如何在 Python plot 中根据给定的 X 轴值找到 Y 轴值？

Question

I have a Python program to plot a set of integers against one for the other.

import matplotlib.pyplot as plt
import numpy as np

line = plt.plot(np.array([0.119, 0.744, 2.225, 3.292]), np.array([0, 100, 400, 1000]))
plt.show()

I need to find the value of the Y axis, for the value "0.261" on the X axis.

I tried the following

xvalues = line[0].get_xdata()
yvalues = line[0].get_ydata()
indexNo = np.where(xvalues == xvalues[1])
print(yvalues[indexNo])

But in the xvalues[1] , I need to provide the index of the value, not the exact value. How can I solve this?

Answer 1

You can use the numpy.interp() function to find the Y value for a given X value. The function takes in three arguments: the X value you want to find the Y value for, the known X values, and the corresponding Y values. It then returns the interpolated Y value. Here's an example of how you can use it in your case:

y_val = np.interp(0.261, xvalues, yvalues)
print(y_val)

This will find the interpolated Y value for X=0.261 using the X and Y values from your line plot.

Answer 2

You can try to fit your xvalues and yvalues into a function, and then use the fitted function to find the y values for arbitrary x values:

# == Necessary Imports =========================================================
import scipy
from scipy.optimize import curve_fit
import numpy as np
import matplotlib
import matplotlib.pyplot as plt


# == Define Function to Fit X and Y points to ===================================
def func(x, a, b, c, offset):
    return  a / np.power(x, b) + c * x + offset

# == Set Initial Values for `func` Parameters ==================================
# Initial values for parameters: `a`, `b`, `c`, `offset`.
initial_parameters = np.array([1.0, 1.0, 1.0, 1.0])

# == X and Y data ==============================================================
# X and Y axes values.
x_data = np.array([0.119, 0.744, 2.225, 3.292])
y_data = np.array([0, 100, 400, 1000])

# == Find `func` Parameters ====================================================
# Curve fit `x_data` and `y_data`
fitted_parameters, pcov = curve_fit(func, x_data, y_data, initial_parameters)

# == Predict Y Values from `x_data` and `func` =================================
model_predictions = func(x_data, *fitted_parameters)

# == Solution Metrics ==========================================================
abs_error = model_predictions.round(3) - x_data
SE = np.square(abs_error)   # Squared errors
MSE = np.mean(SE)           # Mean squared errors
RMSE = np.sqrt(MSE)         # Root Mean Squared Error
r_squared = 1.0 - (np.var(abs_error) / np.var(y_data))

print('Parameters:', fitted_parameters)
print(f'RMSE: {RMSE:.2f}')
print(f'R-squared: {r_squared:.2f}')
print(f'x = 0.261 -> y = {func(0.261, *fitted_parameters):.3f}')
# Parameters: [  0.97721854  -5.22395811 159.66643236 -19.00031993]
# RMSE: 538.87
# R-squared: 0.01
# x = 0.261 -> y = 22.673

for x, true_y in zip(
    [0.119, 0.744, 2.225, 3.292],
    [0, 100, 400, 1000],
):

    calc_y = func(x, *fitted_parameters)
    print(f'x = {x} | true_y = {true_y:.2f} | y_pred = {calc_y:.2f}')

# x = 0.119 | true_y = 0.00 | y_pred = -0.00
# x = 0.744 | true_y = 100.00 | y_pred = 100.00
# x = 2.225 | true_y = 400.00 | y_pred = 400.00
# x = 3.292 | true_y = 1000.00 | y_pred = 1000.00

Given the fitted curve, the value for f(x=0.261) is:

func(0.261, *fitted_parameters)
# 22.673495002167353

You can also plot the fitted function with the original X and Y points:

# == Graphics Output Section ===================================================
def func_scatter_plot(
    x_data,
    y_data,
    fitted_parameters,
    func,
    log_scale: bool = True,
    graph_width: float = 800,
    graph_height: float = 600,
):

    f = plt.figure(figsize=(graph_width/100, graph_height/100), dpi=100)

    axes = f.add_subplot(111)

    # first the raw data as a scatter plot
    axes.plot(x_data, y_data, 'D')

    # Create data for the fitted equation plot
    x_model = np.linspace(min(x_data), max(x_data), 1000)
    y_model = func(x_model, *fitted_parameters)

    # now the model as a line plot
    axes.plot(x_model, y_model)

    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    # Comment this out for default linear scaling
    if log_scale:
        plt.xscale('log')

    plt.show()
    plt.close('all') # clean up after using pyplot


func_scatter_plot(x_data, y_data, fitted_parameters, func, log_scale=False)

Outputs: