def _checkOrth(self, T, TT, eps=0.0001, output=False):
"""check if the basis is orthogonal on a set of points x: TT == T*transpose(T) == c*Identity
INPUT: T: matrix of values of polynomials calculated at common reference points (x)
TT = T * transpose(T)
eps: max numeric error
"""
TTd0 = (-1.*Numeric.identity(Numeric.shape(TT)[0])+1) * TT # TTd0 = TT with 0s on the main diagonal
s = Numeric.sum(Numeric.sum(Numeric.absolute(TTd0)))
minT = MLab.min(MLab.min(T))
maxT = MLab.max(MLab.max(T))
minTTd0 = MLab.min(MLab.min(TTd0))
maxTTd0 = MLab.max(MLab.max(TTd0))
if not s < eps:
out = "NOT ORTHOG, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (minTTd0, maxTTd0, s)
if output:
print out
return False
else:
raise out
elif output:
out = "ORTHOGONAL, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (minTTd0, maxTTd0, s)
print out
return True
def _create_matrix_plot(z_, r_x=0, r_y=0, colorcode=0,
min_area=100000, scale=1):
import numpy.oldnumeric.mlab as ml
# Scale z and find appropriate colormap.
z = z_.copy()
zmax = ml.max(ml.max(z))
zmin = ml.min(ml.min(z))
if (zmin < 0) and (0 < zmax) and (not colorcode):
colormap = create_bipolar_colormap()
zmax = ml.max(asarray([-zmin, zmax]))
z += zmax
z *= (len(colormap)-1)/(2*zmax)
else:
if colorcode == whiteblack:
colormap = create_white_black_colormap()
elif colorcode == blackwhite:
colormap = create_black_white_colormap()
else:
colormap = create_unipolar_colormap()
z -= zmin
if (zmax != zmin):
z *= (len(colormap)-1)/(zmax-zmin)
return _create_scaled_matrix_plot(colormap, z, r_x, r_y,
min_area = min_area, scale = scale)
def _checkOrth(self, T, TT, eps=0.0001, output=False):
"""check if the basis is orthogonal on a set of points x: TT == T*transpose(T) == c*Identity
INPUT: T: matrix of values of polynomials calculated at common reference points (x)
TT = T * transpose(T)
eps: max numeric error
"""
TTd0 = (-1. * Numeric.identity(Numeric.shape(TT)[0]) +
1) * TT # TTd0 = TT with 0s on the main diagonal
s = Numeric.sum(Numeric.sum(Numeric.absolute(TTd0)))
minT = MLab.min(MLab.min(T))
maxT = MLab.max(MLab.max(T))
minTTd0 = MLab.min(MLab.min(TTd0))
maxTTd0 = MLab.max(MLab.max(TTd0))
if not s < eps:
out = "NOT ORTHOG, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (
minTTd0, maxTTd0, s)
if output:
print out
return False
else:
raise out
elif output:
out = "ORTHOGONAL, min(T), max(T):\t%f\t%f\n" % (minT, maxT)
out += " min(TTd0), max(TTd0), sum-abs-el(TTd0):\t%f\t%f\t%f" % (
minTTd0, maxTTd0, s)
print out
return True
def _create_arrow_plot(px, pz, r_x=0, r_y=0,
min_area=100000, scale=1):
import numpy.oldnumeric.mlab as ml
# Scale pz & px
pmax = max( ml.max(ml.max(abs(pz))), ml.max(ml.max(abs(px))))
if (pmax == 0): cst = 0
else: cst = ARROWSIZE/pmax
pz = pz*cst
px = px*cst
return _create_scaled_arrow_plot(px, pz, r_x, r_y,
min_area = min_area, scale = scale)
def legend(text,linetypes=None,lleft=None,color=None,tfont='helvetica',fontsize=14,nobox=0):
"""Construct and place a legend.
Description:
Build a legend and place it on the current plot with an interactive
prompt.
Inputs:
text -- A list of strings which document the curves.
linetypes -- If not given, then the text strings are associated
with the curves in the order they were originally
drawn. Otherwise, associate the text strings with the
corresponding curve types given. See plot for description.
"""
global _hold
global _textcolor
if color is None:
color = _textcolor
else:
_textcolor = color
if color is None:
color = 'black'
sys = gist.plsys()
if sys == 0:
gist.plsys(1)
viewp = gist.viewport()
gist.plsys(sys)
DX = viewp[1] - viewp[0]
DY = viewp[3] - viewp[2]
width = DY / 10.0;
if lleft is None:
lleft = gist.mouse(0,0,"Click on point for lower left coordinate.")
llx = lleft[0]
lly = lleft[1]
else:
llx,lly = lleft[:2]
savesys = gist.plsys()
dx = width / 3.0
legarr = Numeric.arange(llx,llx+width,dx)
legy = Numeric.ones(legarr.shape)
dy = fontsize*points*1.2
deltay = fontsize*points / 2.8
deltax = fontsize*points / 2.6 * DX / DY
ypos = lly + deltay;
if linetypes is None:
linetypes = _GLOBAL_LINE_TYPES[:] # copy them out
gist.plsys(0)
savehold = _hold
_hold = 1
for k in range(len(text)):
plot(legarr,ypos*legy,linetypes[k])
print linetypes[k], text[k]
print llx+width+deltax, ypos-deltay
if text[k] != "":
gist.plt(text[k],llx+width+deltax,ypos-deltay,
color=color,font=tfont,height=fontsize,tosys=0)
ypos = ypos + dy
_hold = savehold
if nobox:
pass
else:
gist.plsys(0)
maxlen = MLab.max(map(len,text))
c1 = (llx-deltax,lly-deltay)
c2 = (llx + width + deltax + fontsize*points* maxlen/1.8 + deltax,
lly + len(text)*dy)
linesx0 = [c1[0],c1[0],c2[0],c2[0]]
linesy0 = [c1[1],c2[1],c2[1],c1[1]]
linesx1 = [c1[0],c2[0],c2[0],c1[0]]
linesy1 = [c2[1],c2[1],c1[1],c1[1]]
gist.pldj(linesx0,linesy0,linesx1,linesy1,color=color)
gist.plsys(savesys)
return
def _create_phasor_movie(z_, r_x=0, r_y=0, min_area=100000, scale=1, ln=0):
import numpy.oldnumeric.mlab as ml
# Make movie memory.
movie = []
frames = 16
z = z_.copy()
if ln:
colormap = create_unipolar_colormap()
# Scale factors for z.
# We're not sure about the lowest zmin value during the calculations.
# So, we make it our own by adding a 'zcst' to each one.
# Log(z**2) gives a (much) nicer plot than log(abs(z)).
# We should get positive values anyhow.
# Supplement to make sure the z isn't zero this really changes
# the feeling of the image.. so not that correct.
zcst = 1e-8
zmax = 2 * np.log(ml.max(ml.max(np.abs(z))) + zcst)
zmin = np.log(zcst) # Around -23.
z_scale = (len(colormap) - 1) / (zmax - zmin)
# Calculate each frame.
for Nr in range(0, frames):
pic = _create_scaled_matrix_plot(
colormap, ((np.log(z.real**2 + zcst) - zmin) * z_scale),
r_x,
r_y,
min_area=min_area,
scale=scale)
movie.append(pic)
z *= np.exp(2j * pi / frames)
else:
colormap = create_bipolar_colormap()
# Scale factors for z.
zmax = ml.max(ml.max(np.abs(z)))
if (zmax == 0):
# in this case, z=0, the middle of the color palet
#(z+zmax)*z_scale) should be = len(colormap)/2
z_scale = (len(colormap) - 1) / 2
zmax = 1
else:
z_scale = (len(colormap) - 1) / (2 * zmax)
# Calculate each frame.
for Nr in range(0, frames):
pic = \
_create_scaled_matrix_plot(
colormap,((z+zmax)*z_scale).real,r_x,r_y,
min_area = min_area, scale = scale)
movie.append(pic)
z *= np.exp(2j * np.pi / frames)
return movie
