def plot_pairwise_ld(m, colorbar=True, ax=None, imshow_kwargs=None):
"""Plot a matrix of genotype linkage disequilibrium values between
all pairs of variants.
Parameters
----------
m : array_like
Array of linkage disequilibrium values in condensed form.
colorbar : bool, optional
If True, add a colorbar to the current figure.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
imshow_kwargs : dict-like, optional
Additional keyword arguments passed through to
:func:`matplotlib.pyplot.imshow`.
Returns
-------
ax : axes
The axes on which the plot was drawn.
"""
import matplotlib.pyplot as plt
# check inputs
m_square = ensure_square(m)
# blank out lower triangle and flip up/down
m_square = np.tril(m_square)[::-1, :]
# set up axes
if ax is None:
# make a square figure with enough pixels to represent each variant
x = m_square.shape[0] / plt.rcParams['figure.dpi']
x = max(x, plt.rcParams['figure.figsize'][0])
fig, ax = plt.subplots(figsize=(x, x))
fig.tight_layout(pad=0)
# setup imshow arguments
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('cmap', 'Greys')
imshow_kwargs.setdefault('vmin', 0)
imshow_kwargs.setdefault('vmax', 1)
# plot as image
im = ax.imshow(m_square, **imshow_kwargs)
# tidy up
ax.set_xticks([])
ax.set_yticks([])
for s in 'bottom', 'right':
ax.spines[s].set_visible(False)
if colorbar:
plt.gcf().colorbar(im, shrink=.5, pad=0)
return ax
def plot_pairwise_ld(m, colorbar=True, ax=None, imshow_kwargs=None):
"""Plot a matrix of genotype linkage disequilibrium values between
all pairs of variants.
Parameters
----------
m : array_like
Array of linkage disequilibrium values in condensed form.
colorbar : bool, optional
If True, add a colorbar to the current figure.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
imshow_kwargs : dict-like, optional
Additional keyword arguments passed through to
:func:`matplotlib.pyplot.imshow`.
Returns
-------
ax : axes
The axes on which the plot was drawn.
"""
import matplotlib.pyplot as plt
# check inputs
m_square = ensure_square(m)
# blank out lower triangle and flip up/down
m_square = np.tril(m_square)[::-1, :]
# set up axes
if ax is None:
# make a square figure with enough pixels to represent each variant
x = m_square.shape[0] / plt.rcParams['savefig.dpi']
x = max(x, plt.rcParams['figure.figsize'][0])
fig, ax = plt.subplots(figsize=(x, x))
fig.tight_layout(pad=0)
# setup imshow arguments
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('cmap', 'Greys')
imshow_kwargs.setdefault('vmin', 0)
imshow_kwargs.setdefault('vmax', 1)
# plot as image
im = ax.imshow(m_square, **imshow_kwargs)
# tidy up
ax.set_xticks([])
ax.set_yticks([])
for s in 'bottom', 'right':
ax.spines[s].set_visible(False)
if colorbar:
plt.gcf().colorbar(im, shrink=.5, pad=0)
return ax
def pcoa(dist):
"""Perform principal coordinate analysis of a distance matrix, a.k.a.
classical multi-dimensional scaling.
Parameters
----------
dist : array_like
Distance matrix in condensed form.
Returns
-------
coords : ndarray, shape (n_samples, n_dimensions)
Transformed coordinates for the samples.
explained_ratio : ndarray, shape (n_dimensions)
Variance explained by each dimension.
"""
import scipy.linalg
# This implementation is based on the skbio.math.stats.ordination.PCoA
# implementation, with some minor adjustments.
# check inputs
dist = ensure_square(dist)
# perform scaling
e_matrix = (dist ** 2) / -2
row_means = e_matrix.mean(axis=1, keepdims=True)
col_means = e_matrix.mean(axis=0, keepdims=True)
matrix_mean = e_matrix.mean()
f_matrix = e_matrix - row_means - col_means + matrix_mean
eigvals, eigvecs = scipy.linalg.eigh(f_matrix)
# deal with eigvals close to zero
close_to_zero = np.isclose(eigvals, 0)
eigvals[close_to_zero] = 0
# sort descending
idxs = eigvals.argsort()[::-1]
eigvals = eigvals[idxs]
eigvecs = eigvecs[:, idxs]
# keep only positive eigenvalues
keep = eigvals >= 0
eigvecs = eigvecs[:, keep]
eigvals = eigvals[keep]
# compute coordinates
coords = eigvecs * np.sqrt(eigvals)
# compute ratio explained
explained_ratio = eigvals / eigvals.sum()
return coords, explained_ratio
def pcoa(dist):
"""Perform principal coordinate analysis of a distance matrix, a.k.a.
classical multi-dimensional scaling.
Parameters
----------
dist : array_like
Distance matrix in condensed form.
Returns
-------
coords : ndarray, shape (n_samples, n_dimensions)
Transformed coordinates for the samples.
explained_ratio : ndarray, shape (n_dimensions)
Variance explained by each dimension.
"""
import scipy.linalg
# This implementation is based on the skbio.math.stats.ordination.PCoA
# implementation, with some minor adjustments.
# check inputs
dist = ensure_square(dist)
# perform scaling
e_matrix = (dist**2) / -2
row_means = np.mean(e_matrix, axis=1, keepdims=True)
col_means = np.mean(e_matrix, axis=0, keepdims=True)
matrix_mean = np.mean(e_matrix)
f_matrix = e_matrix - row_means - col_means + matrix_mean
eigvals, eigvecs = scipy.linalg.eigh(f_matrix)
# deal with eigvals close to zero
close_to_zero = np.isclose(eigvals, 0)
eigvals[close_to_zero] = 0
# sort descending
idxs = eigvals.argsort()[::-1]
eigvals = eigvals[idxs]
eigvecs = eigvecs[:, idxs]
# keep only positive eigenvalues
keep = eigvals >= 0
eigvecs = eigvecs[:, keep]
eigvals = eigvals[keep]
# compute coordinates
coords = eigvecs * np.sqrt(eigvals)
# compute ratio explained
explained_ratio = eigvals / eigvals.sum()
return coords, explained_ratio
def plot_pairwise_distance(dist, labels=None, colorbar=True, ax=None, imshow_kwargs=None):
"""Plot a pairwise distance matrix.
Parameters
----------
dist : array_like
The distance matrix in condensed form.
labels : sequence of strings, optional
Sample labels for the axes.
colorbar : bool, optional
If True, add a colorbar to the current figure.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
imshow_kwargs : dict-like, optional
Additional keyword arguments passed through to
:func:`matplotlib.pyplot.imshow`.
Returns
-------
ax : axes
The axes on which the plot was drawn
"""
import matplotlib.pyplot as plt
# check inputs
dist_square = ensure_square(dist)
# set up axes
if ax is None:
# make a square figure
x = plt.rcParams["figure.figsize"][0]
fig, ax = plt.subplots(figsize=(x, x))
fig.tight_layout()
# setup imshow arguments
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault("interpolation", "none")
imshow_kwargs.setdefault("cmap", "jet")
imshow_kwargs.setdefault("vmin", np.min(dist))
imshow_kwargs.setdefault("vmax", np.max(dist))
# plot as image
im = ax.imshow(dist_square, **imshow_kwargs)
# tidy up
if labels:
ax.set_xticks(range(len(labels)))
ax.set_yticks(range(len(labels)))
ax.set_xticklabels(labels, rotation=90)
ax.set_yticklabels(labels, rotation=0)
else:
ax.set_xticks([])
ax.set_yticks([])
if colorbar:
plt.gcf().colorbar(im, shrink=0.5)
return ax
def plot_pairwise_distance(dist,
labels=None,
colorbar=True,
ax=None,
imshow_kwargs=None):
"""Plot a pairwise distance matrix.
Parameters
----------
dist : array_like
The distance matrix in condensed form.
labels : sequence of strings, optional
Sample labels for the axes.
colorbar : bool, optional
If True, add a colorbar to the current figure.
ax : axes, optional
The axes on which to draw. If not provided, a new figure will be
created.
imshow_kwargs : dict-like, optional
Additional keyword arguments passed through to
:func:`matplotlib.pyplot.imshow`.
Returns
-------
ax : axes
The axes on which the plot was drawn
"""
import matplotlib.pyplot as plt
# check inputs
dist_square = ensure_square(dist)
# set up axes
if ax is None:
# make a square figure
x = plt.rcParams['figure.figsize'][0]
fig, ax = plt.subplots(figsize=(x, x))
fig.tight_layout()
# setup imshow arguments
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('cmap', 'jet')
imshow_kwargs.setdefault('vmin', np.min(dist))
imshow_kwargs.setdefault('vmax', np.max(dist))
# plot as image
im = ax.imshow(dist_square, **imshow_kwargs)
# tidy up
if labels:
ax.set_xticks(range(len(labels)))
ax.set_yticks(range(len(labels)))
ax.set_xticklabels(labels, rotation=90)
ax.set_yticklabels(labels, rotation=0)
else:
ax.set_xticks([])
ax.set_yticks([])
if colorbar:
plt.gcf().colorbar(im, shrink=.5)
return ax
