import Foundation
import OdeInt
import RealModule

public enum ECGSyn {
    public struct Parameters {
        /// The ECG amplitude in mV.
        let range: (Double, Double) = (-0.4, 1.4)

        /// Amplitude of the noise.
        let aNoise: Double = 0.0

        /// The angle of each attractor (P, Q, R, S, T) around the limit cycle, in radians.
        let theta: [Double] = [-70, -15, 0, 15, 100].map { $0 * .pi / 180 }

        /// The position of attractors (P, Q, R, S, T) above or below the z=0 plane.
        let a: [Double] = [1.2, -5, 30, -7.5, 0.75]

        /// Widths of the attractors (P, Q, R, S, T).
        let b: [Double] = [0.25, 0.1, 0.1, 0.1, 0.4]
    }

    public static func generate(params: Parameters, rrSeries: RRSeries<Double>) -> [Double] {
        var rng = rrSeries.rng
        let srInternal = rrSeries.timeParameters.srInternal

        // adjust extrema parameters for mean heart rate
        let hrFact = sqrt(rrSeries.timeParameters.hrMean / 60.0)
        let hrFactSqrt = sqrt(hrFact)

        let ai = params.a
        let bi = params.b.map { $0 * hrFact }
        let ti = zip([hrFactSqrt, hrFact, 1, hrFact, hrFactSqrt], params.theta).map(*)

        let fhi = rrSeries.rrParamaters.fhi

        let nt = rrSeries.count

        let dt = 1.0 / Double(srInternal)
        let ts = (0 ..< nt).map { Double($0) * dt }
        let x0 = SIMD3<Double>(1.0, 0.0, 0.04)

        let result = SIMD3<Double>.integrate(over: ts, y0: x0, tol: 1e-6) { x, t in
            let ta = atan2(x[1], x[0])

            let r0 = 1.0
            let a0 = 1.0 - sqrt(x[0] * x[0] + x[1] * x[1]) / r0

            let w0 = 2 * .pi / rrSeries.valueAt(t)

            let zbase = 0.005 * sin(2 * .pi * fhi * t)

            var dxdt = SIMD3<Double>(a0 * x[0] - w0 * x[1], a0 * x[1] + w0 * x[0], 0.0)

            for i in 0 ..< ti.count {
                let dt = remainder(ta - ti[i], 2 * .pi)

                dxdt[2] += -ai[i] * dt * exp(-0.5 * (dt * dt) / (bi[i] * bi[i]))
            }
            dxdt[2] += -1.0 * (x[2] - zbase)

            return dxdt
        }

        // extract z and downsample to ECG sampling frequency
        let qstep = srInternal / rrSeries.timeParameters.srEcg
        var zresult = stride(from: 0, to: nt, by: qstep).map { result[$0][2] }

        let (zmin, zmax) = zresult.minAndMax()!
        let zrange = zmax - zmin

        // Scale signal between -0.4 and 1.2 mV
        // add uniformly distributed measurement noise
        for i in 0 ..< zresult.count {
            zresult[i] = (params.range.1 - params.range.0) * (zresult[i] - zmin) / zrange + params.range.0
            zresult[i] += params.aNoise * (2.0 * rng.nextDouble() - 1.0)
        }
        return zresult
    }
}