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tREADME.rst - numeric - C++ library with numerical algorithms |
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git clone git://src.adamsgaard.dk/numeric |
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tREADME.rst (4389B) |
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1 ============================================ |
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2 README: ODE integration with complex numbers |
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3 ============================================ |
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4 Exam exercise for *Numerical Methods* by Anders D. Christensen (mail_) |
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5 |
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6 File description |
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7 ---------------- |
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8 - ``Makefile``: Description for GNU Make, handles compilation and execut… |
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9 - ``README.rst`` (this file): Description of numeric implementation and … |
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10 Written with reStructuredText syntax. |
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11 - ``check.cpp``: Function for displaying the state of a condition to std… |
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12 - ``check.h``: Prototype for the check-function. |
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13 - ``functions.h``: Input functions to be evaluated. |
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14 - ``mainA.cpp``: Main source code file for part A. |
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15 - ``ode.cpp``: Constructor and functions for the ODE class, including Ru… |
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16 stepper and driver. |
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17 - ``ode.h``: Header file with the ODE class. This file must be included … |
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18 programs that want to utilize the ODE functionality. |
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19 - ``plot.gp``: Script for plotting all graphs with Gnuplot. |
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20 - ``typedefs.h``: Header file containing definitions of two main types, |
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21 ``Inttype``, a whole-number type, and ``Floattype``, a floating point … |
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22 type. The type definitions can be changed to different lengths and pre… |
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23 The program can be compiled for verbose output by changing the ``verbo… |
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24 variable. |
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25 - ``vector_arithmetic.h``: Operator overloading functions for the ``std:… |
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26 class. |
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27 |
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28 Problem descriptions |
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29 -------------------- |
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30 The four generated executables each demonstrate the ODE solvers function… |
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31 performing the following tasks. The results consist of the console outpu… |
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32 the corresponding plot with filename ``plot<Character>.png``. |
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33 - *A*: Construct an ODE solver that can handle functions with complex va… |
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34 Demonstrate that it solves the real component correctly, by stepping alo… |
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35 a path in the real range. |
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36 - *B*: Demonstrate that the ODE solver can solve the imaginary component… |
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37 stepping along a path in the imaginary range. |
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38 - *C*: Demonstrate the solution of a set of complex equations by stepping |
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39 through the complex plane. |
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40 - *D*: For an integration path in the complex plane, visualize how the |
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41 requirements of absolute- and relative precision are related to the numb… |
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42 integration steps, for a given floating point precision. |
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43 |
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44 Implementation |
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45 -------------- |
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46 This exercise was written in object-oriented C++ for easy reuse. For |
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47 portability, all included classes are from the standard template library. |
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48 |
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49 The necessary ``std::vector`` arithmetic operations where overloaded to … |
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50 element-wise operations, such as vector-scalar multiplication, vector-ve… |
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51 addition, etc. This approach was preferred over using ``std::valarray``,… |
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52 is not dynamically expandable. |
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53 |
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54 When creating a new ODE object, the user specifies the end-points of the… |
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55 range, where the specified system of ordinary differential equations with |
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56 complex values will be solved. The range end-points are complex numbers |
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57 themselves, and the user can thus specify whether the integrator steps t… |
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58 range of real values, imaginary values, or both components in the comple… |
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59 |
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60 The solver steps through the specified range by an adaptive step size, w… |
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61 also a complex number. The user specifies the fraction of the range to b… |
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62 as a start value for the step. The default value is 0.01. |
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63 |
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64 The ODE class contains functions for writing the ODE solution to stdout |
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65 (``ODE::print``) or to a text file (``ODE::write``). The output format i… |
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66 following; the first column is the real part of x, second column the ima… |
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67 part. The subsequent columns do in turn consist of real- and imaginary … |
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68 the variables in the ODE. |
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69 |
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70 The program requires a modern C++ compiler, GNU Make and Gnuplot. It has… |
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71 tested with GCC, Clang and llvm. |
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72 |
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73 Compiliation and execution |
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74 -------------------------- |
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75 To make and execute the program, go to the root folder and type `make`. … |
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76 will compile and execute the programs for part A-D, and plot output grap… |
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77 desired, individual parts can be compiled and executed using `make <Char… |
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78 |
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79 To view the source code in a browser with vim's syntax highlighting, typ… |
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80 html`, and view the files in the `html` folder. The generation of HTML f… |
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81 requires a newer vim for the source code files, and Docutils for the rea… |
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82 |
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83 All output and objects can be removed using `make clean`. |
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84 |
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85 |
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86 |
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87 .. _mail: mailto:[email protected] |
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88 |
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89 #vim: set tw=80 |
