prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Write docs for Optuna optimization
  
  
  </issue>
  <code>
  [start of cupyx/optimizing/_optimize.py]
  1 import contextlib
  2 import math
  3 
  4 
  5 try:
  6     import optuna
  7     _optuna_available = True
  8 except ImportError:
  9     _optuna_available = False
  10 
  11 
  12 from cupy.core import _optimize_config
  13 from cupyx import time
  14 
  15 
  16 def _optimize(
  17         optimize_config, target_func, suggest_func,
  18         default_best, ignore_error=()):
  19     assert isinstance(optimize_config, _optimize_config._OptimizationConfig)
  20     assert callable(target_func)
  21     assert callable(suggest_func)
  22 
  23     def objective(trial):
  24         args = suggest_func(trial)
  25         max_total_time = optimize_config.max_total_time_per_trial
  26         try:
  27             perf = time.repeat(target_func, args, max_duration=max_total_time)
  28             return perf.gpu_times.mean()
  29         except Exception as e:
  30             if isinstance(e, ignore_error):
  31                 return math.inf
  32             else:
  33                 raise e
  34 
  35     study = optuna.create_study()
  36     study.enqueue_trial(default_best)
  37     study.optimize(
  38         objective,
  39         n_trials=optimize_config.max_trials,
  40         timeout=optimize_config.timeout)
  41     return study.best_trial
  42 
  43 
  44 @contextlib.contextmanager
  45 def optimize(*, key=None, **config_dict):
  46     if not _optuna_available:
  47         raise RuntimeError(
  48             'Optuna is required to run optimization. '
  49             'See https://optuna.org/ for the installation instructions.')
  50 
  51     old_context = _optimize_config.get_current_context()
  52     context = _optimize_config.get_new_context(key, _optimize, config_dict)
  53     _optimize_config.set_current_context(context)
  54 
  55     try:
  56         yield context
  57     finally:
  58         _optimize_config.set_current_context(old_context)
  59
  [end of cupyx/optimizing/_optimize.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/cupyx/optimizing/_optimize.py b/cupyx/optimizing/_optimize.py
  --- a/cupyx/optimizing/_optimize.py
  +++ b/cupyx/optimizing/_optimize.py
  @@ -43,6 +43,37 @@
   
   @contextlib.contextmanager
   def optimize(*, key=None, **config_dict):
  +    """Context manager that optimizes kernel launch parameters.
  +
  +    In this context, CuPy's routines find the best kernel launch parameter
  +    values (e.g., the number of threads and blocks). The found values are
  +    cached and reused with keys as the shapes, strides and dtypes of the
  +    given inputs arrays.
  +
  +    Args:
  +        key (string or None): The cache key of optimizations.
  +        max_trials (int): The number of trials that defaults to 100.
  +        timeout (float):
  +            Stops study after the given number of seconds. Default is 1.
  +        max_total_time_per_trial (float):
  +            Repeats measuring the execution time of the routine for the
  +            given number of seconds. Default is 0.1.
  +
  +    Examples
  +    --------
  +    >>> import cupy
  +    >>> from cupyx import optimizing
  +    >>>
  +    >>> x = cupy.arange(100)
  +    >>> with optimizing.optimize():
  +    ...     cupy.sum(x)
  +    ...
  +    array(4950)
  +
  +    .. note::
  +      Optuna (https://optuna.org) installation is required.
  +      Currently it works for reduction operations only.
  +    """
       if not _optuna_available:
           raise RuntimeError(
               'Optuna is required to run optimization. '
  
verification_info: {"golden_diff": "diff --git a/cupyx/optimizing/_optimize.py b/cupyx/optimizing/_optimize.py\n--- a/cupyx/optimizing/_optimize.py\n+++ b/cupyx/optimizing/_optimize.py\n@@ -43,6 +43,37 @@\n \n @contextlib.contextmanager\n def optimize(*, key=None, **config_dict):\n+    \"\"\"Context manager that optimizes kernel launch parameters.\n+\n+    In this context, CuPy's routines find the best kernel launch parameter\n+    values (e.g., the number of threads and blocks). The found values are\n+    cached and reused with keys as the shapes, strides and dtypes of the\n+    given inputs arrays.\n+\n+    Args:\n+        key (string or None): The cache key of optimizations.\n+        max_trials (int): The number of trials that defaults to 100.\n+        timeout (float):\n+            Stops study after the given number of seconds. Default is 1.\n+        max_total_time_per_trial (float):\n+            Repeats measuring the execution time of the routine for the\n+            given number of seconds. Default is 0.1.\n+\n+    Examples\n+    --------\n+    >>> import cupy\n+    >>> from cupyx import optimizing\n+    >>>\n+    >>> x = cupy.arange(100)\n+    >>> with optimizing.optimize():\n+    ...     cupy.sum(x)\n+    ...\n+    array(4950)\n+\n+    .. note::\n+      Optuna (https://optuna.org) installation is required.\n+      Currently it works for reduction operations only.\n+    \"\"\"\n     if not _optuna_available:\n         raise RuntimeError(\n             'Optuna is required to run optimization. '\n", "issue": "Write docs for Optuna optimization\n\n", "before_files": [{"content": "import contextlib\nimport math\n\n\ntry:\n    import optuna\n    _optuna_available = True\nexcept ImportError:\n    _optuna_available = False\n\n\nfrom cupy.core import _optimize_config\nfrom cupyx import time\n\n\ndef _optimize(\n        optimize_config, target_func, suggest_func,\n        default_best, ignore_error=()):\n    assert isinstance(optimize_config, _optimize_config._OptimizationConfig)\n    assert callable(target_func)\n    assert callable(suggest_func)\n\n    def objective(trial):\n        args = suggest_func(trial)\n        max_total_time = optimize_config.max_total_time_per_trial\n        try:\n            perf = time.repeat(target_func, args, max_duration=max_total_time)\n            return perf.gpu_times.mean()\n        except Exception as e:\n            if isinstance(e, ignore_error):\n                return math.inf\n            else:\n                raise e\n\n    study = optuna.create_study()\n    study.enqueue_trial(default_best)\n    study.optimize(\n        objective,\n        n_trials=optimize_config.max_trials,\n        timeout=optimize_config.timeout)\n    return study.best_trial\n\n\n@contextlib.contextmanager\ndef optimize(*, key=None, **config_dict):\n    if not _optuna_available:\n        raise RuntimeError(\n            'Optuna is required to run optimization. '\n            'See https://optuna.org/ for the installation instructions.')\n\n    old_context = _optimize_config.get_current_context()\n    context = _optimize_config.get_new_context(key, _optimize, config_dict)\n    _optimize_config.set_current_context(context)\n\n    try:\n        yield context\n    finally:\n        _optimize_config.set_current_context(old_context)\n", "path": "cupyx/optimizing/_optimize.py"}]}