prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Improve visualization tutorial
  <!-- Please write a clear and concise description of what content in https://optuna.readthedocs.io/ is an issue. -->
  
  I suggest updating the [visualization tutorial](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/005_visualization.html) as follows
  
  - Add missing [`visualization.plot_pareto_front`](https://optuna.readthedocs.io/en/stable/reference/visualization/generated/optuna.visualization.plot_pareto_front.html#optuna.visualization.plot_pareto_front) example; since this function needs multi-objective function unlike other visualization examples, we might need to define such an objective function after the other examples. If adding such an example is not appropriate, at least we need to mention the existence of `visualization.plot_pareto_front`.
  - Mention the availability of matplotlib version in the first paragraph. 
  
  
  </issue>
  <code>
  [start of tutorial/10_key_features/005_visualization.py]
  1 """
  2 .. _visualization:
  3 
  4 Quick Visualization for Hyperparameter Optimization Analysis
  5 ============================================================
  6 
  7 Optuna provides various visualization features in :mod:`optuna.visualization` to analyze optimization results visually.
  8 
  9 This tutorial walks you through this module by visualizing the history of lightgbm model for breast cancer dataset.
  10 """
  11 
  12 ###################################################################################################
  13 import lightgbm as lgb
  14 import numpy as np
  15 import sklearn.datasets
  16 import sklearn.metrics
  17 from sklearn.model_selection import train_test_split
  18 
  19 import optuna
  20 from optuna.visualization import plot_contour
  21 from optuna.visualization import plot_edf
  22 from optuna.visualization import plot_intermediate_values
  23 from optuna.visualization import plot_optimization_history
  24 from optuna.visualization import plot_parallel_coordinate
  25 from optuna.visualization import plot_param_importances
  26 from optuna.visualization import plot_slice
  27 
  28 SEED = 42
  29 
  30 np.random.seed(SEED)
  31 
  32 
  33 ###################################################################################################
  34 # Define the objective function.
  35 def objective(trial):
  36     data, target = sklearn.datasets.load_breast_cancer(return_X_y=True)
  37     train_x, valid_x, train_y, valid_y = train_test_split(data, target, test_size=0.25)
  38     dtrain = lgb.Dataset(train_x, label=train_y)
  39     dvalid = lgb.Dataset(valid_x, label=valid_y)
  40 
  41     param = {
  42         "objective": "binary",
  43         "metric": "auc",
  44         "verbosity": -1,
  45         "boosting_type": "gbdt",
  46         "bagging_fraction": trial.suggest_float("bagging_fraction", 0.4, 1.0),
  47         "bagging_freq": trial.suggest_int("bagging_freq", 1, 7),
  48         "min_child_samples": trial.suggest_int("min_child_samples", 5, 100),
  49     }
  50 
  51     # Add a callback for pruning.
  52     pruning_callback = optuna.integration.LightGBMPruningCallback(trial, "auc")
  53     gbm = lgb.train(
  54         param, dtrain, valid_sets=[dvalid], verbose_eval=False, callbacks=[pruning_callback]
  55     )
  56 
  57     preds = gbm.predict(valid_x)
  58     pred_labels = np.rint(preds)
  59     accuracy = sklearn.metrics.accuracy_score(valid_y, pred_labels)
  60     return accuracy
  61 
  62 
  63 ###################################################################################################
  64 study = optuna.create_study(
  65     direction="maximize",
  66     sampler=optuna.samplers.TPESampler(seed=SEED),
  67     pruner=optuna.pruners.MedianPruner(n_warmup_steps=10),
  68 )
  69 study.optimize(objective, n_trials=100, timeout=600)
  70 
  71 ###################################################################################################
  72 # Plot functions
  73 # --------------
  74 # Visualize the optimization history. See :func:`~optuna.visualization.plot_optimization_history` for the details.
  75 plot_optimization_history(study)
  76 
  77 ###################################################################################################
  78 # Visualize the learning curves of the trials. See :func:`~optuna.visualization.plot_intermediate_values` for the details.
  79 plot_intermediate_values(study)
  80 
  81 ###################################################################################################
  82 # Visualize high-dimensional parameter relationships. See :func:`~optuna.visualization.plot_parallel_coordinate` for the details.
  83 plot_parallel_coordinate(study)
  84 
  85 ###################################################################################################
  86 # Select parameters to visualize.
  87 plot_parallel_coordinate(study, params=["bagging_freq", "bagging_fraction"])
  88 
  89 ###################################################################################################
  90 # Visualize hyperparameter relationships. See :func:`~optuna.visualization.plot_contour` for the details.
  91 plot_contour(study)
  92 
  93 ###################################################################################################
  94 # Select parameters to visualize.
  95 plot_contour(study, params=["bagging_freq", "bagging_fraction"])
  96 
  97 ###################################################################################################
  98 # Visualize individual hyperparameters as slice plot. See :func:`~optuna.visualization.plot_slice` for the details.
  99 plot_slice(study)
  100 
  101 ###################################################################################################
  102 # Select parameters to visualize.
  103 plot_slice(study, params=["bagging_freq", "bagging_fraction"])
  104 
  105 ###################################################################################################
  106 # Visualize parameter importances. See :func:`~optuna.visualization.plot_param_importances` for the details.
  107 plot_param_importances(study)
  108 
  109 ###################################################################################################
  110 # Learn which hyperparameters are affecting the trial duration with hyperparameter importance.
  111 optuna.visualization.plot_param_importances(
  112     study, target=lambda t: t.duration.total_seconds(), target_name="duration"
  113 )
  114 
  115 ###################################################################################################
  116 # Visualize empirical distribution function. See :func:`~optuna.visualization.plot_edf` for the details.
  117 plot_edf(study)
  118
  [end of tutorial/10_key_features/005_visualization.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/tutorial/10_key_features/005_visualization.py b/tutorial/10_key_features/005_visualization.py
  --- a/tutorial/10_key_features/005_visualization.py
  +++ b/tutorial/10_key_features/005_visualization.py
  @@ -7,6 +7,9 @@
   Optuna provides various visualization features in :mod:`optuna.visualization` to analyze optimization results visually.
   
   This tutorial walks you through this module by visualizing the history of lightgbm model for breast cancer dataset.
  +
  +For visualizing multi-objective optimization (i.e., the usage of :func:`optuna.visualization.plot_pareto_front`),
  +please refer to the tutorial of :ref:`multi_objective`.
   """
   
   ###################################################################################################
  @@ -17,6 +20,9 @@
   from sklearn.model_selection import train_test_split
   
   import optuna
  +
  +# You can use Matplotlib instead of Plotly for visualization by simply replacing `optuna.visualization` with
  +# `optuna.visualization.matplotlib` in the following examples.
   from optuna.visualization import plot_contour
   from optuna.visualization import plot_edf
   from optuna.visualization import plot_intermediate_values
  
verification_info: {"golden_diff": "diff --git a/tutorial/10_key_features/005_visualization.py b/tutorial/10_key_features/005_visualization.py\n--- a/tutorial/10_key_features/005_visualization.py\n+++ b/tutorial/10_key_features/005_visualization.py\n@@ -7,6 +7,9 @@\n Optuna provides various visualization features in :mod:`optuna.visualization` to analyze optimization results visually.\n \n This tutorial walks you through this module by visualizing the history of lightgbm model for breast cancer dataset.\n+\n+For visualizing multi-objective optimization (i.e., the usage of :func:`optuna.visualization.plot_pareto_front`),\n+please refer to the tutorial of :ref:`multi_objective`.\n \"\"\"\n \n ###################################################################################################\n@@ -17,6 +20,9 @@\n from sklearn.model_selection import train_test_split\n \n import optuna\n+\n+# You can use Matplotlib instead of Plotly for visualization by simply replacing `optuna.visualization` with\n+# `optuna.visualization.matplotlib` in the following examples.\n from optuna.visualization import plot_contour\n from optuna.visualization import plot_edf\n from optuna.visualization import plot_intermediate_values\n", "issue": "Improve visualization tutorial\n<!-- Please write a clear and concise description of what content in https://optuna.readthedocs.io/ is an issue. -->\r\n\r\nI suggest updating the [visualization tutorial](https://optuna.readthedocs.io/en/stable/tutorial/10_key_features/005_visualization.html) as follows\r\n\r\n- Add missing [`visualization.plot_pareto_front`](https://optuna.readthedocs.io/en/stable/reference/visualization/generated/optuna.visualization.plot_pareto_front.html#optuna.visualization.plot_pareto_front) example; since this function needs multi-objective function unlike other visualization examples, we might need to define such an objective function after the other examples. If adding such an example is not appropriate, at least we need to mention the existence of `visualization.plot_pareto_front`.\r\n- Mention the availability of matplotlib version in the first paragraph. \r\n\n", "before_files": [{"content": "\"\"\"\n.. _visualization:\n\nQuick Visualization for Hyperparameter Optimization Analysis\n============================================================\n\nOptuna provides various visualization features in :mod:`optuna.visualization` to analyze optimization results visually.\n\nThis tutorial walks you through this module by visualizing the history of lightgbm model for breast cancer dataset.\n\"\"\"\n\n###################################################################################################\nimport lightgbm as lgb\nimport numpy as np\nimport sklearn.datasets\nimport sklearn.metrics\nfrom sklearn.model_selection import train_test_split\n\nimport optuna\nfrom optuna.visualization import plot_contour\nfrom optuna.visualization import plot_edf\nfrom optuna.visualization import plot_intermediate_values\nfrom optuna.visualization import plot_optimization_history\nfrom optuna.visualization import plot_parallel_coordinate\nfrom optuna.visualization import plot_param_importances\nfrom optuna.visualization import plot_slice\n\nSEED = 42\n\nnp.random.seed(SEED)\n\n\n###################################################################################################\n# Define the objective function.\ndef objective(trial):\n    data, target = sklearn.datasets.load_breast_cancer(return_X_y=True)\n    train_x, valid_x, train_y, valid_y = train_test_split(data, target, test_size=0.25)\n    dtrain = lgb.Dataset(train_x, label=train_y)\n    dvalid = lgb.Dataset(valid_x, label=valid_y)\n\n    param = {\n        \"objective\": \"binary\",\n        \"metric\": \"auc\",\n        \"verbosity\": -1,\n        \"boosting_type\": \"gbdt\",\n        \"bagging_fraction\": trial.suggest_float(\"bagging_fraction\", 0.4, 1.0),\n        \"bagging_freq\": trial.suggest_int(\"bagging_freq\", 1, 7),\n        \"min_child_samples\": trial.suggest_int(\"min_child_samples\", 5, 100),\n    }\n\n    # Add a callback for pruning.\n    pruning_callback = optuna.integration.LightGBMPruningCallback(trial, \"auc\")\n    gbm = lgb.train(\n        param, dtrain, valid_sets=[dvalid], verbose_eval=False, callbacks=[pruning_callback]\n    )\n\n    preds = gbm.predict(valid_x)\n    pred_labels = np.rint(preds)\n    accuracy = sklearn.metrics.accuracy_score(valid_y, pred_labels)\n    return accuracy\n\n\n###################################################################################################\nstudy = optuna.create_study(\n    direction=\"maximize\",\n    sampler=optuna.samplers.TPESampler(seed=SEED),\n    pruner=optuna.pruners.MedianPruner(n_warmup_steps=10),\n)\nstudy.optimize(objective, n_trials=100, timeout=600)\n\n###################################################################################################\n# Plot functions\n# --------------\n# Visualize the optimization history. See :func:`~optuna.visualization.plot_optimization_history` for the details.\nplot_optimization_history(study)\n\n###################################################################################################\n# Visualize the learning curves of the trials. See :func:`~optuna.visualization.plot_intermediate_values` for the details.\nplot_intermediate_values(study)\n\n###################################################################################################\n# Visualize high-dimensional parameter relationships. See :func:`~optuna.visualization.plot_parallel_coordinate` for the details.\nplot_parallel_coordinate(study)\n\n###################################################################################################\n# Select parameters to visualize.\nplot_parallel_coordinate(study, params=[\"bagging_freq\", \"bagging_fraction\"])\n\n###################################################################################################\n# Visualize hyperparameter relationships. See :func:`~optuna.visualization.plot_contour` for the details.\nplot_contour(study)\n\n###################################################################################################\n# Select parameters to visualize.\nplot_contour(study, params=[\"bagging_freq\", \"bagging_fraction\"])\n\n###################################################################################################\n# Visualize individual hyperparameters as slice plot. See :func:`~optuna.visualization.plot_slice` for the details.\nplot_slice(study)\n\n###################################################################################################\n# Select parameters to visualize.\nplot_slice(study, params=[\"bagging_freq\", \"bagging_fraction\"])\n\n###################################################################################################\n# Visualize parameter importances. See :func:`~optuna.visualization.plot_param_importances` for the details.\nplot_param_importances(study)\n\n###################################################################################################\n# Learn which hyperparameters are affecting the trial duration with hyperparameter importance.\noptuna.visualization.plot_param_importances(\n    study, target=lambda t: t.duration.total_seconds(), target_name=\"duration\"\n)\n\n###################################################################################################\n# Visualize empirical distribution function. See :func:`~optuna.visualization.plot_edf` for the details.\nplot_edf(study)\n", "path": "tutorial/10_key_features/005_visualization.py"}]}