def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None: xb=a
if xe is None: xe=b
x=a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1=a+(b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v,v1=f(x),f(x1)
nk=[]
put(" u = %s N = %d"%(repr(round(dx,3)),N))
put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep "%(f(0,None)))
for k in range(1,6):
tckp,u=splprep([x,v],s=s,per=per,k=k,nest=-1)
tck=splrep(x,v,s=s,per=per,k=k)
uv=splev(dx,tckp)
err1 = abs(uv[1]-f(uv[0]))
err2 = abs(splev(uv[0],tck)-f(uv[0]))
assert_(err1 < 1e-2)
assert_(err2 < 1e-2)
put(" %d : %s %.1e %.1e"%\
(k,repr([round(z,3) for z in uv]),
err1,
err2))
put("Derivatives of parametric cubic spline at u (first function):")
k=3
tckp,u=splprep([x,v],s=s,per=per,k=k,nest=-1)
for d in range(1,k+1):
uv=splev(dx,tckp,d)
put(" %s "%(repr(uv[0])))
def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1 = a + (b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v,v1 = f(x),f(x1)
put(" u = %s N = %d" % (repr(round(dx,3)),N))
put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep " % (f(0,None)))
for k in range(1,6):
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
tck = splrep(x,v,s=s,per=per,k=k)
uv = splev(dx,tckp)
err1 = abs(uv[1]-f(uv[0]))
err2 = abs(splev(uv[0],tck)-f(uv[0]))
assert_(err1 < 1e-2)
assert_(err2 < 1e-2)
put(" %d : %s %.1e %.1e" %
(k,repr([round(z,3) for z in uv]),
err1,
err2))
put("Derivatives of parametric cubic spline at u (first function):")
k = 3
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
for d in range(1,k+1):
uv = splev(dx,tckp,d)
put(" %s " % (repr(uv[0])))
def fitEdge(og,e,VERBOSE=False):
path = og[e[0]][e[1]]['wpath']
#pstart=og.node[e[0]]['wcrd']
#pend = og.node[e[1]]['wcrd']
#path.extend([pend])
#p = [pstart]
#p.extend(path)
ae = np.array(path)
if( ae.shape[0] > 3 ): # there are not enough points to fit with
if( VERBOSE ): print("refitting edge with %d points"%len(path))
s = ae.shape[0]/2.0
fit2 = splprep(ae.transpose(),task=0,full_output =1, s=s)[0]
u = np.array(list(range(ae.shape[0]+1))).\
astype(np.float64)/(ae.shape[0])
# location of spline points
og[e[0]][e[1]]['d0'] = splev(u,fit2[0],der=0)
# first derivative (tangent) of spline
og[e[0]][e[1]]['d1'] =np.array( splev(u,fit2[0],der=1))
# second derivative (curvature) of spline
og[e[0]][e[1]]['d2'] = np.array(splev(u,fit2[0],der=2))
else:
if( VERBOSE ): print("no or insufficient points to fit")
og[e[0]][e[1]]['d0'] = None
og[e[0]][e[1]]['d1'] = None
og[e[0]][e[1]]['d2'] = None
def fitEdge(og, e, VERBOSE=False):
path = og[e[0]][e[1]]['wpath']
#pstart=og.node[e[0]]['wcrd']
#pend = og.node[e[1]]['wcrd']
#path.extend([pend])
#p = [pstart]
#p.extend(path)
ae = np.array(path)
if (ae.shape[0] > 3): # there are not enough points to fit with
if (VERBOSE): print("refitting edge with %d points" % len(path))
s = ae.shape[0] / 2.0
fit2 = splprep(ae.transpose(), task=0, full_output=1, s=s)[0]
u = np.array(list(range(ae.shape[0]+1))).\
astype(np.float64)/(ae.shape[0])
# location of spline points
og[e[0]][e[1]]['d0'] = splev(u, fit2[0], der=0)
# first derivative (tangent) of spline
og[e[0]][e[1]]['d1'] = np.array(splev(u, fit2[0], der=1))
# second derivative (curvature) of spline
og[e[0]][e[1]]['d2'] = np.array(splev(u, fit2[0], der=2))
else:
if (VERBOSE): print("no or insufficient points to fit")
og[e[0]][e[1]]['d0'] = None
og[e[0]][e[1]]['d1'] = None
og[e[0]][e[1]]['d2'] = None
def to_spline(self, smoothing=0, spacing_corrected=False):
"""Return the best-fit periodic parametric 3rd degree b-spline to the data points.
The smoothing parameter is an upper-bound on the mean squared deviation between the
data points and the points produced by the smoothed spline. By default it is 0,
forcing an interpolating spline.
The returned spline is valid over the parametric range [0, num_points+1], where
the value at 0 is the same as the value at num_points+1. If spacing_corrected
is True, then the intermediate points will be placed according to the physical
spacing between them, which is useful in some situations like resampling.
However, it means that the spline evalueated at position N will not necessarialy
give the same point as contour.points[n], unless all of the points are exactly
evenly spaced. Similarly, non-zero values of smoothing will disrupt this property
as well.
Two values are returned: tck and u. 'tck' is a tuple containing the spline c
oefficients, the knots (two lists; x-knots and y-knots), and the degree of
the spline. This 'tck' tuple can be used by the routines in scipy.fitpack.
'u' is a list of the parameter values corresponding to the points in the range.
"""
# the fitpack smoothing parameter is an upper-bound on the TOTAL squared deviation;
# ours is a bound on the MEAN squared deviation. Fix the mismatch:
l = len(self.points)
smoothing = smoothing * l
if spacing_corrected:
interpoint_distances = self.interpoint_distances()
last_to_first = interpoint_distances[0]
interpoint_distances[0] = 0
cumulative_distances = numpy.add.accumulate(interpoint_distances)
u = numpy.empty(l + 1, dtype=float)
u[:-1] = cumulative_distances
u[-1] = cumulative_distances[-1] + last_to_first
u *= l / u[-1]
else:
u = numpy.arange(0, l + 1)
points = numpy.resize(self.points, [l + 1, 2])
points[-1] = points[0]
tck, uout = fitpack.splprep(x=points.transpose(),
u=u,
per=True,
s=smoothing)
return tck, uout
def fitPath(self,maxiter=40, s=20000):
"""fits a least squares spline through the path
find descriptions of maxiter and s from scipy documentation"""
try:
pth = path.getCrds()
pp = [pth[:,0],pth[:,1],pth[:,2]]
if( len(pp[0]) <= 3 ): # there are not enough points to fit with
self.splinePoints = pp
self.splineTangents = None
self.splineCurvature = None
return
else:
s = len(pp[0])/2.0
cont = 1
j=0
while( j < maxiter ):
fit2 = splprep(pp,task=0,full_output =1, s=s)[0]
u = na.array(range(pp[0].shape[0]+1)).\
astype(na.float64)/(pp[0].shape[0])
# location of spline points
self.splinePoints = splev(u,fit2[0],der=0)
# first derivative (tangent) of spline
valsd = splev(u,fit2[0],der=1)
self.splineTangents = na.array(valsd).astype(na.float64)
# second derivative (curvature) of spline
valsc = splev(u,fit2[0],der=2)
self.splineCurvature = na.array(valsc).astype(na.float64)
success = 1 # this doesn't make much sense
if( success ): # how should I be determining success?
break
else:
s = s*0.9
j += 1
return True
except Exception, error:
print "failed in fitPath()",error
def fitPath(self, maxiter=40, s=20000):
"""fits a least squares spline through the path
find descriptions of maxiter and s from scipy documentation"""
try:
pth = path.getCrds()
pp = [pth[:, 0], pth[:, 1], pth[:, 2]]
if (len(pp[0]) <= 3): # there are not enough points to fit with
self.splinePoints = pp
self.splineTangents = None
self.splineCurvature = None
return
else:
s = len(pp[0]) / 2.0
cont = 1
j = 0
while (j < maxiter):
fit2 = splprep(pp, task=0, full_output=1, s=s)[0]
u = na.array(range(pp[0].shape[0]+1)).\
astype(na.float64)/(pp[0].shape[0])
# location of spline points
self.splinePoints = splev(u, fit2[0], der=0)
# first derivative (tangent) of spline
valsd = splev(u, fit2[0], der=1)
self.splineTangents = na.array(valsd).astype(na.float64)
# second derivative (curvature) of spline
valsc = splev(u, fit2[0], der=2)
self.splineCurvature = na.array(valsc).astype(na.float64)
success = 1 # this doesn't make much sense
if (success): # how should I be determining success?
break
else:
s = s * 0.9
j += 1
return True
except Exception, error:
print "failed in fitPath()", error
def distribution_plot(data_groups, filename, axis_title = None, plot_title = None,
colors = default_colors, names = None, axes_at_origin = True, plot_points = False,
fix_xrange = (None, None), scale_factors = None):
"""Plot the 1D distributions of several collections of points to a SVG file.
The distributions of the 1D points in 'data_groups' are estimated with kernel
density estimation, fit to splines, and plotted on numerical axes with an
optional legend.
Parameters:
data_groups -- a list of grouped data points. Each group is a list of numbers,
the distribution of which will be estimated and plotted.
filename -- file to write the SVG out to.
axis_title -- Title for the x-axis.
plot_title -- title for the plot.
colors -- the colors to fill the contours of each group with. Either color
names that are defined in the SVG specification or (r,g,b) triplets are
acceptable. This parameter must be an iterable; if there are not enough
elements for the groups, they will be cycled.
names -- the name of each group. Must be a list as long as contour_groups.
If names is None, then there will be no legend in the output SVG.
axes_at_origin -- if True, then the plot axes will intersect at the origin
(or the nearest point to it in the data plot). Otherwise the axes will
be at the bottom and left of the plot.
plot_points -- if True, dots will be plotted at the location of each
sample.
fix_xrange, fix_yrange -- (min, max) tuples. If either or both values are
None, then the best-fit range given the contours and their positions is
chosen. Setting either or both forces the axis to have that minimum or
maximum point.
scale_factors -- If not None, a list of values by which to scale the heights
of each distribution.
"""
from scipy.interpolate import fitpack
data_groups = [numpy.asarray(data_group, dtype=numpy.float32) for data_group in data_groups]
if not numpy.alltrue([data_group.ndim == 1 for data_group in data_groups]):
raise ValueError('Can only plot distributions in one dimension.')
data_groups = [numpy.asarray(data_group) for data_group in data_groups]
data_ranges = [(g.min(), g.max()) for g in data_groups]
kd_estimators = [kde.gaussian_kde(data_group) for data_group in data_groups]
min = numpy.min([m for m, x in data_ranges])
max = numpy.max([x for m, x in data_ranges])
extra = 0.05*(max - min)
min -= extra
max += extra
#min, max, data_ranges = _kde_range(kd_estimators, data_ranges, 5e-6)
# pin the values to those of fix_xrange, if specified
if fix_xrange[0] is not None:
min = fix_xrange[0]
if fix_xrange[1] is not None:
max = fix_xrange[1]
height = 0
beziers = []
err = numpy.seterr(under='ignore')
# ignore underflow -- KDE can underflow when estimating regions of very low density
if scale_factors is None:
scale_factors = [1]*len(kd_estimators)
for (range_min, range_max), estimator, scale_factor in zip(data_ranges, kd_estimators, scale_factors):
if fix_xrange[0] is not None and range_min < min: range_min=min
if fix_xrange[1] is not None and range_max > max: range_max=max
eval_points = list(numpy.linspace(range_min, range_max, 100, True))
kde_points = estimator.evaluate(eval_points) * scale_factor
data_height = kde_points.max()
if data_height > height: height = data_height
#s = 0.0005 * numpy.min([range_max - range_min, data_height]) / 100
s = 0
spline = fitpack.splprep([eval_points, kde_points], u=eval_points, s=s)[0]
beziers.append(utility_tools.b_spline_to_bezier_series(spline))
numpy.seterr(**err)
data_xrange = [min, max]
data_yrange = [0, height]
equal_axis_spacing = False
plot = plot_class.Plot(_CANVAS_WIDTH, _CANVAS_HEIGHT, data_xrange, data_yrange,
equal_axis_spacing, _LEFT_PAD, _RIGHT_PAD, _TOP_PAD, _BOTTOM_PAD)
legend = True
if names is None:
legend = False
names = ['distribution-%d'%d for d in range(len(data_groups))]
else:
names = [name.replace(' ', '_') for name in names]
if plot_points:
point_radius = 0.005 * (data_xrange[1] - data_xrange[0])
plot.style.add_selector('[class~="point"]', fill='black', stroke=None)
for name, bezier, data_group, estimator, color in zip(names, beziers, data_groups, kd_estimators, itertools.cycle(colors)):
plot.add_bezier(bezier, id=name, svg_class='data density', layer=name)
plot.style.add_selector('[class~="density"][id="%s"]'%name, fill='none', stroke=color)
plot.style.add_selector('[class~="legend"][id="%s"]'%name, fill='none', stroke=color)
if plot_points:
values = numpy.unique(data_group)
for point in zip(values, estimator(values)):
plot.add_circle(point, point_radius, id=None, svg_class="data point", layer=name, in_data_coords=True)
if legend:
legend_x = _CANVAS_WIDTH - _PAD - 80
legend_y = _FONT_SIZE_SMALL * plot_class._TOP_TO_BASELINE + _PAD
line_length = 50
plot.add_legend(legend_x, legend_y, line_length, names, _FONT_SIZE_SMALL)
if plot_title is not None:
plot.add_title(plot_title, _FONT_SIZE)
if axes_at_origin:
positions = (-1,0)
else:
positions = (-1,-1)
plot.add_axes(positions = positions, titles = (axis_title, None), ticsize = _TICSIZE, font_size = _FONT_SIZE_SMALL)
plot.to_svg(filename, plot_title)
return plot
def line_plot(data_groups, filename, axis_titles = (None, None), plot_title = None,
colors = default_colors, names = None, axes_at_origin = True,
fix_xrange = (None, None), fix_yrange = (None, None), bezier=None):
"""Plot smooth lines connecting at given x, y locations to an SVG file.
The resulting SVG will have numerical axes (either centered at the origin, or
placed on the left and bottom of the plot) and optionally a legend.
Parameters:
data_groups -- a list of polylines to be plotted, where each polyline is
placed in a different SVG group and colored differently. Each polyline
is itself a list of [x, y] pairs.
filename -- file to write the SVG out to.
line_width -- Pixel width of the lines to be plotted.
axis_titles -- pair of titles for the x and y axes, respectively.
plot_title -- title for the plot.
colors -- the colors to fill the contours of each group with. Either color
names that are defined in the SVG specification or (r,g,b) triplets are
acceptable. This parameter must be an iterable; if there are not enough
elements for the groups, they will be cycled.
names -- the name of each group. Must be a list as long as contour_groups.
If names is None, then there will be no legend in the output SVG.
axes_at_origin -- if True, then the plot axes will intersect at the origin
(or the nearest point to it in the data plot). Otherwise the axes will
be at the bottom and left of the plot.
fix_xrange, fix_yrange -- (min, max) tuples. If either or both values are
None, then the best-fit range given the contours and their positions is
chosen. Setting either or both forces the axis to have that minimum or
maximum point.
"""
from scipy.interpolate import fitpack
all_points = numpy.array([p for dg in data_groups for p in dg])
plot_width = _CANVAS_WIDTH - _LEFT_PAD - _RIGHT_PAD
plot_height = _CANVAS_HEIGHT - _TOP_PAD - _BOTTOM_PAD
data_xrange, data_yrange = numpy.transpose([all_points.min(axis=0), all_points.max(axis=0)])
fmin, fmax = fix_xrange
if fmin is not None: data_xrange[0] = fmin
if fmax is not None: data_xrange[1] = fmax
fmin, fmax = fix_yrange
if fmin is not None: data_yrange[0] = fmin
if fmax is not None: data_yrange[1] = fmax
equal_axis_spacing = False
plot = plot_class.Plot(_CANVAS_WIDTH, _CANVAS_HEIGHT, data_xrange, data_yrange,
equal_axis_spacing, _LEFT_PAD, _RIGHT_PAD, _TOP_PAD, _BOTTOM_PAD)
legend = True
if names is None:
legend = False
names = ['group-%d'%d for d in range(len(data_groups))]
else:
names = [name.replace(' ', '_') for name in names]
for name, data_group, color in zip(names, data_groups, itertools.cycle(colors)):
if bezier is not None:
spline = fitpack.splprep(numpy.transpose(data_group), s=bezier)[0]
curve = utility_tools.b_spline_to_bezier_series(spline)
plot.add_bezier(curve, id=name, svg_class='data line', layer=name)
else:
plot.add_polyline(data_group, id=name, svg_class='data line', layer=name)
plot.style.add_selector('[id="%s"]'%name, fill='none', stroke=color)
if legend:
legend_x = _CANVAS_WIDTH - _PAD - 80
legend_y = _FONT_SIZE_SMALL * plot_class._TOP_TO_BASELINE + _PAD
line_length = 50
plot.add_legend(legend_x, legend_y, line_length, names, _FONT_SIZE_SMALL, box=False)
if plot_title is not None:
plot.add_title(plot_title, _FONT_SIZE)
if axes_at_origin:
positions = (0,0)
else:
positions = (-1,-1)
plot.add_axes(positions = positions, titles = axis_titles, ticsize = _TICSIZE, font_size = _FONT_SIZE_SMALL)
plot.to_svg(filename, plot_title)
return plot
