def setdata(self, X, V):
A = self.bialtprodeye(2*self.F.J_coords)
"""Note: p, q <= min(n,m)"""
self.data.Brand = 2*(random((A.shape[0],self.data.p))-0.5)
self.data.Crand = 2*(random((A.shape[1],self.data.q))-0.5)
self.data.B = zeros((A.shape[0],self.data.p), Float)
self.data.C = zeros((A.shape[1],self.data.q), Float)
self.data.D = zeros((self.data.q,self.data.p), Float)
U, S, Vh = linalg.svd(A)
self.data.b = U[:,-1:]
self.data.c = num_transpose(Vh)[:,-1:]
if self.update:
self.data.B[:,1] = self.data.b
self.data.C[:,1] = self.data.c
U2, S2, Vh2 = linalg.svd(c_[r_[A, transpose(self.data.C[:,1])], r_[self.data.B[:,1], [[0]]]])
self.data.B[:,2] = U2[0:A.shape[0],-1:]
self.data.C[:,2] = num_transpose(Vh2)[0:A.shape[1],-1:]
self.data.D[0,1] = U2[A.shape[0],-1]
self.data.D[1,0] = num_transpose(Vh2)[A.shape[1],-1]
else:
self.data.B = self.data.Brand
self.data.C = self.data.Crand
def binitbinsfix(binsleft, binsright, x, y): #give bins for binning
nbin = len(binsleft)
xbin = N.zeros(len(binsleft), 'f')
ybin = N.zeros(len(binsleft), 'f')
ybinerr = N.zeros(len(binsleft), 'f')
y = N.take(y, N.argsort(x)) #sort y according to x rankings
x = N.take(x, N.argsort(x))
j = -1
for i in range(len(xbin)):
xmin = binsleft[i]
xmax = binsright[i]
yb = []
for j in range(len(x)):
if x[j] > xmin:
yb.append(y[j])
if x[j] > xmax:
yb = N.array(yb, 'f')
xbin[i] = 0.5 * (xmin + xmax)
try:
ybin[i] = pylab.median(yb)
ybinerr[i] = pylab.std(yb) / N.sqrt(1. * len(yb))
except ZeroDivisionError:
print "warning: ZeroDivision error in binitbinsfix"
ybin[i] = 0.
ybinerr[i] = 0.
break
return xbin, ybin, ybinerr
def binitbins(xmin, xmax, nbin, x, y): #use equally spaced bins
dx = float((xmax - xmin) / (nbin))
xbin = N.arange(xmin, (xmax), dx) + dx / 2.
#print "within binitbins"
#print "xbin = ",xbin
#print "dx = ",dx
#print "xmax = ",xmax
#print "xmin = ",xmin
ybin = N.zeros(len(xbin), 'd')
ybinerr = N.zeros(len(xbin), 'd')
xbinnumb = N.array(len(x), 'd')
x1 = N.compress((x >= xmin) & (x <= xmax), x)
y1 = N.compress((x >= xmin) & (x <= xmax), y)
x = x1
y = y1
xbinnumb = ((x - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
j = -1
for i in range(len(xbin)):
ydata = N.compress(abs(xbinnumb - float(i)) < .5, y)
try:
ybin[i] = N.average(ydata)
#ybin[i]=pylab.median(ydata)
ybinerr[i] = pylab.std(ydata) / N.sqrt(float(len(ydata)))
except ZeroDivisionError:
ybin[i] = 0.
ybinerr[i] = 0.
return xbin, ybin, ybinerr
def horizontalhist(x, xmin, xmax, nbin): #give bins for binning
#nbin=len(bins)
xbin = N.zeros(nbin, 'f')
ybin = N.zeros(nbin, 'f')
ybinerr = N.zeros(nbin, 'f')
dbin = (xmax - xmin) / (1. * nbin)
bins = N.arange(xmin, (xmax + dbin), dbin)
x = N.take(x, N.argsort(x))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((x - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
#print "from within horizontal hist"
#print "bins = ",bins
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
xbin[i] = xmin
yb = 0.
for j in range(len(x)):
if (x[j] > xmin) & (x[j] <= xmax):
yb = yb + 1.
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
#print i,len(xbin),xbin[i],xmin,xmax,ybin[i],bins[i]
xbin[(len(xbin) - 1)] = xbin[(len(xbin) - 2)] + dbin
#xbin=bins
#print "from w/in horizontal hist, ybin = ",ybin
return xbin, ybin, ybinerr
def verticalhist(y, ymin, ymax, nbin): #give bins for binning
#nbin=len(bins)
xbin = N.zeros(nbin, 'f')
ybin = N.zeros(nbin, 'f')
ybinerr = N.zeros(nbin, 'f')
dbin = (ymax - ymin) / (1. * nbin)
bins = N.arange(ymin, (ymax + dbin), dbin)
y = N.take(y, N.argsort(y))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((y - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
yb = 0.
for j in range(len(y)):
if y[j] > xmin:
yb = yb + 1.
if y[j] > xmax:
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
#xbin[i]=0.5*(xmin+xmax)
xbin[i] = xmax
break
drawhist(ybin, xbin)
def scipyhist2(bins, y): #give bins for binning
nbin = len(bins)
xbin = N.zeros(len(bins), 'f')
ybin = N.zeros(len(bins), 'f')
ybinerr = N.zeros(len(bins), 'f')
y = N.take(y, N.argsort(y))
xmin = min(bins)
xmax = max(bins)
xbinnumb = ((y - xmin) * nbin / (xmax - xmin)
) #calculate x bin number for each point
for i in range(len(xbin) - 1):
xmin = bins[i]
xmax = bins[i + 1]
yb = 0.
for j in range(len(y)):
if y[j] > xmin:
yb = yb + 1.
if y[j] > xmax:
ybin[i] = yb
ybinerr[i] = N.sqrt(yb)
xbin[i] = 0.5 * (xmin + xmax)
break
return xbin, ybin, ybinerr
def load_svd(sfile, ufile, vfile):
"""loads dense svd files as output by svdlibc"""
n_s = int(sfile.readline())
S = na.zeros((n_s, n_s), type="Float32") #store S as a column vector
for i in range(n_s):
S[i,i] = float(sfile.readline())
assert sfile.readline() == ''
rows, columns = [int(a) for a in ufile.readline().split()]
U = na.zeros((rows, columns), type="Float32")
row = 0
for line in ufile:
col = 0
for n in line.split():
U[row, col] = float(n)
col += 1
row += 1
rows, columns = [int(a) for a in vfile.readline().split()]
V = na.zeros((rows, columns), type="Float32")
row = 0
for line in vfile:
col = 0
for n in line.split():
V[row, col] = float(n)
col += 1
row += 1
return U, S, V
def histOutline(dataIn, binsIn=None):
"""
Make a histogram that can be plotted with plot() so that
the histogram just has the outline rather than bars as it
usually does.
"""
if (binsIn == None):
(en, eb) = pylab.matplotlib.mlab.hist(dataIn, bins=50, normed=True)
binsIn = eb
else:
(en, eb) = pylab.matplotlib.mlab.hist(dataIn, bins=binsIn)
stepSize = binsIn[1] - binsIn[0]
bins = numarray.zeros(len(eb)*2 + 2, type=numarray.Float)
data = numarray.zeros(len(eb)*2 + 2, type=numarray.Float)
for bb in range(len(binsIn)):
bins[2*bb + 1] = binsIn[bb]
bins[2*bb + 2] = binsIn[bb] + stepSize
data[2*bb + 1] = en[bb]
data[2*bb + 2] = en[bb]
bins[0] = bins[1]
bins[-1] = bins[-2]
data[0] = 0
data[-1] = 0
return (bins, data)
def buildSpearmanCorrelationMatrix(traits, sc):
dim = (len(traits), sc)
matrix = numarray.zeros(dim, MA.Float64)
testMatrix = numarray.zeros(dim, MA.Float64)
def customCmp(a, b):
return cmp(a[1], b[1])
for i in range(len(traits)):
# copy strain data to a temporary list and turn it into
# (strain, expression) pairs
sd = traits[i].strainData
tempList = []
for key in sd.keys():
tempList.append((key, sd[key]))
# sort the temporary list by expression
tempList.sort(customCmp)
for j in range(len(tempList)):
# k is the strain id minus 1
# 1-based strain id -> 0-based column index
k = int(tempList[j][0]) - 1
# j is the rank of the particular strain
matrix[i,k] = j
testMatrix[i,k] = 1
return matrix, testMatrix
def gaussNodes(m, tol=10e-9):
def legendre(t, m):
p0 = 1.0
p1 = t
for k in range(1, m):
p = ((2.0 * k + 1.0) * t * p1 - k * p0) / (1.0 + k)
p0 = p1
p1 = p
dp = m * (p0 - t * p1) / (1.0 - t**2)
return p, dp
A = zeros((m), type=Float64)
x = zeros((m), type=Float64)
nRoots = (m + 1) / 2 # Number of non-neg. roots
for i in range(nRoots):
t = cos(pi * (i + 0.75) / (m + 0.5)) # Approx. root
for j in range(30):
p, dp = legendre(t, m) # Newton-Raphson
dt = -p / dp
t = t + dt # method
if abs(dt) < tol:
x[i] = t
x[m - i - 1] = -t
A[i] = 2.0 / (1.0 - t**2) / (dp**2) # Eq.(6.25)
A[m - i - 1] = A[i]
break
return x, A
def GenLinSystem(poly):
n=len(poly)
N=n*(n-1) /2
rhs=numarray.zeros(N )
a = numarray.zeros( ( N,N) )
c= 0
for i in range(n):
x = numarray.zeros(len(poly) )
x[i]=1
rhs[c]=(poly*x).sum()**2
for J in range(0,n-1):
for K in range(J+1,n):
k = JKtoi(J,K,n)
a[c,k] = (x[J] - x[K]) **2
c+=1
for i in range(n):
for j in range (i+1,n) :
x = numarray.zeros(n )
x[i]=1
x[j]=2
rhs[c]=(poly*x).sum()**2
for J in range(0,n-1):
for K in range(J+1,n):
k = JKtoi(J,K,n)
a[c,k] = (x[J] - x[K]) **2
c+=1
if c >= N:
break
if c >= N:
break
return a, rhs
def numhess(self, x0, ind1=None, ind2=None):
"""Computes second derivative using 2nd order centered finite difference scheme.
MAKE MORE EFFICIENT IN FUTURE (i.e. when an index is in both ind1 and ind2)
Thus, for F: R^n ---> R^m, H is an (m,n1,n2) matrix, where n1, n2 are subsets of [1,...,n]
"""
eps = 1e-3
try:
n1 = len(ind1)
except:
n1 = self.n
ind1 = range(n1)
try:
n2 = len(ind2)
except:
n2 = self.n
ind2 = range(n2)
H = zeros((self.m,n1,n2), Float)
for i in range(n1):
ei = zeros(self.n, Float)
ei[ind1[i]] = 1.0
for j in range(n2):
ej = zeros(self.n, Float)
ej[ind2[j]] = 1.0
if ind1[i] == ind2[j]:
H[:,i,j] = (-1*self.func(x0+2*eps*ei) + 16*self.func(x0+eps*ei) - 30*self.func(x0) + \
16*self.func(x0-eps*ei) - self.func(x0-2*eps*ei))/(12*eps*eps)
else:
H[:,i,j] = (self.func(x0+eps*(ei+ej)) - self.func(x0+eps*(ei-ej)) - \
self.func(x0+eps*(ej-ei)) + self.func(x0-eps*(ei+ej)))/(4*eps*eps)
return H
def hess(func, x0, ind):
"""Computes second derivative using 2nd order centered finite difference scheme."""
eps = 1e-3
n = len(x0)
m = len(ind)
H = zeros((func.m, m, m), Float)
for i in range(m):
ei = zeros(n, Float)
ei[ind[i]] = 1.0
for j in range(i, m):
ej = zeros(n, Float)
ej[ind[j]] = 1.0
if i == j:
H[:, i,
j] = (-1 * func(x0 + 2 * eps * ei) + 16 * func(x0 + eps * ei)
- 30 * func(x0) + 16 * func(x0 - eps * ei) -
func(x0 - 2 * eps * ei)) / (12 * eps * eps)
else:
H[:, i,
j] = H[:, j,
i] = (func(x0 + eps * (ei + ej)) -
func(x0 + eps * (ei - ej)) - func(x0 + eps *
(ej - ei)) +
func(x0 - eps * (ei + ej))) / (4 * eps * eps)
return H
def run_kut5(F, x, y, h):
# Runge-Kutta-Fehlberg formulas
C = array([37.0 / 378, 0.0, 250.0 / 621, 125.0 / 594, 0.0, 512.0 / 1771])
D = array([2825.0 / 27648, 0.0, 18575.0 / 48384, 13525.0 / 55296, 277.0 / 14336, 1.0 / 4])
n = len(y)
K = zeros((6, n), type=Float64)
K[0] = h * F(x, y)
K[1] = h * F(x + 1.0 / 5 * h, y + 1.0 / 5 * K[0])
K[2] = h * F(x + 3.0 / 10 * h, y + 3.0 / 40 * K[0] + 9.0 / 40 * K[1])
K[3] = h * F(x + 3.0 / 5 * h, y + 3.0 / 10 * K[0] - 9.0 / 10 * K[1] + 6.0 / 5 * K[2])
K[4] = h * F(x + h, y - 11.0 / 54 * K[0] + 5.0 / 2 * K[1] - 70.0 / 27 * K[2] + 35.0 / 27 * K[3])
K[5] = h * F(
x + 7.0 / 8 * h,
y
+ 1631.0 / 55296 * K[0]
+ 175.0 / 512 * K[1]
+ 575.0 / 13824 * K[2]
+ 44275.0 / 110592 * K[3]
+ 253.0 / 4096 * K[4],
)
# Initialize arrays {dy} and {E}
E = zeros((n), type=Float64)
dy = zeros((n), type=Float64)
# Compute solution increment {dy} and per-step error {E}
for i in range(6):
dy = dy + C[i] * K[i]
E = E + (C[i] - D[i]) * K[i]
# Compute RMS error e
e = sqrt(sum(E ** 2) / n)
return dy, e
def invwedge(q, n): ind = argmax(abs(q),0)[0] q = q/q[ind] i, j = indtoij(ind) v1 = zeros((n,1), Float) v2 = zeros((n,1), Float) v1[i,0] = 0 v2[j,0] = 0 v1[j,0] = 1 v2[i,0] = 1 for k in range(0,i): if k != j: v1[k,0] = q[ijtoind(i, k),0] for k in range(i+1,n): v1[k,0] = -1*q[ijtoind(k, i),0] for k in range(0,j): v2[k,0] = -1*q[ijtoind(j, k),0] for k in range(j+1,n): if k != i: v2[k,0] = q[ijtoind(k, j),0] return v1, v2
def load_svd(sfile, ufile, vfile):
"""loads dense svd files as output by svdlibc"""
n_s = int(sfile.readline())
S = na.zeros((n_s, n_s), type="Float32") #store S as a column vector
for i in range(n_s):
S[i, i] = float(sfile.readline())
assert sfile.readline() == ''
rows, columns = [int(a) for a in ufile.readline().split()]
U = na.zeros((rows, columns), type="Float32")
row = 0
for line in ufile:
col = 0
for n in line.split():
U[row, col] = float(n)
col += 1
row += 1
rows, columns = [int(a) for a in vfile.readline().split()]
V = na.zeros((rows, columns), type="Float32")
row = 0
for line in vfile:
col = 0
for n in line.split():
V[row, col] = float(n)
col += 1
row += 1
return U, S, V
def hist(binsIn, dataIn, normed=False):
"""
Make a histogram that can be plotted with plot() so that
the histogram just has the outline rather than bars as it
usually does.
Example Usage:
binsIn = numarray.arange(0, 1, 0.1)
angle = pylab.rand(50)
(bins, data) = histOutline(binsIn, angle)
plot(bins, data, 'k-', linewidth=2)
"""
(en, eb) = matplotlib.mlab.hist(dataIn, bins=binsIn, normed=normed)
stepSize = binsIn[1] - binsIn[0]
bins = na.zeros(len(eb) * 2 + 2, type=na.Float)
data = na.zeros(len(eb) * 2 + 2, type=na.Float)
for bb in range(len(binsIn)):
bins[2 * bb + 1] = binsIn[bb]
bins[2 * bb + 2] = binsIn[bb] + stepSize
data[2 * bb + 1] = en[bb]
data[2 * bb + 2] = en[bb]
bins[0] = bins[1]
bins[-1] = bins[-2]
data[0] = 0
data[-1] = 0
return (bins, data)
def calculate_spectrogram(input_array, framesize, hopsize, window_function = numarray.linear_algebra.mlab.hanning, keep_bands_until = 0, axis = 0): """Calculate the spectrogram.""" do_fft = lambda arr: abs(numarray.fft.real_fft(arr, axis = axis))[:keep_bands_until] keep_bands_until = keep_bands_until or int(framesize / 2) input_shape = map(None, numarray.shape(input_array)) window = window_function(framesize) if len(input_shape) > 1: window = transpose(array([list(window)] * input_shape[1])) # print "input_shape:", shape(input_array) zeros_shape = input_shape # this allows for both 1 and 2 dim inputs zeros_shape[0] = framesize / 2 input_array_plus_zeros = numarray.concatenate((numarray.zeros(zeros_shape), input_array, numarray.zeros(zeros_shape))) fft_range = range(0, len(input_array) - framesize, hopsize) fft_array = numarray.zeros(([len(fft_range)] + map(None, numarray.shape(do_fft(window)))), # do_fft(window) is used here because it gives the right shape numarray.Float32) * 1.0 # this *1.0 is necessary! for result_counter, input_counter in enumerate(fft_range): frame = window * input_array_plus_zeros[input_counter : input_counter + framesize] fft_array[result_counter] = 10 * numarray.log10(0.1 + do_fft(frame)) return fft_array
def determinant(a):
"""determinant(a) -> ||a||
*a* may be either rank-2 or rank-3. If it is rank-2, it must square.
>>> A = [[1,2,3], [3,4,5], [5,6,7]]
>>> _isClose(determinant(A), 0)
1
If *a* is rank-3, it is treated as an array of rank-2 matrices and
must be square along the last 2 axes.
>>> A = [[[1, 3], [2j, 3j]], [[2, 4], [4j, 4j]], [[3, 5], [6j, 5j]]]
>>> _isClose(determinant(A), [-3j, -8j, -15j])
1
If *a* is not square along its last two axes, a LinAlgError is raised.
>>> determinant(na.asarray(A)[...,:1])
Traceback (most recent call last):
...
LinearAlgebraError: Array (or it submatrices) must be square
"""
a = na.asarray(a)
_assertRank((2,3), a)
_assertSubmatrixSquareness(a)
stretched = (len(a.shape) == 2)
if stretched:
a = a[na.NewAxis,]
t = _commonType(a)
a = _castCopyAndTranspose(t, a, indices=(0,2,1))
n_cases, n = a.shape[:2]
if _array_kind[t] == 1:
lapack_routine = lapack_lite2.zgetrf
else:
lapack_routine = lapack_lite2.dgetrf
no_pivoting = na.arrayrange(1, n+1)
pivots = na.zeros((n,), 'l')
all_pivots = na.zeros((n_cases, n,), 'l')
sum , not_equal = na.sum, na.not_equal
stride = n * n * a.itemsize()
pivots_stride = n * pivots.itemsize()
view = a[0].view()
view_pivots = all_pivots[0]
a_i = view.copy()
for i in range(n_cases):
if i:
a_i._copyFrom(view)
outcome = lapack_routine(n, n, a_i, n, pivots, 0)
view_pivots._copyFrom(pivots)
view._copyFrom(a_i)
view._byteoffset += stride
view_pivots._byteoffset += pivots_stride
signs = na.where(sum(not_equal(all_pivots, no_pivoting), 1) % 2, -1, 1).astype(t)
for i in range(n):
signs *= a[:,i,i]
if stretched:
signs = signs[0]
return signs
def run_kut5(F, x, y, h):
# Runge-Kutta-Fehlberg formulas
C = array([37./378, 0., 250./621, 125./594, \
0., 512./1771])
D = array([2825./27648, 0., 18575./48384, \
13525./55296, 277./14336, 1./4])
n = len(y)
K = zeros((6, n), type=Float64)
K[0] = h * F(x, y)
K[1] = h * F(x + 1. / 5 * h, y + 1. / 5 * K[0])
K[2] = h * F(x + 3. / 10 * h, y + 3. / 40 * K[0] + 9. / 40 * K[1])
K[3] = h*F(x + 3./5*h, y + 3./10*K[0]- 9./10*K[1] \
+ 6./5*K[2])
K[4] = h*F(x + h, y - 11./54*K[0] + 5./2*K[1] \
- 70./27*K[2] + 35./27*K[3])
K[5] = h*F(x + 7./8*h, y + 1631./55296*K[0] \
+ 175./512*K[1] + 575./13824*K[2] \
+ 44275./110592*K[3] + 253./4096*K[4])
# Initialize arrays {dy} and {E}
E = zeros((n), type=Float64)
dy = zeros((n), type=Float64)
# Compute solution increment {dy} and per-step error {E}
for i in range(6):
dy = dy + C[i] * K[i]
E = E + (C[i] - D[i]) * K[i]
# Compute RMS error e
e = sqrt(sum(E**2) / n)
return dy, e
def invwedge(q, n):
ind = argmax(abs(q), 0)[0]
q = q / q[ind]
i, j = indtoij(ind)
v1 = zeros((n, 1), Float)
v2 = zeros((n, 1), Float)
v1[i, 0] = 0
v2[j, 0] = 0
v1[j, 0] = 1
v2[i, 0] = 1
for k in range(0, i):
if k != j:
v1[k, 0] = q[ijtoind(i, k), 0]
for k in range(i + 1, n):
v1[k, 0] = -1 * q[ijtoind(k, i), 0]
for k in range(0, j):
v2[k, 0] = -1 * q[ijtoind(j, k), 0]
for k in range(j + 1, n):
if k != i:
v2[k, 0] = q[ijtoind(k, j), 0]
return v1, v2
def cluster_vectorspace(self, vectors, trace=False):
assert len(vectors) > 0
# set the parameters to initial values
dimensions = len(vectors[0])
means = self._means
priors = self._priors
if not priors:
priors = self._priors = numarray.ones(self._num_clusters,
numarray.Float64) / self._num_clusters
covariances = self._covariance_matrices
if not covariances:
covariances = self._covariance_matrices = \
[ numarray.identity(dimensions, numarray.Float64)
for i in range(self._num_clusters) ]
# do the E and M steps until the likelihood plateaus
lastl = self._loglikelihood(vectors, priors, means, covariances)
converged = False
while not converged:
if trace: print 'iteration; loglikelihood', lastl
# E-step, calculate hidden variables, h[i,j]
h = numarray.zeros((len(vectors), self._num_clusters),
numarray.Float64)
for i in range(len(vectors)):
for j in range(self._num_clusters):
h[i,j] = priors[j] * self._gaussian(means[j],
covariances[j], vectors[i])
h[i,:] /= sum(h[i,:])
# M-step, update parameters - cvm, p, mean
for j in range(self._num_clusters):
covariance_before = covariances[j]
new_covariance = numarray.zeros((dimensions, dimensions),
numarray.Float64)
new_mean = numarray.zeros(dimensions, numarray.Float64)
sum_hj = 0.0
for i in range(len(vectors)):
delta = vectors[i] - means[j]
new_covariance += h[i,j] * \
numarray.multiply.outer(delta, delta)
sum_hj += h[i,j]
new_mean += h[i,j] * vectors[i]
covariances[j] = new_covariance / sum_hj
means[j] = new_mean / sum_hj
priors[j] = sum_hj / len(vectors)
# bias term to stop covariance matrix being singular
covariances[j] += self._bias * \
numarray.identity(dimensions, numarray.Float64)
# calculate likelihood - FIXME: may be broken
l = self._loglikelihood(vectors, priors, means, covariances)
# check for convergence
if abs(lastl - l) < self._conv_threshold:
converged = True
lastl = l
def getVW(self, A):
# V --> m, W --> n
#print self.data
MLU = linalg.lu_factor(c_[r_[A,transpose(self.data.C)], r_[self.data.B,self.data.D]])
V = linalg.lu_solve(MLU,r_[zeros((self.data.n,self.data.q), Float), eye(self.data.q)])
W = linalg.lu_solve(MLU,r_[zeros((self.data.m,self.data.p), Float), eye(self.data.p)],trans=1)
return V, W
def read_sdd(fin):
"""Read an SDD output file into memory
The SDD output file starts with 2 comment lines, followed by a line whose
contents are C{k n m}. C{k} is the user's selected value for truncation
of the matrices. C{n} is the number of rows in the original matrix, and
C{m} is the number of columns in the original matrix.
Following this line are C{k} values which represent B{D}, a diagonal matrix.
The next n*k values are in the set C{{-1, 0, 1}}, and represent the X
matrix. Following this, logically, are m*k values representng the Y matrix.
If you're confused, read the code; it's pretty simple. (although not
documented anywhere, grumble, grumble)
The odd C{if buf} statements in the read loops are necessary because
SDDPACK seems not to write any lines longer than 96 characters. Thus, each
row may or may not be on the same line.
@param fin: open sdd file
@type fin: File
@returns Tuple (X, D, Y), the three SDD matrices
"""
for i in range(2): fin.readline() #ignore comments at top of sdd file
k, n, m = fin.readline().split()
k = int(k)
n = int(n)
m = int(m)
D = na.zeros((k,k), type="Float32")
print "reading D matrix from SDD file"
for i in range(int(k)):
D[i,i] = float(fin.readline())
X = na.zeros((n, k), type="Int8") #the values are in {-1, 0, 1}
buf = fin.readline().split()
print "reading X matrix from SDD file"
for i in xrange(k):
for j in xrange(n):
if buf:
X[j,i] = int(buf.pop(0)) #do I want j, i reversed? (think so)
else:
buf = fin.readline().split()
X[j,i] = int(buf.pop(0))
assert buf == [] #verify we don't have data left over
Y = na.zeros((m, k), type="Int8") #vals in {-1, 0, 1} still
buf = fin.readline().split()
print "reading Y matrix from SDD file"
for i in xrange(k):
for j in xrange(m):
if buf:
Y[j,i] = int(buf.pop(0))
else:
buf = fin.readline().split()
Y[j,i] = int(buf.pop(0))
assert fin.readline() == '' and buf == [] #verify we done got everything
return (X, D, Y)
def approx_fprime(xk, f, *args):
f0 = apply(f, (xk, ) + args)
grad = Num.zeros((len(xk), ), 'd')
ei = Num.zeros((len(xk), ), 'd')
for k in range(len(xk)):
ei[k] = 1.0
grad[k] = (apply(f, (xk + epsilon * ei, ) + args) - f0) / epsilon
ei[k] = 0.0
return grad
def getnearestgen(self,ra1,dec1,ra2,dec2,j):#measure distances from ra1, dec1 to members in catalog ra2, dec2
sig5=N.zeros(len(ra1),'f')
sig10=N.zeros(len(ra1),'f')
for i in range(len(ra1)):
angdist=my.DA(c.z[j],h100)#kpc/arcsec
dspec=N.sqrt((ra1[i]-ra2)**2+(dec1[i]-dec2)**2)#sorted array of distances in degrees
dspecsort=N.take(dspec,N.argsort(dspec))
sig5[i]=5./(N.pi)/(dspecsort[5]*3600.*angdist/1000.)**2#convert from deg to arcsec, multiply by DA (kpc/arcsec), divide by 1000 to convert to Mpc, index 5 element b/c 0 is itself
sig10[i]=10./(N.pi)/(dspecsort[10]*3600.*angdist/1000.)**2#convert from deg to arcsec, multiply by DA (kpc/arcsec), divide by 1000 to convert to Mpc, index 5 element b/c 0 is itself
return sig5, sig10
def isovalues(isos,isow):
x = numarray.zeros(len(isos))*0. # age
y = numarray.zeros(len(isos))*0. # metallicity
z = numarray.zeros(len(isos))*0. # metallicity
for i in range(len(isos)):
feh,age = iso.scaled2real(isos[i][0],isos[i][1])
y[i] = feh
x[i] = numarray.log10(age)
z[i] = isow[i]
return x,y,z
def Kcorr(self):#calculate K_u(z) (Blanton et al 2003) for each cluster
self.kcorr=N.zeros(len(self.z),'f')
self.dL=N.zeros(len(self.z),'f')
z=N.arange(0.,1.2,.1)
#kc=N.array([0.,0.,.05,.05,.1,.15,.2,.225,.25,.3,.35,.35],'f')#Ku(z)
kc=N.array([0.,0.,.025,.05,.07,.1,.14,.16,.2,.25,.25,.3],'f')#Kg(z)
r=self.z/.01
for i in range(len(self.z)):
self.kcorr[i]=kc[int(r[i])]+(r[i]-int(r[i]))*(kc[int(r[i]+1)]-kc[int(r[i])])
self.dL[i] = my.dL(self.z[i],h100)
def isovalues(isos, isow):
x = numarray.zeros(len(isos)) * 0. # age
y = numarray.zeros(len(isos)) * 0. # metallicity
z = numarray.zeros(len(isos)) * 0. # metallicity
for i in range(len(isos)):
feh, age = iso.scaled2real(isos[i][0], isos[i][1])
y[i] = feh
x[i] = numarray.log10(age)
z[i] = isow[i]
return x, y, z
def readsdsscompleteness(self):
self.nspec05 = N.zeros(len(self.z), 'f')
self.nphot05 = N.zeros(len(self.z), 'f')
self.compl05 = N.zeros(len(self.z), 'f')
self.nspec1 = N.zeros(len(self.z), 'f')
self.nphot1 = N.zeros(len(self.z), 'f')
self.compl1 = N.zeros(len(self.z), 'f')
self.nspec2 = N.zeros(len(self.z), 'f')
self.nphot2 = N.zeros(len(self.z), 'f')
self.compl2 = N.zeros(len(self.z), 'f')
complout = open('sdsscompleteness.dat', 'r')
i = 0
for line in complout:
f = line.split()
#print line
#print f
j = 0
for j in range(len(f)):
f[j] = float(f[j])
print f
(self.nspec05[i], self.nphot05[i], self.compl05[i], self.nspec1[i],
self.nphot1[i], self.compl1[i], self.nspec2[i], self.nphot2[i],
self.compl2[i]) = (f[0], f[1], f[2], f[3], f[4], f[5], f[6], f[7],
f[8])
#print f[0],f[1],f[2],self.nspec05[i],self.nphot05[i],self.compl05[i]
#print line
i = i + 1
complout.close()
print "got ", i, " clusters from sdsscompleteness.dat"
print "min of c.compl05 = ", min(self.compl05)
def sample(snx,sny,plist,background):
#i think that this one just does a little 3 by 3 box
import numarray
#print "sample" , snx , " " , sny
pixellist = numarray.zeros((3,3),type = numarray.Float32)
pixels = numarray.zeros((3,3),type = numarray.Float32)
#print pixellist
cx = round(snx)
cy = round(sny)
for xcor in [cx - 1.0 , cx , cx + 1.0]:
for ycor in [cy - 1.0 , cy , cy + 1.0]:
#print xcor, cx, ycor, cy, xcor-cx+2, ycor-cy+2
x = int(xcor-cx+1)
y = int(ycor-cy+1)
#print x ,y
#reverse x and y because of image
pixellist[x][y] = plist[int(ycor)-1][int(xcor)-1]
#print pixellist
#shift to a 3 x 3 grid
snx = snx - cx + 1
sny = sny - cy + 1
xmin = snx - 0.5
ymin = sny - 0.5
xmax = snx + 0.5
ymax = sny + 0.5
scale = 1.00
#figure out which pixels to measure
tally = 0
counts = 0
vcounts = 0
for pixelx in range(3):
for pixely in range(3):
pymin = pixely - scale / 2.0
pymax = pixely + scale / 2.0
pxmin = pixelx - scale / 2.0
pxmax = pixelx + scale / 2.0
compx = overlap(pxmin,pxmax,xmin,xmax)
compy = overlap(pymin,pymax,ymin,ymax)
coeff = compx * compy
#pixels[pixelx][pixely]
#print coeff, tally
counts = counts + coeff * pixellist[pixelx][pixely]
vcounts = vcounts + pixellist[pixelx][pixely]
tally = tally + coeff
vavcounts = vcounts / 9.0
sum = 0
for pixelx in range(3):
for pixely in range(3):
sum = sum + pow((pixellist[pixelx][pixely]-vavcounts),2)
rms = pow(sum/9.0,0.5)
#rescale the pixels to account for the difference in pixel scale
#print counts
#counts = counts * pow(scale )
print "coeff adds up to " , tally
return [counts,rms]
def _mad3(data):
# adapted from NR function moment
n = len(data[:,0,0])
s = num.zeros(data[0,:,:].shape, num.Float32)
# First pass to get the mean.
for j in range(n): s += data[j,:,:]
ave = s/n
adev = num.zeros(s.shape, num.Float32)
for j in range(n):
num.add(adev, num.fabs(data[j] - ave), adev)
return adev / n
def hess3(func, x0, ind): """Computes third derivative using hess function.""" eps = sqrt(1e-3) n = len(x0) m = len(ind) C = zeros((func.m,m,m,m), Float) for i in range(m): ei = zeros(n, Float) ei[ind[i]] = 1.0 C[i,:,:,:] = (hess(func,x0+eps*ei,ind) - hess(func,x0-eps*ei,ind))/(2*eps) return C
def testInit(self):
a = self.a
b = self.b
assert(a.g == 0.0 and \
na.allclose(a.h, na.zeros(3)) and \
na.allclose(a.K, na.zeros(shape=(3,3)))), \
" Error with standard initialization "
assert(b.g == 2.0 and \
na.allclose(b.h, na.array([1,2,3], type='Float32')) and \
na.allclose(b.K, na.arange(9,shape=(3,3), type='Float32'))), \
" Error with standard initialization with parameter setting"
def plotFitRms(root, polyroot, gcfitdir):
s = starset.StarSet(root)
s.loadPolyfit(polyroot, arcsec=1, accel=0)
years = s.stars[0].years
fitPx = s.getArray('fitXv.p')
fitVx = s.getArray('fitXv.v')
fitPy = s.getArray('fitYv.p')
fitVy = s.getArray('fitYv.v')
t0x = s.getArray('fitXv.t0')
t0y = s.getArray('fitYv.t0')
rmsX = na.zeros(len(s.stars), type=na.Float)
rmsY = na.zeros(len(s.stars), type=na.Float)
rms = na.zeros(len(s.stars), type=na.Float)
cnt = na.zeros(len(s.stars), type=na.Int)
for ee in range(len(years)):
dtX = years[ee] - t0x
dtY = years[ee] - t0y
xfit = fitPx + (dtX * fitVx)
yfit = fitPy + (dtY * fitVy)
x = s.getArrayFromEpoch(ee, 'x')
y = s.getArrayFromEpoch(ee, 'y')
xpix = s.getArrayFromEpoch(ee, 'xpix')
ypix = s.getArrayFromEpoch(ee, 'ypix')
diffx = xfit - x
diffy = yfit - y
diff = na.sqrt(diffx**2 + diffy**2)
idx = (na.where(xpix > -999))[0]
rmsX[idx] += diffx**2
rmsY[idx] += diffy**2
rms[idx] += diff**2
cnt[idx] += 1
rmsX = na.sqrt(rmsX / cnt) * 1000.0
rmsY = na.sqrt(rmsY / cnt) * 1000.0
rms = na.sqrt(rms / cnt) * 1000.0
mag = s.getArray('mag')
x = s.getArray('x')
y = s.getArray('y')
r = na.sqrt(x**2 + y**2)
idx = (na.where(mag < 15))[0]
p.clf()
p.semilogy(r[idx], rms[idx], 'k.')
def hess3(func, x0, ind):
"""Computes third derivative using hess function."""
eps = sqrt(1e-3)
n = len(x0)
m = len(ind)
C = zeros((func.m, m, m, m), Float)
for i in range(m):
ei = zeros(n, Float)
ei[ind[i]] = 1.0
C[i, :, :, :] = (hess(func, x0 + eps * ei, ind) -
hess(func, x0 - eps * ei, ind)) / (2 * eps)
return C
def plotFitRms(root, polyroot, gcfitdir):
s = starset.StarSet(root)
s.loadPolyfit(polyroot, arcsec=1, accel=0)
years = s.stars[0].years
fitPx = s.getArray('fitXv.p')
fitVx = s.getArray('fitXv.v')
fitPy = s.getArray('fitYv.p')
fitVy = s.getArray('fitYv.v')
t0x = s.getArray('fitXv.t0')
t0y = s.getArray('fitYv.t0')
rmsX = na.zeros(len(s.stars), type=na.Float)
rmsY = na.zeros(len(s.stars), type=na.Float)
rms = na.zeros(len(s.stars), type=na.Float)
cnt = na.zeros(len(s.stars), type=na.Int)
for ee in range(len(years)):
dtX = years[ee] - t0x
dtY = years[ee] - t0y
xfit = fitPx + (dtX * fitVx)
yfit = fitPy + (dtY * fitVy)
x = s.getArrayFromEpoch(ee, 'x')
y = s.getArrayFromEpoch(ee, 'y')
xpix = s.getArrayFromEpoch(ee, 'xpix')
ypix = s.getArrayFromEpoch(ee, 'ypix')
diffx = xfit - x
diffy = yfit - y
diff = na.sqrt(diffx**2 + diffy**2)
idx = (na.where(xpix > -999))[0]
rmsX[idx] += diffx**2
rmsY[idx] += diffy**2
rms[idx] += diff**2
cnt[idx] += 1
rmsX = na.sqrt(rmsX / cnt) * 1000.0
rmsY = na.sqrt(rmsY / cnt) * 1000.0
rms = na.sqrt(rms / cnt) * 1000.0
mag = s.getArray('mag')
x = s.getArray('x')
y = s.getArray('y')
r = na.sqrt(x**2 + y**2)
idx = (na.where(mag < 15))[0]
p.clf()
p.semilogy(r[idx], rms[idx], 'k.')
def __init__(self, names, shape, g=None, h=None, K=None):
Potential.__init__(self, names)
self.shape = shape
# set parameters to 0s
self.n = na.sum(shape)
if not g: self.g = 0.0
else: self.g = float(g)
if not h: self.h = na.zeros(shape=(self.n), type='Float32')
else: self.h = na.array(h,shape=(self.n), type='Float32')
if not K: self.K = na.zeros(shape=(self.n, self.n), type='Float32')
else: self.K = na.array(K, shape=(self.n, self.n), type='Float32')
def processBands():
# buffer arrays
red = zeros((ysz,xsz),typecode)
green = zeros((ysz,xsz),typecode)
blue = zeros((ysz,xsz),typecode)
pan = zeros((ysz,xsz),'f')
# read into buffers
GDALReadRaster(redBand._o,xbloff,ybloff,xsz,ysz,xsz,ysz,self.srcDt,red)
GDALReadRaster(greenBand._o,xbloff,ybloff,xsz,ysz,xsz,ysz,self.srcDt,green)
GDALReadRaster(blueBand._o,xbloff,ybloff,xsz,ysz,xsz,ysz,self.srcDt,blue)
GDALReadRaster(panBand._o,xbloff,ybloff,xsz,ysz,xsz,ysz,gdal.GDT_Float32,pan)
# merge
mergeFn(red.astype('f'),green.astype('f'),blue.astype('f'),pan)
def create_predict_table(LCM, agent_set, agents_index, observed_choices_id, data_objects, geographies=[]):
resources = data_objects
mc_choices = sample_choice(LCM.model.probabilities) # monte carlo choice
mc_choices_index = LCM.model_resources.translate("index")[mc_choices]
maxprob_choices = sample_choice(LCM.model.probabilities, method="max_prob") # max prob choice
maxprob_choices_index = LCM.model_resources.translate("index")[maxprob_choices]
results = []
gcs = resources.translate("gridcell")
for geography in geographies:
geos = resources.translate(geography)
# get observed geo_id
obs = copy_dataset(agent_set)
obs.subset_by_index(agents_index)
obs.set_values_of_one_attribute(gcs.id_name[0], observed_choices_id)
resources.merge({"household": obs}) # , "gridcell": gcs, "zone": zones, "faz":fazes})
obs.compute_variables(geos.id_name[0], resources=resources)
obs_geo_ids = obs.get_attribute(geos.id_name[0])
# count simulated choices
sim = copy_dataset(obs)
sim.set_values_of_one_attribute(gcs.id_name[0], gcs.get_id_attribute()[mc_choices_index])
resources.merge({"household": sim})
geos_size = geos.size()
geo_ids = geos.get_id_attribute()
pred_matrix = zeros((geos_size, geos_size))
p_success = zeros((geos_size,)).astype(Float32)
f = 0
for geo_id in geo_ids:
index_in_geo = where(obs_geo_ids == geo_id)[0]
resources.merge({"select_index": index_in_geo})
geos.compute_variables("number_of_select_households", resources=resources)
pred_matrix[f] = geos.get_attribute("number_of_select_households")
if sum(pred_matrix[f]) > 0:
p_success[f] = float(pred_matrix[f, f]) / sum(pred_matrix[f])
sim.increment_version("grid_id") # to trigger recomputation in next iteration
f += 1
print p_success
results.append((pred_matrix.copy(), p_success.copy()))
return results
def create_predict_table(LCM, agent_set, agents_index, observed_choices_id, data_objects, geographies=[]):
resources = data_objects
mc_choices = sample_choice(LCM.model.probabilities) #monte carlo choice
mc_choices_index = LCM.model_resources.translate("index")[mc_choices]
maxprob_choices = sample_choice(LCM.model.probabilities, method="max_prob") #max prob choice
maxprob_choices_index = LCM.model_resources.translate("index")[maxprob_choices]
results = []
gcs = resources.translate("gridcell")
for geography in geographies:
geos = resources.translate(geography)
#get observed geo_id
obs = copy_dataset(agent_set)
obs.subset_by_index(agents_index)
obs.set_values_of_one_attribute(gcs.id_name[0], observed_choices_id)
resources.merge({"household": obs}) #, "gridcell": gcs, "zone": zones, "faz":fazes})
obs.compute_variables(geos.id_name[0], resources=resources)
obs_geo_ids = obs.get_attribute(geos.id_name[0])
#count simulated choices
sim = copy_dataset(obs)
sim.set_values_of_one_attribute(gcs.id_name[0], gcs.get_id_attribute()[mc_choices_index])
resources.merge({"household": sim})
geos_size = geos.size()
geo_ids = geos.get_id_attribute()
pred_matrix = zeros((geos_size, geos_size))
p_success = zeros((geos_size,)).astype(Float32)
f = 0
for geo_id in geo_ids:
index_in_geo = where(obs_geo_ids == geo_id)[0]
resources.merge({"select_index": index_in_geo})
geos.compute_variables("number_of_select_households", resources=resources)
pred_matrix[f] = geos.get_attribute("number_of_select_households")
if sum(pred_matrix[f]) > 0:
p_success[f] = float(pred_matrix[f, f])/sum(pred_matrix[f])
sim.increment_version('grid_id') #to trigger recomputation in next iteration
f += 1
print p_success
results.append((pred_matrix.copy(), p_success.copy()))
return results
def buildPearsonCorrelationMatrix(traits, commonStrains):
dim = (len(traits), len(commonStrains))
matrix = numarray.zeros(dim, MA.Float64)
testMatrix = numarray.zeros(dim, MA.Float64)
for i in range(len(traits)):
sd = traits[i].strainData
keys = sd.keys()
for j in range(0, len(commonStrains)):
if keys.__contains__(commonStrains[j]):
matrix[i,j] = sd[commonStrains[j]]
testMatrix[i,j] = 1
return matrix, testMatrix
def jac(func, x0, ind): """Compute (n-1) x m Jacobian of function func at x0, where n = len(x0) and m = len(ind). ind denotes the indices along which to compute the Jacobian. NOTE: This assumes func has 1 more variable than equations!!.""" eps = 1e-6 n = len(x0) m = len(ind) J = zeros((n-1, m), Float) for i in range(m): ei = zeros(n, Float) ei[ind[i]] = 1.0 J[:,i] = (func(x0+eps*ei)-func(x0-eps*ei))/(2*eps) return J
def diff(self, x0, ind=None):
eps = 1e-6
try:
n = len(ind)
except:
n = self.n
ind = range(n)
J = zeros((self.m, n), Float)
for i in range(n):
ei = zeros(self.n, Float)
ei[ind[i]] = 1.0
J[:,i] = (self.func(x0+eps*ei)-self.func(x0-eps*ei))/(2*eps)
return J
def jac(func, x0, ind):
"""Compute (n-1) x m Jacobian of function func at x0, where n = len(x0) and
m = len(ind). ind denotes the indices along which to compute the
Jacobian. NOTE: This assumes func has 1 more variable than equations!!."""
eps = 1e-6
n = len(x0)
m = len(ind)
J = zeros((n - 1, m), Float)
for i in range(m):
ei = zeros(n, Float)
ei[ind[i]] = 1.0
J[:, i] = (func(x0 + eps * ei) - func(x0 - eps * ei)) / (2 * eps)
return J
def GetCartesianForces(self):
#Control from ASE API?
#Make array of positions
#Get number of atoms
numAtoms = len(self.GetListOfAtoms())
#Debugging
print 'there are %i atoms' % (numAtoms)
#Make a numarray to hold the atoms
positions = numa.zeros((
numAtoms,
3,
), numa.Float64)
#Get the info from each atom and copy it to the numarray
count = 0
tempList = self.GetListOfAtoms()
for k in tempList:
positions[count] = k.GetCartesianPosition()
count = count + 1
#Debugging
print positions
#Run a set positions
cp2k_interface.c_set_pos(positions, self.env_id)
#Run a get to check
positions = numa.zeros((
numAtoms,
3,
), numa.Float64)
cp2k_interface.c_get_pos(positions, self.env_id)
#Debugging
print positions
#Calculate forces (update_forces)
cp2k_interface.c_update_forces(self.env_id)
#Now run a get force
#Use parse tuple to get pyobject
#Junk return
self.forces = num.zeros((numAtoms, 3), num.Float)
return self.forces
def binit(x, y, n): #bin arrays x, y into n bins, returning xbin,ybin
nx = len(x)
y = N.take(y, N.argsort(x)) #sort y according to x rankings
x = N.take(x, N.argsort(x))
xbin = N.zeros(n, 'f')
ybin = N.zeros(n, 'f')
for i in range(n):
nmin = i * int(float(nx) / float(n))
nmax = (i + 1) * int(float(nx) / float(n))
xbin[i] = pylab.median(x[nmin:nmax])
ybin[i] = pylab.median(y[nmin:nmax])
#xbin[i]=N.average(x[nmin:nmax])
#ybin[i]=N.average(y[nmin:nmax])
#ybinerr[i]=scipy.stats.std(y[nmin:nmax])
return xbin, ybin #, ybinerr
def _mad2(data, included):
# adapted from NR function moment
# same as mad3 but ignores zero values
n = len(data[:,0,0])
s = num.zeros(data[0,:,:].shape, num.Float32)
# First pass to get the mean.
for j in range(n): s += data[j,:,:]
ave = s/included
adev = num.zeros(s.shape, num.Float32)
for j in range(n):
d = where(num.fabs(data[j]) > tiny,
num.fabs(data[j] - ave),
0.0)
num.add(adev, d, adev)
return adev / included
def GenLinSystem(poly):
"""
Generates the linear system which allows factorisation of
something like:
(a1 * a+ a2 *b + a3 *c ....) ^2 into:
c1(a-b)^2 + c2(a-c)^2
For the two dimensional bilinear interpolator, get something like:
p2 = numarray.array([3,-1,-1,-1])
which may be solved by:
a,r=GenLinSystem(p2)
la.solve_linear_equations(a,r)
"""
n=len(poly)
# number of pairings
NC=n*(n-1) /2
NP=n*(n+1) /2
# The linear system
rhs = numarray.zeros(NP ,
numarray.Float64)
a = numarray.zeros( ( NP,NC) ,
numarray.Float64)
for i in range(0, n-1):
for j in range (i+1, n):
cdx = CJKtoi(i,j,n)
a[ PJKtoi(i,i,n) , cdx ] =1
a[ PJKtoi(i,j,n) , cdx ] =-2
a[ PJKtoi(j,j,n) , cdx ] =1
# right hand side
for i in range(0, n):
for j in range (i, n):
pdx=PJKtoi(i,j,n)
if i == j:
rhs[pdx]= poly[i]**2
else:
rhs[pdx]= 2 * poly[i] * poly[j]
return a, rhs
def dual_perceptron(x, y):
"""implements a dual form perceptron
as defined in "Support Vector Machines", Cristiani, p.18
@x is a list of i 'numarray.array's that define the input
@y is a list of i correct outputs for x, must be syncronized with x
i.e. y[3] == correct f(x[3])
@n is the learning rate 0 < n < 1"""
a = na.zeros(len(x), na.Float32) #embedding strength = alpha
b = 0 #bias
R = math.pow(max_norm(x), 2)
mistake_free = 0
iteration = 0
while mistake_free == 0 and iteration < 50:
iteration += 1
print "iteration #", iteration
mistake_free = 1
for i in range(len(x)):
sum_lc = 0
for j in range(len(x)):
sum_lc += a[j] * y[j] * na.dot(x[j], x[i]) #+ b
print sum_lc, a, y, x, b
if y[i] * (sum_lc + b) <= 0:
print b, a, sum_lc, y[i]
a[i] += 1
b += y[i] * R
mistake_free = 0
return (a, b)
def r(u): # Boundary condition residuals-- see Eq. (8.7)
r = zeros(len(u),type=Float64)
X,Y = integrate(F,x,initCond(u),xStop,h)
y = Y[len(Y) - 1]
r[0] = y[2]
r[1] = y[3] - 1.0
return r
def LUdecomp(a, tol=1.0e-9):
n = len(a)
seq = array(range(n))
# Set up scale factors
s = zeros((n), type=Float64)
for i in range(n):
s[i] = max(abs(a[i, :]))
for k in range(0, n - 1):
# Row interchange, if needed
p = int(argmax(abs(a[k:n, k]) / s[k:n])) + k
if abs(a[p, k]) < tol:
error.err("Matrix is singular")
if p != k:
swap.swapRows(s, k, p)
swap.swapRows(a, k, p)
swap.swapRows(seq, k, p)
# Elimination
for i in range(k + 1, n):
if a[i, k] != 0.0:
lam = a[i, k] / a[k, k]
a[i, k + 1 : n] = a[i, k + 1 : n] - lam * a[k, k + 1 : n]
a[i, k] = lam
return a, seq
def testHorizontalLinesARGB32(self):
colors = (Qt.red, Qt.green, Qt.blue, Qt.white, Qt.black)
alpha = 0xff000000
red = 0x00ff0000
green = 0x0000ff00
blue = 0x000000ff
white = 0x00ffffff
black = 0x00000000
image = QImage(3, len(colors), QImage.Format_ARGB32)
painter = QPainter(image)
for i, color in enumerate(colors):
painter.setPen(color)
painter.drawLine(0, i, image.width(), i)
del painter
array = np.zeros((image.height(), image.width()), dtype=np.UInt32)
array[0,:] = alpha|red
array[1,:] = alpha|green
array[2,:] = alpha|blue
array[3,:] = alpha|white
array[4,:] = alpha|black
self.assertEqual(np.all(array == toNumpy(image)), True)
self.assertEqual(image == toQImage(array), True)