code: 
  import numpy as np
  from numpy.testing import assert_allclose, assert_array_equal
  import pytest
  
  from scipy.fft import dct, idct, dctn, idctn, dst, idst, dstn, idstn
  import scipy.fft as fft
  from scipy import fftpack
  
  # scipy.fft wraps the fftpack versions but with normalized inverse transforms.
  # So, the forward transforms and definitions are already thoroughly tested in
  # fftpack/test_real_transforms.py
  
  
  @pytest.mark.parametrize("forward, backward", [(dct, idct), (dst, idst)])
  @pytest.mark.parametrize("type", [1, 2, 3, 4])
  @pytest.mark.parametrize("n", [2, 3, 4, 5, 10, 16])
  @pytest.mark.parametrize("axis", [0, 1])
  @pytest.mark.parametrize("norm", [None, 'ortho'])
  def test_identity_1d(forward, backward, type, n, axis, norm):
      # Test the identity f^-1(f(x)) == x
      x = np.random.rand(n, n)
  
      y = forward(x, type, axis=axis, norm=norm)
      z = backward(y, type, axis=axis, norm=norm)
      assert_allclose(z, x)
  
      pad = [(0, 0)] * 2
      pad[axis] = (0, 4)
  
      y2 = np.pad(y, pad, mode='edge')
      z2 = backward(y2, type, n, axis, norm)
      assert_allclose(z2, x)
  
  
  @pytest.mark.parametrize("forward, backward", [(dct, idct), (dst, idst)])
  @pytest.mark.parametrize("type", [1, 2, 3, 4])
  @pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
                                     np.complex64, np.complex128])
  @pytest.mark.parametrize("axis", [0, 1])
  @pytest.mark.parametrize("norm", [None, 'ortho'])
  @pytest.mark.parametrize("overwrite_x", [True, False])
  def test_identity_1d_overwrite(forward, backward, type, dtype, axis, norm,
                                 overwrite_x):
      # Test the identity f^-1(f(x)) == x
      x = np.random.rand(7, 8)
      x_orig = x.copy()
  
      y = forward(x, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
      y_orig = y.copy()
      z = backward(y, type, axis=axis, norm=norm, overwrite_x=overwrite_x)
      if not overwrite_x:
          assert_allclose(z, x, rtol=1e-6, atol=1e-6)
          assert_array_equal(x, x_orig)
          assert_array_equal(y, y_orig)
      else:
          assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
  
  
  @pytest.mark.parametrize("forward, backward", [(dctn, idctn), (dstn, idstn)])
  @pytest.mark.parametrize("type", [1, 2, 3, 4])
  @pytest.mark.parametrize("shape, axes",
                           [
                               ((4, 4), 0),
                               ((4, 4), 1),
                               ((4, 4), None),
                               ((4, 4), (0, 1)),
                               ((10, 12), None),
                               ((10, 12), (0, 1)),
                               ((4, 5, 6), None),
                               ((4, 5, 6), 1),
                               ((4, 5, 6), (0, 2)),
                           ])
  @pytest.mark.parametrize("norm", [None, 'ortho'])
  def test_identity_nd(forward, backward, type, shape, axes, norm):
      # Test the identity f^-1(f(x)) == x
  
      x = np.random.random(shape)
  
      if axes is not None:
          shape = np.take(shape, axes)
  
      y = forward(x, type, axes=axes, norm=norm)
      z = backward(y, type, axes=axes, norm=norm)
      assert_allclose(z, x)
  
      if axes is None:
          pad = [(0, 4)] * x.ndim
      elif isinstance(axes, int):
          pad = [(0, 0)] * x.ndim
          pad[axes] = (0, 4)
      else:
          pad = [(0, 0)] * x.ndim
  
          for a in axes:
              pad[a] = (0, 4)
  
      y2 = np.pad(y, pad, mode='edge')
      z2 = backward(y2, type, shape, axes, norm)
      assert_allclose(z2, x)
  
  
  @pytest.mark.parametrize("forward, backward", [(dctn, idctn), (dstn, idstn)])
  @pytest.mark.parametrize("type", [1, 2, 3, 4])
  @pytest.mark.parametrize("shape, axes",
                           [
                               ((4, 5), 0),
                               ((4, 5), 1),
                               ((4, 5), None),
                           ])
  @pytest.mark.parametrize("dtype", [np.float16, np.float32, np.float64,
                                     np.complex64, np.complex128])
  @pytest.mark.parametrize("norm", [None, 'ortho'])
  @pytest.mark.parametrize("overwrite_x", [False, True])
  def test_identity_nd_overwrite(forward, backward, type, shape, axes, dtype,
                                 norm, overwrite_x):
      # Test the identity f^-1(f(x)) == x
  
      x = np.random.random(shape).astype(dtype)
      x_orig = x.copy()
  
      if axes is not None:
          shape = np.take(shape, axes)
  
      y = forward(x, type, axes=axes, norm=norm)
      y_orig = y.copy()
      z = backward(y, type, axes=axes, norm=norm)
      if overwrite_x:
          assert_allclose(z, x_orig, rtol=1e-6, atol=1e-6)
      else:
          assert_allclose(z, x, rtol=1e-6, atol=1e-6)
          assert_array_equal(x, x_orig)
          assert_array_equal(y, y_orig)
  
  
  @pytest.mark.parametrize("func", ['dct', 'dst', 'dctn', 'dstn'])
  @pytest.mark.parametrize("type", [1, 2, 3, 4])
  @pytest.mark.parametrize("norm", [None, 'ortho'])
  def test_fftpack_equivalience(func, type, norm):
      x = np.random.rand(8, 16)
      fft_res = getattr(fft, func)(x, type, norm=norm)
      fftpack_res = getattr(fftpack, func)(x, type, norm=norm)
  
      assert_allclose(fft_res, fftpack_res)
   #!/usr/bin/env python
  """
  refguide_check.py [OPTIONS] [-- ARGS]
  
  Check for a Scipy submodule whether the objects in its __all__ dict
  correspond to the objects included in the reference guide.
  
  Example of usage::
  
      $ python refguide_check.py optimize
  
  Note that this is a helper script to be able to check if things are missing;
  the output of this script does need to be checked manually.  In some cases
  objects are left out of the refguide for a good reason (it's an alias of
  another function, or deprecated, or ...)
  
  Another use of this helper script is to check validity of code samples
  in docstrings. This is different from doctesting [we do not aim to have
  scipy docstrings doctestable!], this is just to make sure that code in
  docstrings is valid python::
  
      $ python refguide_check.py --doctests optimize
  
  """
  import copy
  import doctest
  import glob
  import inspect
  import io
  import os
  import re
  import shutil
  import sys
  import tempfile
  import warnings
  from argparse import ArgumentParser
  from contextlib import contextmanager, redirect_stderr
  from doctest import NORMALIZE_WHITESPACE, ELLIPSIS, IGNORE_EXCEPTION_DETAIL
  
  import docutils.core
  import numpy as np
  import sphinx
  from docutils.parsers.rst import directives
  from pkg_resources import parse_version
  
  sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', 'doc', 'sphinxext'))
  from numpydoc.docscrape_sphinx import get_doc_object
  
  if parse_version(sphinx.__version__) >= parse_version('1.5'):
      # Enable specific Sphinx directives
      from sphinx.directives import SeeAlso, Only
      directives.register_directive('seealso', SeeAlso)
      directives.register_directive('only', Only)
  else:
      # Remove sphinx directives that don't run without Sphinx environment.
      # Sphinx < 1.5 installs all directives on import...
      directives._directives.pop('versionadded', None)
      directives._directives.pop('versionchanged', None)
      directives._directives.pop('moduleauthor', None)
      directives._directives.pop('sectionauthor', None)
      directives._directives.pop('codeauthor', None)
      directives._directives.pop('toctree', None)
  
  
  BASE_MODULE = "scipy"
  
  PUBLIC_SUBMODULES = [
      'cluster',
      'cluster.hierarchy',
      'cluster.vq',
      'constants',
      'fft',
      'fftpack',
      'fftpack.convolve',
      'integrate',
      'interpolate',
      'io',
      'io.arff',
      'io.wavfile',
      'linalg',
      'linalg.blas',
      'linalg.lapack',
      'linalg.interpolative',
      'misc',
      'ndimage',
      'odr',
      'optimize',
      'signal',
      'signal.windows',
      'sparse',
      'sparse.csgraph',
      'sparse.linalg',
      'spatial',
      'spatial.distance',
      'spatial.transform',
      'special',
      'stats',
      'stats.mstats',
      'stats.contingency',
  ]
  
  # Docs for these modules are included in the parent module
  OTHER_MODULE_DOCS = {
      'fftpack.convolve': 'fftpack',
      'io.wavfile': 'io',
      'io.arff': 'io',
  }
  
  # these names are known to fail doctesting and we like to keep it that way
  # e.g. sometimes pseudocode is acceptable etc
  DOCTEST_SKIPLIST = set([
      'scipy.stats.kstwobign',  # inaccurate cdf or ppf
      'scipy.stats.levy_stable',
      'scipy.special.sinc',  # comes from numpy
      'scipy.misc.who',  # comes from numpy
      'scipy.optimize.show_options',
      'io.rst',   # XXX: need to figure out how to deal w/ mat files
  ])
  
  # these names are not required to be present in ALL despite being in
  # autosummary:: listing
  REFGUIDE_ALL_SKIPLIST = [
      r'scipy\.sparse\.csgraph',
      r'scipy\.sparse\.linalg',
      r'scipy\.spatial\.distance',
      r'scipy\.linalg\.blas\.[sdczi].*',
      r'scipy\.linalg\.lapack\.[sdczi].*',
  ]
  
  # these names are not required to be in an autosummary:: listing
  # despite being in ALL
  REFGUIDE_AUTOSUMMARY_SKIPLIST = [
      r'scipy\.special\..*_roots',  # old aliases for scipy.special.*_roots
      r'scipy\.special\.jn',  # alias for jv
      r'scipy\.ndimage\.sum',   # alias for sum_labels
      r'scipy\.linalg\.solve_lyapunov',  # deprecated name
      r'scipy\.stats\.contingency\.chi2_contingency',
      r'scipy\.stats\.contingency\.expected_freq',
      r'scipy\.stats\.contingency\.margins',
      r'scipy\.stats\.reciprocal',
  ]
  # deprecated windows in scipy.signal namespace
  for name in ('barthann', 'bartlett', 'blackmanharris', 'blackman', 'bohman',
               'boxcar', 'chebwin', 'cosine', 'exponential', 'flattop',
               'gaussian', 'general_gaussian', 'hamming', 'hann', 'hanning',
               'kaiser', 'nuttall', 'parzen', 'slepian', 'triang', 'tukey'):
      REFGUIDE_AUTOSUMMARY_SKIPLIST.append(r'scipy\.signal\.' + name)
  
  HAVE_MATPLOTLIB = False
  
  
  def short_path(path, cwd=None):
      """
      Return relative or absolute path name, whichever is shortest.
      """
      if not isinstance(path, str):
          return path
      if cwd is None:
          cwd = os.getcwd()
      abspath = os.path.abspath(path)
      relpath = os.path.relpath(path, cwd)
      if len(abspath) <= len(relpath):
          return abspath
      return relpath
  
  
  def find_names(module, names_dict):
      # Refguide entries:
      #
      # - 3 spaces followed by function name, and maybe some spaces, some
      #   dashes, and an explanation; only function names listed in
      #   refguide are formatted like this (mostly, there may be some false
      #   positives)
      #
      # - special directives, such as data and function
      #
      # - (scipy.constants only): quoted list
      #
      patterns = [
          r"^\s\s\s([a-z_0-9A-Z]+)(\s+-+.*)?$",
          r"^\.\. (?:data|function)::\s*([a-z_0-9A-Z]+)\s*$"
      ]
  
      if module.__name__ == 'scipy.constants':
          patterns += ["^``([a-z_0-9A-Z]+)``"]
  
      patterns = [re.compile(pattern) for pattern in patterns]
      module_name = module.__name__
  
      for line in module.__doc__.splitlines():
          res = re.search(r"^\s*\.\. (?:currentmodule|module):: ([a-z0-9A-Z_.]+)\s*$", line)
          if res:
              module_name = res.group(1)
              continue
  
          for pattern in patterns:
              res = re.match(pattern, line)
              if res is not None:
                  name = res.group(1)
                  entry = '.'.join([module_name, name])
                  names_dict.setdefault(module_name, set()).add(name)
                  break
  
  
  def get_all_dict(module):
      """Return a copy of the __all__ dict with irrelevant items removed."""
      if hasattr(module, "__all__"):
          all_dict = copy.deepcopy(module.__all__)
      else:
          all_dict = copy.deepcopy(dir(module))
          all_dict = [name for name in all_dict
                      if not name.startswith("_")]
      for name in ['absolute_import', 'division', 'print_function']:
          try:
              all_dict.remove(name)
          except ValueError:
              pass
  
      # Modules are almost always private; real submodules need a separate
      # run of refguide_check.
      all_dict = [name for name in all_dict
                  if not inspect.ismodule(getattr(module, name, None))]
  
      deprecated = []
      not_deprecated = []
      for name in all_dict:
          f = getattr(module, name, None)
          if callable(f) and is_deprecated(f):
              deprecated.append(name)
          else:
              not_deprecated.append(name)
  
      others = set(dir(module)).difference(set(deprecated)).difference(set(not_deprecated))
  
      return not_deprecated, deprecated, others
  
  
  def compare(all_dict, others, names, module_name):
      """Return sets of objects only in __all__, refguide, or completely missing."""
      only_all = set()
      for name in all_dict:
          if name not in names:
              for pat in REFGUIDE_AUTOSUMMARY_SKIPLIST:
                  if re.match(pat, module_name + '.' + name):
                      break
              else:
                  only_all.add(name)
  
      only_ref = set()
      missing = set()
      for name in names:
          if name not in all_dict:
              for pat in REFGUIDE_ALL_SKIPLIST:
                  if re.match(pat, module_name + '.' + name):
                      if name not in others:
                          missing.add(name)
                      break
              else:
                  only_ref.add(name)
  
      return only_all, only_ref, missing
  
  def is_deprecated(f):
      with warnings.catch_warnings(record=True) as w:
          warnings.simplefilter("error")
          try:
              f(**{"not a kwarg":None})
          except DeprecationWarning:
              return True
          except Exception:
              pass
          return False
  
  def check_items(all_dict, names, deprecated, others, module_name, dots=True):
      num_all = len(all_dict)
      num_ref = len(names)
  
      output = ""
  
      output += "Non-deprecated objects in __all__: %i\n" % num_all
      output += "Objects in refguide: %i\n\n" % num_ref
  
      only_all, only_ref, missing = compare(all_dict, others, names, module_name)
      dep_in_ref = set(only_ref).intersection(deprecated)
      only_ref = set(only_ref).difference(deprecated)
  
      if len(dep_in_ref) > 0:
          output += "Deprecated objects in refguide::\n\n"
          for name in sorted(deprecated):
              output += "    " + name + "\n"
  
      if len(only_all) == len(only_ref) == len(missing) == 0:
          if dots:
              output_dot('.')
          return [(None, True, output)]
      else:
          if len(only_all) > 0:
              output += "ERROR: objects in %s.__all__ but not in refguide::\n\n" % module_name
              for name in sorted(only_all):
                  output += "    " + name + "\n"
  
              output += "\nThis issue can be fixed by adding these objects to\n"
              output += "the function listing in __init__.py for this module\n"
  
          if len(only_ref) > 0:
              output += "ERROR: objects in refguide but not in %s.__all__::\n\n" % module_name
              for name in sorted(only_ref):
                  output += "    " + name + "\n"
  
              output += "\nThis issue should likely be fixed by removing these objects\n"
              output += "from the function listing in __init__.py for this module\n"
              output += "or adding them to __all__.\n"
  
          if len(missing) > 0:
              output += "ERROR: missing objects::\n\n"
              for name in sorted(missing):
                  output += "    " + name + "\n"
  
          if dots:
              output_dot('F')
          return [(None, False, output)]
  
  
  def validate_rst_syntax(text, name, dots=True):
      if text is None:
          if dots:
              output_dot('E')
          return False, "ERROR: %s: no documentation" % (name,)
  
      ok_unknown_items = set([
          'mod', 'currentmodule', 'autosummary', 'data',
          'obj', 'versionadded', 'versionchanged', 'module', 'class', 'meth',
          'ref', 'func', 'toctree', 'moduleauthor',
          'sectionauthor', 'codeauthor', 'eq', 'doi', 'DOI', 'arXiv', 'arxiv'
      ])
  
      # Run through docutils
      error_stream = io.StringIO()
  
      def resolve(name, is_label=False):
          return ("http://foo", name)
  
      token = '<RST-VALIDATE-SYNTAX-CHECK>'
  
      docutils.core.publish_doctree(
          text, token,
          settings_overrides = dict(halt_level=5,
                                    traceback=True,
                                    default_reference_context='title-reference',
                                    default_role='emphasis',
                                    link_base='',
                                    resolve_name=resolve,
                                    stylesheet_path='',
                                    raw_enabled=0,
                                    file_insertion_enabled=0,
                                    warning_stream=error_stream))
  
      # Print errors, disregarding unimportant ones
      error_msg = error_stream.getvalue()
      errors = error_msg.split(token)
      success = True
      output = ""
  
      for error in errors:
          lines = error.splitlines()
          if not lines:
              continue
  
          m = re.match(r'.*Unknown (?:interpreted text role|directive type) "(.*)".*$', lines[0])
          if m:
              if m.group(1) in ok_unknown_items:
                  continue
  
          m = re.match(r'.*Error in "math" directive:.*unknown option: "label"', " ".join(lines), re.S)
          if m:
              continue
  
          output += name + lines[0] + "::\n    " + "\n    ".join(lines[1:]).rstrip() + "\n"
          success = False
  
      if not success:
          output += "    " + "-"*72 + "\n"
          for lineno, line in enumerate(text.splitlines()):
              output += "    %-4d    %s\n" % (lineno+1, line)
          output += "    " + "-"*72 + "\n\n"
  
      if dots:
          output_dot('.' if success else 'F')
      return success, output
  
  
  def output_dot(msg='.', stream=sys.stderr):
      stream.write(msg)
      stream.flush()
  
  
  def check_rest(module, names, dots=True):
      """
      Check reStructuredText formatting of docstrings
  
      Returns: [(name, success_flag, output), ...]
      """
  
      try:
          skip_types = (dict, str, unicode, float, int)
      except NameError:
          # python 3
          skip_types = (dict, str, float, int)
  
      results = []
  
      if module.__name__[6:] not in OTHER_MODULE_DOCS:
          results += [(module.__name__,) +
                      validate_rst_syntax(inspect.getdoc(module),
                                          module.__name__, dots=dots)]
  
      for name in names:
          full_name = module.__name__ + '.' + name
          obj = getattr(module, name, None)
  
          if obj is None:
              results.append((full_name, False, "%s has no docstring" % (full_name,)))
              continue
          elif isinstance(obj, skip_types):
              continue
  
          if inspect.ismodule(obj):
              text = inspect.getdoc(obj)
          else:
              try:
                  text = str(get_doc_object(obj))
              except Exception:
                  import traceback
                  results.append((full_name, False,
                                  "Error in docstring format!\n" +
                                  traceback.format_exc()))
                  continue
  
          m = re.search("([\x00-\x09\x0b-\x1f])", text)
          if m:
              msg = ("Docstring contains a non-printable character %r! "
                     "Maybe forgot r\"\"\"?" % (m.group(1),))
              results.append((full_name, False, msg))
              continue
  
          try:
              src_file = short_path(inspect.getsourcefile(obj))
          except TypeError:
              src_file = None
  
          if src_file:
              file_full_name = src_file + ':' + full_name
          else:
              file_full_name = full_name
  
          results.append((full_name,) + validate_rst_syntax(text, file_full_name, dots=dots))
  
      return results
  
  
  ### Doctest helpers ####
  
  # the namespace to run examples in
  DEFAULT_NAMESPACE = {'np': np}
  
  # the namespace to do checks in
  CHECK_NAMESPACE = {
        'np': np,
        'assert_allclose': np.testing.assert_allclose,
        'assert_equal': np.testing.assert_equal,
        # recognize numpy repr's
        'array': np.array,
        'matrix': np.matrix,
        'int64': np.int64,
        'uint64': np.uint64,
        'int8': np.int8,
        'int32': np.int32,
        'float32': np.float32,
        'float64': np.float64,
        'dtype': np.dtype,
        'nan': np.nan,
        'NaN': np.nan,
        'inf': np.inf,
        'Inf': np.inf,}
  
  
  class DTRunner(doctest.DocTestRunner):
      DIVIDER = "\n"
  
      def __init__(self, item_name, checker=None, verbose=None, optionflags=0):
          self._item_name = item_name
          doctest.DocTestRunner.__init__(self, checker=checker, verbose=verbose,
                                         optionflags=optionflags)
  
      def _report_item_name(self, out, new_line=False):
          if self._item_name is not None:
              if new_line:
                  out("\n")
              self._item_name = None
  
      def report_start(self, out, test, example):
          self._checker._source = example.source
          return doctest.DocTestRunner.report_start(self, out, test, example)
  
      def report_success(self, out, test, example, got):
          if self._verbose:
              self._report_item_name(out, new_line=True)
          return doctest.DocTestRunner.report_success(self, out, test, example, got)
  
      def report_unexpected_exception(self, out, test, example, exc_info):
          self._report_item_name(out)
          return doctest.DocTestRunner.report_unexpected_exception(
              self, out, test, example, exc_info)
  
      def report_failure(self, out, test, example, got):
          self._report_item_name(out)
          return doctest.DocTestRunner.report_failure(self, out, test,
                                                      example, got)
  
  class Checker(doctest.OutputChecker):
      obj_pattern = re.compile(r'at 0x[0-9a-fA-F]+>')
      vanilla = doctest.OutputChecker()
      rndm_markers = {'# random', '# Random', '#random', '#Random', "# may vary"}
      stopwords = {'plt.', '.hist', '.show', '.ylim', '.subplot(',
                   'set_title', 'imshow', 'plt.show', '.axis(', '.plot(',
                   '.bar(', '.title', '.ylabel', '.xlabel', 'set_ylim', 'set_xlim',
                   '# reformatted', '.set_xlabel(', '.set_ylabel(', '.set_zlabel(',
                   '.set(xlim=', '.set(ylim=', '.set(xlabel=', '.set(ylabel='}
  
      def __init__(self, parse_namedtuples=True, ns=None, atol=1e-8, rtol=1e-2):
          self.parse_namedtuples = parse_namedtuples
          self.atol, self.rtol = atol, rtol
          if ns is None:
              self.ns = dict(CHECK_NAMESPACE)
          else:
              self.ns = ns
  
      def check_output(self, want, got, optionflags):
          # cut it short if they are equal
          if want == got:
              return True
  
          # skip stopwords in source
          if any(word in self._source for word in self.stopwords):
              return True
  
          # skip random stuff
          if any(word in want for word in self.rndm_markers):
              return True
  
          # skip function/object addresses
          if self.obj_pattern.search(got):
              return True
  
          # ignore comments (e.g. signal.freqresp)
          if want.lstrip().startswith("#"):
              return True
  
          # try the standard doctest
          try:
              if self.vanilla.check_output(want, got, optionflags):
                  return True
          except Exception:
              pass
  
          # OK then, convert strings to objects
          try:
              a_want = eval(want, dict(self.ns))
              a_got = eval(got, dict(self.ns))
          except Exception:
              # Maybe we're printing a numpy array? This produces invalid python
              # code: `print(np.arange(3))` produces "[0 1 2]" w/o commas between
              # values. So, reinsert commas and retry.
              # TODO: handle (1) abberivation (`print(np.arange(10000))`), and
              #              (2) n-dim arrays with n > 1
              s_want = want.strip()
              s_got = got.strip()
              cond = (s_want.startswith("[") and s_want.endswith("]") and
                      s_got.startswith("[") and s_got.endswith("]"))
              if cond:
                  s_want = ", ".join(s_want[1:-1].split())
                  s_got = ", ".join(s_got[1:-1].split())
                  return self.check_output(s_want, s_got, optionflags)
  
              if not self.parse_namedtuples:
                  return False
              # suppose that "want"  is a tuple, and "got" is smth like
              # MoodResult(statistic=10, pvalue=0.1).
              # Then convert the latter to the tuple (10, 0.1),
              # and then compare the tuples.
              try:
                  num = len(a_want)
                  regex = (r'[\w\d_]+\(' +
                           ', '.join([r'[\w\d_]+=(.+)']*num) +
                           r'\)')
                  grp = re.findall(regex, got.replace('\n', ' '))
                  if len(grp) > 1:  # no more than one for now
                      return False
                  # fold it back to a tuple
                  got_again = '(' + ', '.join(grp[0]) + ')'
                  return self.check_output(want, got_again, optionflags)
              except Exception:
                  return False
  
          # ... and defer to numpy
          try:
              return self._do_check(a_want, a_got)
          except Exception:
              # heterog tuple, eg (1, np.array([1., 2.]))
              try:
                  return all(self._do_check(w, g) for w, g in zip(a_want, a_got))
              except (TypeError, ValueError):
                  return False
  
      def _do_check(self, want, got):
          # This should be done exactly as written to correctly handle all of
          # numpy-comparable objects, strings, and heterogeneous tuples
          try:
              if want == got:
                  return True
          except Exception:
              pass
          return np.allclose(want, got, atol=self.atol, rtol=self.rtol)
  
  
  def _run_doctests(tests, full_name, verbose, doctest_warnings):
      """Run modified doctests for the set of `tests`.
  
      Returns: list of [(success_flag, output), ...]
      """
      flags = NORMALIZE_WHITESPACE | ELLIPSIS | IGNORE_EXCEPTION_DETAIL
      runner = DTRunner(full_name, checker=Checker(), optionflags=flags,
                        verbose=verbose)
  
      output = io.StringIO(newline='')
      success = True
      # Redirect stderr to the stdout or output
      tmp_stderr = sys.stdout if doctest_warnings else output
  
      @contextmanager
      def temp_cwd():
          cwd = os.getcwd()
          tmpdir = tempfile.mkdtemp()
          try:
              os.chdir(tmpdir)
              yield tmpdir
          finally:
              os.chdir(cwd)
              shutil.rmtree(tmpdir)
  
      # Run tests, trying to restore global state afterward
      cwd = os.getcwd()
      with np.errstate(), np.printoptions(), temp_cwd() as tmpdir, \
              redirect_stderr(tmp_stderr):
          # try to ensure random seed is NOT reproducible
          np.random.seed(None)
  
          for t in tests:
              t.filename = short_path(t.filename, cwd)
              fails, successes = runner.run(t, out=output.write)
              if fails > 0:
                  success = False
  
      output.seek(0)
      return success, output.read()
  
  
  def check_doctests(module, verbose, ns=None,
                     dots=True, doctest_warnings=False):
      """Check code in docstrings of the module's public symbols.
  
      Returns: list of [(item_name, success_flag, output), ...]
      """
      if ns is None:
          ns = dict(DEFAULT_NAMESPACE)
  
      # Loop over non-deprecated items
      results = []
  
      for name in get_all_dict(module)[0]:
          full_name = module.__name__ + '.' + name
  
          if full_name in DOCTEST_SKIPLIST:
              continue
  
          try:
              obj = getattr(module, name)
          except AttributeError:
              import traceback
              results.append((full_name, False,
                              "Missing item!\n" +
                              traceback.format_exc()))
              continue
  
          finder = doctest.DocTestFinder()
          try:
              tests = finder.find(obj, name, globs=dict(ns))
          except Exception:
              import traceback
              results.append((full_name, False,
                              "Failed to get doctests!\n" +
                              traceback.format_exc()))
              continue
  
          success, output = _run_doctests(tests, full_name, verbose,
                                          doctest_warnings)
  
          if dots:
              output_dot('.' if success else 'F')
  
          results.append((full_name, success, output))
  
          if HAVE_MATPLOTLIB:
              import matplotlib.pyplot as plt
              plt.close('all')
  
      return results
  
  
  def check_doctests_testfile(fname, verbose, ns=None,
                     dots=True, doctest_warnings=False):
      """Check code in a text file.
  
      Mimic `check_doctests` above, differing mostly in test discovery.
      (which is borrowed from stdlib's doctest.testfile here,
       https://github.com/python-git/python/blob/master/Lib/doctest.py)
  
      Returns: list of [(item_name, success_flag, output), ...]
  
      Notes
      -----
  
      refguide can be signalled to skip testing code by adding
      ``#doctest: +SKIP`` to the end of the line. If the output varies or is
      random, add ``# may vary`` or ``# random`` to the comment. for example
  
      >>> plt.plot(...)  # doctest: +SKIP
      >>> random.randint(0,10)
      5 # random
  
      We also try to weed out pseudocode:
      * We maintain a list of exceptions which signal pseudocode,
      * We split the text file into "blocks" of code separated by empty lines
        and/or intervening text.
      * If a block contains a marker, the whole block is then assumed to be
        pseudocode. It is then not being doctested.
  
      The rationale is that typically, the text looks like this:
  
      blah
      <BLANKLINE>
      >>> from numpy import some_module   # pseudocode!
      >>> func = some_module.some_function
      >>> func(42)                  # still pseudocode
      146
      <BLANKLINE>
      blah
      <BLANKLINE>
      >>> 2 + 3        # real code, doctest it
      5
  
      """
      results = []
  
      if ns is None:
          ns = dict(DEFAULT_NAMESPACE)
  
      _, short_name = os.path.split(fname)
      if short_name in DOCTEST_SKIPLIST:
          return results
  
      full_name = fname
      with open(fname, encoding='utf-8') as f:
          text = f.read()
  
      PSEUDOCODE = set(['some_function', 'some_module', 'import example',
                        'ctypes.CDLL',     # likely need compiling, skip it
                        'integrate.nquad(func,'  # ctypes integrate tutotial
                        ])
  
      # split the text into "blocks" and try to detect and omit pseudocode blocks.
      parser = doctest.DocTestParser()
      good_parts = []
      for part in text.split('\n\n'):
          tests = parser.get_doctest(part, ns, fname, fname, 0)
          if any(word in ex.source for word in PSEUDOCODE
                                   for ex in tests.examples):
              # omit it
              pass
          else:
              # `part` looks like a good code, let's doctest it
              good_parts += [part]
  
      # Reassemble the good bits and doctest them:
      good_text = '\n\n'.join(good_parts)
      tests = parser.get_doctest(good_text, ns, fname, fname, 0)
      success, output = _run_doctests([tests], full_name, verbose,
                                      doctest_warnings)
  
      if dots:
          output_dot('.' if success else 'F')
  
      results.append((full_name, success, output))
  
      if HAVE_MATPLOTLIB:
          import matplotlib.pyplot as plt
          plt.close('all')
  
      return results
  
  
  def init_matplotlib():
      global HAVE_MATPLOTLIB
  
      try:
          import matplotlib
          matplotlib.use('Agg')
          HAVE_MATPLOTLIB = True
      except ImportError:
          HAVE_MATPLOTLIB = False
  
  
  def main(argv):
      parser = ArgumentParser(usage=__doc__.lstrip())
      parser.add_argument("module_names", metavar="SUBMODULES", default=[],
                          nargs='*', help="Submodules to check (default: all public)")
      parser.add_argument("--doctests", action="store_true", help="Run also doctests")
      parser.add_argument("-v", "--verbose", action="count", default=0)
      parser.add_argument("--doctest-warnings", action="store_true",
                          help="Enforce warning checking for doctests")
      parser.add_argument("--skip-tutorial", action="store_true",
                          help="Skip running doctests in the tutorial.")
      args = parser.parse_args(argv)
  
      modules = []
      names_dict = {}
  
      if args.module_names:
          args.skip_tutorial = True
      else:
          args.module_names = list(PUBLIC_SUBMODULES)
  
      os.environ['SCIPY_PIL_IMAGE_VIEWER'] = 'true'
  
      module_names = list(args.module_names)
      for name in list(module_names):
          if name in OTHER_MODULE_DOCS:
              name = OTHER_MODULE_DOCS[name]
              if name not in module_names:
                  module_names.append(name)
  
      for submodule_name in module_names:
          module_name = BASE_MODULE + '.' + submodule_name
          __import__(module_name)
          module = sys.modules[module_name]
  
          if submodule_name not in OTHER_MODULE_DOCS:
              find_names(module, names_dict)
  
          if submodule_name in args.module_names:
              modules.append(module)
  
      dots = True
      success = True
      results = []
  
      print("Running checks for %d modules:" % (len(modules),))
  
      if args.doctests or not args.skip_tutorial:
          init_matplotlib()
  
      for module in modules:
          if dots:
              if module is not modules[0]:
                  sys.stderr.write(' ')
              sys.stderr.write(module.__name__ + ' ')
              sys.stderr.flush()
  
          all_dict, deprecated, others = get_all_dict(module)
          names = names_dict.get(module.__name__, set())
  
          mod_results = []
          mod_results += check_items(all_dict, names, deprecated, others, module.__name__)
          mod_results += check_rest(module, set(names).difference(deprecated),
                                    dots=dots)
          if args.doctests:
              mod_results += check_doctests(module, (args.verbose >= 2), dots=dots,
                                            doctest_warnings=args.doctest_warnings)
  
          for v in mod_results:
              assert isinstance(v, tuple), v
  
          results.append((module, mod_results))
  
      if dots:
          sys.stderr.write("\n")
          sys.stderr.flush()
  
      if not args.skip_tutorial:
          base_dir = os.path.join(os.path.abspath(os.path.dirname(__file__)), '..')
          tut_path = os.path.join(base_dir, 'doc', 'source', 'tutorial', '*.rst')
          print('\nChecking tutorial files at %s:' % os.path.relpath(tut_path, os.getcwd()))
          for filename in sorted(glob.glob(tut_path)):
              if dots:
                  sys.stderr.write('\n')
                  sys.stderr.write(os.path.split(filename)[1] + ' ')
                  sys.stderr.flush()
  
              tut_results = check_doctests_testfile(filename, (args.verbose >= 2),
                      dots=dots, doctest_warnings=args.doctest_warnings)
  
              def scratch():
                  pass        # stub out a "module", see below
              scratch.__name__ = filename
              results.append((scratch, tut_results))
  
          if dots:
              sys.stderr.write("\n")
              sys.stderr.flush()
  
      # Report results
      all_success = True
  
      for module, mod_results in results:
          success = all(x[1] for x in mod_results)
          all_success = all_success and success
  
          if success and args.verbose == 0:
              continue
  
          print("")
          print("=" * len(module.__name__))
          print(module.__name__)
          print("=" * len(module.__name__))
          print("")
  
          for name, success, output in mod_results:
              if name is None:
                  if not success or args.verbose >= 1:
                      print(output.strip())
                      print("")
              elif not success or (args.verbose >= 2 and output.strip()):
                  print(name)
                  print("-"*len(name))
                  print("")
                  print(output.strip())
                  print("")
  
      if all_success:
          print("\nOK: refguide and doctests checks passed!")
          sys.exit(0)
      else:
          print("\nERROR: refguide or doctests have errors")
          sys.exit(1)
  
  
  if __name__ == '__main__':
      main(argv=sys.argv[1:])
  
apis: numpy.take numpy.testing.assert_array_equal numpy.random.random numpy.random.rand numpy.testing.assert_allclose numpy.pad
apis: numpy.allclose numpy.random.seed numpy.errstate numpy.printoptions matplotlib.pyplot.close matplotlib.use