Difference between revisions of "Timescalecalculus python library documentation"
(→Defining a time scale) |
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After extracting the files, open a Python instance in its folder and type | After extracting the files, open a Python instance in its folder and type | ||
<pre> >>> from timescalecalculus import *</pre> | <pre> >>> from timescalecalculus import *</pre> | ||
| − | == | + | ==Time scale basics== |
Right now, a [[time scale]] in this library can consist of only a finite list of numbers. Fraction types are available. | Right now, a [[time scale]] in this library can consist of only a finite list of numbers. Fraction types are available. | ||
| − | <pre>>>> ts=[1,2,3,4,5,6,7]</pre> | + | Let $\mathbb{T}=\left\{0,\dfrac{1}{3},\dfrac{1}{2},\dfrac{7}{9},1,2,3,4,5,6,7 \right\}$.<br /> |
| − | The [[forward jump]] $\sigma$ can be used: | + | <pre>>>> ts=[0,Fraction(1,3),Fraction(1,2),Fraction(7,9),1,2,3,4,5,6,7]</pre> |
| − | <pre>>>> sigma(3,ts) | + | The [[forward jump]] $\sigma$ can be used:<br /> |
| − | + | $\sigma(0)=\dfrac{1}{3}$ | |
| − | The [[backward jump]] $\rho$ can be used: | + | <pre>>>> sigma(0,ts) |
| + | Fraction(1, 3)</pre> | ||
| + | $\sigma(4)=5$ | ||
| + | <pre>>>> sigma(4,ts) | ||
| + | 5</pre> | ||
| + | $\sigma(7)=7$ | ||
| + | <pre>>>> sigma(7,ts) | ||
| + | 7</pre> | ||
| + | |||
| + | The [[backward jump]] $\rho$ can be used:<br /> | ||
| + | $\rho(1)=\dfrac{7}{9}$ | ||
| + | <pre>>>> rho(1,ts) | ||
| + | Fraction(7, 9)</pre> | ||
| + | $\rho(3)=2$ | ||
<pre>>>> rho(3,ts) | <pre>>>> rho(3,ts) | ||
2</pre> | 2</pre> | ||
| + | $\rho(0)=0$ | ||
| + | <pre>>>> rho(0,ts) | ||
| + | 0</pre> | ||
The [[delta derivative]] works as expected. The delta derivative of a constant is zero: | The [[delta derivative]] works as expected. The delta derivative of a constant is zero: | ||
<pre>>>> dderivative(lambda x: 1,5,ts) | <pre>>>> dderivative(lambda x: 1,5,ts) | ||
Revision as of 06:22, 23 December 2016
This is the documentation for the Python repository timescalecalculus.
The basics
After extracting the files, open a Python instance in its folder and type
>>> from timescalecalculus import *
Time scale basics
Right now, a time scale in this library can consist of only a finite list of numbers. Fraction types are available.
Let $\mathbb{T}=\left\{0,\dfrac{1}{3},\dfrac{1}{2},\dfrac{7}{9},1,2,3,4,5,6,7 \right\}$.
>>> ts=[0,Fraction(1,3),Fraction(1,2),Fraction(7,9),1,2,3,4,5,6,7]
The forward jump $\sigma$ can be used:
$\sigma(0)=\dfrac{1}{3}$
>>> sigma(0,ts) Fraction(1, 3)
$\sigma(4)=5$
>>> sigma(4,ts) 5
$\sigma(7)=7$
>>> sigma(7,ts) 7
The backward jump $\rho$ can be used:
$\rho(1)=\dfrac{7}{9}$
>>> rho(1,ts) Fraction(7, 9)
$\rho(3)=2$
>>> rho(3,ts) 2
$\rho(0)=0$
>>> rho(0,ts) 0
The delta derivative works as expected. The delta derivative of a constant is zero:
>>> dderivative(lambda x: 1,5,ts) 0
and obeying the delta derivative of squaring function, we see
>>> dderivative(lambda x: x*x,5,ts) 11
The delta exponential is supported. For example if $\mathbb{T}=\{1,2,3,4,5,6,7\}$ then $e_1(3,1)=(1+\mu(1))(1+\mu(2))=(2)(2)=4$ which is correctly computed:
>>> dexpf(lambda x: 1, 3, 1, ts) 4
