Arrays

New in version 1.8.0: from Jonny Saunders, Ryan Ly, and Chris Mungall #1887, linkml-model#181

---

We can divide data types into a few abstract forms (see “Recognizing Structural Forms”). Linked data tools regularly handle scalars, lists, tables, graphs, and trees, but less commonly handle multidimensional arrays. The LinkML metamodel has first-class support to specify them, and its generators are growing first-class support to make those specifications work with array formats and libraries that people actually use.

Types

There are two types of array specification in LinkML:

• NDArrays - “regular” dense multidimensional arrays with shape and dtype constraints

• Coming Soon Labeled Arrays - arrays that use additional arrays as their indices (eg. a set of temperature measurements indexed by latitude and longitude).

NDArrays

Show code cell content Hide code cell content

from linkml.generators import PydanticGenerator
from linkml_runtime.loaders.yaml_loader import YAMLLoader
from linkml_runtime.dumpers.yaml_dumper import YAMLDumper
from IPython.display import display, Markdown
from pathlib import Path
import numpy as np
from rich.console import Console
from rich.theme import Theme
from rich.style import Style
from rich.color import Color

theme = Theme({
    "repr.call": Style(color=Color.from_rgb(110,191,38), bold=True),
    "repr.attrib_name": Style(color="slate_blue1"),
    "repr.number": Style(color="deep_sky_blue1"),
    
})
console = Console(theme=theme)

schemas = Path('.').resolve().parent / '_includes' / 'arrays'

COMPARISON = """
:::::{{tab-set}}
::::{{tab-item}} LinkML
:::{{code-block}} yaml
{linkml}
:::
::::
::::{{tab-item}} pydantic - LoL
:::{{code-block}} python
{pydantic_lol}
:::
::::
::::{{tab-item}} numpydantic
:::{{code-block}} python
{pydantic_npd}
::: 
::::
:::::
"""

def render_module(path, representation='list'):
    generator = PydanticGenerator(str(path), array_representations=[representation])
    module = generator.render()
    return module
    
def compile_module(path, representation='list'):
    generator = PydanticGenerator(str(path), array_representations=[representation])
    module = generator.compile_module()
    return module

def render_class(path, cls, representation='list') -> str:
    module = render_module(path, representation)
    cls = module.classes[cls]
    code = cls.render(black=True)
    return code

def render_comparison(path, cls, string=False) -> str:
    if not isinstance(cls, list):
        cls = [cls]
        
    path = str(path)
    sch = YAMLLoader().load_as_dict(path)
    class_strs = []
    pydantic_strs = []
    npd_strs = []
    
    for a_cls in cls:
        class_def = sch['classes'][a_cls]
        class_def = {a_cls: class_def}
        class_strs.append(YAMLDumper().dumps(class_def))
        pydantic_strs.append(render_class(path, a_cls))
        npd_strs.append(render_class(path, a_cls, representation='numpydantic'))
        
    class_str = "\n".join(class_strs)
    pydantic_str = "\n".join(pydantic_strs)
    npd_str = "\n".join(npd_strs)
    md = COMPARISON.format(linkml=class_str, pydantic_lol=pydantic_str, pydantic_npd=npd_str)
    if string:
        return md
    else:
        display(Markdown(md))
    

NDArrays are a slot-level feature - they augment the usual slot range syntax with an array property.

For example, A class with a data slot which consists of array of integers between 2 and 5 dimensions and its PydanticGenerator array representations look like:

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sch = schemas / 'example.yaml'
render_comparison(sch, 'MyClass')
example_mod = compile_module(sch)
MyClass = getattr(example_mod, 'MyClass')

LinkML

MyClass:
  attributes:
    data:
      range: integer
      array:
        minimum_number_dimensions: 3
        maximum_number_dimensions: 5

pydantic - LoL

class MyClass(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "example"})

    data: Optional[Union[List[List[List[int]]], List[List[List[List[int]]]], List[List[List[List[List[int]]]]]]] = (
        Field(
            default=None,
            json_schema_extra={
                "linkml_meta": {
                    "alias": "data",
                    "array": {"maximum_number_dimensions": 5, "minimum_number_dimensions": 3},
                    "domain_of": ["MyClass"],
                }
            },
        )
    )

numpydantic

class MyClass(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "example"})

    data: Optional[
        Union[NDArray[Shape["*, *, *"], int], NDArray[Shape["*, *, *, *"], int], NDArray[Shape["*, *, *, *, *"], int]]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "data",
                "array": {"maximum_number_dimensions": 5, "minimum_number_dimensions": 3},
                "domain_of": ["MyClass"],
            }
        },
    )

The generated pydantic model can validate all the constraints of the array, serialize it to JSON, and everything else that you’d expect from a pydantic model.

This model correctly validates:

model = MyClass(data=np.ones((5,4,3), dtype=int))
console.print(model)

MyClass(
    data=[
        [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
        [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
        [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
        [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
        [[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]]
    ]
)

But an array with the wrong shape doesn’t:

try:
    MyClass(data=np.ones((1,)))
except Exception as e:
    console.print(e)

Show code cell output Hide code cell output

3 validation errors for MyClass
data.list[list[list[int]]].0
  Input should be a valid list [type=list_type, input_value=1.0, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0
  Input should be a valid list [type=list_type, input_value=1.0, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0
  Input should be a valid list [type=list_type, input_value=1.0, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type

Nor does an array with the wrong type

try:
    MyClass(data=np.random.rand(5,4,3))
except Exception as e:
    console.print(e)

Show code cell output Hide code cell output

180 validation errors for MyClass
data.list[list[list[int]]].0.0.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.36233636819171644, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.0.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.217152298707722, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.0.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6858206989325767, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.1.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.7891735774391294, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.1.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6744892954230731, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.1.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9224301421625795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.2.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.767340513509762, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.2.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.03886717683238927, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.2.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.956820302383326, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.3.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9128771378708389, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.3.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.5170218971685141, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].0.3.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.053137012447675325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.0.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.10293740303989585, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.0.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.7638142564038325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.0.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.15503776574263017, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.1.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9215052746215283, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.1.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.49757261609987335, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.1.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.37909013689001037, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.2.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9088962155150846, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.2.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.5749639236125221, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.2.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.8979019992668682, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.3.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.41552844134205535, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.3.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.35363465174994224, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].1.3.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.8560346943983752, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.0.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.5643950808764403, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.0.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.21746592100388518, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.0.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.2450109402856454, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.1.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.5198211375062816, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.1.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.7773606029679785, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.1.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.08316625236493425, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.2.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6962957134529947, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.2.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.1597128068627085, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.2.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.7666390361417795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.3.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.16505181685486747, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.3.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.8534090454812723, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].2.3.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.2201842194571081, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.0.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.04754925021915235, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.0.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.2880783907540432, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.0.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6146475362262824, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.1.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.49514263005932635, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.1.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.4157474095959117, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.1.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9649935802619418, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.2.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.44694954680644483, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.2.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.4555962411298127, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.2.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.8539541521148573, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.3.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.14599295179188, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.3.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.2764068976690558, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].3.3.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9299288043519114, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.0.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6585414359682743, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.0.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.3437321938486534, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.0.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9469743857109924, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.1.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.023613416842737656, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.1.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9726810845232208, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.1.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.021232860751145388, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.2.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.8308394966594216, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.2.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9343449908831468, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.2.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.6903038003688691, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.3.0
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.164917824048866, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.3.1
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.9589671128259276, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[int]]].4.3.2
  Input should be a valid integer, got a number with a fractional part [type=int_from_float, 
input_value=0.7503093444900333, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/int_from_float
data.list[list[list[list[int]]]].0.0.0
  Input should be a valid list [type=list_type, input_value=0.36233636819171644, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.0.1
  Input should be a valid list [type=list_type, input_value=0.217152298707722, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.0.2
  Input should be a valid list [type=list_type, input_value=0.6858206989325767, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.1.0
  Input should be a valid list [type=list_type, input_value=0.7891735774391294, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.1.1
  Input should be a valid list [type=list_type, input_value=0.6744892954230731, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.1.2
  Input should be a valid list [type=list_type, input_value=0.9224301421625795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.2.0
  Input should be a valid list [type=list_type, input_value=0.767340513509762, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.2.1
  Input should be a valid list [type=list_type, input_value=0.03886717683238927, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.2.2
  Input should be a valid list [type=list_type, input_value=0.956820302383326, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.3.0
  Input should be a valid list [type=list_type, input_value=0.9128771378708389, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.3.1
  Input should be a valid list [type=list_type, input_value=0.5170218971685141, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].0.3.2
  Input should be a valid list [type=list_type, input_value=0.053137012447675325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.0.0
  Input should be a valid list [type=list_type, input_value=0.10293740303989585, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.0.1
  Input should be a valid list [type=list_type, input_value=0.7638142564038325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.0.2
  Input should be a valid list [type=list_type, input_value=0.15503776574263017, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.1.0
  Input should be a valid list [type=list_type, input_value=0.9215052746215283, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.1.1
  Input should be a valid list [type=list_type, input_value=0.49757261609987335, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.1.2
  Input should be a valid list [type=list_type, input_value=0.37909013689001037, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.2.0
  Input should be a valid list [type=list_type, input_value=0.9088962155150846, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.2.1
  Input should be a valid list [type=list_type, input_value=0.5749639236125221, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.2.2
  Input should be a valid list [type=list_type, input_value=0.8979019992668682, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.3.0
  Input should be a valid list [type=list_type, input_value=0.41552844134205535, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.3.1
  Input should be a valid list [type=list_type, input_value=0.35363465174994224, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].1.3.2
  Input should be a valid list [type=list_type, input_value=0.8560346943983752, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.0.0
  Input should be a valid list [type=list_type, input_value=0.5643950808764403, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.0.1
  Input should be a valid list [type=list_type, input_value=0.21746592100388518, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.0.2
  Input should be a valid list [type=list_type, input_value=0.2450109402856454, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.1.0
  Input should be a valid list [type=list_type, input_value=0.5198211375062816, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.1.1
  Input should be a valid list [type=list_type, input_value=0.7773606029679785, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.1.2
  Input should be a valid list [type=list_type, input_value=0.08316625236493425, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.2.0
  Input should be a valid list [type=list_type, input_value=0.6962957134529947, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.2.1
  Input should be a valid list [type=list_type, input_value=0.1597128068627085, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.2.2
  Input should be a valid list [type=list_type, input_value=0.7666390361417795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.3.0
  Input should be a valid list [type=list_type, input_value=0.16505181685486747, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.3.1
  Input should be a valid list [type=list_type, input_value=0.8534090454812723, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].2.3.2
  Input should be a valid list [type=list_type, input_value=0.2201842194571081, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.0.0
  Input should be a valid list [type=list_type, input_value=0.04754925021915235, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.0.1
  Input should be a valid list [type=list_type, input_value=0.2880783907540432, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.0.2
  Input should be a valid list [type=list_type, input_value=0.6146475362262824, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.1.0
  Input should be a valid list [type=list_type, input_value=0.49514263005932635, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.1.1
  Input should be a valid list [type=list_type, input_value=0.4157474095959117, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.1.2
  Input should be a valid list [type=list_type, input_value=0.9649935802619418, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.2.0
  Input should be a valid list [type=list_type, input_value=0.44694954680644483, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.2.1
  Input should be a valid list [type=list_type, input_value=0.4555962411298127, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.2.2
  Input should be a valid list [type=list_type, input_value=0.8539541521148573, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.3.0
  Input should be a valid list [type=list_type, input_value=0.14599295179188, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.3.1
  Input should be a valid list [type=list_type, input_value=0.2764068976690558, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].3.3.2
  Input should be a valid list [type=list_type, input_value=0.9299288043519114, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.0.0
  Input should be a valid list [type=list_type, input_value=0.6585414359682743, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.0.1
  Input should be a valid list [type=list_type, input_value=0.3437321938486534, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.0.2
  Input should be a valid list [type=list_type, input_value=0.9469743857109924, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.1.0
  Input should be a valid list [type=list_type, input_value=0.023613416842737656, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.1.1
  Input should be a valid list [type=list_type, input_value=0.9726810845232208, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.1.2
  Input should be a valid list [type=list_type, input_value=0.021232860751145388, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.2.0
  Input should be a valid list [type=list_type, input_value=0.8308394966594216, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.2.1
  Input should be a valid list [type=list_type, input_value=0.9343449908831468, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.2.2
  Input should be a valid list [type=list_type, input_value=0.6903038003688691, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.3.0
  Input should be a valid list [type=list_type, input_value=0.164917824048866, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.3.1
  Input should be a valid list [type=list_type, input_value=0.9589671128259276, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[int]]]].4.3.2
  Input should be a valid list [type=list_type, input_value=0.7503093444900333, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.0.0
  Input should be a valid list [type=list_type, input_value=0.36233636819171644, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.0.1
  Input should be a valid list [type=list_type, input_value=0.217152298707722, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.0.2
  Input should be a valid list [type=list_type, input_value=0.6858206989325767, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.1.0
  Input should be a valid list [type=list_type, input_value=0.7891735774391294, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.1.1
  Input should be a valid list [type=list_type, input_value=0.6744892954230731, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.1.2
  Input should be a valid list [type=list_type, input_value=0.9224301421625795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.2.0
  Input should be a valid list [type=list_type, input_value=0.767340513509762, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.2.1
  Input should be a valid list [type=list_type, input_value=0.03886717683238927, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.2.2
  Input should be a valid list [type=list_type, input_value=0.956820302383326, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.3.0
  Input should be a valid list [type=list_type, input_value=0.9128771378708389, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.3.1
  Input should be a valid list [type=list_type, input_value=0.5170218971685141, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].0.3.2
  Input should be a valid list [type=list_type, input_value=0.053137012447675325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.0.0
  Input should be a valid list [type=list_type, input_value=0.10293740303989585, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.0.1
  Input should be a valid list [type=list_type, input_value=0.7638142564038325, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.0.2
  Input should be a valid list [type=list_type, input_value=0.15503776574263017, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.1.0
  Input should be a valid list [type=list_type, input_value=0.9215052746215283, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.1.1
  Input should be a valid list [type=list_type, input_value=0.49757261609987335, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.1.2
  Input should be a valid list [type=list_type, input_value=0.37909013689001037, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.2.0
  Input should be a valid list [type=list_type, input_value=0.9088962155150846, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.2.1
  Input should be a valid list [type=list_type, input_value=0.5749639236125221, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.2.2
  Input should be a valid list [type=list_type, input_value=0.8979019992668682, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.3.0
  Input should be a valid list [type=list_type, input_value=0.41552844134205535, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.3.1
  Input should be a valid list [type=list_type, input_value=0.35363465174994224, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].1.3.2
  Input should be a valid list [type=list_type, input_value=0.8560346943983752, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.0.0
  Input should be a valid list [type=list_type, input_value=0.5643950808764403, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.0.1
  Input should be a valid list [type=list_type, input_value=0.21746592100388518, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.0.2
  Input should be a valid list [type=list_type, input_value=0.2450109402856454, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.1.0
  Input should be a valid list [type=list_type, input_value=0.5198211375062816, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.1.1
  Input should be a valid list [type=list_type, input_value=0.7773606029679785, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.1.2
  Input should be a valid list [type=list_type, input_value=0.08316625236493425, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.2.0
  Input should be a valid list [type=list_type, input_value=0.6962957134529947, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.2.1
  Input should be a valid list [type=list_type, input_value=0.1597128068627085, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.2.2
  Input should be a valid list [type=list_type, input_value=0.7666390361417795, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.3.0
  Input should be a valid list [type=list_type, input_value=0.16505181685486747, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.3.1
  Input should be a valid list [type=list_type, input_value=0.8534090454812723, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].2.3.2
  Input should be a valid list [type=list_type, input_value=0.2201842194571081, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.0.0
  Input should be a valid list [type=list_type, input_value=0.04754925021915235, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.0.1
  Input should be a valid list [type=list_type, input_value=0.2880783907540432, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.0.2
  Input should be a valid list [type=list_type, input_value=0.6146475362262824, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.1.0
  Input should be a valid list [type=list_type, input_value=0.49514263005932635, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.1.1
  Input should be a valid list [type=list_type, input_value=0.4157474095959117, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.1.2
  Input should be a valid list [type=list_type, input_value=0.9649935802619418, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.2.0
  Input should be a valid list [type=list_type, input_value=0.44694954680644483, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.2.1
  Input should be a valid list [type=list_type, input_value=0.4555962411298127, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.2.2
  Input should be a valid list [type=list_type, input_value=0.8539541521148573, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.3.0
  Input should be a valid list [type=list_type, input_value=0.14599295179188, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.3.1
  Input should be a valid list [type=list_type, input_value=0.2764068976690558, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].3.3.2
  Input should be a valid list [type=list_type, input_value=0.9299288043519114, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.0.0
  Input should be a valid list [type=list_type, input_value=0.6585414359682743, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.0.1
  Input should be a valid list [type=list_type, input_value=0.3437321938486534, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.0.2
  Input should be a valid list [type=list_type, input_value=0.9469743857109924, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.1.0
  Input should be a valid list [type=list_type, input_value=0.023613416842737656, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.1.1
  Input should be a valid list [type=list_type, input_value=0.9726810845232208, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.1.2
  Input should be a valid list [type=list_type, input_value=0.021232860751145388, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.2.0
  Input should be a valid list [type=list_type, input_value=0.8308394966594216, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.2.1
  Input should be a valid list [type=list_type, input_value=0.9343449908831468, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.2.2
  Input should be a valid list [type=list_type, input_value=0.6903038003688691, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.3.0
  Input should be a valid list [type=list_type, input_value=0.164917824048866, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.3.1
  Input should be a valid list [type=list_type, input_value=0.9589671128259276, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type
data.list[list[list[list[list[int]]]]].4.3.2
  Input should be a valid list [type=list_type, input_value=0.7503093444900333, input_type=float64]
    For further information visit https://errors.pydantic.dev/2.10/v/list_type

Array Library Integration

The most basic kind of array annotations that the pydantic generator can produce are “list of list” style arrays, but most practical uses of arrays require specialized array libraries.

The PydanticGenerator also supports generating array annotations with numpydantic, which allows you to use a single model with an extensible set of array libraries.

To generate numpydantic-style array annotations:

PydanticGenerator('my_schema.yaml', array_representations=['numpydantic'])

Which yields a model like this (and see the examples throughout the rest of this page)

from pydantic import BaseModel
from numpydantic import NDArray, Shape

class MyModel(BaseModel):
    array: NDArray[Shape["3 x, 4 y, * z"], int]

Then use it as you please:

import numpy as np
import dask.array as da
import zarr

# numpy
model = MyModel(array=np.zeros((3, 4, 5), dtype=int))
# dask
model = MyModel(array=da.zeros((3, 4, 5), dtype=int))
# hdf5 datasets
model = MyModel(array=('data.h5', '/nested/dataset'))
# zarr arrays
model = MyModel(array=zarr.zeros((3,4,5), dtype=int))
model = MyModel(array='data.zarr')
model = MyModel(array=('data.zarr', '/nested/dataset'))
# video files
model = MyModel(array="data.mp4")

This makes it possible for your schema to be extremely implementation general - data formats and standards can support many array backends out of the box, reducing coupling between the abstract standard and its concrete implementation. More humble array users get powerful array modeling tools right from a yaml schema.

Tip

To use numpydantic arrays, you’ll need to add it as a dependency in your project.

Schema rendered with numpydantic arrays will include a module-level constant NUMPYDANTIC_VERSION which specifies the minimum version that it was designed for, but if you already depend on linkml in your project you can add the numpydantic extra (eg. pip install linkml[numpydantic]) which will give you a numpydantic dependency that matches the version supported by linkml.

Specification

NDArrays are defined by an ArrayExpression (metamodel docs)

An ArrayExpression has many of the default properties other LinkML expressions have – you can annotate your arrays like the rest of your data. To define the array, an ArrayExpression uses the following unique properties:

Shape

Shape can be specified numerically:

maximum_number_dimensions: int | False | None

Maximum (inclusive) number of dimensions.

When used with dimensions, to differentiate with being unset or None, needs to be set to False explicitly to indicate an “infinite”[1] number of dimensions (see Complex Shaped Arrays)

minimum_number_dimensions: int | None

Minimum (inclusive) number of dimensions.

exact_number_dimensions: int | None

An exact number of dimensions.

Equivalent to minimum_number_dimensions and maximum_number_dimensions being equal ints

dimensions: list[DimensionExpression]

Parameterization of individual dimensions (see below)

Dimensions

Dimensions can be further parameterized by defining dimensions with a list of DimensionExpressions, which accept:

alias: str | None

The name of the dimension

maximum_cardinality: int | None

The maximum size of this dimension (inclusive). If None, no maximum is set

minimum_cardinality: int | None

The minimum size of this dimension (inclusive). If None, no minimum is set

exact_cardinality: int | None

The exact size of this dimension. Equivalent to minimum_cardinality and maximum_cardinality being equal ints

Shape Forms

The combinations of the different ArrayExpression properties imply four NDArray forms:

• Any Shape - Arrays without limits to their shape

• Bounded Shape - Arrays with constraints on the number of dimensions without further parameterization

• Parameterized Shape - Arrays with parameterized dimensions

• Complex Shape - Arrays with both constraints on the number of dimensions and parameterized dimensions

Any

An Any shaped array can take any shape. This is the simplest array form, indicating the mere presence of an array.

An any shaped array is specified with an empty array dictionary:

LinkML

AnyType:
  attributes:
    array:
      range: AnyType
      array: {}

Typed:
  attributes:
    array:
      range: integer
      array: {}

pydantic - LoL

class AnyType(ConfiguredBaseModel):
    array: Optional[AnyShapeArray] = Field(None)

class Typed(ConfiguredBaseModel):
    array: Optional[AnyShapeArray[int]] = Field(None)

numpydantic

class AnyType(ConfiguredBaseModel):
    array: Optional[NDArray] = Field(None)

class Typed(ConfiguredBaseModel):
    array: Optional[NDArray[Any, int]] = Field(None)

The resulting pydantic models use a special AnyShapeArray class injected by pydanticgen’s template system when using the List of List (LoL) representation (see Representations).

Note

In the future, Any shape arrays might also be able to be specified with an explicit None value, e.g.:

MyClass:
  attributes:
    data:
      range: integer
      array:

This is a technical limitation in SchemaView - see linkml-model#189 and #1975

Bounded

We have already seen so-called “Bounded” shaped arrays, which don’t add any additional parameterization beyond the number of their dimensions.

The maximum_, minimum_, and exact_number_dimensions properties can be used in combination to indicate…

A minimum without a maximum, using the AnyShapeArray model internally -

Show code cell source Hide code cell source

sch = schemas / 'bounded_shape.yaml'
render_comparison(sch, 'MinDimensions')

LinkML

MinDimensions:
  attributes:
    array:
      range: integer
      array:
        minimum_number_dimensions: 2

pydantic - LoL

class MinDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[List[AnyShapeArray[int]]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"minimum_number_dimensions": 2},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

numpydantic

class MinDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[NDArray[Shape["*, *, ..."], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"minimum_number_dimensions": 2},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

A maximum without a minimum -

Show code cell source Hide code cell source

sch = schemas / 'bounded_shape.yaml'
render_comparison(sch, 'MaxDimensions')

LinkML

MaxDimensions:
  attributes:
    array:
      range: integer
      array:
        maximum_number_dimensions: 5

pydantic - LoL

class MaxDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[
        Union[
            List[int],
            List[List[int]],
            List[List[List[int]]],
            List[List[List[List[int]]]],
            List[List[List[List[List[int]]]]],
        ]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"maximum_number_dimensions": 5},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

numpydantic

class MaxDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[
        Union[
            NDArray[Shape["*"], int],
            NDArray[Shape["*, *"], int],
            NDArray[Shape["*, *, *"], int],
            NDArray[Shape["*, *, *, *"], int],
            NDArray[Shape["*, *, *, *, *"], int],
        ]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"maximum_number_dimensions": 5},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

An exact number of dimensions -

Show code cell source Hide code cell source

sch = schemas / 'bounded_shape.yaml'
render_comparison(sch, 'ExactDimensions')

LinkML

ExactDimensions:
  attributes:
    array:
      range: integer
      array:
        exact_number_dimensions: 3

pydantic - LoL

class ExactDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[List[List[List[int]]]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"exact_number_dimensions": 3},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

numpydantic

class ExactDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[NDArray[Shape["*, *, *"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"exact_number_dimensions": 3},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

And a range of dimensions -

Show code cell source Hide code cell source

sch = schemas / 'bounded_shape.yaml'
render_comparison(sch, 'RangeDimensions')

LinkML

RangeDimensions:
  attributes:
    array:
      range: integer
      array:
        minimum_number_dimensions: 2
        maximum_number_dimensions: 5

pydantic - LoL

class RangeDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[
        Union[List[List[int]], List[List[List[int]]], List[List[List[List[int]]]], List[List[List[List[List[int]]]]]]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"maximum_number_dimensions": 5, "minimum_number_dimensions": 2},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

numpydantic

class RangeDimensions(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "bounded_shape_array"})

    array: Optional[
        Union[
            NDArray[Shape["*, *"], int],
            NDArray[Shape["*, *, *"], int],
            NDArray[Shape["*, *, *, *"], int],
            NDArray[Shape["*, *, *, *, *"], int],
        ]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"maximum_number_dimensions": 5, "minimum_number_dimensions": 2},
                "domain_of": ["ExactDimensions", "MinDimensions", "MaxDimensions", "RangeDimensions"],
            }
        },
    )

Parameterized

Dimensions can be further parameterized, giving them names and cardinality constraints.

Similarly to bounded arrays, the following demonstrate setting a single-dimensional array with cardinality constraints…

Minimum cardinality:

Show code cell source Hide code cell source

sch = schemas / 'parameterized_shape.yaml'
render_comparison(sch, 'MinCard')

LinkML

MinCard:
  attributes:
    array:
      range: integer
      array:
        dimensions:
        - alias: min_card
          minimum_cardinality: 2

pydantic - LoL

class MinCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[conlist(min_length=2, item_type=int)] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "min_card", "minimum_cardinality": 2}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

numpydantic

class MinCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[NDArray[Shape["2-* min_card"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "min_card", "minimum_cardinality": 2}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

Maximum cardinality:

Show code cell source Hide code cell source

sch = schemas / 'parameterized_shape.yaml'
render_comparison(sch, 'MaxCard')

LinkML

MaxCard:
  attributes:
    array:
      range: integer
      array:
        dimensions:
        - alias: max_card
          maximum_cardinality: 5

pydantic - LoL

class MaxCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[conlist(max_length=5, item_type=int)] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "max_card", "maximum_cardinality": 5}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

numpydantic

class MaxCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[NDArray[Shape["*-5 max_card"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "max_card", "maximum_cardinality": 5}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

Exact cardinality:

Show code cell source Hide code cell source

sch = schemas / 'parameterized_shape.yaml'
render_comparison(sch, 'ExactCard')

LinkML

ExactCard:
  attributes:
    array:
      range: integer
      array:
        dimensions:
        - alias: max_card
          exact_cardinality: 3

pydantic - LoL

class ExactCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[conlist(min_length=3, max_length=3, item_type=int)] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "max_card", "exact_cardinality": 3}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

numpydantic

class ExactCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[NDArray[Shape["3 max_card"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "max_card", "exact_cardinality": 3}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

Cardinality range:

Show code cell source Hide code cell source

sch = schemas / 'parameterized_shape.yaml'
render_comparison(sch, 'RangeCard')

LinkML

RangeCard:
  attributes:
    array:
      range: integer
      array:
        dimensions:
        - alias: min_card
          minimum_cardinality: 2
          maximum_cardinality: 5

pydantic - LoL

class RangeCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[conlist(min_length=2, max_length=5, item_type=int)] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "min_card", "maximum_cardinality": 5, "minimum_cardinality": 2}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

numpydantic

class RangeCard(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[NDArray[Shape["2-5 min_card"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {"dimensions": [{"alias": "min_card", "maximum_cardinality": 5, "minimum_cardinality": 2}]},
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

And they can be used together, for example one can specify

A four dimensional array such that

• The first dimension has at least two items

• The second dimension has at most five items

• The third dimension has between two and five items

• The fourth dimension has exactly six items

Show code cell source Hide code cell source

sch = schemas / 'parameterized_shape.yaml'
render_comparison(sch, 'ParameterizedArray')
parameterized_mod = compile_module(sch)
ParameterizedArray = getattr(parameterized_mod, 'ParameterizedArray')

LinkML

ParameterizedArray:
  attributes:
    array:
      range: integer
      array:
        dimensions:
        - alias: min_card
          minimum_cardinality: 2
        - alias: max_card
          maximum_cardinality: 5
        - alias: range_card
          minimum_cardinality: 2
          maximum_cardinality: 5
        - alias: exact_card
          exact_cardinality: 6

pydantic - LoL

class ParameterizedArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[
        conlist(
            min_length=2,
            item_type=conlist(
                max_length=5,
                item_type=conlist(
                    min_length=2, max_length=5, item_type=conlist(min_length=6, max_length=6, item_type=int)
                ),
            ),
        )
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [
                        {"alias": "min_card", "minimum_cardinality": 2},
                        {"alias": "max_card", "maximum_cardinality": 5},
                        {"alias": "range_card", "maximum_cardinality": 5, "minimum_cardinality": 2},
                        {"alias": "exact_card", "exact_cardinality": 6},
                    ]
                },
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

numpydantic

class ParameterizedArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "parameterized_shape_array"})

    array: Optional[NDArray[Shape["2-* min_card, *-5 max_card, 2-5 range_card, 6 exact_card"], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [
                        {"alias": "min_card", "minimum_cardinality": 2},
                        {"alias": "max_card", "maximum_cardinality": 5},
                        {"alias": "range_card", "maximum_cardinality": 5, "minimum_cardinality": 2},
                        {"alias": "exact_card", "exact_cardinality": 6},
                    ]
                },
                "domain_of": ["MinCard", "MaxCard", "ExactCard", "RangeCard", "ParameterizedArray"],
            }
        },
    )

Which validates each of the constraints separately:

array = np.arange(4*1*2*6,dtype=int).reshape((4,1,2,6))
# array = np.ones((4,1,2,6), dtype=int)

console.print(ParameterizedArray(array=array))

ParameterizedArray(
    array=[
        [[[0, 1, 2, 3, 4, 5], [6, 7, 8, 9, 10, 11]]],
        [[[12, 13, 14, 15, 16, 17], [18, 19, 20, 21, 22, 23]]],
        [[[24, 25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35]]],
        [[[36, 37, 38, 39, 40, 41], [42, 43, 44, 45, 46, 47]]]
    ]
)

Complex

Complex NDArrays combine all three of the prior forms.

For example:

An array with between 5 and 7 dimensions such that…

• The first dimension has at least two items

• The second dimension has at most five items

• The third dimension has between two and five items

• The fourth dimension has exactly six items

Show code cell source Hide code cell source

sch = schemas / 'complex_shape.yaml'
render_comparison(sch, 'ComplexRangeShapeArray')

LinkML

ComplexRangeShapeArray:
  attributes:
    array:
      range: integer
      array:
        minimum_number_dimensions: 5
        maximum_number_dimensions: 7
        dimensions:
        - alias: max_card
          maximum_cardinality: 5
        - alias: min_card
          minimum_cardinality: 2
        - alias: range_card
          minimum_cardinality: 2
          maximum_cardinality: 5
        - alias: exact_card
          exact_cardinality: 6

pydantic - LoL

class ComplexRangeShapeArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "complex_shape_array"})

    array: Optional[
        conlist(
            max_length=5,
            item_type=conlist(
                min_length=2,
                item_type=conlist(
                    min_length=2,
                    max_length=5,
                    item_type=conlist(
                        min_length=6, max_length=6, item_type=Union[List[int], List[List[int]], List[List[List[int]]]]
                    ),
                ),
            ),
        )
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [
                        {"alias": "max_card", "maximum_cardinality": 5},
                        {"alias": "min_card", "minimum_cardinality": 2},
                        {"alias": "range_card", "maximum_cardinality": 5, "minimum_cardinality": 2},
                        {"alias": "exact_card", "exact_cardinality": 6},
                    ],
                    "maximum_number_dimensions": 7,
                    "minimum_number_dimensions": 5,
                },
                "domain_of": [
                    "ComplexAnyShapeArray",
                    "ComplexMaxShapeArray",
                    "ComplexRangeShapeArray",
                    "ComplexExactShapeArray",
                ],
            }
        },
    )

numpydantic

class ComplexRangeShapeArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "complex_shape_array"})

    array: Optional[
        Union[
            NDArray[Shape["*-5 max_card, 2-* min_card, 2-5 range_card, 6 exact_card, *"], int],
            NDArray[Shape["*-5 max_card, 2-* min_card, 2-5 range_card, 6 exact_card, *, *"], int],
            NDArray[Shape["*-5 max_card, 2-* min_card, 2-5 range_card, 6 exact_card, *, *, *"], int],
        ]
    ] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [
                        {"alias": "max_card", "maximum_cardinality": 5},
                        {"alias": "min_card", "minimum_cardinality": 2},
                        {"alias": "range_card", "maximum_cardinality": 5, "minimum_cardinality": 2},
                        {"alias": "exact_card", "exact_cardinality": 6},
                    ],
                    "maximum_number_dimensions": 7,
                    "minimum_number_dimensions": 5,
                },
                "domain_of": [
                    "ComplexAnyShapeArray",
                    "ComplexMaxShapeArray",
                    "ComplexRangeShapeArray",
                    "ComplexExactShapeArray",
                ],
            }
        },
    )

The only place where the syntax of complex arrays differ is that minimum and maximum_number_dimensions are set at the length of the specified dimensions list by default. In order to specify an array with a fixed number of parameterized dimensions with an arbitrary number of additional dimensions, set maximum_number_dimensions to False :

Show code cell source Hide code cell source

sch = schemas / 'complex_shape.yaml'
render_comparison(sch, 'ComplexAnyShapeArray')

LinkML

ComplexAnyShapeArray:
  attributes:
    array:
      range: integer
      array:
        maximum_number_dimensions: false
        dimensions:
        - alias: max_card
          maximum_cardinality: 5

pydantic - LoL

class ComplexAnyShapeArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "complex_shape_array"})

    array: Optional[conlist(max_length=5, item_type=Union[AnyShapeArray[int], int])] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [{"alias": "max_card", "maximum_cardinality": 5}],
                    "maximum_number_dimensions": False,
                },
                "domain_of": [
                    "ComplexAnyShapeArray",
                    "ComplexMaxShapeArray",
                    "ComplexRangeShapeArray",
                    "ComplexExactShapeArray",
                ],
            }
        },
    )

numpydantic

class ComplexAnyShapeArray(ConfiguredBaseModel):
    linkml_meta: ClassVar[LinkMLMeta] = LinkMLMeta({"from_schema": "complex_shape_array"})

    array: Optional[NDArray[Shape["*-5 max_card, ..."], int]] = Field(
        default=None,
        json_schema_extra={
            "linkml_meta": {
                "alias": "array",
                "array": {
                    "dimensions": [{"alias": "max_card", "maximum_cardinality": 5}],
                    "maximum_number_dimensions": False,
                },
                "domain_of": [
                    "ComplexAnyShapeArray",
                    "ComplexMaxShapeArray",
                    "ComplexRangeShapeArray",
                    "ComplexExactShapeArray",
                ],
            }
        },
    )

Generators

Support

At release, only pydanticgen supports arrays, but arrays will be implemented gradually for the rest of the generators.

generator	representation	anyshape	bounded	parameterized	complex
pydantic	List of Lists	Y	Y	Y	Y
pydantic	Numpydantic	Y	Y	Y	Y
… (the rest of em)

Representations

Since arrays are unlike other data types in that they usually require some specialized libraries to handle them, and many formats don’t have a single canonical array type, generators may accommodate multiple array representations.

The basic representation supported by the pydantic generator is the “List of lists” style array representation. This can be used without any additional dependencies beyond pydantic.

Pydanticgen now also supports most common array libraries from a single annotation using numpydantic - a single array specification generates a single pydantic model, but the numpydantic numpydantic.NDArray type abstracts the validation process for an extensible set of array libraries. Use whatever you want as an array, why stop at numpy arrays - currently it also supports hdf5, zarr, video files, and also allows custom array interfaces via subclassing. See the numpydantic docs for more.

See each generator’s documentation page for a summary of the array representations they support.

Implementation Guidance

TODO

Implementation docs for arrays are forthcoming.

For now see ArrayRangeGenerator and ListOfListsArray as the reference implementation

See Also

• How-to: Multidimensional arrays - discussion about the problems with array specification in linked data

• Tricky Choices - Some further discussions of decisions made in the specification

References

• ArrayExpression metamodel specification

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[1]

Of course, Python has a recursion limit and every array library only supports a finite number of dimensions. Infinite in this case just means that the abstract specification sets no limit, and the implementations try and meet that as best they can.