kitpylib.PyMath package

kitpylib.PyMath package#

Module contents#

Submodules#

kitpylib.PyMath.findroot module#

kitpylib.PyMath.findroot.bisection(f, a, b, e, showtimes=False)#

BISECTION#

A function to find roots of f(x)=0 by bisection method. f(a) and f(b) cannot have the same signs.

Parameters#

ffunc

f must be continuous. Python function returning a number.

afloat

Start of the bracketing interval [a,b].

bfloat

End of the bracketing interval [a,b].

efloat

Accuracy

showtimesbool. The default is False.

Show how many times the calculator use to find the root.

Returns#

iterations:

Returns if showtimes is True.

rootfloat

Root of f between a and b.

Examples#

Precise value:

>>> f = lambda x: x**2-1
>>> root = bisection(f, 0, 2, 0.01)
>>> root
1.0

Errors:

>>> root = bisection(f, -2, 2, 0.01)
ValueError: Incorrect input!

Approximate value:

>>> g = lambda x: -x**3-3*x+5
>>> root = bisection(g, 1, 2, 0.01)
>>> root
1.1484375

showtimes is True:

>>> bisection(g, 1, 2, 0.01, showtimes=True)
Finding root in 7 times.
1.1484375

kitpylib.PyMath.mathfuncs module#

kitpylib.PyMath.spf1d module#

class kitpylib.PyMath.spf1d.PC(f, px1, py1)#

Bases: object

== This is a class of the calculation of pedal curves.

Parameters#

f(function), px1, py1(x, y of the point)

Returns#

a, b: x, y of the function

x, y: x, y of pedal curves

Example#

>>> f = lambda x: x**2-1
>>> a = PC(f, 0, 0)
>>> a.a
array([-5.       , -4.9989999, -4.9979998, ...,  4.9979998,  4.9989999,
        5.       ])
kitpylib.PyMath.spf1d.diff1st(f0, x, h=0.01)#

This is the 1st order derivative of a function.

\[f'(x)=(f(x + h) - f(x - h))/(2*h)\]
kitpylib.PyMath.spf1d.diff2nd(f0, x, h=0.01)#

This is the 2nd order derivative of a function.

\[f''(x)=(f(x-h)-2*f(x)+f(x+h))/(h*h)\]

kitpylib.PyMath.spf2d module#

A module for 2d special functions.

kitpylib.PyMath.spf2d.gaus2d(x)#

The 2d Gaussian Function.

kitpylib.PyMath.spf2d.ramp2d(x)#

The 2d ramp function.

kitpylib.PyMath.spf2d.rect2d(x)#

The 2d rectangle function.

kitpylib.PyMath.spf2d.sign2d(x)#

The 2d sign function.

kitpylib.PyMath.spf2d.sinc2d(x)#

The 2d sinc function.

kitpylib.PyMath.spf2d.step2d(x)#

The 2d step function.

kitpylib.PyMath.spf2d.tri2d(x)#

The 2d triangle function.

kitpylib.PyMath.spf3d module#

A module for 3d special functions.

kitpylib.PyMath.spf3d.gaus3d(x, y)#

The 3d Gaussian Function.

kitpylib.PyMath.spf3d.ramp3d(x, y)#

The 3d ramp function.

kitpylib.PyMath.spf3d.rect3d(x, y)#

The 3d rectangle function.

kitpylib.PyMath.spf3d.sign3d(x, y)#

The 3d sign function.

kitpylib.PyMath.spf3d.sinc3d(x, y)#

The 3d sinc function.

kitpylib.PyMath.spf3d.step3d(x, y)#

The 3d step function.

kitpylib.PyMath.spf3d.tri3d(x, y)#

The 3d triangle function.

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