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Merge pull request #15 from QuantumPhysique/refactorInterpolation
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Speed up interpolation
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@braniii
braniii committed Mar 17, 2024
2 parents 95bb210 + bf0417f commit ed75df5
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18 changes: 18 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -12,11 +12,20 @@ adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
[//]: # (### Bugfix 🐛:)
[//]: # (### Other changes:)


## [Unreleased]
### Added Features and Improvements 🙌:
- All new and improved interpolation API, the predictions are now more reliable
- Using the latest flutter 3.19 with upgraded deps
- Compile against Android 14 (SDK34)

### Bugfix 🐛:
- Fix bug, when reloading theme
- Fix bug that the interpolation was not shown for disabled smoothing, #25

### Other changes:
- Disabling interpolation, will now use sigma=2days for extrapolation prediction


## [0.5.0] - 2024-01-25
### Added Features and Improvements 🙌:
Expand All @@ -41,6 +50,15 @@ adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
- Fix f-droid metadata


## [0.4.6] - 2024-01-08
### Bugfix 🐛:
- Fix bug, when using lb and st units

### Other changes:
- Fix version error in 0.4.5
- Fix f-droid metadata


## [0.4.4] - 2023-12-20
### Bugfix 🐛:
- Fix bug, which prevented loading the app without measurements
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321 changes: 3 additions & 318 deletions app/lib/core/interpolation.dart
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@@ -1,312 +1,7 @@
import 'dart:math';

import 'package:flutter/material.dart';
import 'package:flutter_gen/gen_l10n/app_localizations.dart';
import 'package:trale/core/icons.dart';

import 'package:trale/core/measurement.dart';
import 'package:trale/core/preferences.dart';


/// return gaussian with std of 3 days in x [ms]
double gaussian(
double x, {double sigma=72 * 3600 * 1000, double mu=0}
) => sigma == 0
? x - mu == 0
? 1
: 0
: 1 / (sigma * sqrt(2 * pi)) * exp(-1 / 2 * pow(x - mu, 2) / pow(sigma, 2));


/// return fermi-dirac statistic based weight with fermi-edge at 2*width
double regressionWeight({
required double x,
required double mu,
required double width
}) => 1.0 / (
1.0 + exp(
((mu - x) - 2 * width) / width
)
);


/// estimate weights based on measurements
List<double> regressionWeights(int x, List<Measurement> measurements) {
final Preferences pref = Preferences();
final List<double> weights = <double>[
for (final Measurement m in measurements)
regressionWeight(
x: m.dateInMs.toDouble(),
mu: x.toDouble(),
width: pref.interpolStrength.strengthMeasurement * 24 * 3600 * 1000,
)
];

final double totalWeights = weights.reduce(
(double value, double element) => value + element
);
return <double>[
for (final double w in weights)
w / totalWeights
];
}


/// estimate weighted averaged weight
double regressionMeanWeight(int x, List<Measurement> measurements) {
final List<double> weights = regressionWeights(x, measurements);
double meanWeight = 0;
for (int i=0; i <measurements.length; i++){
meanWeight += measurements[i].weight * weights[i];
}
return meanWeight;
}


/// estimate weighted averaged weight
double regressionMeanTime(int x, List<Measurement> measurements) {
final List<double> weights = regressionWeights(x, measurements);
double meanTime = 0;
for (int i=0; i <measurements.length; i++){
meanTime += measurements[i].dateInMs * weights[i];
}
return meanTime;
}

/// estimate change of linear regression
double regressionMeanChange(int x, List<Measurement> measurements) {
final List<double> weights = regressionWeights(x, measurements);
final double tMean = regressionMeanTime(x, measurements);
final double wMean = regressionMeanWeight(x, measurements);
double meanDeltaTime = 0;
double meanDeltaWeight = 0;
double t, w;
for (int i=0; i < measurements.length; i++){
t = measurements[i].dateInMs.toDouble();
w = measurements[i].weight;
meanDeltaWeight += (w - wMean) * (t - tMean) * weights[i];
meanDeltaTime += (t - tMean) * (t - tMean) * weights[i];
}
return meanDeltaWeight / meanDeltaTime;
}


/// estimate intercept of linear regression
double regressionMeanIntercept(int x, List<Measurement> measurements) {
final double tMean = regressionMeanTime(x, measurements);
final double wMean = regressionMeanWeight(x, measurements);
final double cMean = regressionMeanChange(x, measurements);

final double intercept = wMean - cMean * tMean;
return intercept;
}


/// linear regression around time t
Measurement linearRegression(int x, int xref, List<Measurement> measurements) {
final double intercept = regressionMeanIntercept(xref, measurements);
final double change = regressionMeanChange(xref, measurements);
final double weight = change * x + intercept;
const double weightMax = 1000;
final Measurement m = Measurement(
weight: weight < 0
? 0
: weight > weightMax
? weightMax
: weight,
date: DateTime.fromMillisecondsSinceEpoch(x),
isMeasured: true,
);

return m;
}


/// add value of linear regression to list of Measurements
List<Measurement> addLinearRegression(List<Measurement> ms) {
final Preferences pref = Preferences();
final List<Measurement> msRegr = <Measurement>[
for (final Measurement m in ms)
Measurement(
weight: m.weight,
date: m.date,
isMeasured: m.isMeasured,
)
];
final Interpolation interpol = Interpolation(
measures: ms,
extrapolationRange: pref.interpolStrength.strengthMeasurement,
);

// future extrapolation
final int dateFrom = ms.last.dateInMs + interpol.extrapolationStepWidth;
final int dateTo = dateFrom + 2 * interpol.extrapolationRange;
msRegr.addAll(
_createRegressionMeasurements(
ms, dateFrom, dateTo, interpol.extrapolationStepWidth,
),
);
return msRegr;
}

List<Measurement> _createRegressionMeasurements(
List<Measurement> ms, int dateFrom, int dateTo, int stepWidth,
) {
return <Measurement>[
for (int date=dateFrom; date < dateTo + stepWidth; date += stepWidth)
linearRegression(date, dateFrom, ms)
];
}


/// estimate eights based on measurments
List<double> measurementsToWeights(int x, List<Measurement> measurements) {
final Preferences pref = Preferences();
final List<double> weights = <double>[
for (final Measurement m in measurements)
gaussian(
x.toDouble(),
mu: m.dateInMs.toDouble(),
sigma: (
m.isMeasured
? pref.interpolStrength.strengthMeasurement
: pref.interpolStrength.strengthInterpol
) * 24 * 3600 * 1000,
) * (m.isMeasured ? pref.interpolStrength.weight : 1)
];
final double totalWeights = weights.reduce(
(double value, double element) => value + element
);
return <double>[
for (final double w in weights)
w / totalWeights
];
}


/// estimate weighted averaged weight
double meanWeight(int x, List<Measurement> measurements) {
final List<double> weights = measurementsToWeights(x, measurements);
double meanWeight = 0;
for (int i=0; i <measurements.length; i++){
meanWeight += measurements[i].weight * weights[i];
}
return meanWeight;
}


/// x date in milliseconds since epoch, measurements sorted by date
Measurement gaussianInterpol(int x, List<Measurement> measurements){
return Measurement(
weight: meanWeight(x, measurements),
date: DateTime.fromMillisecondsSinceEpoch(x),
isMeasured: false,
);
}

/// x date in milliseconds since epoch, measurements sorted by date
Measurement linearInterpol(int x, List<Measurement> measurements){
if (measurements.length == 1) {
return Measurement(
weight: measurements.first.weight,
date: DateTime.fromMillisecondsSinceEpoch(x),
isMeasured: false,
);
}

final int index = measurements.lastIndexWhere(
(Measurement m) => m.dateInMs <= x
);
int indexBefore, indexAfter;
if (index == -1) {
indexBefore = 0;
indexAfter = 1;
} else if (index == measurements.length - 1) {
indexBefore = measurements.length - 2;
indexAfter = measurements.length - 1;
} else {
indexBefore = index;
indexAfter = index + 1;
}
final Measurement mBefore = measurements[indexBefore];
final Measurement mAfter = measurements[indexAfter];

final double derivative = (
mAfter.weight - mBefore.weight
) / (
mAfter.dateInMs - mBefore.dateInMs
);
final double offset = mAfter.weight - derivative * mAfter.dateInMs;
return Measurement(
weight: derivative * x + offset,
date: DateTime.fromMillisecondsSinceEpoch(x),
isMeasured: false,
);
}


/// Enum with all available interpolation functions
enum InterpolFunc {
/// gaussian
gaussian,
/// stones
linear,
}

/// extend units
extension InterpolFuncExtension on InterpolFunc {
/// get the scaling factor to kg
Function(int, List<Measurement>) get function =>
<InterpolFunc, Function(int, List<Measurement>)>{
InterpolFunc.gaussian: gaussianInterpol,
InterpolFunc.linear: linearInterpol,
}[this]!;
/// get string expression
String get name => toString().split('.').last;
}

/// class for interpolating measurement values
class Interpolation {
/// constructor
Interpolation({
required this.measures,
/// Step width [days]
double extrapolationStepWidth=1,
/// Extrapolation range [days]
double extrapolationRange=0,
}) {
this.extrapolationRange = (extrapolationRange * 24*3600*1000).toInt();
this.extrapolationStepWidth = (
extrapolationStepWidth * 24*3600*1000
).toInt();
}

/// interpolate Measurements
List<Measurement> interpolate(InterpolFunc interpolFunc){
// do not interpolate if empty
if (measures.isEmpty) {
return <Measurement>[];
}

final int dateFrom = measures.first.dateInMs - extrapolationRange;
final int dateTo = measures.last.dateInMs + extrapolationRange;
return <Measurement>[
for (
int date=dateFrom;
date < dateTo + extrapolationStepWidth;
date += extrapolationStepWidth
)
interpolFunc.function(date, measures) as Measurement
];
}

/// extrapolationRange in milliseconds
late int extrapolationRange;
/// step widths in milliseconds
late int extrapolationStepWidth;
/// daily-averaged and sorted Measurements
late List<Measurement> measures;
}

/// Enum with all available interpolation functions
enum InterpolStrength {
Expand All @@ -324,27 +19,17 @@ enum InterpolStrength {
extension InterpolStrengthExtension on InterpolStrength {
/// get the interpolation strength of measurements [days]
double get strengthMeasurement => <InterpolStrength, double>{
InterpolStrength.none: 0.01,
InterpolStrength.none: 2,
InterpolStrength.soft: 2,
InterpolStrength.medium: 4,
InterpolStrength.strong: 7,
}[this]!;

/// get the interpolation strength of measurements [days]
double get strengthInterpol => <InterpolStrength, double>{
InterpolStrength.none: 0,
InterpolStrength.soft: 1,
InterpolStrength.medium: 2,
InterpolStrength.strong: 3,
}[this]!;
double get strengthInterpol => strengthMeasurement / 2;

/// get the ratio how much the measurements are weighted more than interpols
double get weight => <InterpolStrength, double>{
InterpolStrength.none: 1,
InterpolStrength.soft: 10,
InterpolStrength.medium: 5,
InterpolStrength.strong: 3,
}[this]!;
double get weight => 2;

/// get international name
String nameLong (BuildContext context) => <InterpolStrength, String>{
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2 changes: 1 addition & 1 deletion app/lib/core/measurement.dart
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Expand Up @@ -70,7 +70,7 @@ class Measurement {

/// return day in milliseconds since epoch neglecting the hours, minutes
int get dayInMs => DateTime(
date.year, date.month, date.day
date.year, date.month, date.day, 12, // use 1h offset to ignore jumps
).millisecondsSinceEpoch;

/// return date in milliseconds
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