Python中如何将多项式系数表达式加入图例并绘制计算点

1. 多项式系数的格式转换 #

numpy的np.polyfit()返回的系数是从最高次项到常数项排列的（比如9阶拟合返回[c₉, c₈, ..., c₀]），要生成y = c₈x⁸ + c₇x⁷ + … + c₀格式的字符串，只需遍历系数并拼接对应项：

import numpy as np
import matplotlib.pyplot as plt

# 假设已有的测量数据
gain_meas = np.array([10, 12, 14, 16, 18, 20])  # 示例增益数据
pout_meas = np.array([30, 35, 42, 47, 51, 53])   # 示例输出功率数据

# 9阶多项式拟合
order = 9
coeffs = np.polyfit(gain_meas, pout_meas, order)

# 生成多项式字符串
poly_str = "y = "
for exp in range(order, -1, -1):
    coeff = coeffs[order - exp]
    # 处理符号与格式
    if exp == order:
        poly_str += f"{coeff:.4f}x^{exp}"
    else:
        sign = "+" if coeff >= 0 else "-"
        term = f"x^{exp}" if exp != 0 else ""
        poly_str += f" {sign} {abs(coeff):.4f}{term}"

# 替换为美观的Unicode上标（可选）
superscripts = {"^9":"⁹", "^8":"⁸", "^7":"⁷", "^6":"⁶", "^5":"⁵", "^4":"⁴", "^3":"³", "^2":"²", "^1":"", "^0":""}
for k, v in superscripts.items():
    poly_str = poly_str.replace(k, v)
# 处理x^1替换后的多余空格
poly_str = poly_str.replace("x ", "x")

2. 将多项式字符串加入图例 #

绘图时把生成的poly_str作为拟合曲线的图例标签即可：

# 绘制测量数据与拟合曲线
plt.scatter(gain_meas, pout_meas, label="测量数据")
gain_fit = np.linspace(min(gain_meas), max(gain_meas), 100)
pout_fit = np.polyval(coeffs, gain_fit)
plt.plot(gain_fit, pout_fit, label=f"9阶拟合\n{poly_str}")

# 绘制目标输出功率对应增益点（保留原有实现）
target_pout = 52
# 构造多项式方程求解对应增益
eq_coeffs = np.append(coeffs, -target_pout)
roots = np.roots(eq_coeffs)
# 筛选有效实数解
valid_gain = [r.real for r in roots if np.isreal(r) and min(gain_meas) <= r.real <= max(gain_meas)]
plt.scatter(valid_gain, [target_pout]*len(valid_gain), color="red", marker="*", label=f"52dBm对应增益")

plt.xlabel("增益 (dB)")
plt.ylabel("输出功率 (dBm)")
plt.legend()
plt.grid(True)
plt.show()

注意事项 #

• 可调整.4f的小数位数，匹配数据精度需求
• 若不需要Unicode上标，可跳过替换步骤，直接保留x^n格式
• 求解目标增益时，务必筛选实数且在测量范围内的解，避免无效值

内容的提问来源于stack exchange，提问作者blast