def tajima_d(ac, pos=None, start=None, stop=None):
"""Calculate the value of Tajima's D over a given region.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
pos : array_like, int, shape (n_items,), optional
Variant positions, using 1-based coordinates, in ascending order.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
Returns
-------
D : float
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> allel.stats.tajima_d(ac)
3.1445848780213814
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> allel.stats.tajima_d(ac, pos=pos, start=7, stop=25)
3.8779735196179366
"""
# check inputs
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if pos is not None and (start is not None or stop is not None):
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
loc = pos.locate_range(start, stop)
ac = ac[loc]
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# count segregating variants
S = ac.count_segregating()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate Watterson's theta (absolute value)
theta_hat_w_abs = S / a1
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# calculate theta_hat pi (sum differences over variants)
theta_hat_pi_abs = np.sum(mpd)
# N.B., both theta estimates are usually divided by the number of
# (accessible) bases but here we want the absolute difference
d = theta_hat_pi_abs - theta_hat_w_abs
# calculate the denominator (standard deviation)
a2 = np.sum(1 / (np.arange(1, n) ** 2))
b1 = (n + 1) / (3 * (n - 1))
b2 = 2 * (n ** 2 + n + 3) / (9 * n * (n - 1))
c1 = b1 - (1 / a1)
c2 = b2 - ((n + 2) / (a1 * n)) + (a2 / (a1 ** 2))
e1 = c1 / a1
e2 = c2 / (a1 ** 2 + a2)
d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1)))
# finally calculate Tajima's D
D = d / d_stdev
return D
def sequence_divergence(pos, ac1, ac2, an1=None, an2=None, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide divergence between two populations within a
given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy = sequence_divergence(pos, ac1, ac2, start=1, stop=31)
>>> dxy
0.12096774193548387
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
if an1 is not None:
an1 = asarray_ndim(an1, 1)
if an2 is not None:
an2 = asarray_ndim(an2, 1)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# handle start/stop
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac1 = ac1[loc]
ac2 = ac2[loc]
if an1 is not None:
an1 = an1[loc]
if an2 is not None:
an2 = an2[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference between the two populations
mpd = mean_pairwise_difference_between(ac1, ac2, an1=an1, an2=an2, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base, N.B., expect pos is 1-based
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
dxy = mpd_sum / n_bases
return dxy
def watterson_theta(pos, ac, start=None, stop=None, is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.stats.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
def sequence_divergence(pos,
ac1,
ac2,
an1=None,
an2=None,
start=None,
stop=None,
is_accessible=None):
"""Estimate nucleotide divergence between two populations within a
given region, which is the average proportion of sites (including
monomorphic sites not present in the data) that differ between randomly
chosen pairs of chromosomes, one from each population.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
an1 : array_like, int, shape (n_variants,), optional
Allele numbers for the first population. If not provided, will be
calculated from `ac1`.
an2 : array_like, int, shape (n_variants,), optional
Allele numbers for the second population. If not provided, will be
calculated from `ac2`.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy = sequence_divergence(pos, ac1, ac2, start=1, stop=31)
>>> dxy
0.12096774193548387
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
if an1 is not None:
an1 = asarray_ndim(an1, 1)
if an2 is not None:
an2 = asarray_ndim(an2, 1)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# handle start/stop
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac1 = ac1[loc]
ac2 = ac2[loc]
if an1 is not None:
an1 = an1[loc]
if an2 is not None:
an2 = an2[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference between the two populations
mpd = mean_pairwise_difference_between(ac1, ac2, an1=an1, an2=an2, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base, N.B., expect pos is 1-based
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
dxy = mpd_sum / n_bases
return dxy
def sequence_diversity(pos, ac, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide diversity within a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
pi : ndarray, float, shape (n_windows,)
Nucleotide diversity.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> pi = allel.stats.sequence_diversity(pos, ac, start=1, stop=31)
>>> pi
0.13978494623655915
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac = asarray_ndim(ac, 2)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
pi = mpd_sum / n_bases
return pi
def sequence_diversity(pos, ac, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide diversity within a given region, which is the
average proportion of sites (including monomorphic sites not present in the
data) that differ between randomly chosen pairs of chromosomes.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
pi : ndarray, float, shape (n_windows,)
Nucleotide diversity.
Notes
-----
If start and/or stop are not provided, uses the difference between the last
and the first position as a proxy for the total number of sites, which can
overestimate the sequence diversity.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> pi = allel.sequence_diversity(pos, ac, start=1, stop=31)
>>> pi
0.13978494623655915
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac = asarray_ndim(ac, 2)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
pi = mpd_sum / n_bases
return pi
def tajima_d(ac, pos=None, start=None, stop=None, min_sites=3):
"""Calculate the value of Tajima's D over a given region.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
pos : array_like, int, shape (n_items,), optional
Variant positions, using 1-based coordinates, in ascending order.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
min_sites : int, optional
Minimum number of segregating sites for which to calculate a value. If
there are fewer, np.nan is returned. Defaults to 3.
Returns
-------
D : float
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> allel.tajima_d(ac)
3.1445848780213814
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> allel.tajima_d(ac, pos=pos, start=7, stop=25)
3.8779735196179366
"""
# check inputs
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if pos is not None and (start is not None or stop is not None):
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
loc = pos.locate_range(start, stop)
ac = ac[loc]
# count segregating variants
S = ac.count_segregating()
if S < min_sites:
return np.nan
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate Watterson's theta (absolute value)
theta_hat_w_abs = S / a1
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# calculate theta_hat pi (sum differences over variants)
theta_hat_pi_abs = np.sum(mpd)
# N.B., both theta estimates are usually divided by the number of
# (accessible) bases but here we want the absolute difference
d = theta_hat_pi_abs - theta_hat_w_abs
# calculate the denominator (standard deviation)
a2 = np.sum(1 / (np.arange(1, n)**2))
b1 = (n + 1) / (3 * (n - 1))
b2 = 2 * (n**2 + n + 3) / (9 * n * (n - 1))
c1 = b1 - (1 / a1)
c2 = b2 - ((n + 2) / (a1 * n)) + (a2 / (a1**2))
e1 = c1 / a1
e2 = c2 / (a1**2 + a2)
d_stdev = np.sqrt((e1 * S) + (e2 * S * (S - 1)))
# finally calculate Tajima's D
D = d / d_stdev
return D
def watterson_theta(pos, ac, start=None, stop=None,
is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# masking inaccessible sites from pos and ac
pos, ac = mask_inaccessible(is_accessible, pos, ac)
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start-1:stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
def plot_variant_locator(pos,
step=None,
ax=None,
start=None,
stop=None,
flip=False,
line_kwargs=None):
"""
Plot lines indicating the physical genome location of variants from a
single chromosome/contig. By default the top x axis is in variant index
space, and the bottom x axis is in genome position space.
Parameters
----------
pos : array_like
A sorted 1-dimensional array of genomic positions from a single
chromosome/contig.
step : int, optional
Plot a line for every `step` variants.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
start : int, optional
The start position for the region to draw.
stop : int, optional
The stop position for the region to draw.
flip : bool, optional
Flip the plot upside down.
line_kwargs : dict-like
Additional keyword arguments passed through to `plt.Line2D`.
Returns
-------
ax : axes
The axes on which the plot was drawn
"""
import matplotlib.pyplot as plt
# check inputs
pos = SortedIndex(pos, copy=False)
# set up axes
if ax is None:
x = plt.rcParams['figure.figsize'][0]
y = x / 7
fig, ax = plt.subplots(figsize=(x, y))
fig.tight_layout()
# determine x axis limits
if start is None:
start = np.min(pos)
if stop is None:
stop = np.max(pos)
loc = pos.locate_range(start, stop)
pos = pos[loc]
if step is None:
step = len(pos) // 100
ax.set_xlim(start, stop)
# plot the lines
if line_kwargs is None:
line_kwargs = dict()
# line_kwargs.setdefault('linewidth', .5)
n_variants = len(pos)
for i, p in enumerate(pos[::step]):
xfrom = p
xto = (start + ((i * step / n_variants) * (stop - start)))
l = plt.Line2D([xfrom, xto], [0, 1], **line_kwargs)
ax.add_line(l)
# invert?
if flip:
ax.invert_yaxis()
ax.xaxis.tick_top()
else:
ax.xaxis.tick_bottom()
# tidy up
ax.set_yticks([])
ax.xaxis.set_tick_params(direction='out')
for l in 'left', 'right':
ax.spines[l].set_visible(False)
return ax
def plot_variant_locator(pos, step=None, ax=None, start=None,
stop=None, flip=False,
line_kwargs=None):
"""
Plot lines indicating the physical genome location of variants from a
single chromosome/contig. By default the top x axis is in variant index
space, and the bottom x axis is in genome position space.
Parameters
----------
pos : array_like
A sorted 1-dimensional array of genomic positions from a single
chromosome/contig.
step : int, optional
Plot a line for every `step` variants.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
start : int, optional
The start position for the region to draw.
stop : int, optional
The stop position for the region to draw.
flip : bool, optional
Flip the plot upside down.
line_kwargs : dict-like
Additional keyword arguments passed through to `plt.Line2D`.
Returns
-------
ax : axes
The axes on which the plot was drawn
"""
import matplotlib.pyplot as plt
# check inputs
pos = SortedIndex(pos, copy=False)
# set up axes
if ax is None:
x = plt.rcParams['figure.figsize'][0]
y = x / 7
fig, ax = plt.subplots(figsize=(x, y))
fig.tight_layout()
# determine x axis limits
if start is None:
start = np.min(pos)
if stop is None:
stop = np.max(pos)
loc = pos.locate_range(start, stop)
pos = pos[loc]
if step is None:
step = len(pos) // 100
ax.set_xlim(start, stop)
# plot the lines
if line_kwargs is None:
line_kwargs = dict()
# line_kwargs.setdefault('linewidth', .5)
n_variants = len(pos)
for i, p in enumerate(pos[::step]):
xfrom = p
xto = (
start +
((i * step / n_variants) * (stop-start))
)
l = plt.Line2D([xfrom, xto], [0, 1], **line_kwargs)
ax.add_line(l)
# invert?
if flip:
ax.invert_yaxis()
ax.xaxis.tick_top()
else:
ax.xaxis.tick_bottom()
# tidy up
ax.set_yticks([])
ax.xaxis.set_tick_params(direction='out')
for l in 'left', 'right':
ax.spines[l].set_visible(False)
return ax
