ModSimPy/code/modsim.py at master · Bogidon/ModSimPy

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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')

# make sure we have Python 3.6 or better

import sys

if sys.version_info < (3, 6):

logger.warn('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=1.5)

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.integrate import odeint

from scipy.optimize import leastsq

from scipy.optimize import minimize_scalar

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

"""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(kwargs, 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, **kwargs)

if units:

array = array * units

return array

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

"""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` (at least approximately).

If you provide the keyword argument `endpoint=False`, the last value

in the array is `stop-step`.

start: first value

stop: last value

step: space between 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

"""

if stop is None:

stop = start

start = 0

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

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

underride(kwargs, endpoint=True)

# 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 kwargs['endpoint']:

n += 1

array = np.linspace(start, stop, int(n), **kwargs)

if units:

array = array * units

return array

def fit_leastsq(error_func, params, data, **kwargs):

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

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

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

kwargs: any other arguments are passed to leastsq

"""

# to pass `data` to `leastsq`, we have to put it in a tuple

args = (data,)

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

kwargs['full_output'] = True

# run leastsq

best_params, _, _, mesg, ier = leastsq(error_func, x0=params, args=args, **kwargs)

#TODO: check why logging.info is not visible

# check for errors

if ier in [1, 2, 3, 4]:

print("""modsim.py: scipy.optimize.leastsq ran successfully

and returned the following message:\n""" + mesg)

else:

logging.error("""modsim.py: When I ran scipy.optimize.leastsq, something

went wrong, and I got the following message:""")

raise Exception(mesg)

# return the best parameters

return best_params

@property

def dimensionality(self):

"""Unit's dimensionality (e.g. {length: 1, time: -1})

This is a simplified version of this method that does no caching.

returns: dimensionality

"""

dim = self._REGISTRY._get_dimensionality(self._units)

return dim

# monkey patch Unit and Quantity so they use the non-caching

# version of `dimensionality`

pint.unit._Unit.dimensionality = dimensionality

pint.quantity._Quantity.dimensionality = dimensionality

def units_off():

"""Make all quantities behave as if they were dimensionless.

"""

global SAVED_PINT_METHOD

SAVED_PINT_METHOD = UNITS._get_dimensionality

UNITS._get_dimensionality = lambda self: {}

def units_on():

"""Restore the saved behavior of quantities.

"""

UNITS._get_dimensionality = SAVED_PINT_METHOD

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

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

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: OptimizeResult object

(see https://docs.scipy.org/doc/scipy/

reference/generated/scipy.optimize.minimize_scalar.html)

"""

try:

midpoint = np.mean(bounds)

min_func(midpoint, *args)

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)

underride(options, xatol=1e-3)

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 returns is %s""" % res.message

raise Exception(msg)

return res

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

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

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: OptimizeResult object

(see https://docs.scipy.org/doc/scipy/

reference/generated/scipy.optimize.minimize_scalar.html)

"""

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 run_odeint(system, slope_func, **kwargs):

"""Runs a simulation of the system.

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

is an array or Series that specifies the time when the

solution will be computed.

Adds a DataFrame to the System: results

system: System object

slope_func: function that computes slopes

"""

# makes sure `system` contains `ts`

if not hasattr(system, 'ts'):

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

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

or Series that specifies the times when the

solution will be computed:"""

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`

units_off()

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

units_on()

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

# a TimeFrame with appropriate columns and index

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

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

"""

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

return interp1d(series.index, series.values, **options)

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

"""

frame = inspect.currentframe()

caller = frame.f_back

caller.f_globals.update(series)

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

"""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

x0 = np.asarray(x0).flatten()

try:

func(x0, *args)

except Exception as e:

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

running the 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(kwargs, xtol=1e-7)

# run fsolve

units_off()

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

units_on()

return result

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

class Simplot:

"""Provides a simplified interface to matplotlib."""

def __init__(self):

"""Initializes the instance variables."""

# map from Figure to FigureState

self.figure_states = dict()

def get_figure_state(self, figure=None):

"""Gets the state of the current figure.

figure: Figure

returns: FigureState object

"""

if figure is None:

figure = plt.gcf()

try:

return self.figure_states[figure]

except KeyError:

figure_state = FigureState()

self.figure_states[figure] = figure_state

return figure_state

SIMPLOT = Simplot()

class FigureState:

"""Encapsulates information about the current figure."""

def __init__(self):

# map from style tuple to Lines object

self.lines = dict()

def get_line(self, style, kwargs):

"""Gets the line object for a given style tuple.

style: Matplotlib style string

kwargs: dictionary of style options

returns: maplotlib.lines.Lines2D

"""

color = kwargs.get('color')

key = style, color

# if there's no style or color, make a new line,

# and don't store it for future updating.

if key == (None, None):

return self.make_line(style, kwargs)

# otherwise try to look it up, and if it's

# not there, make a new line and store it.

try:

return self.lines[key]

except KeyError:

line = self.make_line(style, kwargs)

self.lines[key] = line

return line

def make_line(self, style, kwargs):

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

if style is None:

lines = plt.plot([], **kwargs)

else:

lines = plt.plot([], style, **kwargs)

return lines[0]

def clear_lines(self):

self.lines = dict()

# TODO: Split plot into simplot(), which adds points to existing lines,

# and plot(), which does not

def plot(*args, **kwargs):

"""Makes line plots.

args can be:

plot(y)

plot(y, style_string)

plot(x, y)

plot(x, y, style_string)

kwargs are the same as for pyplot.plot

If x or y have attributes label and/or units,

label the axes accordingly.

"""

update = kwargs.pop('update', False)

x = None

y = None

style = None

# parse the args the same way plt.plot does:

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

if 'style' in kwargs:

style = kwargs.pop('style')

# get the current line, based on style and kwargs,

# or create a new empty line

figure = plt.gcf()

figure_state = SIMPLOT.get_figure_state(figure)

line = figure_state.get_line(style, kwargs)

# append y to ydata

if update:

ys = np.asarray(y)

else:

ys = line.get_ydata()

ys = np.append(ys, y)

line.set_ydata(ys)

# update xdata

xs = line.get_xdata()

if x is None:

# see if y is something like a Series that has an index

if hasattr(y, 'index'):

x = y.index

# if we still don't have an x, increment the last element of xs

if x is None:

try:

x = xs[-1] + 1

except IndexError:

x = 0

if update:

xs = np.asarray(x)

else:

xs = np.append(xs, x)

line.set_xdata(xs)

#print(line.get_xdata())

#print(line.get_ydata())

axes = plt.gca()

axes.relim()

axes.autoscale_view(True, True, True)

axes.margins(0.02)

figure.canvas.draw()

def contour(df, **options):

"""Makes a contour plot from a DataFrame.

Note: columns and index must be numerical

df: DataFrame

"""

x = results.columns

y = results.index

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

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

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

def newfig(**kwargs):

"""Creates a new figure."""

fig = plt.figure()

fig.set(**kwargs)

fig.canvas.draw()

def savefig(filename, *args, **kwargs):

"""Save the current figure.

filename: string

"""

print('Saving figure to file', filename)

return plt.savefig(filename, *args, **kwargs)

def label_axes(xlabel=None, ylabel=None, title=None, **kwargs):

"""Puts labels and title on the axes.

xlabel: string

ylabel: string

title: string

kwargs: options passed to pyplot

"""

ax = plt.gca()

ax.set_ylabel(ylabel, **kwargs)

ax.set_xlabel(xlabel, **kwargs)

if title is not None:

ax.set_title(title, **kwargs)

# TODO: consider setting labels automatically based on

# object attributes

# label the y axis

#label = getattr(y, 'label', 'y')

#units = getattr(y, 'units', 'dimensionless')

#plt.ylabel('%s (%s)' % (label, units))

xlabel = plt.xlabel

ylabel = plt.ylabel

xscale = plt.xscale

yscale = plt.yscale

xlim = plt.xlim

ylim = plt.ylim

title = plt.title

hlines = plt.hlines

vlines = plt.vlines

fill_between = plt.fill_between

class SubPlots:

def __init__(self, fig, axes_seq):

self.fig = fig

self.axes_seq = axes_seq

self.current_axes_index = 0

def current_axes():

return self.axes_seq(self.current_axes_index)

# TODO: consider making SubPlots iterable

def next_axes(self):

self.current_axes_index += 1

return current_axes()

def subplots(*args, **kwargs):

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

return SubPlots(fig, axes_seq)

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

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, **kwargs)

fig = plt.gcf()

fig.set_figwidth(width)

fig.set_figheight(height)

def legend(**kwargs):

underride(kwargs, loc='best')

plt.legend(**kwargs)

def nolegend():

# TODO

pass

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)

plt.legend(handle_list, label_list)

def decorate(**kwargs):

"""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

defined by Matplotlib. To see the list, run plt.getp(plt.gca())

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')

"""

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

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

legend(loc=loc)

plt.gca().set(**kwargs)

class Array(np.ndarray):

pass

class MySeries(pd.Series):

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, dtype=np.float64)

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, columns=['value'])

return df._repr_html_()

def set(self, **kwargs):

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

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

"""

for name, value in kwargs.items():

self[name] = value

class SweepSeries(MySeries):

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

"""

pass

class TimeSeries(MySeries):

pass

class System(MySeries):

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

"""Initialize the series.

If there are no positional arguments, use kwargs.

If there is one positional argument, copy it.

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)

# TODO: also copy in the kwargs?

else:

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

raise TypeError(msg)

@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#pandas.Series.T """

return self.loc['T']

class State(System):

pass

class Condition(System):

pass

def flip(p=0.5):

return np.random.random() < p

# abs, min, max, pow, sum, round

def abs(*args):