driftwm/sim/flow.py

from __future__ import annotations

from dataclasses import dataclass
from typing import Any

import numpy as np


PAPER_FLOW = {
    "uniform_min": 0.03,
    "uniform_max": 0.24,
    "vortex_base_max": 0.05,
    "vortex_gamma_min": 0.12,
    "vortex_gamma_max": 0.24,
    "vortex_max": 0.36,
    "gradient_base_min": 0.00,
    "gradient_base_max": 0.08,
    "gradient_matrix_min": 0.018,
    "gradient_matrix_max": 0.040,
    "gradient_max": 0.34,
    "turbulent_base_max": 0.05,
    "turbulent_vector_std": 0.105,
    "turbulent_max": 0.34,
    "shear_min": 0.035,
    "shear_max_rate": 0.085,
    "shear_max": 0.38,
    "double_gyre_amp_min": 0.20,
    "double_gyre_amp_max": 0.34,
    "double_gyre_max": 0.36,
    "source_base_max": 0.03,
    "source_strength_min": 0.16,
    "source_strength_max": 0.30,
    "source_max": 0.36,
    "random_fourier_amp_std": 0.045,
    "random_fourier_max": 0.38,
}


@dataclass
class Flow:
    name: str
    flow_id: int

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        raise NotImplementedError

    def metadata(self) -> dict[str, Any]:
        return {"flow_type": self.name, "flow_id": int(self.flow_id)}


@dataclass
class NoFlow(Flow):
    def __init__(self, flow_id: int = 0):
        super().__init__("noflow", flow_id)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        return np.zeros_like(np.asarray(pos, dtype=np.float32))


@dataclass
class UniformFlow(Flow):
    vector: np.ndarray

    def __init__(self, vector: np.ndarray, flow_id: int):
        super().__init__("uniform", flow_id)
        self.vector = np.asarray(vector, dtype=np.float32)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        return np.broadcast_to(self.vector, pos.shape).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out["vector"] = self.vector.astype(float).tolist()
        return out

@dataclass
class VortexFlow(Flow):
    base: np.ndarray
    center: np.ndarray
    gamma: float
    radius_eps: float
    max_speed: float

    def __init__(
        self,
        base: np.ndarray,
        center: np.ndarray,
        gamma: float,
        flow_id: int,
        radius_eps: float = 0.30,
        max_speed: float = 0.50,
        name: str = "vortex",
    ):
        super().__init__(name, flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.center = np.asarray(center, dtype=np.float32)
        self.gamma = float(gamma)
        self.radius_eps = float(radius_eps)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        rel = pos - self.center
        denom = np.sum(rel * rel, axis=-1, keepdims=True) + self.radius_eps**2
        swirl = self.gamma * np.concatenate([-rel[..., 1:2], rel[..., 0:1]], axis=-1) / denom
        vel = self.base + swirl
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update(
            {
                "base": self.base.astype(float).tolist(),
                "center": self.center.astype(float).tolist(),
                "gamma": self.gamma,
            }
        )
        return out


@dataclass
class GradientFlow(Flow):
    base: np.ndarray
    center: np.ndarray
    matrix: np.ndarray
    max_speed: float

    def __init__(self, base: np.ndarray, center: np.ndarray, matrix: np.ndarray, flow_id: int, max_speed: float = 0.55):
        super().__init__("gradient", flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.center = np.asarray(center, dtype=np.float32)
        self.matrix = np.asarray(matrix, dtype=np.float32)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        rel = pos - self.center
        vel = self.base + rel @ self.matrix.T
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update(
            {
                "base": self.base.astype(float).tolist(),
                "center": self.center.astype(float).tolist(),
                "matrix": self.matrix.astype(float).tolist(),
            }
        )
        return out


@dataclass
class TurbulentPatchFlow(Flow):
    base: np.ndarray
    centers: np.ndarray
    vectors: np.ndarray
    sigma: float
    max_speed: float

    def __init__(
        self,
        base: np.ndarray,
        centers: np.ndarray,
        vectors: np.ndarray,
        flow_id: int,
        sigma: float = 1.15,
        max_speed: float = 0.55,
    ):
        super().__init__("turbulent_patch", flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.centers = np.asarray(centers, dtype=np.float32)
        self.vectors = np.asarray(vectors, dtype=np.float32)
        self.sigma = float(sigma)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        rel = pos[..., None, :] - self.centers
        weights = np.exp(-np.sum(rel * rel, axis=-1, keepdims=True) / (2.0 * self.sigma**2))
        perturb = np.sum(weights * self.vectors, axis=-2)
        vel = self.base + perturb
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update({"base": self.base.astype(float).tolist(), "centers": self.centers.astype(float).tolist()})
        return out


@dataclass
class ShearFlow(Flow):
    base: np.ndarray
    center_y: float
    shear: float
    max_speed: float

    def __init__(self, base: np.ndarray, center_y: float, shear: float, flow_id: int, max_speed: float = 0.60):
        super().__init__("shear", flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.center_y = float(center_y)
        self.shear = float(shear)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        vel = np.broadcast_to(self.base, pos.shape).copy()
        vel[..., 0] += self.shear * (pos[..., 1] - self.center_y)
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update({"base": self.base.astype(float).tolist(), "center_y": self.center_y, "shear": self.shear})
        return out


@dataclass
class DoubleGyreFlow(Flow):
    amp: float
    phase: float
    workspace: tuple[float, float, float, float]
    max_speed: float

    def __init__(
        self,
        amp: float,
        phase: float,
        flow_id: int,
        workspace: tuple[float, float, float, float],
        max_speed: float = 0.50,
    ):
        super().__init__("double_gyre", flow_id)
        self.amp = float(amp)
        self.phase = float(phase)
        self.workspace = workspace
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        xmin, xmax, ymin, ymax = self.workspace
        x = (pos[..., 0] - xmin) / max(xmax - xmin, 1e-6)
        y = (pos[..., 1] - ymin) / max(ymax - ymin, 1e-6)
        sx = np.sin(np.pi * x + self.phase)
        cx = np.cos(np.pi * x + self.phase)
        sy = np.sin(2.0 * np.pi * y)
        cy = np.cos(2.0 * np.pi * y)
        vel = np.stack([self.amp * sx * cy, -0.5 * self.amp * cx * sy], axis=-1)
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update({"amp": self.amp, "phase": self.phase})
        return out


@dataclass
class SourceSinkFlow(Flow):
    base: np.ndarray
    centers: np.ndarray
    strengths: np.ndarray
    radius_eps: float
    max_speed: float

    def __init__(
        self,
        name: str,
        base: np.ndarray,
        centers: np.ndarray,
        strengths: np.ndarray,
        flow_id: int,
        radius_eps: float = 0.45,
        max_speed: float = 0.50,
    ):
        super().__init__(name, flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.centers = np.asarray(centers, dtype=np.float32)
        self.strengths = np.asarray(strengths, dtype=np.float32)
        self.radius_eps = float(radius_eps)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        rel = pos[..., None, :] - self.centers
        denom = np.sum(rel * rel, axis=-1, keepdims=True) + self.radius_eps**2
        strength_shape = (1,) * (rel.ndim - 2) + (self.strengths.shape[0], 1)
        radial = np.sum(self.strengths.reshape(strength_shape) * rel / denom, axis=-2)
        vel = self.base + radial
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update(
            {
                "base": self.base.astype(float).tolist(),
                "centers": self.centers.astype(float).tolist(),
                "strengths": self.strengths.astype(float).tolist(),
            }
        )
        return out


@dataclass
class RandomFourierFlow(Flow):
    base: np.ndarray
    k: np.ndarray
    amp: np.ndarray
    phase: np.ndarray
    max_speed: float

    def __init__(
        self,
        base: np.ndarray,
        k: np.ndarray,
        amp: np.ndarray,
        phase: np.ndarray,
        flow_id: int,
        max_speed: float = 0.60,
    ):
        super().__init__("random_fourier", flow_id)
        self.base = np.asarray(base, dtype=np.float32)
        self.k = np.asarray(k, dtype=np.float32)
        self.amp = np.asarray(amp, dtype=np.float32)
        self.phase = np.asarray(phase, dtype=np.float32)
        self.max_speed = float(max_speed)

    def velocity(self, pos: np.ndarray, t: float = 0.0) -> np.ndarray:
        pos = np.asarray(pos, dtype=np.float32)
        flat = pos.reshape(-1, 2)
        arg = flat @ self.k.T + self.phase[None, :]
        # Divergence-free field via stream function psi: v=(dpsi/dy, -dpsi/dx).
        coeff = self.amp[None, :] * np.cos(arg)
        vx = np.sum(coeff * self.k[None, :, 1], axis=1)
        vy = -np.sum(coeff * self.k[None, :, 0], axis=1)
        vel = np.stack([vx, vy], axis=-1).reshape(pos.shape) + self.base
        speed = np.linalg.norm(vel, axis=-1, keepdims=True)
        scale = np.minimum(1.0, self.max_speed / np.maximum(speed, 1e-6))
        return (vel * scale).astype(np.float32)

    def metadata(self) -> dict[str, Any]:
        out = super().metadata()
        out.update({"base": self.base.astype(float).tolist(), "num_modes": int(self.k.shape[0])})
        return out


def _sample_uniform_vector(rng: np.random.Generator, min_speed: float = 0.05, max_speed: float = 0.35) -> np.ndarray:
    speed = rng.uniform(min_speed, max_speed)
    direction = rng.uniform(0.0, 2.0 * np.pi)
    return np.array([speed * np.cos(direction), speed * np.sin(direction)], dtype=np.float32)


def _sample_signed_uniform(rng: np.random.Generator, min_abs: float, max_abs: float) -> float:
    sign = -1.0 if rng.random() < 0.5 else 1.0
    return float(sign * rng.uniform(min_abs, max_abs))


def _route_anchors(workspace: tuple[float, float, float, float]) -> np.ndarray:
    xmin, xmax, ymin, ymax = workspace
    w = xmax - xmin
    h = ymax - ymin
    points = np.array(
        [
            [0.20, 0.20],
            [0.35, 0.35],
            [0.50, 0.50],
            [0.65, 0.65],
            [0.80, 0.80],
            [0.20, 0.80],
            [0.35, 0.65],
            [0.50, 0.50],
            [0.65, 0.35],
            [0.80, 0.20],
            [0.50, 0.25],
            [0.50, 0.75],
            [0.25, 0.50],
            [0.75, 0.50],
        ],
        dtype=np.float32,
    )
    points[:, 0] = xmin + points[:, 0] * w
    points[:, 1] = ymin + points[:, 1] * h
    return points


def _sample_route_center(
    rng: np.random.Generator,
    workspace: tuple[float, float, float, float],
    jitter: float = 0.65,
) -> np.ndarray:
    xmin, xmax, ymin, ymax = workspace
    anchors = _route_anchors(workspace)
    center = anchors[int(rng.integers(0, len(anchors)))] + rng.normal(0.0, jitter, size=2).astype(np.float32)
    return np.array([np.clip(center[0], xmin + 1.2, xmax - 1.2), np.clip(center[1], ymin + 1.2, ymax - 1.2)], dtype=np.float32)


def _sample_route_centers(
    rng: np.random.Generator,
    workspace: tuple[float, float, float, float],
    count: int,
    jitter: float = 0.65,
) -> np.ndarray:
    return np.stack([_sample_route_center(rng, workspace, jitter=jitter) for _ in range(count)], axis=0).astype(np.float32)


def sample_flow(
    flow_type: str,
    rng: np.random.Generator,
    flow_id: int,
    workspace: tuple[float, float, float, float] = (0.0, 10.0, 0.0, 10.0),
) -> Flow:
    flow_type = flow_type.lower()
    profile = PAPER_FLOW
    if flow_type == "noflow":
        return NoFlow(flow_id=0)
    if flow_type == "uniform":
        return UniformFlow(_sample_uniform_vector(rng, profile["uniform_min"], profile["uniform_max"]), flow_id=flow_id)
    if flow_type == "vortex_center":
        center = _sample_route_center(rng, workspace, jitter=0.45)
        base = _sample_uniform_vector(rng, 0.0, profile["vortex_base_max"])
        gamma = _sample_signed_uniform(rng, profile["vortex_gamma_min"], profile["vortex_gamma_max"])
        return VortexFlow(base=base, center=center, gamma=gamma, flow_id=flow_id, max_speed=profile["vortex_max"], name=flow_type)
    if flow_type == "gradient":
        center = _sample_route_center(rng, workspace, jitter=0.35)
        base = _sample_uniform_vector(rng, profile["gradient_base_min"], profile["gradient_base_max"])
        scale = rng.uniform(profile["gradient_matrix_min"], profile["gradient_matrix_max"])
        mat = rng.normal(0.0, 1.0, size=(2, 2)).astype(np.float32)
        mat = mat / max(float(np.linalg.norm(mat)), 1e-6) * scale
        return GradientFlow(base=base, center=center, matrix=mat, flow_id=flow_id, max_speed=profile["gradient_max"])
    if flow_type == "turbulent_patch":
        base = _sample_uniform_vector(rng, 0.0, profile["turbulent_base_max"])
        centers = _sample_route_centers(rng, workspace, count=5, jitter=0.85)
        vectors = rng.normal(0.0, profile["turbulent_vector_std"], size=(5, 2)).astype(np.float32)
        return TurbulentPatchFlow(base=base, centers=centers, vectors=vectors, flow_id=flow_id, max_speed=profile["turbulent_max"])
    if flow_type == "shear":
        xmin, xmax, ymin, ymax = workspace
        base = _sample_uniform_vector(rng, 0.0, profile["turbulent_base_max"])
        center_y = 0.5 * (ymin + ymax)
        shear = _sample_signed_uniform(rng, profile["shear_min"], profile["shear_max_rate"])
        return ShearFlow(base=base, center_y=center_y, shear=shear, flow_id=flow_id, max_speed=profile["shear_max"])
    if flow_type == "double_gyre":
        amp = float(rng.uniform(profile["double_gyre_amp_min"], profile["double_gyre_amp_max"]))
        phase = float(rng.uniform(0.0, 2.0 * np.pi))
        return DoubleGyreFlow(amp=amp, phase=phase, flow_id=flow_id, workspace=workspace, max_speed=profile["double_gyre_max"])
    if flow_type == "source_sink":
        base = _sample_uniform_vector(rng, 0.0, profile["source_base_max"])
        center = _sample_route_centers(rng, workspace, count=1, jitter=0.65)
        strength = np.array([_sample_signed_uniform(rng, profile["source_strength_min"], profile["source_strength_max"])], dtype=np.float32)
        return SourceSinkFlow(
            name="source_sink",
            base=base,
            centers=center,
            strengths=strength,
            flow_id=flow_id,
            max_speed=profile["source_max"],
        )
    if flow_type == "source_sink_pair":
        base = _sample_uniform_vector(rng, 0.0, profile["source_base_max"])
        centers = _sample_route_centers(rng, workspace, count=2, jitter=0.75)
        strength = float(rng.uniform(profile["source_strength_min"], profile["source_strength_max"]))
        if rng.random() < 0.5:
            strength = -strength
        strengths = np.array([strength, -strength], dtype=np.float32)
        return SourceSinkFlow(
            name="source_sink_pair",
            base=base,
            centers=centers,
            strengths=strengths,
            flow_id=flow_id,
            max_speed=profile["source_max"],
        )
    if flow_type == "random_fourier":
        base = _sample_uniform_vector(rng, 0.0, profile["turbulent_base_max"])
        modes = 8
        k = rng.integers(1, 5, size=(modes, 2)).astype(np.float32)
        signs = rng.choice([-1.0, 1.0], size=(modes, 2)).astype(np.float32)
        k = signs * k * (2.0 * np.pi / 10.0)
        amp_std = profile["random_fourier_amp_std"]
        amp = rng.normal(0.0, amp_std, size=(modes,)).astype(np.float32)
        phase = rng.uniform(0.0, 2.0 * np.pi, size=(modes,)).astype(np.float32)
        return RandomFourierFlow(
            base=base,
            k=k,
            amp=amp,
            phase=phase,
            flow_id=flow_id,
            max_speed=profile["random_fourier_max"],
        )
    raise ValueError(f"unknown flow type: {flow_type}")