diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 89efc98d..e6225d95 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -46,12 +46,12 @@ repos:
           - tomli
 
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.4.4
+    rev: v0.4.5
     hooks:
       - id: ruff
         args: [--fix, --exit-non-zero-on-fix]
 
   - repo: https://github.com/RobertCraigie/pyright-python
-    rev: v1.1.363
+    rev: v1.1.364
     hooks:
       - id: pyright
diff --git a/lmo/__init__.py b/lmo/__init__.py
index e0de49e3..dac8c63c 100644
--- a/lmo/__init__.py
+++ b/lmo/__init__.py
@@ -1,31 +1,42 @@
-"""Lmo: Robust statistics with trimmed L-moments and L-comoments."""
-import sys
+"""
+Robust statistics with trimmed L-moments and L-comoments.
+"""
+
+import sys  # noqa: I001
 from typing import TYPE_CHECKING, Final
 
 from ._lm import (
-    l_kurtosis,
     l_loc,
-    l_moment,
-    l_moment_cov,
-    l_moment_influence,
-    l_ratio,
-    l_ratio_influence,
-    l_ratio_se,
     l_scale,
+    l_variation,
     l_skew,
+    l_kurtosis,
+
+    l_kurt,
+    l_moment,
+    l_ratio,
     l_stats,
+
+    l_moment_cov,
+    l_ratio_se,
     l_stats_se,
-    l_variation,
+
+    l_moment_influence,
+    l_ratio_influence,
+
     l_weights,
 )
 from ._lm_co import (
-    l_cokurtosis,
     l_coloc,
-    l_comoment,
-    l_coratio,
-    l_corr,
     l_coscale,
+
+    l_corr,
     l_coskew,
+    l_cokurtosis,
+    l_cokurt,
+
+    l_comoment,
+    l_coratio,
     l_costats,
 )
 from ._meta import get_version as _get_version
@@ -60,6 +71,7 @@
     'l_variation',
     'l_skew',
     'l_kurtosis',
+    'l_kurt',
 
     'l_moment',
     'l_ratio',
@@ -79,6 +91,7 @@
     'l_corr',
     'l_coskew',
     'l_cokurtosis',
+    'l_cokurt',
 
     'l_comoment',
     'l_coratio',
diff --git a/lmo/_lm.py b/lmo/_lm.py
index e28dab8e..f77b38f8 100644
--- a/lmo/_lm.py
+++ b/lmo/_lm.py
@@ -9,29 +9,28 @@
 from . import ostats, pwm_beta
 from ._utils import (
     clean_order,
+    clean_orders,
     clean_trim,
     ensure_axis_at,
     l_stats_orders,
     moments_to_ratio,
     ordered,
     round0,
+    sort_maybe,
 )
 from .linalg import ir_pascal, sandwich, sh_legendre, trim_matrix
+from .typing import (
+    AnyOrder,
+    AnyOrderND,
+    np as lnpt,
+)
 from .typing.compat import TypeVar
 
 
 if TYPE_CHECKING:
     from collections.abc import Callable
 
-    from .typing import (
-        AnyAWeights,
-        AnyFWeights,
-        AnyOrder,
-        AnyOrderND,
-        AnyTrim,
-        LMomentOptions,
-        np as lnpt,
-    )
+    from .typing import AnyAWeights, AnyFWeights, AnyTrim, LMomentOptions
     from .typing.compat import Unpack
 
 
@@ -47,6 +46,7 @@
     'l_variation',
     'l_skew',
     'l_kurtosis',
+    'l_kurt',
 
     'l_moment_cov',
     'l_ratio_se',
@@ -66,13 +66,17 @@
 _Vectorized: TypeAlias = _T_float | npt.NDArray[_T_float]
 _Floating: TypeAlias = np.floating[Any]
 
-_L_WEIGHTS_CACHE: Final[
-    dict[
-        # (n, s, t)
-        tuple[int, int, int] | tuple[int, float, float],
-        lnpt.Array[tuple[int, int], _Floating],
-    ]
-] = {}
+# (dtype.char, n, s, t)
+_CacheKey: TypeAlias = (
+    tuple[str, int, int, int]
+    | tuple[str, int, float, float]
+)
+# `r: _T_order >= 4`
+_CacheArray: TypeAlias = lnpt.Array[tuple[_T_order, _T_size], np.longdouble]
+_Cache: TypeAlias = dict[_CacheKey, _CacheArray[Any, Any]]
+
+# depends on `dtype`, `n`, and `trim`
+_CACHE: Final[_Cache] = {}
 
 
 def _l_weights_pwm(
@@ -87,11 +91,21 @@ def _l_weights_pwm(
     r0 = r + s + t
 
     # `__matmul__` annotations are lacking (`np.matmul` is equivalent to it)
-    w0 = np.matmul(
+    wr = np.matmul(
         sh_legendre(r0, dtype=np.int64 if r0 < 29 else dtype),
         pwm_beta.weights(r0, n, dtype=dtype),
+        dtype=dtype,
     )
-    return np.matmul(trim_matrix(r, trim, dtype=dtype), w0) if s or t else w0
+    if s or t:
+        wr = np.matmul(trim_matrix(r, trim, dtype=dtype), wr, dtype=dtype)
+
+        # ensure that the trimmed ends are 0
+        if s:
+            wr[:, :s] = 0
+        if t:
+            wr[:, -t:] = 0
+
+    return wr
 
 
 def _l_weights_ostat(
@@ -125,13 +139,13 @@ def _l_weights_ostat(
 
 
 def l_weights(
-    r: _T_order,
+    r_max: _T_order,
     n: _T_size,
     /,
     trim: AnyTrim = 0,
     *,
     dtype: _DType[_T_float] = np.float64,
-    cache: bool = False,
+    cache: bool | None = None,
 ) -> lnpt.Array[tuple[_T_order, _T_size], _T_float]:
     r"""
     Projection matrix of the first $r$ (T)L-moments for $n$ samples.
@@ -170,8 +184,16 @@ def l_weights(
         observation vector(s) of size $n$), into (an unbiased estimate of) the
         *generalized trimmed L-moments*, with orders $\le r$.
 
+    Args:
+        r_max: The amount L-moment orders.
+        n: The number of samples.
+        trim: A scalar or 2-tuple with the trim orders. Defaults to 0.
+        dtype: The datatype of the returned weight matrix.
+        cache: Whether to cache the weights. By default, it's enabled i.f.f
+            the trim values are integers, and `r_max + sum(trim) < 24`.
+
     Returns:
-        P_r: 2-D array of shape `(r, n)`.
+        P_r: 2-D array of shape `(r_max, n)`, readonly if `cache=True`
 
     Examples:
         >>> import lmo
@@ -186,55 +208,44 @@ def l_weights(
         - [J.R.M. Hosking (2007) - Some theory and practical uses of trimmed
             L-moments](https://doi.org/10.1016/j.jspi.2006.12.002)
     """
-    if r == 0:
-        return np.empty((r, n), dtype=dtype)
-
-    match clean_trim(trim):
-        case s, t if s < 0 or t < 0:
-            msg = f'trim orders must be >=0, got {trim}'
-            raise ValueError(msg)
-        case s, t:
-            pass
-        case _:  # type: ignore [reportUneccessaryComparison]
-            msg = (
-                f'trim must be a tuple with two non-negative ints or floats, '
-                f'got {trim!r}'
-            )
-            raise TypeError(msg)
-
-    # manual cache lookup, only if cache=False (for testability)
-    # e.g. `functools.cache` would be inefficient for e.g. r=3 with cached r=4
-    cache_key = n, s, t
-    if (
-        cache
-        and cache_key in _L_WEIGHTS_CACHE
-        and (w := _L_WEIGHTS_CACHE[cache_key]).shape[0] <= r
-    ):
-        if w.shape[0] < r:
-            w = w[:r]
-
-        # ignore if r is larger that what's cached
-        if w.shape[0] == r:
-            assert w.shape == (r, n)
-            return w.astype(dtype)
-
-    if r + s + t <= 24 and isinstance(s, int) and isinstance(t, int):
-        w = _l_weights_pwm(r, n, (s, t), dtype=dtype or np.float64)
+    if r_max < 0:
+        msg = f'r must be non-negative, got {r_max}'
+        raise ValueError(msg)
 
-        # ensure that the trimmed ends are 0
-        if s:
-            w[:, :s] = 0
-        if t:
-            w[:, -t:] = 0
-    else:
-        w = _l_weights_ostat(r, n, (s, t), dtype=dtype or np.float64)
+    dtype = np.dtype(dtype)
+    sctype = dtype.type
 
-    if cache:
-        # the pyright error here is due to the fact that the first type param
-        # of `np.ndarray` is invariant (which is incorrect), instead of
-        # being covariant
-        _L_WEIGHTS_CACHE[cache_key] = w  # pyright: ignore[reportArgumentType]
+    if r_max == 0:
+        return np.empty((0, n), dtype=sctype)
 
+    s, t = clean_trim(trim)
+
+    if (n_min := r_max + s + t) > n:
+        msg = f'expected n >= r + s + t, got {n} < {n_min}'
+        raise ValueError(msg)
+
+    key = dtype.char, n, s, t
+    if (_w := _CACHE.get(key)) is not None and _w.shape[0] >= r_max:
+        w = cast(lnpt.Array[tuple[_T_order, _T_size], _T_float], _w)
+    else:
+        # when caching, use at least 4 orders, to avoid cache misses
+        _r_max = 4 if cache and r_max < 4 else r_max
+
+        _cache_default = False
+        if r_max + s + t <= 24 and isinstance(s, int) and isinstance(t, int):
+            w = _l_weights_pwm(_r_max, n, trim=(s, t), dtype=sctype)
+            _cache_default = True
+        else:
+            w = _l_weights_ostat(_r_max, n, trim=(s, t), dtype=sctype)
+
+        if cache or cache is None and _cache_default:
+            w.setflags(write=False)
+            # be wary of a potential race condition
+            if key not in _CACHE or w.shape[0] >= _CACHE[key].shape[0]:
+                _CACHE[key] = w
+
+    if w.shape[0] > r_max:
+        w = w[:r_max]
     return w
 
 
@@ -292,8 +303,8 @@ def l_moment(
     dtype: _DType[_T_float] = np.float64,
     fweights: AnyFWeights | None = None,
     aweights: AnyAWeights | None = None,
-    sort: lnpt.SortKind | None = None,
-    cache: bool = False,
+    sort: lnpt.SortKind | bool = True,
+    cache: bool | None = None,
 ) -> _Vectorized[_T_float]:
     r"""
     Estimates the generalized trimmed L-moment $\lambda^{(s, t)}_r$ from
@@ -348,12 +359,14 @@ def l_moment(
             All `aweights` must be `>=0`, and the sum must be nonzero.
 
             The algorithm is similar to that for weighted quantiles.
-        sort ('quicksort' | 'heapsort' | 'stable'):
+        sort (True | False | 'quicksort' | 'heapsort' | 'stable'):
             Sorting algorithm, see [`numpy.sort`][numpy.sort].
+            Set to `False` if the array is already sorted.
         cache:
             Set to `True` to speed up future L-moment calculations that have
             the same number of observations in `a`, equal `trim`, and equal or
-            smaller `r`.
+            smaller `r`. By default, it will cache i.f.f. the trim is integral,
+            and $r + s + t \le 24$. Set to `False` to always disable caching.
 
     Returns:
         l:
@@ -403,8 +416,11 @@ def l_moment(
     x_k = ensure_axis_at(x_k, axis, -1)
     n = x_k.shape[-1]
 
-    _r = np.asarray(r)
-    r_max = clean_order(np.max(_r))
+    if np.isscalar(r):
+        _r = np.array(clean_order(cast(AnyOrder, r)))
+    else:
+        _r = clean_orders(cast(AnyOrderND, r))
+    r_min, r_max = np.min(_r), int(np.max(_r))
 
     # TODO @jorenham: nan handling, see:
     # https://github.com/jorenham/Lmo/issues/70
@@ -420,12 +436,10 @@ def l_moment(
 
     l_r = np.inner(l_weights(r_max, n, st, dtype=dtype, cache=cache), x_k)
 
-    # we like 0-based indexing; so if P_r starts at r=1, prepend all 1's
-    # for r=0 (any zeroth moment is defined to be 1)
-    l_r = np.r_[np.ones((1, *l_r.shape[1:]), dtype=l_r.dtype), l_r]
+    if r_min > 0:
+        return l_r.take(_r - 1, 0)
 
-    # l[r] fails when r is e.g. a tuple (valid sequence).
-    return l_r.take(_r, 0)
+    return np.r_[np.ones((1, *l_r.shape[1:]), l_r.dtype), l_r].take(_r, 0)
 
 
 @overload
@@ -910,6 +924,9 @@ def l_kurtosis(
     return l_ratio(a, 4, 2, trim=trim, axis=axis, dtype=dtype, **kwds)
 
 
+l_kurt = l_kurtosis
+
+
 def l_moment_cov(
     a: lnpt.AnyArrayFloat,
     r_max: AnyOrder,
@@ -1103,7 +1120,7 @@ def l_moment_influence(
     /,
     trim: AnyTrim = 0,
     *,
-    sort: lnpt.SortKind | None = 'quicksort',
+    sort: lnpt.SortKind | bool = True,
     tol: float = 1e-8,
 ) -> Callable[[_T_x], _T_x]:
     r"""
@@ -1132,11 +1149,9 @@ def l_moment_influence(
     _r = clean_order(r)
     s, t = clean_trim(trim)
 
-    x_k = np.array(a, copy=True)
-    if sort:
-        x_k.sort(kind=sort)
+    x_k = np.array(a, copy=bool(sort))
+    x_k = sort_maybe(x_k, sort=sort, inplace=True)
 
-    x_k = np.sort(np.asarray(a), kind=sort)
     n = len(x_k)
 
     w_k = l_weights(_r, n, (s, t))[-1]
@@ -1173,7 +1188,7 @@ def l_ratio_influence(
     /,
     trim: AnyTrim = 0,
     *,
-    sort: lnpt.SortKind = 'quicksort',
+    sort: lnpt.SortKind | bool = True,
     tol: float = 1e-8,
 ) -> Callable[[_T_x], _T_x]:
     r"""
@@ -1202,12 +1217,12 @@ def l_ratio_influence(
     """
     _r, _s = clean_order(r), clean_order(s, name='s')
 
-    _x = np.array(a, copy=True)
-    _x.sort(kind=sort)
+    _x = np.array(a, copy=bool(sort))
+    _x = sort_maybe(_x, sort=sort, inplace=True)
     n = len(_x)
 
-    eif_r = l_moment_influence(_x, _r, trim, sort=None, tol=0)
-    eif_k = l_moment_influence(_x, _s, trim, sort=None, tol=0)
+    eif_r = l_moment_influence(_x, _r, trim, sort=False, tol=0)
+    eif_k = l_moment_influence(_x, _s, trim, sort=False, tol=0)
 
     l_r, l_k = cast(
         tuple[float, float],
diff --git a/lmo/_lm_co.py b/lmo/_lm_co.py
index ba91101f..ac1adb97 100644
--- a/lmo/_lm_co.py
+++ b/lmo/_lm_co.py
@@ -27,6 +27,7 @@
     'l_corr',
     'l_coskew',
     'l_cokurtosis',
+    'l_cokurt',
 )
 
 
@@ -48,9 +49,9 @@ def l_comoment(
     trim: AnyTrim = 0,
     *,
     dtype: _DType[_T_float] = np.float64,
-    rowvar: bool = True,
+    rowvar: bool | None = None,
     sort: lnpt.SortKind | None = None,
-    cache: bool = False,
+    cache: bool | None = None,
 ) -> lnpt.Array[Any, _T_float]:
     r"""
     Multivariate extension of [`lmo.l_moment`][lmo.l_moment].
@@ -109,20 +110,22 @@ def l_comoment(
                 Useful for fitting heavy-tailed distributions, such as the
                 Cauchy distribution.
         rowvar:
-            If `rowvar` is True (default), then each row (axis 0) represents a
+            If `True`, then each row (axis 0) represents a
             variable, with observations in the columns (axis 1).
-            Otherwise, the relationship is transposed: each column represents
+            If `False`, the relationship is transposed: each column represents
             a variable, while the rows contain observations.
+            If `None` (default), it is determined from the shape of `a`.
         dtype:
             Floating type to use in computing the L-moments. Default is
             [`numpy.float64`][numpy.float64].
 
-        sort ('quick' | 'stable' | 'heap'):
+        sort ('quicksort' | 'heapsort' | 'stable'):
             Sorting algorithm, see [`numpy.sort`][numpy.sort].
         cache:
             Set to `True` to speed up future L-moment calculations that have
             the same number of observations in `a`, equal `trim`, and equal or
-            smaller `r`.
+            smaller `r`. By default, it will cache i.f.f. the trim is integral,
+            and $r + s + t \le 24$. Set to `False` to always disable caching.
 
     Returns:
         L: Array of shape `(*r.shape, m, m)` with r-th L-comoments.
@@ -133,29 +136,39 @@ def l_comoment(
 
         >>> import lmo, numpy as np
         >>> rng = np.random.default_rng(12345)
-        >>> x = rng.multivariate_normal([0, 0], [[6, -3], [-3, 3.5]], 99).T
+        >>> x = rng.multivariate_normal([0, 0], [[6, -3], [-3, 3.5]], 99)
         >>> lmo.l_comoment(x, 2)
         array([[ 1.2766793 , -0.83299947],
                [-0.71547941,  1.05990727]])
 
         The diagonal contains the univariate L-moments:
 
-        >>> lmo.l_moment(x, 2, axis=-1)
+        >>> lmo.l_moment(x, 2, axis=0)
         array([1.2766793 , 1.05990727])
 
+        The orientation (`rowvar`) is automatically determined, unless
+        explicitly specified.
+
+        >>> lmo.l_comoment(x, 2).shape
+        (2, 2)
+        >>> lmo.l_comoment(x.T, 2).shape
+        (2, 2)
+        >>> lmo.l_comoment(x, 2, rowvar=False).shape
+        (2, 2)
+        >>> lmo.l_comoment(x.T, 2, rowvar=True).shape
+        (2, 2)
+
     References:
         - [R. Serfling & P. Xiao (2007) - A Contribution to Multivariate
           L-Moments: L-Comoment Matrices](https://doi.org/10.1016/j.jmva.2007.01.008)
     """
-    x = np.array(
-        a,
-        order='C' if rowvar else 'F',
-        subok=True,
-        ndmin=2,
-    )
+    x = np.array(a, subok=True, ndmin=2)
     if x.ndim != 2:
         msg = f'sample array must be 2-D, got shape {x.shape}'
         raise ValueError(msg)
+
+    if rowvar is None:
+        rowvar = x.shape[0] < x.shape[1]
     if not rowvar:
         x = x.T
     m, n = x.shape
@@ -165,15 +178,15 @@ def l_comoment(
     else:
         _r = clean_orders(cast(AnyOrderND, r))
 
+    if not m:
+        return np.empty((*np.shape(_r), 0, 0), dtype=dtype)
+
     r_min = int(np.min(_r))
     r_max = int(np.max(_r))
 
     if r_min == r_max == 0 and _r.ndim == 0:
         return np.identity(m, dtype=dtype)
 
-    if not m:
-        return np.empty((*np.shape(_r), 0, 0), dtype=dtype)
-
     # projection/hat matrix of shape (r_max - r_min, n)
     p_k = l_weights(r_max, n, trim=trim, dtype=dtype, cache=cache)
     if r_min > 1:
@@ -184,7 +197,7 @@ def l_comoment(
 
     for j in range(m):
         # *concomitants* of x[i] w.r.t. x[j] for all i
-        x_kij = ordered(x, x[j], axis=-1, sort=sort)
+        x_kij = ordered(x, x[j], axis=-1, sort=sort or True)
         l_kij[:, :, j] = np.inner(p_k, x_kij)
 
     if r_min == 0:
@@ -417,3 +430,6 @@ def l_cokurtosis(
         - [`lmo.l_kurtosis`][lmo.l_kurtosis]
     """
     return l_coratio(a, 4, 2, trim=trim, dtype=dtype, **kwds)
+
+
+l_cokurt = l_cokurtosis
diff --git a/lmo/_utils.py b/lmo/_utils.py
index 54d2cd06..2fddd6f2 100644
--- a/lmo/_utils.py
+++ b/lmo/_utils.py
@@ -21,6 +21,7 @@
     'l_stats_orders',
     'moments_to_ratio',
     'moments_to_stats_cov',
+    'sort_maybe',
     'ordered',
     'plotting_positions',
     'round0',
@@ -138,6 +139,25 @@ def _sort_like(
     )
 
 
+def sort_maybe(
+    x: lnpt.Array[_T_shape1, _T_number],
+    /,
+    axis: int = -1,
+    *,
+    sort: bool | lnpt.SortKind = True,
+    inplace: bool = False,
+) -> lnpt.Array[_T_shape1, _T_number]:
+    if not sort:
+        return x
+
+    kind = sort if isinstance(sort, str) else None
+
+    if inplace:
+        x.sort(axis=axis, kind=kind)
+        return x
+    return np.sort(x, axis=axis, kind=kind)
+
+
 def ordered(  # noqa: C901
     x: lnpt.AnyArrayFloat,
     y: lnpt.AnyArrayFloat | None = None,
@@ -147,7 +167,7 @@ def ordered(  # noqa: C901
     *,
     fweights: AnyFWeights | None = None,
     aweights: AnyAWeights | None = None,
-    sort: lnpt.SortKind | None = None,
+    sort: lnpt.SortKind | bool = True,
 ) -> lnpt.Array[lnpt.AtLeast1D, lnpt.Float]:
     """
     Calculate `n = len(x)` order stats of `x`, optionally weighted.
@@ -173,8 +193,16 @@ def ordered(  # noqa: C901
             _z = np.apply_along_axis(np.add, axis, 1j * _x, _y)
 
     # apply the ordering
-    i_kk = np.argsort(_z, axis=axis, kind=sort)
-    x_kk = _sort_like(_x, i_kk, axis=axis)
+    if sort or sort is None:  # pyright: ignore[reportUnnecessaryComparison]
+        kind = sort if isinstance(sort, str) else None
+        i_kk = np.argsort(_z, axis=axis, kind=kind)
+        x_kk = _sort_like(_x, i_kk, axis=axis)
+    else:
+        if axis is None:
+            i_kk = np.arange(len(_z))
+        else:
+            i_kk = np.mgrid[tuple(slice(0, j) for j in _z.shape)][axis]
+        x_kk = _x
 
     # prepare observation weights
     w_kk = None
diff --git a/lmo/contrib/scipy_stats.py b/lmo/contrib/scipy_stats.py
index 6b78d3e5..7fc3f84b 100644
--- a/lmo/contrib/scipy_stats.py
+++ b/lmo/contrib/scipy_stats.py
@@ -589,6 +589,8 @@ def l_kurtosis(
         """
         return float(self.l_ratio(4, 2, *args, trim=trim, **kwds))
 
+    l_kurt = l_kurtosis
+
     def l_moments_cov(
         self,
         r_max: int,
@@ -1448,6 +1450,8 @@ def l_skew(self, trim: AnyTrim = 0) -> float:  # noqa: D102
     def l_kurtosis(self, trim: AnyTrim = 0) -> float:  # noqa: D102
         return self.dist.l_kurtosis(*self.args, trim=trim, **self.kwds)
 
+    l_kurt = l_kurtosis
+
     def l_moments_cov(  # noqa: D102
         self,
         r_max: int,
diff --git a/lmo/distributions.py b/lmo/distributions.py
index 2526ce29..f9b67c1c 100644
--- a/lmo/distributions.py
+++ b/lmo/distributions.py
@@ -861,6 +861,8 @@ def l_kurtosis(self, trim: AnyTrim | None = None) -> float:
         """
         return float(self.l_ratio(4, 2, trim=trim))
 
+    l_kurt = l_kurtosis
+
     # `rv_continuous` and `rv_frozen` compatibility
 
     @property
diff --git a/lmo/pwm_beta.py b/lmo/pwm_beta.py
index ef606c51..8184a025 100644
--- a/lmo/pwm_beta.py
+++ b/lmo/pwm_beta.py
@@ -88,7 +88,6 @@ def cov(
     r: _R,
     /,
     axis: None = ...,
-    *,
     dtype: _DType[_F] = np.float64,
     **kwds: Any,
 ) -> lnpt.Array[tuple[_R, _R], _F]: ...
@@ -119,7 +118,7 @@ def cov(
         r: The amount of orders to evaluate, i.e. $k = 0, \dots, r - 1$.
         axis: The axis along which to calculate the covariance matrices.
         dtype: Desired output floating data type.
-        **kwargs: Additional keywords to pass to `lmo.stats.ordered`.
+        **kwds: Additional keywords to pass to `lmo.stats.ordered`.
 
     Returns:
         S_b: Variance-covariance matrix/tensor of shape `(r, r)` or (r, r, n)
diff --git a/lmo/typing/_core.py b/lmo/typing/_core.py
index 9fb26919..453b262e 100644
--- a/lmo/typing/_core.py
+++ b/lmo/typing/_core.py
@@ -22,8 +22,8 @@ class LMomentOptions(TypedDict, total=False):
     Use as e.g. `**kwds: Unpack[LMomentOptions]` (on `python<3.11`) or
     `**kwds: *LMomentOptions` (on `python>=3.11`).
     """
-    sort: lnpt.SortKind
-    cache: bool
+    sort: lnpt.SortKind | bool
+    cache: bool | None
     fweights: AnyFWeights
     aweights: AnyAWeights
 
@@ -34,5 +34,5 @@ class LComomentOptions(TypedDict, total=False):
     `**kwds: *LComomentOptions` (on `python>=3.11`).
     """
     sort: lnpt.SortKind
-    cache: bool
-    rowvar: bool
+    cache: bool | None
+    rowvar: bool | None
diff --git a/poetry.lock b/poetry.lock
index 9e4bdf4c..ecb740fe 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 1.8.2 and should not be changed by hand.
+# This file is automatically @generated by Poetry 1.8.3 and should not be changed by hand.
 
 [[package]]
 name = "appnope"
@@ -618,13 +618,13 @@ test = ["coverage[toml]", "ddt (>=1.1.1,!=1.4.3)", "mock", "mypy", "pre-commit",
 
 [[package]]
 name = "griffe"
-version = "0.45.0"
+version = "0.45.1"
 description = "Signatures for entire Python programs. Extract the structure, the frame, the skeleton of your project, to generate API documentation or find breaking changes in your API."
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "griffe-0.45.0-py3-none-any.whl", hash = "sha256:90fe5c90e1b0ca7dd6fee78f9009f4e01b37dbc9ab484a9b2c1578915db1e571"},
-    {file = "griffe-0.45.0.tar.gz", hash = "sha256:85cb2868d026ea51c89bdd589ad3ccc94abc5bd8d5d948e3d4450778a2a05b4a"},
+    {file = "griffe-0.45.1-py3-none-any.whl", hash = "sha256:12194c10ae07a7f46708741ad78419362cf8e5c883f449c7c48de1686611b853"},
+    {file = "griffe-0.45.1.tar.gz", hash = "sha256:84ce9243a9e63c07d55563a735a0d07ef70b46c455616c174010e7fc816f4648"},
 ]
 
 [package.dependencies]
@@ -642,13 +642,13 @@ files = [
 
 [[package]]
 name = "hypothesis"
-version = "6.102.4"
+version = "6.102.6"
 description = "A library for property-based testing"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "hypothesis-6.102.4-py3-none-any.whl", hash = "sha256:013df31b04a4daede13756f497e60e451963d86f426395a79f99c5d692919bbd"},
-    {file = "hypothesis-6.102.4.tar.gz", hash = "sha256:59b4d144346d5cffb482cc1bafbd21b13ff31608e8c4b3e4630339aee3e87763"},
+    {file = "hypothesis-6.102.6-py3-none-any.whl", hash = "sha256:ef281ba8b2626ebade9f463fbe8851ae6ff6ae4a8621a9e54c7c2477a97ccff0"},
+    {file = "hypothesis-6.102.6.tar.gz", hash = "sha256:ef5655b4ca349082241ab55f899a34ea6d75cc336a7b07356680909059db1349"},
 ]
 
 [package.dependencies]
@@ -658,10 +658,10 @@ numpy = {version = ">=1.17.3", optional = true, markers = "extra == \"numpy\""}
 sortedcontainers = ">=2.1.0,<3.0.0"
 
 [package.extras]
-all = ["backports.zoneinfo (>=0.2.1)", "black (>=19.10b0)", "click (>=7.0)", "crosshair-tool (>=0.0.54)", "django (>=3.2)", "dpcontracts (>=0.4)", "hypothesis-crosshair (>=0.0.2)", "lark (>=0.10.1)", "libcst (>=0.3.16)", "numpy (>=1.17.3)", "pandas (>=1.1)", "pytest (>=4.6)", "python-dateutil (>=1.4)", "pytz (>=2014.1)", "redis (>=3.0.0)", "rich (>=9.0.0)", "tzdata (>=2024.1)"]
+all = ["backports.zoneinfo (>=0.2.1)", "black (>=19.10b0)", "click (>=7.0)", "crosshair-tool (>=0.0.54)", "django (>=3.2)", "dpcontracts (>=0.4)", "hypothesis-crosshair (>=0.0.4)", "lark (>=0.10.1)", "libcst (>=0.3.16)", "numpy (>=1.17.3)", "pandas (>=1.1)", "pytest (>=4.6)", "python-dateutil (>=1.4)", "pytz (>=2014.1)", "redis (>=3.0.0)", "rich (>=9.0.0)", "tzdata (>=2024.1)"]
 cli = ["black (>=19.10b0)", "click (>=7.0)", "rich (>=9.0.0)"]
 codemods = ["libcst (>=0.3.16)"]
-crosshair = ["crosshair-tool (>=0.0.54)", "hypothesis-crosshair (>=0.0.2)"]
+crosshair = ["crosshair-tool (>=0.0.54)", "hypothesis-crosshair (>=0.0.4)"]
 dateutil = ["python-dateutil (>=1.4)"]
 django = ["django (>=3.2)"]
 dpcontracts = ["dpcontracts (>=0.4)"]
@@ -829,13 +829,13 @@ files = [
 
 [[package]]
 name = "jupyter-client"
-version = "8.6.1"
+version = "8.6.2"
 description = "Jupyter protocol implementation and client libraries"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "jupyter_client-8.6.1-py3-none-any.whl", hash = "sha256:3b7bd22f058434e3b9a7ea4b1500ed47de2713872288c0d511d19926f99b459f"},
-    {file = "jupyter_client-8.6.1.tar.gz", hash = "sha256:e842515e2bab8e19186d89fdfea7abd15e39dd581f94e399f00e2af5a1652d3f"},
+    {file = "jupyter_client-8.6.2-py3-none-any.whl", hash = "sha256:50cbc5c66fd1b8f65ecb66bc490ab73217993632809b6e505687de18e9dea39f"},
+    {file = "jupyter_client-8.6.2.tar.gz", hash = "sha256:2bda14d55ee5ba58552a8c53ae43d215ad9868853489213f37da060ced54d8df"},
 ]
 
 [package.dependencies]
@@ -847,7 +847,7 @@ traitlets = ">=5.3"
 
 [package.extras]
 docs = ["ipykernel", "myst-parser", "pydata-sphinx-theme", "sphinx (>=4)", "sphinx-autodoc-typehints", "sphinxcontrib-github-alt", "sphinxcontrib-spelling"]
-test = ["coverage", "ipykernel (>=6.14)", "mypy", "paramiko", "pre-commit", "pytest", "pytest-cov", "pytest-jupyter[client] (>=0.4.1)", "pytest-timeout"]
+test = ["coverage", "ipykernel (>=6.14)", "mypy", "paramiko", "pre-commit", "pytest (<8.2.0)", "pytest-cov", "pytest-jupyter[client] (>=0.4.1)", "pytest-timeout"]
 
 [[package]]
 name = "jupyter-core"
@@ -1242,13 +1242,13 @@ cache = ["platformdirs"]
 
 [[package]]
 name = "mkdocs-material"
-version = "9.5.23"
+version = "9.5.24"
 description = "Documentation that simply works"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "mkdocs_material-9.5.23-py3-none-any.whl", hash = "sha256:ffd08a5beaef3cd135aceb58ded8b98bbbbf2b70e5b656f6a14a63c917d9b001"},
-    {file = "mkdocs_material-9.5.23.tar.gz", hash = "sha256:4627fc3f15de2cba2bde9debc2fd59b9888ef494beabfe67eb352e23d14bf288"},
+    {file = "mkdocs_material-9.5.24-py3-none-any.whl", hash = "sha256:e12cd75954c535b61e716f359cf2a5056bf4514889d17161fdebd5df4b0153c6"},
+    {file = "mkdocs_material-9.5.24.tar.gz", hash = "sha256:02d5aaba0ee755e707c3ef6e748f9acb7b3011187c0ea766db31af8905078a34"},
 ]
 
 [package.dependencies]
@@ -1326,13 +1326,13 @@ python-legacy = ["mkdocstrings-python-legacy (>=0.2.1)"]
 
 [[package]]
 name = "mkdocstrings-python"
-version = "1.10.2"
+version = "1.10.3"
 description = "A Python handler for mkdocstrings."
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "mkdocstrings_python-1.10.2-py3-none-any.whl", hash = "sha256:e8e596b37f45c09b67bec253e035fe18988af5bbbbf44e0ccd711742eed750e5"},
-    {file = "mkdocstrings_python-1.10.2.tar.gz", hash = "sha256:38a4fd41953defb458a107033440c229c7e9f98f35a24e84d888789c97da5a63"},
+    {file = "mkdocstrings_python-1.10.3-py3-none-any.whl", hash = "sha256:11ff6d21d3818fb03af82c3ea6225b1534837e17f790aa5f09626524171f949b"},
+    {file = "mkdocstrings_python-1.10.3.tar.gz", hash = "sha256:321cf9c732907ab2b1fedaafa28765eaa089d89320f35f7206d00ea266889d03"},
 ]
 
 [package.dependencies]
@@ -1461,7 +1461,6 @@ optional = false
 python-versions = ">=3.9"
 files = [
     {file = "pandas-2.2.2-cp310-cp310-macosx_10_9_x86_64.whl", hash = "sha256:90c6fca2acf139569e74e8781709dccb6fe25940488755716d1d354d6bc58bce"},
-    {file = "pandas-2.2.2-cp310-cp310-macosx_11_0_arm64.whl", hash = "sha256:c7adfc142dac335d8c1e0dcbd37eb8617eac386596eb9e1a1b77791cf2498238"},
     {file = "pandas-2.2.2-cp310-cp310-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:4abfe0be0d7221be4f12552995e58723c7422c80a659da13ca382697de830c08"},
     {file = "pandas-2.2.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:8635c16bf3d99040fdf3ca3db669a7250ddf49c55dc4aa8fe0ae0fa8d6dcc1f0"},
     {file = "pandas-2.2.2-cp310-cp310-musllinux_1_1_aarch64.whl", hash = "sha256:40ae1dffb3967a52203105a077415a86044a2bea011b5f321c6aa64b379a3f51"},
@@ -1475,14 +1474,12 @@ files = [
     {file = "pandas-2.2.2-cp311-cp311-musllinux_1_1_x86_64.whl", hash = "sha256:0cace394b6ea70c01ca1595f839cf193df35d1575986e484ad35c4aeae7266c1"},
     {file = "pandas-2.2.2-cp311-cp311-win_amd64.whl", hash = "sha256:873d13d177501a28b2756375d59816c365e42ed8417b41665f346289adc68d24"},
     {file = "pandas-2.2.2-cp312-cp312-macosx_10_9_x86_64.whl", hash = "sha256:9dfde2a0ddef507a631dc9dc4af6a9489d5e2e740e226ad426a05cabfbd7c8ef"},
-    {file = "pandas-2.2.2-cp312-cp312-macosx_11_0_arm64.whl", hash = "sha256:e9b79011ff7a0f4b1d6da6a61aa1aa604fb312d6647de5bad20013682d1429ce"},
     {file = "pandas-2.2.2-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:1cb51fe389360f3b5a4d57dbd2848a5f033350336ca3b340d1c53a1fad33bcad"},
     {file = "pandas-2.2.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:eee3a87076c0756de40b05c5e9a6069c035ba43e8dd71c379e68cab2c20f16ad"},
     {file = "pandas-2.2.2-cp312-cp312-musllinux_1_1_aarch64.whl", hash = "sha256:3e374f59e440d4ab45ca2fffde54b81ac3834cf5ae2cdfa69c90bc03bde04d76"},
     {file = "pandas-2.2.2-cp312-cp312-musllinux_1_1_x86_64.whl", hash = "sha256:43498c0bdb43d55cb162cdc8c06fac328ccb5d2eabe3cadeb3529ae6f0517c32"},
     {file = "pandas-2.2.2-cp312-cp312-win_amd64.whl", hash = "sha256:d187d355ecec3629624fccb01d104da7d7f391db0311145817525281e2804d23"},
     {file = "pandas-2.2.2-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:0ca6377b8fca51815f382bd0b697a0814c8bda55115678cbc94c30aacbb6eff2"},
-    {file = "pandas-2.2.2-cp39-cp39-macosx_11_0_arm64.whl", hash = "sha256:9057e6aa78a584bc93a13f0a9bf7e753a5e9770a30b4d758b8d5f2a62a9433cd"},
     {file = "pandas-2.2.2-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:001910ad31abc7bf06f49dcc903755d2f7f3a9186c0c040b827e522e9cef0863"},
     {file = "pandas-2.2.2-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:66b479b0bd07204e37583c191535505410daa8df638fd8e75ae1b383851fe921"},
     {file = "pandas-2.2.2-cp39-cp39-musllinux_1_1_aarch64.whl", hash = "sha256:a77e9d1c386196879aa5eb712e77461aaee433e54c68cf253053a73b7e49c33a"},
@@ -1842,13 +1839,13 @@ diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pyright"
-version = "1.1.363"
+version = "1.1.364"
 description = "Command line wrapper for pyright"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "pyright-1.1.363-py3-none-any.whl", hash = "sha256:d3b8d73c8d230e26cc3523862f3398032a0c39a00d7bb69dc0f595f8e888fd01"},
-    {file = "pyright-1.1.363.tar.gz", hash = "sha256:00a8f0ae0e339473bb0488f8a2a2dcdf574e94a16cd7b4390d49d144714d8db2"},
+    {file = "pyright-1.1.364-py3-none-any.whl", hash = "sha256:865f1e02873c5dc7427c95acf53659a118574010e6fb364e27e47ec5c46a9f26"},
+    {file = "pyright-1.1.364.tar.gz", hash = "sha256:612a2106a4078ec57efc22b5620729e9bdf4a3c17caba013b534bd33f7d08e5a"},
 ]
 
 [package.dependencies]
@@ -1860,13 +1857,13 @@ dev = ["twine (>=3.4.1)"]
 
 [[package]]
 name = "pytest"
-version = "8.2.0"
+version = "8.2.1"
 description = "pytest: simple powerful testing with Python"
 optional = false
 python-versions = ">=3.8"
 files = [
-    {file = "pytest-8.2.0-py3-none-any.whl", hash = "sha256:1733f0620f6cda4095bbf0d9ff8022486e91892245bb9e7d5542c018f612f233"},
-    {file = "pytest-8.2.0.tar.gz", hash = "sha256:d507d4482197eac0ba2bae2e9babf0672eb333017bcedaa5fb1a3d42c1174b3f"},
+    {file = "pytest-8.2.1-py3-none-any.whl", hash = "sha256:faccc5d332b8c3719f40283d0d44aa5cf101cec36f88cde9ed8f2bc0538612b1"},
+    {file = "pytest-8.2.1.tar.gz", hash = "sha256:5046e5b46d8e4cac199c373041f26be56fdb81eb4e67dc11d4e10811fc3408fd"},
 ]
 
 [package.dependencies]
@@ -1986,7 +1983,6 @@ files = [
     {file = "PyYAML-6.0.1-cp311-cp311-win_amd64.whl", hash = "sha256:bf07ee2fef7014951eeb99f56f39c9bb4af143d8aa3c21b1677805985307da34"},
     {file = "PyYAML-6.0.1-cp312-cp312-macosx_10_9_x86_64.whl", hash = "sha256:855fb52b0dc35af121542a76b9a84f8d1cd886ea97c84703eaa6d88e37a2ad28"},
     {file = "PyYAML-6.0.1-cp312-cp312-macosx_11_0_arm64.whl", hash = "sha256:40df9b996c2b73138957fe23a16a4f0ba614f4c0efce1e9406a184b6d07fa3a9"},
-    {file = "PyYAML-6.0.1-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:a08c6f0fe150303c1c6b71ebcd7213c2858041a7e01975da3a99aed1e7a378ef"},
     {file = "PyYAML-6.0.1-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:6c22bec3fbe2524cde73d7ada88f6566758a8f7227bfbf93a408a9d86bcc12a0"},
     {file = "PyYAML-6.0.1-cp312-cp312-musllinux_1_1_x86_64.whl", hash = "sha256:8d4e9c88387b0f5c7d5f281e55304de64cf7f9c0021a3525bd3b1c542da3b0e4"},
     {file = "PyYAML-6.0.1-cp312-cp312-win32.whl", hash = "sha256:d483d2cdf104e7c9fa60c544d92981f12ad66a457afae824d146093b8c294c54"},
@@ -2246,62 +2242,62 @@ use-chardet-on-py3 = ["chardet (>=3.0.2,<6)"]
 
 [[package]]
 name = "ruff"
-version = "0.4.4"
+version = "0.4.5"
 description = "An extremely fast Python linter and code formatter, written in Rust."
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "ruff-0.4.4-py3-none-macosx_10_12_x86_64.whl", hash = "sha256:29d44ef5bb6a08e235c8249294fa8d431adc1426bfda99ed493119e6f9ea1bf6"},
-    {file = "ruff-0.4.4-py3-none-macosx_11_0_arm64.whl", hash = "sha256:c4efe62b5bbb24178c950732ddd40712b878a9b96b1d02b0ff0b08a090cbd891"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:4c8e2f1e8fc12d07ab521a9005d68a969e167b589cbcaee354cb61e9d9de9c15"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_armv7l.manylinux2014_armv7l.whl", hash = "sha256:60ed88b636a463214905c002fa3eaab19795679ed55529f91e488db3fe8976ab"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:b90fc5e170fc71c712cc4d9ab0e24ea505c6a9e4ebf346787a67e691dfb72e85"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_ppc64.manylinux2014_ppc64.whl", hash = "sha256:8e7e6ebc10ef16dcdc77fd5557ee60647512b400e4a60bdc4849468f076f6eef"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_ppc64le.manylinux2014_ppc64le.whl", hash = "sha256:b9ddb2c494fb79fc208cd15ffe08f32b7682519e067413dbaf5f4b01a6087bcd"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_s390x.manylinux2014_s390x.whl", hash = "sha256:c51c928a14f9f0a871082603e25a1588059b7e08a920f2f9fa7157b5bf08cfe9"},
-    {file = "ruff-0.4.4-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:b5eb0a4bfd6400b7d07c09a7725e1a98c3b838be557fee229ac0f84d9aa49c36"},
-    {file = "ruff-0.4.4-py3-none-musllinux_1_2_aarch64.whl", hash = "sha256:b1867ee9bf3acc21778dcb293db504692eda5f7a11a6e6cc40890182a9f9e595"},
-    {file = "ruff-0.4.4-py3-none-musllinux_1_2_armv7l.whl", hash = "sha256:1aecced1269481ef2894cc495647392a34b0bf3e28ff53ed95a385b13aa45768"},
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+    {file = "watchdog-4.0.1.tar.gz", hash = "sha256:eebaacf674fa25511e8867028d281e602ee6500045b57f43b08778082f7f8b44"},
 ]
 
 [package.extras]
@@ -2568,4 +2566,4 @@ pandas = ["pandas"]
 [metadata]
 lock-version = "2.0"
 python-versions = ">=3.10,<3.14"
-content-hash = "711845b916c770c2006ec8cd5cbf09c4c9ba80a083f635706d0a620b50e9148a"
+content-hash = "1588274b645e001ea4b541217a3f80b783139b27472272889292f966f6042240"
diff --git a/pyproject.toml b/pyproject.toml
index e40d4c8e..304460eb 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,7 +5,7 @@ build-backend = "poetry.core.masonry.api"
 
 [tool.poetry]
 name = "lmo"
-version = "0.13.2"
+version = "0.14.0"
 description = "L-Moments for robust statistics & inference."
 authors = ["Joren Hammudoglu <jhammudoglu@gmail.com>"]
 readme = "README.md"
@@ -49,15 +49,15 @@ optype = "^0.4.0"
 codespell = "^2.2.6"
 hypothesis = {version = "^6.102.4", extras = ["numpy"]}
 pre-commit = "^3.7.1"
-pyright = "^1.1.363"
-pytest = "^8.2.0"
+pyright = "^1.1.364"
+pytest = "^8.2.1"
 pytest-doctestplus = "^1.2.1"
-ruff = "^0.4.4"
+ruff = "^0.4.5"
 tomli = {version = "^2.0.1", python = "<3.11"}
 
 [tool.poetry.group.docs.dependencies]
 mkdocs = "^1.6.0"
-mkdocs-material = "^9.5.23"
+mkdocs-material = "^9.5.24"
 mkdocs-include-markdown-plugin = "^6.0.6"
 mkdocstrings = {version = "^0.25.1", extras = ["python"]}
 mkdocs-git-revision-date-localized-plugin = "^1.2.5"
@@ -87,7 +87,7 @@ numpy = "<=2"
 optional = true
 [tool.poetry.group.numpy2.dependencies]
 numpy = {version = ">=2.0.0rc2", allow-prereleases = true}
-scipy = ">=1.13.0"
+scipy = ">=1.13.1"
 
 [tool.poetry.extras]
 pandas = ["pandas"]
@@ -172,7 +172,6 @@ extend-exclude = [
 ]
 
 [tool.ruff.lint]
-ignore-init-module-imports = true
 preview = true
 select = [
     "F",        # pyflakes
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 00000000..3350ec3c
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,25 @@
+# ruff: noqa: SLF001
+# pyright: reportPrivateUsage=false
+import contextlib
+from collections.abc import Iterator
+
+import pytest
+
+from lmo import _lm
+
+
+@contextlib.contextmanager
+def tmp_cache() -> Iterator[_lm._Cache]:
+    cache_tmp: _lm._Cache = {}
+    cache_old, _lm._CACHE = _lm._CACHE, cache_tmp
+    try:
+        yield cache_tmp
+    finally:
+        _lm._CACHE = cache_old
+
+
+@pytest.fixture(name='tmp_cache')
+def tmp_cache_fixture():
+    with tmp_cache() as cache:
+        assert not cache
+        yield cache
diff --git a/tests/test_weights.py b/tests/test_weights.py
index aa0929bd..88f60121 100644
--- a/tests/test_weights.py
+++ b/tests/test_weights.py
@@ -1,78 +1,166 @@
+import functools
+from typing import Any
+
 import numpy as np
+import pytest
 from hypothesis import (
     given,
     strategies as st,
 )
+from hypothesis.extra import numpy as hnp
+from numpy.testing import (
+    assert_allclose as _assert_allclose,
+    assert_array_equal,
+)
+
+from lmo import l_weights
+from .conftest import tmp_cache
 
-from lmo._lm import l_weights
+
+# matches np.allclose
+assert_allclose = functools.partial(_assert_allclose, rtol=1e-5, atol=1e-8)
 
 
-MAX_N = 1 << 10
 MAX_R = 8
 MAX_T = 4
+MIN_N = MAX_R + MAX_T * 2 + 1
+MAX_N = 1 << 8
+
 
-st_n = st.integers(MAX_R + MAX_T * 2 + 1, MAX_N)
+st_n = st.integers(MIN_N, MAX_N)
 st_r = st.integers(1, MAX_R)
 
-st_t_f = st.floats(0, MAX_T, exclude_min=True)
-st_t_i = st.integers(1, MAX_T)
-st_t_i0 = st.integers(0, MAX_T)
+st_i_eq0 = st.just(0)
+st_i_ge0 = st.integers(0, MAX_T)
+st_i_gt0 = st.integers(1, MAX_T)
+
+st_i2_eq0 = st.tuples(st.just(0), st.just(0))
+st_i2_ge0 = st.tuples(st.integers(0, MAX_T), st.integers(0, MAX_T))
+st_i2_gt0 = st.tuples(st.integers(1, MAX_T), st.integers(1, MAX_T))
 
-st_trim_i = st.tuples(st_t_i, st_t_i)
-st_trim_i0 = st.tuples(st_t_i0, st_t_i0)
+st_i12_eq0 = st_i_eq0 | st_i2_eq0
+st_i12_ge0 = st_i_ge0 | st_i2_ge0
+st_i12_gt0 = st_i_gt0 | st_i2_gt0
 
+st_floating = hnp.floating_dtypes(sizes=[32, 64])
 
-@given(n=st_n, r=st_r, trim0=st.just((0, 0)))
-def test_l_weights_alias(n, r, trim0):
-    w_l = l_weights(r, n)
-    w_tl = l_weights(r, n, trim0)
 
-    assert np.array_equal(w_l, w_tl)
+@given(n=st_n, trim=st_i12_eq0)
+def test_empty(n: int, trim: int | tuple[int, int]):
+    w = l_weights(0, n, trim, cache=False)
+    assert w.shape == (0, n)
 
 
-@given(n=st_n, r=st_r, trim=st_trim_i0)
-def test_l_weights_basic(n, r, trim):
-    w = l_weights(r, n, trim)
+@given(n=st_n, r=st_r, trim=st_i12_eq0)
+def test_untrimmed(n: int, r: int, trim: int | tuple[int, int]):
+    w_l = l_weights(r, n, cache=False)
+    w_tl = l_weights(r, n, trim, cache=False)
+
+    assert_array_equal(w_l, w_tl)
+
+
+@given(n=st_n, r=st_r, trim=st_i12_ge0)
+def test_default(n: int, r: int, trim: int | tuple[int, int]):
+    w = l_weights(r, n, trim, cache=False)
 
     assert w.shape == (r, n)
-    assert np.all(np.isfinite(n))
+    assert np.all(np.isfinite(w))
     assert w.dtype.type is np.float64
 
 
-# symmetries only apply for symmetric trimming, for obvious reasons
-@given(n=st_n, t=st_t_i0)
-def test_l_weights_symmetry(n, t):
-    w = l_weights(MAX_R, n, (t, t))
+@given(n=st_n, r=st_r, trim=st_i12_ge0, dtype=st_floating)
+def test_dtype(
+    n: int,
+    r: int,
+    trim: int | tuple[int, int],
+    dtype: np.dtype[np.floating[Any]],
+):
+    w = l_weights(r, n, trim, dtype=dtype, cache=False)
+
+    assert np.all(np.isfinite(w))
+    assert w.dtype.type is dtype.type
+
+
+@given(n=st_n, t=st_i_ge0)
+def test_symmetry(n: int, t: int):
+    w = l_weights(MAX_R, n, (t, t), cache=False)
 
     w_evn_lhs, w_evn_rhs = w[::2], w[::2, ::-1]
-    assert np.allclose(w_evn_lhs, w_evn_rhs)
+    assert_allclose(w_evn_lhs, w_evn_rhs)
 
     w_odd_lhs, w_odd_rhs = w[1::2], w[1::2, ::-1]
-    assert np.allclose(w_odd_lhs, -w_odd_rhs)
+    assert_allclose(w_odd_lhs, -w_odd_rhs)
 
 
 def test_l_weights_symmetry_large_even_r():
-    w = l_weights(16, MAX_N * 2)
+    w = l_weights(16, MAX_N * 2, cache=False)
 
     w_evn_lhs, w_evn_rhs = w[::2], w[::2, ::-1]
-    assert np.allclose(w_evn_lhs, w_evn_rhs)
+    assert_allclose(w_evn_lhs, w_evn_rhs)
 
 
-@given(n=st_n, r=st_r, trim=st_trim_i)
-def test_l_weights_trim(n, r, trim):
-    w = l_weights(r, n, trim)
+@given(n=st_n, r=st_r, trim=st_i2_gt0)
+def test_trim(n: int, r: int, trim: tuple[int, int]):
+    w = l_weights(r, n, trim, cache=False)
 
     tl, tr = trim
     assert tl > 0
     assert tr > 0
 
-    assert np.allclose(w[:, :tl], 0)
-    assert np.allclose(w[:, n - tr :], 0)
+    assert_allclose(w[:, :tl], 0)
+    assert_allclose(w[:, n - tr :], 0)
 
 
-@given(n=st_n, r=st.integers(2, MAX_R), trim=st_trim_i0)
-def test_tl_weights_sum(n, r, trim):
-    w = l_weights(r, n, trim)
+@given(n=st_n, r=st.integers(2, MAX_R), trim=st_i12_ge0)
+def test_sum(n: int, r: int, trim: int | tuple[int, int]):
+    w = l_weights(r, n, trim, cache=False)
     w_sum = w.sum(axis=-1)
 
-    assert np.allclose(w_sum, np.eye(r, 1).ravel())
+    assert_allclose(w_sum, np.eye(r, 1).ravel())
+
+
+@given(n=st_n, r=st.integers(4, MAX_R), trim=st_i12_ge0)
+def test_uncached(n: int, r: int, trim: int | tuple[int, int]):
+    with tmp_cache() as cache:
+        w0 = l_weights(r, n, trim, cache=False)
+        w1 = l_weights(r, n, trim, cache=False)
+
+        assert not cache
+        assert w0 is not w1
+        assert_array_equal(w0, w1)
+
+
+@given(n=st_n, r=st.integers(4, MAX_R), trim=st_i12_ge0, dtype=st_floating)
+def test_cached(
+    n: int,
+    r: int,
+    trim: int | tuple[int, int],
+    dtype: np.dtype[np.floating[Any]],
+):
+    s, t = trim if isinstance(trim, tuple) else (trim, trim)
+    cache_key = dtype.char, n, s, t
+
+    with tmp_cache() as cache:
+        assert not cache
+
+        w0 = l_weights(r, n, trim, dtype=dtype, cache=True)
+        assert w0.dtype.char == cache_key[0]
+        assert cache
+        assert cache_key in cache
+        w0_cached = cache[cache_key]
+
+        # cached weights should be readonly
+        w0_orig = w0[0, 0]
+        with pytest.raises(
+            ValueError,
+            match='assignment destination is read-only',
+        ):
+            w0[0, 0] = w0_orig + 1
+        assert w0[0, 0] == w0_orig
+
+        w1 = l_weights(r, n, trim, dtype=dtype, cache=True)
+        w1_cached = cache[cache_key]
+        assert w0_cached is w1_cached
+
+        # this requires `r>=4` and `r == r_cached`
+        assert w0 is w1