Python numpy.histogram() Examples

def intersectionAndUnion(imPred, imLab, numClass=150):
    """
    Computes the intersection and Union for all the classes between two images
    :param imPred: Predictions image
    :param imLab: Ground-truth image
    :param numClass: Number of semantic classes. Default:150
    :return: Intersection and union for all the classes
    """
    # Remove classes from unlabeled pixels in gt image.
    # We should not penalize detections in unlabeled portions of the image.
    imPred = imPred * (imLab > 0).long()

    # Compute area intersection:
    intersection = imPred * (imPred == imLab).long()
    (area_intersection, _) = np.histogram(intersection, bins=numClass, range=(1, numClass))

    # Compute area union:
    (area_pred, _) = np.histogram(imPred, bins=numClass, range=(1, numClass))
    (area_lab, _) = np.histogram(imLab, bins=numClass, range=(1, numClass))
    area_union = area_pred + area_lab - area_intersection

    IoU = area_intersection / (area_union + 1e-10)

    return IoU 

def histogram(t, L):
    """
    A: If t is a list of tensors/np.ndarrays, B is executed for all, yielding len(ts) histograms, which are summed
    per bin
    B: convert t to numpy, count bins.
    :param t: tensor or list of tensor, each expected to be in [0, L)
    :param L: number of symbols
    :return: length-L array, containing at l the number of values mapping to to symbol l
    """
    if isinstance(t, list):
        ts = t
        histograms = np.stack((histogram(t, L) for t in ts), axis=0)  # get array (len(ts) x L)
        return np.sum(histograms, 0)
    assert 0 <= t.min() and t.max() < L, (t.min(), t.max())
    a = tensor_to_np(t)
    counts, _ = np.histogram(a, np.arange(L+1))  # +1 because np.histogram takes bin edges, including rightmost edge
    return counts


# Gradients -------------------------------------------------------------------- 

def _hist_bin_scott(x, range):
    """
    Scott histogram bin estimator.

    The binwidth is proportional to the standard deviation of the data
    and inversely proportional to the cube root of data size
    (asymptotically optimal).

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    del range  # unused
    return (24.0 * np.pi**0.5 / x.size)**(1.0 / 3.0) * np.std(x) 

def hist_chars(x, m=None, M=None, width=50):
    '''
    Prints a one-line histogram with one char per bin.  The bin count is
    quantized into only a few values and scaled to create a visual
    representation.  Min and max values are displayed on the ends.
    '''
    (h, hbins, m, M) = _gethist(x, width, m, M)
    nchars = len(_strhist_chars)
    if np.any(h > 0):
        hmin = np.min(h)
        hmax  = np.max(h)
        hchar = np.round((nchars-1)*(h - hmin)/(hmax - hmin))
        hstr = ''.join([_strhist_chars[int(i)] for i in hchar])
    else:
        hstr = ' ' * width
    return '% .5f |%s| %.5f' % (m, hstr, M) 

def _hist_bin_rice(x, range):
    """
    Rice histogram bin estimator.

    Another simple estimator with no normality assumption. It has better
    performance for large data than Sturges, but tends to overestimate
    the number of bins. The number of bins is proportional to the cube
    root of data size (asymptotically optimal). The estimate depends
    only on size of the data.

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    del range  # unused
    return x.ptp() / (2.0 * x.size ** (1.0 / 3)) 

def test_outliers(self):
        # Check that outliers are not tallied
        a = np.arange(10) + .5

        # Lower outliers
        h, b = histogram(a, range=[0, 9])
        assert_equal(h.sum(), 9)

        # Upper outliers
        h, b = histogram(a, range=[1, 10])
        assert_equal(h.sum(), 9)

        # Normalization
        h, b = histogram(a, range=[1, 9], density=True)
        assert_almost_equal((h * np.diff(b)).sum(), 1, decimal=15)

        # Weights
        w = np.arange(10) + .5
        h, b = histogram(a, range=[1, 9], weights=w, density=True)
        assert_equal((h * np.diff(b)).sum(), 1)

        h, b = histogram(a, bins=8, range=[1, 9], weights=w)
        assert_equal(h, w[1:-1]) 

def _hist_bin_sturges(x, range):
    """
    Sturges histogram bin estimator.

    A very simplistic estimator based on the assumption of normality of
    the data. This estimator has poor performance for non-normal data,
    which becomes especially obvious for large data sets. The estimate
    depends only on size of the data.

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    del range  # unused
    return x.ptp() / (np.log2(x.size) + 1.0) 

def threshold(self, morph):
        """Find the threshold value for a given morphology
        """
        _morph = morph[morph > 0]
        _bins = 50
        # Decrease the bin size for sources with a small number of pixels
        if _morph.size < 500:
            _bins = max(np.int(_morph.size / 10), 1)
            if _bins == 1:
                return 0, _bins
        hist, bins = np.histogram(np.log10(_morph).reshape(-1), _bins)
        cutoff = np.where(hist == 0)[0]
        # If all of the pixels are used there is no need to threshold
        if len(cutoff) == 0:
            return 0, _bins
        return 10 ** bins[cutoff[-1]], _bins 

def test_bool_conversion(self):
        # gh-12107
        # Reference integer histogram
        a = np.array([1, 1, 0], dtype=np.uint8)
        int_hist, int_edges = np.histogram(a)

        # Should raise an warning on booleans
        # Ensure that the histograms are equivalent, need to suppress
        # the warnings to get the actual outputs
        with suppress_warnings() as sup:
            rec = sup.record(RuntimeWarning, 'Converting input from .*')
            hist, edges = np.histogram([True, True, False])
            # A warning should be issued
            assert_equal(len(rec), 1)
            assert_array_equal(hist, int_hist)
            assert_array_equal(edges, int_edges) 

def _hist_bin_sqrt(x, range):
    """
    Square root histogram bin estimator.

    Bin width is inversely proportional to the data size. Used by many
    programs for its simplicity.

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    del range  # unused
    return x.ptp() / np.sqrt(x.size) 

def test_gen_radius(self):
        r"""Test gen_radius method.

        Approach: Ensures the output is set, of the correct type, length, and units.
        Check distributional agreement.
        """
        plan_pop = self.fixture
        n = 10000
        radii = plan_pop.gen_radius(n)

        # ensure the units are length
        self.assertEqual((radii/u.km).decompose().unit, u.dimensionless_unscaled)
        # radius > 0
        self.assertTrue(np.all(radii.value > 0))
        self.assertTrue(np.all(np.isfinite(radii.value)))

        h = np.histogram(radii.to('earthRad').value,bins=plan_pop.Rs)
        np.testing.assert_allclose(plan_pop.Rvals.sum()*h[0]/float(n),plan_pop.Rvals,rtol=0.05) 

def test_gen_sma(self):
        r"""Test gen_sma method.

        Approach: Ensures the output is set, of the correct type, length, and units.
        Check that they are in the correct range and follow the distribution.
        """

        plan_pop = self.fixture
        n = 10000
        sma = plan_pop.gen_sma(n)

        # ensure the units are length
        self.assertEqual((sma/u.km).decompose().unit, u.dimensionless_unscaled)
        # sma > 0
        self.assertTrue(np.all(sma.value >= 0))
        # sma >= arange[0], sma <= arange[1]
        self.assertTrue(np.all(sma - plan_pop.arange[0] >= 0))
        self.assertTrue(np.all(plan_pop.arange[1] - sma >= 0))

        h = np.histogram(sma.to('AU').value,100,density=True)
        hx = np.diff(h[1])/2.+h[1][:-1]
        hp = plan_pop.dist_sma(hx)

        chi2 = scipy.stats.chisquare(h[0],hp)
        self.assertGreaterEqual(chi2[1],0.95) 

def test_gen_plan_params(self):
        r"""Test generated planet parameters:
        Expected: all 1 R_E, all p = 0.67, e = 0, and uniform a,e in arange,erange
        """

        obj = EarthTwinHabZone2(constrainOrbits=False,erange=[0.1,0.5],**self.spec)

        x = 10000

        a, e, p, Rp = obj.gen_plan_params(x)
        
        assert(np.all(p == 0.367))
        assert(np.all(Rp == 1.0*u.R_earth))

        for param,param_range in zip([a.value,e],[obj.arange.value,obj.erange]):
            h = np.histogram(param,100,density=True)
            chi2 = scipy.stats.chisquare(h[0],[1.0/np.diff(param_range)[0]]*len(h[0]))
            self.assertGreater(chi2[1], 0.95) 

def test_gen_sma(self):
        r"""Test gen_sma method.

        Approach: Ensures the output is set, of the correct type, length, and units.
        Check that they are in the correct range and follow the distribution.
        """

        plan_pop = self.fixture
        n = 10000
        sma = plan_pop.gen_sma(n)

        # ensure the units are length
        self.assertEqual((sma/u.km).decompose().unit, u.dimensionless_unscaled)
        # sma > 0
        self.assertTrue(np.all(sma.value >= 0))
        # sma >= arange[0], sma <= arange[1]
        self.assertTrue(np.all(sma - plan_pop.arange[0] >= 0))
        self.assertTrue(np.all(plan_pop.arange[1] - sma >= 0))

        h = np.histogram(sma.to('AU').value,100,density=True)
        hx = np.diff(h[1])/2.+h[1][:-1]
        hp = plan_pop.dist_sma(hx)

        chi2 = scipy.stats.chisquare(h[0],hp)
        self.assertGreaterEqual(chi2[1],0.95) 

def test_gen_plan_params(self):
        r"""Test generated planet parameters:
        Expected: all 1 R_E, all p = 0.67, e = 0, and uniform a in arange
        """

        obj = EarthTwinHabZone1(**self.spec)

        x = 10000

        a, e, p, Rp = obj.gen_plan_params(x)
        
        assert(np.all(e == 0))
        assert(np.all(p == 0.367))
        assert(np.all(Rp == 1.0*u.R_earth))

        h = np.histogram(a.to('AU').value,100,density=True)
        chi2 = scipy.stats.chisquare(h[0],[1.0/np.diff(obj.arange.to('AU').value)[0]]*len(h[0]))
        self.assertGreater(chi2[1], 0.95) 

def read_image(self,im):
    if self.i >= self.k :
      self.i = 0
    try:
      img = Image.open(im)
      osize = img.size
      img.thumbnail((self.resample,self.resample))
      v = [float(p)/float(img.size[0]*img.size[1])*100  for p in np.histogram(np.asarray(img))[0]]
      if self.size :
        v += [osize[0], osize[1]]
      i = self.i
      self.i += 1
      return [i, v, im]
    except Exception as e:
      print("Error reading ",im,e)
      return [None, None, None] 

def get_hardness_distribution(gtG, max_dist, min_dist, rng, trials, bins, nodes,
                              n_ori, step_size):
  heuristic_fn = lambda node_ids, node_id: \
    heuristic_fn_vec(nodes[node_ids, :], nodes[[node_id], :], n_ori, step_size)
  num_nodes = gtG.num_vertices()
  gt_dists = []; h_dists = [];
  for i in range(trials):
    end_node_id = rng.choice(num_nodes)
    gt_dist = gt.topology.shortest_distance(gt.GraphView(gtG, reversed=True),
                                            source=gtG.vertex(end_node_id),
                                            target=None, max_dist=max_dist)
    gt_dist = np.array(gt_dist.get_array())
    ind = np.where(np.logical_and(gt_dist <= max_dist, gt_dist >= min_dist))[0]
    gt_dist = gt_dist[ind]
    h_dist = heuristic_fn(ind, end_node_id)[:,0]
    gt_dists.append(gt_dist)
    h_dists.append(h_dist)
  gt_dists = np.concatenate(gt_dists)
  h_dists = np.concatenate(h_dists)
  hardness = 1. - h_dists*1./gt_dists
  hist, _ = np.histogram(hardness, bins)
  hist = hist.astype(np.float64)
  hist = hist / np.sum(hist)
  return hist 

def read_image(self,im):
    if self.i >= self.k :
      self.i = 0
    try:
      img = Image.open(im)
      osize = img.size
      img.thumbnail((self.resample,self.resample))
      v = [float(p)/float(img.size[0]*img.size[1])*100  for p in np.histogram(np.asarray(img))[0]]
      if self.size :
        v += [osize[0], osize[1]]
      pbar.update(1)
      i = self.i
      self.i += 1
      return [i, v, im]
    except Exception as e:
      print("Error reading ",im,e)
      return [None, None, None] 

def compareHistograms(image,x,y,w,h, ppl):
	#temporary crop detected target
	tempCrop = image[x:x+w, y:y+h]
	#generate temporary histogram to compare to existant ones
	tempHist = generateHistogram(tempCrop)
	
	if(len(ppl) > 0):
		b = checkSimilarity(tempHist, ppl, image)
		if(b):
			return (b.x, b.y, b.w, b.h, b.color, b.label)
		else:
			return None
	else:
		return None
	
	return None 

def test_bin_edge_cases(self):
        # Ensure that floating-point computations correctly place edge cases.
        arr = np.array([337, 404, 739, 806, 1007, 1811, 2012])
        hist, edges = np.histogram(arr, bins=8296, range=(2, 2280))
        mask = hist > 0
        left_edges = edges[:-1][mask]
        right_edges = edges[1:][mask]
        for x, left, right in zip(arr, left_edges, right_edges):
            assert_(x >= left)
            assert_(x < right) 

def test_error_binnum_type (self):
        # Tests if right Error is raised if bins argument is float
        vals = np.linspace(0.0, 1.0, num=100)
        histogram(vals, 5)
        assert_raises(TypeError, histogram, vals, 2.4) 

def _hist_bin_fd(x, range):
    """
    The Freedman-Diaconis histogram bin estimator.

    The Freedman-Diaconis rule uses interquartile range (IQR) to
    estimate binwidth. It is considered a variation of the Scott rule
    with more robustness as the IQR is less affected by outliers than
    the standard deviation. However, the IQR depends on fewer points
    than the standard deviation, so it is less accurate, especially for
    long tailed distributions.

    If the IQR is 0, this function returns 1 for the number of bins.
    Binwidth is inversely proportional to the cube root of data size
    (asymptotically optimal).

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """
    del range  # unused
    iqr = np.subtract(*np.percentile(x, [75, 25]))
    return 2.0 * iqr * x.size ** (-1.0 / 3.0) 

def test_density(self):
        # Check that the integral of the density equals 1.
        n = 100
        v = np.random.rand(n)
        a, b = histogram(v, density=True)
        area = np.sum(a * np.diff(b))
        assert_almost_equal(area, 1)

        # Check with non-constant bin widths
        v = np.arange(10)
        bins = [0, 1, 3, 6, 10]
        a, b = histogram(v, bins, density=True)
        assert_array_equal(a, .1)
        assert_equal(np.sum(a * np.diff(b)), 1)

        # Test that passing False works too
        a, b = histogram(v, bins, density=False)
        assert_array_equal(a, [1, 2, 3, 4])

        # Variale bin widths are especially useful to deal with
        # infinities.
        v = np.arange(10)
        bins = [0, 1, 3, 6, np.inf]
        a, b = histogram(v, bins, density=True)
        assert_array_equal(a, [.1, .1, .1, 0.])

        # Taken from a bug report from N. Becker on the numpy-discussion
        # mailing list Aug. 6, 2010.
        counts, dmy = np.histogram(
            [1, 2, 3, 4], [0.5, 1.5, np.inf], density=True)
        assert_equal(counts, [.25, 0]) 

def _hist_bin_stone(x, range):
    """
    Histogram bin estimator based on minimizing the estimated integrated squared error (ISE).

    The number of bins is chosen by minimizing the estimated ISE against the unknown true distribution.
    The ISE is estimated using cross-validation and can be regarded as a generalization of Scott's rule.
    https://en.wikipedia.org/wiki/Histogram#Scott.27s_normal_reference_rule

    This paper by Stone appears to be the origination of this rule.
    http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/34.pdf

    Parameters
    ----------
    x : array_like
        Input data that is to be histogrammed, trimmed to range. May not
        be empty.
    range : (float, float)
        The lower and upper range of the bins.

    Returns
    -------
    h : An estimate of the optimal bin width for the given data.
    """

    n = x.size
    ptp_x = np.ptp(x)
    if n <= 1 or ptp_x == 0:
        return 0

    def jhat(nbins):
        hh = ptp_x / nbins
        p_k = np.histogram(x, bins=nbins, range=range)[0] / n
        return (2 - (n + 1) * p_k.dot(p_k)) / hh

    nbins_upper_bound = max(100, int(np.sqrt(n)))
    nbins = min(_range(1, nbins_upper_bound + 1), key=jhat)
    if nbins == nbins_upper_bound:
        warnings.warn("The number of bins estimated may be suboptimal.", RuntimeWarning, stacklevel=2)
    return ptp_x / nbins 

def test_top_sparse3(self):
        shape, rank, k, factors, x, x_indices, x_vals = \
                utils.generate_dataset()
        model = utils.parafac(factors)
        for beta in [1.0, 2.0, 1.5]:
            for factor in range(3):
                # Generate the top numerator for the reference dense method
                einstr = utils.generate_dense(rank, factor)
                # Get all factors that aren't the current factor
                mode_factors = [a for j, a in enumerate(factors) if j != factor]
                mode_factors += [x * (model ** (beta - 2.)), ]
                top_d = np.einsum(einstr, *mode_factors)

                # Now get the top numerator for the sparse method
                top_s = np.zeros(factors[factor].shape, dtype=np.float32)
                utils.top_sparse3(x_indices, x_vals, top_s, beta, factor, *factors)

                # Now get the top numerator for the sparse method using numba
                top_n = np.zeros(factors[factor].shape, dtype=np.float32)
                utils.top_sparse3_numba(x_indices, x_vals, top_n, beta, factor, *factors)

                print(top_d, top_s, top_n)
                print(top_d - top_n)
                print(np.histogram(np.abs((top_d - top_n) / top_d)))
                result = np.allclose(top_d, top_s, rtol=1e-2, atol=1e-2)
                self.assertTrue(result)
                result = np.allclose(top_d, top_n, rtol=1e-2, atol=1e-2)
                self.assertTrue(result) 

def histo_summary(self, tag, values, step, bins=1000):
        """Log a histogram of the tensor of values."""

        # Create a histogram using numpy
        counts, bin_edges = np.histogram(values, bins=bins)

        # Fill the fields of the histogram proto
        hist = tf.HistogramProto()
        hist.min = float(np.min(values))
        hist.max = float(np.max(values))
        hist.num = int(np.prod(values.shape))
        hist.sum = float(np.sum(values))
        hist.sum_squares = float(np.sum(values**2))

        # Drop the start of the first bin
        bin_edges = bin_edges[1:]

        # Add bin edges and counts
        for edge in bin_edges:
            hist.bucket_limit.append(edge)
        for c in counts:
            hist.bucket.append(c)

        # Create and write Summary
        summary = tf.Summary(value=[tf.Summary.Value(tag=tag, histo=hist)])
        self.writer.add_summary(summary, step)
        self.writer.flush() 

def histo_summary(self, tag, values, step, bins=1000):
        """Log a histogram of the tensor of values."""

        # Create a histogram using numpy
        counts, bin_edges = np.histogram(values, bins=bins)

        # Fill the fields of the histogram proto
        hist = tf.HistogramProto()
        hist.min = float(np.min(values))
        hist.max = float(np.max(values))
        hist.num = int(np.prod(values.shape))
        hist.sum = float(np.sum(values))
        hist.sum_squares = float(np.sum(values**2))

        # Drop the start of the first bin
        bin_edges = bin_edges[1:]

        # Add bin edges and counts
        for edge in bin_edges:
            hist.bucket_limit.append(edge)
        for c in counts:
            hist.bucket.append(c)

        # Create and write Summary
        summary = tf.Summary(value=[tf.Summary.Value(tag=tag, histo=hist)])
        self.writer.add_summary(summary, step)
        self.writer.flush() 

def add_hist_image_summary(values, bins, name):
  """Adds a tf.summary.image for a histogram plot of the values.

  Plots the histogram of values and creates a tf image summary.

  Args:
    values: a 1-D float32 tensor containing the values.
    bins: bin edges which will be directly passed to np.histogram.
    name: name for the image summary.
  """

  def hist_plot(values, bins):
    """Numpy function to plot hist."""
    fig = plt.figure(frameon=False)
    ax = fig.add_subplot('111')
    y, x = np.histogram(values, bins=bins)
    ax.plot(x[:-1], y)
    ax.set_ylabel('count')
    ax.set_xlabel('value')
    fig.canvas.draw()
    width, height = fig.get_size_inches() * fig.get_dpi()
    image = np.fromstring(
        fig.canvas.tostring_rgb(), dtype='uint8').reshape(
            1, int(height), int(width), 3)
    return image
  hist_plot = tf.py_func(hist_plot, [values, bins], tf.uint8)
  tf.summary.image(name, hist_plot) 

def histo_summary(self, tag, values, step, bins=1000):
        """Log a histogram of the tensor of values."""

        # Create a histogram using numpy
        counts, bin_edges = np.histogram(values, bins=bins)

        # Fill the fields of the histogram proto
        hist = tf.HistogramProto()
        hist.min = float(np.min(values))
        hist.max = float(np.max(values))
        hist.num = int(np.prod(values.shape))
        hist.sum = float(np.sum(values))
        hist.sum_squares = float(np.sum(values ** 2))

        # Drop the start of the first bin
        bin_edges = bin_edges[1:]

        # Add bin edges and counts
        for edge in bin_edges:
            hist.bucket_limit.append(edge)
        for c in counts:
            hist.bucket.append(c)

        # Create and write Summary
        summary = tf.Summary(value=[tf.Summary.Value(tag=tag, histo=hist)])
        self.writer.add_summary(summary, step)
        self.writer.flush() 

def compute_class_weights(self, histogram):
        '''
        Helper function to compute the class weights
        :param histogram: distribution of class samples
        :return: None, but updates the classWeights variable
        '''
        normHist = histogram / np.sum(histogram)
        for i in range(self.classes):
            self.classWeights[i] = 1 / (np.log(self.normVal + normHist[i]))