def fix(x):
"""
Rounds towards zero.
x_rounded = fix(x) rounds the elements of x to the nearest integers
towards zero.
For negative numbers is equivalent to ceil and for positive to floor.
"""
dim = numerix.shape(x)
if numerix.mlab.rank(x)==2:
y = reshape(x,(1,dim[0]*dim[1]))[0]
y = y.tolist()
elif numerix.mlab.rank(x)==1:
y = x
else:
y = [x]
for i in range(len(y)):
if y[i]>0:
y[i] = floor(y[i])
else:
y[i] = ceil(y[i])
if numerix.mlab.rank(x)==2:
x = reshape(y,dim)
elif numerix.mlab.rank(x)==0:
x = y[0]
return x
def fix(x):
"""
Rounds towards zero.
x_rounded = fix(x) rounds the elements of x to the nearest integers
towards zero.
For negative numbers is equivalent to ceil and for positive to floor.
"""
dim = numerix.shape(x)
if numerix.mlab.rank(x)==2:
y = reshape(x,(1,dim[0]*dim[1]))[0]
y = y.tolist()
elif numerix.mlab.rank(x)==1:
y = x
else:
y = [x]
for i in range(len(y)):
if y[i]>0:
y[i] = floor(y[i])
else:
y[i] = ceil(y[i])
if numerix.mlab.rank(x)==2:
x = reshape(y,dim)
elif numerix.mlab.rank(x)==0:
x = y[0]
return x
def polyval(p,x):
"""
y = polyval(p,x)
p is a vector of polynomial coeffients and y is the polynomial
evaluated at x.
Example code to remove a polynomial (quadratic) trend from y:
p = polyfit(x, y, 2)
trend = polyval(p, x)
resid = y - trend
See also polyfit
"""
x = asarray(x)+0.
p = reshape(p, (len(p),1))
X = vander(x,len(p))
y = matrixmultiply(X,p)
return reshape(y, x.shape)
def polyval(p, x):
"""
y = polyval(p,x)
p is a vector of polynomial coeffients and y is the polynomial
evaluated at x.
Example code to remove a polynomial (quadratic) trend from y:
p = polyfit(x, y, 2)
trend = polyval(p, x)
resid = y - trend
See also polyfit
"""
x = asarray(x) + 0.
p = reshape(p, (len(p), 1))
X = vander(x, len(p))
y = matrixmultiply(X, p)
return reshape(y, x.shape)
def locate_label(self, linecontour, labelwidth):
"""find a good place to plot a label (relatively flat
part of the contour) and the angle of rotation for the
text object
"""
nsize= len(linecontour)
if labelwidth > 1:
xsize = int(ceil(nsize/labelwidth))
else:
xsize = 1
if xsize == 1:
ysize = nsize
else:
ysize = labelwidth
XX = resize(array(linecontour)[:,0],(xsize, ysize))
YY = resize(array(linecontour)[:,1],(xsize,ysize))
yfirst = YY[:,0]
ylast = YY[:,-1]
xfirst = XX[:,0]
xlast = XX[:,-1]
s = (reshape(yfirst, (xsize,1))-YY)*(reshape(xlast,(xsize,1))-reshape(xfirst,(xsize,1)))-(reshape(xfirst,(xsize,1))-XX)*(reshape(ylast,(xsize,1))-reshape(yfirst,(xsize,1)))
L=sqrt((xlast-xfirst)**2+(ylast-yfirst)**2)
dist = add.reduce(([(abs(s)[i]/L[i]) for i in range(xsize)]),-1)
x,y,ind = self.get_label_coords(dist, XX, YY, ysize, labelwidth)
angle = arctan2(ylast - yfirst, xlast - xfirst)
rotation = angle[ind]*180/pi
if rotation > 90:
rotation = rotation -180
if rotation < -90:
rotation = 180 + rotation
dind = list(linecontour).index((x,y))
return x,y, rotation, dind
def polyfit(x,y,N):
"""
Do a best fit polynomial of order N of y to x. Return value is a
vector of polynomial coefficients [pk ... p1 p0]. Eg, for N=2
p2*x0^2 + p1*x0 + p0 = y1
p2*x1^2 + p1*x1 + p0 = y1
p2*x2^2 + p1*x2 + p0 = y2
.....
p2*xk^2 + p1*xk + p0 = yk
Method: if X is a the Vandermonde Matrix computed from x (see
http://mathworld.wolfram.com/VandermondeMatrix.html), then the
polynomial least squares solution is given by the 'p' in
X*p = y
where X is a len(x) x N+1 matrix, p is a N+1 length vector, and y
is a len(x) x 1 vector
This equation can be solved as
p = (XT*X)^-1 * XT * y
where XT is the transpose of X and -1 denotes the inverse.
For more info, see
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html,
but note that the k's and n's in the superscripts and subscripts
on that page. The linear algebra is correct, however.
See also polyval
"""
x = asarray(x)+0.
y = asarray(y)+0.
y = reshape(y, (len(y),1))
X = Matrix(vander(x, N+1))
Xt = Matrix(transpose(X))
c = array(linear_algebra.inverse(Xt*X)*Xt*y) # convert back to array
c.shape = (N+1,)
return c
def polyfit(x, y, N):
"""
Do a best fit polynomial of order N of y to x. Return value is a
vector of polynomial coefficients [pk ... p1 p0]. Eg, for N=2
p2*x0^2 + p1*x0 + p0 = y1
p2*x1^2 + p1*x1 + p0 = y1
p2*x2^2 + p1*x2 + p0 = y2
.....
p2*xk^2 + p1*xk + p0 = yk
Method: if X is a the Vandermonde Matrix computed from x (see
http://mathworld.wolfram.com/VandermondeMatrix.html), then the
polynomial least squares solution is given by the 'p' in
X*p = y
where X is a len(x) x N+1 matrix, p is a N+1 length vector, and y
is a len(x) x 1 vector
This equation can be solved as
p = (XT*X)^-1 * XT * y
where XT is the transpose of X and -1 denotes the inverse.
For more info, see
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html,
but note that the k's and n's in the superscripts and subscripts
on that page. The linear algebra is correct, however.
See also polyval
"""
x = asarray(x) + 0.
y = asarray(y) + 0.
y = reshape(y, (len(y), 1))
X = Matrix(vander(x, N + 1))
Xt = Matrix(transpose(X))
c = array(linear_algebra.inverse(Xt * X) * Xt * y) # convert back to array
c.shape = (N + 1, )
return c
