prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Fix second image in KElbowVisualizer documentation
  The second image that was added to the `KElbowVisualizer` documentation in PR #635 is not rendering correctly because the `elbow_is_behind.png` file is not generated by the `elbow.py` file, but was added separately.
  
  - [x] Expand `KElbowVisualizer` documentation in `elbow.rst`
  - [x] Add example showing how to hide timing and use `calinski_harabaz` scoring metric
  - [x] Update `elbow.py` to generate new image for the documentation.
  
  
  
  
  </issue>
  <code>
  [start of docs/api/cluster/elbow.py]
  1 # Clustering Evaluation Imports
  2 from functools import partial
  3 
  4 from sklearn.cluster import MiniBatchKMeans
  5 from sklearn.datasets import make_blobs as sk_make_blobs
  6 
  7 from yellowbrick.cluster import KElbowVisualizer
  8 
  9 # Helpers for easy dataset creation
  10 N_SAMPLES = 1000
  11 N_FEATURES = 12
  12 SHUFFLE = True
  13 
  14 # Make blobs partial
  15 make_blobs = partial(sk_make_blobs, n_samples=N_SAMPLES, n_features=N_FEATURES, shuffle=SHUFFLE)
  16 
  17 
  18 if __name__ == '__main__':
  19     # Make 8 blobs dataset
  20     X, y = make_blobs(centers=8)
  21 
  22     # Instantiate the clustering model and visualizer
  23     # Instantiate the clustering model and visualizer
  24     visualizer = KElbowVisualizer(MiniBatchKMeans(), k=(4,12))
  25 
  26     visualizer.fit(X) # Fit the training data to the visualizer
  27     visualizer.poof(outpath="images/elbow.png") # Draw/show/poof the data
  28
  [end of docs/api/cluster/elbow.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/docs/api/cluster/elbow.py b/docs/api/cluster/elbow.py
  --- a/docs/api/cluster/elbow.py
  +++ b/docs/api/cluster/elbow.py
  @@ -1,27 +1,55 @@
  -# Clustering Evaluation Imports
  -from functools import partial
  +#!/usr/bin/env python
   
  -from sklearn.cluster import MiniBatchKMeans
  -from sklearn.datasets import make_blobs as sk_make_blobs
  +"""
  +Generate images for the elbow plot documentation.
  +"""
   
  -from yellowbrick.cluster import KElbowVisualizer
  +# Import necessary modules
  +import matplotlib.pyplot as plt
   
  -# Helpers for easy dataset creation
  -N_SAMPLES = 1000
  -N_FEATURES = 12
  -SHUFFLE = True
  +from sklearn.cluster import KMeans
  +from sklearn.datasets import make_blobs
  +from yellowbrick.cluster import KElbowVisualizer
   
  -# Make blobs partial
  -make_blobs = partial(sk_make_blobs, n_samples=N_SAMPLES, n_features=N_FEATURES, shuffle=SHUFFLE)
   
  +def draw_elbow(path="images/elbow.png"):
  +    # Generate synthetic dataset with 8 blobs
  +    X, y = make_blobs(
  +        centers=8, n_features=12, n_samples=1000,
  +        shuffle=True, random_state=42
  +    )
   
  -if __name__ == '__main__':
  -    # Make 8 blobs dataset
  -    X, y = make_blobs(centers=8)
  +    # Create a new figure to draw the clustering visualizer on
  +    _, ax = plt.subplots()
   
       # Instantiate the clustering model and visualizer
  +    model = KMeans()
  +    visualizer = KElbowVisualizer(model, ax=ax, k=(4,12))
  +
  +    visualizer.fit(X)                # Fit the data to the visualizer
  +    visualizer.poof(outpath=path)    # Draw/show/poof the data
  +
  +
  +def draw_calinski_harabaz(path="images/calinski_harabaz.png"):
  +    # Generate synthetic dataset with 8 blobs
  +    X, y = make_blobs(
  +        centers=8, n_features=12, n_samples=1000,
  +        shuffle=True, random_state=42
  +    )
  +
  +    # Create a new figure to draw the clustering visualizer on
  +    _, ax = plt.subplots()
  +
       # Instantiate the clustering model and visualizer
  -    visualizer = KElbowVisualizer(MiniBatchKMeans(), k=(4,12))
  +    model = KMeans()
  +    visualizer = KElbowVisualizer(
  +        model, ax=ax, k=(4,12),
  +        metric='calinski_harabaz', timings=False
  +    )
  +    visualizer.fit(X)                # Fit the data to the visualizer
  +    visualizer.poof(outpath=path)    # Draw/show/poof the data
   
  -    visualizer.fit(X) # Fit the training data to the visualizer
  -    visualizer.poof(outpath="images/elbow.png") # Draw/show/poof the data
  +
  +if __name__ == '__main__':
  +    draw_elbow()
  +    draw_calinski_harabaz()
  
verification_info: {"golden_diff": "diff --git a/docs/api/cluster/elbow.py b/docs/api/cluster/elbow.py\n--- a/docs/api/cluster/elbow.py\n+++ b/docs/api/cluster/elbow.py\n@@ -1,27 +1,55 @@\n-# Clustering Evaluation Imports\n-from functools import partial\n+#!/usr/bin/env python\n \n-from sklearn.cluster import MiniBatchKMeans\n-from sklearn.datasets import make_blobs as sk_make_blobs\n+\"\"\"\n+Generate images for the elbow plot documentation.\n+\"\"\"\n \n-from yellowbrick.cluster import KElbowVisualizer\n+# Import necessary modules\n+import matplotlib.pyplot as plt\n \n-# Helpers for easy dataset creation\n-N_SAMPLES = 1000\n-N_FEATURES = 12\n-SHUFFLE = True\n+from sklearn.cluster import KMeans\n+from sklearn.datasets import make_blobs\n+from yellowbrick.cluster import KElbowVisualizer\n \n-# Make blobs partial\n-make_blobs = partial(sk_make_blobs, n_samples=N_SAMPLES, n_features=N_FEATURES, shuffle=SHUFFLE)\n \n+def draw_elbow(path=\"images/elbow.png\"):\n+    # Generate synthetic dataset with 8 blobs\n+    X, y = make_blobs(\n+        centers=8, n_features=12, n_samples=1000,\n+        shuffle=True, random_state=42\n+    )\n \n-if __name__ == '__main__':\n-    # Make 8 blobs dataset\n-    X, y = make_blobs(centers=8)\n+    # Create a new figure to draw the clustering visualizer on\n+    _, ax = plt.subplots()\n \n     # Instantiate the clustering model and visualizer\n+    model = KMeans()\n+    visualizer = KElbowVisualizer(model, ax=ax, k=(4,12))\n+\n+    visualizer.fit(X)                # Fit the data to the visualizer\n+    visualizer.poof(outpath=path)    # Draw/show/poof the data\n+\n+\n+def draw_calinski_harabaz(path=\"images/calinski_harabaz.png\"):\n+    # Generate synthetic dataset with 8 blobs\n+    X, y = make_blobs(\n+        centers=8, n_features=12, n_samples=1000,\n+        shuffle=True, random_state=42\n+    )\n+\n+    # Create a new figure to draw the clustering visualizer on\n+    _, ax = plt.subplots()\n+\n     # Instantiate the clustering model and visualizer\n-    visualizer = KElbowVisualizer(MiniBatchKMeans(), k=(4,12))\n+    model = KMeans()\n+    visualizer = KElbowVisualizer(\n+        model, ax=ax, k=(4,12),\n+        metric='calinski_harabaz', timings=False\n+    )\n+    visualizer.fit(X)                # Fit the data to the visualizer\n+    visualizer.poof(outpath=path)    # Draw/show/poof the data\n \n-    visualizer.fit(X) # Fit the training data to the visualizer\n-    visualizer.poof(outpath=\"images/elbow.png\") # Draw/show/poof the data\n+\n+if __name__ == '__main__':\n+    draw_elbow()\n+    draw_calinski_harabaz()\n", "issue": "Fix second image in KElbowVisualizer documentation\nThe second image that was added to the `KElbowVisualizer` documentation in PR #635 is not rendering correctly because the `elbow_is_behind.png` file is not generated by the `elbow.py` file, but was added separately.\r\n\r\n- [x] Expand `KElbowVisualizer` documentation in `elbow.rst`\r\n- [x] Add example showing how to hide timing and use `calinski_harabaz` scoring metric\r\n- [x] Update `elbow.py` to generate new image for the documentation.\r\n\r\n\r\n\n", "before_files": [{"content": "# Clustering Evaluation Imports\nfrom functools import partial\n\nfrom sklearn.cluster import MiniBatchKMeans\nfrom sklearn.datasets import make_blobs as sk_make_blobs\n\nfrom yellowbrick.cluster import KElbowVisualizer\n\n# Helpers for easy dataset creation\nN_SAMPLES = 1000\nN_FEATURES = 12\nSHUFFLE = True\n\n# Make blobs partial\nmake_blobs = partial(sk_make_blobs, n_samples=N_SAMPLES, n_features=N_FEATURES, shuffle=SHUFFLE)\n\n\nif __name__ == '__main__':\n    # Make 8 blobs dataset\n    X, y = make_blobs(centers=8)\n\n    # Instantiate the clustering model and visualizer\n    # Instantiate the clustering model and visualizer\n    visualizer = KElbowVisualizer(MiniBatchKMeans(), k=(4,12))\n\n    visualizer.fit(X) # Fit the training data to the visualizer\n    visualizer.poof(outpath=\"images/elbow.png\") # Draw/show/poof the data\n", "path": "docs/api/cluster/elbow.py"}]}