func
func
Various analytical functions for testing the methods.
- quinn.func.funcs.blundell(xx, datanoise=0.0)[source]
Classical example from Blundell et al. [1].
\[f(x)=x+0.3 \sin(2\pi(x+\sigma\:{\cal N}(0,1)))+0.3 \sin(4\pi(x+\sigma\:{\cal N}(0,1)))+\sigma\:{\cal N}(0,1)\]- Parameters:
xx (np.ndarray) – Input array \(x\) of size (N,d).
datanoise (float, optional) – Standard deviation \(\sigma\) of i.i.d. gaussian noise, both on the input and output.
- Returns:
Output array of size (N,d).
- Return type:
np.ndarray
Note
This function is typically used in d=1 setting.
- quinn.func.funcs.Sine(xx, datanoise=0.0)[source]
Simple sum of sines function
\[f(x)=\sin(x_1)+...+\sin(x_d) + \sigma \: {\cal N} (0,1)\]- Parameters:
xx (np.ndarray) – Input array \(x\) of size (N,d).
datanoise (float, optional) – Standard deviation \(\sigma\) of i.i.d. gaussian noise.
- Returns:
Output array of size (N,1).
- Return type:
np.ndarray
- quinn.func.funcs.Summation(xx, datanoise=0.0)[source]
Summation function.
\[f(x)=x_1 + x_2 + \dots + x_d + \sigma \: {\cal N} (0,1)\]- Parameters:
xx (np.ndarray) – Input array \(x\) of size (N,d).
datanoise (float, optional) – Standard deviation \(\sigma\) of i.i.d. gaussian noise, both on the input and output.
- Returns:
Output array of size (N,d).
- Return type:
np.ndarray
- quinn.func.funcs.Sine10(xx, datanoise=0.02)[source]
Sum of sines function with 10 outputs
\[\begin{split}f_1(x)=\sin(x_1)+...+\sin(x_d) + \sigma \: {\cal N} (0,1)\\ \dots \qquad\qquad\qquad\qquad\\ f_{10}(x)=\sin(x_1)+...+\sin(x_d) + \sigma \: {\cal N} (0,1)\end{split}\]- Parameters:
xx (np.ndarray) – Input array \(x\) of size (N,d).
datanoise (float, optional) – Standard deviation \(\sigma\) of i.i.d. gaussian noise.
- Returns:
Output array of size (N,10).
- Return type:
np.ndarray
- quinn.func.funcs.Ackley(x, datanoise=0.02)[source]
Ackley4 or Modified Ackley function from https://arxiv.org/pdf/1308.4008v1.pdf.
\[f(x)=\sum_{i=1}^{d-1} \left(\exp(-0.2)\sqrt{x_i^2+x_{i+1}^2} + 3 (\cos{2x_i}+\sin{2x_{i+1}})\right) + \sigma \: {\cal N} (0,1)\]- Parameters:
xx (np.ndarray) – Input array \(x\) of size (N,d).
datanoise (float, optional) – Standard deviation \(\sigma\) of i.i.d. gaussian noise.
- Returns:
Output array of size (N,1).
- Return type:
np.ndarray