#include <Fractals.h>
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| NewtonFractal (double detailFactor=1, double _min=-1.0, double _max=1.0, int _maxIter=100, double _tol=1e-5) |
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Matrix< double > | operator() () const |
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Newton fractals
- Examples
- numerics/TestFractals.cpp.
◆ NewtonFractal()
NewtonFractal::NewtonFractal |
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double |
detailFactor = 1 , |
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double |
_min = -1.0 , |
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double |
_max = 1.0 , |
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int |
_maxIter = 100 , |
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double |
_tol = 1e-5 |
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) |
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inline |
Default constructor
- Parameters
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detailFactor | determines how detailed the fractal is displayed |
_min | min value (chose from [-1, 1]) |
_max | max value (chose from [-1, 1]) |
_maxIter | number maximum iterations for newton algorithm |
_tol | tolerance used for newton algoirthm |
◆ fun()
static Matrix< double > NewtonFractal::fun |
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const Matrix< double > & |
x | ) |
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inlinestaticprivate |
Newton fractal function
$$ \begin{pmatrix} x_0^3 - 3x_0 \cdot x_1^2 - 1 \\ -x_1^3 + 3x_0^2 \cdot x_1 \end{pmatrix} $$
- Parameters
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- Returns
- evaluated value
◆ jac()
static Matrix< double > NewtonFractal::jac |
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const Matrix< double > & |
x | ) |
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inlinestaticprivate |
Helper, jacobian matrix of fun
$$ \begin{pmatrix} 3 x_0^2 x_1^2 & -6 x_0x_1\\ 6 x_0 x_1 & 3 x_0^2 - 3x_1^2 \end{pmatrix} $$
- Parameters
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x | current value (2 dimensional) |
- Returns
- 2 by 2 jacobian matrix evaluated in x
◆ operator()()
Matrix< double > NewtonFractal::operator() |
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const |
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inline |
◆ detail
double NewtonFractal::detail |
detail factor for approximation
◆ maxIter
int NewtonFractal::maxIter = 100 |
max number iterations for newton algorithm
◆ tol
double NewtonFractal::tol = 1e-5 |
tolerance used for newton algorithm
◆ xMax
double NewtonFractal::xMax = 1.0 |
◆ xMin
double NewtonFractal::xMin = -1.0 |
start and end value on x-axis
◆ yMax
double NewtonFractal::yMax = 1.0 |
◆ yMin
double NewtonFractal::yMin = -1.0 |
start and end value on y-axis
The documentation for this class was generated from the following file: