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""" Basic functions for manipulating 2d arrays
"""
__all__ = ['diag','diagflat','eye','fliplr','flipud','rot90','tri','triu',
'tril','vander','histogram2d']
from numpy.core.numeric import asanyarray, int_, equal, subtract, arange, \
zeros, arange, greater_equal, multiply, ones, asarray
def fliplr(m):
""" returns an array m with the rows preserved and columns flipped
in the left/right direction. Works on the first two dimensions of m.
"""
m = asanyarray(m)
if m.ndim < 2:
raise ValueError, "Input must be >= 2-d."
return m[:, ::-1]
def flipud(m):
""" returns an array with the columns preserved and rows flipped in
the up/down direction. Works on the first dimension of m.
"""
m = asanyarray(m)
if m.ndim < 1:
raise ValueError, "Input must be >= 1-d."
return m[::-1,...]
def rot90(m, k=1):
""" returns the array found by rotating m by k*90
degrees in the counterclockwise direction. Works on the first two
dimensions of m.
"""
m = asanyarray(m)
if m.ndim < 2:
raise ValueError, "Input must >= 2-d."
k = k % 4
if k == 0: return m
elif k == 1: return fliplr(m).transpose()
elif k == 2: return fliplr(flipud(m))
else: return fliplr(m.transpose()) # k==3
def eye(N, M=None, k=0, dtype=float):
""" eye returns a N-by-M 2-d array where the k-th diagonal is all ones,
and everything else is zeros.
"""
if M is None: M = N
m = equal(subtract.outer(arange(N), arange(M)),-k)
if m.dtype != dtype:
return m.astype(dtype)
def diag(v, k=0):
""" returns a copy of the the k-th diagonal if v is a 2-d array
or returns a 2-d array with v as the k-th diagonal if v is a
1-d array.
"""
v = asarray(v)
s = v.shape
if len(s)==1:
n = s[0]+abs(k)
res = zeros((n,n), v.dtype)
if (k>=0):
i = arange(0,n-k)
fi = i+k+i*n
else:
i = arange(0,n+k)
fi = i+(i-k)*n
res.flat[fi] = v
return res
elif len(s)==2:
N1,N2 = s
if k >= 0:
M = min(N1,N2-k)
i = arange(0,M)
fi = i+k+i*N2
else:
M = min(N1+k,N2)
i = arange(0,M)
fi = i + (i-k)*N2
return v.flat[fi]
else:
raise ValueError, "Input must be 1- or 2-d."
def diagflat(v,k=0):
try:
wrap = v.__array_wrap__
except AttributeError:
wrap = None
v = asarray(v).ravel()
s = len(v)
n = s + abs(k)
res = zeros((n,n), v.dtype)
if (k>=0):
i = arange(0,n-k)
fi = i+k+i*n
else:
i = arange(0,n+k)
fi = i+(i-k)*n
res.flat[fi] = v
if not wrap:
return res
return wrap(res)
def tri(N, M=None, k=0, dtype=float):
""" returns a N-by-M array where all the diagonals starting from
lower left corner up to the k-th are all ones.
"""
if M is None: M = N
m = greater_equal(subtract.outer(arange(N), arange(M)),-k)
if m.dtype != dtype:
return m.astype(dtype)
def tril(m, k=0):
""" returns the elements on and below the k-th diagonal of m. k=0 is the
main diagonal, k > 0 is above and k < 0 is below the main diagonal.
"""
m = asanyarray(m)
out = multiply(tri(m.shape[0], m.shape[1], k=k, dtype=int),m)
return out
def triu(m, k=0):
""" returns the elements on and above the k-th diagonal of m. k=0 is the
main diagonal, k > 0 is above and k < 0 is below the main diagonal.
"""
m = asanyarray(m)
out = multiply((1-tri(m.shape[0], m.shape[1], k-1, int)),m)
return out
# borrowed from John Hunter and matplotlib
def vander(x, N=None):
"""
X = vander(x,N=None)
The Vandermonde matrix of vector x. The i-th column of X is the
the i-th power of x. N is the maximum power to compute; if N is
None it defaults to len(x).
"""
x = asarray(x)
if N is None: N=len(x)
X = ones( (len(x),N), x.dtype)
for i in range(N-1):
X[:,i] = x**(N-i-1)
return X
def histogram2d(x,y, bins=10, range=None, normed=False):
"""histogram2d(x,y, bins=10, range=None, normed=False) -> H, xedges, yedges
Compute the 2D histogram from samples x,y.
Parameters
----------
x,y: 1D data series. Both arrays must have the same length.
bins: Number of bins -or- [nbin x, nbin y] -or-
[bin edges] -or- [x bin edges, y bin edges].
range: A sequence of lower and upper bin edges (default: [min, max]).
normed: True or False.
The histogram array is a count of the number of samples in each
two dimensional bin.
Setting normed to True returns a density rather than a bin count.
Data falling outside of the edges are not counted.
"""
import numpy as np
try:
N = len(bins)
except TypeError:
N = 1
bins = [bins]
x = asarray(x)
y = asarray(y)
if range is None:
xmin, xmax = x.min(), x.max()
ymin, ymax = y.min(), y.max()
else:
xmin, xmax = range[0]
ymin, ymax = range[1]
if N == 2:
if np.isscalar(bins[0]):
xnbin = bins[0]
xedges = np.linspace(xmin, xmax, xnbin+1)
else:
xedges = asarray(bins[0], float)
xnbin = len(xedges)-1
if np.isscalar(bins[1]):
ynbin = bins[1]
yedges = np.linspace(ymin, ymax, ynbin+1)
else:
yedges = asarray(bins[1], float)
ynbin = len(yedges)-1
elif N == 1:
ynbin = xnbin = bins[0]
xedges = np.linspace(xmin, xmax, xnbin+1)
yedges = np.linspace(ymin, ymax, ynbin+1)
else:
yedges = asarray(bins, float)
xedges = yedges.copy()
ynbin = len(yedges)-1
xnbin = len(xedges)-1
dxedges = np.diff(xedges)
dyedges = np.diff(yedges)
# Flattened histogram matrix (1D)
hist = np.zeros((xnbin)*(ynbin), int)
# Count the number of sample in each bin (1D)
xbin = np.digitize(x,xedges)
ybin = np.digitize(y,yedges)
# Values that fall on an edge are put in the right bin.
# For the rightmost bin, we want values equal to the right
# edge to be counted in the last bin, and not as an outlier.
xdecimal = int(-np.log10(dxedges.min()))+6
ydecimal = int(-np.log10(dyedges.min()))+6
on_edge_x = np.where(np.around(x,xdecimal) == np.around(xedges[-1], xdecimal))[0]
on_edge_y = np.where(np.around(y,ydecimal) == np.around(yedges[-1], ydecimal))[0]
xbin[on_edge_x] -= 1
ybin[on_edge_y] -= 1
# Remove the true outliers
outliers = (xbin==0) | (xbin==xnbin+1) | (ybin==0) | (ybin == ynbin+1)
xbin = xbin[outliers==False] - 1
ybin = ybin[outliers==False] - 1
# Compute the sample indices in the flattened histogram matrix.
if xnbin >= ynbin:
xy = ybin*(xnbin) + xbin
else:
xy = xbin*(ynbin) + ybin
# Compute the number of repetitions in xy and assign it to the flattened
# histogram matrix.
flatcount = np.bincount(xy)
indices = np.arange(len(flatcount))
hist[indices] = flatcount
shape = np.sort([xnbin, ynbin])
# Shape into a proper matrix
histmat = hist.reshape(shape)
if (shape == (ynbin, xnbin)).all():
histmat = histmat.T
if normed:
diff2 = np.outer(dxedges, dyedges)
histmat = histmat / diff2 / histmat.sum()
return histmat, xedges, yedges
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