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Practical Programming and Numerical Methods 2020.

NB

(12/8) Re-examination: those of you who did the exam the first time and just forgot to upload the link should simply upload the link to the university's examination server at the re-examination time; those of you who did not do the exam should find their project (using the same algorithm) in [this reshuffled list].
(2/6) Go ahead, the list of projects is ready.
(1/6) Tomorrow the list of examination projects (see the link above) will be reshuffled one last time. You will find the project assigned to you using the following algorithm: take the last two digits of your student-number and interpret it as a two-digit number, X; now, the index of your exercise is (X mod N) where N is the number of projects in the list, N equals the index of the last project plus one (since numbering starts with zero). If your student-number ends with 00, your project is #0, if your student-number ends with 01, your project is #1, ..., if your student-number ends with 21, your project is #21, if your student-number ends with 22, your project is #0, ...
Consider the examination project as yet another homework, only this time individually assigned. Check that 'make clean' cleans the project and 'make' builds it. Check that I will be able to see and clone your project without logging in.
If you want, you may create a short report in LaTeX. But you don't have to, if your output files and/or figures are indicative enough.

Send me an email if you need a clarification of the formulation of your poject.
(12/5) In your wiki page you must create a small table with the points that you have earned for the homeworks. Something like this:

A B C Σ_ABC

1 Interpolation 6 3 1 10

2 Linear Equations 5 1 0 6

... ... ... ... ...

10 Neural Networks 6 0 0 6

Total points 71
(12/5) An examination project from the (preliminary) list above will be assigned to you randomly in the beginning of the examination period. The project should be done in a separate, easily identifiable, directory (say, "Exam"). Consider it as just another homework problem. Do it with Makefile and everything like you did the homework problems.
(11/5) At the official examination time (2-3/6) you have to login to the examination server and upload the link to your repository as if it were your examination project. The actual deadline to finish your homeworks and your examination project is 21/6. Your last push should be no later than 21/6. In exceptional circumstances you might be able to get a few days dispensation (talk to me).
(4/3) The "path-to-dll" example is added to the "solutions". It shows how to run mono if your dlls are in different locations.
(3/3) The interface example "ivector3d" in now in the "solutions" folder.
(3/3) I have created a folder—"solutions", the link is above—where I am going to put examples of "perfect" solutions to exercises as I see it.
(28/2) Go to our Wiki page (linke above), put yourself in the ListOfParticipants, and create a link to your repository.
(26/2) The integrator quad.o8av[→] is slightly improved, I believe, so you might want to download the new version.
(30/1) The grey color of an item below indicates that the item is not yet finished.
(29/1) After the popular vote we go csharp-mono this year.
First meeting: 29/1

Schedule

F	Onsdag	12 - 15	Auditorium D4 (1531-219)	uge 5-14, 16-20
F	Fredag	13 - 16	Auditorium G1 (1532-116)	uge 5-14, 16-20

Plan

[→] Introduction: POSIX/UNIX systems; Programming languages; Free/Open software.
[→] Compiling, linking, and running programs with C#-mono; POSIX make utility and makefiles;
[→] Structure of a C#-program; Main method; Primitive types; Conditionals and loops; Scope of variables; Simple output.
[→] Arrays; Classes and structs; Vector class.
[→] Input/output: standard streams, redirections, piping; file streams; command-line arguments. Distributed version control systems; git.
[→] Scientific plots with gnuplot.
[→] Functional programming: passing functions as parameters (delegates, anonymous delegates, generic delegate System.Func, lambda expressions); Closures; Numerical integration routine quad.o8av;
[→] Passing functions as parameters part 2: ordinary differential equations (ODE): A Runge-Kutta ODE integration routine ode.rk23;
[→] Making scientific reports with LaTeX and Gnuplot: LaTex basics: math, figures; Gnuplot's cairolatex terminal.
Interpolation 1 [chapter.pdf] [problem "interpolation"]
- Polynomial interpolation;
- Spline interpolation: linear, quadratic, cubic splines;
- Object-oriented and functional programming styles.
Interpolation 2
- Sub-splines: Akima and monotone;
- Other forms of interpolation;
- Multivariate interpolation;
Linear equations [chapter.pdf] [problem "linear-equations"]
- Triangular systems, back-substitution, forward-substitution;
- QR-decomposition: modified Gram-Schmidt algorithm, Householder reflection algorithm, Givens rotation algorithm;
- LU-decomposition: Doolittle algorithm;
- Cholesky decomposition;
- Determinant of a matrix;
- Matrix inverse.
Ordinary least-squares problem [chapter.pdf] [problem "least-squares"]
- Least-squares problem;
- Least-squares solution with QR-decomposition;
- Ordinary least-squares fit; fit errors and covariance matrix.
Eigenvalue decomposition [chapter.pdf] [problem "eigenvalues"]
- Eigenvalues and eigenvectors;
- Eigenvalue decomposition;
- QR/QL algoritm;
- Jacobi eigenvalue algorithm;
- Rank-1 and Rank-2 updates of symmetric eigenvalue problem;
- Singular value decomposition;
Ordinary differential equations (ODE) - 1 [chapter.pdf] [problem "ODE"]
- One-step (Runge-Kutta) methods;
- Error estimate;
- Adaptive step-size strategy;
Ordinary differential equations (ODE) - 2
- Implicit, multi-step, and predictor-corrector methods;
Numerical integration (quadratures) - 1 [chapter.pdf] [problem "numerical integration"]
- Riemann sums: rectangle and trapezium rules;
- Quadratures with equally spaced abscissas (Newton-Cotes quadratures);
- Adaptive algorithms with equally spaced abscissas;
Numerical integration (quadratures) - 2
- Quadratures with optimized nodes (Gauss quadratures);
- Variable transformation quadratures;
Nonlinear equations / root-finding [chapter.pdf] [problem "Roots"]
- Modified Newton's method with backtracking linesearch;
- Quasi-Newton methods: Broyden update;
Minimization - 1/2 [chapter.pdf] [problem "Minimization"]
- Modified Newton's method with backtracking linesearch;
- Quasi-Newton methods: Broyden and SR1 updates;
Minimization - 2/2
- Dowhill simplex method (Nelder-Mead);
- Globally convergent methods;
Monte Carlo integration [chapter.pdf] [problem "Monte Carlo"]
- Plain Monte Carlo sampling;
- Stratified and Importance sampling;
- Quasi-random sequences;
Multiprocessing [chapter.pdf] [System.Threading] [dotnet parallel programming]
- Programs and threads; Multithreading;
- Symmetric multiprocessing;
- Parallel computing;
- Csharp tools for multiprocessing;
Artificial Neural Networks [Wikibook "Artificial Neural Networks"] [problem "Neural Network"]
- Artificial neurons and neural networks;
- Three-layer feed-forward neural networks; input, output, and hidden neurons;
- Network training;
Power methods and Kryslov subspaces (linear algebra) [chapter "Power methods"] [chapter "Eigenvalues"]
- Power and inverse iteration methods;
- Arnoldi and Lanczos methods;
- GMRES (Generalized Minimum RESidual) method for solving systems of linear equations.;
- Matrix updates;
Fast Fourier transform and applications [chapter "FFT"]
- Discrete Fourier Transform and applications
- Fast Fourier Transform: Danielson-Lanczos lemma and Cooley-Tukey algorithm;

References

D.V.Fedorov, Introduction to numerical methods, [1M pdf file].
Howto install mono on macOS [→];
Csharp syntax [→];
Csharp documentation from Microsoft [→];
Gnuplot documentation [→];
L^AT_EX wikibook [→];

	A	B	C	Σ_ABC
1 Interpolation	6	3	1	10
2 Linear Equations	5	1	0	6
...	...	...	...	...
10 Neural Networks	6	0	0	6
Total points				71