Computational Photonics

Dr. Thomas Kaiser

Tools for Scientific Computing

• MATLAB – commercial (and expensive!)

– high level language

– focus on linear algebra (MATrix LABoratory)

– excellent IDE, but buggy graphics

– many specialized toolboxes

• Octave (GNU Clone of MATLAB) – free software

– high level language, quasi-identical to MATLAB

– same core features, less specials

– less comfortable IDE

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Tools for Scientific Computing

• Python 3 – free software

– high level, general purpose language

– excellent IDEs and developing tools (Spyder, Ipython, Jupyter)

– becomes de facto standard for scientific computing and data science

– many packages with excellent functionalities (SciPy, NumPy, matplotlib, ...)

– Distributions manage packages (updates etc) recommended: Anaconda (has all recommended tools above on board)

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Tools for Scientific Computing

• MATLAB, Octave and Python are Interpreter

languages!

• Compiler languages for scientific computing:

– C / C++

– Fortran

– [Java, C#, ObjectPascal, Basic, ...]

• Compiled programs are usually faster in runtime,

but slower in development

• Solution: using pre-compiled numerical core

routines (LAPACK/BLAS, Intel MKL, FFTW, ...)

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Recap / Quick Intro: MATLAB Syntax

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see live presentation / syntax recap material

Recap: Basic Numerical Operations

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see also m-file with live presentation of high-level concepts

and tasks for self-studying recap online

Differentiation

• left-, right-sided, central, higher order, ...

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Integration

• Rectangle, Gaussian, Simpson quadrature, ...

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Root finding

• Bisection, Secant method, Newton method, ...

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secant method regula falsi

Finding extremal points

• Steepest descent, Downhill-Simplex, ...

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Linear system of equations

• Gauss-Jordan elimination, LU-decomposition,...

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Eigenvalues, -vectors

• Householder, QR method, ...

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Discrete Fourier Transform

• Fast Fourier Transform, Shannon-theorem, ...

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Ordinary Differential Eqations

• Euler, Runge-Kutta method, ...

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