prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  update path handling in examples/preprocessing/otp.py
  all of our `data_path` functions now return `pathlib.Path` objects, which allows things like the following:
  
  https://github.com/mne-tools/mne-python/blob/37a9e5587443109515a85cdc4396af4e014ecf82/examples/datasets/brainstorm_data.py#L32-L35
  
  Compare this to the old pattern (using `os.path.join`, often imported as `op.join`):
  
  ```py
  raw_path = os.path.join(data_path, 'MEG', 'bst_raw',
                          'subj001_somatosensory_20111109_01_AUX-f.ds')
  ```
  
  or the *really* old pattern (using the `+` operator on plain strings):
  
  ```py
  raw_path = (data_path + '/MEG/bst_raw/' +
              'subj001_somatosensory_20111109_01_AUX-f.ds')
  ```
  
  Update the paths in the file mentioned in the issue title to use the new pathlib-style, which is considered the modern, best-practice way to handle file paths.
  
  
  </issue>
  <code>
  [start of examples/preprocessing/otp.py]
  1 # -*- coding: utf-8 -*-
  2 """
  3 .. _ex-otp:
  4 
  5 ===========================================================
  6 Plot sensor denoising using oversampled temporal projection
  7 ===========================================================
  8 
  9 This demonstrates denoising using the OTP algorithm :footcite:`LarsonTaulu2018`
  10 on data with with sensor artifacts (flux jumps) and random noise.
  11 """
  12 # Author: Eric Larson <larson.eric.d@gmail.com>
  13 #
  14 # License: BSD-3-Clause
  15 
  16 # %%
  17 
  18 import os.path as op
  19 import mne
  20 import numpy as np
  21 
  22 from mne import find_events, fit_dipole
  23 from mne.datasets.brainstorm import bst_phantom_elekta
  24 from mne.io import read_raw_fif
  25 
  26 print(__doc__)
  27 
  28 # %%
  29 # Plot the phantom data, lowpassed to get rid of high-frequency artifacts.
  30 # We also crop to a single 10-second segment for speed.
  31 # Notice that there are two large flux jumps on channel 1522 that could
  32 # spread to other channels when performing subsequent spatial operations
  33 # (e.g., Maxwell filtering, SSP, or ICA).
  34 
  35 dipole_number = 1
  36 data_path = bst_phantom_elekta.data_path()
  37 raw = read_raw_fif(
  38     op.join(data_path, 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif'))
  39 raw.crop(40., 50.).load_data()
  40 order = list(range(160, 170))
  41 raw.copy().filter(0., 40.).plot(order=order, n_channels=10)
  42 
  43 # %%
  44 # Now we can clean the data with OTP, lowpass, and plot. The flux jumps have
  45 # been suppressed alongside the random sensor noise.
  46 
  47 raw_clean = mne.preprocessing.oversampled_temporal_projection(raw)
  48 raw_clean.filter(0., 40.)
  49 raw_clean.plot(order=order, n_channels=10)
  50 
  51 
  52 # %%
  53 # We can also look at the effect on single-trial phantom localization.
  54 # See the :ref:`tut-brainstorm-elekta-phantom`
  55 # for more information. Here we use a version that does single-trial
  56 # localization across the 17 trials are in our 10-second window:
  57 
  58 def compute_bias(raw):
  59     events = find_events(raw, 'STI201', verbose=False)
  60     events = events[1:]  # first one has an artifact
  61     tmin, tmax = -0.2, 0.1
  62     epochs = mne.Epochs(raw, events, dipole_number, tmin, tmax,
  63                         baseline=(None, -0.01), preload=True, verbose=False)
  64     sphere = mne.make_sphere_model(r0=(0., 0., 0.), head_radius=None,
  65                                    verbose=False)
  66     cov = mne.compute_covariance(epochs, tmax=0, method='oas',
  67                                  rank=None, verbose=False)
  68     idx = epochs.time_as_index(0.036)[0]
  69     data = epochs.get_data()[:, :, idx].T
  70     evoked = mne.EvokedArray(data, epochs.info, tmin=0.)
  71     dip = fit_dipole(evoked, cov, sphere, n_jobs=None, verbose=False)[0]
  72     actual_pos = mne.dipole.get_phantom_dipoles()[0][dipole_number - 1]
  73     misses = 1000 * np.linalg.norm(dip.pos - actual_pos, axis=-1)
  74     return misses
  75 
  76 
  77 bias = compute_bias(raw)
  78 print('Raw bias: %0.1fmm (worst: %0.1fmm)'
  79       % (np.mean(bias), np.max(bias)))
  80 bias_clean = compute_bias(raw_clean)
  81 print('OTP bias: %0.1fmm (worst: %0.1fmm)'
  82       % (np.mean(bias_clean), np.max(bias_clean),))
  83 
  84 # %%
  85 # References
  86 # ----------
  87 # .. footbibliography::
  88
  [end of examples/preprocessing/otp.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/examples/preprocessing/otp.py b/examples/preprocessing/otp.py
  --- a/examples/preprocessing/otp.py
  +++ b/examples/preprocessing/otp.py
  @@ -15,7 +15,6 @@
   
   # %%
   
  -import os.path as op
   import mne
   import numpy as np
   
  @@ -34,8 +33,7 @@
   
   dipole_number = 1
   data_path = bst_phantom_elekta.data_path()
  -raw = read_raw_fif(
  -    op.join(data_path, 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif'))
  +raw = read_raw_fif(data_path / 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif')
   raw.crop(40., 50.).load_data()
   order = list(range(160, 170))
   raw.copy().filter(0., 40.).plot(order=order, n_channels=10)
  
verification_info: {"golden_diff": "diff --git a/examples/preprocessing/otp.py b/examples/preprocessing/otp.py\n--- a/examples/preprocessing/otp.py\n+++ b/examples/preprocessing/otp.py\n@@ -15,7 +15,6 @@\n \n # %%\n \n-import os.path as op\n import mne\n import numpy as np\n \n@@ -34,8 +33,7 @@\n \n dipole_number = 1\n data_path = bst_phantom_elekta.data_path()\n-raw = read_raw_fif(\n-    op.join(data_path, 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif'))\n+raw = read_raw_fif(data_path / 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif')\n raw.crop(40., 50.).load_data()\n order = list(range(160, 170))\n raw.copy().filter(0., 40.).plot(order=order, n_channels=10)\n", "issue": "update path handling in examples/preprocessing/otp.py\nall of our `data_path` functions now return `pathlib.Path` objects, which allows things like the following:\r\n\r\nhttps://github.com/mne-tools/mne-python/blob/37a9e5587443109515a85cdc4396af4e014ecf82/examples/datasets/brainstorm_data.py#L32-L35\r\n\r\nCompare this to the old pattern (using `os.path.join`, often imported as `op.join`):\r\n\r\n```py\r\nraw_path = os.path.join(data_path, 'MEG', 'bst_raw',\r\n                        'subj001_somatosensory_20111109_01_AUX-f.ds')\r\n```\r\n\r\nor the *really* old pattern (using the `+` operator on plain strings):\r\n\r\n```py\r\nraw_path = (data_path + '/MEG/bst_raw/' +\r\n            'subj001_somatosensory_20111109_01_AUX-f.ds')\r\n```\r\n\r\nUpdate the paths in the file mentioned in the issue title to use the new pathlib-style, which is considered the modern, best-practice way to handle file paths.\r\n\n", "before_files": [{"content": "# -*- coding: utf-8 -*-\n\"\"\"\n.. _ex-otp:\n\n===========================================================\nPlot sensor denoising using oversampled temporal projection\n===========================================================\n\nThis demonstrates denoising using the OTP algorithm :footcite:`LarsonTaulu2018`\non data with with sensor artifacts (flux jumps) and random noise.\n\"\"\"\n# Author: Eric Larson <larson.eric.d@gmail.com>\n#\n# License: BSD-3-Clause\n\n# %%\n\nimport os.path as op\nimport mne\nimport numpy as np\n\nfrom mne import find_events, fit_dipole\nfrom mne.datasets.brainstorm import bst_phantom_elekta\nfrom mne.io import read_raw_fif\n\nprint(__doc__)\n\n# %%\n# Plot the phantom data, lowpassed to get rid of high-frequency artifacts.\n# We also crop to a single 10-second segment for speed.\n# Notice that there are two large flux jumps on channel 1522 that could\n# spread to other channels when performing subsequent spatial operations\n# (e.g., Maxwell filtering, SSP, or ICA).\n\ndipole_number = 1\ndata_path = bst_phantom_elekta.data_path()\nraw = read_raw_fif(\n    op.join(data_path, 'kojak_all_200nAm_pp_no_chpi_no_ms_raw.fif'))\nraw.crop(40., 50.).load_data()\norder = list(range(160, 170))\nraw.copy().filter(0., 40.).plot(order=order, n_channels=10)\n\n# %%\n# Now we can clean the data with OTP, lowpass, and plot. The flux jumps have\n# been suppressed alongside the random sensor noise.\n\nraw_clean = mne.preprocessing.oversampled_temporal_projection(raw)\nraw_clean.filter(0., 40.)\nraw_clean.plot(order=order, n_channels=10)\n\n\n# %%\n# We can also look at the effect on single-trial phantom localization.\n# See the :ref:`tut-brainstorm-elekta-phantom`\n# for more information. Here we use a version that does single-trial\n# localization across the 17 trials are in our 10-second window:\n\ndef compute_bias(raw):\n    events = find_events(raw, 'STI201', verbose=False)\n    events = events[1:]  # first one has an artifact\n    tmin, tmax = -0.2, 0.1\n    epochs = mne.Epochs(raw, events, dipole_number, tmin, tmax,\n                        baseline=(None, -0.01), preload=True, verbose=False)\n    sphere = mne.make_sphere_model(r0=(0., 0., 0.), head_radius=None,\n                                   verbose=False)\n    cov = mne.compute_covariance(epochs, tmax=0, method='oas',\n                                 rank=None, verbose=False)\n    idx = epochs.time_as_index(0.036)[0]\n    data = epochs.get_data()[:, :, idx].T\n    evoked = mne.EvokedArray(data, epochs.info, tmin=0.)\n    dip = fit_dipole(evoked, cov, sphere, n_jobs=None, verbose=False)[0]\n    actual_pos = mne.dipole.get_phantom_dipoles()[0][dipole_number - 1]\n    misses = 1000 * np.linalg.norm(dip.pos - actual_pos, axis=-1)\n    return misses\n\n\nbias = compute_bias(raw)\nprint('Raw bias: %0.1fmm (worst: %0.1fmm)'\n      % (np.mean(bias), np.max(bias)))\nbias_clean = compute_bias(raw_clean)\nprint('OTP bias: %0.1fmm (worst: %0.1fmm)'\n      % (np.mean(bias_clean), np.max(bias_clean),))\n\n# %%\n# References\n# ----------\n# .. footbibliography::\n", "path": "examples/preprocessing/otp.py"}]}