quantities, strip the units

x0 = [magnitude(x) for x in params]

# override `full_output` so we get a message if something goes wrong

options['full_output'] = True

# run leastsq

with units_off():

best_params, cov_x, infodict, mesg, ier = leastsq(error_func,

x0=x0, args=args, **options)

details = ModSimSeries(infodict)

details.set(cov_x=cov_x, mesg=mesg, ier=ier)

# if we got a Params object, we should return a Params object

if isinstance(params, Params):

best_params = Params(Series(best_params, params.index))

# return the best parameters and details

return best_params, details

def min_bounded(min_func, bounds, *args, **options):

"""Finds the input value that minimizes `min_func`.

Wrapper for https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html

min_func: computes the function to be minimized

bounds: sequence of two values, lower and upper bounds of the

range to be searched

args: any additional positional arguments are passed to min_func

options: any keyword arguments are passed as options to minimize_scalar

returns: ModSimSeries object

"""

# try:

# print(bounds[0])

# min_func(bounds[0], *args)

# except Exception as e:

# msg = """Before running scipy.integrate.min_bounded, I tried

# running the slope function you provided with the

# initial conditions in system and t=0, and I got

# the following error:"""

# logger.error(msg)

# raise(e)

underride(options, xatol=1e-3)

# TODO: Do we need to remove units from bounds?

with units_off():

res = minimize_scalar(min_func,

bracket=bounds,

bounds=bounds,

args=args,

method='bounded',

options=options)

if not res.success:

msg = """scipy.optimize.minimize_scalar did not succeed.

The message it returned is %s""" % res.message

raise Exception(msg)

return ModSimSeries(res)

def max_bounded(max_func, bounds, *args, **options):

"""Finds the input value that maximizes `max_func`.

Wrapper for https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize_scalar.html

min_func: computes the function to be maximized

bounds: sequence of two values, lower and upper bounds of the

range to be searched

args: any additional positional arguments are passed to max_func

options: any keyword arguments are passed as options to minimize_scalar

returns: ModSimSeries object

"""

def min_func(*args):

return -max_func(*args)

res = min_bounded(min_func, bounds, *args, **options)

# we have to negate the function value before returning res

res.fun = -res.fun

return res

def minimize(min_func, x0, *args, **options):

"""Finds the input value that minimizes `min_func`.

Wrapper for https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html

min_func: computes the function to be minimized

x0: initial guess

args: any additional positional arguments are passed to min_func

options: any keyword arguments are passed as options to minimize_scalar

returns: ModSimSeries object

"""

underride(options, tol=1e-3)

with units_off():

res = scipy.optimize.minimize(min_func, x0, *args, **options)

return ModSimSeries(res)

def run_odeint(system, slope_func, **options):

"""Integrates an ordinary differential equation.

`system` should contain system parameters and `ts`, which

is an array or Series that specifies the time when the

solution will be computed.

system: System object

slope_func: function that computes slopes

returns: TimeFrame

"""

# make sure `system` contains `ts`

if not hasattr(system, 'ts'):

msg = """It looks like `system` does not contain `ts`

as a system variable. `ts` should be an array

or Series that specifies the times when the

solution will be computed:"""

raise ValueError(msg)

# make sure `system` contains `init`

if not hasattr(system, 'init'):

msg = """It looks like `system` does not contain `init`

as a system variable. `init` should be a State

object that specifies the initial condition:"""

raise ValueError(msg)

# make the system parameters available as globals

unpack(system)

# try running the slope function with the initial conditions

try:

slope_func(init, ts[0], system)

except Exception as e:

msg = """Before running scipy.integrate.odeint, I tried

running the slope function you provided with the

initial conditions in system and t=0, and I got

the following error:"""

logger.error(msg)

raise(e)

# when odeint calls slope_func, it should pass `system` as

# the third argument. To make that work, we have to make a

# tuple with a single element and pass the tuple to odeint as `args`

args = (system,)

# now we're ready to run `odeint` with `init` and `ts` from `system`

with units_off():

array = odeint(slope_func, list(init), ts, args, **options)

# the return value from odeint is an array, so let's pack it into

# a TimeFrame with appropriate columns and index

frame = TimeFrame(array, columns=init.index, index=ts, dtype=np.float64)

return frame

def run_ode_solver(system, slope_func, **options):

"""Computes a numerical solution to a differential equation.

`system` must contain `init` with initial conditions,

`t_0` with the start time, and `t_end` with the end time.

It can contain any other parameters required by the slope function.

`options` can be any legal options of `scipy.integrate.solve_ivp`

system: System object

slope_func: function that computes slopes

returns: TimeFrame

"""

# make sure `system` contains `init`

if not hasattr(system, 'init'):

msg = """It looks like `system` does not contain `init`

as a system variable. `init` should be a State

object that specifies the initial condition:"""

raise ValueError(msg)

# make sure `system` contains `t_end`

if not hasattr(system, 't_end'):

msg = """It looks like `system` does not contain `t_end`

as a system variable. `t_end` should be the

final time:"""

raise ValueError(msg)

# make the system parameters available as globals

unpack(system)

# the default value for t_0 is 0

t_0 = getattr(system, 't_0', 0)

# try running the slope function with the initial conditions

# try:

# slope_func(init, t_0, system)

# except Exception as e:

# msg = """Before running scipy.integrate.solve_ivp, I tried

# running the slope function you provided with the

# initial conditions in `system` and `t=t_0` and I got

# the following error:"""

# logger.error(msg)

# raise(e)

# wrap the slope function to reverse the arguments and add `system`

f = lambda t, y: slope_func(y, t, system)

def wrap_event(event):

"""Wrap the event functions.

Make events terminal by default.

"""

wrapped = lambda t, y: event(y, t, system)

wrapped.terminal = getattr(event, 'terminal', True)

wrapped.direction = getattr(event, 'direction', 0)

return wrapped

# wrap the event functions so they take the right arguments

events = options.pop('events', [])

try:

events = [wrap_event(event) for event in events]

except TypeError:

events = wrap_event(events)

# remove dimensions from the initial conditions.

# we need this because otherwise `init` gets copied into the

# results array along with its units

# try:

# y_0 = [magnitude(x) for x in init]

# except TypeError:

# y_0 = [magnitude(init)]

y_0 = [magnitude(x) for x in init]

# run the solver

with units_off():

bunch = solve_ivp(f, [t_0, t_end], y_0, events=events, **options)

# separate the results from the details

y = bunch.pop('y')

t = bunch.pop('t')

details = ModSimSeries(bunch)

# pack the results into a TimeFrame

results = TimeFrame(np.transpose(y), index=t, columns=init.index)

return results, details

def fsolve(func, x0, *args, **options):

"""Return the roots of the (non-linear) equations

defined by func(x) = 0 given a starting estimate.

Uses scipy.optimize.fsolve, with extra error-checking.

func: function to find the roots of

x0: scalar or array, initial guess

args: additional positional arguments are passed along to fsolve,

which passes them along to func

returns: solution as an array

"""

# make sure we can run the given function with x0

try:

func(x0, *args)

except Exception as e:

msg = """Before running scipy.optimize.fsolve, I tried

running the error function you provided with the x0

you provided, and I got the following error:"""

logger.error(msg)

raise(e)

# make the tolerance more forgiving than the default

underride(options, xtol=1e-6)

x0 = magnitude(x0)

# run fsolve

with units_off():

result = scipy.optimize.fsolve(func, x0, args=args, **options)

return result

def crossings(series, value):

"""Find the labels where the series passes through value.

The labels in series must be increasing numerical values.

series: Series

value: number

returns: sequence of labels

"""

interp = InterpolatedUnivariateSpline(series.index, series-value)

return interp.roots()

def interpolate(series, **options):

"""Creates an interpolation function.

series: Series object

options: any legal options to scipy.interpolate.interp1d

returns: function that maps from the index of the series to values

"""

# TODO: add error checking for nonmonotonicity

if sum(series.index.isnull()):

msg = """The Series you passed to interpolate contains

NaN values in the index, which would result in

undefined behavior. So I'm putting a stop to that."""

raise ValueError(msg)

# make the interpolate function extrapolate past the ends of

# the range, unless `options` already specifies a value for `fill_value`

underride(options, fill_value='extrapolate')

# call interp1d, which returns a new function object

interp_func = interp1d(series.index, series.values, **options)

units = getattr(series, 'units', None)

if units:

return lambda x: Quantity(interp_func(x), units)

else:

return interp_func

def interp_inverse(series, **options):

"""Interpolate the inverse function of a Series.

series: Series object, represents a mapping from `a` to `b`

kind: string, which kind of iterpolation

options: keyword arguments passed to interpolate

returns: interpolation object, can be used as a function

from `b` to `a`

"""

inverse = Series(series.index, index=series.values)

T = interpolate(inverse, **options)

return T

def unpack(series):

"""Make the names in `series` available as globals.

series: Series with variables names in the index

"""

# TODO: Make this a context manager, so the syntax is

# with series:

# and maybe even add an __exit__ that copies changes back

frame = inspect.currentframe()

caller = frame.f_back

caller.f_globals.update(series)

def source_code(obj):

"""Prints the source code for a given object.

obj: function or method object

"""

print(inspect.getsource(obj))

def underride(d, **options):

"""Add key-value pairs to d only if key is not in d.

If d is None, create a new dictionary.

d: dictionary

options: keyword args to add to d

"""

if d is None:

d = {}

for key, val in options.items():

d.setdefault(key, val)

return d

def plot(*args, **options):

"""Makes line plots.

args can be:

plot(y)

plot(y, style_string)

plot(x, y)

plot(x, y, style_string)

options are the same as for pyplot.plot

"""

# TODO: add lines to REPLOT_CACHE

x, y, style = parse_plot_args(*args, **options)

if isinstance(x, pd.DataFrame) or isinstance(y, pd.DataFrame):

raise ValueError("modsimpy.plot can't handle DataFrames.")

if x is None:

if isinstance(y, np.ndarray):

x = np.arange(len(y))

if isinstance(y, pd.Series):

x = y.index

y = y.values

x = magnitudes(x)

y = magnitudes(y)

underride(options, linewidth=3, alpha=0.6)

if style is not None:

lines = plt.plot(x, y, style, **options)

else:

lines = plt.plot(x, y, **options)

return lines

REPLOT_CACHE = {}

def replot(*args, **options):

"""

try:

label = options['label']

except KeyError:

raise ValueError('To use replot, you must provide a label argument.')

axes = plt.gca()

key = (axes, label)

if key not in REPLOT_CACHE:

lines = plot(*args, **options)

if len(lines) != 1:

raise ValueError('Replot only works with a single plotted element.')

REPLOT_CACHE[key] = lines[0]

return lines

line = REPLOT_CACHE[key]

x, y, style = parse_plot_args(*args, **options)

line.set_xdata(x)

line.set_ydata(y)

def parse_plot_args(*args, **options):

"""Parse the args the same way plt.plot does."""

x = None

y = None

style = None

if len(args) == 1:

y = args[0]

elif len(args) == 2:

if isinstance(args[1], str):

y, style = args

else:

x, y = args

elif len(args) == 3:

x, y, style = args

return x, y, style

def contour(df, **options):

"""Makes a contour plot from a DataFrame.

Note: columns and index must be numerical

df: DataFrame

"""

x = df.columns

y = df.index

X, Y = np.meshgrid(x, y)

cs = plt.contour(X, Y, df, **options)

plt.clabel(cs, inline=1, fontsize=10)

def savefig(filename, **options):

"""Save the current figure.

Keyword arguments are passed along to plt.savefig

https://matplotlib.org/api/_as_gen/matplotlib.pyplot.savefig.html

filename: string

"""

print('Saving figure to file', filename)

plt.savefig(filename, **options)

def decorate(**options):

"""Decorate the current axes.

Call decorate with keyword arguments like

decorate(title='Title',

xlabel='x',

ylabel='y')

The keyword arguments can be any of the axis properties

https://matplotlib.org/api/axes_api.html

In addition, you can use `legend=False` to suppress the legend.

And you can use `loc` to indicate the location of the legend

(the default value is 'best')

"""

loc = options.pop('loc', 'best')

if options.pop('legend', True):

legend(loc=loc)

plt.gca().set(**options)

plt.tight_layout()

def legend(**options):

"""Draws a legend only if there is at least one labeled item.

options are passed to plt.legend()

https://matplotlib.org/api/_as_gen/matplotlib.pyplot.legend.html

"""

underride(options, loc='best')

ax = plt.gca()

handles, labels = ax.get_legend_handles_labels()

ax.legend(handles, labels, **options)

def remove_from_legend(bad_labels):

"""Removes some labels from the legend.

bad_labels: sequence of strings

"""

ax = plt.gca()

handles, labels = ax.get_legend_handles_labels()

handle_list, label_list = [], []

for handle, label in zip(handles, labels):

if label not in bad_labels:

handle_list.append(handle)

label_list.append(label)

ax.legend(handle_list, label_list)

# TODO: Either finish SubPlots or remove it

class SubPlots:

def __init__(self, fig, axes_seq):

self.fig = fig

self.axes_seq = axes_seq

self.current_axes_index = 0

def current_axes(self):

return self.axes_seq(self.current_axes_index)

# TODO: consider making SubPlots iterable

def next_axes(self):

self.current_axes_index += 1

return self.current_axes()

def subplots(*args, **options):

fig, axes_seq = plt.subplots(*args, **options)

return SubPlots(fig, axes_seq)

def subplot(nrows, ncols, plot_number, **options):

figsize = {(2, 1): (8, 8),

(3, 1): (8, 10)}

key = nrows, ncols

default = (8, 5.5)

width, height = figsize.get(key, default)

plt.subplot(nrows, ncols, plot_number, **options)

fig = plt.gcf()

fig.set_figwidth(width)

fig.set_figheight(height)

class ModSimSeries(pd.Series):

"""Modified version of a Pandas Series,

with a few changes to make it more suited to our purpose.

In particular:

1. I provide a more consistent __init__ method.

2. Series provides two special variables called

`dt` and `T` that cause problems if we try to use those names

as variables. I override them so they can be used variable names.

3. Series doesn't provide a good _repr_html, so it doesn't look

good in Jupyter notebooks.

4. ModSimSeries provides a set() method that takes keyword arguments.

"""

def __init__(self, *args, **kwargs):

"""Initialize a Series.

Note: this cleans up a weird Series behavior, which is

that Series() and Series([]) yield different results.

See: https://github.com/pandas-dev/pandas/issues/16737

"""

if args or kwargs:

underride(kwargs, copy=True)

super().__init__(*args, **kwargs)

else:

super().__init__([], dtype=np.float64)

def _repr_html_(self):

"""Returns an HTML representation of the series.

Mostly used for Jupyter notebooks.

"""

df = pd.DataFrame(self.values, index=self.index, columns=['values'])

return df._repr_html_()

def __copy__(self, deep=True):

series = super().copy(deep=deep)

return self.__class__(series)

copy = __copy__

def set(self, **kwargs):

"""Uses keyword arguments to update the Series in place.

Example: series.set(a=1, b=2)

"""

for name, value in kwargs.items():

self[name] = value

@property

def dt(self):

"""Intercept the Series accessor object so we can use `dt`

as a row label and access it using dot notation.

https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.dt.html

"""

return self.loc['dt']

@property

def T(self):

"""Intercept the Series accessor object so we can use `T`

as a row label and access it using dot notation.

https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.T.html

"""

return self.loc['T']

def get_first_label(series):

"""Returns the label of the first element."""

return series.index[0]

def get_last_label(series):

"""Returns the label of the first element."""

return series.index[-1]

def get_index_label(series, i):

"""Returns the ith label in the index."""

return series.index[i]

def get_first_value(series):

"""Returns the value of the first element."""

return series.values[0]

def get_last_value(series):

"""Returns the value of the first element."""

return series.values[-1]

def gradient(series):

"""Computes the numerical derivative of a series."""

a = np.gradient(series, series.index)

return TimeSeries(a, series.index)

class TimeSeries(ModSimSeries):

"""Represents a mapping from times to values."""

pass

class SweepSeries(ModSimSeries):

"""Represents a mapping from parameter values to metrics."""

pass

class System(ModSimSeries):

"""Contains system variables and their values.

Takes keyword arguments and stores them as rows.

"""

def __init__(self, *args, **kwargs):

"""Initialize the series.

If there are no positional arguments, use kwargs.

If there is one positional argument, copy it and add

in the kwargs.

More than one positional argument is an error.

"""

if len(args) == 0:

super().__init__(list(kwargs.values()), index=kwargs)

elif len(args) == 1:

super().__init__(*args, copy=True)

self.set(**kwargs)

else:

msg = '__init__() takes at most one positional argument'

raise TypeError(msg)

class State(System):

"""Contains state variables and their values.

Takes keyword arguments and stores them as rows.

"""

pass

class Condition(System):

"""Represents the condition of a system.

Condition objects are often used to construct a System object.

"""

pass

class Params(System):

"""Represents a set of parameters.

"""

pass

def compute_abs_diff(seq):

xs = np.asarray(seq)

diff = np.ediff1d(xs, np.nan)

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ModSimPy/code/modsim.py at master · gitMilan/ModSimPy · GitHub

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