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 select(condlist, choicelist, default=0):
""" Return an array composed of different elements of choicelist
depending on the list of conditions.
condlist is a list of condition arrays containing ones or zeros
choicelist is a list of choice arrays (of the "same" size as the
arrays in condlist). The result array has the "same" size as the
arrays in choicelist. If condlist is [c0, ..., cN-1] then choicelist
must be of length N. The elements of the choicelist can then be
represented as [v0, ..., vN-1]. The default choice if none of the
conditions are met is given as the default argument.
The conditions are tested in order and the first one statisfied is
used to select the choice. In other words, the elements of the
output array are found from the following tree (notice the order of
the conditions matters):
if c0: v0
elif c1: v1
elif c2: v2
...
elif cN-1: vN-1
else: default
Note that one of the condition arrays must be large enough to handle
the largest array in the choice list.
"""
n = len(condlist)
n2 = len(choicelist)
if n2 != n:
raise ValueError, "list of cases must be same length as list of conditions"
choicelist.insert(0, default)
S = 0
pfac = 1
for k in range(1, n+1):
S += k * pfac * asarray(condlist[k-1])
if k < n:
pfac *= (1-asarray(condlist[k-1]))
# handle special case of a 1-element condition but
# a multi-element choice
if type(S) in ScalarType or max(asarray(S).shape)==1:
pfac = asarray(1)
for k in range(n2+1):
pfac = pfac + asarray(choicelist[k])
if type(S) in ScalarType:
S = S*ones(asarray(pfac).shape, type(S))
else:
S = S*ones(asarray(pfac).shape, S.dtype)
return choose(S, tuple(choicelist))
def select(condlist, choicelist, default=0):
"""Return an array composed of different elements in choicelist,
depending on the list of conditions.
:Parameters:
condlist : list of N boolean arrays of length M
The conditions C_0 through C_(N-1) which determine
from which vector the output elements are taken.
choicelist : list of N arrays of length M
Th vectors V_0 through V_(N-1), from which the output
elements are chosen.
:Returns:
output : 1-dimensional array of length M
The output at position m is the m-th element of the first
vector V_n for which C_n[m] is non-zero. Note that the
output depends on the order of conditions, since the
first satisfied condition is used.
Equivalent to:
output = []
for m in range(M):
output += [V[m] for V,C in zip(values,cond) if C[m]]
or [default]
"""
n = len(condlist)
n2 = len(choicelist)
if n2 != n:
raise ValueError, "list of cases must be same length as list of conditions"
choicelist = [default] + choicelist
S = 0
pfac = 1
for k in range(1, n + 1):
S += k * pfac * asarray(condlist[k - 1])
if k < n:
pfac *= (1 - asarray(condlist[k - 1]))
# handle special case of a 1-element condition but
# a multi-element choice
if type(S) in ScalarType or max(asarray(S).shape) == 1:
pfac = asarray(1)
for k in range(n2 + 1):
pfac = pfac + asarray(choicelist[k])
if type(S) in ScalarType:
S = S * ones(asarray(pfac).shape, type(S))
else:
S = S * ones(asarray(pfac).shape, S.dtype)
return choose(S, tuple(choicelist))
def polyint(p, m=1, k=None):
"""Return the mth analytical integral of the polynomial p.
If k is None, then zero-valued constants of integration are used.
otherwise, k should be a list of length m (or a scalar if m=1) to
represent the constants of integration to use for each integration
(starting with k[0])
"""
m = int(m)
if m < 0:
raise ValueError, "Order of integral must be positive (see polyder)"
if k is None:
k = NX.zeros(m, float)
k = atleast_1d(k)
if len(k) == 1 and m > 1:
k = k[0]*NX.ones(m, float)
if len(k) < m:
raise ValueError, \
"k must be a scalar or a rank-1 array of length 1 or >m."
if m == 0:
return p
else:
truepoly = isinstance(p, poly1d)
p = NX.asarray(p)
y = NX.zeros(len(p)+1, float)
y[:-1] = p*1.0/NX.arange(len(p), 0, -1)
y[-1] = k[0]
val = polyint(y, m-1, k=k[1:])
if truepoly:
val = poly1d(val)
return val
def smooth(x,window_len=11,window='hanning'):
"""smooth the data using a window with requested size.
This method is based on the convolution of a scaled window with the signal.
The signal is prepared by introducing reflected copies of the signal
(with the window size) in both ends so that transient parts are minimized
in the begining and end part of the output signal.
input:
x: the input signal
window_len: the dimension of the smoothing window; should be an odd integer
window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
flat window will produce a moving average smoothing.
output:
the smoothed signal
example:
t=linspace(-2,2,0.1)
x=sin(t)+randn(len(t))*0.1
y=smooth(x)
see also:
numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve
scipy.signal.lfilter
TODO: the window parameter could be the window itself if an array instead of a string
"""
from numpy.core.numeric import ones
import numpy
x = numpy.array(x)
if x.ndim != 1:
raise ValueError, "smooth only accepts 1 dimension arrays."
if x.size < window_len:
#if len(x) < window_len:
raise ValueError, "Input vector needs to be bigger than window size."
if window_len<3:
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
s=numpy.r_[2*x[0]-x[window_len:1:-1],x,2*x[-1]-x[-1:-window_len:-1]]
#print(len(s))
if window == 'flat': #moving average
w=ones(window_len,'d')
else:
w=eval('numpy.'+window+'(window_len)')
y=numpy.convolve(w/w.sum(),s,mode='same')
return y[window_len-1:-window_len+1]
def lpc(self, x0 = None, X=None, weights = None):
''' Will return the scaled curve if self._lpcParameters['scaled'] = True, to return the curve on the same scale as the originally input data, call getCurve with unscale = True
Arguments
---------
x0 : 2-dim numpy.array containing #rows equal to number of explicitly defined start points
and #columns equal to dimension of the feature space points; seeds for the start points algorithm
X : 2-dim numpy.array containing #rows equal to number of data points and #columns equal to dimension
of the feature space points
weights : see self._followxSingleDirection docs
'''
if X is None:
if self.Xi is None:
raise ValueError, 'Data points have not yet been set in this LPCImpl instance. Either supply as X parameter to this function or call setDataPoints'
else:
self.setDataPoints(X)
N = self.Xi.shape[0]
if self._lpcParameters['binary'] or weights is None:
self._weights = ones(N, dtype = float)
else:
self._weights = array(weights, dtype = float)
if self._weights.shape != (N):
raise ValueError, 'Weights must be one dimensional of vector of weights with size equal to the sample size'
self._selectStartPoints(x0)
#TODO add initialization relevant for other branches
m = self.x0.shape[0] #how many starting points were actually generated
way = self._lpcParameters['way']
self._curve = [self._followx(self.x0[j], way = way, weights = self._weights) for j in range(m)]
return self._curve
def gmmEM(data, K, it,show=False,usekmeans=True):
#data += finfo(float128).eps*100
centroid = kmeans2(data, K)[0] if usekmeans else ((max(data) - min(data))*random_sample((K,data.shape[1])) + min(data))
N = data.shape[0]
gmm = GaussianMM(centroid)
if show: gmm.draw(data)
while it > 0:
print it," iterations remaining"
it = it - 1
# e-step
gausses = zeros((K, N), dtype = data.dtype)
for k in range(0, K):
gausses[k] = gmm.c[k]*mulnormpdf(data, gmm.mean[k], gmm.covm[k])
sums = sum(gausses, axis=0)
if count_nonzero(sums) != sums.size:
raise "Divide by Zero"
gausses /= sums
# m step
sg = sum(gausses, axis=1)
if count_nonzero(sg) != sg.size:
raise "Divide by Zero"
gmm.c = ones(sg.shape) / N * sg
for k in range(0, K):
gmm.mean[k] = sum(data * gausses[k].reshape((-1,1)), axis=0) / sg[k]
d = data - gmm.mean[k]
d1 = d.transpose()*gausses[k]
gmm.covm[k]=dot(d1,d)/sg[k]
if show: gmm.draw(data)
return gmm
def vander(x, N=None):
"""
Generate a Van der Monde matrix.
The columns of the output matrix are decreasing powers of the input
vector. Specifically, the i-th output column is the input vector to
the power of ``N - i - 1``. Such a matrix with a geometric progression
in each row is named Van Der Monde, or Vandermonde matrix, from
Alexandre-Theophile Vandermonde.
Parameters
----------
x : array_like
1-D input array.
N : int, optional
Order of (number of columns in) the output. If `N` is not specified,
a square array is returned (``N = len(x)``).
Returns
-------
out : ndarray
Van der Monde matrix of order `N`. The first column is ``x^(N-1)``,
the second ``x^(N-2)`` and so forth.
References
----------
.. [1] Wikipedia, "Vandermonde matrix",
http://en.wikipedia.org/wiki/Vandermonde_matrix
Examples
--------
>>> x = np.array([1, 2, 3, 5])
>>> N = 3
>>> np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> x = np.array([1, 2, 3, 5])
>>> np.vander(x)
array([[ 1, 1, 1, 1],
[ 8, 4, 2, 1],
[ 27, 9, 3, 1],
[125, 25, 5, 1]])
"""
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 vander(x, N=None):
"""
Generate a Van der Monde matrix.
The columns of the output matrix are decreasing powers of the input
vector. Specifically, the i-th output column is the input vector to
the power of ``N - i - 1``. Such a matrix with a geometric progression
in each row is named Van Der Monde, or Vandermonde matrix, from
Alexandre-Theophile Vandermonde.
Parameters
----------
x : array_like
1-D input array.
N : int, optional
Order of (number of columns in) the output. If `N` is not specified,
a square array is returned (``N = len(x)``).
Returns
-------
out : ndarray
Van der Monde matrix of order `N`. The first column is ``x^(N-1)``,
the second ``x^(N-2)`` and so forth.
References
----------
.. [1] Wikipedia, "Vandermonde matrix",
http://en.wikipedia.org/wiki/Vandermonde_matrix
Examples
--------
>>> x = np.array([1, 2, 3, 5])
>>> N = 3
>>> np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> x = np.array([1, 2, 3, 5])
>>> np.vander(x)
array([[ 1, 1, 1, 1],
[ 8, 4, 2, 1],
[ 27, 9, 3, 1],
[125, 25, 5, 1]])
"""
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 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 hamming(M):
"""hamming(M) returns the M-point Hamming window.
"""
if M < 1:
return array([])
if M == 1:
return ones(1, float)
n = arange(0, M)
return 0.54 - 0.46 * cos(2.0 * pi * n / (M - 1))
def readFile(self, filePath, fileSize):
'''
file format
---------------------------
index1 xx.xxx yy.yyy
index2 xx.xxx yy.yyy
index3 xx.xxx yy.yyy
---------------------------
we eliminate the 'index' and extract two values into a set.
'''
try:
__fpath = filePath
# path of the file
__size = fileSize
# number of data items in file
# these values may subject to change depending on the data.txt format
__firstValStart = 2
__firstValEnd = 12
__secondValStart = 13
__secondValEnd = 22
from numpy import float64
# 3 columns. bias value, first value, second value
__array = ones((__size, 3), float64)
f = open(__fpath,
mode='r',
buffering=1,
encoding=None,
errors=None,
newline=None,
closefd=True)
print('reading data from file....')
for i in range(0, __size):
line = f.readline()
__firstValue = line[__firstValStart:__firstValEnd]
__secondValue = line[__secondValStart:__secondValEnd]
__array[i, 1] = __firstValue
__array[i, 2] = __secondValue
#print(__array[i,1],__array[i,2]);
print('data reading complete....')
return __array
except IOError:
pass
def tranNBO(trainMatrix,trainCategory):
numTrainDocs = len(trainMatrix)
numWords = len(trainMatrix[0])
pAbusive = sum(trainCategory)/float(numTrainDocs) #某个类发生的概率
p0Num = ones(numWords)
p1Num = ones(numWords) #初始样本个数为1，防止条件概率为0，影响结果
p0Denom = 2.0
p1Denom = 2.0
for i in range(numTrainDocs):
if trainCategory[i] == 1:
p1Num += trainMatrix[i]
p1Denom += sum(trainMatrix[i])
else:
p0Num += trainMatrix[i]
p0Denom += sum(trainMatrix[i])
p1Vect = log(p1Num/p1Denom) #计算类标签为1时，其它属性发生的条件概率
p0Vect = log(p0Num/p0Denom) #计算类标签为0时，其它属性发生的条件概率
return p0Vect,p1Vect,pAbusive #返回条件概率喝类标签为1的概率
def blackman(M):
"""blackman(M) returns the M-point Blackman window.
"""
if M < 1:
return array([])
if M == 1:
return ones(1, float)
n = arange(0,M)
return 0.42-0.5*cos(2.0*pi*n/(M-1)) + 0.08*cos(4.0*pi*n/(M-1))
def hamming(M):
"""hamming(M) returns the M-point Hamming window.
"""
if M < 1:
return array([])
if M == 1:
return ones(1,float)
n = arange(0,M)
return 0.54-0.46*cos(2.0*pi*n/(M-1))
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 __init__(self,
policy,
learner,
predictionAgent,
lr=array([.11]),
x0=array([25 * ones(10)]),
gamma=.995):
super(RateAgent, self).__init__(policy, predictionAgent, lr=lr, x0=x0)
self.gamma = gamma
self.learner = self.inicLearner(learner)
def readFile(self, filePath,fileSize):
'''
file format
---------------------------
index1 xx.xxx yy.yyy
index2 xx.xxx yy.yyy
index3 xx.xxx yy.yyy
---------------------------
we eliminate the 'index' and extract two values into a set.
'''
try:
__fpath=filePath; # path of the file
__size=fileSize; # number of data items in file
# these values may subject to change depending on the data.txt format
__firstValStart=2;
__firstValEnd=12;
__secondValStart=13;
__secondValEnd=22;
from numpy import float64
# 3 columns. bias value, first value, second value
__array= ones((__size,3),float64);
f=open(__fpath, mode='r', buffering=1, encoding=None, errors=None, newline=None, closefd=True);
print('reading data from file....');
for i in range(0,__size):
line= f.readline();
__firstValue= line[__firstValStart:__firstValEnd];
__secondValue=line[__secondValStart:__secondValEnd];
__array[i,1]= __firstValue
__array[i,2]= __secondValue;
#print(__array[i,1],__array[i,2]);
print('data reading complete....');
return __array;
except IOError:
pass
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 logisticRegression(trainData, trainLabels, testData, testLabels):
#adjust the data, adding the 'free parameter' to the train data
trainDataWithFreeParam = hstack((trainData.copy(), ones(trainData.shape[0])[:,newaxis]))
testDataWithFreeParam = hstack((testData.copy(), ones(testData.shape[0])[:,newaxis]))
alpha = 10
oldW = zeros(trainDataWithFreeParam.shape[1])
newW = ones(trainDataWithFreeParam.shape[1])
iteration = 0
trainDataWithFreeParamTranspose = transpose(trainDataWithFreeParam)
alphaI = alpha * identity(oldW.shape[0])
while not array_equal(oldW, newW):
if iteration == 100:
break
oldW = newW.copy()
yVect = yVector(oldW, trainDataWithFreeParam)
r = R(yVect)
firstTerm = inv(alphaI + dot(dot(trainDataWithFreeParamTranspose, r), trainDataWithFreeParam))
secondTerm = dot(trainDataWithFreeParamTranspose, (yVect-trainLabels)) + alpha * oldW
newW = oldW - dot(firstTerm, secondTerm)
iteration += 1
#see how well we did
numCorrect = 0
for x,t in izip(testDataWithFreeParam, testLabels):
if yScalar(newW, x) >= 0.5:
if t == 1:
numCorrect += 1
else:
if t == 0:
numCorrect += 1
return float(numCorrect) / float(len(testLabels))
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 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 stocGradAscent0(dataMatrix, classLabels):
"""
随机梯度上升
"""
m, n = np.shape(dataMatrix)
#固定学习率
alpha = 0.01
weights = ones(n)
for i in range(m):
#梯度上升矢量公式
h = sigmoid(sum(dataMatrix[i] * weights)) #向量
error = classLabels[i] - h #向量
weights = weights + alpha * error * dataMatrix[i]
# numpy.append(arr, values, axis=None):就是arr和values会重新组合成一个新的数组，做为返回值。
# 当axis无定义时，是横向加成，返回总是为一维数组
return weights
def problem1(data, figureDir, figureName, targetValue):
figureOutLoc = os.path.join(figureDir, '1', figureName + ".eps")
if os.path.exists(figureOutLoc):
return
if not os.path.exists(os.path.dirname(figureOutLoc)):
os.makedirs(os.path.dirname(figureOutLoc))
trainList = []
testList = []
for l in range(151):
w = doubleU(phi(data[TRAIN]), l, tListToTVector(data[TRAIN_LABELS]))
trainMSE = MSE(data[TRAIN], w, data[TRAIN_LABELS])
testMSE = MSE(data[TEST], w, data[TEST_LABELS])
trainList.append(trainMSE)
testList.append(testMSE)
trainArray = squeeze(row_stack(trainList))
testArray = squeeze(row_stack(testList))
#find the best l value on the test set
targetArray = targetValue * ones(151, dtype=numpy.float64)
targetDiffArray = testArray - targetArray
bestL = argmin(targetDiffArray)
lArray = arange(151).reshape(-1)
plt.plot(lArray, trainArray, '-', label="Train")
plt.plot(lArray, testArray, '--', label="Test")
plt.plot(lArray, targetArray, ':', label="Target")
plt.title(figureName)
plt.xlabel("lambda")
plt.ylabel("MSE")
plt.ylim(ymax = min((plt.ylim()[1], 7.0)))
#add a label showing the min value, and annotate it's lvalue
if series == 'wine':
annotateOffset = .02
else:
annotateOffset = .2
plt.annotate("Best lambda value = " + str(bestL) + " MSE = %.3f" %testList[bestL],
xy=(bestL, testArray[bestL]),
xytext=(bestL + 10, testArray[bestL] - annotateOffset),
bbox=dict(boxstyle="round", fc="0.8"),
arrowprops=dict(arrowstyle="->"))
plt.legend(loc=0)
plt.savefig(figureOutLoc)
plt.clf()
def vander(x, N=None):
"""
Generate a Van der Monde matrix.
The columns of the output matrix are decreasing powers of the input
vector. Specifically, the i-th output column is the input vector to
the power of ``N - i - 1``.
Parameters
----------
x : array_like
Input array.
N : int, optional
Order of (number of columns in) the output.
Returns
-------
out : ndarray
Van der Monde matrix of order `N`. The first column is ``x^(N-1)``,
the second ``x^(N-2)`` and so forth.
Examples
--------
>>> x = np.array([1, 2, 3, 5])
>>> N = 3
>>> np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
"""
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 vander(x, N=None):
"""
Generate a Van der Monde matrix.
The columns of the output matrix are decreasing powers of the input
vector. Specifically, the i-th output column is the input vector to
the power of ``N - i - 1``.
Parameters
----------
x : array_like
Input array.
N : int, optional
Order of (number of columns in) the output.
Returns
-------
out : ndarray
Van der Monde matrix of order `N`. The first column is ``x^(N-1)``,
the second ``x^(N-2)`` and so forth.
Examples
--------
>>> x = np.array([1, 2, 3, 5])
>>> N = 3
>>> np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
"""
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 roots(p):
""" Return the roots of the polynomial coefficients in p.
The values in the rank-1 array p are coefficients of a polynomial.
If the length of p is n+1 then the polynomial is
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError,"Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = _eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def stocGradAscent1(dataMatrix, classLabels, numIter=150):
"""
改进的随机梯度上升
"""
m, n = np.shape(dataMatrix)
weights = ones(n)
for j in range(m):
dataIndex = list(range(m))
for i in range(m):
#每次都降低alpha的大小
alpha = 4 / (1.0 + j + i) + 0.01
#随机选择样本
randIndex = int(np.random.uniform(0, len(dataIndex)))
#随机选择一个样本计算h
h = sigmoid(sum(dataMatrix[randIndex] * weights))
#计算误差
error = classLabels[randIndex] - h
#更新回归系数
weights = weights + alpha * error * dataMatrix[randIndex]
#删除已使用版本
del (dataIndex[randIndex])
return weights
def problem2(data, figureDir, dataName, l, maxNumRepetitions, minSampleSize, targetValue):
if os.path.exists(getProblem2FigureLoc(figureDir, dataName, l, maxNumRepetitions)):
#this implies that all figures before it have been created already, so we don't need to repeat them
return
MSEValues = [[] for x in xrange(minSampleSize, len(data[TRAIN]) + 1)]
sampleSizeValueList = range(minSampleSize, len(data[TRAIN]) + 1, 1)
sampleSizeValueArray = array(sampleSizeValueList)
targetArray = targetValue * ones(len(sampleSizeValueList), dtype=numpy.float64)
for repeatNum in range(1, maxNumRepetitions+1):
#randomly choose ordering of the samples for this run
#make the range of indexes, then shuffle them into a random order
randomlySortedIndexes = range(len(data[TRAIN]))
shuffle(randomlySortedIndexes)
#start with a sample size of one, go to the total training set
for sampleSizeIndex, sampleSize in enumerate(sampleSizeValueList):
curSampleIndexesList = randomlySortedIndexes[:sampleSize]
curTrainSample = selectSample(data[TRAIN], curSampleIndexesList)
curTrainLabelSample = selectSample(data[TRAIN_LABELS], curSampleIndexesList)
w = doubleU(phi(curTrainSample), l, tListToTVector(curTrainLabelSample))
curSampleMSE = MSE(data[TEST], w, data[TEST_LABELS])
MSEValues[sampleSizeIndex].append(squeeze(curSampleMSE))
#have a sample size of 0 is meaningless
curRepeatMeanMSEValues = array([mean(array(x, dtype=numpy.float64)) for x in MSEValues])
plt.plot(sampleSizeValueArray, curRepeatMeanMSEValues, '-', label="Learning curve")
plt.plot(sampleSizeValueArray, targetArray, '--', label="Target MSE")
plt.title("lamba = " + str(l) + " - " + str(repeatNum) + " repetitions")
plt.xlabel("Sample Size - minimum " + str(minSampleSize))
plt.ylabel("MSE on Full Test Set")
plt.xlim(xmin=targetValue - .5)
plt.legend(loc=0)
plt.savefig(getProblem2FigureLoc(figureDir, dataName, l, repeatNum))
plt.clf()
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 nonzero(a != 0)
def roots(self, p, nsing):
"""
Return nsing roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Compute polynomial values.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
"""
import numpy.core.numeric as NX
# If input is scalar, this makes it an array
p = np.core.atleast_1d(p)
if len(p.shape) != 1:
raise ValueError("Input must be a rank-1 array.")
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = np.diag(NX.ones((N - 2, ), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
#power = Power(A)
#for i in range(nsing):
# power.iterate(np.random.rand(len(A)))
roots = scipy.sparse.linalg.eigs(A, k=nsing)[0]
#roots = power.u
else:
roots = NX.array([])
return roots
def vander(x, N=None):
"""
Generate a Van der Monde matrix.
The columns of the output matrix are decreasing powers of the input
vector. Specifically, the `i`-th output column is the input vector
raised element-wise to the power of ``N - i - 1``. Such a matrix with
a geometric progression in each row is named for Alexandre-Theophile
Vandermonde.
Parameters
----------
x : array_like
1-D input array.
N : int, optional
Order of (number of columns in) the output. If `N` is not specified,
a square array is returned (``N = len(x)``).
Returns
-------
out : ndarray
Van der Monde matrix of order `N`. The first column is ``x^(N-1)``,
the second ``x^(N-2)`` and so forth.
Examples
--------
>>> x = np.array([1, 2, 3, 5])
>>> N = 3
>>> np.vander(x, N)
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> np.column_stack([x**(N-1-i) for i in range(N)])
array([[ 1, 1, 1],
[ 4, 2, 1],
[ 9, 3, 1],
[25, 5, 1]])
>>> x = np.array([1, 2, 3, 5])
>>> np.vander(x)
array([[ 1, 1, 1, 1],
[ 8, 4, 2, 1],
[ 27, 9, 3, 1],
[125, 25, 5, 1]])
The determinant of a square Vandermonde matrix is the product
of the differences between the values of the input vector:
>>> np.linalg.det(np.vander(x))
48.000000000000043
>>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)
48
"""
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 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 roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Evaluate a polynomial at a point.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError("Input must be a rank-1 array.")
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N - 2, ), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def masked_all_like(arr):
"""Returns an empty masked array of the same shape and dtype as the array `a`,
where all the data are masked."""
a = masked_array(numeric.empty_like(arr),
mask=numeric.ones(arr.shape, bool_))
return a
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 roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like of shape(M,)
Rank-1 array of polynomial co-efficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError:
When `p` cannot be converted to a rank-1 array.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> print np.roots(coeff)
[-0.3125+0.46351241j -0.3125-0.46351241j]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError, "Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1]) + 1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N - 2, ), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def __train__(self, data, labels):
o=ones((data.shape[0],1))
h=hstack((data, o))
pseudoX=pinv(h)
self.w=dot(pseudoX, labels.reshape((-1,1)))
def __init__(self, fm_train, N, max):
self.sigma = IntegerRange(1, max+1)
A = []
B = []
#Fair transition matrix
A = ones([37,37])/(37*1.0)
# print A
# Not fair transition matrix
# for i in range(N):
# transition = []
# for j in range(N):
# if(i == j):
# transition.append(1.0/10000000)
# else:
# transition.append(1.0/(N-1))
# A.append(transition)
# now data are divided in order to obtain a starting emission values for each state.
# number of partition basing on the number of states
#
# npartition = int(len(fm_train)/N)
#
#
# # for the first N-1 states
# for i in range(N-1):
# submatrix = fm_train[i*npartition:((1+i)*npartition)-1]
# occurrences = Counter(submatrix)
# emission = [0.0]*(max)
#
# for key in occurrences.keys():
# emission[key-1] = occurrences[key-1]
#
#
# emission = array(emission) / (sum(emission))
#
# # The matrix is too sparse so an adjustement is needed: all value equal to 0 will be set to 0.0001
# # and the normal value will be adjusted in order to have th e sum of emission equal to 1!
#
# numberofzeros = list(emission).count(0)
# adjvalue = (numberofzeros * 0.0001) / (emission != 0).sum()
#
# for i in range(0,len(emission)):
# if emission[i] == 0:
# emission[i] = 0.0001
# else:
# emission[i] -= adjvalue
#
#
#
# B.append(list(emission))
#
# # the last state is computed apart because it can have different number of values!
# submatrix = fm_train[N-1*npartition:len(fm_train)-1]
# occurrences = Counter(submatrix)
# emission = [0.0]*(max)
#
# print occurrences
#
# for key in occurrences.keys():
# emission[key-1] = occurrences[key-1]
#
#
# emission = array(emission) / (sum(emission))
#
# # The matrix is too sparse so an adjustement is needed: all value equal to 0 will be set to 0.0001
# # and the normal value will be adjusted in order to have th e sum of emission equal to 1!
#
# numberofzeros = list(emission).count(0)
# adjvalue = numberofzeros * 0.0001 / (emission != 0).sum()
#
# for i in range(0,len(emission)):
# if emission[i] == 0:
# emission[i] = 0.0001
# else:
# emission[i] -= adjvalue
#
# B.append(list(emission))
# The emission distribution is computed basing on the output range, each state has singl range value where the probability
# is equal and the other values have 0.0001 prob percentage
B = []
partition = int(max/N)
# get occurrences of each value
occurrences_count = Counter(fm_train)
occurrences_prob = zeros(264)
for i in occurrences_count.keys():
occurrences_prob[i] = occurrences_count[i]
# the first state is an outlier and it is treated separately
emission = zeros(max)
emission[1:68] = occurrences_prob[1:68]/sum(occurrences_prob[1:68])
B.append(emission)
for i in range(18,53):
emission = ones(max) * 0.0001
emission[i*partition:(i+1)*partition] = (occurrences_prob[i*partition:(i+1)*partition]/sum(occurrences_prob[i*partition:(i+1)*partition])) - (((max - partition)*0.0001)/partition)
print sum(emission)
B.append(emission)
# last state is an outlier too
emission = zeros(max)
emission[209:264] = occurrences_prob[209:264]/sum(occurrences_prob[209:264])
B.append(emission)
# # Adjusting the NaN values of the emission matrix
# for i in range(N):
# if(any(numpy.isnan(B[i]))):
# B[i]= list(ones(max) / max)
#
# adj_prob = (1-((max-partition)*0.0001))/partition
# for i in range(N):
# emission = ones(max)*0.0001
# emission[i*partition:(i+1)*partition] = adj_prob
# print sum(emission)
# B.append(emission)
print "B = %s" % B
pi = [1.0/37]*37
self.m = HMMFromMatrices(self.sigma, DiscreteDistribution(self.sigma), A, list(B), pi)
train = EmissionSequence(self.sigma, fm_train)
trainstart = time.time()
self.m.baumWelch(train)
trainend = time.time()
print 'HMM train time'
print trainend - trainstart
def average(a, axis=None, weights=None, returned=False):
"""Average the array over the given axis. If the axis is None,
average over all dimensions of the array. Equivalent to
a.mean(axis) and to
a.sum(axis) / size(a, axis)
If weights are given, result is:
sum(a * weights,axis) / sum(weights,axis),
where the weights must have a's shape or be 1D with length the
size of a in the given axis. Integer weights are converted to
Float. Not specifying weights is equivalent to specifying
weights that are all 1.
If 'returned' is True, return a tuple: the result and the sum of
the weights or count of values. The shape of these two results
will be the same.
Raises ZeroDivisionError if appropriate. (The version in MA does
not -- it returns masked values).
"""
if axis is None:
a = array(a).ravel()
if weights is None:
n = add.reduce(a)
d = len(a) * 1.0
else:
w = array(weights).ravel() * 1.0
n = add.reduce(multiply(a, w))
d = add.reduce(w)
else:
a = array(a)
ash = a.shape
if ash == ():
a.shape = (1, )
if weights is None:
n = add.reduce(a, axis)
d = ash[axis] * 1.0
if returned:
d = ones(n.shape) * d
else:
w = array(weights, copy=False) * 1.0
wsh = w.shape
if wsh == ():
wsh = (1, )
if wsh == ash:
n = add.reduce(a * w, axis)
d = add.reduce(w, axis)
elif wsh == (ash[axis], ):
ni = ash[axis]
r = [newaxis] * ni
r[axis] = slice(None, None, 1)
w1 = eval("w[" + repr(tuple(r)) + "]*ones(ash, float)")
n = add.reduce(a * w1, axis)
d = add.reduce(w1, axis)
else:
raise ValueError, 'averaging weights have wrong shape'
if not isinstance(d, ndarray):
if d == 0.0:
raise ZeroDivisionError, 'zero denominator in average()'
if returned:
return n / d, d
else:
return n / d
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 masked_all(shape, dtype=float_):
"""Returns an empty masked array of the given shape and dtype,
where all the data are masked."""
a = masked_array(numeric.empty(shape, dtype),
mask=numeric.ones(shape, bool_))
return a
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by::
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like
Rank-1 array of polynomial coefficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError :
When `p` cannot be converted to a rank-1 array.
See also
--------
poly : Find the coefficients of a polynomial with a given sequence
of roots.
polyval : Evaluate a polynomial at a point.
polyfit : Least squares polynomial fit.
poly1d : A one-dimensional polynomial class.
Notes
-----
The algorithm relies on computing the eigenvalues of the
companion matrix [1]_.
References
----------
.. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:
Cambridge University Press, 1999, pp. 146-7.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> np.roots(coeff)
array([-0.3125+0.46351241j, -0.3125-0.46351241j])
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError("Input must be a rank-1 array.")
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def roots(p):
"""
Return the roots of a polynomial with coefficients given in p.
The values in the rank-1 array `p` are coefficients of a polynomial.
If the length of `p` is n+1 then the polynomial is described by
p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
Parameters
----------
p : array_like of shape(M,)
Rank-1 array of polynomial co-efficients.
Returns
-------
out : ndarray
An array containing the complex roots of the polynomial.
Raises
------
ValueError:
When `p` cannot be converted to a rank-1 array.
Examples
--------
>>> coeff = [3.2, 2, 1]
>>> print np.roots(coeff)
[-0.3125+0.46351241j -0.3125-0.46351241j]
"""
# If input is scalar, this makes it an array
p = atleast_1d(p)
if len(p.shape) != 1:
raise ValueError,"Input must be a rank-1 array."
# find non-zero array entries
non_zero = NX.nonzero(NX.ravel(p))[0]
# Return an empty array if polynomial is all zeros
if len(non_zero) == 0:
return NX.array([])
# find the number of trailing zeros -- this is the number of roots at 0.
trailing_zeros = len(p) - non_zero[-1] - 1
# strip leading and trailing zeros
p = p[int(non_zero[0]):int(non_zero[-1])+1]
# casting: if incoming array isn't floating point, make it floating point.
if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
p = p.astype(float)
N = len(p)
if N > 1:
# build companion matrix and find its eigenvalues (the roots)
A = diag(NX.ones((N-2,), p.dtype), -1)
A[0, :] = -p[1:] / p[0]
roots = eigvals(A)
else:
roots = NX.array([])
# tack any zeros onto the back of the array
roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
return roots
def polyint(p, m=1, k=None):
"""
Return an antiderivative (indefinite integral) of a polynomial.
The returned order `m` antiderivative `P` of polynomial `p` satisfies
:math:`\\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`
integration constants `k`. The constants determine the low-order
polynomial part
.. math:: \\frac{k_{m-1}}{0!} x^0 + \\ldots + \\frac{k_0}{(m-1)!}x^{m-1}
of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.
Parameters
----------
p : {array_like, poly1d}
Polynomial to differentiate.
A sequence is interpreted as polynomial coefficients, see `poly1d`.
m : int, optional
Order of the antiderivative. (Default: 1)
k : {None, list of `m` scalars, scalar}, optional
Integration constants. They are given in the order of integration:
those corresponding to highest-order terms come first.
If ``None`` (default), all constants are assumed to be zero.
If `m = 1`, a single scalar can be given instead of a list.
See Also
--------
polyder : derivative of a polynomial
poly1d.integ : equivalent method
Examples
--------
The defining property of the antiderivative:
>>> p = np.poly1d([1,1,1])
>>> P = np.polyint(p)
>>> P
poly1d([ 0.33333333, 0.5 , 1. , 0. ])
>>> np.polyder(P) == p
True
The integration constants default to zero, but can be specified:
>>> P = np.polyint(p, 3)
>>> P(0)
0.0
>>> np.polyder(P)(0)
0.0
>>> np.polyder(P, 2)(0)
0.0
>>> P = np.polyint(p, 3, k=[6,5,3])
>>> P
poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ])
Note that 3 = 6 / 2!, and that the constants are given in the order of
integrations. Constant of the highest-order polynomial term comes first:
>>> np.polyder(P, 2)(0)
6.0
>>> np.polyder(P, 1)(0)
5.0
>>> P(0)
3.0
"""
m = int(m)
if m < 0:
raise ValueError("Order of integral must be positive (see polyder)")
if k is None:
k = NX.zeros(m, float)
k = atleast_1d(k)
if len(k) == 1 and m > 1:
k = k[0]*NX.ones(m, float)
if len(k) < m:
raise ValueError(
"k must be a scalar or a rank-1 array of length 1 or >m.")
truepoly = isinstance(p, poly1d)
p = NX.asarray(p)
if m == 0:
if truepoly:
return poly1d(p)
return p
else:
# Note: this must work also with object and integer arrays
y = NX.concatenate((p.__truediv__(NX.arange(len(p), 0, -1)), [k[0]]))
val = polyint(y, m - 1, k=k[1:])
if truepoly:
return poly1d(val)
return val
import sys
fr=open('D:\eclipse_workspace\Classify\data\data.txt')
macList=['c0:38:96:25:5b:c3','e0:05:c5:ba:80:40','b0:d5:9d:46:a3:9b','42:a5:89:51:c7:dd']
X=empty((4,60),numpy.int8)
for line in fr:
parts=line.split(',')
try:
poi=macList.index(parts[2])
print('poi',poi)
if poi!='-1':
print('try parts[2]:',parts[2])
lie=int(parts[-1].strip())-1
X[poi,lie] = parts[1]
except :
pass
#print('haha',parts[2])
else:
print('no error')
print("final:",type(list),type(1),type(macList))
print(X)
w=ones((4,1))
b=1
print(transpose(w))
z=dot(transpose(w),X)+1
y1=zeros((30,1))
y2=ones((30,1))
y=row_stack((y1,y2))
print(y)
#plt.plot(list)
#plt.show()
def polyint(p, m=1, k=None):
"""
Return an antiderivative (indefinite integral) of a polynomial.
The returned order `m` antiderivative `P` of polynomial `p` satisfies
:math:`\\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`
integration constants `k`. The constants determine the low-order
polynomial part
.. math:: \\frac{k_{m-1}}{0!} x^0 + \\ldots + \\frac{k_0}{(m-1)!}x^{m-1}
of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.
Parameters
----------
p : array_like or poly1d
Polynomial to differentiate.
A sequence is interpreted as polynomial coefficients, see `poly1d`.
m : int, optional
Order of the antiderivative. (Default: 1)
k : list of `m` scalars or scalar, optional
Integration constants. They are given in the order of integration:
those corresponding to highest-order terms come first.
If ``None`` (default), all constants are assumed to be zero.
If `m = 1`, a single scalar can be given instead of a list.
See Also
--------
polyder : derivative of a polynomial
poly1d.integ : equivalent method
Examples
--------
The defining property of the antiderivative:
>>> p = np.poly1d([1,1,1])
>>> P = np.polyint(p)
>>> P
poly1d([ 0.33333333, 0.5 , 1. , 0. ])
>>> np.polyder(P) == p
True
The integration constants default to zero, but can be specified:
>>> P = np.polyint(p, 3)
>>> P(0)
0.0
>>> np.polyder(P)(0)
0.0
>>> np.polyder(P, 2)(0)
0.0
>>> P = np.polyint(p, 3, k=[6,5,3])
>>> P
poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ])
Note that 3 = 6 / 2!, and that the constants are given in the order of
integrations. Constant of the highest-order polynomial term comes first:
>>> np.polyder(P, 2)(0)
6.0
>>> np.polyder(P, 1)(0)
5.0
>>> P(0)
3.0
"""
m = int(m)
if m < 0:
raise ValueError("Order of integral must be positive (see polyder)")
if k is None:
k = NX.zeros(m, float)
k = atleast_1d(k)
if len(k) == 1 and m > 1:
k = k[0] * NX.ones(m, float)
if len(k) < m:
raise ValueError(
"k must be a scalar or a rank-1 array of length 1 or >m.")
truepoly = isinstance(p, poly1d)
p = NX.asarray(p)
if m == 0:
if truepoly:
return poly1d(p)
return p
else:
# Note: this must work also with object and integer arrays
y = NX.concatenate((p.__truediv__(NX.arange(len(p), 0, -1)), [k[0]]))
val = polyint(y, m - 1, k=k[1:])
if truepoly:
return poly1d(val)
return val
def _followxSingleDirection( self,
x,
direction = Direction.FORWARD,
forward_curve = None,
last_eigenvector = None,
weights = 1.):
'''Generates a partial lpc curve dictionary from the start point, x.
Arguments
---------
x : 1-dim, length m, numpy.array of floats, start point for the algorithm when m is dimension of feature space
direction : bool, proceeds in Direction.FORWARD or Direction.BACKWARD from this point (just sets sign for first eigenvalue)
forward_curve : dictionary as returned by this function, is used to detect crossing of the curve under construction with a
previously constructed curve
last_eigenvector : 1-dim, length m, numpy.array of floats, a unit vector that defines the initial direction, relative to
which the first eigenvector is biased and initial cos_neu_neu is calculated
weights : 1-dim, length n numpy.array of observation weights (can also be used to exclude
individual observations from the computation by setting their weight to zero.),
where n is the number of feature points
'''
x0 = copy(x)
N = self.Xi.shape[0]
d = self.Xi.shape[1]
it = self._lpcParameters['it']
h = array(self._lpcParameters['h'])
t0 = self._lpcParameters['t0']
rho0 = self._lpcParameters['rho0']
save_xd = empty((it,d))
eigen_vecd = empty((it,d))
c0 = ones(it)
cos_alt_neu = ones(it)
cos_neu_neu = ones(it)
lamb = empty(it) #NOTE this is named 'lambda' in the original R code
rho = zeros(it)
high_rho_points = empty((0,d))
count_points = 0
for i in range(it):
kernel_weights = self._kernd(self.Xi, x0, c0[i]*h) * weights
mu_x = average(self.Xi, axis = 0, weights = kernel_weights)
sum_weights = sum(kernel_weights)
mean_sub = self.Xi - mu_x
cov_x = dot( dot(transpose(mean_sub), numpy.diag(kernel_weights)), mean_sub) / sum_weights
#assert (abs(cov_x.transpose() - cov_x)/abs(cov_x.transpose() + cov_x) < 1e-6).all(), 'Covariance matrix not symmetric, \n cov_x = {0}, mean_sub = {1}'.format(cov_x, mean_sub)
save_xd[i] = mu_x #save first point of the branch
count_points += 1
#calculate path length
if i==0:
lamb[0] = 0
else:
lamb[i] = lamb[i-1] + sqrt(sum((mu_x - save_xd[i-1])**2))
#calculate eigenvalues/vectors
#(sorted_eigen_cov is a list of tuples containing eigenvalue and associated eigenvector, sorted descending by eigenvalue)
eigen_cov = eigh(cov_x)
sorted_eigen_cov = zip(eigen_cov[0],map(ravel,vsplit(eigen_cov[1].transpose(),len(eigen_cov[1]))))
sorted_eigen_cov.sort(key = lambda elt: elt[0], reverse = True)
eigen_norm = sqrt(sum(sorted_eigen_cov[0][1]**2))
eigen_vecd[i] = direction * sorted_eigen_cov[0][1] / eigen_norm #Unit eigenvector corresponding to largest eigenvalue
#rho parameters
rho[i] = sorted_eigen_cov[1][0] / sorted_eigen_cov[0][0] #Ratio of two largest eigenvalues
if i != 0 and rho[i] > rho0 and rho[i-1] <= rho0:
high_rho_points = vstack((high_rho_points, x0))
#angle between successive eigenvectors
if i==0 and last_eigenvector is not None:
cos_alt_neu[i] = direction * dot(last_eigenvector, eigen_vecd[i])
if i > 0:
cos_alt_neu[i] = dot(eigen_vecd[i], eigen_vecd[i-1])
#signum flipping
if cos_alt_neu[i] < 0:
eigen_vecd[i] = -eigen_vecd[i]
cos_neu_neu[i] = -cos_alt_neu[i]
else:
cos_neu_neu[i] = cos_alt_neu[i]
#angle penalization
pen = self._lpcParameters['pen']
if pen > 0:
if i == 0 and last_eigenvector is not None:
a = abs(cos_alt_neu[i])**pen
eigen_vecd[i] = a * eigen_vecd[i] + (1-a) * last_eigenvector
if i > 0:
a = abs(cos_alt_neu[i])**pen
eigen_vecd[i] = a * eigen_vecd[i] + (1-a) * eigen_vecd[i-1]
#check curve termination criteria
if i not in (0, it-1):
#crossing
cross = self._lpcParameters['cross']
if forward_curve is None:
full_curve_points = save_xd[0:i+1]
else:
full_curve_points = vstack((forward_curve['save_xd'],save_xd[0:i+1])) #inefficient, initialize then append?
if not cross:
prox = where(ravel(cdist(full_curve_points,[mu_x])) <= mean(h))[0]
if len(prox) != max(prox) - min(prox) + 1:
break
#convergence
convergence_at = self._lpcParameters['convergence_at']
conv_ratio = abs(lamb[i] - lamb[i-1]) / (2 * (lamb[i] + lamb[i-1]))
if conv_ratio < convergence_at:
break
#boundary
boundary = self._lpcParameters['boundary']
if conv_ratio < boundary:
c0[i+1] = 0.995 * c0[i]
else:
c0[i+1] = min(1.01*c0[i], 1)
#step along in direction eigen_vecd[i]
x0 = mu_x + t0 * eigen_vecd[i]
#trim output in the case where convergence occurs before 'it' iterations
curve = { 'save_xd': save_xd[0:count_points],
'eigen_vecd': eigen_vecd[0:count_points],
'cos_neu_neu': cos_neu_neu[0:count_points],
'rho': rho[0:count_points],
'high_rho_points': high_rho_points,
'lamb': lamb[0:count_points],
'c0': c0[0:count_points]
}
return curve
