Problems P1-P7
These seven problems are introduced studied in the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
- dcgpy.generate_P1()
Generates the problem P1 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = x^5 - \pi x^3 + x\]x is sampled in ten equally spaced points in [1,3].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P1() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P2()
Generates the problem P2 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = x^5 - \pi x^3 + \frac{\pi}{x}\]x is sampled in ten equally spaced points in [0.1,5].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P2() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P3()
Generates the problem P3 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = \frac{e x^5 + x^3}{x+1}\]x is sampled in ten equally spaced points in [-0.9,1].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P3() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P4()
Generates the problem P4 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = \sin(\pi x) + \frac 1x\]x is sampled in ten equally spaced points in [-1,1].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P4() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P5()
Generates the problem P5 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = e x^5 - \pi x^3 + x\]x is sampled in ten equally spaced points in [1,3].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P5() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P6()
Generates the problem P6 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = \frac{e x^2 - 1}{\pi (x + 2)}\]x is sampled in ten equally spaced points in [-2.1,1].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P6() >>> plt.plot(X,Y, '.')
- dcgpy.generate_P7()
Generates the problem P7 from the paper:
Izzo, Dario, Francesco Biscani, and Alessio Mereta. “Differentiable genetic programming.” European Conference on Genetic Programming. Springer, 2017.
The functional form of such a problem is:
\[y = \cos(\pi x) + \sin(e x)\]x is sampled in ten equally spaced points in [-1,1].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_P7() >>> plt.plot(X,Y, '.')