Understanding the Problem

When analyzing large NumPy datasets in Python, you often need to verify whether a matrix consists strictly of allowed values—such as zeros (0) and missing values (np.nan). However, standard comparison operations in Python often yield counter-intuitive results when np.nan is involved.

Why the Original Approach Fails

In the original code snippet, two fundamental issues prevent the expected logical check from working:

  • NaN Inequality: According to the IEEE 754 floating-point standard, np.nan is never equal to anything, including itself. Therefore, m0 == np.nan will evaluate to False for every single element. You must use np.isnan() to detect NaN values.
  • Logical AND vs. OR: The condition (m0 == 0) & (m0 == np.nan) checks if an element is simultaneously equal to zero AND equal to NaN, which is logically impossible. What you actually want is a bitwise OR (|).
  • Performance Overhead of np.unique: Calling np.unique() forces NumPy to sort the array elements, which adds an unnecessary O(N log N) computational overhead for large matrices.

Solution 1: Simple Vectorized Expression (Recommended)

The cleanest and most idiomatic way to handle this in NumPy is to check that every element is either equal to 0 or is a NaN using bitwise logical operators:

import numpy as np

def contains_only_zeros_and_nans(arr):
    return np.all((arr == 0) | np.isnan(arr))

# Example usage:
m = np.array([[0, 3, 4, 5], [1, 2, 0, 0], [0, 0, np.nan, 2], [np.nan, 3, 3, np.nan]])
n = np.array([[0, np.nan, 0, 0], [0, np.nan, 0, 0], [0, 0, np.nan, 0], [np.nan, np.nan, np.nan, np.nan]])

print(contains_only_zeros_and_nans(m))  # Output: False
print(contains_only_zeros_and_nans(n))  # Output: True

Solution 2: Memory-Efficient Approach for Huge Matrices

If you are working with extremely large arrays, computing (arr == 0) | np.isnan(arr) creates temporary boolean arrays in memory. To reduce memory allocation, you can combine np.logical_or with np.isnan:

def contains_only_zeros_and_nans_low_mem(arr):
    return np.logical_or(arr == 0, np.isnan(arr)).all()

Solution 3: Early-Exit Short-Circuiting with Numba

Standard NumPy vectorized functions process the entire matrix before returning a boolean result. If a matrix has billions of elements and the very first value is invalid (e.g., 5), NumPy will still evaluate the remaining elements.

For maximum performance on massive datasets, you can use Numba to create a short-circuiting loop that exits as soon as an invalid entry is encountered:

import numba as nb
import numpy as np

@nb.njit
def contains_only_zeros_and_nans_numba(arr):
    flat = arr.flat
    for i in range(flat.size):
        val = flat[i]
        if val != 0 and not np.isnan(val):
            return False
    return True

# Usage remains identical
print(contains_only_zeros_and_nans_numba(n))  # Output: True

Summary

To accurately check for zeros and NaNs in NumPy, always avoid direct equality comparisons with np.nan. For small-to-medium matrices, standard vectorized operations like np.all((arr == 0) | np.isnan(arr)) offer the best readability. For massive multi-gigabyte arrays, consider Numba for fast short-circuiting evaluation.