在同一图形上有不同x范围的两幅图，具有渐近性

Question

我正在绘制一个函数的曲线，它在p点是正切的，我想独立地管理曲线和切线的xlim。在此代码中，切线半长应为1：

from sympy import init_printing, symbols, N, plot
from sympy import diff
from sympy import log, cos, atan

init_printing()
x = symbols('x')

# Plot a tangent at point (p_x, p_y), of length l
def plot_line(p_x, p_y, x, a, l):
    # Compute b, build tangent expression
    b = p_y - a*p_x
    t = a*x + b
    
    # Limit line length
    r = atan(a) # angle in rad
    dx = N(l*cos(r)) # half range for x
    lims = {'xlim': (p_x-dx, p_x+dx)}
    
    # Build plot
    t_plot = plot(t, show=False, **lims)
    return t_plot

# Function
y = 2.1*log(x)

# Point
px = 7
py = y.subs(x, px)

# Plot curve and point
marker = {'args': [px, py, 'bo']}
lims = {'xlim': (0,10), 'ylim': (0,5)}
plots = plot(y, markers=[marker], show=False, **lims)

# Find derivative, plot tangent
y_d = diff(y)
a = y_d.subs(x, px)
plots.extend(plot_line(px, py, x, a, 1))

# Finalize and show plots
plots.aspect_ratio=(1,1)
plots.show()

但事实并非如此..。

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Answer 1

SymPy的plot()函数签名类似于以下内容：

plot(expr, range, **kwargs)

其中range是一个三元元组：(symbol, min_val, max_val)。plot函数将计算从min_val到max_val的expr。

**kwargs之一是xlim，它是一个2元素元组：xlim=(x_min, x_max)。它用于限制从x_min到x_max沿x轴的可视化.尽管如此，由plot函数计算的数值还是从min_val到max_val。

尽管如此，您需要从xlim内部删除plot_line并提供range参数：

from sympy import init_printing, symbols, N, plot
from sympy import diff
from sympy import log, cos, atan

init_printing()
x = symbols('x')

# Plot a tangent at point (p_x, p_y), of length l
def plot_line(p_x, p_y, x, a, l):
    # Compute b, build tangent expression
    b = p_y - a*p_x
    t = a*x + b
    
    # Limit line length
    r = atan(a) # angle in rad
    dx = N(l*cos(r)) # half range for x
    
    # Build plot
    # Need to provide the range to limit the line length
    t_plot = plot(t, (x, p_x-dx, p_x+dx), show=False)
    return t_plot

# Function
y = 2.1*log(x)

# Point
px = 7
py = y.subs(x, px)

# Plot curve and point
marker = {'args': [px, py, 'bo']}
lims = {'xlim': (0,10), 'ylim': (0,5)}
plots = plot(y, markers=[marker], show=False, **lims)

# Find derivative, plot tangent
y_d = diff(y)
a = y_d.subs(x, px)
plots.extend(plot_line(px, py, x, a, 1))

# Finalize and show plots
plots.aspect_ratio=(1,1)
plots.show()

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