1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
|
""" Basic functions for manipulating 2d arrays
"""
__all__ = ['diag','diagflat','eye','fliplr','flipud','rot90','tri','triu',
'tril','vander','histogram2d']
from numpy.core.numeric import asanyarray, 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).swapaxes(0,1)
elif k == 2: return fliplr(flipud(m))
else: return fliplr(m.swapaxes(0,1)) # 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:
m = m.astype(dtype)
return m
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):
"""Return a 2D array whose k'th diagonal is a flattened v and all other
elements are zero.
Examples
--------
>>> diagflat([[1,2],[3,4]]])
array([[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]])
>>> diagflat([1,2], 1)
array([[0, 1, 0],
[0, 0, 2],
[0, 0, 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)
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):
"""
Generate the Vandermonde matrix of vector x.
The i-th column of X is the the (N-i)-1-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, weights=None):
"""histogram2d(x,y, bins=10, range=None, normed=False) -> H, xedges, yedges
Compute the 2D histogram from samples x,y.
:Parameters:
- `x,y` : Sample arrays (1D).
- `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` : Boolean, if False, return the number of samples in each bin,
if True, returns the density.
- `weights` : An array of weights. The weights are normed only if normed
is True. Should weights.sum() not equal N, the total bin count \
will not be equal to the number of samples.
:Return:
- `hist` : Histogram array.
- `xedges, yedges` : Arrays defining the bin edges.
Example:
>>> x = random.randn(100,2)
>>> hist2d, xedges, yedges = histogram2d(x, bins = (6, 7))
:SeeAlso: histogramdd
"""
from numpy import histogramdd
try:
N = len(bins)
except TypeError:
N = 1
if N != 1 and N != 2:
xedges = yedges = asarray(bins, float)
bins = [xedges, yedges]
hist, edges = histogramdd([x,y], bins, range, normed, weights)
return hist, edges[0], edges[1]
|
