| from tqdm.auto import trange | |
| import gradio as gr | |
| import pandas as pd | |
| import numpy as np | |
| import plotly.express as px | |
| def make_plot(proj_dir, type_sequence, w, difficulty_distribution_padding, progress=gr.Progress(track_tqdm=True)): | |
| base = 1.01 | |
| index_len = 800 | |
| index_offset = 150 | |
| d_range = 10 | |
| d_offset = 1 | |
| r_repetitions = 1 | |
| f_repetitions = 2.3 | |
| max_repetitions = 200000 | |
| type_block = dict() | |
| type_count = dict() | |
| last_t = type_sequence[0] | |
| type_block[last_t] = 1 | |
| type_count[last_t] = 1 | |
| for t in type_sequence[1:]: | |
| type_count[t] = type_count.setdefault(t, 0) + 1 | |
| if t != last_t: | |
| type_block[t] = type_block.setdefault(t, 0) + 1 | |
| last_t = t | |
| if 2 in type_count and 2 in type_block: | |
| f_repetitions = round(type_count[2] / type_block[2] + 1, 1) | |
| def stability2index(stability): | |
| return int(round(np.log(stability) / np.log(base)) + index_offset) | |
| def init_stability(d): | |
| return max(((d - w[2]) / w[3] + 2) * w[1] + w[0], np.power(base, -index_offset)) | |
| def cal_next_recall_stability(s, r, d, response): | |
| if response == 1: | |
| return s * (1 + np.exp(w[6]) * (11 - d) * np.power(s, w[7]) * (np.exp((1 - r) * w[8]) - 1)) | |
| else: | |
| return w[9] * np.power(d, w[10]) * np.power(s, w[11]) * np.exp((1 - r) * w[12]) | |
| stability_list = np.array([np.power(base, i - index_offset) for i in range(index_len)]) | |
| print(f"terminal stability: {stability_list.max(): .2f}") | |
| df = pd.DataFrame(columns=["retention", "difficulty", "repetitions"]) | |
| for percentage in trange(96, 70, -2, desc='Repetition vs Retention plot'): | |
| recall = percentage / 100 | |
| repetitions_list = np.zeros((d_range, index_len)) | |
| repetitions_list[:, :-1] = max_repetitions | |
| for d in range(d_range, 0, -1): | |
| s0 = init_stability(d) | |
| s0_index = stability2index(s0) | |
| diff = max_repetitions | |
| while diff > 0.1: | |
| s0_repetitions = repetitions_list[d - 1][s0_index] | |
| for s_index in range(index_len - 2, -1, -1): | |
| stability = stability_list[s_index]; | |
| interval = max(1, round(stability * np.log(recall) / np.log(0.9))) | |
| p_recall = np.power(0.9, interval / stability) | |
| recall_s = cal_next_recall_stability(stability, p_recall, d, 1) | |
| forget_d = min(d + d_offset, 10) | |
| forget_s = cal_next_recall_stability(stability, p_recall, forget_d, 0) | |
| recall_s_index = min(stability2index(recall_s), index_len - 1) | |
| forget_s_index = min(max(stability2index(forget_s), 0), index_len - 1) | |
| recall_repetitions = repetitions_list[d - 1][recall_s_index] + r_repetitions | |
| forget_repetitions = repetitions_list[forget_d - 1][forget_s_index] + f_repetitions | |
| exp_repetitions = p_recall * recall_repetitions + (1.0 - p_recall) * forget_repetitions | |
| if exp_repetitions < repetitions_list[d - 1][s_index]: | |
| repetitions_list[d - 1][s_index] = exp_repetitions | |
| diff = s0_repetitions - repetitions_list[d - 1][s0_index] | |
| df.loc[0 if pd.isnull(df.index.max()) else df.index.max() + 1] = [recall, d, s0_repetitions] | |
| df.sort_values(by=["difficulty", "retention"], inplace=True) | |
| df.to_csv(proj_dir/"expected_repetitions.csv", index=False) | |
| print("expected_repetitions.csv saved.") | |
| optimal_retention_list = np.zeros(10) | |
| df2 = pd.DataFrame() | |
| for d in range(1, d_range + 1): | |
| retention = df[df["difficulty"] == d]["retention"] | |
| repetitions = df[df["difficulty"] == d]["repetitions"] | |
| optimal_retention = retention.iat[repetitions.argmin()] | |
| optimal_retention_list[d - 1] = optimal_retention | |
| df2 = df2.append( | |
| pd.DataFrame({'retention': retention, 'expected repetitions': repetitions, 'd': d, 'r': optimal_retention})) | |
| fig = px.line(df2, x="retention", y="expected repetitions", color='d', log_y=True) | |
| print(f"\n-----suggested retention: {np.inner(difficulty_distribution_padding, optimal_retention_list):.2f}-----") | |
| suggested_retention_markdown = f"""# Suggested Retention: `{np.inner(difficulty_distribution_padding, optimal_retention_list):.2f}`""" | |
| return fig, suggested_retention_markdown | |