NumPy floating point error: Overflow encountered in double_scalars

The Error

The ‘Overflow encountered in double_scalars’ error in NumPy is commonly encountered when working with large or very small float numbers that exceed the limits of floating-point precision in the given data type (typically double). Let’s explore some solutions to address this issue.

The Solutions

Use a Larger Data Type

Float64 (double precision) is the default NumPy floating-point data type and can lead to overflow. To avoid this, explicitly specify a larger data type like ‘float128’.

1. Identify the operation that causes overflow.
2. Change the data type of the involved arrays to ‘float128’ or a similar higher-precision type.
3. Rerun the operation to see if the error is resolved.

import numpy as np

# Assume 'a' and 'b' are large numbers.
a = np.array([1e300], dtype='float128')
b = np.array([1e100], dtype='float128')

# Performing a potentially overflowing operation
result = a * b
print(result)

Note: Higher-precision floating-point types may increase memory usage and computational time.

Use NumPy Functions with Built-in Overflow Checks

Solution description: NumPy offers functions that have built-in overflow handling, such as numpy.logaddexp and numpy.logaddexp2 for logarithms:

1. Locate the function with potential for overflow.
2. Replace it with its NumPy counterpart that has built-in checks.
3. Verify that the error is resolved.

import numpy as np

# When computing log(x + y) for large x and y to prevent overflow:
x = 1e300
y = 1e300

# Use the NumPy function with built-in overflow checks
result = np.logaddexp(x, y)
print(result)

Note: These functions are only applicable to specific operations and might not be available for all cases where overflow can occur.

Scale Your Data

Manually scale the inputs to mitigate the risk of overflow. This is often done when the magnitude of the data might be too large.

1. Identify if input scaling is applicable to your operation.
2. Choose an appropriate scale factor.
3. Multiply your inputs by the scale factor before the operation.
4. Adjust the output accordingly if necessary.

import numpy as np

scale_factor = 1e-300

a = np.array([1e300]) * scale_factor
b = np.array([1e100]) * scale_factor

# Perform the scaled operation
result = a * b

# If needed, reverse the scaling
result *= (1 / scale_factor**2)
print(result)

Note: Choosing an incorrect scale factor can lead to underflow or loss of precision.

Incremental Computation

For iterative processes, consider breaking down the computation into smaller, incremental steps that prevent the intermediate results from becoming too large:

1. Analyze the algorithm for incremental computation potential.
2. Refactor the code to accumulate the result iteratively.
3. Ensure each step’s result is within floating-point capacity.

import numpy as np

# Imagine a situation where iterating addition causes overflow
# Instead of direct summation, use an incremental loop
total = np.float64(0)
for i in range(1, 100000):
    total += np.float64(i * 1e100)

print(total)

Note: Incremental computation can be slower due to the loop overhead, but it can help control the numerical scale of intermediate values.

Error Handling with Try/Catch

Use Python’s exception handling to catch overflow errors and handle them appropriately:

1. Identify the code block where overflow may occur.
2. Encapsulate it within a try-except block.
3. Implement an appropriate response to the exception.

import numpy as np

try:
    # Imagine 'a' and 'b' are large values causing overflow
    a = np.array([1e300])
    b = np.array([1e300])
    result = a * b
except FloatingPointError:
    print('Overflow encountered. Consider using a different approach.')

Note: Exception handling will not solve the overflow issue but provides a way to manage the outcome when it occurs.

Final Words

The ‘Overflow encountered in double_scalars’ error can often be mitigated through a variety of strategies depending on the context of the operation that causes it. Importantly, developers must choose an appropriate solution based on accuracy requirements, performance considerations, and the specific numerical computation at hand.