From e93c33730745a1543628fc4a55e776ad78e0a7b2 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 00:51:37 -0400 Subject: [PATCH 01/13] fix conflict during rebase --- src/galax/potential/_src/scf/__init__.py | 11 + src/galax/potential/_src/scf/bfe.py | 192 ++++++++++++++++++ src/galax/potential/_src/scf/bfe_helper.py | 91 +++++++++ src/galax/potential/_src/scf/coeffs.py | 108 ++++++++++ src/galax/potential/_src/scf/coeffs_helper.py | 64 ++++++ src/galax/potential/_src/scf/gegenbauer.py | 102 ++++++++++ src/galax/potential/_src/scf/utils.py | 102 ++++++++++ tests/potential/scf/test_coeff_helper.py | 76 +++++++ tests/potential/scf/test_coeffs.py | 42 ++++ tests/potential/scf/test_gegenbauer.py | 85 ++++++++ tests/potential/scf/test_utils.py | 145 +++++++++++++ 11 files changed, 1018 insertions(+) create mode 100644 src/galax/potential/_src/scf/__init__.py create mode 100644 src/galax/potential/_src/scf/bfe.py create mode 100644 src/galax/potential/_src/scf/bfe_helper.py create mode 100644 src/galax/potential/_src/scf/coeffs.py create mode 100644 src/galax/potential/_src/scf/coeffs_helper.py create mode 100644 src/galax/potential/_src/scf/gegenbauer.py create mode 100644 src/galax/potential/_src/scf/utils.py create mode 100644 tests/potential/scf/test_coeff_helper.py create mode 100644 tests/potential/scf/test_coeffs.py create mode 100644 tests/potential/scf/test_gegenbauer.py create mode 100644 tests/potential/scf/test_utils.py diff --git a/src/galax/potential/_src/scf/__init__.py b/src/galax/potential/_src/scf/__init__.py new file mode 100644 index 000000000..a62b0ea67 --- /dev/null +++ b/src/galax/potential/_src/scf/__init__.py @@ -0,0 +1,11 @@ +from . import bfe, bfe_helper, coeffs, coeffs_helper +from .bfe import * +from .bfe_helper import * +from .coeffs import * +from .coeffs_helper import * + +__all__: list[str] = [] +__all__ += bfe.__all__ +__all__ += bfe_helper.__all__ +__all__ += coeffs.__all__ +__all__ += coeffs_helper.__all__ diff --git a/src/galax/potential/_src/scf/bfe.py b/src/galax/potential/_src/scf/bfe.py new file mode 100644 index 000000000..9cdefb47f --- /dev/null +++ b/src/galax/potential/_src/scf/bfe.py @@ -0,0 +1,192 @@ +"""Self-Consistent Field Potential.""" + +__all__ = ["SCFPotential", "STnlmSnapshotParameter"] + +from collections.abc import Callable +from functools import partial +from typing import Any + +import equinox as eqx +import jax +import jax.numpy as jnp +from jaxtyping import Array, Float + +import galax.typing as gt +from .bfe_helper import phi_nl_vec, rho_nl as calculate_rho_nl +from .coeffs import compute_coeffs_discrete +from .gegenbauer import GegenbauerCalculator +from .utils import cartesian_to_spherical, real_Ylm +from galax.potential._src.core import AbstractPotential +from galax.potential._src.param import AbstractParameter, ParameterField + +############################################################################## + + +class SCFPotential(AbstractPotential): + r"""Self-Consistent Field (SCF) potential. + + A gravitational potential represented as a basis function expansion. This + uses the self-consistent field (SCF) method of Hernquist & Ostriker (1992) + and Lowing et al. (2011), and represents all coefficients as real + quantities. + + Parameters + ---------- + m : numeric + Scale mass. + r_s : numeric + Scale length. + Snlm : Array[float, (nmax+1, lmax+1, lmax+1)] | Callable + Array of coefficients for the cos() terms of the expansion. This should + be a 3D array with shape `(nmax+1, lmax+1, lmax+1)`, where `nmax` is the + number of radial expansion terms and `lmax` is the number of spherical + harmonic `l` terms. If a callable is provided, it should accept a + single argument `t` and return the array of coefficients for that time. + Tnlm : Array[float, (nmax+1, lmax+1, lmax+1)] | Callable + Array of coefficients for the sin() terms of the expansion. This should + be a 3D array with shape `(nmax+1, lmax+1, lmax+1)`, where `nmax` is the + number of radial expansion terms and `lmax` is the number of spherical + harmonic `l` terms. If a callable is provided, it should accept a + single argument `t` and return the array of coefficients for that time. + units : iterable + Unique list of non-reducable units that specify (at minimum) the length, + mass, time, and angle units. + """ + + m: AbstractParameter = ParameterField(dimensions="mass") + r_s: AbstractParameter = ParameterField(dimensions="length") + Snlm: AbstractParameter = ParameterField(dimensions="dimensionless") + Tnlm: AbstractParameter = ParameterField(dimensions="dimensionless") + + nmax: int = eqx.field(init=False, static=True, repr=False) + lmax: int = eqx.field(init=False, static=True, repr=False) + _ultra_sph: GegenbauerCalculator = eqx.field(init=False, static=True, repr=False) + + def __post_init__(self) -> None: + super().__post_init__() + + # shape parameters + shape = self.Snlm(0).shape + object.__setattr__(self, "nmax", shape[0] - 1) + object.__setattr__(self, "lmax", shape[1] - 1) + + # gegenbauer calculator + object.__setattr__(self, "_ultra_sph", GegenbauerCalculator(self.nmax)) + + # ========================================================================== + + @partial(jax.jit, inline=True) + def _potential( + self, xyz: gt.BatchQVec3, t: gt.BatchableRealQScalar, / + ) -> gt.VecN | gt.FloatScalar: + r_s = self.r_s(t) + r, theta, phi = cartesian_to_spherical(xyz).T + + s = jnp.atleast_1d(r / r_s) # ([n],[l],[m],[N]) + theta = jnp.atleast_1d(theta)[None, None, None] # ([n],[l],[m],[N]) + phi = jnp.atleast_1d(phi)[None, None, None] # ([n],[l],[m],[N]) + + ns = jnp.arange(self.nmax + 1)[:, None, None] # (n, [l], [m]) + ls = jnp.arange(self.lmax + 1)[None, :, None] # ([n], l, [m]) + phi_nl = phi_nl_vec(s, ns, ls, self._ultra_sph) # (n, l, [m], N) + + li, mi = jnp.tril_indices(self.lmax + 1) # (l*(l+1)//2,) + shape = (1, self.lmax + 1, self.lmax + 1, 1) # ([n], l, m, [N]) + midx = jnp.zeros(shape, dtype=int).at[:, li, mi, 0].set(mi) # ([n], l, m, [N]) + + Ylm = jnp.zeros(shape[:-1] + (len(s),)) + Ylm = Ylm.at[0, li, mi, :].set( + real_Ylm(theta[:, 0, 0, :], li[..., None], mi[..., None]) + ) + + Snlm = self.Snlm(t, r_s=r_s)[..., None] + Tnlm = self.Tnlm(t, r_s=r_s)[..., None] + + out = (self._G * self.m(t) / r_s) * jnp.sum( + Ylm * phi_nl * (Snlm * jnp.cos(midx * phi) + Tnlm * jnp.sin(midx * phi)), + axis=(0, 1, 2), + ) + return out[0] if len(xyz.shape) == 1 else out + + @partial(jax.jit, inline=True) + @eqx.filter_vmap(in_axes=(None, 1, None)) # type: ignore[misc] # on `q` axis 1 + def _density(self, q: gt.LengthVec3, /, t: gt.RealQScalar) -> Float[Array, "N"]: # type: ignore[name-defined] + """Compute the density at the given position(s).""" + r, theta, phi = cartesian_to_spherical(q) + r_s = self.r_s(t) + s = jnp.atleast_1d(r / r_s)[:, None, None, None] + theta = jnp.atleast_1d(theta)[:, None, None, None] + phi = jnp.atleast_1d(phi)[:, None, None, None] + + ns = jnp.arange(self.nmax + 1)[:, None, None] # (n, [l], [m]) + ls = jnp.arange(self.lmax + 1)[None, :, None] # ([n], l, [m]) + + phi_nl = calculate_rho_nl(s, ns[None], ls[None], gegenbauer=self._ultra_sph) + + li, mi = jnp.tril_indices(self.lmax + 1) # (l*(l+1)//2,) + shape = (1, 1, self.lmax + 1, self.lmax + 1) + midx = jnp.zeros(shape, dtype=int).at[:, :, li, mi].set(mi) + Ylm = jnp.zeros((len(theta), 1, self.lmax + 1, self.lmax + 1)) + Ylm = Ylm.at[:, li, mi, :].set(real_Ylm(li[None], mi[None], theta[:, :, 0, 0])) + + Snlm = self.Snlm(t, r_s=r_s)[None] + Tnlm = self.Tnlm(t, r_s=r_s)[None] + + out = (self._G * self.m(t) / r_s) * jnp.sum( + Ylm * phi_nl * (Snlm * jnp.cos(midx * phi) + Tnlm * jnp.sin(midx * phi)), + axis=(1, 2, 3), + ) + return out[0] if len(q.shape) == 1 else out + + +# ============================================================================= + + +class STnlmSnapshotParameter(AbstractParameter): # type: ignore[misc] + """Parameter for the STnlm coefficients.""" + + snapshot: Callable[ # type: ignore[name-defined] + [Float[Array, "N"]], + tuple[Float[Array, "3 N"], Float[Array, "N"]], + ] + """Cartesian coordinates of the snapshot. + + This should be a callable that accepts a single argument `t` and returns + the cartesian coordinates and the masses of the snapshot at that time. + """ + + nmax: int = eqx.field(static=True, converter=int) + """Radial expansion term.""" + + lmax: int = eqx.field(static=True, converter=int) + """Spherical harmonic term.""" + + def __call__( + self, t: gt.TimeScalar, *, r_s: gt.LengthScalar, **_: Any + ) -> tuple[ + Float[Array, "{self.nmax}+1 {self.lmax}+1 {self.lmax}+1"], + Float[Array, "{self.nmax}+1 {self.lmax}+1 {self.lmax}+1"], + ]: + """Return the coefficients at the given time(s). + + Parameters + ---------- + t : float | Array[float, ()] + Time at which to evaluate the coefficients. + r_s : float | Array[float, ()] + Scale length of the potential at the given time(s. + **kwargs : Any + Additional keyword arguments are ignored. + + Returns + ------- + Snlm : Array[float, (nmax+1, lmax+1, lmax+1)] + The value of the cosine expansion coefficient. + Tnlm : Array[float, (nmax+1, lmax+1, lmax+1)] + The value of the sine expansion coefficient. + """ + xyz, m = self.snapshot(t) + coeffs: tuple[Array, Array] = compute_coeffs_discrete( + xyz, m, nmax=self.nmax, lmax=self.lmax, r_s=r_s + ) + return coeffs diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py new file mode 100644 index 000000000..9c36321fb --- /dev/null +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -0,0 +1,91 @@ +"""Self-Consistent Field Potential.""" + +__all__: list[str] = [] + +from functools import partial + +import jax +from jaxtyping import Array, Float + +from .coeffs_helper import normalization_Knl +from .utils import psi_of_r +from galax.potential._src.scf.gegenbauer import GegenbauerCalculator +from galax.typing import IntLike + + +@partial(jax.jit, static_argnames=("gegenbauer",)) +def rho_nl( + s: Float[Array, "N"], n: int, l: int, *, gegenbauer: GegenbauerCalculator +) -> Float[Array, "N"]: + r"""Radial density expansion terms. + + Parameters + ---------- + s : Array[float, (n,)] + Scaled radius :math:`r/r_s`. + n : int + Radial expansion term. + l : int + Spherical harmonic term. + gegenbauer : GegenbauerCalculator, keyword-only + Gegenbauer calculator. This is used to compute the Gegenbauer + polynomials efficiently. + + Returns + ------- + Array[float, (n,)] + """ + return ( + jnp.sqrt(4 * jnp.pi) + * (normalization_Knl(n=n, l=l) / (2 * jnp.pi)) + * (s**l / (s * (1 + s) ** (2 * l + 3))) + * gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + ) + + +# ====================================================================== + + +@partial(jax.jit, static_argnames=("gegenbauer",)) +def phi_nl( + s: Float[Array, "samples"], n: IntLike, l: IntLike, gegenbauer: GegenbauerCalculator +) -> Float[Array, "samples"]: + r"""Angular density expansion terms. + + Parameters + ---------- + s : Array[float, (n_samples,)] + Scaled radius :math:`r/r_s`. + n : int + Radial expansion term. + l : int + Spherical harmonic term. + gegenbauer : GegenbauerCalculator, keyword-only + Gegenbauer calculator. This is used to compute the Gegenbauer + polynomials efficiently. + + Returns + ------- + Array[float, (n_samples,)] + + Examples + -------- + >>> import jax.numpy as jnp + >>> from galax.potential._src.scf.gegenbauer import GegenbauerCalculator + >>> gegenbauer = GegenbauerCalculator(100) + >>> phi_nl(0.5, 1, 1, gegenbauer=gegenbauer) + Array(0.5, dtype=float32) + >>> phi_nl(jnp.array([0.5, 0.5]), 1, 1, gegenbauer=gegenbauer) + Array([0.5, 0.5], dtype=float32) + """ + return ( + -jnp.sqrt(4 * jnp.pi) + * (s**l / (1.0 + s) ** (2 * l + 1)) + * gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + ) + + +phi_nl_vec = jnp.vectorize(phi_nl, signature="(n),(),()->(n)", excluded=(3,)) + +phi_nl_grad = jax.jit(jnp.vectorize(jax.grad(phi_nl, argnums=0), excluded=(3,))) +r"""Derivative :math:`\frac{d}{dr} \phi_{nl}`.""" diff --git a/src/galax/potential/_src/scf/coeffs.py b/src/galax/potential/_src/scf/coeffs.py new file mode 100644 index 000000000..bcf92b0cf --- /dev/null +++ b/src/galax/potential/_src/scf/coeffs.py @@ -0,0 +1,108 @@ +"""Self-Consistent Field Potential.""" + +__all__ = ["compute_coeffs_discrete"] + + +from functools import partial + +import jax +import jax.numpy as jnp +from jaxtyping import Array, Float + +import galax.typing as gt +from .bfe_helper import phi_nl_vec +from .coeffs_helper import expansion_coeffs_Anl_discrete +from .gegenbauer import GegenbauerCalculator +from .utils import cartesian_to_spherical, real_Ylm + + +@partial(jax.jit, static_argnames=("nmax", "lmax", "gegenbauer")) +def compute_coeffs_discrete( + xyz: Float[Array, "samples 3"], + mass: Float[Array, "samples"], # type: ignore[name-defined] + *, + nmax: gt.IntLike, + lmax: gt.IntLike, + r_s: gt.FloatQScalar, + gegenbauer: GegenbauerCalculator | None = None, +) -> tuple[ + Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], + Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], +]: + """Compute expansion coefficients for the SCF potential. + + Compute the expansion coefficients for representing the density distribution + of input points as a basis function expansion. The points, ``xyz``, are + assumed to be samples from the density distribution. + + This is Equation 15 of Lowing et al. (2011). + + Parameters + ---------- + xyz : Array[float, (n_samples, 3)] + Samples from the density distribution. + :todo:`unit support` + mass : Array[float, (n_samples,)] + Mass of each sample. + :todo:`unit support` + nmax : int + Maximum value of ``n`` for the radial expansion. + lmax : int + Maximum value of ``l`` for the spherical harmonics. + r_s : numeric + Scale radius. + :todo:`unit support` + + gegenbauer : GegenbauerCalculator, optional + Gegenbauer calculator. This is used to compute the Gegenbauer + polynomials efficiently. If not provided, a new calculator will be + created. + + Returns + ------- + Snlm : Array[float, (nmax+1, lmax+1, lmax+1)] + The value of the cosine expansion coefficient. + Tnlm : Array[float, (nmax+1, lmax+1, lmax+1)] + The value of the sine expansion coefficient. + """ + if gegenbauer is None: + ggncalc = GegenbauerCalculator(nmax=nmax) + elif gegenbauer.nmax < nmax: + msg = "gegenbauer.nmax != nmax" + raise ValueError(msg) + else: + ggncalc = gegenbauer + + rthetaphi = cartesian_to_spherical(xyz) + r = rthetaphi[..., 0] + theta = rthetaphi[..., 1] + phi = rthetaphi[..., 2] + s = r / r_s + + ns = jnp.arange(nmax + 1)[:, None] # (n, l) + ls = jnp.arange(lmax + 1)[None, :] # (n, l) + + Anl_til = expansion_coeffs_Anl_discrete(ns, ls) # (n, l) + phinl = phi_nl_vec(s, ns, ls, ggncalc) # (n, l, N) + + li, mi = jnp.tril_indices(lmax + 1) # (l*(l+1)//2,) + lm = jnp.zeros((lmax + 1, lmax + 1), dtype=int).at[li, mi].set(li) # (l, m) + ms = jnp.zeros((lmax + 1, lmax + 1), dtype=int).at[li, mi].set(mi) # (l, m) + # TODO: this is VERY SLOW. Can we do better? + Ylm = real_Ylm(theta, lm, ms, m_max=100) # (l, m, N) + + delta = jax.lax.select(ms == 0, jnp.ones_like(ms), jnp.zeros_like(ms)) # (l, m) + mvalid = jnp.zeros((lmax + 1, lmax + 1)).at[li, mi].set(1) # select m <= l + + tmp = ( # (n, l, m, N) using broadcasting + mvalid[None, :, :, None] + * (2 - delta[None, :, :, None]) + * Anl_til[:, :, None, None] + * mass[None, None, None, :] + * phinl[:, :, None, :] + * Ylm[None, :, :, :] + ) + Snlm = jnp.sum(tmp * jnp.cos(ms[None, :, :, None] * phi[None, None, None]), axis=-1) + Tnlm = jnp.sum(tmp * jnp.sin(ms[None, :, :, None] * phi[None, None, None]), axis=-1) + + return Snlm, Tnlm diff --git a/src/galax/potential/_src/scf/coeffs_helper.py b/src/galax/potential/_src/scf/coeffs_helper.py new file mode 100644 index 000000000..775ff73de --- /dev/null +++ b/src/galax/potential/_src/scf/coeffs_helper.py @@ -0,0 +1,64 @@ +"""Self-Consistent Field Potential.""" + +__all__: list[str] = [] + +from typing import overload + +from jax.scipy.special import gamma +from jaxtyping import Array, Float, Integer + +import quaxed.numpy as jnp + +from .utils import factorial + + +@overload +def normalization_Knl(n: int, l: int) -> float: ... + + +@overload +def normalization_Knl(n: Array, l: Array) -> Array: ... + + +def normalization_Knl( + n: Integer[Array, "*#shape"] | int, l: Integer[Array, "*#shape"] | int +) -> Float[Array, "*shape"] | float: + """SCF normalization factor. + + Parameters + ---------- + n : int + Radial expansion term. + l : int + Spherical harmonic term. + + Returns + ------- + float + """ + return 0.5 * n * (n + 4 * l + 3.0) + (l + 1) * (2 * l + 1) + + +def expansion_coeffs_Anl_discrete( + n: Integer[Array, "*#shape"], l: Integer[Array, "*#shape"] +) -> Float[Array, "*shape"]: + """Return normalization factor for the coefficients. + + Equation 16 of Lowing et al. (2011). + + Parameters + ---------- + n : int + Radial expansion term. + l : int + spherical harmonic term. + + Returns + ------- + float + """ + Knl = normalization_Knl(n=n, l=l) + prefac = -(2 ** (8.0 * l + 6)) / (4 * jnp.pi * Knl) + numerator = factorial(n) * (n + 2 * l + 1.5) * gamma(2 * l + 1.5) ** 2 + denominator = gamma(n + 4.0 * l + 3.0) + return prefac * (numerator / denominator) diff --git a/src/galax/potential/_src/scf/gegenbauer.py b/src/galax/potential/_src/scf/gegenbauer.py new file mode 100644 index 000000000..fe2749079 --- /dev/null +++ b/src/galax/potential/_src/scf/gegenbauer.py @@ -0,0 +1,102 @@ +"""Gegenbauer polynomials.""" + +__all__ = ["GegenbauerCalculator"] + +from functools import partial +from typing import Protocol, runtime_checkable + +import equinox as eqx +import jax +import sympy as sp +import sympy2jax +from jax.scipy.special import gamma + +from .utils import factorial +from galax.typing import FloatLike, IntLike, VecN +from galax.utils._jax import vectorize_method + + +@runtime_checkable +class AbstractGegenbauerDerivativeTerm(Protocol): + def __call__(self, x: VecN, alpha: float) -> VecN: ... + + +def _compute_weight_function_derivatives( + nmax: int, +) -> tuple[AbstractGegenbauerDerivativeTerm, ...]: + """Compute the nth derivative of the weight function for the Gegenbauer polynomials. + + .. warning:: + + This function is still VERY slow for nmax > 7. + + .. todo:: + + This isn't quite Equation 22.2.3 of Abramowitz & Stegun (1972). + + It's too costly to have JAX compute the Gegenbauer polynomials directly, so + we instead compute the nth derivative of the weight function, and then + use the recurrence relation to compute the Gegenbauer polynomials. + """ + # Make Symbols + x: sp.Symbol = sp.Symbol("x") + n: sp.Symbol = sp.Symbol("n", integer=True) + alpha: sp.Symbol = sp.Symbol("alpha", positive=True) + + # weight function for the Gegenbauer polynomials + weight = (1 - x**2) ** (n + alpha - 0.5) + + # Compute the nth derivative term for the Gegenbauer polynomials + # start with the 0th derivative + fn_sympy: sp.Expr = sp.simplify(sp.diff(weight, x, 0)) + func_list = [] + for i in range(nmax + 1): + # Symbolic computation of the nth derivative + if i > 0: + fn_sympy = sp.simplify(sp.diff(fn_sympy, x, 1)) + # Convert to a JAX function + fn_jax = sympy2jax.SymbolicModule(fn_sympy) + # Re-arrange the arguments + fn_jax_save = lambda x, alpha, n=i, fn=fn_jax: fn( # noqa: E731 + x=x, alpha=alpha, n=n + ) + func_list.append(fn_jax_save) + return tuple(func_list) + + +class GegenbauerCalculator(eqx.Module): # type: ignore[misc] + """Gegenbauer (ultraspherical) polynomial.""" + + nmax: int + """Maximum order of the Gegenbauer polynomials.""" + + _weights: tuple[AbstractGegenbauerDerivativeTerm, ...] = eqx.field( + init=False, static=True, repr=False + ) + """Tuple of weights for nth derivative of the Gegenbauer polynomials. + + This is computed in the __post_init__ method. + """ + + def __post_init__(self) -> None: + object.__setattr__( + self, "_weights", _compute_weight_function_derivatives(self.nmax) + ) + + # TODO: switch requires integer n, but everything else already vectorized + @partial(jax.jit, static_argnames=("n", "alpha")) + @vectorize_method(signature="(),(),()->()") + def __call__( + self, n: IntLike, alpha: IntLike | FloatLike, x: FloatLike | VecN + ) -> FloatLike | VecN: + r"""Calculate :math:`C_n^\alpha(x)`.""" + # # TODO: the Gegenbauer polynomials have limits on valid inputs + nth_deriv = jax.lax.switch(n, self._weights, x, alpha) + + # TODO: write out full mathematical derivation + factor0 = ((-1.0) ** n) / ((2**n) * factorial(n)) + factor1 = (gamma(alpha + 0.5) * gamma(n + 2.0 * alpha)) / ( + gamma(2.0 * alpha) * gamma(alpha + n + 0.5) + ) + factor2 = (1.0 - x**2) ** (-alpha + 0.5) + return factor0 * factor1 * factor2 * nth_deriv diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py new file mode 100644 index 000000000..6847c366a --- /dev/null +++ b/src/galax/potential/_src/scf/utils.py @@ -0,0 +1,102 @@ +"""Utility Functions.""" + +from functools import partial +from typing import TypeAlias, TypeVar, cast + +import jax +from jax import lax +from jax._src.numpy.util import promote_args_inexact +from jax.scipy.special import sph_harm +from jaxtyping import ArrayLike, Shaped + +import quaxed.numpy as jnp + +import galax.typing as gt + +BatchableIntLike: TypeAlias = Shaped[gt.IntLike, "*#batch"] + +T = TypeVar("T", bound=ArrayLike) + + +@partial(jax.jit) +@partial(jax.numpy.vectorize, signature="(3)->(3)") +def cartesian_to_spherical(xyz: gt.Vec3, /) -> gt.Vec3: + """Convert Cartesian coordinates to spherical coordinates. + + Parameters + ---------- + xyz : Array[float, (3,)] + Cartesian coordinates in the form (x, y, z). + + Returns + ------- + r_theta_phi : Array[float, (3,)] + Spherical radius. + Inclination (polar) angle in [0, pi] from North to South pole. + Azimuthal angle in [-pi, pi] + """ + r = jnp.sqrt(jnp.sum(xyz**2, axis=0)) # spherical radius + # TODO: this is a hack to avoid the ambiguity at r==0. This should be done better. + theta = jax.lax.select( + r == 0, jnp.zeros_like(r), jnp.arccos(xyz[2] / r) + ) # inclination angle + phi = jnp.arctan2(xyz[1], xyz[0]) # azimuthal angle + return jnp.array([r, theta, phi]) + + +# TODO: replace with upstream, when available +def factorial(n: T) -> T: + """Factorial helper function.""" + (n,) = promote_args_inexact("factorial", n) + return cast("T", xp.where(n < 0, 0, lax.exp(lax.lgamma(n + 1)))) + + +def psi_of_r(r: T) -> T: + r""":math:`\psi(r) = (r-1)/(r+1)`. + + Equation 9 of Lowing et al. (2011). + """ + return cast("T", (r - 1.0) / (r + 1.0)) + + +# ============================================================================= + + +@partial(jax.numpy.vectorize, signature="(n),(),()->(n)", excluded=(3,)) +@partial(jax.jit, static_argnames=("m_max",)) # TODO: should l,m be static? +def _real_Ylm(theta: gt.VecN, l: gt.IntLike, m: gt.IntLike, m_max: int) -> gt.VecN: + # TODO: sph_harm only supports scalars, even though it returns an array! + theta = xp.atleast_1d(theta) + return sph_harm( + m, xp.atleast_1d(l), theta=xp.zeros_like(theta), phi=theta, n_max=m_max + ).real + + +@partial(jax.jit, static_argnames=("m_max",)) +def real_Ylm( + theta: gt.FloatAnyShape, l: BatchableIntLike, m: BatchableIntLike, m_max: int = 100 +) -> gt.FloatAnyShape: + r"""Get the spherical harmonic :math:`Y_{lm}(\theta)` of the polar angle. + + This is different than the scipy (and thus JAX) convention, which is + :math:`Y_{lm}(\theta, \phi)`. + Note that scipy also uses the opposite convention for theta, phi where + theta is the azimuthal angle and phi is the polar angle. + + Parameters + ---------- + theta : Array[float, (*shape, N)] + Polar angle in [0, pi]. + l, m : int | Array[int, ()] + Spherical harmonic terms. l in [0,lmax], m in [0,l]. + m_max : int, optional + Maximum order of the spherical harmonic expansion. + + Returns + ------- + Array[float, (l, m, N)] + Spherical harmonic. The shape is batched using the vectorization signature + ``(n),(),()->(n)``. + """ + # TODO: raise an error if m > m_max + return _real_Ylm(theta, l, m, m_max) diff --git a/tests/potential/scf/test_coeff_helper.py b/tests/potential/scf/test_coeff_helper.py new file mode 100644 index 000000000..0190b3520 --- /dev/null +++ b/tests/potential/scf/test_coeff_helper.py @@ -0,0 +1,76 @@ +"""Test the Gegenbauer class.""" + +import jax +import numpy as np +import pytest + +import quaxed.numpy as jnp + +from galax.potential._src.scf.bfe_helper import rho_nl +from galax.potential._src.scf.coeffs_helper import ( + expansion_coeffs_Anl_discrete, + normalization_Knl, +) +from galax.potential._src.scf.gegenbauer import GegenbauerCalculator + + +def test_normalization_Knl(): + """Test the ``normalization_Knl`` function. + + .. todo:: + + This test is not very good. It should be improved. + """ + assert normalization_Knl(0, 0) == 1 + assert normalization_Knl(1, 0) == 3 + assert normalization_Knl(2, 0) == 6 + assert normalization_Knl(0, 1) == 6 + assert normalization_Knl(0, 2) == 15 + assert normalization_Knl(1, 1) == 10 + + +# ============================================================================= + + +def test_expansion_coeffs_Anl_discrete(): + """Test the ``expansion_coeffs_Anl_discrete`` function. + + .. todo:: + + This test is not very good. It should be improved. + """ + np.testing.assert_allclose(expansion_coeffs_Anl_discrete(0, 0), -3) + np.testing.assert_allclose( + expansion_coeffs_Anl_discrete(1, 0), -0.555555, rtol=1e-5 + ) + + +# ============================================================================= + + +@jax.jit +def compare_rho_nl(s, n, l): + """Compare the ``rho_nl`` function.""" + gc = GegenbauerCalculator(10) + + mock = rho_nl(s, n, l, gegenbauer=gc) + observed = jax.lax.stop_gradient(mock) + + return -jnp.sum((observed - mock) ** 2) + + +@pytest.mark.skip(reason="TODO") +def test_rho_nl(): + """Test the ``rho_nl`` function.""" + s = jnp.linspace(0, 4, 100, dtype=float) + n = jnp.array([1.0]) + l = jnp.array([2.0]) + + first_deriv = jax.jacfwd(compare_rho_nl)(s, n, l) + assert first_deriv == 0 + + +@pytest.mark.skip(reason="TODO") +def test_phi_nl(): + """Test the ``phi_nl`` function.""" + raise NotImplementedError diff --git a/tests/potential/scf/test_coeffs.py b/tests/potential/scf/test_coeffs.py new file mode 100644 index 000000000..f7ef28220 --- /dev/null +++ b/tests/potential/scf/test_coeffs.py @@ -0,0 +1,42 @@ +"""Test the Coefficient Calculations.""" + +import gala.potential as gp +import numpy as np + +import quaxed.numpy as jnp + +import galax.potential as gpx + + +def test_compute_coeffs_discrete(): + """Test the ``normalization_Knl`` function. + + .. todo:: + + This test is not very good. It should be improved. + """ + # Setup + rng = np.random.default_rng(42) + particle_xyz = rng.normal(0.0, 5.0, size=(3, 10_000)) + particle_xyz[2] = np.abs(particle_xyz[2]) + particle_xyz = jnp.array(particle_xyz) + + particle_mass = jnp.ones(particle_xyz.shape[1]) + particle_mass = 1e12 * particle_mass / particle_mass.sum() + + nmax = 2 + lmax = 3 + r_s = 10 + + # Gala + gala_Snlm, gala_Tnlm = gp.scf.compute_coeffs_discrete( + np.array(particle_xyz), np.array(particle_mass), nmax=nmax, lmax=lmax, r_s=r_s + ) + + # Galdynamix + Snlm, Tnlm = gpx.scf.compute_coeffs_discrete( + particle_xyz, particle_mass, nmax=nmax, lmax=lmax, r_s=r_s + ) + + np.testing.assert_allclose(Snlm, gala_Snlm, rtol=1e-7) + np.testing.assert_allclose(Tnlm, gala_Tnlm, rtol=1e-7) diff --git a/tests/potential/scf/test_gegenbauer.py b/tests/potential/scf/test_gegenbauer.py new file mode 100644 index 000000000..3a982083c --- /dev/null +++ b/tests/potential/scf/test_gegenbauer.py @@ -0,0 +1,85 @@ +"""Test the Gegenbauer class.""" + +from types import LambdaType + +import numpy as np +import pytest +from scipy.special import gegenbauer as gegenbauer_sp + +import quaxed.numpy as jnp + +from galax.potential._src.scf.gegenbauer import ( + GegenbauerCalculator, + _compute_weight_function_derivatives, +) + + +class TestGegenbauerCalculator: + """Test the GegenbauerCalculator class.""" + + def test_compute_weight_function_derivatives(self): + """Test the ``_compute_weight_function_derivatives`` function. + + ..todo:: + + This test is not very good, since it doesn't actually check the + correctness of the output. It just checks that the function runs. + + """ + nmax = 5 + terms = _compute_weight_function_derivatives(nmax) + assert len(terms) == nmax + 1 + + x = jnp.linspace(0.02, 0.99, 10000) + alpha = 2 + got = terms[0](x, alpha) + assert got.shape == x.shape + + @pytest.mark.parametrize("nmax", [0, 2, 6]) + def test_init(self, nmax): + """Test initializing the GegenbauerCalculator.""" + gc = GegenbauerCalculator(nmax) + assert gc.nmax == nmax + + # Check the pre-computed weights + assert isinstance(gc._weights, tuple) + assert len(gc._weights) == nmax + 1 + assert all(isinstance(w, LambdaType) for w in gc._weights) + + # @pytest.mark.parametrize("nmax", [0, 1, 2, 3, 4, 5, 6]) + def test_call(self): + """Test the functor.""" + # Setup + nmax = 5 + x = jnp.linspace(0.02, 0.99, 10000) + gc = GegenbauerCalculator(nmax) + + # # n > nmax should raise an error + # with pytest.raises(ValueError): + # gc(6, 0, x) + + # With ints and floats + got = gc(1, 0, x) + assert got == pytest.approx(gegenbauer_sp(n=1, alpha=0)(x), rel=1e-8) + + def test_call_vectorized(self): + """Test the functor with vectorized arguments.""" + # Setup + nmax = 5 + x = jnp.linspace(0.02, 0.99, 10000) + gc = GegenbauerCalculator(nmax) + + n = jnp.array([3, 5]) + alpha = 1.5 + got = gc(n, alpha, x[:, None]) + expected = np.c_[ + gegenbauer_sp(n=3, alpha=alpha)(np.array(x)), + gegenbauer_sp(n=5, alpha=alpha)(np.array(x)), + ] + assert got.shape == expected.shape + assert got == pytest.approx(expected, rel=1e-8) + + @pytest.mark.skip(reason="TODO with `hypothesis`") + def test_validity(self): + """Test the regions of validity of the Gegenbauer calculator.""" + raise NotImplementedError diff --git a/tests/potential/scf/test_utils.py b/tests/potential/scf/test_utils.py new file mode 100644 index 000000000..97ad675f4 --- /dev/null +++ b/tests/potential/scf/test_utils.py @@ -0,0 +1,145 @@ +"""Test :mod:`galax.potential._src.scf.utils`.""" + +import hypothesis +import hypothesis.extra.numpy as hnp +import jax +import numpy as np +import numpy.typing as npt +import scipy.special as sp +from hypothesis import assume, given, strategies as st + +import quaxed.numpy as jnp + +from galax.potential._src.scf.utils import ( + cartesian_to_spherical, + factorial, + psi_of_r, + real_Ylm, +) + + +# TODO: use hnp.floating_dtypes() +# TODO: test more batch dimensions +def xyz_strategy() -> st.SearchStrategy[np.ndarray]: + return hnp.arrays( + dtype=np.float64, + shape=st.tuples(st.integers(1, 100), st.integers(3, 3)), + elements=st.floats(-10, 10, allow_subnormal=False, allow_nan=False), + ) + + +@given(xyz_strategy()) +def test_cartesian_to_spherical(xyz): + """Test the ``cartesian_to_spherical`` function.""" + assume(np.all(xyz.sum(axis=1) != 0)) + + n = len(xyz) + xyz = jnp.asarray(xyz) + + rthetaphi = cartesian_to_spherical(xyz) + r = rthetaphi[..., 0] + theta = rthetaphi[..., 1] + phi = rthetaphi[..., 2] + + # Check + assert r.shape == (n,) + assert theta.shape == (n,) + assert phi.shape == (n,) + + assert jnp.all(r >= 0) + assert jnp.all(theta >= 0) & jnp.all(theta <= jnp.pi) + assert jnp.all(phi >= -jnp.pi) & jnp.all(phi <= jnp.pi) + + +def test_cartesian_to_spherical_jac(): + """Test the ``cartesian_to_spherical`` function.""" + # Scalar + xyz = jnp.asarray([1, 0, 0], dtype=float) + assert xyz.shape == (3,) + + output = jax.jacfwd(cartesian_to_spherical)(xyz) + np.testing.assert_array_equal( + output, [[1.0, 0.0, 0.0], [-0.0, -0.0, -1.0], [0.0, 1.0, 0.0]] + ) + + # Vector + xyz = jnp.asarray([[1, 0, 0], [0, 1, 0]], dtype=float) + assert xyz.shape == (2, 3) + + output = jax.jacfwd(cartesian_to_spherical)(xyz) + assert output.shape == (2, 3, 2, 3) # WTF? + np.testing.assert_array_equal( + output[0, :, 0, :], [[1.0, 0.0, 0.0], [-0.0, -0.0, -1.0], [0.0, 1.0, 0.0]] + ) + np.testing.assert_array_equal( + output[1, :, 1, :], [[0.0, 1.0, 0.0], [0.0, 0.0, -1.0], [-1.0, 0.0, 0.0]] + ) + + +# ============================================================================= + + +@given( + n=st.integers(0, 100) + | hnp.arrays(dtype=int, shape=hnp.array_shapes(), elements=st.integers(0, 100)) +) +def test_factorial(n: int | npt.NDArray[np.int_]): + """Test the ``factorial`` function.""" + got = factorial(jnp.asarray(n)) + expected = sp.factorial(n) + np.testing.assert_allclose(got, expected) + + +# ============================================================================= + + +@given( + r=st.floats(0, 100) + | hnp.arrays(dtype=float, shape=hnp.array_shapes(), elements=st.floats(0, 100)), +) +def test_psi_of_r(r): + """Test the ``psi_of_r`` function.""" + got = psi_of_r(r) + expected = (r - 1) / (r + 1) + np.testing.assert_allclose(got, expected) + + +# ============================================================================= + + +def test_Ylm_jitting(): + """Test the ``real_Ylm`` function.""" + got = real_Ylm(5, 0, np.pi) + expected = np.real(sp.sph_harm(0, 5, 0, np.pi)) + np.testing.assert_allclose(got, expected) + + +@hypothesis.settings(deadline=500) +@given(l=st.integers(1, 25), m=st.integers(1, 25), theta=st.floats(0, np.pi)) +def test_real_Ylm(l, m, theta): + """Test the ``real_Ylm`` function.""" + assume(theta != 0) + assume(m <= l) + got = real_Ylm(l, m, theta) + expected = np.real(sp.sph_harm(m, l, 0, theta)) + np.testing.assert_allclose(got, expected) + + +# # TODO: mark as slow +# # TODO: test batch dimensions of l, m, theta +# @hypothesis.settings(deadline=500) +# @given( +# l=st.integers(1, 25), +# m=st.integers(1, 25), +# theta=hnp.arrays( +# dtype=np.float64, +# shape=st.integers(1, 100), +# elements=st.floats(1e-5, np.pi, allow_subnormal=False, allow_nan=False), +# ), +# ) +# def test_real_Ylm_vec(l, m, theta): +# """Test the ``real_Ylm`` function.""" +# assume(m <= l) +# got = real_Ylm(l, m, theta) +# expected = np.real(sp.sph_harm(m, l, 0, theta)) +# np.testing.assert_allclose(got, expected) From 476a29a4323f463138424b26ac8bc7fad501d972 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Sun, 22 Jun 2025 23:22:27 -0400 Subject: [PATCH 02/13] conflict --- src/galax/typing.py | 153 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 153 insertions(+) create mode 100644 src/galax/typing.py diff --git a/src/galax/typing.py b/src/galax/typing.py new file mode 100644 index 000000000..5d3778a14 --- /dev/null +++ b/src/galax/typing.py @@ -0,0 +1,153 @@ +"""Type hints for galax.""" + +# TODO: Finalize variable names and make everything public. +__all__: list[str] = [] + +from typing import TypeAlias + +import astropy.units as u +from jaxtyping import Array, Float, Integer, Shaped + +from unxt import Quantity + +# ============================================================================= + +Shape: TypeAlias = tuple[int, ...] +Dimension: TypeAlias = u.PhysicalType +Unit: TypeAlias = u.Unit | u.UnitBase | u.CompositeUnit +UnitEquivalency: TypeAlias = u.Equivalency + +# ============================================================================= +# Scalars + +# An integer scalar. +IntScalar = Integer[Array, ""] +IntQScalar = Integer[Quantity, ""] +IntLike = IntScalar | int + +# A float scalar. +FloatScalar = Float[Array, ""] +FloatQScalar = Float[Quantity, ""] + +FloatLike = FloatScalar | float | int +"""A float(/int) or float scalar.""" + +# A float or integer scalar. +RealScalar = FloatScalar | IntScalar +RealQScalar = FloatQScalar | IntQScalar + +# A float or integer or float(/int) scalar. +RealScalarLike = FloatLike | IntLike + + +# ============================================================================= +# Vectors + +# ----------------------------------------------------------------------------- +# Shaped + +# 1-vector +Vec1 = Float[Array, "1"] +QVec1 = Float[Quantity, "1"] + +# A 3-vector, e.g. q=(x, y, z) or p=(vx, vy, vz). +Vec3 = Float[Array, "3"] +QVec3 = Float[Quantity, "3"] + +Vec4 = Float[Array, "4"] +"""A 4-vector e.g. w=(t, x, y, z).""" + +Vec6 = Float[Array, "6"] +"""A 6-vector e.g. w=(x, y, z, vx, vy, vz).""" + +Vec7 = Float[Array, "7"] +"""A 7-vector e.g. w=(x, y, z, vx, vy, vz, t).""" + +VecN = Float[Array, "N"] +"""An (N,)-vector.""" + +# ----------------- +# Specific + +# Time vector +VecTime = Float[Array, "time"] +QVecTime = Float[Quantity, "time"] +VecTime1 = Float[Vec1, "time"] +VecTime3 = Float[Vec3, "time"] +VecTime6 = Float[Vec6, "time"] +VecTime7 = Float[Vec7, "time"] + +# ----------------------------------------------------------------------------- +# Vector Batches + +# ----------------- +# Scalars + +BatchFloatScalar = Shaped[FloatScalar, "*batch"] + +BatchableFloatQScalar = Shaped[FloatQScalar, "*#batch"] + +BatchFloatQScalar = Shaped[FloatQScalar, "*batch"] + +BatchRealQScalar = Shaped[RealQScalar, "*batch"] +BatchableRealScalar = Shaped[RealScalar, "*#batch"] +BatchableRealQScalar = Shaped[RealQScalar, "*#batch"] + +BatchableRealScalarLike = BatchableRealScalar | RealScalarLike + +# ----------------- +# Batched + +# Zero or more batches of 3-vectors. +BatchVec3 = Shaped[Vec3, "*batch"] +BatchQVec3 = Shaped[QVec3, "*batch"] + +# Zero or more batches of 6-vectors +BatchVec6 = Shaped[Vec6, "*batch"] + +# Zero or more batches of 7-vectors +BatchVec7 = Shaped[Vec7, "*batch"] + +# ----------------- +# Specific + +BatchVecTime = Shaped[VecTime, "*batch"] +BatchVecTime6 = Shaped[VecTime6, "*batch"] +BatchVecTime7 = Shaped[VecTime7, "*batch"] +BatchQVecTime = Shaped[QVecTime, "*batch"] + +# ----------------- +# Any Shape + +FloatAnyShape = Float[Array, "..."] +FloatQAnyShape = Float[Quantity, "..."] + + +# ============================================================================= +# Matrices + +QMatrix33 = Float[Quantity, "3 3"] +BatchQMatrix33 = Shaped[QMatrix33, "*batch"] + + +# ============================================================================= + +MassScalar = Shaped[Quantity["mass"], ""] +MassBatchScalar = Shaped[Quantity["mass"], "*batch"] +MassBatchableScalar = Shaped[Quantity["mass"], "*#batch"] + +TimeScalar = Shaped[Quantity["time"], ""] +TimeBatchScalar = Shaped[Quantity["time"], "*batch"] +TimeBatchableScalar = Shaped[Quantity["time"], "*#batch"] + +LengthScalar = Shaped[Quantity["length"], ""] +LengthVec3 = Shaped[Quantity["length"], "3"] +LengthBatchVec3 = Shaped[LengthVec3, "*batch"] +LengthBatchableVec3 = Shaped[LengthVec3, "*#batch"] + +SpeedVec3: TypeAlias = Shaped[Quantity["speed"], "3"] +SpeedBatchVec3: TypeAlias = Shaped[SpeedVec3, "*batch"] +SpeedBatchableVec3: TypeAlias = Shaped[SpeedVec3, "*#batch"] + +SpecificEnergyScalar = Float[Quantity["specific_energy"], ""] +SpecificEnergyBatchScalar = Float[Quantity["specific_energy"], "*batch"] From 0e5c7a734e739236eadd9f2e1f947e108044f7bc Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 00:49:17 -0400 Subject: [PATCH 03/13] Remove GegenbauerCalculator and implement eval_gegenbauer, remove typing --- src/galax/potential/_src/scf/bfe.py | 9 +- src/galax/potential/_src/scf/bfe_helper.py | 26 ++-- src/galax/potential/_src/scf/coeffs.py | 18 +-- src/galax/potential/_src/scf/gegenbauer.py | 102 -------------- src/galax/potential/_src/scf/utils.py | 6 +- src/galax/typing.py | 153 --------------------- 6 files changed, 16 insertions(+), 298 deletions(-) delete mode 100644 src/galax/potential/_src/scf/gegenbauer.py delete mode 100644 src/galax/typing.py diff --git a/src/galax/potential/_src/scf/bfe.py b/src/galax/potential/_src/scf/bfe.py index 9cdefb47f..95ecef5d3 100644 --- a/src/galax/potential/_src/scf/bfe.py +++ b/src/galax/potential/_src/scf/bfe.py @@ -14,7 +14,6 @@ import galax.typing as gt from .bfe_helper import phi_nl_vec, rho_nl as calculate_rho_nl from .coeffs import compute_coeffs_discrete -from .gegenbauer import GegenbauerCalculator from .utils import cartesian_to_spherical, real_Ylm from galax.potential._src.core import AbstractPotential from galax.potential._src.param import AbstractParameter, ParameterField @@ -60,7 +59,6 @@ class SCFPotential(AbstractPotential): nmax: int = eqx.field(init=False, static=True, repr=False) lmax: int = eqx.field(init=False, static=True, repr=False) - _ultra_sph: GegenbauerCalculator = eqx.field(init=False, static=True, repr=False) def __post_init__(self) -> None: super().__post_init__() @@ -70,9 +68,6 @@ def __post_init__(self) -> None: object.__setattr__(self, "nmax", shape[0] - 1) object.__setattr__(self, "lmax", shape[1] - 1) - # gegenbauer calculator - object.__setattr__(self, "_ultra_sph", GegenbauerCalculator(self.nmax)) - # ========================================================================== @partial(jax.jit, inline=True) @@ -88,7 +83,7 @@ def _potential( ns = jnp.arange(self.nmax + 1)[:, None, None] # (n, [l], [m]) ls = jnp.arange(self.lmax + 1)[None, :, None] # ([n], l, [m]) - phi_nl = phi_nl_vec(s, ns, ls, self._ultra_sph) # (n, l, [m], N) + phi_nl = phi_nl_vec(s, ns, ls) # (n, l, [m], N) li, mi = jnp.tril_indices(self.lmax + 1) # (l*(l+1)//2,) shape = (1, self.lmax + 1, self.lmax + 1, 1) # ([n], l, m, [N]) @@ -121,7 +116,7 @@ def _density(self, q: gt.LengthVec3, /, t: gt.RealQScalar) -> Float[Array, "N"]: ns = jnp.arange(self.nmax + 1)[:, None, None] # (n, [l], [m]) ls = jnp.arange(self.lmax + 1)[None, :, None] # ([n], l, [m]) - phi_nl = calculate_rho_nl(s, ns[None], ls[None], gegenbauer=self._ultra_sph) + phi_nl = calculate_rho_nl(s, ns[None], ls[None]) li, mi = jnp.tril_indices(self.lmax + 1) # (l*(l+1)//2,) shape = (1, 1, self.lmax + 1, self.lmax + 1) diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py index 9c36321fb..89d911ee9 100644 --- a/src/galax/potential/_src/scf/bfe_helper.py +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -9,13 +9,13 @@ from .coeffs_helper import normalization_Knl from .utils import psi_of_r -from galax.potential._src.scf.gegenbauer import GegenbauerCalculator +from spexial import eval_gegenbauer from galax.typing import IntLike -@partial(jax.jit, static_argnames=("gegenbauer",)) +@jax.jit def rho_nl( - s: Float[Array, "N"], n: int, l: int, *, gegenbauer: GegenbauerCalculator + s: Float[Array, "N"], n: int, l: int, *, ) -> Float[Array, "N"]: r"""Radial density expansion terms. @@ -27,9 +27,6 @@ def rho_nl( Radial expansion term. l : int Spherical harmonic term. - gegenbauer : GegenbauerCalculator, keyword-only - Gegenbauer calculator. This is used to compute the Gegenbauer - polynomials efficiently. Returns ------- @@ -39,16 +36,16 @@ def rho_nl( jnp.sqrt(4 * jnp.pi) * (normalization_Knl(n=n, l=l) / (2 * jnp.pi)) * (s**l / (s * (1 + s) ** (2 * l + 3))) - * gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + * eval_gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) ) # ====================================================================== -@partial(jax.jit, static_argnames=("gegenbauer",)) +@jax.jit def phi_nl( - s: Float[Array, "samples"], n: IntLike, l: IntLike, gegenbauer: GegenbauerCalculator + s: Float[Array, "samples"], n: IntLike, l: IntLike, ) -> Float[Array, "samples"]: r"""Angular density expansion terms. @@ -60,9 +57,6 @@ def phi_nl( Radial expansion term. l : int Spherical harmonic term. - gegenbauer : GegenbauerCalculator, keyword-only - Gegenbauer calculator. This is used to compute the Gegenbauer - polynomials efficiently. Returns ------- @@ -71,17 +65,15 @@ def phi_nl( Examples -------- >>> import jax.numpy as jnp - >>> from galax.potential._src.scf.gegenbauer import GegenbauerCalculator - >>> gegenbauer = GegenbauerCalculator(100) - >>> phi_nl(0.5, 1, 1, gegenbauer=gegenbauer) + >>> phi_nl(0.5, 1, 1) Array(0.5, dtype=float32) - >>> phi_nl(jnp.array([0.5, 0.5]), 1, 1, gegenbauer=gegenbauer) + >>> phi_nl(jnp.array([0.5, 0.5]), 1, 1) Array([0.5, 0.5], dtype=float32) """ return ( -jnp.sqrt(4 * jnp.pi) * (s**l / (1.0 + s) ** (2 * l + 1)) - * gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + * eval_gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) ) diff --git a/src/galax/potential/_src/scf/coeffs.py b/src/galax/potential/_src/scf/coeffs.py index bcf92b0cf..aec969b95 100644 --- a/src/galax/potential/_src/scf/coeffs.py +++ b/src/galax/potential/_src/scf/coeffs.py @@ -12,11 +12,10 @@ import galax.typing as gt from .bfe_helper import phi_nl_vec from .coeffs_helper import expansion_coeffs_Anl_discrete -from .gegenbauer import GegenbauerCalculator from .utils import cartesian_to_spherical, real_Ylm -@partial(jax.jit, static_argnames=("nmax", "lmax", "gegenbauer")) +@partial(jax.jit, static_argnames=("nmax", "lmax")) def compute_coeffs_discrete( xyz: Float[Array, "samples 3"], mass: Float[Array, "samples"], # type: ignore[name-defined] @@ -24,7 +23,6 @@ def compute_coeffs_discrete( nmax: gt.IntLike, lmax: gt.IntLike, r_s: gt.FloatQScalar, - gegenbauer: GegenbauerCalculator | None = None, ) -> tuple[ Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], @@ -53,11 +51,6 @@ def compute_coeffs_discrete( Scale radius. :todo:`unit support` - gegenbauer : GegenbauerCalculator, optional - Gegenbauer calculator. This is used to compute the Gegenbauer - polynomials efficiently. If not provided, a new calculator will be - created. - Returns ------- Snlm : Array[float, (nmax+1, lmax+1, lmax+1)] @@ -65,13 +58,6 @@ def compute_coeffs_discrete( Tnlm : Array[float, (nmax+1, lmax+1, lmax+1)] The value of the sine expansion coefficient. """ - if gegenbauer is None: - ggncalc = GegenbauerCalculator(nmax=nmax) - elif gegenbauer.nmax < nmax: - msg = "gegenbauer.nmax != nmax" - raise ValueError(msg) - else: - ggncalc = gegenbauer rthetaphi = cartesian_to_spherical(xyz) r = rthetaphi[..., 0] @@ -83,7 +69,7 @@ def compute_coeffs_discrete( ls = jnp.arange(lmax + 1)[None, :] # (n, l) Anl_til = expansion_coeffs_Anl_discrete(ns, ls) # (n, l) - phinl = phi_nl_vec(s, ns, ls, ggncalc) # (n, l, N) + phinl = phi_nl_vec(s, ns, ls) # (n, l, N) li, mi = jnp.tril_indices(lmax + 1) # (l*(l+1)//2,) lm = jnp.zeros((lmax + 1, lmax + 1), dtype=int).at[li, mi].set(li) # (l, m) diff --git a/src/galax/potential/_src/scf/gegenbauer.py b/src/galax/potential/_src/scf/gegenbauer.py deleted file mode 100644 index fe2749079..000000000 --- a/src/galax/potential/_src/scf/gegenbauer.py +++ /dev/null @@ -1,102 +0,0 @@ -"""Gegenbauer polynomials.""" - -__all__ = ["GegenbauerCalculator"] - -from functools import partial -from typing import Protocol, runtime_checkable - -import equinox as eqx -import jax -import sympy as sp -import sympy2jax -from jax.scipy.special import gamma - -from .utils import factorial -from galax.typing import FloatLike, IntLike, VecN -from galax.utils._jax import vectorize_method - - -@runtime_checkable -class AbstractGegenbauerDerivativeTerm(Protocol): - def __call__(self, x: VecN, alpha: float) -> VecN: ... - - -def _compute_weight_function_derivatives( - nmax: int, -) -> tuple[AbstractGegenbauerDerivativeTerm, ...]: - """Compute the nth derivative of the weight function for the Gegenbauer polynomials. - - .. warning:: - - This function is still VERY slow for nmax > 7. - - .. todo:: - - This isn't quite Equation 22.2.3 of Abramowitz & Stegun (1972). - - It's too costly to have JAX compute the Gegenbauer polynomials directly, so - we instead compute the nth derivative of the weight function, and then - use the recurrence relation to compute the Gegenbauer polynomials. - """ - # Make Symbols - x: sp.Symbol = sp.Symbol("x") - n: sp.Symbol = sp.Symbol("n", integer=True) - alpha: sp.Symbol = sp.Symbol("alpha", positive=True) - - # weight function for the Gegenbauer polynomials - weight = (1 - x**2) ** (n + alpha - 0.5) - - # Compute the nth derivative term for the Gegenbauer polynomials - # start with the 0th derivative - fn_sympy: sp.Expr = sp.simplify(sp.diff(weight, x, 0)) - func_list = [] - for i in range(nmax + 1): - # Symbolic computation of the nth derivative - if i > 0: - fn_sympy = sp.simplify(sp.diff(fn_sympy, x, 1)) - # Convert to a JAX function - fn_jax = sympy2jax.SymbolicModule(fn_sympy) - # Re-arrange the arguments - fn_jax_save = lambda x, alpha, n=i, fn=fn_jax: fn( # noqa: E731 - x=x, alpha=alpha, n=n - ) - func_list.append(fn_jax_save) - return tuple(func_list) - - -class GegenbauerCalculator(eqx.Module): # type: ignore[misc] - """Gegenbauer (ultraspherical) polynomial.""" - - nmax: int - """Maximum order of the Gegenbauer polynomials.""" - - _weights: tuple[AbstractGegenbauerDerivativeTerm, ...] = eqx.field( - init=False, static=True, repr=False - ) - """Tuple of weights for nth derivative of the Gegenbauer polynomials. - - This is computed in the __post_init__ method. - """ - - def __post_init__(self) -> None: - object.__setattr__( - self, "_weights", _compute_weight_function_derivatives(self.nmax) - ) - - # TODO: switch requires integer n, but everything else already vectorized - @partial(jax.jit, static_argnames=("n", "alpha")) - @vectorize_method(signature="(),(),()->()") - def __call__( - self, n: IntLike, alpha: IntLike | FloatLike, x: FloatLike | VecN - ) -> FloatLike | VecN: - r"""Calculate :math:`C_n^\alpha(x)`.""" - # # TODO: the Gegenbauer polynomials have limits on valid inputs - nth_deriv = jax.lax.switch(n, self._weights, x, alpha) - - # TODO: write out full mathematical derivation - factor0 = ((-1.0) ** n) / ((2**n) * factorial(n)) - factor1 = (gamma(alpha + 0.5) * gamma(n + 2.0 * alpha)) / ( - gamma(2.0 * alpha) * gamma(alpha + n + 0.5) - ) - factor2 = (1.0 - x**2) ** (-alpha + 0.5) - return factor0 * factor1 * factor2 * nth_deriv diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py index 6847c366a..f3c2e3e40 100644 --- a/src/galax/potential/_src/scf/utils.py +++ b/src/galax/potential/_src/scf/utils.py @@ -11,7 +11,7 @@ import quaxed.numpy as jnp -import galax.typing as gt +import galax._custom_types as gt BatchableIntLike: TypeAlias = Shaped[gt.IntLike, "*#batch"] @@ -74,8 +74,8 @@ def _real_Ylm(theta: gt.VecN, l: gt.IntLike, m: gt.IntLike, m_max: int) -> gt.Ve @partial(jax.jit, static_argnames=("m_max",)) def real_Ylm( - theta: gt.FloatAnyShape, l: BatchableIntLike, m: BatchableIntLike, m_max: int = 100 -) -> gt.FloatAnyShape: + theta: gt.SzAny, l: BatchableIntLike, m: BatchableIntLike, m_max: int = 100 +) -> gt.SzAny: r"""Get the spherical harmonic :math:`Y_{lm}(\theta)` of the polar angle. This is different than the scipy (and thus JAX) convention, which is diff --git a/src/galax/typing.py b/src/galax/typing.py deleted file mode 100644 index 5d3778a14..000000000 --- a/src/galax/typing.py +++ /dev/null @@ -1,153 +0,0 @@ -"""Type hints for galax.""" - -# TODO: Finalize variable names and make everything public. -__all__: list[str] = [] - -from typing import TypeAlias - -import astropy.units as u -from jaxtyping import Array, Float, Integer, Shaped - -from unxt import Quantity - -# ============================================================================= - -Shape: TypeAlias = tuple[int, ...] -Dimension: TypeAlias = u.PhysicalType -Unit: TypeAlias = u.Unit | u.UnitBase | u.CompositeUnit -UnitEquivalency: TypeAlias = u.Equivalency - -# ============================================================================= -# Scalars - -# An integer scalar. -IntScalar = Integer[Array, ""] -IntQScalar = Integer[Quantity, ""] -IntLike = IntScalar | int - -# A float scalar. -FloatScalar = Float[Array, ""] -FloatQScalar = Float[Quantity, ""] - -FloatLike = FloatScalar | float | int -"""A float(/int) or float scalar.""" - -# A float or integer scalar. -RealScalar = FloatScalar | IntScalar -RealQScalar = FloatQScalar | IntQScalar - -# A float or integer or float(/int) scalar. -RealScalarLike = FloatLike | IntLike - - -# ============================================================================= -# Vectors - -# ----------------------------------------------------------------------------- -# Shaped - -# 1-vector -Vec1 = Float[Array, "1"] -QVec1 = Float[Quantity, "1"] - -# A 3-vector, e.g. q=(x, y, z) or p=(vx, vy, vz). -Vec3 = Float[Array, "3"] -QVec3 = Float[Quantity, "3"] - -Vec4 = Float[Array, "4"] -"""A 4-vector e.g. w=(t, x, y, z).""" - -Vec6 = Float[Array, "6"] -"""A 6-vector e.g. w=(x, y, z, vx, vy, vz).""" - -Vec7 = Float[Array, "7"] -"""A 7-vector e.g. w=(x, y, z, vx, vy, vz, t).""" - -VecN = Float[Array, "N"] -"""An (N,)-vector.""" - -# ----------------- -# Specific - -# Time vector -VecTime = Float[Array, "time"] -QVecTime = Float[Quantity, "time"] -VecTime1 = Float[Vec1, "time"] -VecTime3 = Float[Vec3, "time"] -VecTime6 = Float[Vec6, "time"] -VecTime7 = Float[Vec7, "time"] - -# ----------------------------------------------------------------------------- -# Vector Batches - -# ----------------- -# Scalars - -BatchFloatScalar = Shaped[FloatScalar, "*batch"] - -BatchableFloatQScalar = Shaped[FloatQScalar, "*#batch"] - -BatchFloatQScalar = Shaped[FloatQScalar, "*batch"] - -BatchRealQScalar = Shaped[RealQScalar, "*batch"] -BatchableRealScalar = Shaped[RealScalar, "*#batch"] -BatchableRealQScalar = Shaped[RealQScalar, "*#batch"] - -BatchableRealScalarLike = BatchableRealScalar | RealScalarLike - -# ----------------- -# Batched - -# Zero or more batches of 3-vectors. -BatchVec3 = Shaped[Vec3, "*batch"] -BatchQVec3 = Shaped[QVec3, "*batch"] - -# Zero or more batches of 6-vectors -BatchVec6 = Shaped[Vec6, "*batch"] - -# Zero or more batches of 7-vectors -BatchVec7 = Shaped[Vec7, "*batch"] - -# ----------------- -# Specific - -BatchVecTime = Shaped[VecTime, "*batch"] -BatchVecTime6 = Shaped[VecTime6, "*batch"] -BatchVecTime7 = Shaped[VecTime7, "*batch"] -BatchQVecTime = Shaped[QVecTime, "*batch"] - -# ----------------- -# Any Shape - -FloatAnyShape = Float[Array, "..."] -FloatQAnyShape = Float[Quantity, "..."] - - -# ============================================================================= -# Matrices - -QMatrix33 = Float[Quantity, "3 3"] -BatchQMatrix33 = Shaped[QMatrix33, "*batch"] - - -# ============================================================================= - -MassScalar = Shaped[Quantity["mass"], ""] -MassBatchScalar = Shaped[Quantity["mass"], "*batch"] -MassBatchableScalar = Shaped[Quantity["mass"], "*#batch"] - -TimeScalar = Shaped[Quantity["time"], ""] -TimeBatchScalar = Shaped[Quantity["time"], "*batch"] -TimeBatchableScalar = Shaped[Quantity["time"], "*#batch"] - -LengthScalar = Shaped[Quantity["length"], ""] -LengthVec3 = Shaped[Quantity["length"], "3"] -LengthBatchVec3 = Shaped[LengthVec3, "*batch"] -LengthBatchableVec3 = Shaped[LengthVec3, "*#batch"] - -SpeedVec3: TypeAlias = Shaped[Quantity["speed"], "3"] -SpeedBatchVec3: TypeAlias = Shaped[SpeedVec3, "*batch"] -SpeedBatchableVec3: TypeAlias = Shaped[SpeedVec3, "*#batch"] - -SpecificEnergyScalar = Float[Quantity["specific_energy"], ""] -SpecificEnergyBatchScalar = Float[Quantity["specific_energy"], "*batch"] From 052d0e9d3844a475b9d6cddd2a60c1eb6a64e52a Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 00:57:25 -0400 Subject: [PATCH 04/13] gegenbauer tests --- tests/potential/scf/test_coeff_helper.py | 7 +- tests/potential/scf/test_gegenbauer.py | 85 ------------------------ 2 files changed, 2 insertions(+), 90 deletions(-) delete mode 100644 tests/potential/scf/test_gegenbauer.py diff --git a/tests/potential/scf/test_coeff_helper.py b/tests/potential/scf/test_coeff_helper.py index 0190b3520..ef496a4ec 100644 --- a/tests/potential/scf/test_coeff_helper.py +++ b/tests/potential/scf/test_coeff_helper.py @@ -1,4 +1,4 @@ -"""Test the Gegenbauer class.""" +"""Test Gegenbauer utils.""" import jax import numpy as np @@ -11,8 +11,6 @@ expansion_coeffs_Anl_discrete, normalization_Knl, ) -from galax.potential._src.scf.gegenbauer import GegenbauerCalculator - def test_normalization_Knl(): """Test the ``normalization_Knl`` function. @@ -51,9 +49,8 @@ def test_expansion_coeffs_Anl_discrete(): @jax.jit def compare_rho_nl(s, n, l): """Compare the ``rho_nl`` function.""" - gc = GegenbauerCalculator(10) - mock = rho_nl(s, n, l, gegenbauer=gc) + mock = rho_nl(s, n, l) observed = jax.lax.stop_gradient(mock) return -jnp.sum((observed - mock) ** 2) diff --git a/tests/potential/scf/test_gegenbauer.py b/tests/potential/scf/test_gegenbauer.py deleted file mode 100644 index 3a982083c..000000000 --- a/tests/potential/scf/test_gegenbauer.py +++ /dev/null @@ -1,85 +0,0 @@ -"""Test the Gegenbauer class.""" - -from types import LambdaType - -import numpy as np -import pytest -from scipy.special import gegenbauer as gegenbauer_sp - -import quaxed.numpy as jnp - -from galax.potential._src.scf.gegenbauer import ( - GegenbauerCalculator, - _compute_weight_function_derivatives, -) - - -class TestGegenbauerCalculator: - """Test the GegenbauerCalculator class.""" - - def test_compute_weight_function_derivatives(self): - """Test the ``_compute_weight_function_derivatives`` function. - - ..todo:: - - This test is not very good, since it doesn't actually check the - correctness of the output. It just checks that the function runs. - - """ - nmax = 5 - terms = _compute_weight_function_derivatives(nmax) - assert len(terms) == nmax + 1 - - x = jnp.linspace(0.02, 0.99, 10000) - alpha = 2 - got = terms[0](x, alpha) - assert got.shape == x.shape - - @pytest.mark.parametrize("nmax", [0, 2, 6]) - def test_init(self, nmax): - """Test initializing the GegenbauerCalculator.""" - gc = GegenbauerCalculator(nmax) - assert gc.nmax == nmax - - # Check the pre-computed weights - assert isinstance(gc._weights, tuple) - assert len(gc._weights) == nmax + 1 - assert all(isinstance(w, LambdaType) for w in gc._weights) - - # @pytest.mark.parametrize("nmax", [0, 1, 2, 3, 4, 5, 6]) - def test_call(self): - """Test the functor.""" - # Setup - nmax = 5 - x = jnp.linspace(0.02, 0.99, 10000) - gc = GegenbauerCalculator(nmax) - - # # n > nmax should raise an error - # with pytest.raises(ValueError): - # gc(6, 0, x) - - # With ints and floats - got = gc(1, 0, x) - assert got == pytest.approx(gegenbauer_sp(n=1, alpha=0)(x), rel=1e-8) - - def test_call_vectorized(self): - """Test the functor with vectorized arguments.""" - # Setup - nmax = 5 - x = jnp.linspace(0.02, 0.99, 10000) - gc = GegenbauerCalculator(nmax) - - n = jnp.array([3, 5]) - alpha = 1.5 - got = gc(n, alpha, x[:, None]) - expected = np.c_[ - gegenbauer_sp(n=3, alpha=alpha)(np.array(x)), - gegenbauer_sp(n=5, alpha=alpha)(np.array(x)), - ] - assert got.shape == expected.shape - assert got == pytest.approx(expected, rel=1e-8) - - @pytest.mark.skip(reason="TODO with `hypothesis`") - def test_validity(self): - """Test the regions of validity of the Gegenbauer calculator.""" - raise NotImplementedError From 872003dd888b3797690f9feb32b1cd69147fbc67 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 01:03:49 -0400 Subject: [PATCH 05/13] remove galax.typing --- src/galax/potential/_src/params/base.py | 4 ++-- src/galax/potential/_src/params/constant.py | 2 +- src/galax/potential/_src/scf/bfe.py | 2 +- src/galax/potential/_src/scf/bfe_helper.py | 2 +- src/galax/potential/_src/scf/coeffs.py | 2 +- 5 files changed, 6 insertions(+), 6 deletions(-) diff --git a/src/galax/potential/_src/params/base.py b/src/galax/potential/_src/params/base.py index 4b289207a..0c6ec6c94 100644 --- a/src/galax/potential/_src/params/base.py +++ b/src/galax/potential/_src/params/base.py @@ -26,7 +26,7 @@ def __call__( Parameters ---------- - t : `~galax.typing.BBtQuSz0` + t : `~galax._custom_types.BBtQuSz0` Time(s) at which to compute the parameter value. ustrip : Unit | None Unit to strip from the parameter value. @@ -62,7 +62,7 @@ def __call__( Parameters ---------- - t : `~galax.typing.BBtQuSz0` + t : `~galax._custom_types.BBtQuSz0` The time(s) at which to compute the parameter value. ustrip : Unit | None The unit to strip from the parameter value. If None, the diff --git a/src/galax/potential/_src/params/constant.py b/src/galax/potential/_src/params/constant.py index 630e22799..71d6b3113 100644 --- a/src/galax/potential/_src/params/constant.py +++ b/src/galax/potential/_src/params/constant.py @@ -135,7 +135,7 @@ def __call__( Parameters ---------- - t : `~galax.typing.BBtQuSz0`, optional + t : `~galax._custom_types.BBtQuSz0`, optional This is ignored and is thus optional. Note that for most :class:`~galax.potential.AbstractParameter` the time is required. ustrip : Unit | None diff --git a/src/galax/potential/_src/scf/bfe.py b/src/galax/potential/_src/scf/bfe.py index 95ecef5d3..037b4e05a 100644 --- a/src/galax/potential/_src/scf/bfe.py +++ b/src/galax/potential/_src/scf/bfe.py @@ -11,7 +11,7 @@ import jax.numpy as jnp from jaxtyping import Array, Float -import galax.typing as gt +import galax._custom_types as gt from .bfe_helper import phi_nl_vec, rho_nl as calculate_rho_nl from .coeffs import compute_coeffs_discrete from .utils import cartesian_to_spherical, real_Ylm diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py index 89d911ee9..5d4186b9c 100644 --- a/src/galax/potential/_src/scf/bfe_helper.py +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -10,7 +10,7 @@ from .coeffs_helper import normalization_Knl from .utils import psi_of_r from spexial import eval_gegenbauer -from galax.typing import IntLike +import galax._custom_types as gt @jax.jit diff --git a/src/galax/potential/_src/scf/coeffs.py b/src/galax/potential/_src/scf/coeffs.py index aec969b95..42f836804 100644 --- a/src/galax/potential/_src/scf/coeffs.py +++ b/src/galax/potential/_src/scf/coeffs.py @@ -9,7 +9,7 @@ import jax.numpy as jnp from jaxtyping import Array, Float -import galax.typing as gt +import galax._custom_types as gt from .bfe_helper import phi_nl_vec from .coeffs_helper import expansion_coeffs_Anl_discrete from .utils import cartesian_to_spherical, real_Ylm From 93b784fba7341e5737116420d4614c7cd90b3124 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 01:08:01 -0400 Subject: [PATCH 06/13] correct types --- src/galax/potential/_src/scf/utils.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py index f3c2e3e40..66315662d 100644 --- a/src/galax/potential/_src/scf/utils.py +++ b/src/galax/potential/_src/scf/utils.py @@ -13,14 +13,14 @@ import galax._custom_types as gt -BatchableIntLike: TypeAlias = Shaped[gt.IntLike, "*#batch"] +BatchableIntSz0: TypeAlias = Shaped[gt.IntSz0, "*#batch"] T = TypeVar("T", bound=ArrayLike) @partial(jax.jit) @partial(jax.numpy.vectorize, signature="(3)->(3)") -def cartesian_to_spherical(xyz: gt.Vec3, /) -> gt.Vec3: +def cartesian_to_spherical(xyz: gt.FloatSz3, /) -> gt.FloatSz3: """Convert Cartesian coordinates to spherical coordinates. Parameters @@ -64,7 +64,7 @@ def psi_of_r(r: T) -> T: @partial(jax.numpy.vectorize, signature="(n),(),()->(n)", excluded=(3,)) @partial(jax.jit, static_argnames=("m_max",)) # TODO: should l,m be static? -def _real_Ylm(theta: gt.VecN, l: gt.IntLike, m: gt.IntLike, m_max: int) -> gt.VecN: +def _real_Ylm(theta: gt.SzN, l: gt.IntSz0, m: gt.IntSz0, m_max: int) -> gt.SzN: # TODO: sph_harm only supports scalars, even though it returns an array! theta = xp.atleast_1d(theta) return sph_harm( @@ -74,7 +74,7 @@ def _real_Ylm(theta: gt.VecN, l: gt.IntLike, m: gt.IntLike, m_max: int) -> gt.Ve @partial(jax.jit, static_argnames=("m_max",)) def real_Ylm( - theta: gt.SzAny, l: BatchableIntLike, m: BatchableIntLike, m_max: int = 100 + theta: gt.SzAny, l: BatchableIntSz0, m: BatchableIntSz0, m_max: int = 100 ) -> gt.SzAny: r"""Get the spherical harmonic :math:`Y_{lm}(\theta)` of the polar angle. From 72053c8cc67f968016b7eb9f8eab96640f23df7c Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 01:40:20 -0400 Subject: [PATCH 07/13] more typing fixes; add spexial dependency --- pyproject.toml | 1 + src/galax/potential/_src/scf/bfe.py | 14 ++++++++------ src/galax/potential/_src/scf/bfe_helper.py | 5 +++-- src/galax/potential/_src/scf/coeffs.py | 6 +++--- 4 files changed, 15 insertions(+), 11 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index 093590ed4..599bfff8e 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -53,6 +53,7 @@ "wadler_lindig>=0.1.6", "xmmutablemap>=0.1", "zeroth>=1.0", + "spexial @ git+https://github.com/JAXtronomy/spexial.git@main", ] [project.optional-dependencies] diff --git a/src/galax/potential/_src/scf/bfe.py b/src/galax/potential/_src/scf/bfe.py index 037b4e05a..16dc37403 100644 --- a/src/galax/potential/_src/scf/bfe.py +++ b/src/galax/potential/_src/scf/bfe.py @@ -15,8 +15,9 @@ from .bfe_helper import phi_nl_vec, rho_nl as calculate_rho_nl from .coeffs import compute_coeffs_discrete from .utils import cartesian_to_spherical, real_Ylm -from galax.potential._src.core import AbstractPotential -from galax.potential._src.param import AbstractParameter, ParameterField +from galax.potential import AbstractPotential +from galax.potential._src.params.base import AbstractParameter +from galax.potential._src.params.field import ParameterField ############################################################################## @@ -72,8 +73,8 @@ def __post_init__(self) -> None: @partial(jax.jit, inline=True) def _potential( - self, xyz: gt.BatchQVec3, t: gt.BatchableRealQScalar, / - ) -> gt.VecN | gt.FloatScalar: + self, xyz: gt.BtQuSz3, t: gt.BtQuSz0, / + ) -> gt.SzN | gt.FloatSz0: r_s = self.r_s(t) r, theta, phi = cartesian_to_spherical(xyz).T @@ -105,7 +106,7 @@ def _potential( @partial(jax.jit, inline=True) @eqx.filter_vmap(in_axes=(None, 1, None)) # type: ignore[misc] # on `q` axis 1 - def _density(self, q: gt.LengthVec3, /, t: gt.RealQScalar) -> Float[Array, "N"]: # type: ignore[name-defined] + def _density(self, q: gt.QuSz3, /, t: gt.QuSz0) -> Float[Array, "N"]: # type: ignore[name-defined] """Compute the density at the given position(s).""" r, theta, phi = cartesian_to_spherical(q) r_s = self.r_s(t) @@ -157,13 +158,14 @@ class STnlmSnapshotParameter(AbstractParameter): # type: ignore[misc] """Spherical harmonic term.""" def __call__( - self, t: gt.TimeScalar, *, r_s: gt.LengthScalar, **_: Any + self, t: gt.QuSz0, *, r_s: gt.QuSz0, **_: Any ) -> tuple[ Float[Array, "{self.nmax}+1 {self.lmax}+1 {self.lmax}+1"], Float[Array, "{self.nmax}+1 {self.lmax}+1 {self.lmax}+1"], ]: """Return the coefficients at the given time(s). + TODO: are the types correct here? Should they be quantity specific? Parameters ---------- t : float | Array[float, ()] diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py index 5d4186b9c..34e39839e 100644 --- a/src/galax/potential/_src/scf/bfe_helper.py +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -5,6 +5,7 @@ from functools import partial import jax +import jax.numpy as jnp from jaxtyping import Array, Float from .coeffs_helper import normalization_Knl @@ -15,7 +16,7 @@ @jax.jit def rho_nl( - s: Float[Array, "N"], n: int, l: int, *, + s: Float[Array, "N"], n: int, l: int, ) -> Float[Array, "N"]: r"""Radial density expansion terms. @@ -45,7 +46,7 @@ def rho_nl( @jax.jit def phi_nl( - s: Float[Array, "samples"], n: IntLike, l: IntLike, + s: Float[Array, "samples"], n: gt.IntSz0, l: gt.IntSz0, ) -> Float[Array, "samples"]: r"""Angular density expansion terms. diff --git a/src/galax/potential/_src/scf/coeffs.py b/src/galax/potential/_src/scf/coeffs.py index 42f836804..5d354cd5c 100644 --- a/src/galax/potential/_src/scf/coeffs.py +++ b/src/galax/potential/_src/scf/coeffs.py @@ -20,9 +20,9 @@ def compute_coeffs_discrete( xyz: Float[Array, "samples 3"], mass: Float[Array, "samples"], # type: ignore[name-defined] *, - nmax: gt.IntLike, - lmax: gt.IntLike, - r_s: gt.FloatQScalar, + nmax: gt.IntSz0, + lmax: gt.IntSz0, + r_s: gt.FloatQuSz0, ) -> tuple[ Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], Float[Array, "{nmax}+1 {lmax}+1 {lmax}+1"], From c00a5ed147193ffb02e55ed8c80e8301445560e9 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Thu, 9 Oct 2025 13:10:46 -0400 Subject: [PATCH 08/13] conflict --- pyproject.toml | 2 + src/galax/potential/_src/scf/bfe_helper.py | 2 +- src/galax/potential/_src/scf/utils.py | 8 +- tests/potential/scf/test_coeffs.py | 2 +- uv.lock | 1854 ++++++++++---------- 5 files changed, 959 insertions(+), 909 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index 599bfff8e..2b37ff389 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -54,6 +54,8 @@ "xmmutablemap>=0.1", "zeroth>=1.0", "spexial @ git+https://github.com/JAXtronomy/spexial.git@main", + "hypothesis>=6.135.14", + "gala>=1.9.1", ] [project.optional-dependencies] diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py index 34e39839e..74821129d 100644 --- a/src/galax/potential/_src/scf/bfe_helper.py +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -44,7 +44,7 @@ def rho_nl( # ====================================================================== -@jax.jit +@partial(jax.jit, static_argnames=("n", "l")) def phi_nl( s: Float[Array, "samples"], n: gt.IntSz0, l: gt.IntSz0, ) -> Float[Array, "samples"]: diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py index 66315662d..d0fe72103 100644 --- a/src/galax/potential/_src/scf/utils.py +++ b/src/galax/potential/_src/scf/utils.py @@ -48,7 +48,7 @@ def cartesian_to_spherical(xyz: gt.FloatSz3, /) -> gt.FloatSz3: def factorial(n: T) -> T: """Factorial helper function.""" (n,) = promote_args_inexact("factorial", n) - return cast("T", xp.where(n < 0, 0, lax.exp(lax.lgamma(n + 1)))) + return cast("T", jnp.where(n < 0, 0, jnp.exp(lax.lgamma(n + 1)))) def psi_of_r(r: T) -> T: @@ -66,9 +66,9 @@ def psi_of_r(r: T) -> T: @partial(jax.jit, static_argnames=("m_max",)) # TODO: should l,m be static? def _real_Ylm(theta: gt.SzN, l: gt.IntSz0, m: gt.IntSz0, m_max: int) -> gt.SzN: # TODO: sph_harm only supports scalars, even though it returns an array! - theta = xp.atleast_1d(theta) + theta = jnp.atleast_1d(theta) return sph_harm( - m, xp.atleast_1d(l), theta=xp.zeros_like(theta), phi=theta, n_max=m_max + m, jnp.atleast_1d(l), theta=jnp.zeros_like(theta), phi=theta, n_max=m_max ).real @@ -90,7 +90,7 @@ def real_Ylm( l, m : int | Array[int, ()] Spherical harmonic terms. l in [0,lmax], m in [0,l]. m_max : int, optional - Maximum order of the spherical harmonic expansion. + Maximum order of the spherical harmonic ejnpansion. 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b/src/galax/potential/_src/scf/utils.py @@ -48,7 +48,7 @@ def cartesian_to_spherical(xyz: gt.FloatSz3, /) -> gt.FloatSz3: def factorial(n: T) -> T: """Factorial helper function.""" (n,) = promote_args_inexact("factorial", n) - return cast("T", jnp.where(n < 0, 0, jnp.exp(lax.lgamma(n + 1)))) + return cast("T", jnp.where(n < 0, 0, lax.exp(lax.lgamma(n + 1)))) def psi_of_r(r: T) -> T: @@ -90,7 +90,7 @@ def real_Ylm( l, m : int | Array[int, ()] Spherical harmonic terms. l in [0,lmax], m in [0,l]. m_max : int, optional - Maximum order of the spherical harmonic ejnpansion. + Maximum order of the spherical harmonic expansion. Returns ------- From 058052e29a08a4732a37f28790c75a394bb9e7ef Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 15:23:01 -0400 Subject: [PATCH 10/13] we don't need to define the factorial --- src/galax/potential/_src/scf/coeffs_helper.py | 5 +---- src/galax/potential/_src/scf/utils.py | 9 --------- tests/potential/scf/test_utils.py | 15 --------------- 3 files changed, 1 insertion(+), 28 deletions(-) diff --git a/src/galax/potential/_src/scf/coeffs_helper.py b/src/galax/potential/_src/scf/coeffs_helper.py index 775ff73de..a073255b5 100644 --- a/src/galax/potential/_src/scf/coeffs_helper.py +++ b/src/galax/potential/_src/scf/coeffs_helper.py @@ -4,14 +4,11 @@ from typing import overload -from jax.scipy.special import gamma +from jax.scipy.special import gamma, factorial from jaxtyping import Array, Float, Integer import quaxed.numpy as jnp -from .utils import factorial - - @overload def normalization_Knl(n: int, l: int) -> float: ... diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py index 207eeece0..aba85e1ef 100644 --- a/src/galax/potential/_src/scf/utils.py +++ b/src/galax/potential/_src/scf/utils.py @@ -5,7 +5,6 @@ import jax from jax import lax -from jax._src.numpy.util import promote_args_inexact from jax.scipy.special import sph_harm from jaxtyping import ArrayLike, Shaped @@ -43,14 +42,6 @@ def cartesian_to_spherical(xyz: gt.FloatSz3, /) -> gt.FloatSz3: phi = jnp.arctan2(xyz[1], xyz[0]) # azimuthal angle return jnp.array([r, theta, phi]) - -# TODO: replace with upstream, when available -def factorial(n: T) -> T: - """Factorial helper function.""" - (n,) = promote_args_inexact("factorial", n) - return cast("T", jnp.where(n < 0, 0, lax.exp(lax.lgamma(n + 1)))) - - def psi_of_r(r: T) -> T: r""":math:`\psi(r) = (r-1)/(r+1)`. diff --git a/tests/potential/scf/test_utils.py b/tests/potential/scf/test_utils.py index 97ad675f4..6141ba455 100644 --- a/tests/potential/scf/test_utils.py +++ b/tests/potential/scf/test_utils.py @@ -12,7 +12,6 @@ from galax.potential._src.scf.utils import ( cartesian_to_spherical, - factorial, psi_of_r, real_Ylm, ) @@ -79,20 +78,6 @@ def test_cartesian_to_spherical_jac(): # ============================================================================= -@given( - n=st.integers(0, 100) - | hnp.arrays(dtype=int, shape=hnp.array_shapes(), elements=st.integers(0, 100)) -) -def test_factorial(n: int | npt.NDArray[np.int_]): - """Test the ``factorial`` function.""" - got = factorial(jnp.asarray(n)) - expected = sp.factorial(n) - np.testing.assert_allclose(got, expected) - - -# ============================================================================= - - @given( r=st.floats(0, 100) | hnp.arrays(dtype=float, shape=hnp.array_shapes(), elements=st.floats(0, 100)), From f9dc960c0b6692629e1ee18960d66cbbc79c71b3 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Mon, 23 Jun 2025 15:52:40 -0400 Subject: [PATCH 11/13] more changes --- src/galax/potential/_src/scf/utils.py | 16 +++------------- tests/potential/scf/test_utils.py | 1 - 2 files changed, 3 insertions(+), 14 deletions(-) diff --git a/src/galax/potential/_src/scf/utils.py b/src/galax/potential/_src/scf/utils.py index aba85e1ef..3c40a5415 100644 --- a/src/galax/potential/_src/scf/utils.py +++ b/src/galax/potential/_src/scf/utils.py @@ -4,13 +4,12 @@ from typing import TypeAlias, TypeVar, cast import jax -from jax import lax -from jax.scipy.special import sph_harm from jaxtyping import ArrayLike, Shaped import quaxed.numpy as jnp import galax._custom_types as gt +from galax.potential._src.builtin.multipole import compute_Ylm BatchableIntSz0: TypeAlias = Shaped[gt.IntSz0, "*#batch"] @@ -53,16 +52,6 @@ def psi_of_r(r: T) -> T: # ============================================================================= -@partial(jax.numpy.vectorize, signature="(n),(),()->(n)", excluded=(3,)) -@partial(jax.jit, static_argnames=("m_max",)) # TODO: should l,m be static? -def _real_Ylm(theta: gt.SzN, l: gt.IntSz0, m: gt.IntSz0, m_max: int) -> gt.SzN: - # TODO: sph_harm only supports scalars, even though it returns an array! - theta = jnp.atleast_1d(theta) - return sph_harm( - m, jnp.atleast_1d(l), theta=jnp.zeros_like(theta), phi=theta, n_max=m_max - ).real - - @partial(jax.jit, static_argnames=("m_max",)) def real_Ylm( theta: gt.SzAny, l: BatchableIntSz0, m: BatchableIntSz0, m_max: int = 100 @@ -90,4 +79,5 @@ def real_Ylm( ``(n),(),()->(n)``. """ # TODO: raise an error if m > m_max - return _real_Ylm(theta, l, m, m_max) + _real_Ylm, _ = compute_Ylm(l, m, theta=theta, phi=jnp.zeros_like(theta), l_max=m_max) + return _real_Ylm diff --git a/tests/potential/scf/test_utils.py b/tests/potential/scf/test_utils.py index 6141ba455..5c19768e0 100644 --- a/tests/potential/scf/test_utils.py +++ b/tests/potential/scf/test_utils.py @@ -4,7 +4,6 @@ import hypothesis.extra.numpy as hnp import jax import numpy as np -import numpy.typing as npt import scipy.special as sp from hypothesis import assume, given, strategies as st From 92bc71bc55265d9d2d1e220e5348adde54ac8e2f Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Thu, 9 Oct 2025 13:13:30 -0400 Subject: [PATCH 12/13] uvlock --- uv.lock | 1856 +++++++++++++++++++++++++++---------------------------- 1 file changed, 904 insertions(+), 952 deletions(-) diff --git a/uv.lock b/uv.lock index 0991b5496..1450454f5 100644 --- a/uv.lock +++ b/uv.lock @@ -1,9 +1,5 @@ version = 1 -<<<<<<< HEAD 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"sha256:4ba39e99954848a63c200d4fe2c2b65707609bbb82ed62a1a5d61880bfa0a502", size = 4236 }, +] \ No newline at end of file From 3f12e64ff1ec95f94d8cd340d1f2b603bb6b0fb3 Mon Sep 17 00:00:00 2001 From: Aditya Vijaykumar Date: Thu, 9 Oct 2025 13:21:13 -0400 Subject: [PATCH 13/13] vectorization attempt --- src/galax/potential/_src/scf/bfe_helper.py | 37 ++++++++++------------ 1 file changed, 17 insertions(+), 20 deletions(-) diff --git a/src/galax/potential/_src/scf/bfe_helper.py b/src/galax/potential/_src/scf/bfe_helper.py index 74821129d..cf5ebf2af 100644 --- a/src/galax/potential/_src/scf/bfe_helper.py +++ b/src/galax/potential/_src/scf/bfe_helper.py @@ -10,14 +10,12 @@ from .coeffs_helper import normalization_Knl from .utils import psi_of_r -from spexial import eval_gegenbauer +from spexial import eval_gegenbauers import galax._custom_types as gt -@jax.jit -def rho_nl( - s: Float[Array, "N"], n: int, l: int, -) -> Float[Array, "N"]: +def rho_nl(n: gt.IntSz0, l: gt.IntSz0, s: gt.FloatSz0, +) -> gt.FloatSz0: r"""Radial density expansion terms. Parameters @@ -37,31 +35,32 @@ def rho_nl( jnp.sqrt(4 * jnp.pi) * (normalization_Knl(n=n, l=l) / (2 * jnp.pi)) * (s**l / (s * (1 + s) ** (2 * l + 3))) - * eval_gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + * eval_gegenbauers(n, 2 * l + 1.5, psi_of_r(s)) ) +rho_nl_jit_vec = jax.jit( + jax.vmap( jax.vmap(rho_nl, in_axes=(None, 0, None),), in_axes=(None, None, 0)), static_argnames="n" +) # ====================================================================== -@partial(jax.jit, static_argnames=("n", "l")) -def phi_nl( - s: Float[Array, "samples"], n: gt.IntSz0, l: gt.IntSz0, -) -> Float[Array, "samples"]: +def phi_nl(n: gt.IntSz0, l: gt.IntSz0, s: gt.FloatSz0, +) -> gt.FloatSz0: r"""Angular density expansion terms. Parameters ---------- - s : Array[float, (n_samples,)] - Scaled radius :math:`r/r_s`. n : int - Radial expansion term. + Max Radial expansion term. l : int Spherical harmonic term. + s : Float + Scaled radius :math:`r/r_s`. Returns ------- - Array[float, (n_samples,)] + Array[float, (n + 1,)] Examples -------- @@ -74,11 +73,9 @@ def phi_nl( return ( -jnp.sqrt(4 * jnp.pi) * (s**l / (1.0 + s) ** (2 * l + 1)) - * eval_gegenbauer(n, 2 * l + 1.5, psi_of_r(s)) + * eval_gegenbauers(n, 2 * l + 1.5, psi_of_r(s)) ) - -phi_nl_vec = jnp.vectorize(phi_nl, signature="(n),(),()->(n)", excluded=(3,)) - -phi_nl_grad = jax.jit(jnp.vectorize(jax.grad(phi_nl, argnums=0), excluded=(3,))) -r"""Derivative :math:`\frac{d}{dr} \phi_{nl}`.""" +phi_nl_jit_vec = jax.jit( + jax.vmap( jax.vmap(phi_nl, in_axes=(None, 0, None),), in_axes=(None, None, 0)), static_argnames="n" +) \ No newline at end of file