Amplitude–Rate Interpolator

Linearly interpolate measured daily rate versus balance amplitude without extrapolating outside caller-supplied observations.

Description

Amplitude-dependent rate interpolation reads a supplied measurement curve.

Amplitude-dependent rate interpolation reads a supplied measurement curve. Piecewise linear interpolation describes values between neighboring observations.^[1]

Linearly interpolate measured daily rate versus balance amplitude without extrapolating outside caller-supplied observations.

When to use Amplitude–Rate Interpolator

Use this tool to linearly interpolate measured daily rate versus balance amplitude without extrapolating outside caller-supplied observations.

Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.

How to use Amplitude–Rate Interpolator and understand its results

Choose a supported reference focus or prepare the watch measurements, evidence and explicit limits requested. Confirm units and date conventions before running.
Enter observations, targetAmplitudeDegrees using the field table and calculation rules, then run the tool.
Read bracketingAmplitudesDegrees, maximumObservedRateSecondsPerDay, minimumObservedRateSecondsPerDay, observedAmplitudeRangeDegrees, observationCount, targetRateSecondsPerDay. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
observations	Rows contain [amplitude in degrees, rate in seconds per day].	list of list of number	Required
targetAmplitudeDegrees	Target amplitude (deg)	number; minimum: 0	Required

Enter at least two [positive amplitude degrees,finite signed rate seconds/day] rows and an in-range target. Sort rows by amplitude, reject duplicates, and interpolate within adjacent brackets. Return target rate, brackets, amplitude range, rate extrema and count.

rate=lowerRate+(target−lowerAmplitude)/(upperAmplitude−lowerAmplitude)×rateDifference

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
bracketingAmplitudesDegrees	Bracketing amplitudes (deg)	list of number
maximumObservedRateSecondsPerDay	Maximum observed rate (s/day)	number
minimumObservedRateSecondsPerDay	Minimum observed rate (s/day)	number
observedAmplitudeRangeDegrees	Observed amplitude range (deg)	list of number
observationCount	Observation count	integer; minimum: 2
targetRateSecondsPerDay	Interpolated rate (s/day)	number

json

{
  "input": {
    "observations": [
      [
        200,
        0
      ],
      [
        240,
        4
      ],
      [
        280,
        12
      ]
    ],
    "targetAmplitudeDegrees": 250
  },
  "output": {
    "bracketingAmplitudesDegrees": [
      240,
      280
    ],
    "maximumObservedRateSecondsPerDay": 12,
    "minimumObservedRateSecondsPerDay": 0,
    "observedAmplitudeRangeDegrees": [
      200,
      280
    ],
    "observationCount": 3,
    "targetRateSecondsPerDay": 6
  }
}

Limitations and assumptions

No extrapolation, physical curve or complete isochronism diagnosis is fitted.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Matrices are limited to 128 rows and 128 entries per row; other lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Isochronism Amplitude Rate Slope Calculator: Measure the endpoint rate change and slope between two caller-supplied amplitude observations; this does not turn a two-point slope into a complete isochronism curve. For a complementary task, use Daily Rate Average Comparison: Compare an unweighted arithmetic mean of daily rates with a duration-weighted mean for explicitly supplied measurement intervals.

References

Amplitude–Rate Interpolator — tool.io

Similar or alternative tools

Isochronism Amplitude Rate Slope Calculator
Measure the endpoint rate change and slope between two caller-supplied amplitude observations; this does not turn a two-point slope into a complete isochronism curve.
Daily Rate Average Comparison
Compare an unweighted arithmetic mean of daily rates with a duration-weighted mean for explicitly supplied measurement intervals.