def simple_gaussian_kernel(X):
# cut off exponent at -500 to prevent overflow errors
if type(X) == Numeric.ArrayType:
Numeric.putmask(X, X < -500, -500)
elif X < -500:
X = -500
return exp(X)
def gaussian(dist, stddev):
X = -dist**2 / (2 * stddev**2)
# cut off exponent at -500 to prevent overflow errors
if type(X) == Numeric.ArrayType:
Numeric.putmask(X, X < -500, -500)
elif X < -500:
X = -500
return exp(X)
def leftDrag(self, event):
"""
Event handler for LMB drag event.
@param event: A Qt mouse event.
@type event: U{B{QMouseEvent}<http://doc.trolltech.com/4/qmouseevent.html>}
"""
dScale = .025 # This works nicely. Mark 2008-01-29.
delta = self.prevY - event.y()
self.prevY = event.y()
factor = exp(dScale * delta)
#print "y, py =", event.y(), self.prevY, ", delta =", delta, ", factor=", factor
self.glpane.rescale_around_point(factor)
self.glpane.gl_update()
return
def leftDrag(self, event):
"""
Event handler for LMB drag event.
@param event: A Qt mouse event.
@type event: U{B{QMouseEvent}<http://doc.trolltech.com/4/qmouseevent.html>}
"""
dScale = .025 # This works nicely. Mark 2008-01-29.
delta = self.prevY - event.y()
self.prevY = event.y()
factor = exp(dScale * delta)
#print "y, py =", event.y(), self.prevY, ", delta =", delta, ", factor=", factor
self.glpane.rescale_around_point(factor)
self.glpane.gl_update()
return
def f(param, t): return param[0]*exp(-param[1]/t)
def f2(param, t): return 1e13*exp(-param[0]/t)
def func(self, param, t):
return self.N * param[0] * (1 / exp(param[0] * t))
def iagaussian(s,mu,sigma):
""" o Purpose
Generate a 2D Gaussian image.
o Synopsis
g = iagaussian(s,mu,sigma)
o Input
s: [rows columns]
mu: Mean vector. 2D point (x;y). Point of maximum value.
sigma: covariance matrix (square). [ Sx^2 Sxy; Syx Sy^2]
o Output
g:
o Description
A 2D Gaussian image is an image with a Gaussian distribution. It can be used to generate test patterns or Gaussian filters both for spatial and frequency domain. The integral of the gaussian function is 1.0.
o Examples
import Numeric
f = iagaussian([8,4], [3,1], [[1,0],[0,1]])
print Numeric.array2string(f, precision=4, suppress_small=1)
g = ianormalize(f, [0,255]).astype(Numeric.UnsignedInt8)
print g
f = iagaussian(100, 50, 10*10)
g = ianormalize(f, [0,1])
g,d = iaplot(g)
showfig(g)
f = iagaussian([50,50], [25,10], [[10*10,0],[0,20*20]])
g = ianormalize(f, [0,255]).astype(Numeric.UnsignedInt8)
iashow(g)
"""
from Numeric import asarray,product,arange,NewAxis,transpose,matrixmultiply,reshape,concatenate,resize,sum,zeros,Float,ravel,pi,sqrt,exp
from LinearAlgebra import inverse,determinant
if type(sigma).__name__ in ['int', 'float', 'complex']: sigma = [sigma]
s, mu, sigma = asarray(s), asarray(mu), asarray(sigma)
if (product(s) == max(s)):
x = arange(product(s))
d = x - mu
if len(d.shape) == 1:
tmp1 = d[:,NewAxis]
tmp3 = d
else:
tmp1 = transpose(d)
tmp3 = tmp1
if len(sigma) == 1:
tmp2 = 1./sigma
else:
tmp2 = inverse(sigma)
k = matrixmultiply(tmp1, tmp2) * tmp3
else:
aux = arange(product(s))
x, y = iaind2sub(s, aux)
xx = reshape(concatenate((x,y)), (2, product(x.shape)))
d = transpose(xx) - resize(reshape(mu,(len(mu),1)), (s[0]*s[1],len(mu)))
if len(sigma) == 1:
tmp = 1./sigma
else:
tmp = inverse(sigma)
k = matrixmultiply(d, tmp) * d
k = sum(transpose(k))
g = zeros(s, Float)
aux = ravel(g)
if len(sigma) == 1:
tmp = sigma
else:
tmp = determinant(sigma)
aux[:] = 1./(2*pi*sqrt(tmp)) * exp(-1./2 * k)
return g
def func(self, param, t):
return param[0] * param[1] * param[1] * t * (1 / exp(param[1] * t))
def func(self, param, t):
return self.N*param[0]*param[1]*power(param[1]*t, param[0]-1)*\
(1/exp(power(param[1]*t, param[0])))
def combinations(n, k):
"""Returns the number of ways of choosing k items from n.
"""
return exp(lgam(n+1) - lgam(k+1) - lgam(n-k+1))
def f2(param, t):
return 1e13 * exp(-param[0] / t)
def f(param, t):
return param[0] * exp(-param[1] / t)
def f(t):
s1 = sin(2 * pi * t)
e1 = exp(-t)
return absolute(multiply(s1, e1)) + .05
def f(t):
s1 = sin(2*pi*t)
e1 = exp(-t)
return absolute(multiply(s1,e1))+.05