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API reference

polars-llm registers an llm namespace on every Polars expression. Import the package once and the namespace becomes available on any expression that resolves to a string column (the prompt).

import polars as pl
import polars_llm  # noqa: F401  — registers the `.llm` namespace

Chat verbs

Method Provider Mode
chat Any compatible client sync
achat Any compatible client async
openai OpenAI sync
aopenai OpenAI async
anthropic Anthropic sync
aanthropic Anthropic async
gemini Google Gemini sync
agemini Google Gemini async

Chat verbs return a Utf8 column with the model's response. With schema=, they return a struct column matching the Pydantic model.

Embedding verbs

Method Provider Mode
embed Any compatible client sync
aembed Any compatible client async
openai_embed OpenAI Embeddings sync
aopenai_embed OpenAI Embeddings async
gemini_embed Google Gemini sync
agemini_embed Google Gemini async

Embedding verbs return a List[Float64] column.

TypeSafe decision verbs

Method Provider Mode
typesafe TypeSafe System One sync
atypesafe TypeSafe System One async

The source expression is evaluated as TypeSafe state. Pass questions= with any mix of Choice, Score, and Noul questions. These methods return a nested struct with one answer field per question; with_metadata=True also includes the model, token usage, elapsed time, and error. Install them with pip install "polars-llm[typesafe]" on Python 3.10 or newer.

Vector helpers

Method Description
cosine Compute cosine similarity with another vector expression or a literal vector. No provider call is made.

Nearest-neighbor joins

polars_llm also registers an .ann namespace on DataFrames. Use df.ann.knn(other, ...) to return the closest rows from another DataFrame. Both vector columns must have matching dimensions and use List[Float32/64] or Array[Float32/64, dim] values.

polars_llm._ann.Ann

DataFrame namespace for approximate / exact nearest-neighbour joins.

Source code in polars_llm/_ann.py
@pl.api.register_dataframe_namespace("ann")
class Ann:
    """DataFrame namespace for approximate / exact nearest-neighbour joins."""

    def __init__(self, df: pl.DataFrame) -> None:
        self._df = df

    def knn(
        self,
        other: pl.DataFrame,
        *,
        on: str | None = None,
        left_on: str | None = None,
        right_on: str | None = None,
        k: int = 5,
        metric: Metric = "cosine",
        backend: Backend = "auto",
        flat: bool = True,
        suffix: str = "_right",
        rank_name: str = "rank",
        score_name: str = "score",
        **backend_kwargs: Any,
    ) -> pl.DataFrame:
        """Top-K nearest-neighbour join against ``other``.

        Each row in ``self`` is matched against ``other`` using the chosen
        ``metric``; the result holds the ``k`` closest neighbours per row.

        Parameters
        ----------
        other:
            The right-hand DataFrame to search.
        on, left_on, right_on:
            Vector column name(s). Use ``on="vector"`` when both DataFrames
            share the column name, otherwise pass ``left_on`` and ``right_on``.
        k:
            Number of neighbours to return. Clamped to ``len(other)``.
        metric:
            ``"cosine"`` (default), ``"ip"``, or ``"l2"``. Lower score = closer.
        backend:
            ``"auto"`` (brute force up to a few x 10^4 right rows, otherwise
            usearch when installed), ``"brute"``, or ``"usearch"``.
        flat:
            ``True`` (default) returns a flat join of ``len(self) * k`` rows
            with all columns from both sides plus ``rank`` / ``score``.
            ``False`` returns ``len(self)`` rows with a ``neighbors``
            ``List[Struct]`` column carrying the right-side rows.
        suffix:
            Collision suffix for right-side columns (only used when ``flat``).
        rank_name, score_name:
            Names of the rank/score columns added to the output.
        **backend_kwargs:
            Forwarded to ``usearch.index.Index`` (e.g. ``connectivity``,
            ``expansion_add``, ``expansion_search``, ``dtype``).
        """
        import numpy as np  # noqa: F401  -- ensures numpy is installed

        left_col, right_col = _resolve_keys(on, left_on, right_on)
        left_vec = _to_matrix(self._df, left_col)
        right_vec = _to_matrix(other, right_col)
        if left_vec.shape[1] != right_vec.shape[1]:
            raise ValueError(
                f"polars-llm: vector dim mismatch: left {left_vec.shape[1]} != right {right_vec.shape[1]}.",
            )
        if other.height == 0:
            raise ValueError("polars-llm: `other` is empty; cannot run knn.")
        if k < 1:
            raise ValueError(f"polars-llm: `k` must be >= 1, got {k}.")

        chosen = _pick_backend(backend, other.height)
        if chosen == "brute":
            indices, scores = _brute_search(left_vec, right_vec, k, metric)
        else:
            indices, scores = _usearch_search(left_vec, right_vec, k, metric, **backend_kwargs)

        return _assemble(
            self._df,
            other,
            indices,
            scores,
            flat=flat,
            suffix=suffix,
            rank_name=rank_name,
            score_name=score_name,
        )

knn(other, *, on=None, left_on=None, right_on=None, k=5, metric='cosine', backend='auto', flat=True, suffix='_right', rank_name='rank', score_name='score', **backend_kwargs)

Top-K nearest-neighbour join against other.

Each row in self is matched against other using the chosen metric; the result holds the k closest neighbours per row.

Parameters:

Name Type Description Default
other DataFrame

The right-hand DataFrame to search.

required
on str | None

Vector column name(s). Use on="vector" when both DataFrames share the column name, otherwise pass left_on and right_on.

None
left_on str | None

Vector column name(s). Use on="vector" when both DataFrames share the column name, otherwise pass left_on and right_on.

None
right_on str | None

Vector column name(s). Use on="vector" when both DataFrames share the column name, otherwise pass left_on and right_on.

None
k int

Number of neighbours to return. Clamped to len(other).

5
metric Metric

"cosine" (default), "ip", or "l2". Lower score = closer.

'cosine'
backend Backend

"auto" (brute force up to a few x 10^4 right rows, otherwise usearch when installed), "brute", or "usearch".

'auto'
flat bool

True (default) returns a flat join of len(self) * k rows with all columns from both sides plus rank / score. False returns len(self) rows with a neighbors List[Struct] column carrying the right-side rows.

True
suffix str

Collision suffix for right-side columns (only used when flat).

'_right'
rank_name str

Names of the rank/score columns added to the output.

'rank'
score_name str

Names of the rank/score columns added to the output.

'rank'
**backend_kwargs Any

Forwarded to usearch.index.Index (e.g. connectivity, expansion_add, expansion_search, dtype).

{}
Source code in polars_llm/_ann.py
def knn(
    self,
    other: pl.DataFrame,
    *,
    on: str | None = None,
    left_on: str | None = None,
    right_on: str | None = None,
    k: int = 5,
    metric: Metric = "cosine",
    backend: Backend = "auto",
    flat: bool = True,
    suffix: str = "_right",
    rank_name: str = "rank",
    score_name: str = "score",
    **backend_kwargs: Any,
) -> pl.DataFrame:
    """Top-K nearest-neighbour join against ``other``.

    Each row in ``self`` is matched against ``other`` using the chosen
    ``metric``; the result holds the ``k`` closest neighbours per row.

    Parameters
    ----------
    other:
        The right-hand DataFrame to search.
    on, left_on, right_on:
        Vector column name(s). Use ``on="vector"`` when both DataFrames
        share the column name, otherwise pass ``left_on`` and ``right_on``.
    k:
        Number of neighbours to return. Clamped to ``len(other)``.
    metric:
        ``"cosine"`` (default), ``"ip"``, or ``"l2"``. Lower score = closer.
    backend:
        ``"auto"`` (brute force up to a few x 10^4 right rows, otherwise
        usearch when installed), ``"brute"``, or ``"usearch"``.
    flat:
        ``True`` (default) returns a flat join of ``len(self) * k`` rows
        with all columns from both sides plus ``rank`` / ``score``.
        ``False`` returns ``len(self)`` rows with a ``neighbors``
        ``List[Struct]`` column carrying the right-side rows.
    suffix:
        Collision suffix for right-side columns (only used when ``flat``).
    rank_name, score_name:
        Names of the rank/score columns added to the output.
    **backend_kwargs:
        Forwarded to ``usearch.index.Index`` (e.g. ``connectivity``,
        ``expansion_add``, ``expansion_search``, ``dtype``).
    """
    import numpy as np  # noqa: F401  -- ensures numpy is installed

    left_col, right_col = _resolve_keys(on, left_on, right_on)
    left_vec = _to_matrix(self._df, left_col)
    right_vec = _to_matrix(other, right_col)
    if left_vec.shape[1] != right_vec.shape[1]:
        raise ValueError(
            f"polars-llm: vector dim mismatch: left {left_vec.shape[1]} != right {right_vec.shape[1]}.",
        )
    if other.height == 0:
        raise ValueError("polars-llm: `other` is empty; cannot run knn.")
    if k < 1:
        raise ValueError(f"polars-llm: `k` must be >= 1, got {k}.")

    chosen = _pick_backend(backend, other.height)
    if chosen == "brute":
        indices, scores = _brute_search(left_vec, right_vec, k, metric)
    else:
        indices, scores = _usearch_search(left_vec, right_vec, k, metric, **backend_kwargs)

    return _assemble(
        self._df,
        other,
        indices,
        scores,
        flat=flat,
        suffix=suffix,
        rank_name=rank_name,
        score_name=score_name,
    )

polars_llm.Llm

polars_llm.llm.Llm

Expression namespace for calling LLMs and embedding models per row.

Source code in polars_llm/llm.py
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@pl.api.register_expr_namespace("llm")
class Llm:
    """Expression namespace for calling LLMs and embedding models per row."""

    def __init__(self, prompt: pl.Expr) -> None:
        self._prompt = prompt

    # ---- input shaping ----
    def _input_struct(self, system: str | pl.Expr | None) -> pl.Expr:
        if system is None:
            sys_expr: pl.Expr = pl.lit(None, dtype=pl.Utf8)
        elif isinstance(system, pl.Expr):
            sys_expr = system.cast(pl.Utf8)
        else:
            sys_expr = pl.lit(str(system))
        return pl.struct(self._prompt.alias("prompt"), sys_expr.alias("system"))

    # ---- internal chat dispatch ----
    def _chat(
        self,
        chat: Any,
        *,
        system: str | pl.Expr | None,
        schema: Any | None,
        retries: int,
        backoff: float,
        cache: bool,
        with_metadata: bool,
        on_error: OnError,
    ) -> pl.Expr:
        if schema is not None:
            chat = chat.with_structured_output(schema)

        def runner(rows: list[tuple[Any, Any]]) -> list[dict[str, Any]]:
            return chat_batch_sync(chat, rows, retries=retries, backoff=backoff, cache=cache)

        return chat_map_batches(
            self._input_struct(system),
            runner,
            with_metadata=with_metadata,
            on_error=on_error,
            structured=schema is not None,
        )

    def _achat(
        self,
        chat: Any,
        *,
        system: str | pl.Expr | None,
        schema: Any | None,
        retries: int,
        backoff: float,
        max_concurrency: int | None,
        cache: bool,
        with_metadata: bool,
        on_error: OnError,
    ) -> pl.Expr:
        if schema is not None:
            chat = chat.with_structured_output(schema)

        def runner(rows: list[tuple[Any, Any]]) -> list[dict[str, Any]]:
            return _arun(
                chat_batch_async(
                    chat,
                    rows,
                    retries=retries,
                    backoff=backoff,
                    max_concurrency=max_concurrency,
                    cache=cache,
                ),
            )

        return chat_map_batches(
            self._input_struct(system),
            runner,
            with_metadata=with_metadata,
            on_error=on_error,
            structured=schema is not None,
        )

    # ---- internal embed dispatch ----
    def _embed(
        self,
        embedder: Any,
        *,
        retries: int,
        backoff: float,
        cache: bool,
        chunk_size: int | None,
        dim: int | None,
        with_metadata: bool,
        on_error: OnError,
    ) -> pl.Expr:
        def runner(texts: list[Any]) -> list[dict[str, Any]]:
            return embed_batch_sync(
                embedder,
                texts,
                retries=retries,
                backoff=backoff,
                cache=cache,
                chunk_size=chunk_size,
            )

        return embed_map_batches(
            self._prompt,
            runner,
            with_metadata=with_metadata,
            on_error=on_error,
            dim=dim,
        )

    def _aembed(
        self,
        embedder: Any,
        *,
        retries: int,
        backoff: float,
        max_concurrency: int | None,
        cache: bool,
        chunk_size: int | None,
        dim: int | None,
        with_metadata: bool,
        on_error: OnError,
    ) -> pl.Expr:
        def runner(texts: list[Any]) -> list[dict[str, Any]]:
            return _arun(
                embed_batch_async(
                    embedder,
                    texts,
                    retries=retries,
                    backoff=backoff,
                    max_concurrency=max_concurrency,
                    cache=cache,
                    chunk_size=chunk_size,
                ),
            )

        return embed_map_batches(
            self._prompt,
            runner,
            with_metadata=with_metadata,
            on_error=on_error,
            dim=dim,
        )

    # ---- internal TypeSafe dispatch ----
    def _typesafe(
        self,
        *,
        questions: Mapping[str, Any],
        model: str | None,
        client: Any,
        retries: int,
        backoff: float,
        cache: bool,
        with_metadata: bool,
        on_error: OnError,
        client_kwargs: dict[str, Any],
    ) -> pl.Expr:
        client_cls: Any = None if client is not None else _require("typesafe", TypeSafeClient, "typesafe")

        def runner(states: list[Any]) -> list[dict[str, Any]]:
            active_client = client if client is not None else client_cls(**client_kwargs)
            try:
                return typesafe_batch_sync(
                    active_client,
                    states,
                    questions=questions,
                    model=model,
                    retries=retries,
                    backoff=backoff,
                    cache=cache,
                )
            finally:
                if client is None:
                    active_client.close()

        return typesafe_map_batches(
            self._prompt,
            runner,
            questions=questions,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def _atypesafe(
        self,
        *,
        questions: Mapping[str, Any],
        model: str | None,
        client: Any,
        retries: int,
        backoff: float,
        max_concurrency: int | None,
        cache: bool,
        with_metadata: bool,
        on_error: OnError,
        client_kwargs: dict[str, Any],
    ) -> pl.Expr:
        client_cls: Any = None if client is not None else _require("typesafe", AsyncTypeSafeClient, "typesafe")

        async def run(states: list[Any]) -> list[dict[str, Any]]:
            active_client = client if client is not None else client_cls(**client_kwargs)
            try:
                return await typesafe_batch_async(
                    active_client,
                    states,
                    questions=questions,
                    model=model,
                    retries=retries,
                    backoff=backoff,
                    max_concurrency=max_concurrency,
                    cache=cache,
                )
            finally:
                if client is None:
                    await active_client.aclose()

        def runner(states: list[Any]) -> list[dict[str, Any]]:
            return _arun(run(states))

        return typesafe_map_batches(
            self._prompt,
            runner,
            questions=questions,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ============================================================
    # Public chat verbs
    # ============================================================

    # ---- Provider-agnostic ----
    def chat(
        self,
        *,
        client: Any,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
    ) -> pl.Expr:
        """Run chat completions with any LangChain-compatible client.

        ``client`` must provide ``invoke``. When ``schema`` is supplied it
        must also provide ``with_structured_output``. Use this method for
        providers without a dedicated convenience verb, or for custom and
        preconfigured chat clients.
        """
        return self._chat(
            client,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def achat(
        self,
        *,
        client: Any,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
    ) -> pl.Expr:
        """Run chat completions concurrently with any compatible client.

        ``client`` must provide ``ainvoke``. When ``schema`` is supplied it
        must also provide ``with_structured_output``.
        """
        return self._achat(
            client,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ---- OpenAI ----
    def openai(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run an OpenAI chat completion per row, sync."""
        chat = _make_chat("openai", model, client, model_kwargs)
        return self.chat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def aopenai(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run OpenAI chat completions concurrently across the batch."""
        chat = _make_chat("openai", model, client, model_kwargs)
        return self.achat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ---- Anthropic ----
    def anthropic(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run an Anthropic chat completion per row, sync."""
        chat = _make_chat("anthropic", model, client, model_kwargs)
        return self.chat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def aanthropic(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run Anthropic chat completions concurrently across the batch."""
        chat = _make_chat("anthropic", model, client, model_kwargs)
        return self.achat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ---- Gemini ----
    def gemini(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run a Gemini chat completion per row, sync."""
        chat = _make_chat("gemini", model, client, model_kwargs)
        return self.chat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def agemini(
        self,
        *,
        model: str | None = None,
        system: str | pl.Expr | None = None,
        schema: Any | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Run Gemini chat completions concurrently across the batch."""
        chat = _make_chat("gemini", model, client, model_kwargs)
        return self.achat(
            client=chat,
            system=system,
            schema=schema,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ---- TypeSafe System One ----
    def typesafe(
        self,
        *,
        questions: Mapping[str, Any],
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **client_kwargs: Any,
    ) -> pl.Expr:
        """Evaluate TypeSafe Choice, Score, and Noul questions per row.

        The expression is the TypeSafe ``state``. ``questions`` may contain
        ``typesafe_sdk`` question objects or raw question dictionaries. By
        default the result is a nested Struct containing the named answers;
        ``with_metadata=True`` also includes model, token usage, timing, and
        per-row errors. If ``client`` is omitted, remaining keyword arguments
        are forwarded to ``typesafe_sdk.TypeSafeClient``.
        """
        return self._typesafe(
            questions=questions,
            model=model,
            client=client,
            retries=retries,
            backoff=backoff,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
            client_kwargs=client_kwargs,
        )

    def atypesafe(
        self,
        *,
        questions: Mapping[str, Any],
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **client_kwargs: Any,
    ) -> pl.Expr:
        """Evaluate TypeSafe questions concurrently across each batch.

        Uses ``typesafe_sdk.AsyncTypeSafeClient`` unless an async ``client``
        is supplied. ``max_concurrency`` caps in-flight row evaluations.
        """
        return self._atypesafe(
            questions=questions,
            model=model,
            client=client,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            with_metadata=with_metadata,
            on_error=on_error,
            client_kwargs=client_kwargs,
        )

    # ============================================================
    # Public embed verbs
    # ============================================================

    # ---- Provider-agnostic ----
    def embed(
        self,
        *,
        client: Any,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
    ) -> pl.Expr:
        """Compute embeddings with any LangChain-compatible client.

        ``client`` must provide ``embed_query`` and, when ``chunk_size`` is
        supplied, ``embed_documents``.
        """
        return self._embed(
            client,
            retries=retries,
            backoff=backoff,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def aembed(
        self,
        *,
        client: Any,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
    ) -> pl.Expr:
        """Compute embeddings concurrently with any compatible client.

        ``client`` must provide ``aembed_query`` and, when ``chunk_size`` is
        supplied, ``aembed_documents``.
        """
        return self._aembed(
            client,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def openai_embed(
        self,
        *,
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Compute OpenAI embeddings per row, sync.

        Pass ``chunk_size=N`` to batch ``N`` rows into a single
        ``embed_documents`` call (cheaper / faster for corpus-style embedding).
        Pass ``dim=N`` to return ``Array(Float64, N)`` instead of the default
        ``List(Float64)`` (catches dim drift, plays nicely with vector libs).
        """
        embedder = _make_embed("openai", model, client, model_kwargs)
        return self.embed(
            client=embedder,
            retries=retries,
            backoff=backoff,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def aopenai_embed(
        self,
        *,
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Compute OpenAI embeddings concurrently across the batch.

        Pass ``chunk_size=N`` to batch ``N`` rows per ``aembed_documents``
        call; ``max_concurrency`` then caps in-flight chunk calls. Pass
        ``dim=N`` to return ``Array(Float64, N)`` instead of ``List(Float64)``.
        """
        embedder = _make_embed("openai", model, client, model_kwargs)
        return self.aembed(
            client=embedder,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def gemini_embed(
        self,
        *,
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Compute Gemini embeddings per row, sync.

        Pass ``chunk_size=N`` to batch ``N`` rows into a single
        ``embed_documents`` call. Pass ``dim=N`` to return
        ``Array(Float64, N)`` instead of ``List(Float64)``.
        """
        embedder = _make_embed("gemini", model, client, model_kwargs)
        return self.embed(
            client=embedder,
            retries=retries,
            backoff=backoff,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    def agemini_embed(
        self,
        *,
        model: str | None = None,
        client: Any = None,
        retries: int = 0,
        backoff: float = 0.0,
        max_concurrency: int | None = None,
        cache: bool = False,
        chunk_size: int | None = None,
        dim: int | None = None,
        with_metadata: bool = False,
        on_error: OnError = "null",
        **model_kwargs: Any,
    ) -> pl.Expr:
        """Compute Gemini embeddings concurrently across the batch.

        Pass ``chunk_size=N`` to batch ``N`` rows per ``aembed_documents``
        call; ``max_concurrency`` then caps in-flight chunk calls. Pass
        ``dim=N`` to return ``Array(Float64, N)`` instead of ``List(Float64)``.
        """
        embedder = _make_embed("gemini", model, client, model_kwargs)
        return self.aembed(
            client=embedder,
            retries=retries,
            backoff=backoff,
            max_concurrency=max_concurrency,
            cache=cache,
            chunk_size=chunk_size,
            dim=dim,
            with_metadata=with_metadata,
            on_error=on_error,
        )

    # ============================================================
    # Vector helpers (no provider call)
    # ============================================================

    def cosine(self, other: pl.Expr | pl.Series | list[float] | tuple[float, ...]) -> pl.Expr:
        """Cosine similarity between this vector column and ``other``.

        Accepts both ``Array(Float64, dim)`` and ``List(Float64)`` inputs;
        they are cast to ``List`` internally so the math is uniform. ``other``
        may be a ``pl.Expr`` (e.g. ``pl.col("vector_b")``), a ``pl.Series``,
        or a literal Python list/tuple of floats (broadcast against every
        row). Returns a ``Float64`` expression.

        Lowers to native Polars arithmetic — no API call is made. Rows where
        either vector is null produce ``null``; rows where either vector is
        all-zero produce ``NaN`` (0/0).
        """
        list_dtype = pl.List(pl.Float64)
        a = self._prompt.cast(list_dtype)
        if isinstance(other, pl.Expr):
            b: pl.Expr = other.cast(list_dtype)
        elif isinstance(other, pl.Series):
            b = pl.lit(other).cast(list_dtype)
        elif isinstance(other, list | tuple):
            b = pl.lit(pl.Series("", [list(other)], dtype=list_dtype))
        else:
            raise TypeError(
                f"polars-llm: `cosine` expects a pl.Expr, pl.Series, or list of floats; got {type(other).__name__}",
            )
        dot = (a * b).list.sum()
        norm_a = (a * a).list.sum().sqrt()
        norm_b = (b * b).list.sum().sqrt()
        return dot / (norm_a * norm_b)

chat(*, client, system=None, schema=None, retries=0, backoff=0.0, cache=False, with_metadata=False, on_error='null')

Run chat completions with any LangChain-compatible client.

client must provide invoke. When schema is supplied it must also provide with_structured_output. Use this method for providers without a dedicated convenience verb, or for custom and preconfigured chat clients.

Source code in polars_llm/llm.py
def chat(
    self,
    *,
    client: Any,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
) -> pl.Expr:
    """Run chat completions with any LangChain-compatible client.

    ``client`` must provide ``invoke``. When ``schema`` is supplied it
    must also provide ``with_structured_output``. Use this method for
    providers without a dedicated convenience verb, or for custom and
    preconfigured chat clients.
    """
    return self._chat(
        client,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

achat(*, client, system=None, schema=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, with_metadata=False, on_error='null')

Run chat completions concurrently with any compatible client.

client must provide ainvoke. When schema is supplied it must also provide with_structured_output.

Source code in polars_llm/llm.py
def achat(
    self,
    *,
    client: Any,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
) -> pl.Expr:
    """Run chat completions concurrently with any compatible client.

    ``client`` must provide ``ainvoke``. When ``schema`` is supplied it
    must also provide ``with_structured_output``.
    """
    return self._achat(
        client,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

openai(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run an OpenAI chat completion per row, sync.

Source code in polars_llm/llm.py
def openai(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run an OpenAI chat completion per row, sync."""
    chat = _make_chat("openai", model, client, model_kwargs)
    return self.chat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

aopenai(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run OpenAI chat completions concurrently across the batch.

Source code in polars_llm/llm.py
def aopenai(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run OpenAI chat completions concurrently across the batch."""
    chat = _make_chat("openai", model, client, model_kwargs)
    return self.achat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

anthropic(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run an Anthropic chat completion per row, sync.

Source code in polars_llm/llm.py
def anthropic(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run an Anthropic chat completion per row, sync."""
    chat = _make_chat("anthropic", model, client, model_kwargs)
    return self.chat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

aanthropic(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run Anthropic chat completions concurrently across the batch.

Source code in polars_llm/llm.py
def aanthropic(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run Anthropic chat completions concurrently across the batch."""
    chat = _make_chat("anthropic", model, client, model_kwargs)
    return self.achat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

gemini(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run a Gemini chat completion per row, sync.

Source code in polars_llm/llm.py
def gemini(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run a Gemini chat completion per row, sync."""
    chat = _make_chat("gemini", model, client, model_kwargs)
    return self.chat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

agemini(*, model=None, system=None, schema=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, with_metadata=False, on_error='null', **model_kwargs)

Run Gemini chat completions concurrently across the batch.

Source code in polars_llm/llm.py
def agemini(
    self,
    *,
    model: str | None = None,
    system: str | pl.Expr | None = None,
    schema: Any | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Run Gemini chat completions concurrently across the batch."""
    chat = _make_chat("gemini", model, client, model_kwargs)
    return self.achat(
        client=chat,
        system=system,
        schema=schema,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
    )

typesafe(*, questions, model=None, client=None, retries=0, backoff=0.0, cache=False, with_metadata=False, on_error='null', **client_kwargs)

Evaluate TypeSafe Choice, Score, and Noul questions per row.

The expression is the TypeSafe state. questions may contain typesafe_sdk question objects or raw question dictionaries. By default the result is a nested Struct containing the named answers; with_metadata=True also includes model, token usage, timing, and per-row errors. If client is omitted, remaining keyword arguments are forwarded to typesafe_sdk.TypeSafeClient.

Source code in polars_llm/llm.py
def typesafe(
    self,
    *,
    questions: Mapping[str, Any],
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **client_kwargs: Any,
) -> pl.Expr:
    """Evaluate TypeSafe Choice, Score, and Noul questions per row.

    The expression is the TypeSafe ``state``. ``questions`` may contain
    ``typesafe_sdk`` question objects or raw question dictionaries. By
    default the result is a nested Struct containing the named answers;
    ``with_metadata=True`` also includes model, token usage, timing, and
    per-row errors. If ``client`` is omitted, remaining keyword arguments
    are forwarded to ``typesafe_sdk.TypeSafeClient``.
    """
    return self._typesafe(
        questions=questions,
        model=model,
        client=client,
        retries=retries,
        backoff=backoff,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
        client_kwargs=client_kwargs,
    )

atypesafe(*, questions, model=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, with_metadata=False, on_error='null', **client_kwargs)

Evaluate TypeSafe questions concurrently across each batch.

Uses typesafe_sdk.AsyncTypeSafeClient unless an async client is supplied. max_concurrency caps in-flight row evaluations.

Source code in polars_llm/llm.py
def atypesafe(
    self,
    *,
    questions: Mapping[str, Any],
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **client_kwargs: Any,
) -> pl.Expr:
    """Evaluate TypeSafe questions concurrently across each batch.

    Uses ``typesafe_sdk.AsyncTypeSafeClient`` unless an async ``client``
    is supplied. ``max_concurrency`` caps in-flight row evaluations.
    """
    return self._atypesafe(
        questions=questions,
        model=model,
        client=client,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        with_metadata=with_metadata,
        on_error=on_error,
        client_kwargs=client_kwargs,
    )

embed(*, client, retries=0, backoff=0.0, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null')

Compute embeddings with any LangChain-compatible client.

client must provide embed_query and, when chunk_size is supplied, embed_documents.

Source code in polars_llm/llm.py
def embed(
    self,
    *,
    client: Any,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
) -> pl.Expr:
    """Compute embeddings with any LangChain-compatible client.

    ``client`` must provide ``embed_query`` and, when ``chunk_size`` is
    supplied, ``embed_documents``.
    """
    return self._embed(
        client,
        retries=retries,
        backoff=backoff,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

aembed(*, client, retries=0, backoff=0.0, max_concurrency=None, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null')

Compute embeddings concurrently with any compatible client.

client must provide aembed_query and, when chunk_size is supplied, aembed_documents.

Source code in polars_llm/llm.py
def aembed(
    self,
    *,
    client: Any,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
) -> pl.Expr:
    """Compute embeddings concurrently with any compatible client.

    ``client`` must provide ``aembed_query`` and, when ``chunk_size`` is
    supplied, ``aembed_documents``.
    """
    return self._aembed(
        client,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

openai_embed(*, model=None, client=None, retries=0, backoff=0.0, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null', **model_kwargs)

Compute OpenAI embeddings per row, sync.

Pass chunk_size=N to batch N rows into a single embed_documents call (cheaper / faster for corpus-style embedding). Pass dim=N to return Array(Float64, N) instead of the default List(Float64) (catches dim drift, plays nicely with vector libs).

Source code in polars_llm/llm.py
def openai_embed(
    self,
    *,
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Compute OpenAI embeddings per row, sync.

    Pass ``chunk_size=N`` to batch ``N`` rows into a single
    ``embed_documents`` call (cheaper / faster for corpus-style embedding).
    Pass ``dim=N`` to return ``Array(Float64, N)`` instead of the default
    ``List(Float64)`` (catches dim drift, plays nicely with vector libs).
    """
    embedder = _make_embed("openai", model, client, model_kwargs)
    return self.embed(
        client=embedder,
        retries=retries,
        backoff=backoff,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

aopenai_embed(*, model=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null', **model_kwargs)

Compute OpenAI embeddings concurrently across the batch.

Pass chunk_size=N to batch N rows per aembed_documents call; max_concurrency then caps in-flight chunk calls. Pass dim=N to return Array(Float64, N) instead of List(Float64).

Source code in polars_llm/llm.py
def aopenai_embed(
    self,
    *,
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Compute OpenAI embeddings concurrently across the batch.

    Pass ``chunk_size=N`` to batch ``N`` rows per ``aembed_documents``
    call; ``max_concurrency`` then caps in-flight chunk calls. Pass
    ``dim=N`` to return ``Array(Float64, N)`` instead of ``List(Float64)``.
    """
    embedder = _make_embed("openai", model, client, model_kwargs)
    return self.aembed(
        client=embedder,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

gemini_embed(*, model=None, client=None, retries=0, backoff=0.0, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null', **model_kwargs)

Compute Gemini embeddings per row, sync.

Pass chunk_size=N to batch N rows into a single embed_documents call. Pass dim=N to return Array(Float64, N) instead of List(Float64).

Source code in polars_llm/llm.py
def gemini_embed(
    self,
    *,
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Compute Gemini embeddings per row, sync.

    Pass ``chunk_size=N`` to batch ``N`` rows into a single
    ``embed_documents`` call. Pass ``dim=N`` to return
    ``Array(Float64, N)`` instead of ``List(Float64)``.
    """
    embedder = _make_embed("gemini", model, client, model_kwargs)
    return self.embed(
        client=embedder,
        retries=retries,
        backoff=backoff,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

agemini_embed(*, model=None, client=None, retries=0, backoff=0.0, max_concurrency=None, cache=False, chunk_size=None, dim=None, with_metadata=False, on_error='null', **model_kwargs)

Compute Gemini embeddings concurrently across the batch.

Pass chunk_size=N to batch N rows per aembed_documents call; max_concurrency then caps in-flight chunk calls. Pass dim=N to return Array(Float64, N) instead of List(Float64).

Source code in polars_llm/llm.py
def agemini_embed(
    self,
    *,
    model: str | None = None,
    client: Any = None,
    retries: int = 0,
    backoff: float = 0.0,
    max_concurrency: int | None = None,
    cache: bool = False,
    chunk_size: int | None = None,
    dim: int | None = None,
    with_metadata: bool = False,
    on_error: OnError = "null",
    **model_kwargs: Any,
) -> pl.Expr:
    """Compute Gemini embeddings concurrently across the batch.

    Pass ``chunk_size=N`` to batch ``N`` rows per ``aembed_documents``
    call; ``max_concurrency`` then caps in-flight chunk calls. Pass
    ``dim=N`` to return ``Array(Float64, N)`` instead of ``List(Float64)``.
    """
    embedder = _make_embed("gemini", model, client, model_kwargs)
    return self.aembed(
        client=embedder,
        retries=retries,
        backoff=backoff,
        max_concurrency=max_concurrency,
        cache=cache,
        chunk_size=chunk_size,
        dim=dim,
        with_metadata=with_metadata,
        on_error=on_error,
    )

cosine(other)

Cosine similarity between this vector column and other.

Accepts both Array(Float64, dim) and List(Float64) inputs; they are cast to List internally so the math is uniform. other may be a pl.Expr (e.g. pl.col("vector_b")), a pl.Series, or a literal Python list/tuple of floats (broadcast against every row). Returns a Float64 expression.

Lowers to native Polars arithmetic — no API call is made. Rows where either vector is null produce null; rows where either vector is all-zero produce NaN (0/0).

Source code in polars_llm/llm.py
def cosine(self, other: pl.Expr | pl.Series | list[float] | tuple[float, ...]) -> pl.Expr:
    """Cosine similarity between this vector column and ``other``.

    Accepts both ``Array(Float64, dim)`` and ``List(Float64)`` inputs;
    they are cast to ``List`` internally so the math is uniform. ``other``
    may be a ``pl.Expr`` (e.g. ``pl.col("vector_b")``), a ``pl.Series``,
    or a literal Python list/tuple of floats (broadcast against every
    row). Returns a ``Float64`` expression.

    Lowers to native Polars arithmetic — no API call is made. Rows where
    either vector is null produce ``null``; rows where either vector is
    all-zero produce ``NaN`` (0/0).
    """
    list_dtype = pl.List(pl.Float64)
    a = self._prompt.cast(list_dtype)
    if isinstance(other, pl.Expr):
        b: pl.Expr = other.cast(list_dtype)
    elif isinstance(other, pl.Series):
        b = pl.lit(other).cast(list_dtype)
    elif isinstance(other, list | tuple):
        b = pl.lit(pl.Series("", [list(other)], dtype=list_dtype))
    else:
        raise TypeError(
            f"polars-llm: `cosine` expects a pl.Expr, pl.Series, or list of floats; got {type(other).__name__}",
        )
    dot = (a * b).list.sum()
    norm_a = (a * a).list.sum().sqrt()
    norm_b = (b * b).list.sum().sqrt()
    return dot / (norm_a * norm_b)