Model selection#

https://miro.medium.com/max/1125/1*_7OPgojau8hkiPUiHoGK_w.png

Underfitting#

  • the model is too simple

  • the number of parameters is too low

Overfitting#

  • the model is too complex

  • the number of parameters is too large

Train and test#

The common way to reveal overfitting is to use train and test datasets.

  • training dataset \(\mathcal D_{\mathrm{train}} = (\boldsymbol X_{\mathrm{train}}, \boldsymbol y_{\mathrm{train}})\) is used on learning stage:

\[ \mathcal L_{\mathrm{train}}(\boldsymbol \theta) = \frac 1{N_{\mathrm{train}}}\sum\limits_{(\boldsymbol x_i, y_i) \in \mathcal D_{\mathrm{train}}} \ell(y_i, f_{\boldsymbol \theta}(\boldsymbol x_i)) \to \min\limits_{\boldsymbol \theta} \]
  • test dataset \(\mathcal D_{\mathrm{test}} = (\boldsymbol X_{\mathrm{test}}, \boldsymbol y_{\mathrm{test}})\) used for evlaluation of model’s quality:

\[ \mathcal L_{\mathrm{test}}(\boldsymbol \theta) = \frac 1{N_{\mathrm{test}}}\sum\limits_{(\boldsymbol x_i, y_i) \in \mathcal D_{\mathrm{test}}} \ell(y_i, f_{\boldsymbol \theta}(\boldsymbol x_i)) \]
https://vitalflux.com/wp-content/uploads/2020/12/overfitting-and-underfitting-wrt-model-error-vs-complexity.png

A classical example#

  • Ground truth: \(y(x) = \frac 1{1 + 25x^2}\), \(-2\leqslant x \leqslant 2\)

  • Polynomial regression model: \(f_{\boldsymbol \theta}(x) = \sum\limits_{k=0}^n \theta_k x^k\)

  • Training set: \(X = \Big\{x_i = 4\frac{i-1}{N-1} - 2\Big\}_{i=1}^N\)

  • Test set: \(\tilde X = \Big\{\tilde x_i = 4\frac{i-0.5}{N-1} - 2\Big\}_{i=1}^{N-1}\)

  • Loss function — MSE:

    \[ \mathcal L_{\mathrm{train}}(\boldsymbol \theta, X) = \frac 1N \sum\limits_{i=1}^N (f_{\boldsymbol \theta}(x_i) - y_i)^2 \to \min\limits_{\boldsymbol \theta} \]
  • What is happening with test loss

    \[ \mathcal L_{\mathrm{test}}(\boldsymbol \theta, \tilde X) = \frac 1N \sum\limits_{i=1}^N (f_{\boldsymbol \theta}(\tilde x_i) - \tilde y_i)^2 \]

as \(n\) grows?

Error in callback <function _draw_all_if_interactive at 0x7f91dc2b6fc0> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/.local/lib/python3.12/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
    338     pass
    339 else:
--> 340     return printer(obj)
    341 # Finally look for special method names
    342 method = get_real_method(obj, self.print_method)

File ~/.local/lib/python3.12/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_svg.py:1287, in RendererSVG.get_text_width_height_descent(self, s, prop, ismath)
   1285 def get_text_width_height_descent(self, s, prop, ismath):
   1286     # docstring inherited
-> 1287     return self._text2path.get_text_width_height_descent(s, prop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/textpath.py:52, in TextToPath.get_text_width_height_descent(self, s, prop, ismath)
     49 fontsize = prop.get_size_in_points()
     51 if ismath == "TeX":
---> 52     return TexManager().get_text_width_height_descent(s, fontsize)
     54 scale = fontsize / self.FONT_SCALE
     56 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 1100x600 with 1 Axes>
Error in callback <function _draw_all_if_interactive at 0x7f91dc2b6fc0> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/.local/lib/python3.12/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
    338     pass
    339 else:
--> 340     return printer(obj)
    341 # Finally look for special method names
    342 method = get_real_method(obj, self.print_method)

File ~/.local/lib/python3.12/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_svg.py:1287, in RendererSVG.get_text_width_height_descent(self, s, prop, ismath)
   1285 def get_text_width_height_descent(self, s, prop, ismath):
   1286     # docstring inherited
-> 1287     return self._text2path.get_text_width_height_descent(s, prop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/textpath.py:52, in TextToPath.get_text_width_height_descent(self, s, prop, ismath)
     49 fontsize = prop.get_size_in_points()
     51 if ismath == "TeX":
---> 52     return TexManager().get_text_width_height_descent(s, fontsize)
     54 scale = fontsize / self.FONT_SCALE
     56 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 1100x600 with 1 Axes>
Error in callback <function _draw_all_if_interactive at 0x7f91dc2b6fc0> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/pyplot.py:197, in _draw_all_if_interactive()
    195 def _draw_all_if_interactive() -> None:
    196     if matplotlib.is_interactive():
--> 197         draw_all()

File ~/.local/lib/python3.12/site-packages/matplotlib/_pylab_helpers.py:132, in Gcf.draw_all(cls, force)
    130 for manager in cls.get_all_fig_managers():
    131     if force or manager.canvas.figure.stale:
--> 132         manager.canvas.draw_idle()

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:1893, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1891 if not self._is_idle_drawing:
   1892     with self._idle_draw_cntx():
-> 1893         self.draw(*args, **kwargs)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:388, in FigureCanvasAgg.draw(self)
    385 # Acquire a lock on the shared font cache.
    386 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    387       else nullcontext()):
--> 388     self.figure.draw(self.renderer)
    389     # A GUI class may be need to update a window using this draw, so
    390     # don't forget to call the superclass.
    391     super().draw()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_agg.py:213, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    211 _api.check_in_list(["TeX", True, False], ismath=ismath)
    212 if ismath == "TeX":
--> 213     return super().get_text_width_height_descent(s, prop, ismath)
    215 if ismath:
    216     ox, oy, width, height, descent, font_image = \
    217         self.mathtext_parser.parse(s, self.dpi, prop)

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:652, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    648 fontsize = prop.get_size_in_points()
    650 if ismath == 'TeX':
    651     # todo: handle properties
--> 652     return self.get_texmanager().get_text_width_height_descent(
    653         s, fontsize, renderer=self)
    655 dpi = self.points_to_pixels(72)
    656 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /usr/local/lib/python3.12/subprocess.py:466, in check_output(timeout, *popenargs, **kwargs)
    464     kwargs['input'] = empty
--> 466 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    467            **kwargs).stdout

File /usr/local/lib/python3.12/subprocess.py:548, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    546     kwargs['stderr'] = PIPE
--> 548 with Popen(*popenargs, **kwargs) as process:
    549     try:

File /usr/local/lib/python3.12/subprocess.py:1026, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize, process_group)
   1023             self.stderr = io.TextIOWrapper(self.stderr,
   1024                     encoding=encoding, errors=errors)
-> 1026     self._execute_child(args, executable, preexec_fn, close_fds,
   1027                         pass_fds, cwd, env,
   1028                         startupinfo, creationflags, shell,
   1029                         p2cread, p2cwrite,
   1030                         c2pread, c2pwrite,
   1031                         errread, errwrite,
   1032                         restore_signals,
   1033                         gid, gids, uid, umask,
   1034                         start_new_session, process_group)
   1035 except:
   1036     # Cleanup if the child failed starting.

File /usr/local/lib/python3.12/subprocess.py:1950, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session, process_group)
   1949         err_msg = os.strerror(errno_num)
-> 1950     raise child_exception_type(errno_num, err_msg, err_filename)
   1951 raise child_exception_type(err_msg)

FileNotFoundError: [Errno 2] No such file or directory: 'latex'

The above exception was the direct cause of the following exception:

RuntimeError                              Traceback (most recent call last)
File ~/.local/lib/python3.12/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
    338     pass
    339 else:
--> 340     return printer(obj)
    341 # Finally look for special method names
    342 method = get_real_method(obj, self.print_method)

File ~/.local/lib/python3.12/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File ~/.local/lib/python3.12/site-packages/matplotlib/backend_bases.py:2164, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2161     # we do this instead of `self.figure.draw_without_rendering`
   2162     # so that we can inject the orientation
   2163     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2164         self.figure.draw(renderer)
   2165 if bbox_inches:
   2166     if bbox_inches == "tight":

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/figure.py:3154, in Figure.draw(self, renderer)
   3151         # ValueError can occur when resizing a window.
   3153 self.patch.draw(renderer)
-> 3154 mimage._draw_list_compositing_images(
   3155     renderer, self, artists, self.suppressComposite)
   3157 for sfig in self.subfigs:
   3158     sfig.draw(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File ~/.local/lib/python3.12/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:3034, in _AxesBase.draw(self, renderer)
   3031     for spine in self.spines.values():
   3032         artists.remove(spine)
-> 3034 self._update_title_position(renderer)
   3036 if not self.axison:
   3037     for _axis in self._axis_map.values():

File ~/.local/lib/python3.12/site-packages/matplotlib/axes/_base.py:2978, in _AxesBase._update_title_position(self, renderer)
   2976 top = max(top, bb.ymax)
   2977 if title.get_text():
-> 2978     ax.yaxis.get_tightbbox(renderer)  # update offsetText
   2979     if ax.yaxis.offsetText.get_text():
   2980         bb = ax.yaxis.offsetText.get_tightbbox(renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1336, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1333     renderer = self.figure._get_renderer()
   1334 ticks_to_draw = self._update_ticks()
-> 1336 self._update_label_position(renderer)
   1338 # go back to just this axis's tick labels
   1339 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2609, in YAxis._update_label_position(self, renderer)
   2605     return
   2607 # get bounding boxes for this axis and any siblings
   2608 # that have been set by `fig.align_ylabels()`
-> 2609 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2610 x, y = self.label.get_position()
   2611 if self.label_position == 'left':

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:2161, in Axis._get_tick_boxes_siblings(self, renderer)
   2159 axis = ax._axis_map[name]
   2160 ticks_to_draw = axis._update_ticks()
-> 2161 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2162 bboxes.extend(tlb)
   2163 bboxes2.extend(tlb2)

File ~/.local/lib/python3.12/site-packages/matplotlib/axis.py:1315, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1313 if renderer is None:
   1314     renderer = self.figure._get_renderer()
-> 1315 return ([tick.label1.get_window_extent(renderer)
   1316          for tick in ticks if tick.label1.get_visible()],
   1317         [tick.label2.get_window_extent(renderer)
   1318          for tick in ticks if tick.label2.get_visible()])

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:956, in Text.get_window_extent(self, renderer, dpi)
    951     raise RuntimeError(
    952         "Cannot get window extent of text w/o renderer. You likely "
    953         "want to call 'figure.draw_without_rendering()' first.")
    955 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 956     bbox, info, descent = self._get_layout(self._renderer)
    957     x, y = self.get_unitless_position()
    958     x, y = self.get_transform().transform((x, y))

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
    370 ys = []
    372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
    374     renderer, "lp", self._fontproperties,
    375     ismath="TeX" if self.get_usetex() else False, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
     66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
     67 # Cached based on a copy of fontprop so that later in-place mutations of
     68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
     70     weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)

File ~/.local/lib/python3.12/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
     73 @functools.lru_cache(4096)
     74 def _get_text_metrics_with_cache_impl(
     75         renderer_ref, text, fontprop, ismath, dpi):
     76     # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77     return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/backends/backend_svg.py:1287, in RendererSVG.get_text_width_height_descent(self, s, prop, ismath)
   1285 def get_text_width_height_descent(self, s, prop, ismath):
   1286     # docstring inherited
-> 1287     return self._text2path.get_text_width_height_descent(s, prop, ismath)

File ~/.local/lib/python3.12/site-packages/matplotlib/textpath.py:52, in TextToPath.get_text_width_height_descent(self, s, prop, ismath)
     49 fontsize = prop.get_size_in_points()
     51 if ismath == "TeX":
---> 52     return TexManager().get_text_width_height_descent(s, fontsize)
     54 scale = fontsize / self.FONT_SCALE
     56 if ismath:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File ~/.local/lib/python3.12/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 1100x600 with 1 Axes>

The overfitting is a big problem in ML because an overfitted model makes poor predictions. The first signal of the overfitting: \(\mathcal L_{\mathrm{train}} \ll \mathcal L_{\mathrm{test}}\).

Cross validation#

https://scikit-learn.org/stable/_images/grid_search_cross_validation.png

TODO

  • Add some text and original pictures

  • Make Runge example interactive

  • Show underfitting and overfitting on some real datasets

  • Use comparison of k-NN and linear regression as it is done in the section 2.3 of [Hastie et al., 2009]