def __train__(self, data, labels):
l = labels.reshape((-1,1))
self.__trainingData__ = data
self.__trainingLabels__ = l
N = len(l)
H = zeros((N,N))
for i in range(N):
for j in range(N):
H[i,j] = self.__trainingLabels__[i]*self.__trainingLabels__[j]*self.__kernelFunc__(self.__trainingData__[i],self.__trainingData__[j])
f = -1.0*ones(labels.shape)
lb = zeros(labels.shape)
ub = self.C * ones(labels.shape)
Aeq = labels
beq = 0.0
suppressOut = True
if suppressOut:
devnull = open('/dev/null', 'w')
oldstdout_fno = os.dup(sys.stdout.fileno())
os.dup2(devnull.fileno(), 1)
p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
r = p.solve('cvxopt_qp')
if suppressOut:
os.dup2(oldstdout_fno, 1)
lim = 1e-4
r.xf[where(abs(r.xf)<lim)] = 0
self.__lambdas__ = r.xf
nonzeroindexes = where(r.xf>lim)[0]
# l1 = nonzeroindexes[0]
# self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
self.numSupportVectors = len(nonzeroindexes)
def triu(m, k=0):
"""
Upper triangle of an array.
Return a copy of a matrix with the elements below the `k`-th diagonal
zeroed.
Please refer to the documentation for `tril` for further details.
See Also
--------
tril : lower triangle of an array
Examples
--------
>>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k-1, dtype=bool)
return where(mask, zeros(1, m.dtype), m)
def calcN(classKernels, trainLabels):
N = zeros((len(trainLabels), len(trainLabels)))
for i, l in enumerate(unique(trainLabels)):
numExamplesWithLabel = len(where(trainLabels == l)[0])
Idiff = identity(numExamplesWithLabel, Float64) - (1.0 / numExamplesWithLabel) * ones(numExamplesWithLabel, Float64)
firstDot = dot(classKernels[i], Idiff)
labelTerm = dot(firstDot, transpose(classKernels[i]))
N += labelTerm
N = nan_to_num(N)
#make N more numerically stable
#if I had more time, I would train this parameter, but I don't
additionToN = ((mean(diag(N)) + 1) / 100.0) * identity(N.shape[0], Float64)
N += additionToN
#make sure N is invertable
for i in range(1000):
try:
inv(N)
except LinAlgError:
#doing this to make sure the maxtrix is invertable
#large value supported by section titled
#"numerical issues and regularization" in the paper
N += additionToN
return N
def triu(m, k=0):
"""
Upper triangle of an array.
Return a copy of a matrix with the elements below the `k`-th diagonal
zeroed.
Please refer to the documentation for `tril` for further details.
See Also
--------
tril : lower triangle of an array
Examples
--------
>>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k - 1, dtype=bool)
return where(mask, zeros(1, m.dtype), m)
def train(self, data, labels):
l = labels.reshape((-1,1))
xy = data * l
H = dot(xy,transpose(xy))
f = -1.0*ones(labels.shape)
lb = zeros(labels.shape)
ub = self.C * ones(labels.shape)
Aeq = labels
beq = 0.0
p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
r = p.solve('cvxopt_qp')
r.xf[where(r.xf<1e-3)] = 0
self.w = dot(r.xf*labels,data)
nonzeroindexes = where(r.xf>1e-4)[0]
l1 = nonzeroindexes[0]
self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
self.numSupportVectors = len(nonzeroindexes)
def bartlett(M):
"""bartlett(M) returns the M-point Bartlett window.
"""
if M < 1:
return array([])
if M == 1:
return ones(1, float)
n = arange(0,M)
return where(less_equal(n,(M-1)/2.0),2.0*n/(M-1),2.0-2.0*n/(M-1))
def tril(m, k=0):
"""
Lower triangle of an array.
Return a copy of an array with elements above the `k`-th diagonal zeroed.
For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two
axes.
Parameters
----------
m : array_like, shape (..., M, N)
Input array.
k : int, optional
Diagonal above which to zero elements. `k = 0` (the default) is the
main diagonal, `k < 0` is below it and `k > 0` is above.
Returns
-------
tril : ndarray, shape (..., M, N)
Lower triangle of `m`, of same shape and data-type as `m`.
See Also
--------
triu : same thing, only for the upper triangle
Examples
--------
>>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
>>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))
array([[[ 0, 0, 0, 0, 0],
[ 5, 6, 0, 0, 0],
[10, 11, 12, 0, 0],
[15, 16, 17, 18, 0]],
[[20, 0, 0, 0, 0],
[25, 26, 0, 0, 0],
[30, 31, 32, 0, 0],
[35, 36, 37, 38, 0]],
[[40, 0, 0, 0, 0],
[45, 46, 0, 0, 0],
[50, 51, 52, 0, 0],
[55, 56, 57, 58, 0]]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k, dtype=bool)
return where(mask, m, zeros(1, m.dtype))
def __train__(self, data, labels):
l = labels.reshape((-1,1))
xy = data * l
H = dot(xy,transpose(xy))
f = -1.0*ones(labels.shape)
lb = zeros(labels.shape)
ub = self.C * ones(labels.shape)
Aeq = labels
beq = 0.0
devnull = open('/dev/null', 'w')
oldstdout_fno = os.dup(sys.stdout.fileno())
os.dup2(devnull.fileno(), 1)
p = QP(matrix(H),f.tolist(),lb=lb.tolist(),ub=ub.tolist(),Aeq=Aeq.tolist(),beq=beq)
r = p.solve('cvxopt_qp')
os.dup2(oldstdout_fno, 1)
lim = 1e-4
r.xf[where(r.xf<lim)] = 0
self.w = dot(r.xf*labels,data)
nonzeroindexes = where(r.xf>lim)[0]
l1 = nonzeroindexes[0]
self.w0 = 1.0/labels[l1]-dot(self.w,data[l1])
self.numSupportVectors = len(nonzeroindexes)
def getClassKernels(fullKernelMatrix, trainLabels):
#create a matrix where rows correspond to all examples
#and columns correspond to examples of a specific class
#so if l is the total number of examples, and lj is the number of examples in class j
#then we're creating an l x lj matrix
uniqueLabels = unique(trainLabels)
ret = []
for l in uniqueLabels:
labelIndexes = where(trainLabels == l)[0]
k = zeros((len(fullKernelMatrix), len(labelIndexes)))
for r in range(len(k)):
for c in range(len(k[r])):
k[r][c] = fullKernelMatrix[r][labelIndexes[c]]
ret.append(k)
return ret
def triu(m, k=0):
"""
Upper triangle of an array.
Return a copy of an array with the elements below the `k`-th diagonal
zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the final
two axes.
Please refer to the documentation for `tril` for further details.
See Also
--------
tril : lower triangle of an array
Examples
--------
>>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 0, 8, 9],
[ 0, 0, 12]])
>>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))
array([[[ 0, 1, 2, 3, 4],
[ 0, 6, 7, 8, 9],
[ 0, 0, 12, 13, 14],
[ 0, 0, 0, 18, 19]],
[[20, 21, 22, 23, 24],
[ 0, 26, 27, 28, 29],
[ 0, 0, 32, 33, 34],
[ 0, 0, 0, 38, 39]],
[[40, 41, 42, 43, 44],
[ 0, 46, 47, 48, 49],
[ 0, 0, 52, 53, 54],
[ 0, 0, 0, 58, 59]]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k-1, dtype=bool)
return where(mask, zeros(1, m.dtype), m)
def fix(x, y=None):
"""
Round to nearest integer towards zero.
Round an array of floats element-wise to nearest integer towards zero.
The rounded values are returned as floats.
Parameters
----------
x : array_like
An array of floats to be rounded
y : ndarray, optional
Output array
Returns
-------
out : ndarray of floats
The array of rounded numbers
See Also
--------
trunc, floor, ceil
around : Round to given number of decimals
Examples
--------
>>> np.fix(3.14)
3.0
>>> np.fix(3)
3.0
>>> np.fix([2.1, 2.9, -2.1, -2.9])
array([ 2., 2., -2., -2.])
"""
x = nx.asanyarray(x)
y1 = nx.floor(x)
y2 = nx.ceil(x)
if y is None:
y = nx.asanyarray(y1)
y[...] = nx.where(x >= 0, y1, y2)
return y
def fix(x, y=None):
"""
Round to nearest integer towards zero.
Round an array of floats element-wise to nearest integer towards zero.
The rounded values are returned as floats.
Parameters
----------
x : array_like
An array of floats to be rounded
y : ndarray, optional
Output array
Returns
-------
out : ndarray of floats
The array of rounded numbers
See Also
--------
trunc, floor, ceil
around : Round to given number of decimals
Examples
--------
>>> np.fix(3.14)
3.0
>>> np.fix(3)
3.0
>>> np.fix([2.1, 2.9, -2.1, -2.9])
array([ 2., 2., -2., -2.])
"""
x = nx.asanyarray(x)
y1 = nx.floor(x)
y2 = nx.ceil(x)
if y is None:
y = nx.asanyarray(y1)
y[...] = nx.where(x >= 0, y1, y2)
return y
def tril(m, k=0):
"""
Lower triangle of an array.
Return a copy of an array with elements above the `k`-th diagonal zeroed.
Parameters
----------
m : array_like, shape (M, N)
Input array.
k : int, optional
Diagonal above which to zero elements. `k = 0` (the default) is the
main diagonal, `k < 0` is below it and `k > 0` is above.
Returns
-------
tril : ndarray, shape (M, N)
Lower triangle of `m`, of same shape and data-type as `m`.
See Also
--------
triu : same thing, only for the upper triangle
Examples
--------
>>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k, dtype=bool)
return where(mask, m, zeros(1, m.dtype))
def tril(m, k=0):
"""
Lower triangle of an array.
Return a copy of an array with elements above the `k`-th diagonal zeroed.
Parameters
----------
m : array_like, shape (M, N)
Input array.
k : int, optional
Diagonal above which to zero elements. `k = 0` (the default) is the
main diagonal, `k < 0` is below it and `k > 0` is above.
Returns
-------
tril : ndarray, shape (M, N)
Lower triangle of `m`, of same shape and data-type as `m`.
See Also
--------
triu : same thing, only for the upper triangle
Examples
--------
>>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)
array([[ 0, 0, 0],
[ 4, 0, 0],
[ 7, 8, 0],
[10, 11, 12]])
"""
m = asanyarray(m)
mask = tri(*m.shape[-2:], k=k, dtype=bool)
return where(mask, m, zeros(1, m.dtype))
def sinhc(x):
x = np.asanyarray(x)
y = where(x == 0, 1.0e-20, x)
return np.sinh(y)/y
def mask_indices(n, mask_func, k=0):
"""
Return the indices to access (n, n) arrays, given a masking function.
Assume `mask_func` is a function that, for a square array a of size
``(n, n)`` with a possible offset argument `k`, when called as
``mask_func(a, k)`` returns a new array with zeros in certain locations
(functions like `triu` or `tril` do precisely this). Then this function
returns the indices where the non-zero values would be located.
Parameters
----------
n : int
The returned indices will be valid to access arrays of shape (n, n).
mask_func : callable
A function whose call signature is similar to that of `triu`, `tril`.
That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.
`k` is an optional argument to the function.
k : scalar
An optional argument which is passed through to `mask_func`. Functions
like `triu`, `tril` take a second argument that is interpreted as an
offset.
Returns
-------
indices : tuple of arrays.
The `n` arrays of indices corresponding to the locations where
``mask_func(np.ones((n, n)), k)`` is True.
See Also
--------
triu, tril, triu_indices, tril_indices
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
These are the indices that would allow you to access the upper triangular
part of any 3x3 array:
>>> iu = np.mask_indices(3, np.triu)
For example, if `a` is a 3x3 array:
>>> a = np.arange(9).reshape(3, 3)
>>> a
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
>>> a[iu]
array([0, 1, 2, 4, 5, 8])
An offset can be passed also to the masking function. This gets us the
indices starting on the first diagonal right of the main one:
>>> iu1 = np.mask_indices(3, np.triu, 1)
with which we now extract only three elements:
>>> a[iu1]
array([1, 2, 5])
"""
m = ones((n,n), int)
a = mask_func(m, k)
return where(a != 0)
def triu_indices(n, k=0, m=None):
"""
Return the indices for the upper-triangle of an (n, m) array.
Parameters
----------
n : int
The size of the arrays for which the returned indices will
be valid.
k : int, optional
Diagonal offset (see `triu` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple, shape(2) of ndarrays, shape(`n`)
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array. Can be used
to slice a ndarray of shape(`n`, `n`).
See also
--------
tril_indices : similar function, for lower-triangular.
mask_indices : generic function accepting an arbitrary mask function.
triu, tril
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
upper triangular part starting at the main diagonal, and one starting two
diagonals further right:
>>> iu1 = np.triu_indices(4)
>>> iu2 = np.triu_indices(4, 2)
Here is how they can be used with a sample array:
>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
>>> a[iu1]
array([ 0, 1, 2, 3, 5, 6, 7, 10, 11, 15])
And for assigning values:
>>> a[iu1] = -1
>>> a
array([[-1, -1, -1, -1],
[ 4, -1, -1, -1],
[ 8, 9, -1, -1],
[12, 13, 14, -1]])
These cover only a small part of the whole array (two diagonals right
of the main one):
>>> a[iu2] = -10
>>> a
array([[ -1, -1, -10, -10],
[ 4, -1, -1, -10],
[ 8, 9, -1, -1],
[ 12, 13, 14, -1]])
"""
return where(~tri(n, m, k=k - 1, dtype=bool))
def sinhc(x):
x = np.asanyarray(x)
y = where(x == 0, 1.0e-20, x)
return np.sinh(y)/y
def triu_indices(n, k=0, m=None):
"""
Return the indices for the upper-triangle of an (n, m) array.
Parameters
----------
n : int
The size of the arrays for which the returned indices will
be valid.
k : int, optional
Diagonal offset (see `triu` for details).
m : int, optional
.. versionadded:: 1.9.0
The column dimension of the arrays for which the returned
arrays will be valid.
By default `m` is taken equal to `n`.
Returns
-------
inds : tuple, shape(2) of ndarrays, shape(`n`)
The indices for the triangle. The returned tuple contains two arrays,
each with the indices along one dimension of the array. Can be used
to slice a ndarray of shape(`n`, `n`).
See also
--------
tril_indices : similar function, for lower-triangular.
mask_indices : generic function accepting an arbitrary mask function.
triu, tril
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
Compute two different sets of indices to access 4x4 arrays, one for the
upper triangular part starting at the main diagonal, and one starting two
diagonals further right:
>>> iu1 = np.triu_indices(4)
>>> iu2 = np.triu_indices(4, 2)
Here is how they can be used with a sample array:
>>> a = np.arange(16).reshape(4, 4)
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Both for indexing:
>>> a[iu1]
array([ 0, 1, 2, 3, 5, 6, 7, 10, 11, 15])
And for assigning values:
>>> a[iu1] = -1
>>> a
array([[-1, -1, -1, -1],
[ 4, -1, -1, -1],
[ 8, 9, -1, -1],
[12, 13, 14, -1]])
These cover only a small part of the whole array (two diagonals right
of the main one):
>>> a[iu2] = -10
>>> a
array([[ -1, -1, -10, -10],
[ 4, -1, -1, -10],
[ 8, 9, -1, -1],
[ 12, 13, 14, -1]])
"""
return where(~tri(n, m, k=k-1, dtype=bool))
def sinc(x):
"""sinc(x) returns sin(pi*x)/(pi*x) at all points of array x.
"""
y = pi* where(x == 0, 1.0e-20, x)
return sin(y)/y
def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
"""histogramdd(sample, bins=10, range=None, normed=False, weights=None)
Return the N-dimensional histogram of the sample.
Parameters:
sample : sequence or array
A sequence containing N arrays or an NxM array. Input data.
bins : sequence or scalar
A sequence of edge arrays, a sequence of bin counts, or a scalar
which is the bin count for all dimensions. Default is 10.
range : sequence
A sequence of lower and upper bin edges. Default is [min, max].
normed : boolean
If False, return the number of samples in each bin, if True,
returns the density.
weights : array
Array of weights. The weights are normed only if normed is True.
Should the sum of the weights not equal N, the total bin count will
not be equal to the number of samples.
Returns:
hist : array
Histogram array.
edges : list
List of arrays defining the lower bin edges.
SeeAlso:
histogram
Example
>>> x = random.randn(100,3)
>>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))
"""
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = atleast_2d(sample).T
N, D = sample.shape
nbin = empty(D, int)
edges = D * [None]
dedges = D * [None]
if weights is not None:
weights = asarray(weights)
try:
M = len(bins)
if M != D:
raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
except TypeError:
bins = D * [bins]
# Select range for each dimension
# Used only if number of bins is given.
if range is None:
smin = atleast_1d(array(sample.min(0), float))
smax = atleast_1d(array(sample.max(0), float))
else:
smin = zeros(D)
smax = zeros(D)
for i in arange(D):
smin[i], smax[i] = range[i]
# Make sure the bins have a finite width.
for i in arange(len(smin)):
if smin[i] == smax[i]:
smin[i] = smin[i] - .5
smax[i] = smax[i] + .5
# Create edge arrays
for i in arange(D):
if isscalar(bins[i]):
nbin[i] = bins[i] + 2 # +2 for outlier bins
edges[i] = linspace(smin[i], smax[i], nbin[i] - 1)
else:
edges[i] = asarray(bins[i], float)
nbin[i] = len(edges[i]) + 1 # +1 for outlier bins
dedges[i] = diff(edges[i])
nbin = asarray(nbin)
# Compute the bin number each sample falls into.
Ncount = {}
for i in arange(D):
Ncount[i] = digitize(sample[:, i], edges[i])
# Using digitize, 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.
outliers = zeros(N, int)
for i in arange(D):
# Rounding precision
decimal = int(-log10(dedges[i].min())) + 6
# Find which points are on the rightmost edge.
on_edge = where(
around(sample[:, i], decimal) == around(edges[i][-1], decimal))[0]
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1
# Flattened histogram matrix (1D)
hist = zeros(nbin.prod(), float)
# Compute the sample indices in the flattened histogram matrix.
ni = nbin.argsort()
shape = []
xy = zeros(N, int)
for i in arange(0, D - 1):
xy += Ncount[ni[i]] * nbin[ni[i + 1:]].prod()
xy += Ncount[ni[-1]]
# Compute the number of repetitions in xy and assign it to the flattened histmat.
if len(xy) == 0:
return zeros(nbin - 2, int), edges
flatcount = bincount(xy, weights)
a = arange(len(flatcount))
hist[a] = flatcount
# Shape into a proper matrix
hist = hist.reshape(sort(nbin))
for i in arange(nbin.size):
j = ni[i]
hist = hist.swapaxes(i, j)
ni[i], ni[j] = ni[j], ni[i]
# Remove outliers (indices 0 and -1 for each dimension).
core = D * [slice(1, -1)]
hist = hist[core]
# Normalize if normed is True
if normed:
s = hist.sum()
for i in arange(D):
shape = ones(D, int)
shape[i] = nbin[i] - 2
hist = hist / dedges[i].reshape(shape)
hist /= s
return hist, edges
def sinc(x):
"""sinc(x) returns sin(pi*x)/(pi*x) at all points of array x.
"""
y = pi * where(x == 0, 1.0e-20, x)
return sin(y) / y
def mask_indices(n,mask_func,k=0):
"""Return the indices to access (n,n) arrays, given a masking function.
Assume mask_func() is a function that, for a square array a of size (n,n)
with a possible offset argument k, when called as mask_func(a,k) returns a
new array with zeros in certain locations (functions like triu() or tril()
do precisely this). Then this function returns the indices where the
non-zero values would be located.
Parameters
----------
n : int
The returned indices will be valid to access arrays of shape (n,n).
mask_func : callable
A function whose api is similar to that of numpy.tri{u,l}. That is,
mask_func(x,k) returns a boolean array, shaped like x. k is an optional
argument to the function.
k : scalar
An optional argument which is passed through to mask_func(). Functions
like tri{u,l} take a second argument that is interpreted as an offset.
Returns
-------
indices : an n-tuple of index arrays.
The indices corresponding to the locations where mask_func(ones((n,n)),k)
is True.
Notes
-----
.. versionadded:: 1.4.0
Examples
--------
These are the indices that would allow you to access the upper triangular
part of any 3x3 array:
>>> iu = mask_indices(3,np.triu)
For example, if `a` is a 3x3 array:
>>> a = np.arange(9).reshape(3,3)
>>> a
array([[0, 1, 2],
[3, 4, 5],
[6, 7, 8]])
Then:
>>> a[iu]
array([0, 1, 2, 4, 5, 8])
An offset can be passed also to the masking function. This gets us the
indices starting on the first diagonal right of the main one:
>>> iu1 = mask_indices(3,np.triu,1)
with which we now extract only three elements:
>>> a[iu1]
array([1, 2, 5])
"""
m = ones((n,n),int)
a = mask_func(m,k)
return where(a != 0)
def histogramdd(sample, bins=10, range=None, normed=False, weights=None):
"""histogramdd(sample, bins=10, range=None, normed=False, weights=None)
Return the N-dimensional histogram of the sample.
Parameters:
sample : sequence or array
A sequence containing N arrays or an NxM array. Input data.
bins : sequence or scalar
A sequence of edge arrays, a sequence of bin counts, or a scalar
which is the bin count for all dimensions. Default is 10.
range : sequence
A sequence of lower and upper bin edges. Default is [min, max].
normed : boolean
If False, return the number of samples in each bin, if True,
returns the density.
weights : array
Array of weights. The weights are normed only if normed is True.
Should the sum of the weights not equal N, the total bin count will
not be equal to the number of samples.
Returns:
hist : array
Histogram array.
edges : list
List of arrays defining the lower bin edges.
SeeAlso:
histogram
Example
>>> x = random.randn(100,3)
>>> hist3d, edges = histogramdd(x, bins = (5, 6, 7))
"""
try:
# Sample is an ND-array.
N, D = sample.shape
except (AttributeError, ValueError):
# Sample is a sequence of 1D arrays.
sample = atleast_2d(sample).T
N, D = sample.shape
nbin = empty(D, int)
edges = D*[None]
dedges = D*[None]
if weights is not None:
weights = asarray(weights)
try:
M = len(bins)
if M != D:
raise AttributeError, 'The dimension of bins must be a equal to the dimension of the sample x.'
except TypeError:
bins = D*[bins]
# Select range for each dimension
# Used only if number of bins is given.
if range is None:
smin = atleast_1d(array(sample.min(0), float))
smax = atleast_1d(array(sample.max(0), float))
else:
smin = zeros(D)
smax = zeros(D)
for i in arange(D):
smin[i], smax[i] = range[i]
# Make sure the bins have a finite width.
for i in arange(len(smin)):
if smin[i] == smax[i]:
smin[i] = smin[i] - .5
smax[i] = smax[i] + .5
# Create edge arrays
for i in arange(D):
if isscalar(bins[i]):
nbin[i] = bins[i] + 2 # +2 for outlier bins
edges[i] = linspace(smin[i], smax[i], nbin[i]-1)
else:
edges[i] = asarray(bins[i], float)
nbin[i] = len(edges[i])+1 # +1 for outlier bins
dedges[i] = diff(edges[i])
nbin = asarray(nbin)
# Compute the bin number each sample falls into.
Ncount = {}
for i in arange(D):
Ncount[i] = digitize(sample[:,i], edges[i])
# Using digitize, 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.
outliers = zeros(N, int)
for i in arange(D):
# Rounding precision
decimal = int(-log10(dedges[i].min())) +6
# Find which points are on the rightmost edge.
on_edge = where(around(sample[:,i], decimal) == around(edges[i][-1], decimal))[0]
# Shift these points one bin to the left.
Ncount[i][on_edge] -= 1
# Flattened histogram matrix (1D)
hist = zeros(nbin.prod(), float)
# Compute the sample indices in the flattened histogram matrix.
ni = nbin.argsort()
shape = []
xy = zeros(N, int)
for i in arange(0, D-1):
xy += Ncount[ni[i]] * nbin[ni[i+1:]].prod()
xy += Ncount[ni[-1]]
# Compute the number of repetitions in xy and assign it to the flattened histmat.
if len(xy) == 0:
return zeros(nbin-2, int), edges
flatcount = bincount(xy, weights)
a = arange(len(flatcount))
hist[a] = flatcount
# Shape into a proper matrix
hist = hist.reshape(sort(nbin))
for i in arange(nbin.size):
j = ni[i]
hist = hist.swapaxes(i,j)
ni[i],ni[j] = ni[j],ni[i]
# Remove outliers (indices 0 and -1 for each dimension).
core = D*[slice(1,-1)]
hist = hist[core]
# Normalize if normed is True
if normed:
s = hist.sum()
for i in arange(D):
shape = ones(D, int)
shape[i] = nbin[i]-2
hist = hist / dedges[i].reshape(shape)
hist /= s
return hist, edges
def inv_by_gauss_elimination(mat):
"""Caculate inverse matrix by gauss elimination.
Parameters
----------
mat : ndarray
matrix.
Returns
-------
mat_inv : ndarray
inverse matrix.
mat_null : ndarray
null space matrix.
"""
n_row, n_col = mat.shape
if n_row != n_col:
raise ValueError("n_row and n_col are different.")
data = GF2array(hstack([mat, eye(n_row)]))
n_null_dim = 0
mat_null = array([])
# Row echelon form
for idx_row_src in range(n_row - 1):
idx_pivot_candidate = where(data[idx_row_src:,
idx_row_src] == 1)[0]
if len(idx_pivot_candidate) > 0:
idx_pivot = idx_pivot_candidate[0] + idx_row_src
else:
n_null_dim += 1
continue
if idx_pivot != idx_row_src:
tmp = data[idx_row_src, :].copy()
data[idx_row_src, :] = data[idx_pivot, :]
data[idx_pivot, :] = tmp
for idx_row_dst in range(idx_row_src + 1, n_row):
data[idx_row_dst, :] += (data[idx_row_src, :] *
data[idx_row_dst, idx_row_src])
if np.sum(data[-1, :n_col]) == 0:
n_null_dim += 1
# inverse matrix
for idx_row_src in range(n_row - 1, 0, -1):
for idx_row_dst in range(idx_row_src - 1, -1, -1):
data[idx_row_dst, :] += (data[idx_row_src, :] *
data[idx_row_dst, idx_row_src])
# Find Null space
if n_null_dim > 0:
mat_diag = data[:, :n_col]
mat_null = vstack([
mat_diag[:n_row - n_null_dim, -n_null_dim:],
GF2array(eye(n_null_dim))
])
mat_inv = data[-n_row:, -n_col:]
return mat_inv, mat_null