Advanced Topics

This section covers customization options beyond the basic fit() call: loading pre-computed control points as an initialization, pinning specific control points during training, and more. These features are useful when you have prior knowledge about the shape of the Bézier simplex or want to perform incremental refinement.

Initial control points

You can provide initial control points with a file. The file should contain a list of control points. The file format should be pickled pytorch (.pt), comma-separated values (.csv), tab-separated values (.tsv), JSON (.json), or YAML (.yml or .yaml).

Pickled PyTorch

See PyTorch documentation for details:

CSV

"(2, 0)", 0.0, 0.1
"(1, 1)", 1.0, 1.1
"(0, 2)", 2.0, 2.1

TSV

"(2, 0)"     0.0     0.1
"(1, 1)"     1.0     1.1
"(0, 2)"     2.0     2.1

JSON

{
  "(2, 0)": [0.0, 0.1],
  "(1, 1)": [1.0, 1.1],
  "(0, 2)": [2.0, 2.1]
}

YAML

(2, 0): [0.0, 0.1]
(1, 1): [1.0, 1.1]
(0, 2): [2.0, 2.1]

Partial training

Function fit() provides some arguments for partial training, i.e., train some of control points while the others are fixed.

import torch
import torch_bsf

ts = torch.tensor(  # parameters on a simplex
   [
      [8/8, 0/8],
      [7/8, 1/8],
      [6/8, 2/8],
      [5/8, 3/8],
      [4/8, 4/8],
      [3/8, 5/8],
      [2/8, 6/8],
      [1/8, 7/8],
      [0/8, 8/8],
   ]
)
xs = 1 - ts * ts  # values corresponding to the parameters

# Initialize 2D control points of a Bezier triangle of degree 3
init = {
   # index: value
   (3, 0): [0.0, 0.1],
   (2, 1): [1.0, 1.1],
   (1, 2): [2.0, 2.1],
   (0, 3): [3.0, 3.1],
}

# Or, generate random control points in [0, 1)
init = torch_bsf.bezier_simplex.rand(n_params=2, n_values=2, degree=3)

# Or, load control points from a file
init = torch_bsf.bezier_simplex.load("control_points.yml")

# Train the edge of a Bezier curve while its vertices are fixed
bs = torch_bsf.fit(
   params=ts,  # input observations (training data)
   values=xs,  # output observations (training data)
   init=init,  # initial values of control points
   fix=[[3, 0], [0, 3]],  # fix vertices of the Bezier curve
)

# Predict by the trained model
t = [
   [0.2, 0.8],
   [0.7, 0.3],
]
x = bs(t)
print(x)