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Open toolKullback Leibler Divergence Calculator
Calculate directed KL divergence D(P || Q) and list the contribution from each support element. Provide Probability vector P, Probability vector Q, Logarithm base to compute results directly in your browser. Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
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How the Kullback Leibler Divergence Calculator Works & Core Formula
The Kullback Leibler Divergence Calculator evaluates Probability vector P, Probability vector Q, Logarithm base in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Calculate directed KL divergence D(P || Q) and list the contribution from each support element.
Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Kullback Leibler Divergence Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Kullback Leibler Divergence Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Probability vector P | 0.5,0.5 | Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12. | Required workspace parameter |
| Input: Probability vector Q | 0.25,0.75 | Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12. | Required workspace parameter |
| Input: Logarithm base | 2 | Range: 1.000000001 to 1000000.0 | Required workspace parameter |
| Worked Case 1: Baseline run (Probability vector P = 0.5,0.5) | Preloaded / test values | Calculate directed KL divergence D(P || Q) and list the contribution from each support element | Probability vector P = 0.5,0.5; Probability vector Q = 0.25,0.75; Logarithm base = 2. Output: KL divergence D(P || Q): 0.207518749639; Component terms: 0.5, -0.292481250361; Logarithm base: 2. |
| Worked Case 2: Comparison scenario (Jensen Shannon Divergence Calculator) | Preloaded / test values | Calculate directed KL divergence D(P || Q) and list the contribution from each support element | Probability vector P = 1,0; Probability vector Q = 0,1; Logarithm base = 2. Output: KL divergence D(P || Q): Infinity; Component terms: Infinity, 0; Logarithm base: 2. |
Step-by-Step Guide to Using the Kullback Leibler Divergence Calculator
Follow these three steps to configure Probability vector P, Probability vector Q, Logarithm base, verify unit and boundary rules, and export your Kullback Leibler Divergence Calculator output.
Enter the inputs
Start with probability vector p. Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12.
Input and settings
Check units and mode
Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Tool result
Calculate and save
Select Calculate, check the labelled result, then use Copy result or Download result.txt.
Review the details
Practical Worked Examples for Kullback Leibler Divergence Calculator
These concrete scenarios illustrate how the Kullback Leibler Divergence Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Probability vector P = 0.5,0.5)
Probability vector P = 0.5,0.5; Probability vector Q = 0.25,0.75; Logarithm base = 2. Output: KL divergence D(P || Q): 0.207518749639; Component terms: 0.5, -0.292481250361; Logarithm base: 2.
Comparison scenario (Jensen Shannon Divergence Calculator)
Probability vector P = 1,0; Probability vector Q = 0,1; Logarithm base = 2. Output: KL divergence D(P || Q): Infinity; Component terms: Infinity, 0; Logarithm base: 2.
Boundary & unit check (Kullback Leibler Divergence Calculator)
When solving for 'kullback leibler divergence calculator', verify that Probability vector P, Probability vector Q, Logarithm base use consistent units and stay within the documented scope: Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
How to Read and Verify the Kullback Leibler Divergence Calculator Output
The output panel reports the exact result derived from Probability vector P, Probability vector Q, Logarithm base alongside any unit or formatting notes.
Every calculation follows the rule: Calculate directed KL divergence D(P || Q) and list the contribution from each support element. Because JavaScript uses IEEE 754 double-precision floating-point arithmetic, numeric outputs display up to 12 significant digits where applicable.
Always cross-check the displayed result against the scope note (Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur) before applying the value to production specifications, financial models, or lab records.
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Kullback Leibler Divergence Calculator output.
Operational scope: Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Kullback Leibler Divergence Calculator
Answers about using Kullback Leibler Divergence Calculator and understanding its results.
What formula or rule does the Kullback Leibler Divergence Calculator use?
The Kullback Leibler Divergence Calculator applies the rule: Calculate directed KL divergence D(P || Q) and list the contribution from each support element. Enter Probability vector P, Probability vector Q, Logarithm base into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Kullback Leibler Divergence Calculator?
Yes. Provide Probability vector P, Probability vector Q, Logarithm base using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Kullback Leibler Divergence Calculator?
Both vectors share support, are nonnegative and sum to 1 within 1e-10. Base must exceed 1. A zero P term contributes zero; P > 0 with Q = 0 yields Infinity. Inputs are not silently normalized and direction matters. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Kullback Leibler Divergence Calculator free and does it keep my inputs private?
Yes. All calculations for the Kullback Leibler Divergence Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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