Tutorial¶

from curves import Derivative Curves ======

as Identity (eye)¶

>>> from curves import Curve, lin
>>> eye = Curve()

>>> eye(123.456)
123.456

>>> f = eye + 5
>>> f(10)
15

>>> set(eye(x) - x  for x in lin(-5, 5))
{0}

as Constants¶

>>> from curves import Curve

>>> f = Curve(1) + Curve(7)
>>> f(123.456)
8

>>> f = eye + Curve(7)
>>> f(3)
10

as Functions¶

>>> from math import exp, pi
>>> exp = Curve(exp)
>>> exp
exp

>>> exp(1.)
2.718281828459045

such prepared functions are available as

>>> from curves import Curve, lin
>>> from curves.functions import sin, cos
>>> sin
sin

>>> f = sin ** 2 + cos ** 2
>>> f
sin ** 2 + cos ** 2

>>> f(123.456)
1.0

>>> set(round(f(x), 12) for x in lin(-pi, pi))
{1.0}

as Variables¶

>>> from curves import X  #  same as Curves('X')
>>> X
X

used to build polynomials

>>> p = X ** 2 + 2 * X - 3
>>> p
X ** 2 + 2 * X - 3

>>> p(1)
0

>>> p(-1)
-4

Compositions¶

>>> from math import exp, sqrt, pi, log
>>> from curves import Curve
>>> exp = Curve(exp)
>>> exp
exp

>>> X = Curve('X')
>>> X
X

>>> f = exp(X)  # same as exp @ X
>>> f
exp(X)

>>> phi = 1 / sqrt(2 * pi) * exp(-(X ** 2) / 2)  # std normal density
>>> phi(0)
0.3989422804014327

>>> phi(1)
0.24197072451914337

>>> g = exp @ log
>>> round(g(123.456), 12)
123.456

Inplace Operations¶

>>> from curves import X

>>> X += 2
>>> X
X + 2

>>> X(1)
3

>>> X -= 2
>>> X
X

>>> X(1)
1

>>> X -= 2
>>> X
X - 2

>>> X(1)
-1

Operators¶

Derivative¶

>>> from curves import Curve, Integral, Derivative, plotter

>>> f = Curve('X') ** 2
>>> df = Derivative(f)
>>> df(6)
12.0...

Integral¶

>>> F = Integral(f, a=0)
>>> F(6)
72.0...

>>> plotter[-5: 5](f, Derivative(f), Integral(f))

Plotting¶

>>> from math import sqrt, pi

>>> from curves import Curve, X, plot, lin
>>> from curves.functions import exp, sin, cos, ramp, step
>>> from curves.operators import Integral, Derivative

set x values

>>> x = lin(-5, 5, num=500)  # x values from -1 to 1

define the function

>>> std_norm_pdf = 1 / sqrt(2 * pi) * exp(-(X ** 2) / 2)

and plot it

>>> plot(x, phi=std_norm_pdf)

as simple as

>>> plot(x, sin, -sin, cos, -cos)

And even labels with LaTeX labels are possible

>>> curves = {r"$\phi(t)$": std_norm_pdf,
...           r"$\Phi(t)$": Integral(std_norm_pdf, -10)}
>>> plot(x, **curves, ylim=[-1/2, 3/2], figsize=(10, 5))

$_images/latex.png$

or

>>> f = X ** 2
>>> curves = {
...     r"$\phi(t)$": std_norm_pdf,
...     f"${str(f).replace(' ** ', '^')}$": f,
...     r"$\sin(t)$": (1 + sin) / 4
... }
>>> plot(x, **curves, ylim=[-1/2, 3/2], figsize=(10, 5))

and so

>>> from matplotlib import pyplot as plt

>>> x = lin(-1, 2)
>>> plt.figure(figsize=(10, 5))
>>> plt.subplot(121)
>>> plot(x, ramp, Derivative(ramp), ylim=[-1, 2], aspect=True, show=False)
>>> plt.subplot(122)
>>> plot(x, step, Integral(step), ylim=[-1, 2], aspect=True, show=False)