Trio/Dependencies/LoopKit/LoopKit/InsulinKit/InsulinMath.swift

//
//  InsulinMath.swift
//  Naterade
//
//  Created by Nathan Racklyeft on 1/30/16.
//  Copyright © 2016 Nathan Racklyeft. All rights reserved.
//

import Foundation
import HealthKit


extension DoseEntry {
    private func continuousDeliveryInsulinOnBoard(at date: Date, model: InsulinModel, delta: TimeInterval) -> Double {
        let doseDuration = endDate.timeIntervalSince(startDate)  // t1
        let time = date.timeIntervalSince(startDate)
        var iob: Double = 0
        var doseDate = TimeInterval(0)  // i

        repeat {
            let segment: Double

            if doseDuration > 0 {
                segment = max(0, min(doseDate + delta, doseDuration) - doseDate) / doseDuration
            } else {
                segment = 1
            }

            iob += segment * model.percentEffectRemaining(at: time - doseDate)
            doseDate += delta
        } while doseDate <= min(floor((time + model.delay) / delta) * delta, doseDuration)

        return iob
    }

    func insulinOnBoard(at date: Date, model: InsulinModel, delta: TimeInterval) -> Double {
        let time = date.timeIntervalSince(startDate)
        guard time >= 0 else {
            return 0
        }

        // Consider doses within the delta time window as momentary
        if endDate.timeIntervalSince(startDate) <= 1.05 * delta {
            return netBasalUnits * model.percentEffectRemaining(at: time)
        } else {
            return netBasalUnits * continuousDeliveryInsulinOnBoard(at: date, model: model, delta: delta)
        }
    }

    private func continuousDeliveryGlucoseEffect(at date: Date, model: InsulinModel, delta: TimeInterval) -> Double {
        let doseDuration = endDate.timeIntervalSince(startDate)  // t1
        let time = date.timeIntervalSince(startDate)
        var value: Double = 0
        var doseDate = TimeInterval(0)  // i

        repeat {
            let segment: Double

            if doseDuration > 0 {
                segment = max(0, min(doseDate + delta, doseDuration) - doseDate) / doseDuration
            } else {
                segment = 1
            }

            value += segment * (1.0 - model.percentEffectRemaining(at: time - doseDate))
            doseDate += delta
        } while doseDate <= min(floor((time + model.delay) / delta) * delta, doseDuration)

        return value
    }

    func glucoseEffect(at date: Date, model: InsulinModel, insulinSensitivity: Double, delta: TimeInterval) -> Double {
        let time = date.timeIntervalSince(startDate)

        guard time >= 0 else {
            return 0
        }

        // Consider doses within the delta time window as momentary
        if endDate.timeIntervalSince(startDate) <= 1.05 * delta {
            return netBasalUnits * -insulinSensitivity * (1.0 - model.percentEffectRemaining(at: time))
        } else {
            return netBasalUnits * -insulinSensitivity * continuousDeliveryGlucoseEffect(at: date, model: model, delta: delta)
        }
    }

    func trimmed(from start: Date? = nil, to end: Date? = nil, syncIdentifier: String? = nil) -> DoseEntry {

        let originalDuration = endDate.timeIntervalSince(startDate)

        let startDate = max(start ?? .distantPast, self.startDate)
        let endDate = max(startDate, min(end ?? .distantFuture, self.endDate))

        var trimmedDeliveredUnits: Double? = deliveredUnits
        var trimmedValue: Double = value

        if originalDuration > .ulpOfOne && (startDate > self.startDate || endDate < self.endDate) {
            let updatedActualDelivery = unitsInDeliverableIncrements * (endDate.timeIntervalSince(startDate) / originalDuration)
            if deliveredUnits != nil {
                trimmedDeliveredUnits = updatedActualDelivery
            }
            if case .units = unit  {
                trimmedValue = updatedActualDelivery
            }
        }

        return DoseEntry(
            type: type,
            startDate: startDate,
            endDate: endDate,
            value: trimmedValue,
            unit: unit,
            deliveredUnits: trimmedDeliveredUnits,
            description: description,
            syncIdentifier: syncIdentifier,
            scheduledBasalRate: scheduledBasalRate,
            insulinType: insulinType,
            automatic: automatic,
            isMutable: isMutable,
            wasProgrammedByPumpUI: wasProgrammedByPumpUI
        )
    }
}


/**
 It takes a MM x22 pump about 40s to deliver 1 Unit while bolusing
 See: http://www.healthline.com/diabetesmine/ask-dmine-speed-insulin-pumps#3

 The x23 and newer pumps can deliver at 2x, 3x, and 4x that speed, targeting
 a maximum 5-minute delivery for all boluses (8U - 25U)

 A basal rate of 30 U/hour (near-max) would deliver an additional 0.5 U/min.
 */
private let MaximumReservoirDropPerMinute = 6.5


extension Collection where Element: ReservoirValue {
    /**
     Converts a continuous, chronological sequence of reservoir values to a sequence of doses

     This is an O(n) operation.

     - returns: An array of doses
     */
    var doseEntries: [DoseEntry] {
        var doses: [DoseEntry] = []
        var previousValue: Element?

        let numberFormatter = NumberFormatter()
        numberFormatter.numberStyle = .decimal
        numberFormatter.maximumFractionDigits = 3

        for value in self {
            if let previousValue = previousValue {
                let volumeDrop = previousValue.unitVolume - value.unitVolume
                let duration = value.startDate.timeIntervalSince(previousValue.startDate)

                if duration > 0 && 0 <= volumeDrop && volumeDrop <= MaximumReservoirDropPerMinute * duration.minutes {
                    doses.append(DoseEntry(
                        type: .tempBasal,
                        startDate: previousValue.startDate,
                        endDate: value.startDate,
                        value: volumeDrop,
                        unit: .units
                    ))
                }
            }

            previousValue = value
        }

        return doses
    }

    /**
     Whether a span of chronological reservoir values is considered continuous and therefore reliable.
     
     Reservoir values of 0 are automatically considered unreliable due to the assumption that an unknown amount of insulin can be delivered after the 0 marker.

     - parameter startDate:       The beginning of the interval in which to validate continuity
     - parameter endDate:         The end of the interval in which to validate continuity
     - parameter maximumDuration: The maximum interval to consider reliable for a reservoir-derived dose
     
     - returns: Whether the reservoir values meet the critera for continuity
     */
    func isContinuous(from start: Date?, to end: Date, within maximumDuration: TimeInterval) -> Bool {
        guard let firstValue = self.first else {
            return false
        }

        // The first value has to be at least as old as the start date, as a reference point.
        let startDate = start ?? firstValue.endDate
        guard firstValue.endDate <= startDate else {
            return false
        }

        var lastValue = firstValue

        for value in self {
            defer {
                lastValue = value
            }

            // Volume and interval validation only applies for values in the specified range,
            guard value.endDate >= startDate && value.startDate <= end else {
                continue
            }

            // We can't trust 0. What else was delivered?
            guard value.unitVolume > 0 else {
                return false
            }

            // Rises in reservoir volume indicate a rewind + prime, and primes
            // can be easily confused with boluses.
            // Small rises (1 U) can be ignored as they're indicative of a mixed-precision sequence.
            guard value.unitVolume <= lastValue.unitVolume + 1 else {
                return false
            }

            // Ensure no more than the maximum interval has passed
            guard value.startDate.timeIntervalSince(lastValue.endDate) <= maximumDuration else {
                return false
            }
        }

        return true
    }
}


extension DoseEntry {
    /// Annotates a dose with the context of the scheduled basal rate
    ///
    /// If the dose crosses a schedule boundary, it will be split into multiple doses so each dose has a
    /// single scheduled basal rate.
    ///
    /// - Parameter basalSchedule: The basal rate schedule to apply
    /// - Returns: An array of annotated doses
    fileprivate func annotated(with basalSchedule: BasalRateSchedule) -> [DoseEntry] {
        switch type {
        case .tempBasal, .suspend, .resume:
            guard scheduledBasalRate == nil else {
                return [self]
            }
            break
        case .basal, .bolus:
            return [self]
        }

        var doses: [DoseEntry] = []
        let basalItems = basalSchedule.between(start: startDate, end: endDate)

        for (index, basalItem) in basalItems.enumerated() {
            let startDate: Date
            let endDate: Date

            // If we're splitting into multiple entries, keep the syncIdentifier unique
            var syncIdentifier = self.syncIdentifier
            if syncIdentifier != nil, basalItems.count > 1 {
                syncIdentifier! += " \(index + 1)/\(basalItems.count)"
            }

            if index == 0 {
                startDate = self.startDate
            } else {
                startDate = basalItem.startDate
            }

            if index == basalItems.count - 1 {
                endDate = self.endDate
            } else {
                endDate = basalItems[index + 1].startDate
            }

            var dose = trimmed(from: startDate, to: endDate, syncIdentifier: syncIdentifier)

            dose.scheduledBasalRate = HKQuantity(unit: DoseEntry.unitsPerHour, doubleValue: basalItem.value)

            doses.append(dose)
        }

        return doses
    }
    
    /// Annotates a dose with the specified insulin type.
    ///
    /// - Parameter insulinType: The insulin type to annotate the dose with.
    /// - Returns: A dose annotated with the insulin model
    public func annotated(with insulinType: InsulinType) -> DoseEntry {
        return DoseEntry(
            type: type,
            startDate: startDate,
            endDate: endDate,
            value: value,
            unit: unit,
            deliveredUnits: deliveredUnits,
            description: description,
            syncIdentifier: syncIdentifier,
            scheduledBasalRate: scheduledBasalRate,
            insulinType: insulinType,
            isMutable: isMutable,
            wasProgrammedByPumpUI: wasProgrammedByPumpUI
        )
    }
}

extension DoseEntry {
    /// Calculates the timeline of glucose effects for a temp basal dose
    /// Use case: predict glucose effects of zero temping
    ///
    /// - Parameters:
    ///   - insulinModelProvider: A factory that can provide an insulin model given an insulin type
    ///   - longestEffectDuration: The longest duration that a dose could be active.
    ///   - defaultInsulinModelSetting: The model of insulin activity over time
    ///   - insulinSensitivity: The schedule of glucose effect per unit of insulin
    ///   - basalRateSchedule: The schedule of basal rates
    /// - Returns: An array of glucose effects for the duration of the temp basal dose plus the duration of insulin action
    public func tempBasalGlucoseEffects(
        insulinModelProvider: InsulinModelProvider,
        longestEffectDuration: TimeInterval,
        insulinSensitivity: InsulinSensitivitySchedule,
        basalRateSchedule: BasalRateSchedule
        ) -> [GlucoseEffect] {

        guard case .tempBasal = type else {
            return []
        }
        
        let netTempBasalDoses = self.annotated(with: basalRateSchedule)

        return netTempBasalDoses.glucoseEffects(insulinModelProvider: insulinModelProvider, longestEffectDuration: longestEffectDuration, insulinSensitivity: insulinSensitivity)
    }

    fileprivate var resolvingDelivery: DoseEntry {
        guard !isMutable, deliveredUnits == nil else {
            return self
        }

        let resolvedUnits: Double

        if case .units = unit {
            resolvedUnits = value
        } else {
            switch type {
            case .tempBasal:
                resolvedUnits = unitsInDeliverableIncrements
            case .basal:
                resolvedUnits = programmedUnits
            default:
                return self
            }
        }
        return DoseEntry(type: type, startDate: startDate, endDate: endDate, value: value, unit: unit, deliveredUnits: resolvedUnits, description: description, syncIdentifier: syncIdentifier, scheduledBasalRate: scheduledBasalRate, insulinType: insulinType, isMutable: isMutable, wasProgrammedByPumpUI: wasProgrammedByPumpUI)
    }
}

extension Collection where Element == DoseEntry {

    /**
     Maps a timeline of dose entries with overlapping start and end dates to a timeline of doses that represents actual insulin delivery.

     - returns: An array of reconciled insulin delivery history, as TempBasal and Bolus records
     */
    func reconciled() -> [DoseEntry] {

        var reconciled: [DoseEntry] = []

        var lastSuspend: DoseEntry?
        var lastBasal: DoseEntry?

        for dose in self {
            switch dose.type {
            case .bolus:
                reconciled.append(dose)
            case .basal, .tempBasal:
                if lastSuspend == nil, let last = lastBasal {
                    let endDate = Swift.min(last.endDate, dose.startDate)

                    // Ignore 0-duration doses
                    if endDate > last.startDate {
                        reconciled.append(last.trimmed(from: nil, to: endDate, syncIdentifier: last.syncIdentifier))
                    }
                } else if let suspend = lastSuspend, dose.type == .tempBasal {
                    // Handle missing resume. Basal following suspend, with no resume.
                    reconciled.append(DoseEntry(
                        type: suspend.type,
                        startDate: suspend.startDate,
                        endDate: dose.startDate,
                        value: suspend.value,
                        unit: suspend.unit,
                        description: suspend.description ?? dose.description,
                        syncIdentifier: suspend.syncIdentifier,
                        insulinType: suspend.insulinType,
                        isMutable: suspend.isMutable,
                        wasProgrammedByPumpUI: suspend.wasProgrammedByPumpUI
                    ))
                    lastSuspend = nil
                }

                lastBasal = dose
            case .resume:
                if let suspend = lastSuspend {

                    reconciled.append(DoseEntry(
                        type: suspend.type,
                        startDate: suspend.startDate,
                        endDate: dose.startDate,
                        value: suspend.value,
                        unit: suspend.unit,
                        description: suspend.description ?? dose.description,
                        syncIdentifier: suspend.syncIdentifier,
                        insulinType: suspend.insulinType,
                        isMutable: suspend.isMutable,
                        wasProgrammedByPumpUI: suspend.wasProgrammedByPumpUI
                    ))

                    lastSuspend = nil

                    // Continue temp basals that may have started before suspending
                    if let last = lastBasal {
                        if last.endDate > dose.endDate {
                            lastBasal = DoseEntry(
                                type: last.type,
                                startDate: dose.endDate,
                                endDate: last.endDate,
                                value: last.value,
                                unit: last.unit,
                                description: last.description,
                                // We intentionally use the resume's identifier, as the basal entry has already been entered
                                syncIdentifier: dose.syncIdentifier,
                                insulinType: last.insulinType,
                                automatic: last.automatic,
                                isMutable: last.isMutable,
                                wasProgrammedByPumpUI: last.wasProgrammedByPumpUI
                            )
                        } else {
                            lastBasal = nil
                        }
                    }
                }
            case .suspend:
                if let last = lastBasal {

                    reconciled.append(DoseEntry(
                        type: last.type,
                        startDate: last.startDate,
                        endDate: Swift.min(last.endDate, dose.startDate),
                        value: last.value,
                        unit: last.unit,
                        description: last.description,
                        syncIdentifier: last.syncIdentifier,
                        insulinType: last.insulinType,
                        isMutable: last.isMutable,
                        wasProgrammedByPumpUI: last.wasProgrammedByPumpUI
                    ))

                    if last.endDate <= dose.startDate {
                        lastBasal = nil
                    }
                }

                lastSuspend = dose
            }
        }

        if let suspend = lastSuspend {
            reconciled.append(suspend)
        } else if let last = lastBasal, last.endDate > last.startDate {
            reconciled.append(last)
        }

        return reconciled.map { $0.resolvingDelivery }
    }

    /// Annotates a sequence of dose entries with the configured basal rate schedule.
    ///
    /// Doses which cross time boundaries in the basal rate schedule are split into multiple entries.
    ///
    /// - Parameter basalSchedule: The basal rate schedule
    /// - Returns: An array of annotated dose entries
    func annotated(with basalSchedule: BasalRateSchedule) -> [DoseEntry] {
        var annotatedDoses: [DoseEntry] = []

        for dose in self {
            annotatedDoses += dose.annotated(with: basalSchedule)
        }

        return annotatedDoses
    }
    
    /**
     Calculates the total insulin delivery for a collection of doses

     - returns: The total insulin insulin, in Units
     */
    var totalDelivery: Double {
        return reduce(0) { (total, dose) -> Double in
            return total + dose.unitsInDeliverableIncrements
        }
    }

    /**
     Calculates the timeline of insulin remaining for a collection of doses

     - parameter insulinModelProvider:  A factory that can provide an insulin model given an insulin type
     - parameter longestEffectDuration: The longest duration that a dose could be active.
     - parameter start:                 The date to start the timeline
     - parameter end:                   The date to end the timeline
     - parameter delta:                 The differential between timeline entries

     - returns: A sequence of insulin amount remaining
     */
    func insulinOnBoard(
        insulinModelProvider: InsulinModelProvider,
        longestEffectDuration: TimeInterval,
        from start: Date? = nil,
        to end: Date? = nil,
        delta: TimeInterval = TimeInterval(minutes: 5)
    ) -> [InsulinValue] {
        guard let (start, end) = LoopMath.simulationDateRangeForSamples(self, from: start, to: end, duration: longestEffectDuration, delta: delta) else {
            return []
        }

        var date = start
        var values = [InsulinValue]()

        repeat {
            let value = reduce(0) { (value, dose) -> Double in
                return value + dose.insulinOnBoard(at: date, model: insulinModelProvider.model(for: dose.insulinType), delta: delta)
            }

            values.append(InsulinValue(startDate: date, value: value))
            date = date.addingTimeInterval(delta)
        } while date <= end

        return values
    }

    /// Calculates the timeline of glucose effects for a collection of doses
    ///
    /// - Parameters:
    ///   - insulinModelProvider: A factory that can provide an insulin model given an insulin type
    ///   - longestEffectDuration: The longest duration that a dose could be active.
    ///   - insulinSensitivity: The schedule of glucose effect per unit of insulin
    ///   - start: The earliest date of effects to return
    ///   - end: The latest date of effects to return
    ///   - delta: The interval between returned effects
    /// - Returns: An array of glucose effects for the duration of the doses
    public func glucoseEffects(
        insulinModelProvider: InsulinModelProvider,
        longestEffectDuration: TimeInterval,
        insulinSensitivity: InsulinSensitivitySchedule,
        from start: Date? = nil,
        to end: Date? = nil,
        delta: TimeInterval = TimeInterval(/* minutes: */60 * 5)
    ) -> [GlucoseEffect] {
        guard let (start, end) = LoopMath.simulationDateRangeForSamples(self.filter({ entry in
            entry.netBasalUnits != 0
        }), from: start, to: end, duration: longestEffectDuration, delta: delta) else {
            return []
        }

        var date = start
        var values = [GlucoseEffect]()
        let unit = HKUnit.milligramsPerDeciliter

        repeat {
            let value = reduce(0) { (value, dose) -> Double in
                return value + dose.glucoseEffect(at: date, model: insulinModelProvider.model(for: dose.insulinType), insulinSensitivity: insulinSensitivity.quantity(at: dose.startDate).doubleValue(for: unit), delta: delta)
            }

            values.append(GlucoseEffect(startDate: date, quantity: HKQuantity(unit: unit, doubleValue: value)))
            date = date.addingTimeInterval(delta)
        } while date <= end

        return values
    }

    /// Applies the current basal schedule to a collection of reconciled doses in chronological order
    ///
    /// The scheduled basal rate is associated doses that override it, for later derivation of net delivery
    ///
    /// - Parameters:
    ///   - basalSchedule: The active basal schedule during the dose delivery
    ///   - start: The earliest date to apply the basal schedule
    ///   - end: The latest date to include. Doses must end before this time to be included.
    ///   - insertingBasalEntries: Whether basal doses should be created from the schedule. Pass true only for pump models that do not report their basal rates in event history.
    /// - Returns: An array of doses, 
    func overlayBasalSchedule(_ basalSchedule: BasalRateSchedule, startingAt start: Date, endingAt end: Date = .distantFuture, insertingBasalEntries: Bool) -> [DoseEntry] {
        let dateFormatter = ISO8601DateFormatter()  // GMT-based ISO formatting
        var newEntries = [DoseEntry]()
        var lastBasal: DoseEntry?

        if insertingBasalEntries {
            // Create a placeholder entry at our start date, so we know the correct duration of the
            // inserted basal entries
            lastBasal = DoseEntry(resumeDate: start)
        }

        for dose in self {
            switch dose.type {
            case .tempBasal, .basal, .suspend:
                // Only include entries if they have ended by the end date, since they may be cancelled
                guard dose.endDate <= end else {
                    continue
                }

                if let lastBasal = lastBasal {
                    if insertingBasalEntries {
                        // For older pumps which don't report the start/end of scheduled basal delivery,
                        // generate a basal entry from the specified schedule.
                        for scheduled in basalSchedule.between(start: lastBasal.endDate, end: dose.startDate) {
                            // Generate a unique identifier based on the start/end timestamps
                            let start = Swift.max(lastBasal.endDate, scheduled.startDate)
                            let end = Swift.min(dose.startDate, scheduled.endDate)

                            guard end.timeIntervalSince(start) > .ulpOfOne else {
                                continue
                            }

                            let syncIdentifier = "BasalRateSchedule \(dateFormatter.string(from: start)) \(dateFormatter.string(from: end))"

                            newEntries.append(DoseEntry(
                                type: .basal,
                                startDate: start,
                                endDate: end,
                                value: scheduled.value,
                                unit: .unitsPerHour,
                                syncIdentifier: syncIdentifier,
                                scheduledBasalRate: HKQuantity(unit: .internationalUnitsPerHour, doubleValue: scheduled.value),
                                insulinType: lastBasal.insulinType,
                                automatic: lastBasal.automatic
                            ))
                        }
                    }
                }

                lastBasal = dose

                // Only include the last basal entry if has ended by our end date
                if let lastBasal = lastBasal {
                    newEntries.append(lastBasal)
                }
            case .resume:
                assertionFailure("No resume events should be present in reconciled doses")
            case .bolus:
                newEntries.append(dose)
            }
        }

        return newEntries
    }

    /// Creates an array of DoseEntry values by unioning another array, de-duplicating by syncIdentifier
    ///
    /// - Parameter otherDoses: An array of doses to union
    /// - Returns: A new array of doses
    func appendedUnion(with otherDoses: [DoseEntry]) -> [DoseEntry] {
        var union: [DoseEntry] = []
        var syncIdentifiers: Set<String> = []

        for dose in (self + otherDoses) {
            if let syncIdentifier = dose.syncIdentifier {
                let (inserted, _) = syncIdentifiers.insert(syncIdentifier)
                if !inserted {
                    continue
                }
            }

            union.append(dose)
        }

        return union
    }
}


extension BidirectionalCollection where Element == DoseEntry {
    /// The endDate of the last basal dose in the collection
    var lastBasalEndDate: Date? {
        for dose in self.reversed() {
            if dose.type == .basal || dose.type == .tempBasal || dose.type == .resume {
                return dose.endDate
            }
        }

        return nil
    }
}