Resolving TypeError: can't multiply sequence by non-int of type 'numpy.float64' in Matplotlib

Problem Background and Error Analysis

When performing data visualization with Matplotlib, linear regression fitting is a common analytical technique. However, users often encounter the TypeError: can't multiply sequence by non-int of type 'numpy.float64' error when attempting to plot the best-fit line. The core issue lies in data type mismatch, specifically the unsupported multiplication operation between Python lists and NumPy floating-point numbers.

Detailed Error Cause Analysis

In the original code, variables x and y are defined as Python lists:

x = [0.46,0.59,0.68,0.99,0.39,0.31,1.09,0.77,0.72,0.49,0.55,0.62,0.58,0.88,0.78]
y = [0.315,0.383,0.452,0.650,0.279,0.215,0.727,0.512,0.478,0.335,0.365,0.424,0.390,0.585,0.511]

When calling np.polyfit(x, y, 1), the function returns slope m and intercept b as numpy.float64 scalar values. The problem occurs when executing the m*x + b line of code.

In standard Python, list multiplication with integers produces list repetition:

>>> 2 * [1, 2, 3]
[1, 2, 3, 1, 2, 3]

While list multiplication with floats raises TypeError:

>>> 1.5 * [1, 2, 3]
TypeError: can't multiply sequence by non-int of type 'float'

Special Behavior of NumPy

Interestingly, NumPy scalars exhibit special behavior when multiplied with Python lists. When using numpy.float64 values with lists, NumPy truncates the float to an integer and then performs standard list repetition:

>>> np.float64(0.5) * [1, 2, 3]
[]
>>> np.float64(1.5) * [1, 2, 3]
[1, 2, 3]
>>> np.float64(2.5) * [1, 2, 3]
[1, 2, 3, 1, 2, 3]

This implicit type conversion behavior can be confusing, as users expect element-wise multiplication rather than list repetition.

Complete Solution

To properly resolve this issue, convert Python lists to NumPy arrays:

import matplotlib.pyplot as plt
from scipy import stats
import numpy as np

# Convert lists to NumPy arrays
x = np.array([0.46,0.59,0.68,0.99,0.39,0.31,1.09,0.77,0.72,0.49,0.55,0.62,0.58,0.88,0.78])
y = np.array([0.315,0.383,0.452,0.650,0.279,0.215,0.727,0.512,0.478,0.335,0.365,0.424,0.390,0.585,0.511])

xerr = [0.01]*15
yerr = [0.001]*15

plt.rc('font', family='serif', size=13)
m, b = np.polyfit(x, y, 1)
plt.plot(x,y,'s',color='#0066FF')
plt.plot(x, m*x + b, 'r-')  # Now works correctly
plt.errorbar(x,y,xerr=xerr,yerr=0,linestyle="None",color='black')
plt.xlabel('$\Delta t$ $(s)$',fontsize=20)
plt.ylabel('$\Delta p$ $(hPa)$',fontsize=20)
plt.autoscale(enable=True, axis=u'both', tight=False)
plt.grid(False)
plt.xlim(0.2,1.2)
plt.ylim(0,0.8)
plt.show()

Importance of Data Type Conversion

In scientific computing and data analysis, proper use of data types is crucial. NumPy arrays provide efficient numerical operations and support element-wise operations, which are essential for linear regression fitting. In contrast, Python lists are better suited for storing heterogeneous data but are less efficient for numerical computations.

Similar type errors frequently occur when handling user input. For example, input obtained through the input() function is string type by default and requires explicit conversion:

# Error example
user_input = input("Enter a number: ")
result = user_input * 2.5  # Raises TypeError

# Correct approach
user_input = float(input("Enter a number: "))
result = user_input * 2.5  # Works correctly

Best Practice Recommendations

To avoid similar data type errors, we recommend:

1. Prefer NumPy arrays over Python lists for numerical computations
2. Perform timely data type conversions when handling user input or file data
3. Use the type() function to check variable data types
4. Add type assertions or checks before critical computation steps

By understanding the inherent differences in data types and conversion mechanisms, you can significantly improve code robustness and maintainability.