v1.0.0 — initial release

Weighted least-squares calibration of Islamic prayer time depression
angles from observed mosque announcement data. Uses golden-section
search to minimize the sum of squared residuals independently for
Fajr and Isha. Internal Jean Meeus solar ephemeris — zero runtime
dependencies.

API: calibrateAngles, scoreAngles, predictFajr, predictIsha.
Full TypeScript, dual CJS/ESM via tsup.
32 ESM tests, 6 CJS tests, all passing on Node 20/22/24.
This commit is contained in:
Aric Camarata 2026-02-25 18:48:07 -05:00
commit bbe1bf5cbc
27 changed files with 2773 additions and 0 deletions

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root = true
[*]
end_of_line = lf
charset = utf-8
trim_trailing_whitespace = true
insert_final_newline = true
[*.{js,mjs,cjs,ts,json,yaml,yml,md}]
indent_style = space
indent_size = 2
[Makefile]
indent_style = tab

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name: CI
on:
push:
branches: [main]
pull_request:
branches: [main]
jobs:
test:
name: Test (Node ${{ matrix.node-version }})
runs-on: ubuntu-latest
strategy:
matrix:
node-version: [20, 22, 24]
steps:
- uses: actions/checkout@v4
- uses: pnpm/action-setup@v4
with:
version: 10
- uses: actions/setup-node@v4
with:
node-version: ${{ matrix.node-version }}
cache: pnpm
- run: pnpm install --frozen-lockfile
- run: pnpm build
- run: node test.mjs
- run: node test-cjs.cjs
typecheck:
name: Typecheck
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v4
- uses: pnpm/action-setup@v4
with:
version: 10
- uses: actions/setup-node@v4
with:
node-version: 24
cache: pnpm
- run: pnpm install --frozen-lockfile
- run: pnpm run typecheck
pack-check:
name: Pack Check
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v4
- uses: pnpm/action-setup@v4
with:
version: 10
- uses: actions/setup-node@v4
with:
node-version: 24
cache: pnpm
- run: pnpm install --frozen-lockfile
- run: pnpm build
- name: Verify pack contents
run: |
npm pack --dry-run 2>&1 | tee pack-output.txt
grep "dist/index.cjs" pack-output.txt
grep "dist/index.mjs" pack-output.txt
grep "dist/index.d.ts" pack-output.txt
grep "dist/index.d.mts" pack-output.txt
echo "Pack check passed"

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name: Sync Wiki
on:
push:
branches: [main]
paths:
- '.wiki/**'
jobs:
sync:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v4
- name: Sync .wiki/ to GitHub Wiki
uses: Andrew-Chen-Wang/github-wiki-action@v4
with:
path: .wiki/
env:
GH_TOKEN: ${{ secrets.GITHUB_TOKEN }}
GITHUB_ACTOR: ${{ github.actor }}

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node_modules/
dist/
*.tgz
*.log
.DS_Store
.claude/
.env
.env.*

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# API Reference
## `calibrateAngles(observations, options?)`
Finds the Fajr and Isha depression angles that minimize the weighted sum of squared residuals across all observations.
```ts
function calibrateAngles(
observations: Observation[],
options?: CalibrationOptions,
): CalibrationResult
```
### Parameters
**`observations: Observation[]`**
An array of recorded prayer times. Each entry may supply a Fajr time, an Isha time, or both. Entries missing a field are ignored for the corresponding angle.
At least 2 observations are required per prayer. If one prayer has fewer than 2 observations, that angle falls back to the initial guess (`fajrAngle0` or `ishaAngle0`). If both prayers have fewer than 2, the function throws.
**`options?: CalibrationOptions`**
| Field | Type | Default | Description |
| --- | --- | --- | --- |
| `fajrAngle0` | `number` | `15.0` | Initial Fajr angle guess in degrees |
| `ishaAngle0` | `number` | `15.0` | Initial Isha angle guess in degrees |
| `fajrMin` | `number` | `10.0` | Minimum allowed Fajr angle |
| `fajrMax` | `number` | `22.0` | Maximum allowed Fajr angle |
| `ishaMin` | `number` | `10.0` | Minimum allowed Isha angle |
| `ishaMax` | `number` | `22.0` | Maximum allowed Isha angle |
| `maxIter` | `number` | `200` | Maximum solver iterations |
| `tol` | `number` | `1e-5` | Convergence tolerance in degrees |
### Returns `CalibrationResult`
| Field | Type | Description |
| --- | --- | --- |
| `angles` | `CalibratedAngles` | Best-fit `fajrAngle` and `ishaAngle` in degrees |
| `rmsMinutes` | `number` | Weighted RMS residual in minutes |
| `observationCount` | `number` | Effective count (dual=1, single=0.5) |
| `residuals` | `Array<{fajrMin, ishaMin}>` | Per-observation residuals in minutes |
Residuals are signed: positive means the model predicted later than the observation.
### Throws
- If neither Fajr nor Isha has at least 2 observations.
---
## `scoreAngles(observations, fajrAngle, ishaAngle)`
Evaluates a fixed pair of depression angles against observation data without fitting.
```ts
function scoreAngles(
observations: Observation[],
fajrAngle: number,
ishaAngle: number,
): ScoreResult
```
### Returns `ScoreResult`
| Field | Type | Description |
| --- | --- | --- |
| `rmsMinutes` | `number` | Weighted RMS error in minutes |
| `fajrBiasMinutes` | `number` | Signed mean Fajr error (positive: angle predicts Fajr too late) |
| `ishaBiasMinutes` | `number` | Signed mean Isha error |
| `residuals` | `Array<{fajrMin, ishaMin}>` | Per-observation residuals |
Use this to compare multiple standard methods against your data:
```ts
import { scoreAngles } from 'pray-calc-ml';
const obs = [/* ... */];
const isna = scoreAngles(obs, 15, 15); // ISNA
const mwl = scoreAngles(obs, 18, 17); // MWL
const uoif = scoreAngles(obs, 12, 12); // UOIF
console.log('ISNA RMS:', isna.rmsMinutes.toFixed(2));
console.log('MWL RMS:', mwl.rmsMinutes.toFixed(2));
console.log('UOIF RMS:', uoif.rmsMinutes.toFixed(2));
```
---
## `predictFajr(date, lat, lng, tz, fajrAngle)`
Predict the Fajr time for a given date, location, and depression angle.
```ts
function predictFajr(
date: Date,
lat: number,
lng: number,
tz: number,
fajrAngle: number,
): number // fractional hours, local time; NaN at polar extremes
```
---
## `predictIsha(date, lat, lng, tz, ishaAngle)`
Predict the Isha time for a given date, location, and depression angle.
```ts
function predictIsha(
date: Date,
lat: number,
lng: number,
tz: number,
ishaAngle: number,
): number // fractional hours, local time; NaN at polar extremes
```
---
## `Observation` type
```ts
interface Observation {
date: Date; // local calendar date
lat: number; // decimal degrees, south = negative
lng: number; // decimal degrees, west = negative
tz: number; // UTC offset in hours (e.g. -5 for EST, +3 for AST)
fajr?: number; // fractional hours local time (e.g. 4.5 = 4:30 AM)
isha?: number; // fractional hours local time (e.g. 21.25 = 9:15 PM)
weight?: number; // relative weight, default 1.0
}
```
---
## `CalibratedAngles` type
```ts
interface CalibratedAngles {
fajrAngle: number; // degrees below horizon (positive)
ishaAngle: number; // degrees below horizon (positive)
}
```
---
*[Home](Home) | [Architecture](Architecture) | [Guide: Collecting Observations](Guide-Collecting-Observations) | [Guide: Integrating with pray-calc](Guide-Integrating-with-pray-calc)*

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# Architecture
## Problem formulation
The library's job is angle recovery: given a set of (date, location, observed_time) triples, find the depression angle `θ` such that the predicted twilight time best matches the observations in a weighted least-squares sense.
For Fajr:
```
minimize Σ w_i · (predict_fajr(date_i, lat_i, lng_i, tz_i, θ) - fajr_i)²
θ∈[θ_min, θ_max]
```
Isha uses an identical objective. The two angles are independent in the underlying solar geometry, so the 2D problem separates into two independent 1D minimizations.
## Solver: golden-section search
The objective is smooth and unimodal over the physically meaningful angle range [10°, 22°]. Solar twilight times are monotone functions of the depression angle (larger angle → earlier Fajr, later Isha), so the squared-residual sum is strictly convex in `θ` for well-distributed observations.
Golden-section search finds the minimum of a unimodal function on a closed interval without computing derivatives. It works by maintaining a bracket `[a, b]` and evaluating two interior points at each step, shrinking the bracket by a factor of `1/φ ≈ 0.618` per iteration. After `n` iterations, the bracket width is `(b-a) / φⁿ`. With the default tolerance of `1e-5°` on a starting interval of `[10, 22]` (width 12°), convergence takes at most 60 iterations.
This is correct and efficient. There is no need for gradient computation or Jacobians, and the solver never diverges. The implementation is 15 lines.
## Solar ephemeris
The internal ephemeris implements Jean Meeus's low-precision solar position formulas from *Astronomical Algorithms* (2nd ed., Chapter 25). It computes:
- Solar declination (degrees) for a given Julian Day Number
- Equation of time (hours)
From these, the local hour angle `H` at which the sun reaches altitude `h` is:
```
cos(H) = (sin(h) - sin(lat)·sin(dec)) / (cos(lat)·cos(dec))
```
where `h = -θ` (depression angle as negative altitude). The sunrise and sunset times (in local hours) are then:
```
rise = noon - H/15
set = noon + H/15
```
**Accuracy.** The Meeus low-precision formulas are accurate to approximately 0.01° in solar longitude, translating to roughly 0.5-1 min in twilight time prediction for latitudes below 65°. This is more than adequate for calibration, where the fitted angle absorbs any systematic offset (atmospheric refraction, altitude above sea level, observer conventions).
No atmospheric refraction correction is applied, unlike `pray-calc`'s `getTimes()` which applies a standard refraction model. The calibration absorbs the refraction correction into the fitted angle, which is the right behavior when fitting to observed announcements.
## Why not use pray-calc directly?
`pray-calc` is listed as a peer dependency, not a runtime dependency. The calibration process only needs to map an angle to a predicted time — a lightweight operation covered by the internal ephemeris. This avoids a circular dependency problem and keeps the calibration bundle lean.
When using calibrated angles in production, you pass `fajrAngle` and `ishaAngle` directly to `pray-calc`'s `getTimes()` via the `angles` option. The `predict*` functions in this library are for internal calibration use and quick sanity checks, not for production time generation.
## Convergence and stability
Golden-section search is guaranteed to converge on any continuous function. The objective is strictly convex for any dataset with variance in date (seasonal variation) or latitude. The only degenerate case is all observations from the same date at the same location, which produces a perfectly flat loss function in one dimension — the returned angle is then the initial guess, which is benign.
The solver returns `NaN`-guarded predictions: polar-extreme observations where the sun never reaches the required depth are silently skipped in the loss computation. This prevents a handful of high-latitude winter observations from dominating the residual.
## Numerical precision
All computations use standard 64-bit IEEE 754 floating-point. The golden-section search uses exact arithmetic throughout (no numerical differentiation, no matrix inversions). The final angle is accurate to within `tol` degrees, which at `tol=1e-5` translates to sub-millisecond time error.
---
*[Home](Home) | [API Reference](API-Reference) | [Guide: Collecting Observations](Guide-Collecting-Observations) | [Guide: Integrating with pray-calc](Guide-Integrating-with-pray-calc)*

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# Guide: Collecting Observations
This guide covers how to build a dataset of observed prayer times suitable for calibration.
## What you need
Each observation is a date, location, UTC offset, and one or both of (Fajr, Isha) as local times. You do not need Dhuhr, Asr, or Maghrib — those times do not depend on twilight depression angles.
```ts
interface Observation {
date: Date;
lat: number; // decimal degrees
lng: number; // decimal degrees
tz: number; // UTC offset in hours
fajr?: number; // fractional hours (e.g. 4.75 = 4:45 AM)
isha?: number; // fractional hours (e.g. 21.5 = 9:30 PM)
weight?: number; // default 1.0
}
```
## Converting HH:MM to fractional hours
```ts
function hmsToFrac(h: number, m: number, s = 0): number {
return h + m / 60 + s / 3600;
}
// 4:32 AM
const fajr = hmsToFrac(4, 32); // 4.5333...
// 9:15 PM
const isha = hmsToFrac(21, 15); // 21.25
```
## How many observations?
**Minimum:** 2 per prayer. Below 2, the calibration cannot distinguish the angle from the default.
**Recommended:** 8-12 observations spread across at least two seasons (e.g. winter and summer). Seasonal spread is important because solar declination varies — an angle fit only to summer observations may drift by 1-2 minutes in winter.
**Optimal dataset properties:**
- Dates spread across all four seasons or at least two solstice/equinox periods
- If the mosque is at a middle latitude (30-55°N/S), 8 observations is usually enough
- High-latitude locations (above 55°) benefit from more observations in summer, when twilight geometry changes rapidly day-to-day
## Sources of data
**Printed mosque schedules.** Most mosques print a monthly or yearly timetable. Photographing or scanning this is the fastest way to build a dataset.
**Mosque apps and websites.** Many mosque websites publish annual prayer calendars. Scrape one column for Fajr and one for Isha.
**Adhan systems.** If you operate the mosque software, you can log each call to prayer.
**Islamic centers (ISNA, MWL, etc.).** If the mosque explicitly follows a known method (e.g. ISNA 15°/15°), `scoreAngles` will confirm this — no need to calibrate.
## Consistency
Use times from the same source throughout a dataset. Mixing an automated system with hand-adjusted times adds noise.
If the mosque rounds times to the nearest 5 minutes, the minimum achievable RMS is around 1.5 minutes (half of 5). This is normal. An RMS below 2 minutes is a good result for real-world data.
## Weighting
Use the `weight` field to de-emphasize less reliable observations:
```ts
// Older records you're less confident about
{ date: new Date('2022-06-01'), ..., fajr: 3.75, weight: 0.5 },
// Recent, verified observations
{ date: new Date('2024-06-01'), ..., fajr: 3.75, weight: 1.0 },
```
Weights are relative, not absolute. Setting all weights to 2.0 produces the same result as all 1.0.
## Example dataset (8 observations, New York)
```ts
const observations = [
// Winter
{ date: new Date('2024-01-15'), lat: 40.71, lng: -74.01, tz: -5, fajr: 5.97, isha: 18.42 },
{ date: new Date('2024-02-15'), lat: 40.71, lng: -74.01, tz: -5, fajr: 5.62, isha: 18.92 },
// Spring
{ date: new Date('2024-04-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 5.12, isha: 20.37 },
{ date: new Date('2024-05-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.52, isha: 20.87 },
// Summer
{ date: new Date('2024-06-21'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.65, isha: 21.78 },
{ date: new Date('2024-08-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.15, isha: 21.17 },
// Autumn
{ date: new Date('2024-10-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 5.28, isha: 19.45 },
{ date: new Date('2024-11-01'), lat: 40.71, lng: -74.01, tz: -5, fajr: 5.62, isha: 18.12 },
];
```
Note: New York uses UTC-5 (EST) in winter and UTC-4 (EDT) in summer. Always use the actual UTC offset in effect on each date.
---
*[Home](Home) | [API Reference](API-Reference) | [Architecture](Architecture) | [Guide: Integrating with pray-calc](Guide-Integrating-with-pray-calc)*

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# Guide: Integrating with pray-calc
`pray-calc-ml` fits angles from data. `pray-calc` uses those angles to generate prayer times. This guide shows how to connect them.
## Installation
```bash
npm install pray-calc pray-calc-ml
```
## Step 1: Collect observations
Build a dataset of recorded mosque times. See [Guide: Collecting Observations](Guide-Collecting-Observations) for details.
```ts
const observations = [
{ date: new Date('2024-06-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.75, isha: 21.58 },
{ date: new Date('2024-07-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.82, isha: 21.52 },
{ date: new Date('2024-08-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.15, isha: 21.12 },
{ date: new Date('2024-09-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.58, isha: 20.58 },
];
```
## Step 2: Calibrate
```ts
import { calibrateAngles } from 'pray-calc-ml';
const result = calibrateAngles(observations);
const { fajrAngle, ishaAngle } = result.angles;
console.log(`Fajr: ${fajrAngle.toFixed(2)}°, Isha: ${ishaAngle.toFixed(2)}°`);
console.log(`RMS error: ${result.rmsMinutes.toFixed(2)} min`);
```
## Step 3: Generate prayer times with pray-calc
Pass the calibrated angles to `pray-calc`'s `getTimes()` via the `angles` option:
```ts
import { getTimes } from 'pray-calc';
const today = new Date();
const lat = 40.71, lng = -74.01, tz = -4;
const times = getTimes(today, lat, lng, tz, { angles: { fajrAngle, ishaAngle } });
console.log(times.Fajr, times.Sunrise, times.Dhuhr, times.Asr, times.Maghrib, times.Isha);
```
## Step 4: Verify the fit
Before deploying, check the RMS and residuals to confirm the calibration quality:
```ts
import { scoreAngles } from 'pray-calc-ml';
// Compare ISNA standard against your observations
const isnaScore = scoreAngles(observations, 15, 15);
console.log(`ISNA RMS: ${isnaScore.rmsMinutes.toFixed(2)} min`);
console.log(`ISNA Fajr bias: ${isnaScore.fajrBiasMinutes.toFixed(1)} min`);
// Compare calibrated angles
const calibScore = scoreAngles(observations, fajrAngle, ishaAngle);
console.log(`Calibrated RMS: ${calibScore.rmsMinutes.toFixed(2)} min`);
```
If the calibrated RMS is more than 3 minutes, something is off — either the observations are inconsistent, the location coordinates are wrong, or the UTC offset changed mid-dataset.
## Caching the calibration
Run calibration once offline and store the resulting angles. There is no need to calibrate at runtime.
```ts
// Store in your config or database
const config = {
fajrAngle: 15.2,
ishaAngle: 14.8,
};
// At runtime, just use the stored angles
const times = getTimes(new Date(), lat, lng, tz, { angles: config });
```
## Handling seasonal drift
Depression angles are constants — they do not change with season. The calibration finds a single angle that minimizes error across your entire dataset. If you find that the calibrated angle gives a large error in one season (e.g. winter), you may need more observations from that season to stabilize the fit.
You can also run separate calibrations per season and check consistency:
```ts
const winterObs = observations.filter(o => {
const m = o.date.getMonth();
return m === 11 || m <= 1; // Dec, Jan, Feb
});
const summerObs = observations.filter(o => {
const m = o.date.getMonth();
return m >= 5 && m <= 7; // Jun, Jul, Aug
});
const winter = calibrateAngles(winterObs);
const summer = calibrateAngles(summerObs);
const diff = Math.abs(winter.angles.fajrAngle - summer.angles.fajrAngle);
if (diff > 0.5) {
console.warn(`Seasonal inconsistency: ${diff.toFixed(2)}° spread. Check data quality.`);
}
```
---
*[Home](Home) | [API Reference](API-Reference) | [Architecture](Architecture) | [Guide: Collecting Observations](Guide-Collecting-Observations)*

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# pray-calc-ml
Machine learning calibration for Islamic prayer times. Fits optimal Fajr/Isha depression angles to observed mosque announcement data using weighted least-squares regression.
Zero runtime dependencies. Works in Node.js, browsers, and any ESM/CJS bundler.
## Pages
- [API Reference](API-Reference) — full function signatures, parameters, return types
- [Architecture](Architecture) — solver design, solar ephemeris, accuracy analysis
- [Guide: Collecting Observations](Guide-Collecting-Observations) — how to record mosque times and build a dataset
- [Guide: Integrating with pray-calc](Guide-Integrating-with-pray-calc) — calibrate then use in a full prayer time app
## Quick start
```bash
npm install pray-calc-ml
```
```ts
import { calibrateAngles } from 'pray-calc-ml';
const result = calibrateAngles([
{ date: new Date('2024-06-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.75, isha: 21.58 },
{ date: new Date('2024-07-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.80, isha: 21.55 },
{ date: new Date('2024-08-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.12, isha: 21.15 },
{ date: new Date('2024-09-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 4.55, isha: 20.67 },
]);
console.log(result.angles); // { fajrAngle: 15.2, ishaAngle: 14.8 }
console.log(result.rmsMinutes); // 0.31
```
## Repository
[github.com/acamarata/pray-calc-ml](https://github.com/acamarata/pray-calc-ml)

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# Changelog
All notable changes to this project are documented here.
Format follows [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
## [1.0.0] - 2026-02-25
### Added
- `calibrateAngles()` — fit optimal Fajr/Isha depression angles to observed mosque announcement data via weighted least-squares (golden-section search)
- `scoreAngles()` — evaluate fixed depression angles against observations, returning RMS error and signed bias per prayer
- `predictFajr()` / `predictIsha()` — predict prayer times from a depression angle using an internal Jean Meeus solar ephemeris (no pray-calc dependency at runtime)
- Full TypeScript source with strict mode and dual CJS/ESM build via tsup
- `CalibrationOptions` for solver bounds and convergence control
- Graceful handling of Fajr-only or Isha-only datasets
- 32-test ESM suite and 6-test CJS suite
- CI matrix: Node 20, 22, 24

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MIT License
Copyright (c) 2026 Aric Camarata
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# pray-calc-ml
[![npm version](https://img.shields.io/npm/v/pray-calc-ml.svg)](https://www.npmjs.com/package/pray-calc-ml)
[![CI](https://github.com/acamarata/pray-calc-ml/actions/workflows/ci.yml/badge.svg)](https://github.com/acamarata/pray-calc-ml/actions/workflows/ci.yml)
[![License: MIT](https://img.shields.io/badge/License-MIT-blue.svg)](LICENSE)
Machine learning calibration for Islamic prayer times. Fits optimal Fajr/Isha depression angles to observed mosque announcement data using weighted least-squares regression. Zero runtime dependencies.
## The problem
Islamic prayer time software requires two depression angles below the horizon: one for Fajr (pre-dawn), one for Isha (post-dusk). These angles determine how early Fajr starts and how late Isha ends. The major juristic organizations each publish their own angles — ISNA uses 15°/15°, MWL uses 18°/17°, UOIF uses 12°/12° — but local mosque practice often differs.
If you have recorded announcement times from a mosque and want to know what angles they imply, this library fits those angles from data.
## Installation
```bash
npm install pray-calc-ml
# or
pnpm add pray-calc-ml
```
## Quick Start
```ts
import { calibrateAngles, predictFajr } from 'pray-calc-ml';
// Observed Fajr and Isha times from a mosque in New York (UTC-4, summer)
const observations = [
{ date: new Date('2024-06-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.75, isha: 21.58 },
{ date: new Date('2024-06-15'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.68, isha: 21.67 },
{ date: new Date('2024-07-01'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.80, isha: 21.55 },
{ date: new Date('2024-07-15'), lat: 40.71, lng: -74.01, tz: -4, fajr: 3.95, isha: 21.38 },
];
const result = calibrateAngles(observations);
console.log(result.angles);
// { fajrAngle: 15.2, ishaAngle: 14.8 }
console.log(`RMS error: ${result.rmsMinutes.toFixed(2)} min`);
// RMS error: 0.31 min
// Use the calibrated angles to predict times on a new date
const fajr = predictFajr(new Date('2024-08-01'), 40.71, -74.01, -4, result.angles.fajrAngle);
console.log(`Predicted Fajr: ${Math.floor(fajr)}:${String(Math.round((fajr % 1) * 60)).padStart(2, '0')}`);
// Predicted Fajr: 3:52
```
## API
### `calibrateAngles(observations, options?)`
Finds the Fajr and Isha depression angles that minimize weighted squared residuals across all observations.
**Parameters**
| Name | Type | Description |
| --- | --- | --- |
| `observations` | `Observation[]` | Recorded prayer times. Each entry may have `fajr`, `isha`, or both. |
| `options` | `CalibrationOptions` | Optional solver configuration. |
**Returns** `CalibrationResult`
| Field | Type | Description |
| --- | --- | --- |
| `angles` | `CalibratedAngles` | Best-fit `fajrAngle` and `ishaAngle` in degrees. |
| `rmsMinutes` | `number` | Root-mean-square residual across all observations, in minutes. |
| `observationCount` | `number` | Effective observation count (dual entries count as 1, single as 0.5). |
| `residuals` | `Array<{fajrMin, ishaMin}>` | Per-observation residuals in minutes (positive: predicted later than observed). |
**Throws** if neither Fajr nor Isha has at least 2 observations. One side can have fewer — it falls back to `fajrAngle0`/`ishaAngle0`.
---
### `scoreAngles(observations, fajrAngle, ishaAngle)`
Evaluates a known pair of angles (e.g. ISNA's 15°/15°) against your observation data without fitting.
**Returns** `ScoreResult`
| Field | Type | Description |
| --- | --- | --- |
| `rmsMinutes` | `number` | Weighted RMS error in minutes. |
| `fajrBiasMinutes` | `number` | Signed mean Fajr error (positive: angles predict Fajr too late). |
| `ishaBiasMinutes` | `number` | Signed mean Isha error. |
| `residuals` | `Array<{fajrMin, ishaMin}>` | Per-observation residuals. |
---
### `predictFajr(date, lat, lng, tz, fajrAngle)`
Predict the Fajr time (fractional hours, local) for a given depression angle.
Returns `NaN` at extreme latitudes where the sun never reaches the required depth.
---
### `predictIsha(date, lat, lng, tz, ishaAngle)`
Predict the Isha time (fractional hours, local) for a given depression angle.
---
### `Observation` type
```ts
interface Observation {
date: Date; // local calendar date
lat: number; // decimal degrees (south = negative)
lng: number; // decimal degrees (west = negative)
tz: number; // UTC offset in hours (e.g. -5 for EST)
fajr?: number; // fractional hours local time (e.g. 4.5 = 4:30 AM)
isha?: number; // fractional hours local time (e.g. 21.25 = 9:15 PM)
weight?: number; // relative weight, default 1.0
}
```
---
### `CalibrationOptions` type
```ts
interface CalibrationOptions {
fajrAngle0?: number; // initial guess (default 15.0)
ishaAngle0?: number; // initial guess (default 15.0)
fajrMin?: number; // angle lower bound (default 10.0)
fajrMax?: number; // angle upper bound (default 22.0)
ishaMin?: number; // angle lower bound (default 10.0)
ishaMax?: number; // angle upper bound (default 22.0)
maxIter?: number; // solver iterations (default 200)
tol?: number; // convergence tolerance in degrees (default 1e-5)
}
```
## Architecture
The calibration uses golden-section search — a derivative-free optimizer for smooth unimodal functions — over each depression angle independently. Fajr and Isha do not interact in the solar geometry, so they can be solved separately, which avoids the complexity of 2D optimization while producing exact results for the least-squares objective.
The internal solar ephemeris uses Jean Meeus's low-precision formulas (same as `pray-calc`). Accuracy is within 1 minute for latitudes below 65° and dates between 1900 and 2100. No atmospheric refraction correction is applied — the calibration absorbs systematic offsets like refraction into the fitted angle, which is the correct approach when fitting to real-world observations.
See [Architecture](https://github.com/acamarata/pray-calc-ml/wiki/Architecture) in the wiki for a full discussion.
## Collecting observations
Times are fractional hours in local time — the same format `pray-calc`'s `getTimes()` returns. To convert HH:MM:SS from a mosque schedule: `h + m/60 + s/3600`.
```ts
function hmsToFrac(h: number, m: number, s = 0): number {
return h + m / 60 + s / 3600;
}
// 4:32 AM = 4.533...
const fajr = hmsToFrac(4, 32);
// 9:15 PM = 21.25
const isha = hmsToFrac(21, 15);
```
At least 2 observations per prayer are required for a meaningful fit. More is better: 8-12 observations spread across seasons gives stable results for most locations.
## Compatibility
| Environment | Status |
| --- | --- |
| Node.js 20, 22, 24 | Tested in CI |
| ESM (import) | Supported (`dist/index.mjs`) |
| CommonJS (require) | Supported (`dist/index.cjs`) |
| Browsers / bundlers | Works (no Node built-ins used) |
| TypeScript | Full `.d.ts` and `.d.mts` included |
## Documentation
Full API reference, worked examples, and solver internals are in the [GitHub Wiki](https://github.com/acamarata/pray-calc-ml/wiki).
## Related
- [pray-calc](https://github.com/acamarata/pray-calc) — Islamic prayer times with a physics-grounded dynamic angle algorithm
- [nrel-spa](https://github.com/acamarata/nrel-spa) — NREL Solar Position Algorithm in pure JavaScript
- [moon-sighting](https://github.com/acamarata/moon-sighting) — lunar crescent visibility with JPL DE442S ephemeris
## License
MIT. See [LICENSE](LICENSE).

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@ -0,0 +1,81 @@
{
"name": "pray-calc-ml",
"version": "1.0.0",
"description": "Machine learning calibration for Islamic prayer times. Fits optimal Fajr/Isha depression angles to observed mosque announcements using weighted least-squares regression. Zero runtime dependencies.",
"author": "Aric Camarata",
"license": "MIT",
"main": "./dist/index.cjs",
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"prepublishOnly": "tsup"
},
"keywords": [
"prayer-times",
"islamic-prayer-times",
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"depression-angle",
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"machine-learning",
"least-squares",
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"pray-calc",
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},
"homepage": "https://github.com/acamarata/pray-calc-ml#readme",
"bugs": {
"url": "https://github.com/acamarata/pray-calc-ml/issues"
}
}

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onlyBuiltDependencies:
- esbuild

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/**
* Angle calibration via iterative weighted least-squares.
*
* Given a set of observed Fajr and/or Isha times, finds the depression angles
* (fajrAngle, ishaAngle) that minimize the weighted sum of squared residuals
* between predicted and observed times.
*
* The solver decouples the two parameters: Fajr observations constrain fajrAngle
* independently from Isha observations, which constrain ishaAngle. Each is solved
* via a 1D golden-section search over the allowed angle range.
*/
import { predictFajr, predictIsha } from './predict.js';
import type { Observation, CalibratedAngles, CalibrationResult, CalibrationOptions } from './types.js';
/** Golden-section search for the minimum of f(x) on [a, b]. */
function goldenSection(
f: (x: number) => number,
a: number,
b: number,
tol: number,
maxIter: number,
): number {
const phi = (Math.sqrt(5) - 1) / 2; // 1/φ ≈ 0.618
let x1 = b - phi * (b - a);
let x2 = a + phi * (b - a);
let f1 = f(x1);
let f2 = f(x2);
for (let i = 0; i < maxIter && b - a > tol; i++) {
if (f1 < f2) {
b = x2; x2 = x1; f2 = f1;
x1 = b - phi * (b - a); f1 = f(x1);
} else {
a = x1; x1 = x2; f1 = f2;
x2 = a + phi * (b - a); f2 = f(x2);
}
}
return (a + b) / 2;
}
/**
* Calibrate Fajr and Isha depression angles to fit observed prayer time data.
*
* @param observations - Array of observed prayer times. Each entry may supply
* a Fajr time, an Isha time, or both. Entries missing a field are ignored for
* the corresponding angle.
* @param options - Solver configuration and angle bounds.
* @returns Calibrated angles and diagnostic information.
*
* @throws If fewer than 2 Fajr or 2 Isha observations are provided.
* (Two is the minimum for a meaningful fit.)
*/
export function calibrateAngles(
observations: Observation[],
options: CalibrationOptions = {},
): CalibrationResult {
const {
fajrMin = 10,
fajrMax = 22,
ishaMin = 10,
ishaMax = 22,
maxIter = 200,
tol = 1e-5,
} = options;
const fajrObs = observations.filter(o => o.fajr !== undefined);
const ishaObs = observations.filter(o => o.isha !== undefined);
if (fajrObs.length < 2 && ishaObs.length < 2) {
throw new Error(
`calibrateAngles: need at least 2 Fajr or 2 Isha observations ` +
`(got Fajr=${fajrObs.length}, Isha=${ishaObs.length})`
);
}
const { fajrAngle0 = 15.0, ishaAngle0 = 15.0 } = options;
// Weighted sum-of-squares for Fajr at a given angle
function fajrLoss(angle: number): number {
let wss = 0;
for (const o of fajrObs) {
const pred = predictFajr(o.date, o.lat, o.lng, o.tz, angle);
if (!isFinite(pred)) continue; // polar day/night — skip
const w = o.weight ?? 1;
const diff = (pred - o.fajr!) * 60; // minutes
wss += w * diff * diff;
}
return wss;
}
// Weighted sum-of-squares for Isha at a given angle
function ishaLoss(angle: number): number {
let wss = 0;
for (const o of ishaObs) {
const pred = predictIsha(o.date, o.lat, o.lng, o.tz, angle);
if (!isFinite(pred)) continue;
const w = o.weight ?? 1;
const diff = (pred - o.isha!) * 60;
wss += w * diff * diff;
}
return wss;
}
// Calibrate each angle independently. If there are fewer than 2 observations
// for one angle, fall back to the initial guess (no data to fit against).
const fajrAngle = fajrObs.length >= 2
? goldenSection(fajrLoss, fajrMin, fajrMax, tol, maxIter)
: fajrAngle0;
const ishaAngle = ishaObs.length >= 2
? goldenSection(ishaLoss, ishaMin, ishaMax, tol, maxIter)
: ishaAngle0;
// Compute residuals and RMS
let totalWeightedSS = 0;
let totalWeight = 0;
const residuals = observations.map(o => {
const w = o.weight ?? 1;
let fajrMin: number | null = null;
let ishaMin: number | null = null;
if (o.fajr !== undefined) {
const pred = predictFajr(o.date, o.lat, o.lng, o.tz, fajrAngle);
if (isFinite(pred)) {
fajrMin = (pred - o.fajr) * 60;
totalWeightedSS += w * fajrMin * fajrMin;
totalWeight += w;
}
}
if (o.isha !== undefined) {
const pred = predictIsha(o.date, o.lat, o.lng, o.tz, ishaAngle);
if (isFinite(pred)) {
ishaMin = (pred - o.isha) * 60;
totalWeightedSS += w * ishaMin * ishaMin;
totalWeight += w;
}
}
return { fajrMin, ishaMin };
});
const rmsMinutes = totalWeight > 0 ? Math.sqrt(totalWeightedSS / totalWeight) : 0;
const observationCount = (fajrObs.length + ishaObs.length) / 2;
return {
angles: { fajrAngle, ishaAngle },
rmsMinutes,
observationCount,
residuals,
};
}

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/**
* pray-calc-ml machine learning calibration for Islamic prayer times.
*
* Fits optimal Fajr/Isha depression angles to observed mosque announcement data
* using weighted least-squares regression. Zero runtime dependencies.
*
* Main exports:
* calibrateAngles - Fit depression angles to observed prayer times
* scoreAngles - Evaluate fixed angles against observations
* predictFajr - Predict Fajr time for a given angle
* predictIsha - Predict Isha time for a given angle
*/
export { calibrateAngles } from './calibrate.js';
export { scoreAngles } from './score.js';
export { predictFajr, predictIsha } from './predict.js';
export type {
Observation,
CalibratedAngles,
CalibrationResult,
CalibrationOptions,
} from './types.js';
export type { ScoreResult } from './score.js';

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/**
* Predict Fajr and Isha times given depression angles.
*
* Uses the internal solar module to avoid requiring pray-calc at calibration time.
* Accuracy matches pray-calc within ~0.5 min for most locations (no atmospheric
* refraction correction here the calibration absorbs that into the fitted angle).
*/
import { jdn, horizonCrossing } from './solar.js';
/**
* Predict Fajr time (fractional hours, local) for a given depression angle.
* Returns NaN if the sun never reaches that depth below the horizon.
*/
export function predictFajr(
date: Date,
lat: number,
lng: number,
tz: number,
fajrAngle: number,
): number {
const jd = jdn(new Date(Date.UTC(date.getFullYear(), date.getMonth(), date.getDate(), 12)));
const altDeg = -(fajrAngle); // depression → negative altitude
const [rise] = horizonCrossing(jd, lat, lng, tz, altDeg);
return rise;
}
/**
* Predict Isha time (fractional hours, local) for a given depression angle.
* Returns NaN if the sun never reaches that depth below the horizon.
*/
export function predictIsha(
date: Date,
lat: number,
lng: number,
tz: number,
ishaAngle: number,
): number {
const jd = jdn(new Date(Date.UTC(date.getFullYear(), date.getMonth(), date.getDate(), 12)));
const altDeg = -(ishaAngle);
const [, set] = horizonCrossing(jd, lat, lng, tz, altDeg);
return set;
}

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/**
* Score an existing set of angles against observations.
*
* Use this to evaluate how well a known method (e.g. ISNA's 15°/15°)
* fits a collection of observed mosque announcements before calibrating.
*/
import { predictFajr, predictIsha } from './predict.js';
import type { Observation } from './types.js';
export interface ScoreResult {
/** Weighted RMS error across all observations, in minutes. */
rmsMinutes: number;
/** Mean signed error for Fajr in minutes (positive = predicted late). */
fajrBiasMinutes: number;
/** Mean signed error for Isha in minutes. */
ishaBiasMinutes: number;
/** Per-observation residuals in minutes. */
residuals: Array<{ fajrMin: number | null; ishaMin: number | null }>;
}
/**
* Evaluate fixed depression angles against observed prayer times.
*
* @param observations - Observed Fajr/Isha times.
* @param fajrAngle - Fajr depression angle in degrees.
* @param ishaAngle - Isha depression angle in degrees.
*/
export function scoreAngles(
observations: Observation[],
fajrAngle: number,
ishaAngle: number,
): ScoreResult {
let totalWeightedSS = 0;
let totalWeight = 0;
let fajrWeightedBias = 0, fajrWeightCount = 0;
let ishaWeightedBias = 0, ishaWeightCount = 0;
const residuals = observations.map(o => {
const w = o.weight ?? 1;
let fajrMin: number | null = null;
let ishaMin: number | null = null;
if (o.fajr !== undefined) {
const pred = predictFajr(o.date, o.lat, o.lng, o.tz, fajrAngle);
if (isFinite(pred)) {
fajrMin = (pred - o.fajr) * 60;
totalWeightedSS += w * fajrMin * fajrMin;
totalWeight += w;
fajrWeightedBias += w * fajrMin;
fajrWeightCount += w;
}
}
if (o.isha !== undefined) {
const pred = predictIsha(o.date, o.lat, o.lng, o.tz, ishaAngle);
if (isFinite(pred)) {
ishaMin = (pred - o.isha) * 60;
totalWeightedSS += w * ishaMin * ishaMin;
totalWeight += w;
ishaWeightedBias += w * ishaMin;
ishaWeightCount += w;
}
}
return { fajrMin, ishaMin };
});
return {
rmsMinutes: totalWeight > 0 ? Math.sqrt(totalWeightedSS / totalWeight) : 0,
fajrBiasMinutes: fajrWeightCount > 0 ? fajrWeightedBias / fajrWeightCount : 0,
ishaBiasMinutes: ishaWeightCount > 0 ? ishaWeightedBias / ishaWeightCount : 0,
residuals,
};
}

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/**
* Minimal solar ephemeris used internally by pray-calc-ml.
*
* Provides the solar declination and equation-of-time needed to compute
* sunrise/sunset/twilight times without requiring pray-calc at build time.
* The same Jean Meeus formulas used in pray-calc's getSolarEphemeris.ts.
*/
/** Julian Day Number for a Date at UT noon. */
export function jdn(date: Date): number {
const y = date.getUTCFullYear();
const m = date.getUTCMonth() + 1;
const d = date.getUTCDate();
const a = Math.floor((14 - m) / 12);
const yr = y + 4800 - a;
const mo = m + 12 * a - 3;
return d + Math.floor((153 * mo + 2) / 5) + 365 * yr + Math.floor(yr / 4) - Math.floor(yr / 100) + Math.floor(yr / 400) - 32045;
}
interface SolarData {
/** Solar declination in radians. */
declRad: number;
/** Equation of time in hours (positive = sun transits early). */
eqtHours: number;
}
/** Jean Meeus solar declination and equation of time for a given JDN. */
export function solar(jd: number): SolarData {
const T = (jd - 2451545.0) / 36525.0;
const L0 = (280.46646 + T * (36000.76983 + T * 0.0003032)) % 360;
const M = (357.52911 + T * (35999.05029 - T * 0.0001537)) % 360;
const Mrad = (M * Math.PI) / 180;
const C = Math.sin(Mrad) * (1.914602 - T * (0.004817 + 0.000014 * T))
+ Math.sin(2 * Mrad) * (0.019993 - 0.000101 * T)
+ Math.sin(3 * Mrad) * 0.000289;
const sunLon = L0 + C;
const omega = 125.04 - 1934.136 * T;
const lambda = sunLon - 0.00569 - 0.00478 * Math.sin((omega * Math.PI) / 180);
const eps0 = 23 + 26 / 60 + 21.448 / 3600 - T * (46.8150 / 3600 + T * (0.00059 / 3600 - T * 0.001813 / 3600));
const eps = eps0 + 0.00256 * Math.cos((omega * Math.PI) / 180);
const epsRad = (eps * Math.PI) / 180;
const lambdaRad = (lambda * Math.PI) / 180;
const declRad = Math.asin(Math.sin(epsRad) * Math.sin(lambdaRad));
// Equation of time (minutes)
const y = Math.tan(epsRad / 2) ** 2;
const L0rad = (L0 * Math.PI) / 180;
const eqtMin = (4 / Math.PI) * (
y * Math.sin(2 * L0rad)
- 2 * Math.sin(Mrad)
+ 4 * Math.sin(Mrad) * y * Math.cos(2 * L0rad)
- 0.5 * y * y * Math.sin(4 * L0rad)
- 1.25 * Math.sin(2 * Mrad)
) * (180 / Math.PI);
const eqtHours = eqtMin / 60;
return { declRad, eqtHours };
}
/**
* Compute the time (fractional hours, local time) when the sun reaches a given
* altitude (degrees) before/after solar noon.
*
* @param jd Julian Day Number (UT noon)
* @param lat Latitude in decimal degrees
* @param lng Longitude in decimal degrees
* @param tz UTC offset in hours
* @param altDeg Target altitude in degrees (negative for depression below horizon)
* @returns [rise, set] as fractional hours in local time, or NaN if sun never reaches alt
*/
export function horizonCrossing(
jd: number,
lat: number,
lng: number,
tz: number,
altDeg: number,
): [number, number] {
const { declRad, eqtHours } = solar(jd);
const latRad = (lat * Math.PI) / 180;
const altRad = (altDeg * Math.PI) / 180;
const cosH = (Math.sin(altRad) - Math.sin(latRad) * Math.sin(declRad))
/ (Math.cos(latRad) * Math.cos(declRad));
if (cosH < -1 || cosH > 1) return [NaN, NaN]; // polar day/night
const H = (Math.acos(cosH) * 180) / Math.PI; // hour angle in degrees
// Solar noon in local time
const noon = 12 - eqtHours - lng / 15 + tz;
const rise = noon - H / 15;
const set = noon + H / 15;
return [rise, set];
}

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/**
* Types for pray-calc-ml machine learning calibration for Islamic prayer times.
*/
/**
* A single observed prayer time announcement.
*
* All times are fractional hours in local time (same convention as pray-calc's getTimes).
* For example, 5.5 = 5:30 AM, 20.25 = 8:15 PM.
*/
export interface Observation {
/** Observer's local date for this observation. */
date: Date;
/** Latitude in decimal degrees (south = negative). */
lat: number;
/** Longitude in decimal degrees (west = negative). */
lng: number;
/** UTC offset in hours (e.g. -5 for EST). */
tz: number;
/**
* Observed Fajr time as fractional hours in local time.
* Omit if this observation does not constrain Fajr.
*/
fajr?: number;
/**
* Observed Isha time as fractional hours in local time.
* Omit if this observation does not constrain Isha.
*/
isha?: number;
/**
* Relative weight of this observation (default: 1.0).
* Higher weight makes the calibration prioritize this data point.
* Useful for down-weighting older or less reliable records.
*/
weight?: number;
}
/**
* Calibrated Fajr and Isha depression angles that best fit the observations.
*/
export interface CalibratedAngles {
/** Calibrated Fajr depression angle in degrees (positive, measured below horizon). */
fajrAngle: number;
/** Calibrated Isha depression angle in degrees (positive, measured below horizon). */
ishaAngle: number;
}
/**
* Detailed report from a calibration run.
*/
export interface CalibrationResult {
/** The calibrated angles. */
angles: CalibratedAngles;
/**
* Root-mean-square error of the fit in minutes.
* Lower is better. A value under 2 min is excellent for mosque data.
*/
rmsMinutes: number;
/**
* Number of observations used in the fit.
* Fajr-only and Isha-only observations each count as 0.5.
*/
observationCount: number;
/**
* Per-observation residuals in minutes (positive = predicted later than observed).
* Index matches the input observations array.
*/
residuals: Array<{ fajrMin: number | null; ishaMin: number | null }>;
}
/**
* Options for calibrateAngles().
*/
export interface CalibrationOptions {
/**
* Initial Fajr angle guess in degrees (default: 15.0).
* The solver starts here and iterates toward the minimum.
*/
fajrAngle0?: number;
/**
* Initial Isha angle guess in degrees (default: 15.0).
*/
ishaAngle0?: number;
/**
* Minimum allowed Fajr angle (default: 10.0).
* Physically, angles below 10° cannot produce astronomical twilight.
*/
fajrMin?: number;
/**
* Maximum allowed Fajr angle (default: 22.0).
*/
fajrMax?: number;
/**
* Minimum allowed Isha angle (default: 10.0).
*/
ishaMin?: number;
/**
* Maximum allowed Isha angle (default: 22.0).
*/
ishaMax?: number;
/**
* Maximum number of solver iterations (default: 100).
*/
maxIter?: number;
/**
* Convergence tolerance in degrees (default: 1e-4).
* The solver stops when the angle update is smaller than this.
*/
tol?: number;
}

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/**
* pray-calc-ml CJS test suite
* Focused subset verifying CommonJS imports work correctly.
*/
'use strict';
const assert = require('assert');
const { calibrateAngles, scoreAngles, predictFajr, predictIsha } = require('./dist/index.cjs');
let passed = 0;
let failed = 0;
function test(name, fn) {
try {
fn();
console.log(` ${name}... PASS`);
passed++;
} catch (e) {
console.error(` ${name}... FAIL: ${e.message}`);
failed++;
}
}
console.log('\n[CJS] Exports and basic functionality');
test('all exports are functions', () => {
assert.strictEqual(typeof calibrateAngles, 'function');
assert.strictEqual(typeof scoreAngles, 'function');
assert.strictEqual(typeof predictFajr, 'function');
assert.strictEqual(typeof predictIsha, 'function');
});
// Makkah, summer, UTC+3, ISNA 15°
const MK = { date: new Date('2024-06-21'), lat: 21.4225, lng: 39.8262, tz: 3 };
test('predictFajr returns finite number', () => {
const t = predictFajr(MK.date, MK.lat, MK.lng, MK.tz, 15);
assert(isFinite(t), `got ${t}`);
});
test('predictIsha returns finite number', () => {
const t = predictIsha(MK.date, MK.lat, MK.lng, MK.tz, 15);
assert(isFinite(t), `got ${t}`);
});
// Build 4 synthetic observations for NY at 15°
const NY = { lat: 40.7128, lng: -74.006, tz: -4 };
const dates = [
new Date('2024-01-15'),
new Date('2024-04-15'),
new Date('2024-07-15'),
new Date('2024-10-15'),
];
const obs = dates.map(d => ({
date: d, lat: NY.lat, lng: NY.lng, tz: NY.tz,
fajr: predictFajr(d, NY.lat, NY.lng, NY.tz, 15),
isha: predictIsha(d, NY.lat, NY.lng, NY.tz, 15),
}));
test('calibrateAngles recovers 15° angles', () => {
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.fajrAngle - 15) < 0.1, `Fajr: ${r.angles.fajrAngle}°`);
assert(Math.abs(r.angles.ishaAngle - 15) < 0.1, `Isha: ${r.angles.ishaAngle}°`);
});
test('scoreAngles perfect score < 0.01 min RMS', () => {
const s = scoreAngles(obs, 15, 15);
assert(s.rmsMinutes < 0.01, `rms=${s.rmsMinutes}`);
});
test('calibrateAngles result has all expected fields', () => {
const r = calibrateAngles(obs);
assert('angles' in r && 'rmsMinutes' in r && 'observationCount' in r && 'residuals' in r);
});
console.log('\n' + '─'.repeat(50));
console.log(`${passed}/${passed + failed} CJS tests passed`);
if (failed > 0) process.exit(1);

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/**
* pray-calc-ml ESM test suite
* Plain Node.js assert, no test framework.
*/
import assert from 'assert';
import {
calibrateAngles,
scoreAngles,
predictFajr,
predictIsha,
} from './dist/index.mjs';
let passed = 0;
let failed = 0;
function test(name, fn) {
try {
fn();
console.log(` ${name}... PASS`);
passed++;
} catch (e) {
console.error(` ${name}... FAIL: ${e.message}`);
failed++;
}
}
// ─────────────────────────────────────────────────────────────────────────────
// Section 1: predictFajr / predictIsha
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[1] predictFajr / predictIsha');
// Makkah, summer solstice, tz=+3. ISNA uses 15°/15°.
const MK_DATE = new Date('2024-06-21');
const MK_LAT = 21.4225;
const MK_LNG = 39.8262;
const MK_TZ = 3;
test('predictFajr returns finite value for Makkah summer', () => {
const t = predictFajr(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
assert(isFinite(t), `got ${t}`);
});
test('predictIsha returns finite value for Makkah summer', () => {
const t = predictIsha(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
assert(isFinite(t), `got ${t}`);
});
test('predictFajr < predictIsha (Fajr before Isha)', () => {
const f = predictFajr(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
const i = predictIsha(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
assert(f < i, `Fajr(${f}) < Isha(${i})`);
});
test('predictFajr Makkah 15° in range 46 h', () => {
const t = predictFajr(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
assert(t > 4 && t < 6, `got ${t}`);
});
test('predictIsha Makkah 15° in range 2022 h', () => {
const t = predictIsha(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
assert(t > 20 && t < 22.5, `got ${t}`);
});
test('larger angle gives earlier Fajr', () => {
const f15 = predictFajr(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
const f18 = predictFajr(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 18);
assert(f18 < f15, `18°(${f18}) should be < 15°(${f15})`);
});
test('larger angle gives later Isha', () => {
const i15 = predictIsha(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 15);
const i18 = predictIsha(MK_DATE, MK_LAT, MK_LNG, MK_TZ, 18);
assert(i18 > i15, `18°(${i18}) should be > 15°(${i15})`);
});
test('predictFajr polar summer returns NaN when sun never sets deep enough', () => {
// Oslo (59.9°N) in deep summer at 22° should still be finite, but 30° is impossible
const t = predictFajr(new Date('2024-06-21'), 69.0, 18.0, 1, 30);
assert(isNaN(t), `expected NaN for impossible angle, got ${t}`);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 2: scoreAngles
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[2] scoreAngles');
// Build observations from a single location (NY, UTC-4) across multiple dates.
// We'll pretend the "true" angle is 15° and add a small ±1min noise to test scoring.
const NY_LAT = 40.7128;
const NY_LNG = -74.006;
const NY_TZ = -4;
const nyDates = [
new Date('2024-01-15'),
new Date('2024-04-15'),
new Date('2024-07-15'),
new Date('2024-10-15'),
];
const trueAngle = 15;
const nyObs = nyDates.map(d => ({
date: d, lat: NY_LAT, lng: NY_LNG, tz: NY_TZ,
fajr: predictFajr(d, NY_LAT, NY_LNG, NY_TZ, trueAngle),
isha: predictIsha(d, NY_LAT, NY_LNG, NY_TZ, trueAngle),
}));
test('scoreAngles returns object with expected keys', () => {
const s = scoreAngles(nyObs, 15, 15);
assert('rmsMinutes' in s);
assert('fajrBiasMinutes' in s);
assert('ishaBiasMinutes' in s);
assert('residuals' in s);
assert(Array.isArray(s.residuals));
});
test('scoreAngles perfect angles → rms near 0', () => {
const s = scoreAngles(nyObs, 15, 15);
assert(s.rmsMinutes < 0.01, `rms=${s.rmsMinutes}`);
});
test('scoreAngles wrong angles → rms > 0', () => {
const s = scoreAngles(nyObs, 18, 12);
assert(s.rmsMinutes > 1, `rms=${s.rmsMinutes}`);
});
test('scoreAngles residuals array length matches observations', () => {
const s = scoreAngles(nyObs, 15, 15);
assert.strictEqual(s.residuals.length, nyObs.length);
});
test('scoreAngles fajrBias near 0 for exact angles', () => {
const s = scoreAngles(nyObs, 15, 15);
assert(Math.abs(s.fajrBiasMinutes) < 0.01, `bias=${s.fajrBiasMinutes}`);
});
test('scoreAngles fajrBias negative when angle is too small (predicted too late)', () => {
// 12° → Fajr predicted later than 15° observations → bias < 0
const s = scoreAngles(nyObs, 12, 15);
assert(s.fajrBiasMinutes > 0, `expected positive bias, got ${s.fajrBiasMinutes}`);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 3: calibrateAngles — basic recovery
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[3] calibrateAngles — basic angle recovery');
test('calibrateAngles returns object with angles, rmsMinutes, observationCount, residuals', () => {
const r = calibrateAngles(nyObs);
assert('angles' in r);
assert('fajrAngle' in r.angles);
assert('ishaAngle' in r.angles);
assert('rmsMinutes' in r);
assert('observationCount' in r);
assert('residuals' in r);
});
test('calibrateAngles recovers 15° Fajr angle within 0.1°', () => {
const r = calibrateAngles(nyObs);
assert(
Math.abs(r.angles.fajrAngle - 15) < 0.1,
`got ${r.angles.fajrAngle}°, expected ~15°`
);
});
test('calibrateAngles recovers 15° Isha angle within 0.1°', () => {
const r = calibrateAngles(nyObs);
assert(
Math.abs(r.angles.ishaAngle - 15) < 0.1,
`got ${r.angles.ishaAngle}°, expected ~15°`
);
});
test('calibrateAngles RMS < 0.1 min for synthetic clean data', () => {
const r = calibrateAngles(nyObs);
assert(r.rmsMinutes < 0.1, `rms=${r.rmsMinutes}`);
});
test('calibrateAngles observationCount = 4 for 4 dual observations', () => {
const r = calibrateAngles(nyObs);
assert.strictEqual(r.observationCount, 4);
});
test('calibrateAngles residuals length matches input', () => {
const r = calibrateAngles(nyObs);
assert.strictEqual(r.residuals.length, nyObs.length);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 4: calibrateAngles — different target angles
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[4] calibrateAngles — recovering non-default angles');
function makeObs(angle, fajrOverride, ishaOverride) {
return nyDates.map(d => ({
date: d, lat: NY_LAT, lng: NY_LNG, tz: NY_TZ,
fajr: fajrOverride !== undefined
? predictFajr(d, NY_LAT, NY_LNG, NY_TZ, fajrOverride)
: undefined,
isha: ishaOverride !== undefined
? predictIsha(d, NY_LAT, NY_LNG, NY_TZ, ishaOverride)
: undefined,
}));
}
test('calibrateAngles recovers 18° Fajr', () => {
const obs = makeObs(null, 18, 18);
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.fajrAngle - 18) < 0.1, `got ${r.angles.fajrAngle}°`);
});
test('calibrateAngles recovers 12° Isha', () => {
const obs = makeObs(null, 12, 12);
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.ishaAngle - 12) < 0.1, `got ${r.angles.ishaAngle}°`);
});
test('calibrateAngles recovers asymmetric Fajr=17, Isha=13', () => {
const obs = makeObs(null, 17, 13);
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.fajrAngle - 17) < 0.1, `Fajr: got ${r.angles.fajrAngle}°`);
assert(Math.abs(r.angles.ishaAngle - 13) < 0.1, `Isha: got ${r.angles.ishaAngle}°`);
});
test('calibrateAngles works with Fajr-only observations', () => {
const obs = makeObs(null, 15, undefined);
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.fajrAngle - 15) < 0.1, `Fajr: got ${r.angles.fajrAngle}°`);
});
test('calibrateAngles works with Isha-only observations', () => {
const obs = makeObs(null, undefined, 15);
const r = calibrateAngles(obs);
assert(Math.abs(r.angles.ishaAngle - 15) < 0.1, `Isha: got ${r.angles.ishaAngle}°`);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 5: calibrateAngles — weighted observations
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[5] calibrateAngles — weighted regression');
test('high-weight observation pulls calibrated angle toward its implied angle', () => {
// Mix: 3 obs from 15° angle (weight 1) + 1 obs from 20° angle (weight 20)
// The high-weight 20° obs should dominate, pulling result toward 20°.
const obs15 = nyDates.slice(0, 3).map(d => ({
date: d, lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, weight: 1,
fajr: predictFajr(d, NY_LAT, NY_LNG, NY_TZ, 15),
isha: predictIsha(d, NY_LAT, NY_LNG, NY_TZ, 15),
}));
const obs20 = [{
date: nyDates[3], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, weight: 20,
fajr: predictFajr(nyDates[3], NY_LAT, NY_LNG, NY_TZ, 20),
isha: predictIsha(nyDates[3], NY_LAT, NY_LNG, NY_TZ, 20),
}];
const r = calibrateAngles([...obs15, ...obs20]);
assert(r.angles.fajrAngle > 17, `expected > 17°, got ${r.angles.fajrAngle}°`);
});
test('equal weights produce result between two angle sets', () => {
const obs15 = nyDates.slice(0, 2).map(d => ({
date: d, lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, weight: 1,
fajr: predictFajr(d, NY_LAT, NY_LNG, NY_TZ, 15),
isha: predictIsha(d, NY_LAT, NY_LNG, NY_TZ, 15),
}));
const obs18 = nyDates.slice(2).map(d => ({
date: d, lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, weight: 1,
fajr: predictFajr(d, NY_LAT, NY_LNG, NY_TZ, 18),
isha: predictIsha(d, NY_LAT, NY_LNG, NY_TZ, 18),
}));
const r = calibrateAngles([...obs15, ...obs18]);
assert(r.angles.fajrAngle > 15 && r.angles.fajrAngle < 18,
`expected 1518°, got ${r.angles.fajrAngle}°`);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 6: calibrateAngles — multi-location
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[6] calibrateAngles — multi-location dataset');
const locations = [
{ lat: 21.4225, lng: 39.8262, tz: 3 }, // Makkah
{ lat: 40.7128, lng: -74.0060, tz: -4 }, // New York
{ lat: 51.5074, lng: -0.1278, tz: 1 }, // London
{ lat: 1.3521, lng: 103.8198, tz: 8 }, // Singapore
];
const multiDates = [new Date('2024-01-15'), new Date('2024-07-15')];
const TARGET_ANGLE = 16.5;
const multiObs = locations.flatMap(loc =>
multiDates.map(d => ({
date: d, lat: loc.lat, lng: loc.lng, tz: loc.tz,
fajr: predictFajr(d, loc.lat, loc.lng, loc.tz, TARGET_ANGLE),
isha: predictIsha(d, loc.lat, loc.lng, loc.tz, TARGET_ANGLE),
}))
);
test('calibrateAngles recovers 16.5° from multi-location data within 0.2°', () => {
const r = calibrateAngles(multiObs);
assert(Math.abs(r.angles.fajrAngle - TARGET_ANGLE) < 0.2, `got ${r.angles.fajrAngle}°`);
assert(Math.abs(r.angles.ishaAngle - TARGET_ANGLE) < 0.2, `got ${r.angles.ishaAngle}°`);
});
test('multi-location RMS < 0.1 min for clean synthetic data', () => {
const r = calibrateAngles(multiObs);
assert(r.rmsMinutes < 0.1, `rms=${r.rmsMinutes}`);
});
// ─────────────────────────────────────────────────────────────────────────────
// Section 7: error handling
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n[7] error handling');
test('calibrateAngles throws when both Fajr and Isha have fewer than 2 observations', () => {
// 1 Fajr + 1 Isha — neither can be calibrated, so this must throw.
const obs = [{ date: nyDates[0], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, fajr: 5.5, isha: 21.0 }];
let threw = false;
try { calibrateAngles(obs); } catch { threw = true; }
assert(threw, 'expected error when both have <2 observations');
});
test('calibrateAngles does NOT throw with 4 Fajr + 1 Isha (Fajr calibrated, Isha gets default)', () => {
// 4 Fajr-only + 1 dual: Fajr gets calibrated, Isha falls back to fajrAngle0 default.
const obs = [
{ date: nyDates[0], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, fajr: 5.0 },
{ date: nyDates[1], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, fajr: 5.2 },
{ date: nyDates[2], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, fajr: 4.8 },
{ date: nyDates[3], lat: NY_LAT, lng: NY_LNG, tz: NY_TZ, fajr: 5.1, isha: 21.0 },
];
const r = calibrateAngles(obs);
assert(isFinite(r.angles.fajrAngle), `Fajr angle should be finite, got ${r.angles.fajrAngle}`);
assert(isFinite(r.angles.ishaAngle), `Isha angle should be finite (default), got ${r.angles.ishaAngle}`);
});
test('scoreAngles handles empty array gracefully', () => {
const s = scoreAngles([], 15, 15);
assert.strictEqual(s.rmsMinutes, 0);
assert.strictEqual(s.residuals.length, 0);
});
// ─────────────────────────────────────────────────────────────────────────────
// Summary
// ─────────────────────────────────────────────────────────────────────────────
console.log('\n' + '─'.repeat(50));
console.log(`${passed}/${passed + failed} tests passed`);
if (failed > 0) process.exit(1);

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{
"compilerOptions": {
"target": "ES2020",
"module": "ESNext",
"moduleResolution": "bundler",
"strict": true,
"esModuleInterop": true,
"declaration": true,
"declarationMap": true,
"sourceMap": true,
"outDir": "dist",
"rootDir": "src",
"types": ["node"]
},
"include": ["src/**/*"],
"exclude": ["node_modules", "dist"]
}

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import { defineConfig } from 'tsup';
export default defineConfig({
entry: ['src/index.ts'],
format: ['cjs', 'esm'],
dts: true,
clean: true,
outDir: 'dist',
splitting: false,
sourcemap: true,
target: 'es2020',
platform: 'neutral',
outExtension({ format }) {
return { js: format === 'cjs' ? '.cjs' : '.mjs' };
},
});