def plot():
e = Symbol('e')
y = Symbol('y')
n = Symbol('n')
generalized_vc_bounds = (original_vc_bound, rademacher_penalty_bound)
growth_function_bound = generate_growth_function_bound(50)
p1 = plot(original_vc_bound(n, 0.05, growth_function_bound), (n,100, 15000), show=False, line_color = 'black')
p2 = plot(rademacher_penalty_bound(n, 0.05, growth_function_bound), (n,100, 15000), show=False, line_color = 'blue')
plot_implicit(Eq(e, parrondo_van_den_broek_right(e, n, 0.05, growth_function_bound)), (n,100, 15000), (e,0,5))
# plot_implicit(Eq(e, devroye(e, n, 0.05, growth_function_bound)), (n,100, 1000), (e,0,5))
p1.extend(p2)
p1.show()
def plot_and_save(expr, *args, **kwargs):
name = kwargs.pop('name', '')
dir = kwargs.pop('dir', None)
p = plot_implicit(expr, *args, **kwargs)
p.save(tmp_file(dir=dir, name=name))
# Close the plot to avoid a warning from matplotlib
p._backend.close()
def test_region_and():
matplotlib = import_module("matplotlib",
min_module_version="1.1.0",
catch=(RuntimeError, ))
if not matplotlib:
skip("Matplotlib not the default backend")
from matplotlib.testing.compare import compare_images
test_directory = os.path.dirname(os.path.abspath(__file__))
try:
temp_dir = mkdtemp()
TmpFileManager.tmp_folder(temp_dir)
x, y = symbols("x y")
r1 = (x - 1)**2 + y**2 < 2
r2 = (x + 1)**2 + y**2 < 2
test_filename = tmp_file(dir=temp_dir, name="test_region_and")
cmp_filename = os.path.join(test_directory, "test_region_and.png")
p = plot_implicit(r1 & r2, x, y)
p.save(test_filename)
compare_images(cmp_filename, test_filename, 0.005)
test_filename = tmp_file(dir=temp_dir, name="test_region_or")
cmp_filename = os.path.join(test_directory, "test_region_or.png")
p = plot_implicit(r1 | r2, x, y)
p.save(test_filename)
compare_images(cmp_filename, test_filename, 0.005)
test_filename = tmp_file(dir=temp_dir, name="test_region_not")
cmp_filename = os.path.join(test_directory, "test_region_not.png")
p = plot_implicit(~r1, x, y)
p.save(test_filename)
compare_images(cmp_filename, test_filename, 0.005)
test_filename = tmp_file(dir=temp_dir, name="test_region_xor")
cmp_filename = os.path.join(test_directory, "test_region_xor.png")
p = plot_implicit(r1 ^ r2, x, y)
p.save(test_filename)
compare_images(cmp_filename, test_filename, 0.005)
finally:
TmpFileManager.cleanup()
def draw(self, xmin, xmax, ymin, ymax):
x = symbols('x')
y = symbols('y')
function = self.equation('x', 'y', False)
as1, as2 = self.asymptote('x', 'y', False)
p1 = plot_implicit(function, (x, xmin, xmax), (y, ymin, ymax),
title='Graph of the Hyperbola',
line_color='blue',
show=False)
p2 = plot_implicit(as1, (x, xmin, xmax), (y, ymin, ymax),
line_color='crimson',
show=False)
p3 = plot_implicit(as2, (x, xmin, xmax), (y, ymin, ymax),
line_color='crimson',
show=False)
p1.append(p2[0])
p1.append(p3[0])
p1.show()
def plot_equation(eq: Equality, x_var=None, y_var=None, ):
# 创建plot但不绘制
plot = plot_implicit(eq, x_var, y_var, show=False)
# 自己初始化一个绘制引擎
matplot = MatplotlibBackend(plot)
# backend 给每个plot创建一个单独的坐标系，所以要取出坐标系来单独设置
ax: Axes = matplot.ax[0]
ax.set_aspect('equal')
ax.grid(True)
matplot.show()
def plot():
e = Symbol('e')
y = Symbol('y')
n = Symbol('n')
generalized_vc_bounds = (original_vc_bound, rademacher_penalty_bound)
growth_function_bound = generate_growth_function_bound(50)
p1 = plot(original_vc_bound(n, 0.05, growth_function_bound),
(n, 100, 15000),
show=False,
line_color='black')
p2 = plot(rademacher_penalty_bound(n, 0.05, growth_function_bound),
(n, 100, 15000),
show=False,
line_color='blue')
plot_implicit(
Eq(e, parrondo_van_den_broek_right(e, n, 0.05, growth_function_bound)),
(n, 100, 15000), (e, 0, 5))
# plot_implicit(Eq(e, devroye(e, n, 0.05, growth_function_bound)), (n,100, 1000), (e,0,5))
p1.extend(p2)
p1.show()
def ezplot(expr, color):
try:
plot = plot_implicit(self.parseEquation(expr, x, y),
(x, varXBegin, varXEnd),
(y, varYBegin, varYEnd),
show=False,
line_color=color)
except Exception as e:
plot = None
if not plot:
print("Failed to plot expression: ", expr)
return plot
def plotXhh(mh1_0, mh2_0, r, Xhh_cut, mh1_min, mh1_max, mh2_min, mh2_max,
color):
mh1, mh2 = sp.symbols('mh1 mh2')
sg_expr = ((mh1 - mh1_0) / (r * mh1))**2 + ((mh2 - mh2_0) / (r * mh2))**2
sg_eq = sp.Eq(sg_expr, Xhh_cut**2)
plot = sp.plot_implicit(sg_eq,
x_var=(mh1, mh1_min, mh1_max),
y_var=(mh2, mh2_min, mh2_max),
show=False,
axis_center=(mh1_min, mh2_min))
x, y = zip(*[(x_int.mid, y_int.mid)
for x_int, y_int in plot[0].get_points()[0]])
x, y = list(x), list(y)
plt.plot(x, y, '.', markersize=0.5, color=color)
def draw_plots():
x, y = sy.symbols('x, y')
func1 = sy.Or(sy.Eq(x**2 + y**2 - 4, 0), sy.Eq(x**4 - y - 4, 0))
func2 = sy.Or(sy.Eq((x - 1)**2 + y**2 - 9, 0),
sy.Eq(sy.tan(x - 1) - y**3, 0))
func3 = sy.Or(sy.Eq(x**2 + y**2 - 4, 0), sy.Eq(x**2 + y**2 - 1, 0))
sy.plot_implicit(func1)
sy.plot_implicit(func2, (x, -4, 6), (y, -5, 5))
sy.plot_implicit(func3)
import matplotlib.patches as patches
init_printing()
var('x,y', real=True)
f = (x - 0.5)**3 - 4 * (x - 0.5)**2 + 3 * (x - 0.5) + 1 + 2.5
# pts criticos
pc = solve(f.diff())
p = plot(f, (x, 0.5, 3.25), line_color='blue', show=False)
q = plot(-0.5, (x, -0.5, 3.75), line_color='none', show=False)
p.extend(q)
q = plot(5, (x, -0.5, 3.75), line_color='none', show=False)
p.extend(q)
q = plot_implicit(y <= f, (x, 0.5, 3.25), (y, 0, 5),
show=False,
line_color="gray")
p.extend(q)
p.xlabel = '$x$'
p.ylabel = '$y$'
p.save('fig_geointdef.png')
fig = p._backend.fig
ax = fig.axes[0]
ax.grid('on')
ax.set_xticks([0.5, 3.25])
ax.set_xticklabels(["$a$", "$b$"])
ax.set_yticks([float(f.subs(x, 0.5)), float(f.subs(x, 3.25))])
ax.set_yticklabels([])
ax.text(3.25, 2.5, "$y=f(x)$")
from sympy import plot_implicit, cos, sin, symbols, Eq, And, plot
from sympy.parsing.sympy_parser import parse_expr
points = []
for i in xrange(0,10):
for j in xrange(0,10):
points.append(complex(i,j))
p = 20000
x,y = symbols('x y')
func = ''
for i in xrange(len(points) - 1):
func += ('((x-'+str(points[i].real)+')**2 + (y-'+str(points[i].imag)+')**2)*')
func += ('((x-'+str(points[len(points)-1].real)+')**2 + (y-'+str(points[len(points)-1].imag)+')**2)')
func += ('-' + str(p**2))
print(func)
print(Eq(parse_expr(func)))
plot_implicit(Eq(parse_expr(func)), (x,-10,10), (y,-10,10))
L = (a + c) / 2.0
R = (c + b) / 2.0
Fa = func.subs(x, a)
Fb = func.subs(x, b)
Fc = func.subs(x, c)
FL = func.subs(x, L)
FR = func.subs(x, R)
Fmin = min(Fa, Fb, Fc, FL, FR)
if Fmin == Fa or Fmin == FL:
b = c
c = L
elif Fmin == Fb or Fmin == FR:
a = c
c = R
elif Fmin == Fc:
a = L
b = R
print(c)
sp.plot(func, (x, -1, 4), line_color='r')
x, y = sp.symbols("x y")
hp = sp.plot_implicit(sp.Eq(x**2 + y**2, 4), (x, -3, 3), (y, -3, 3))
fig = hp._backend.fig
ax = hp._backend.ax
xx = yy = np.linspace(-3, 3)
ax.plot(xx, yy) # y = x
ax.plot([0], [0], 'o') # Point (0,0)
ax.set_aspect('equal', 'datalim')
fig.canvas.draw()
#!/usr/bin/env python
# -*- coding: utf-8 -*-
import sympy as sym
if __name__ == "__main__":
x, y = sym.symbols('x, y')
f = x**2 + y**2 - 1
g = sym.tan(x * y + 0.5) - x**2
args = (x, -2, 2), (y, -2, 2)
curve_f = sym.plot_implicit(sym.Eq(f, 0), *args, show=False)
curve_g = sym.plot_implicit(sym.Eq(g, 0), *args, show=False)
curve_g.extend(curve_f)
curve_g.show()
"""
你是公司营销系统的工程师。
你们某个商品的购买概率和补贴额的关系为，p(x) = 0.05 x + 0.2。
该商品原价 m 为 16 元，成本价 c 为 8 元，求利润最大的补贴额应该是多少？
"""
from sympy import expand, symbols, plot_implicit, Eq
import math
from sympy.abc import x, y
p1 = plot_implicit(Eq(-0.0025 * x**2 + 0.38 * x + 1.56, y))
x = symbols('x')
print(expand((16 - 8 - 0.05 * x - 0.2) * (0.05 * x + 0.2)))
def getSubsidy(k, b, m, c):
rx = [-k, k * (m - c) - b, b * (m - c)]
# -系数 (m-c-kx-0.2)*(kx+0.2)
# (16-8-0.05x-0.2)*(0.05x+0.2)
rpx = [-2 * k, k * (m - c) - b]
return -rpx[1] / rpx[0]
# print(getSubsidy(0.05, 0.2, 16, 8))
for i in range(time):
x_list.append(x_list[i] + (x_movement(x_list[i], y_list[i])) * dt)
y_list.append(y_list[i] + (y_movement(x_list[i], y_list[i])) * dt)
ax.plot(x_list, y_list, color="black")
# Quiverplot
# create a grid and set the dir vecs
X, Y = np.meshgrid(x_line, y_line)
x_dir, y_dir = x_movement(X, Y), y_movement(X, Y)
# prepare the colour and normalization factor
norm = np.sqrt(x_dir**2 + y_dir**2)
#Normalize
if normalize:
x_dir /= norm
y_dir /= norm
plt.quiver(X, Y, x_dir, y_dir, norm, pivot='mid')
# Plot Nullclines
p1 = sm.plot_implicit(dot_x_Equal, (x, x_min, x_max), (y, y_min, y_max),
show=False)
p2 = sm.plot_implicit(dot_y_Equal, (x, x_min, x_max), (y, y_min, y_max),
show=False)
move_sympyplot_to_axes(p1, ax)
move_sympyplot_to_axes(p2, ax)
plt.show()
M_t, a, psi, G, theta, z, x, y = sp.var('M_t, a, psi, G, theta, Z, X, Y')
C = sp.var(['C_' + str(i) for i in range(10)])
#criando as bordas da seção transversal (triângulo)
f = sp.Matrix([
y + sp.sqrt(3) * x - 2 * a,
y - sp.sqrt(3) * x - 2 * a,
y - a,
])
p2 = []
for i in f:
p1 = sp.plot_implicit(sp.Eq(i.subs({a: 1}), 0), (x, -4, 4), (y, -4, 4))
p2.append(p1)
[p2[0].extend(i) for i in p2]
p2[0].show()
#criação de psi dada no exercício
psi, alpha, mu, g = sp.var('psi, alpha, mu, G')
theta = sp.Function('theta')(x, y, z)
psi = -g * theta.diff(z) * ((x**2 + y**2) / 2 - (x**3 - 3 * x * y**2) /
(2 * a) - 2 * a**2 / 27)
T = sp.zeros(3)
T[0, 1] = T[1, 0] = +psi.diff(y, ).simplify()
filter (1 pole, 1 zero) to be used in a series connection...
p2 is always a hyperbola that goes trough 0 and 1. For continuity around
w=0.5*pi, we seem to have to use the lower arm (the one that goes through 0).
However, that solution tends to grow large for small w.
..hmm - this soltuion is very small around w=pi/2
but with the upper arm, there's a intersection only for certain values of w
..maybe the 1 pole / 1 zero idea is not really good, after all and we should
stick to 1 pole / 0 zero
"""
from sympy import plot_implicit, symbols, sin, cos, tan, pi
w = 0.45 * pi # cutoff frequency
# intermediate parameters:
s = sin(w)
c = cos(w)
t = tan((w - pi) / 4)
#define symbols and equations:
x, y = symbols('x y') # x=b0, y=b1
a = x + y - 1 # a = a1 = b0+b1-1
e1 = 2 * (1 - c) * (x + y - x * y - 1) + x**2 + y**2
e2 = t * (x + a * y + (y + a * x) * c) - s * (a * x - y)
# plot the two conics:
p1 = plot_implicit(e1, (x, -2, 2), (y, -2, 2))
p2 = plot_implicit(e2, (x, -2, 2), (y, -2, 2))
#p2 = plot_implicit(e2)
from sympy import plot_implicit, symbols, Eq, solve
x, y = symbols('x y')
eq = Eq((x**2 + y**2 - 1)**3 - (x**2) * (y**3))
plot_implicit(eq)
def plot_and_save(name):
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
#implicit plot tests
plot_implicit(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2)).save(tmp_file(name))
plot_implicit(Eq(y**2, x**3 - x), (x, -5, 5),
(y, -4, 4)).save(tmp_file(name))
plot_implicit(y > 1 / x, (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y < 1 / tan(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y >= 2 * sin(x) * cos(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y <= x**2, (x, -3, 3),
(y, -1, 5)).save(tmp_file(name))
#Test all input args for plot_implicit
plot_implicit(Eq(y**2, x**3 - x)).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False, points=500).save(tmp_file())
plot_implicit(y > x, (x, -5, 5)).save(tmp_file())
plot_implicit(And(y > exp(x), y > x + 2)).save(tmp_file())
plot_implicit(Or(y > x, y > -x)).save(tmp_file())
plot_implicit(x**2 - 1, (x, -5, 5)).save(tmp_file())
plot_implicit(x**2 - 1).save(tmp_file())
plot_implicit(y > x, depth=-5).save(tmp_file())
plot_implicit(y > x, depth=5).save(tmp_file())
plot_implicit(y > cos(x), adaptive=False).save(tmp_file())
plot_implicit(y < cos(x), adaptive=False).save(tmp_file())
plot_implicit(And(y > cos(x), Or(y > x, Eq(y, x)))).save(tmp_file())
plot_implicit(y - cos(pi / x)).save(tmp_file())
#Test plots which cannot be rendered using the adaptive algorithm
#TODO: catch the warning.
plot_implicit(Eq(y, re(cos(x) + I*sin(x)))).save(tmp_file(name))
with warnings.catch_warnings(record=True) as w:
plot_implicit(x**2 - 1, legend='An implicit plot').save(tmp_file())
assert len(w) == 1
assert issubclass(w[-1].category, UserWarning)
assert 'No labeled objects found' in str(w[0].message)
def plot(self, filename, input_epsilon):
"""
------------------------------------------------------------------
moving_delta_epsilon: If the associated proof has been finished,
it will create a gif of the delta-epsilon lines.
------------------------------------------------------------------
Parameters:
filename - where to save graph
------------------------------------------------------------------
"""
# we need to consider the following cases:
# delta epsilon proofs => regular DONE
# N/M or both option
# mins on delta/epsilon/N/M?
# issues/things to consider:
# vertical delta lines not working
# too much memory being consumed due to plotting.
# directory vs. file
x = sm.Symbol('x')
y = sm.Symbol('y')
graphs_extend = []
# if proof is done
if self.current_equation == self.epsilon:
# find delta/epsilon bounds
input_delta = self.delta_exp.subs(self.epsilon, input_epsilon)
# is it delta?
if str(self.delta) == 'delta':
# is it bounded?
if self.delta_bound != 0 and input_delta > self.delta_bound:
input_delta = self.delta_bound
# create bounds
x_upper_bound = self.x0 + input_delta
x_lower_bound = self.x0 - input_delta
x_dim = (x, self.x0 - input_delta * 3,
self.x0 + input_delta * 3)
# is it N?
else:
if self.x0 == sm.oo:
x_lower_bound = input_delta
x_upper_bound = None
x_dim = (x, x_lower_bound - x_lower_bound * 0.5,
x_lower_bound + x_lower_bound * 0.5)
else:
x_lower_bound = None
x_upper_bound = input_delta
x_dim = (x, x_upper_bound - x_upper_bound * 0.5,
x_upper_bound + x_upper_bound * 0.5)
# is it epsilon?
if str(self.epsilon) == 'epsilon':
y_upper_bound = self.limit + input_epsilon
y_lower_bound = self.limit - input_epsilon
graphs_extend.append(
splot(y_lower_bound, show=False, line_color="red"))
graphs_extend.append(
splot(y_upper_bound, show=False, line_color="red"))
y_dim = (y, self.limit - input_epsilon * 3,
self.limit + input_epsilon * 3)
# is it M?
else:
if self.limit == sm.oo:
y_lower_bound = input_epsilon
graphs_extend.append(
splot(y_lower_bound, show=False, line_color="red"))
y_dim = (y, y_lower_bound - y_lower_bound * 0.5,
y_lower_bound + y_lower_bound * 0.5)
else:
y_upper_bound = input_epsilon
graphs_extend.append(
splot(y_upper_bound, show=False, line_color="red"))
y_dim = (y, y_upper_bound - y_upper_bound * 0.5,
y_upper_bound + y_upper_bound * 0.5)
# create graphs for the x axis
graphs_extend.append(
plot_implicit(sm.Eq(x, x_upper_bound),
x_dim,
y_dim,
line_color="blue",
show=False))
graphs_extend.append(
plot_implicit(sm.Eq(x, x_lower_bound),
x_dim,
y_dim,
line_color="blue",
show=False))
fx_graph = splot(self.fx,
show=False,
xlim=(x_dim[1], x_dim[2]),
ylim=(y_dim[1], y_dim[2]),
line_color="black")
# merge graphs
for graph in graphs_extend:
fx_graph.extend(graph)
fx_graph.save(filename)
def main():
vca = VCA(eps=0.005, max_dimension=4)
vca.fit(np.array([[-1, 0], [1, 0], [0, 1], [0, -1]]))
print vca.components_
for fn in vca.components_:
plot_implicit(fn)
import sympy as sp
import pandas as pd
import matplotlib
x, y = sp.symbols('x y')
f = sp.sin(x - 0.4 * y) - x + y**2
g = (y + 0.1)**2 + x**2 - 0.7
plot = sp.plot_implicit(sp.Eq(f, 0), show=False, line_color='blue')
plot.extend(sp.plot_implicit(sp.Eq(g, 0), show=False, line_color='green'))
plot.show()
def newton_system(x, y, f, g, x0, y0):
dfdx = f.diff(x)
dfdy = f.diff(y)
dgdx = g.diff(x)
dgdy = g.diff(y)
d = dfdx * dgdy - dgdx * dfdy
dx = f * dgdy - g * dfdy
dy = dfdx * g - dgdx * f
xs, ys, norms, fs, gs = [], [], [], [], []
xk, yk = x0, y0
while True:
new_x = xk - (dx / d).evalf(subs={x: xk, y: yk})
new_y = yk - (dy / d).evalf(subs={x: xk, y: yk})
xs.append(new_x)
ys.append(new_y)
break
xk = xk_1
yk = yk_1
k += 1
data = xx, yy, differ, val_f, val_g
columns = ["x_k", "y_k", "norma", "f(x_k, y_k)", "g(x_k, y_k)"]
df = pd.DataFrame(data, columns).T
df.columns.name = "k"
return df, val
x, y = sp.symbols('x y')
plt1 = sp.plot_implicit(sp.Eq((y + 0.1)**2 + x**2 - 0.2, 0), (x, -0.7, 0.7),
(y, -0.7, 0.7),
show=False)
plt2 = sp.plot_implicit(sp.Eq(x - y**2 - 0.37731, 0), (x, -1, 1), (y, -1, 1),
show=False)
plt1.extend(plt2)
plt1.show()
#(y + 0.1) ** 2 + x ** 2 = 0.2
#x - y ** 2 = 0.37731
f = lambda x, y: (y + 0.1)**2 + x**2 - 0.2
g = lambda x, y: x - y**2 - 0.37731
df_x = lambda x, y: 2 * x
df_y = lambda x, y: 2 * y + 0.2
dg_x = lambda x: 1
dg_y = lambda y: -2 * y
eps = 0.00001
def plot_and_save():
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
#implicit plot tests
plot_implicit(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2)).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), (x, -5, 5),
(y, -4, 4)).save(tmp_file())
plot_implicit(y > 1 / x, (x, -5, 5),
(y, -2, 2)).save(tmp_file())
plot_implicit(y < 1 / tan(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file())
plot_implicit(y >= 2 * sin(x) * cos(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file())
plot_implicit(y <= x**2, (x, -3, 3),
(y, -1, 5)).save(tmp_file())
#Test all input args for plot_implicit
plot_implicit(Eq(y**2, x**3 - x)).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False, points = 500).save(tmp_file())
plot_implicit(y > x, (x, -5, 5)).save(tmp_file())
plot_implicit(And(y > exp(x), y > x + 2)).save(tmp_file())
plot_implicit(Or(y > x, y > -x)).save(tmp_file())
plot_implicit(x**2 - 1, (x, -5, 5)).save(tmp_file())
plot_implicit(x**2 - 1).save(tmp_file())
plot_implicit(y > x, depth = -5).save(tmp_file())
plot_implicit(y > x, depth = 5).save(tmp_file())
plot_implicit(y > cos(x), adaptive=False).save(tmp_file())
plot_implicit(y < cos(x), adaptive=False).save(tmp_file())
plot_implicit(And(y > cos(x), Or(y > x, Eq(y, x)))).save(tmp_file())
#Test plots which cannot be rendered using the adaptive algorithm
#TODO: catch the warning.
plot_implicit(Eq(y, re(cos(x) + I*sin(x)))).save(tmp_file())
QDA_score = np.diag(QDA(mu0, mu1, cov0, cov1, data.T))
QDA_result = np.array(QDA_score > 0)
# LDA plot
w = (mu1 - mu0).T.dot(np.linalg.inv(cov))
b = -1 / 2 * ((mu1.T).dot(np.linalg.inv(cov)).dot(mu1) -
(mu0.T).dot(np.linalg.inv(cov)).dot(mu0))[0][0]
x = np.arange(0, 6, 0.1)
y = (w[0, 0] * x + b) / (-w[0, 1])
plt.scatter(x=data[:, 0], y=data[:, 1], c=LDA_result.reshape(-1))
plt.plot(x, y)
plt.xlabel('data[:,0]')
plt.ylabel('data[:,1]')
plt.title('LDA')
plt.show()
# QDA plot
from sympy import plot_implicit, cos, sin, symbols, Eq, And
x, y = symbols('x y')
X = np.array([x, y]).reshape((2, 1))
diff1 = np.linalg.inv(cov0) - np.linalg.inv(cov1)
diff2 = np.linalg.inv(cov0).dot(mu0) - np.linalg.inv(cov1).dot(mu1)
threshold = 1/2*((mu1.T).dot(np.linalg.inv(cov)).dot(mu1)-(mu0.T).dot(np.linalg.inv(cov)).dot(mu0))[0][0] + \
1/2*np.log(np.linalg.det(cov1)/np.linalg.det(cov0))
expr = 1 / 2 * (X.T.dot(diff1).dot(X)) - X.T.dot(diff2) - threshold
plt2 = plot_implicit(Eq(expr[0, 0], 0), (x, -5, 5), (y, -6, 6))
plt2._backend.ax.scatter(data_0[:, 0], data_0[:, 1], label='data_0')
plt2._backend.ax.scatter(data_1[:, 0], data_1[:, 1], label='data_1')
plt2._backend.save('plt2.png')
import numpy as np
from scipy.stats import beta
from sympy import symbols, plot_implicit, Eq, solve, S, solveset
n, p = symbols('n p')
eq = Eq(n * p * (1 - p)**(n - 1) - 0.05)
plt = plot_implicit(eq, x_var=(n, 1, 30), y_var=(p, 0.0001, .9999))
ns = range(15, 17)
eps = .01
sols = [solve(Eq(n * p * (1 - p)**(n - 1) - eps), p) for n in ns]
ps = [s[1] if len(s) > 1 else s[0] for s in sols]
[p * n for p, n in zip(ps, ns)]
beta, n, j, k = symbols('beta n j k')
eq = beta**(j - n) / (2 + j) * Product(1 - 1 / {1 + k}, (k, n + 1, j))
s = Sum(eq, (j, n + 1, oo))
p = 1 / (1 + n) + s
def u(rho):
if rho == 1:
return lambda c: np.log(c + 1)
else:
return lambda c: ((c + 1)**(1 - rho) - 1) / (1 - rho)
def vq(out, beta):
return out / (1 - beta)
# Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat.
# Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat.
# Every package must provide at least 5 units of protein, at least 9 units of carbohydrates, and no more than 8 units of fat.
# Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
# a. Write a system of inequalities to express the conditions of the problem.
# b. Graph the feasible region of the system.
# https://www.desmos.com/
from sympy import symbols, plot_implicit, plot
from sympy.plotting import plot_parametric
x_rng = 15
y_rng = 15
x, y = symbols('x, y')
exprs = [[x + y >= 5, 'b'], [2 * x + y >= 10, 'r'], [x + y <= 8, 'g']]
p = plot_implicit( exprs[ 0 ][ 0 ], ( x, -x_rng, x_rng ), ( y, -y_rng, y_rng ),\
line_color = exprs[ 0 ][ 1 ], show = False )
p.extend( plot_implicit( exprs[ 1 ][ 0 ], ( x, -x_rng, x_rng ), ( y, -y_rng, y_rng ),\
line_color = exprs[ 1 ][ 1 ], show = False ) )
p.extend( plot_implicit( exprs[ 2 ][ 0 ], ( x, -x_rng, x_rng ), ( y, -y_rng, y_rng ),\
line_color = exprs[ 2 ][ 1 ], show = False ) )
p.show()
def test_line_color():
x, y = symbols("x, y")
p = plot_implicit(x**2 + y**2 - 1, line_color="green", show=False)
assert p._series[0].line_color == "green"
p = plot_implicit(x**2 + y**2 - 1, line_color="r", show=False)
assert p._series[0].line_color == "r"
def test_line_color():
x, y = symbols('x, y')
p = plot_implicit(x**2 + y**2 - 1, line_color="green", show=False)
assert p._series[0].line_color == "green"
p = plot_implicit(x**2 + y**2 - 1, line_color='r', show=False)
assert p._series[0].line_color == "r"
from sympy import symbols, plot_implicit, Eq, plot_parametric
from math import sqrt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
x, y, t = symbols('x y t')
if True:
p = plot_implicit(Eq(y * y + 3 * x * y - x * x * x + 4 * x, 1),
(x, -4.6, 7.8), (y, -6.4, 9.4),
adaptive=False,
depth=1,
points=2000,
line_color='grey',
show=False,
xlabel='$x$',
ylabel='$y$')
p.show()
if False: # circle
p = plot_implicit(Eq(x * x + y * y, 1), (x, -1.4, 1.4), (y, -1.4, 1.4),
adaptive=False,
depth=1,
points=2000,
line_color='grey',
show=False,
xlabel='',
ylabel='',
aspect_ratio=(1, 1))
p1 = plot_parametric((1 - 9 * t, 3 * t), show=False)
p.append(p1[0])
x_2 - a / 2,
x_2 + a / 2,
])
f_2 = sp.Matrix([
x_3 - b / 2,
x_3 + b / 2,
])
#aux=list( sp.utilities.iterables.subsets(f,3) ) # combina 2 a 2
#display(psi)
p2 = []
for i in f_1:
# display(psi.subs({'x_2':sp.solve(i,x_2)[0]}).simplify())
p1 = sp.plot_implicit(sp.Eq(i.subs({a: 2}), 0), (x_2, -4, 4), (x_3, -4, 4))
p2.append(p1)
for i in f_2:
# display(psi.subs({'x_3':sp.solve(i,x_3)[0]}).simplify())
p1 = sp.plot_implicit(sp.Eq(i.subs({b: 2}), 0), (x_2, -4, 4), (x_3, -4, 4))
p2.append(p1)
[p2[0].extend(i) for i in p2]
p2[0].show()
#%%
psi_t = ((2**5) * (a**2) * (b**2)) / (sp.pi**4) * ((-1)**(
(k + l) / 2 - 1)) / (k * l * ((k**2 * b**2) + (l**2 * a**2))) * sp.cos(
(k * x_2 * sp.pi) / a) * sp.cos((l * x_3 * sp.pi) / b)
def graph(self):
warnings.filterwarnings("ignore",
category=MatplotlibDeprecationWarning)
plot_implicit(self.display_equation.subs(e, E),
title="Grafico di " +
str(self.display_equation.subs(e, E)))
# -*- coding: utf-8 -*-
"""
Created on Fri Aug 19 13:57:17 2016
@author: karol
"""
from sympy import plot_implicit, And, Eq, symbols
from sympy.solvers import solve
madera, aluminio = symbols('madera aluminio')
frm = madera - 6
fra = aluminio - 4
frv = madera*6 + aluminio*8 - 48
fgt = madera*180 + aluminio*90
e1 = Eq(madera - 6, 0)
e3 = Eq(madera*6 + aluminio*8 - 48, 0)
sol = solve([Eq(frm, 0), Eq(frv, 0)], [madera, aluminio])
val_opt = fgt.subs(sol)
plot = plot_implicit(And(frm <= 0, fra <= 0, frv <= 0), (madera, -1, 10),
(aluminio, -1, 10), line_color='orange', show=False)
plot.extend(plot_implicit(Eq(fgt, val_opt), (madera, -1, 10),
(aluminio, -1, 10), line_color='blue', show=False))
plot.show()
def plot_and_save(name):
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
#implicit plot tests
plot_implicit(Eq(y, cos(x)), (x, -5, 5), (y, -2, 2)).save(tmp_file(name))
plot_implicit(Eq(y**2, x**3 - x), (x, -5, 5),
(y, -4, 4)).save(tmp_file(name))
plot_implicit(y > 1 / x, (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y < 1 / tan(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y >= 2 * sin(x) * cos(x), (x, -5, 5),
(y, -2, 2)).save(tmp_file(name))
plot_implicit(y <= x**2, (x, -3, 3),
(y, -1, 5)).save(tmp_file(name))
#Test all input args for plot_implicit
plot_implicit(Eq(y**2, x**3 - x)).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False).save(tmp_file())
plot_implicit(Eq(y**2, x**3 - x), adaptive=False, points=500).save(tmp_file())
plot_implicit(y > x, (x, -5, 5)).save(tmp_file())
plot_implicit(And(y > exp(x), y > x + 2)).save(tmp_file())
plot_implicit(Or(y > x, y > -x)).save(tmp_file())
plot_implicit(x**2 - 1, (x, -5, 5)).save(tmp_file())
plot_implicit(x**2 - 1).save(tmp_file())
plot_implicit(y > x, depth=-5).save(tmp_file())
plot_implicit(y > x, depth=5).save(tmp_file())
plot_implicit(y > cos(x), adaptive=False).save(tmp_file())
plot_implicit(y < cos(x), adaptive=False).save(tmp_file())
plot_implicit(And(y > cos(x), Or(y > x, Eq(y, x)))).save(tmp_file())
plot_implicit(y - cos(pi / x)).save(tmp_file())
#Test plots which cannot be rendered using the adaptive algorithm
#TODO: catch the warning.
plot_implicit(Eq(y, re(cos(x) + I*sin(x)))).save(tmp_file(name))
import os
from sympy import plot_implicit, symbols, Eq
# Instead 'Stars' write your path to exe. file
os.system("C:/Users/Lydsyf/PycharmProjects/Mini-Project/bin/Debug/Stars.exe")
with open("data.txt", 'r') as f:
data = f.readlines()
a = [float(i) for i in data[0].split()]
x, y = symbols('x y')
p = plot_implicit(Eq(a[0] * x**2 + a[1]*x*y + a[2] * y**2 + a[3] * x + a[4] * y + a[5], 0),
x_var=(x, -100, 100), y_var=(y, -100, 100), show=False, title='Minimum area ellipse')
for i in range(len(data)-1):
a = [float(i) for i in data[i+1].split()]
p1 = plot_implicit((x - a[0])**2 + (y - a[1])**2 <= 1,
x_var=(x, -100, 100), y_var=(y, -100, 100), show=False, line_color='red')
p.append(p1[0])
p.show()
# %%
N_t
theta_t
# %%
#sp.series(theta_t, x=N, x0=1, n=3)
print(sp.latex(sp.series(N_t, x=theta, x0=0, n=5)))
# %%
x = sp.symbols('x')
sp.series(sp.sqrt(1-x), x=x, x0=0, n=4)
# %%
i = 1.336
g = 2.689e-5
print((i-1)/2/g/i)
# %%
%matplotlib qt
sp.plot_implicit(sp.Eq((index-1)/gamma/index/2, 5000), (index, 1, 2), (gamma, 2e-5, 4e-5))
w
def eqy(x, y):
return numpy.sqrt((1 - a * (x ** 2)) / 2)
# Вычисление матрицы Якоби
def W(x, y):
return numpy.array([
[(1 + numpy.tan(x * y + m) ** 2) * y - 1, (1 + numpy.tan(x * y + m) ** 2) * x],
[2 * a * x, 4 * y]
])
# Графики исходных уравнений
plots = sympy.plot_implicit(sympy.Eq(eq1, 0), (x, -2, 2), (y, -2, 2), line_color="blue", show=False)
plots.extend(sympy.plot_implicit(sympy.Eq(eq2, 0), (x, -2, 2), (y, -2, 2), line_color="red", show=False))
# plots.show()
iters = 0
def SimpleSolve(x0, y0):
global iters
iters = 0
(x, y) = (x0, y0)
while True:
iters += 1
oldx = x
oldy = y
