The FieldML Evaluator Graph¶

A Document is more than a mesh — it's a graph of named evaluators. This notebook walks through the evaluator subtypes and how they compose.

In [ ]:

from pyfieldml import datasets

doc = datasets.load_unit_cube()

from pyfieldml import datasets doc = datasets.load_unit_cube()

Types vs evaluators¶

A Document contains:

• Types: BooleanType, EnsembleType, ContinuousType, MeshType.
• Evaluators: the graph that produces values over those types.

In [ ]:

print("Types:")
for name in doc.region.continuous:
    print("  continuous :", name)
for name in doc.region.ensembles:
    print("  ensemble   :", name)
for name in doc.region.meshes:
    print("  mesh       :", name)

print("Types:") for name in doc.region.continuous: print(" continuous :", name) for name in doc.region.ensembles: print(" ensemble :", name) for name in doc.region.meshes: print(" mesh :", name)

Evaluator subtypes¶

Count by kind:

In [ ]:

from collections import Counter

kinds = Counter(type(ev).__name__ for ev in doc.region.evaluators.values())
for k, n in kinds.items():
    print(f"  {k:25s}  x{n}")

from collections import Counter kinds = Counter(type(ev).__name__ for ev in doc.region.evaluators.values()) for k, n in kinds.items(): print(f" {k:25s} x{n}")

Probing a coordinate field¶

Even a unit cube has a full evaluator graph you can probe at any parametric location:

In [ ]:

import numpy as np

coords = doc.field("coordinates")
xi = np.array([[0.25, 0.25, 0.25], [0.5, 0.5, 0.5], [0.75, 0.75, 0.75]])
for point in xi:
    val = coords.evaluate(element=1, xi=point)
    print(f"xi={point}  ->  {val}")

import numpy as np coords = doc.field("coordinates") xi = np.array([[0.25, 0.25, 0.25], [0.5, 0.5, 0.5], [0.75, 0.75, 0.75]]) for point in xi: val = coords.evaluate(element=1, xi=point) print(f"xi={point} -> {val}")

Jacobians¶

For a unit-cube mesh the identity map means the Jacobian is the identity matrix everywhere:

In [ ]:

J = coords.jacobian(element=1, xi=(0.5, 0.5, 0.5))
print("Jacobian at centroid:")
print(J)

J = coords.jacobian(element=1, xi=(0.5, 0.5, 0.5)) print("Jacobian at centroid:") print(J)