def generate_plot_lattice_bounds(case, p_vals, x_variable, y_variable, range_x, range_y, resolution):
V = case.vertices_2D_slice(p_vals, x_variable, y_variable, range_x=range_x, range_y=range_y, log_out=True)
path = mt.path.Path(V)
bbox = path.get_extents()
fraction_x = (bbox.max[0] - bbox.min[0]) / (log10(range_x[1]) - log10(range_x[0]))
fraction_y = (bbox.max[1] - bbox.min[1]) / (log10(range_y[1]) - log10(range_y[0]))
resolution_x = int(resolution * fraction_x) + 2
resolution_y = int(resolution * fraction_y) + 2
x = np.linspace(bbox.min[0], bbox.max[0], resolution_x)
y = np.linspace(bbox.min[1], bbox.max[1], resolution_y)
points = [bbox.min, (bbox.min[0], bbox.max[1]), bbox.max, (bbox.max[0], bbox.min[1])]
return (points, x, y, path)
def generate_plot_lattice_bounds_new(case, p_vals, x_variable, y_variable, range_x, range_y, resolution):
V = case.vertices_2D_slice(p_vals, x_variable, y_variable,
range_x=range_x, range_y=range_y,
log_out=True)
path=mt.path.Path(V)
bbox=path.get_extents()
## fraction_x = (bbox.max[0]-bbox.min[0])/(log10(range_x[1])-log10(range_x[0]))
## fraction_y = (bbox.max[1]-bbox.min[1])/(log10(range_y[1])-log10(range_y[0]))
## resolution_x = int(resolution*fraction_x)+2
## resolution_y = int(resolution*fraction_y)+2
x=np.linspace(log10(range_x[0]), log10(range_x[1]), resolution)
y=np.linspace(log10(range_y[0]), log10(range_y[1]), resolution)
i= 0
j = 0
x_indices = []
y_indices = []
for xi in x[:-1]:
if xi > bbox.min[0]:
break
i += 1
x_indices.append(max(0, i-1))
for xi in x[i:-1]:
if xi > bbox.max[0]:
break
i += 1
x_indices.append(min(len(y), i+1))
for yi in y[:-1]:
if yi > bbox.min[1]:
break
j += 1
y_indices.append(max(0, j-1))
for yi in y[j:-1]:
if yi > bbox.max[1]:
break
j += 1
y_indices.append(min(len(y), j+1))
return (x_indices,y_indices,path)
def draw_2D_positive_roots(self, ax, p_vals, x_variable, y_variable, range_x,
range_y, color_dict=None, colorbar=True,
resolution=100, cmap=mt.cm.jet,
included_cases=None):
if color_dict is None:
color_dict = dict()
p_bounds = dict(p_vals)
p_bounds[x_variable] = range_x
p_bounds[y_variable] = range_y
hatched_cases = []
if included_cases is not None:
included_cases = [i.case_number for i in self(included_cases)]
if self.number_of_cases < 1e5:
valid_cases = self.valid_cases(p_bounds=p_bounds)
hatched_cases = [i for i in valid_cases if i not in included_cases]
valid_cases = [i for i in valid_cases if i in included_cases]
else:
valid_cases = [i for i in included_cases if self(i).is_valid(p_bounds=p_bounds)]
valid_nonstrict = []
else:
valid_cases = self.valid_cases(p_bounds=p_bounds)
ssystems = list()
for case_number in valid_cases:
case = self(case_number)
if isinstance(case, CyclicalCase) is True:
V = case.vertices_2D_slice(p_vals, x_variable, y_variable,
range_x=[range_x[0]/2, range_x[1]*2],
range_y=[range_y[0]/2, range_y[1]*2],
log_out=True)
for subcase in V:
path=mt.path.Path(V[subcase], closed=False)
ssystems.append((path, case))
else:
V = case.vertices_2D_slice(p_vals, x_variable, y_variable,
range_x=[range_x[0]/2, range_x[1]*2],
range_y=[range_y[0]/2, range_y[1]*2],
log_out=True)
path=mt.path.Path(V, closed=False)
ssystems.append((path, case.ssystem.remove_algebraic_constraints()))
x = np.linspace(log10(range_x[0]), log10(range_x[1]), resolution)
y = np.linspace(log10(range_y[0]), log10(range_y[1]), resolution)
X, Y = np.meshgrid(x, y)
Z=np.zeros((len(x), len(y)), dtype=np.int)
Z = Z - 1
values = dict()
params = VariablePool(p_vals)
for i in xrange(len(y)):
yi = y[i]
params[y_variable] = 10**yi
for j in xrange(len(x)):
xj = x[j]
params[x_variable] = 10**xj
Zj = []
for path, system in ssystems:
if path.contains_point((xj, yi)):
roots = system.positive_roots(params)
if isinstance(roots, dict) is True:
for subcase in roots:
Zj.append(roots[subcase])
else:
Zj.append(roots)
Zj.sort()
nums = [num for num in Zj]
if len(nums) == 0:
continue
key = str(nums[0])
for index in xrange(1, len(nums)):
key += ','+str(nums[index])
try:
Z[i,j] = values[key]
except KeyError:
Z[i,j] = len(values)
values[key] = len(values)
colors = dict()
for i in values:
colors[values[i]] = cmap(values[i]/(len(values)))
if i in color_dict:
colors[values[i]] = color_dict[i]
fc = [colors[i] for i in xrange(len(values))]
cf=ax.contourf(X, Y, Z, cmap=None,
levels=[-2, -1] + [i for i in xrange(len(values)+1)],
colors = ['k'] + fc + ['k'])
colors = {key:colors[values[key]] for key in values}
if colorbar is True:
c_ax,kw=mt.colorbar.make_axes(ax)
c_ax.set_aspect(15)
self.draw_region_colorbar(c_ax, colors)
ax.set_xlim([log10(min(range_x)), log10(max(range_x))])
ax.set_ylim([log10(min(range_y)), log10(max(range_y))])
if x_variable in self._latex:
x_variable = '$'+self._latex[x_variable]+'$'
if y_variable in self._latex:
y_variable = '$'+self._latex[y_variable]+'$'
ax.set_xlabel(r'$\log_{10}$(' + x_variable + ')')
ax.set_ylabel(r'$\log_{10}$(' + y_variable + ')')
return cf, colors
def draw_2D_routh_index(self, ax, p_vals, x_variable, y_variable, range_x, range_y, color_dict=None,
colorbar=True, resolution=100, cmap=mt.cm.Spectral_r):
if color_dict is None:
color_dict = dict()
p_bounds = dict(p_vals)
p_bounds[x_variable] = range_x
p_bounds[y_variable] = range_y
valid_cases = self.valid_cases(p_bounds=p_bounds)
ssystems = list()
for case_number in valid_cases:
case = self(case_number)
V = case.vertices_2D_slice(p_vals, x_variable, y_variable,
range_x=[range_x[0]/2, range_x[1]*2], range_y=[range_y[0]/2, range_y[1]*2],
log_out=True)
path=mt.path.Path(V, closed=False)
ssystems.append((path, case.ssystem.remove_algebraic_constraints()))
x = np.linspace(log10(range_x[0]), log10(range_x[1]), resolution)
y = np.linspace(log10(range_y[0]), log10(range_y[1]), resolution)
X, Y = np.meshgrid(x, y)
Z=np.zeros((len(x), len(y)), dtype=np.int)
values = dict()
params = VariablePool(p_vals)
Zj = set()
for i in xrange(len(y)):
yi = y[i]
params[y_variable] = 10**yi
for j in xrange(len(x)):
xj = x[j]
params[x_variable] = 10**xj
Zj.clear()
for path, ssystem in ssystems:
if path.contains_point((xj, yi)):
Zj.add(ssystem.routh_index(params))
nums = [num for num in Zj]
if len(nums) == 0:
continue
key = str(nums[0])
for index in xrange(1, len(nums)):
key += ','+str(nums[index])
try:
Z[i,j] = values[key]
except KeyError:
Z[i,j] = len(values)
values[key] = len(values)
colors = dict()
for i in values:
colors[values[i]] = cmap(values[i]/(len(values)))
if i in color_dict:
colors[values[i]] = color_dict[i]
fc = [colors[i] for i in xrange(len(values))]
cf=ax.contourf(X, Y, Z, cmap=None,
levels=[-1] + [i for i in xrange(len(values)+1)],
colors = fc + ['k'])
colors = {key:colors[values[key]] for key in values}
if colorbar is True:
c_ax,kw=mt.colorbar.make_axes(ax)
c_ax.set_aspect(15)
self.draw_region_colorbar(c_ax, colors)
ax.set_xlim([log10(min(range_x)), log10(max(range_x))])
ax.set_ylim([log10(min(range_y)), log10(max(range_y))])
if x_variable in self._latex:
x_variable = '$'+self._latex[x_variable]+'$'
if y_variable in self._latex:
y_variable = '$'+self._latex[y_variable]+'$'
ax.set_xlabel(r'$\log_{10}$(' + x_variable + ')')
ax.set_ylabel(r'$\log_{10}$(' + y_variable + ')')
return cf, colors