Shear gp meeting 04/03

Recap of meeting 03 / 04

Clarification

Recall a similar definition of \(\beta\) with units, the unitless version is

\[\beta \equiv \frac{-1}{4L} \ln \rho\] So \[\rho \equiv \exp(-4L \beta)\] where \(L\) is the extent of the features

Normalization

 L = np.sqrt(
  (x.max() - x.min() + 1) ** 2 + \
  (y.max() - y.min() + 1) ** 2
) 

to reflect that we assume isotropic features

Kernel plots ...

Progress with Cython code ...

• \(\kappa\kappa\) kernel can be imported
• can be sampled
• probably buggy
• debug before implementing the rest of the kernels

Cython and Python Kernel plot comparison

Same coordinates, slightly different values

Other Python kernel plots

Weird features disappeared

Blue is for positive definiteness

\(Cov(\kappa, \gamma_1)\) is weird

Next steps for debugging

• go through Cython implementation
• plan how to test pieces of Cython implementation
• test Python implementation for groups of terms

more thoughts needed for next step

• modify the gradient function of the new Cython kernels