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Re: The possibility integration in Python without an equation, just an array-like file

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  Re: The possibility integration in Python without an equation, just an array-like file Johannes Schneider <johannes.schneider@galileo-press.de> - 2014-05-16 17:01 +0200
    Re: The possibility integration in Python without an equation, just an array-like file duncan smith <buzzard@invalid.invalid> - 2014-05-16 19:01 +0100

#71664 — Re: The possibility integration in Python without an equation, just an array-like file

If you do not have a closed form for T(E) you cannot calculate the exact 
value of I(V).

Anyway. Assuming T is integrable you can approximate I(V).

1. Way to do:
interpolate T(E) by a polynomial P and integrate P. For this you need 
the equation (coefficients and exponents) of P. Integrating is easy 
after that.

2. other way:
Use Stair-functions: you can approximate the Value of IV() by the sum 
over T(E_i) * (E_{i+1} - E_i) s.t. E_0 = E_F-\frac{eV}{2} and E_n = 
E_F+\frac{eV}{2}.


3 one more way:
use a computer algebra system like sage.

bg,
Johannes

On 16.05.2014 10:49, Enlong Liu wrote:
> Dear All,
>
> I have a question about the integration with Python. The equation is as
> below:
> and I want to get values of I with respect of V. E_F is known. But for
> T(E), I don't have explicit equation, but a .dat file containing
> two columns, the first is E, and the second is T(E). It is also in the
> attachment for reference. So is it possible to do integration in Python?
>
> Thanks a lot for your help!
>
> Best regards,
> ​
>
> --
> Faculty of Engineering@K.U. Leuven
> BIOTECH@TU Dresden
> Email:liuenlong20@gmail.com <mailto:liuenlong20@gmail.com>;
> enlong.liu@student.kuleuven.be <mailto:enlong.liu@student.kuleuven.be>;
> enlong.liu@biotech.tu-dresden.de <mailto:enlong.liu@biotech.tu-dresden.de>
> Mobile Phone: +4917666191322
> Mailing Address: Zi. 0108R, Budapester Straße 24, 01069, Dresden, Germany
>
>



-- 
Johannes Schneider
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johannes.schneider@galileo-press.de
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#71667

On 16/05/14 16:01, Johannes Schneider wrote:
> If you do not have a closed form for T(E) you cannot calculate the exact
> value of I(V).
>
> Anyway. Assuming T is integrable you can approximate I(V).
>
> 1. Way to do:
> interpolate T(E) by a polynomial P and integrate P. For this you need
> the equation (coefficients and exponents) of P. Integrating is easy
> after that.
>
> 2. other way:
> Use Stair-functions: you can approximate the Value of IV() by the sum
> over T(E_i) * (E_{i+1} - E_i) s.t. E_0 = E_F-\frac{eV}{2} and E_n =
> E_F+\frac{eV}{2}.
>

snip]

Or piecewise polynomials (splines).

Duncan

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