Description
Sum natural logarithms of retentionFractions for logRetention and exponentiate for retainedFraction.
A ratio compares quantities under a stated numerator and denominator. Fractions, percentage numerals, and percentage-point changes use different conventions, and changing a part can also change its whole. Unit consistency, zero denominators, rounding, and the order of adjustments determine the result.
Sum natural logarithms of retentionFractions for logRetention and exponentiate for retainedFraction.
When to use this tool
Use Chained Retention Log Loss Term when you need this specific ratio, allocation, transformation, interval, or adjustment-order calculation with an explicit base.
How to use the tool and how it works
- Enter retentionFractions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logRetention, retainedFraction. Use the output convention below.
Sum natural logarithms of retentionFractions for logRetention and exponentiate for retainedFraction. Require every factor greater than zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| retentionFractions | Retention Fractions | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logRetention | Natural log of the product; zero for no factors. | Required. Finite number. |
| retainedFraction | Retained Fraction | Required. Finite number. |
{
"input": {
"retentionFractions": [
0.5,
0.5
]
},
"output": {
"logRetention": -1.3862943611198906,
"retainedFraction": 0.25
}
}Limitations and assumptions
- An empty list gives log zero and retained fraction one. Very small products can underflow to zero while logRetention remains useful; factors are supplied rather than measured process outcomes.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Check numerator, denominator, units, and adjustment order before comparing results. Use a complete allocation or physical mixture model when a single arithmetic term leaves relevant constraints unspecified.
References
Similar or alternative tools
- Fractional Retention Removed Share Amount
Return retained=initial*retainedFraction and removed=initial-retained.
- Concentration Addition Exact Volume Basis
Use an explicitly measured final volume rather than assuming additive component volumes.