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import numpy as np
def solver(u0_batch, t_coordinate, nu, rho):
"""Solves the 1D reaction diffusion equation for all times in t_coordinate.
Args:
u0_batch (np.ndarray): Initial condition [batch_size, N],
where batch_size is the number of different initial conditions,
and N is the number of spatial grid points.
t_coordinate (np.ndarray): Time coordinates of shape [T+1].
It begins with t_0=0 and follows the time steps t_1, ..., t_T.
nu (float): The parameter nu in the equation.
rho (float): The parameter rho in the equation.
Returns:
solutions (np.ndarray): Shape [batch_size, T+1, N].
solutions[:, 0, :] contains the initial conditions (u0_batch),
solutions[:, i, :] contains the solutions at time t_coordinate[i].
"""
# TODO: Implement the solver for 1D reaction diffusion equation
# Hints:
# 1. Consider using PyTorch or JAX with GPU acceleration for improved performance
# 2. Remember to handle data types and device placement appropriately
return solutions
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