def extend_solutions(sols):
"""
To each solution in sols, adds L1 and L2 with values 1,
and zz2 and zz3 with values zero.
"""
from phcpy.solutions import make_solution, coordinates
result = []
for sol in sols:
(vars, vals) = coordinates(sol)
vars = vars + ['L1', 'L2', 'zz2', 'zz3']
vals = vals + [1, 1, 0, 0]
extsol = make_solution(vars, vals)
result.append(extsol)
return result
def solution_plane(rows, cols, sol):
"""
Returns a sympy matrix with as many rows
as the value of rows and with as many columns
as the value of columns, using the string
represention of a solution in sol.
"""
from phcpy.solutions import coordinates
result = zeros((rows, cols), dtype=complex)
for k in range(cols):
result[k][k] = 1
(vars, vals) = coordinates(sol)
for (name, value) in zip(vars, vals):
i, j = indices(name)
result[i - 1][j - 1] = value
return result
def solution_plane(rows, cols, sol):
"""
Returns a sympy matrix with as many rows
as the value of rows and with as many columns
as the value of columns, using the string
represention of a solution in sol.
"""
from phcpy.solutions import coordinates
result = zeros((rows, cols), dtype=complex)
for k in range(cols):
result[k][k] = 1
(vars, vals) = coordinates(sol)
for (name, value) in zip(vars, vals):
i, j = indices(name)
result[i-1][j-1] = value
return result
def plot(self):
"""
Plots a coordinate of the list of solutions.
"""
from phcpy.solutions import coordinates
dim = self.dim
self.cnv.create_line(0, dim / 2, dim, dim / 2) # x coordinate axis
self.cnv.create_line(dim / 2, 0, dim / 2, dim) # y coordinate axis
(realmin, realmax, imagmin, imagmax) = windowsize(self.sols, self.idx)
dimreal = max(abs(realmin), abs(realmax))
dimimag = max(abs(imagmin), abs(imagmax))
factor = dim / 2 - 10 # the origin is at (dim/2, dim/2)
for sol in self.sols:
(names, values) = coordinates(sol)
val = values[self.idx]
xpt = dim / 2 + (val.real / dimreal) * factor
ypt = dim / 2 + (val.imag / dimimag) * factor
self.cnv.create_oval(xpt-3, ypt-3, \
xpt+3, ypt+3, fill='red')
def plot(self):
"""
Plots a coordinate of the list of solutions.
"""
from phcpy.solutions import coordinates
dim = self.dim
self.cnv.create_line(0, dim/2, dim, dim/2) # x coordinate axis
self.cnv.create_line(dim/2, 0, dim/2, dim) # y coordinate axis
(realmin, realmax, imagmin, imagmax) = windowsize(self.sols, self.idx)
dimreal = max(abs(realmin), abs(realmax))
dimimag = max(abs(imagmin), abs(imagmax))
factor = dim/2 - 10 # the origin is at (dim/2, dim/2)
for sol in self.sols:
(names, values) = coordinates(sol)
val = values[self.idx]
xpt = dim/2 + (val.real/dimreal)*factor
ypt = dim/2 + (val.imag/dimimag)*factor
self.cnv.create_oval(xpt-3, ypt-3, \
xpt+3, ypt+3, fill='red')
def windowsize(sols, idx):
"""
Returns the minimal and maximal value of the
real and imaginary parts of the coordinate with index idx
of the list of solutions in sols, as a tuple of 4 values:
(realmin, realmax, imagmin, imagmax).
"""
from phcpy.solutions import coordinates
(realmin, realmax, imagmin, imagmax) = (0, 0, 0, 0)
for sol in sols:
(names, values) = coordinates(sol)
val = values[idx]
if val.real < realmin:
realmin = val.real
if val.real > realmax:
realmax = val.real
if val.imag < imagmin:
imagmin = val.imag
if val.imag > imagmax:
imagmax = val.imag
return (realmin, realmax, imagmin, imagmax)
def windowsize(sols, idx):
"""
Returns the minimal and maximal value of the
real and imaginary parts of the coordinate with index idx
of the list of solutions in sols, as a tuple of 4 values:
(realmin, realmax, imagmin, imagmax).
"""
from phcpy.solutions import coordinates
(realmin, realmax, imagmin, imagmax) = (0, 0, 0, 0)
for sol in sols:
(names, values) = coordinates(sol)
val = values[idx]
if val.real < realmin:
realmin = val.real
if val.real > realmax:
realmax = val.real
if val.imag < imagmin:
imagmin = val.imag
if val.imag > imagmax:
imagmax = val.imag
return (realmin, realmax, imagmin, imagmax)
def special_solutions(pols, slope):
"""
Given in pols the polynomials for the line intersecting a circle
for a general slope s, solves the problem for a special numerical
value for s, given in the slope.
The value of the slope is added as last coordinate to each solution.
"""
from phcpy.solver import solve
from phcpy.solutions import make_solution, coordinates
special = []
for pol in pols:
rpl = pol.replace('s', '(' + str(slope) + ')')
special.append(rpl)
sols = solve(special, silent=True)
result = []
for sol in sols:
(vars, vals) = coordinates(sol)
vars.append('s')
vals.append(slope)
extsol = make_solution(vars, vals)
result.append(extsol)
return result