Project: s41467-024-47831-2 | Function: main (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
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user: Complete this Python function:

**DESCRIPTION:** Bio-inspired virtual growth algorithm implementing stochastic microstructure generation with frequency-controlled building blocks, entropy-based cell selection, and probability-driven growth simulation for creating irregular architected materials with spatially varying properties

**KEY TERMS:** {
  "frequency_hints": "target frequency combinations of basic building blocks",
  "aug_candidates": "augmented set of candidate blocks with rotations",
  "full_mesh": "symbolic representation of growing microstructure",
  "entropies": "Shannon entropy for measuring cell uncertainty",
  "admissible_blocks": "blocks satisfying adjacency rules",
  "block_count": "frequency tracking for each finite element",
  "probs": "probability distribution for block selection"
}

**CONTEXT CODE:** """
Authors:
- Yingqi Jia (yingqij2@illinois.edu)
- Ke Liu (liuke@pku.edu.cn)
- Xiaojia Shelly Zhang (zhangxs@illinois.edu)

Sponsor:
- David C. Crawford Faculty Scholar Award from the Department of Civil and
  Environmental Engineering and Grainger College of Engineering at the
  University of Illinois

Citations:
- Jia, Y., Liu, K., Zhang, X.S., 2024. Modulate stress distribution with
  bio-inspired irregular architected materials towards optimal tissue support.
  Nature Communications 15, 4072. https://doi.org/10.1038/s41467-024-47831-2
- Jia, Y., Liu, K., Zhang, X.S., 2024. Topology optimization of irregular
  multiscale structures with tunable responses using a virtual growth rule.
  Computer Methods in Applied Mechanics and Engineering 425, 116864.
  https://doi.org/10.1016/j.cma.2024.116864
"""

import os
import time
import datetime
import pytz
from tqdm import tqdm

import numpy as np

from virtual_growth.adjacency_rules import (
    augment_candidates, find_admissible_blocks_2d, find_admissible_blocks_3d)
from virtual_growth.post_processing import (
    compute_final_frequency, plot_microstructure_2d, plot_microstructure_3d,
    plot_microstructure_gif)
from utils.array_list_operations import find_indices


def main(mesh_size, elem_size, candidates, frequency_hints,
         d=1, m=6, n=0, periodic=False, num_tries=1, print_frequency=True,
         make_figure=True, make_gif=True, color="#96ADFC", data_path="",
         save_path="", fig_name="microstructure.jpg",
         gif_name="microstructure.mp4", save_mesh=False, save_mesh_path="",
         save_mesh_name="symbolic_graph.npy"):
    """
    The main function for generating microstructures.
    Inputs:
        mesh_size: A tuple containing numbers of elements in the z-, y- and
                   x-directions (y- and x-directions for 2D) in the mesh.
        elem_size: A tuple containing numbers of cells in the z-, y- and
                   x-directions (y- and x-directions for 2D) in each element.
        candidates: A list containing names of candidate blocks.
        frequency_hints: A 2D array containing frequency hints of candidate
                         blocks. Each row repents frequency hints of one
                         finite element.
        d: One half length of each side of the kernal cube (3D) or one half
           thickness of the arm (2D).
        m: Length of the arm.
        n: Offset of the center (only for 2D).
        periodic: Activate the periodic constaint or not.
        num_tries: Allowable attemps to generate the microstructure.
        print_frequency: Print the frequency distribution or not.
        make_figure: Make the figure of the microstructure or not.
        make_gif: Make the gif of the history of microstructure generation or not.
        data_path: The path for storing the information of blocks and rules.
        save_path: The path for storing the microstructure.
        fig_name: The image name for storing the microstructure.
        gif_name: The gif name for storing the history of microstructure generation.
        save_mesh: Save the symbolic mesh or not.
        save_mesh_path: The path for storing the symbolic mesh.
        save_mesh_name: The name for storing the symbolic mesh.
    """
    raise NotImplementedError("Function has been masked for testing purposes")

    # Pre-check
    # -------------------------------------------------------------------------
    computation_start_time = time.time()
    start_time_info = "Program start time: "+datetime.datetime.now(
        pytz.timezone("America/Chicago")).strftime("%Y-%m-%d %H:%M:%S")
    print(start_time_info)

    if frequency_hints.shape[1] != len(candidates):
        raise ValueError(
            "Candidate blocks and frequency hints are incompatible.")

    if np.count_nonzero(
        np.isclose(np.sum(frequency_hints, axis=1), 1.0)
    ) != frequency_hints.shape[0]:
        raise ValueError("Sum of frequency hints is inequal to 1.")

    if len(mesh_size) != len(elem_size):
        raise ValueError("Dimensions of the mesh and element are incompatible.")

    num_elems = np.prod(mesh_size)  # Number of elements in the mesh
    num_cells_elem = np.prod(elem_size)  # Number of cells in each element
    num_cells = num_elems * num_cells_elem  # Number of all cells in the mesh

    if frequency_hints.shape[0] != num_elems:
        raise ValueError("The number of elements and frequency hints"
                         "are incompatible.")

    if (make_figure or make_gif) and save_path != "" and not os.path.exists(save_path):
        os.makedirs(save_path)

    if save_mesh and save_mesh_path != "" and not os.path.exists(save_mesh_path):
        os.makedirs(save_mesh_path)

    # Prepare for the virtual growth
    # -------------------------------------------------------------------------
    # Compute numbers of all cells in each direction
    dim = len(mesh_size)
    if dim == 2:
        num_cells_y = mesh_size[0] * elem_size[0]
        num_cells_x = mesh_size[1] * elem_size[1]
    elif dim == 3:
        num_cells_z = mesh_size[0] * elem_size[0]
        num_cells_y = mesh_size[1] * elem_size[1]
        num_cells_x = mesh_size[2] * elem_size[2]

    # Compute numbers of all elements in each direction
    all_cells = np.arange(num_cells)
    if dim == 2:
        y_cell, x_cell = np.divmod(all_cells, num_cells_x)
        y_elem, _ = np.divmod(y_cell, elem_size[0])
        x_elem, _ = np.divmod(x_cell, elem_size[1])
        all_elems = y_elem*mesh_size[1] + x_elem
    elif dim == 3:
        z_cell, temp = np.divmod(all_cells, num_cells_x*num_cells_y)
        y_cell, x_cell = np.divmod(temp, num_cells_x)
        z_elem, _ = np.divmod(z_cell, elem_size[0])
        y_elem, _ = np.divmod(y_cell, elem_size[1])
        x_elem, _ = np.divmod(x_cell, elem_size[2])
        all_elems = z_elem*mesh_size[1]*mesh_size[2] + y_elem*mesh_size[2] + x_elem

    # Import data
    names = np.load(data_path + "unique_names.npy")
    rules = np.load(data_path + "pair_rules_encoded.npy")
    rotation_table = np.load(data_path + "rotation_table_encoded.npy")


Complete the function implementation replacing "raise NotImplementedError".