TheAlgorithms/Python · error · ValueError

log10(0) is undefined.

Error message

log10(0) is undefined.

What it means

Raised by inverse_document_frequency in word_frequency_functions.py when smoothing=True and the total number of documents n is 0. With smoothing the formula is 1 + log10(n/(1+df)), and log10(0) is mathematically undefined, so the function refuses rather than returning -inf.

Source

Thrown at machine_learning/word_frequency_functions.py:113

    smoothing, if True return the idf-smooth
    @returns : log10(N/df) or 1+log10(N/1+df)
    @examples :
    >>> inverse_document_frequency(3, 0)
    Traceback (most recent call last):
     ...
    ValueError: log10(0) is undefined.
    >>> inverse_document_frequency(1, 3)
    0.477
    >>> inverse_document_frequency(0, 3)
    Traceback (most recent call last):
     ...
    ZeroDivisionError: df must be > 0
    >>> inverse_document_frequency(0, 3,True)
    1.477
    """
    if smoothing:
        if n == 0:
            raise ValueError("log10(0) is undefined.")
        return round(1 + log10(n / (1 + df)), 3)

    if df == 0:
        raise ZeroDivisionError("df must be > 0")
    elif n == 0:
        raise ValueError("log10(0) is undefined.")
    return round(log10(n / df), 3)


def tf_idf(tf: int, idf: int) -> float:
    """
    Combine the term frequency
    and inverse document frequency functions to
    calculate the originality of a term. This
    'originality' is calculated by multiplying
    the term frequency and the inverse document
    frequency : tf-idf = TF * IDF
    @params : tf, the term frequency, and idf, the inverse document

View on GitHub (pinned to f5988cc097)

Solutions

1. Ensure the corpus is non-empty before computing IDF: check n > 0 at the call site.
2. Load/index documents before running the TF-IDF pipeline.
3. If an empty corpus is legitimate in your flow, skip IDF computation for those terms rather than calling the function.

Example fix

# before
idf = inverse_document_frequency(n_docs, df, True)  # n_docs == 0

# after
idf = inverse_document_frequency(n_docs, df, True) if n_docs > 0 else None

if n_docs > 0:
    idf = inverse_document_frequency(n_docs, df, True)
else:
    idf = None  # empty corpus: no IDF defined

When it happens

Trigger: Calling inverse_document_frequency(0, df, True) - i.e. n=0 with the smoothing flag set. Note df=0 with smoothing is fine because the denominator becomes 1+df.

Common situations: Computing IDF over an empty corpus during unit tests, before documents are loaded, or when a filtering step removes all documents from a shard.

Related errors

• df must be > 0
• Expected a_coeffs to have {self.order + 1} elements for {sel
• Expected b_coeffs to have {self.order + 1} elements for {sel
• k must not be negative
• n must not be negative

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/c59c94a2d7f30b2a. Report an issue: GitHub.