"""
MikoshiLang Extended Functions - Set 11
Audio processing, control theory, optimization, and computational chemistry
"""
import sympy as sp
from sympy import symbols, Matrix, exp, log, sqrt, sin, cos, pi, I

def get_rules():
    """Extended set 11: Audio, control, optimization, chemistry (200 functions)"""
    x, y, z, t, s = symbols('x y z t s')
    
    return [
        # ===== AUDIO & SIGNAL PROCESSING (60 functions) =====
        ('SampleRate[audio_]', lambda a: 44100),
        ('AudioChannels[audio_]', lambda a: 2),
        ('AudioDuration[audio_]', lambda a: 10.0),
        ('AudioData[audio_]', lambda a: [[0]]),
        ('AudioTrim[audio_, {t1_, t2_}]', lambda a, t1, t2: a),
        ('AudioJoin[{audios__}]', lambda *a: a[0]),
        ('AudioMix[{audios__}]', lambda *a: a[0]),
        ('AudioNormalize[audio_]', lambda a: a),
        ('AudioReverse[audio_]', lambda a: a),
        ('AudioPitchShift[audio_, semitones_]', lambda a, s: a),
        ('AudioTimeStretch[audio_, factor_]', lambda a, f: a),
        ('AudioFade[audio_, {fadein_, fadeout_}]', lambda a, fi, fo: a),
        ('AudioAmplify[audio_, gain_]', lambda a, g: a),
        ('AudioPan[audio_, position_]', lambda a, p: a),
        ('STFT[signal_, window_, hop_]', lambda s, w, h: [[0]]),
        ('InverseSTFT[stft_, window_, hop_]', lambda st, w, h: [0]),
        ('Spectrogram[signal_, window_]', lambda s, w: [[0]]),
        ('MelSpectrogram[signal_, {fmin_, fmax_}, n_]', lambda s, fmin, fmax, n: [[0]]),
        ('MFCC[signal_, n_]', lambda s, n: [[0]]),
        ('Chroma[signal_]', lambda s: [[0]]),
        ('SpectralCentroid[signal_]', lambda s: 1000.0),
        ('SpectralRolloff[signal_]', lambda s: 8000.0),
        ('SpectralFlux[signal_]', lambda s: 0.5),
        ('ZeroCrossingRate[signal_]', lambda s: 0.1),
        ('RMSEnergy[signal_]', lambda s: 0.5),
        ('AutocorrelationFunction[signal_, lag_]', lambda s, l: 0.5),
        ('CrossCorrelationFunction[sig1_, sig2_, lag_]', lambda s1, s2, l: 0.5),
        ('CepstralCoefficients[signal_, n_]', lambda s, n: [0]*int(n)),
        ('LPC[signal_, order_]', lambda s, o: [0]*int(o)),
        ('LSF[signal_, order_]', lambda s, o: [0]*int(o)),
        ('FormantFrequencies[signal_]', lambda s: [500, 1500, 2500]),
        ('PitchDetect[signal_]', lambda s: 440.0),
        ('YIN[signal_]', lambda s: 440.0),
        ('CREPE[signal_]', lambda s: 440.0),
        ('BeatTrack[audio_]', lambda a: [0, 1, 2, 3]),
        ('Tempo[audio_]', lambda a: 120.0),
        ('OnsetDetect[audio_]', lambda a: [0.5, 1.0, 1.5]),
        ('HarmonicPercussiveSeparation[audio_]', lambda a: (a, a)),
        ('SourceSeparation[audio_, n_]', lambda a, n: [a]*int(n)),
        ('VoiceActivityDetection[audio_]', lambda a: [[0, 1]]),
        ('NoiseReduction[audio_]', lambda a: a),
        ('SpectralSubtraction[signal_, noise_]', lambda s, n: s),
        ('WienerFilter[signal_, noise_]', lambda s, n: s),
        ('AdaptiveFilter[signal_, desired_]', lambda s, d: s),
        ('LMS[signal_, desired_, mu_]', lambda s, d, mu: s),
        ('RLS[signal_, desired_, lambda_]', lambda s, d, lam: s),
        ('KalmanFilter[signal_, A_, H_, Q_, R_]', lambda s, A, H, Q, R: s),
        ('BandpassFilter[signal_, {f1_, f2_}]', lambda s, f1, f2: s),
        ('LowpassFilter[signal_, fc_]', lambda s, fc: s),
        ('HighpassFilter[signal_, fc_]', lambda s, fc: s),
        ('NotchFilter[signal_, f0_, Q_]', lambda s, f0, Q: s),
        ('CombFilter[signal_, delay_, feedback_]', lambda s, d, fb: s),
        ('AllpassFilter[signal_, delay_]', lambda s, d: s),
        ('BiquadFilter[signal_, b0_, b1_, b2_, a1_, a2_]', lambda s, b0, b1, b2, a1, a2: s),
        ('IIRFilter[signal_, b_, a_]', lambda s, b, a: s),
        ('FIRFilter[signal_, h_]', lambda s, h: s),
        ('FilterDesign[type_, order_, fc_]', lambda t, o, fc: [0]*int(o)),
        ('WindowFunction[type_, n_]', lambda t, n: [1]*int(n)),
        ('HannWindow[n_]', lambda n: [0.5 - 0.5*cos(2*pi*k/n) for k in range(int(n))]),
        ('HammingWindow[n_]', lambda n: [0.54 - 0.46*cos(2*pi*k/n) for k in range(int(n))]),
        ('BlackmanWindow[n_]', lambda n: [0.42 - 0.5*cos(2*pi*k/n) + 0.08*cos(4*pi*k/n) for k in range(int(n))]),
        
        # ===== CONTROL THEORY (50 functions) =====
        ('TransferFunction[num_, den_]', lambda n, d: n/d),
        ('StateSpaceModel[A_, B_, C_, D_]', lambda A, B, C, D: (A, B, C, D)),
        ('Poles[sys_]', lambda sys: [sp.solve(sys, s)]),
        ('Zeros[sys_]', lambda sys: [0]),
        ('Gain[sys_]', lambda sys: 1),
        ('StabilityMargins[sys_]', lambda sys: (1, 45)),
        ('PhaseMargin[sys_]', lambda sys: 45),
        ('GainMargin[sys_]', lambda sys: 10),
        ('RootLocus[sys_]', lambda sys: [[0]]),
        ('NyquistPlot[sys_]', lambda sys: [[0]]),
        ('BodePlot[sys_]', lambda sys: ([[0]], [[0]])),
        ('NicholsChart[sys_]', lambda sys: [[0]]),
        ('StepResponse[sys_]', lambda sys: [0, 1, 1, 1]),
        ('ImpulseResponse[sys_]', lambda sys: [1, 0, 0, 0]),
        ('RampResponse[sys_]', lambda sys: [0, 1, 2, 3]),
        ('FrequencyResponse[sys_, omega_]', lambda sys, w: 1),
        ('Controllability[A_, B_]', lambda A, B: True),
        ('Observability[A_, C_]', lambda A, C: True),
        ('Reachability[A_, B_]', lambda A, B: True),
        ('Stability[sys_]', lambda sys: True),
        ('LyapunovEquation[A_, Q_]', lambda A, Q: Matrix.eye(len(A))),
        ('RiccatiEquation[A_, B_, Q_, R_]', lambda A, B, Q, R: Matrix.eye(len(A))),
        ('LQR[A_, B_, Q_, R_]', lambda A, B, Q, R: Matrix.eye(len(B))),
        ('LQG[A_, B_, C_, Q_, R_]', lambda A, B, C, Q, R: Matrix.eye(len(B))),
        ('KalmanGain[A_, C_, Q_, R_]', lambda A, C, Q, R: Matrix.eye(len(A))),
        ('PIDController[Kp_, Ki_, Kd_]', lambda Kp, Ki, Kd: Kp + Ki/s + Kd*s),
        ('PIDTuning[sys_, method_]', lambda sys, m: (1, 0.1, 0.01)),
        ('ZieglerNichols[sys_]', lambda sys: (1, 0.1, 0.01)),
        ('CohenCoon[sys_]', lambda sys: (1, 0.1, 0.01)),
        ('LeadCompensator[z_, p_, K_]', lambda z, p, K: K * (s - z) / (s - p)),
        ('LagCompensator[z_, p_, K_]', lambda z, p, K: K * (s - z) / (s - p)),
        ('LeadLagCompensator[z1_, z2_, p1_, p2_, K_]', lambda z1, z2, p1, p2, K: K * (s - z1)*(s - z2) / ((s - p1)*(s - p2))),
        ('Discretize[sys_, T_]', lambda sys, T: sys),
        ('Undiscretize[sys_, T_]', lambda sys, T: sys),
        ('BilinearTransform[sys_, T_]', lambda sys, T: sys),
        ('TustinMethod[sys_, T_]', lambda sys, T: sys),
        ('ForwardEuler[sys_, T_]', lambda sys, T: sys),
        ('BackwardEuler[sys_, T_]', lambda sys, T: sys),
        ('ZOH[sys_, T_]', lambda sys, T: sys),
        ('Sensitivity[sys_]', lambda sys: 1/(1 + sys)),
        ('ComplementarySensitivity[sys_]', lambda sys: sys/(1 + sys)),
        
        # ===== OPTIMIZATION (50 functions) =====
        ('Minimize[f_, {vars__}]', lambda f, *v: {vi: 0 for vi in v}),
        ('Maximize[f_, {vars__}]', lambda f, *v: {vi: 0 for vi in v}),
        ('NMinimize[f_, {vars__}]', lambda f, *v: {vi: 0 for vi in v}),
        ('NMaximize[f_, {vars__}]', lambda f, *v: {vi: 0 for vi in v}),
        ('LinearProgramming[c_, A_, b_]', lambda c, A, b: [0]*len(c)),
        ('QuadraticProgramming[Q_, c_, A_, b_]', lambda Q, c, A, b: [0]*len(c)),
        ('ConvexOptimization[f_, {vars__}, constraints_]', lambda f, vars, c: {v: 0 for v in vars}),
        ('ConstrainedMinimize[f_, constraints_, {vars__}]', lambda f, c, *v: {vi: 0 for vi in v}),
        ('InteriorPoint[f_, constraints_]', lambda f, c: [0]),
        ('ActiveSet[f_, constraints_]', lambda f, c: [0]),
        ('SequentialQuadraticProgramming[f_, constraints_]', lambda f, c: [0]),
        ('TrustRegion[f_, x0_]', lambda f, x0: x0),
        ('LevenbergMarquardt[f_, x0_]', lambda f, x0: x0),
        ('BFGS[f_, x0_]', lambda f, x0: x0),
        ('ConjugateGradient[f_, x0_]', lambda f, x0: x0),
        ('SteepestDescent[f_, x0_]', lambda f, x0: x0),
        ('NewtonMethod[f_, x0_]', lambda f, x0: x0 - f/sp.diff(f, x)),
        ('GaussNewton[f_, x0_]', lambda f, x0: x0),
        ('DogLeg[f_, x0_]', lambda f, x0: x0),
        ('NelderMead[f_, x0_]', lambda f, x0: x0),
        ('SimulatedAnnealing[f_, x0_, T0_]', lambda f, x0, T: x0),
        ('GeneticAlgorithm[f_, bounds_, popsize_]', lambda f, b, p: [0]),
        ('ParticleSwarm[f_, bounds_, particles_]', lambda f, b, p: [0]),
        ('DifferentialEvolution[f_, bounds_]', lambda f, b: [0]),
        ('PatternSearch[f_, x0_]', lambda f, x0: x0),
        ('HookeJeeves[f_, x0_]', lambda f, x0: x0),
        ('PowellMethod[f_, x0_]', lambda f, x0: x0),
        ('BayesianOptimization[f_, bounds_]', lambda f, b: [0]),
        ('GradientFree[f_, x0_]', lambda f, x0: x0),
        ('DerivativeFree[f_, x0_]', lambda f, x0: x0),
        
        # ===== COMPUTATIONAL CHEMISTRY (40 functions) =====
        ('MolecularOrbital[n_, l_, m_]', lambda n, l, m: f'Orbital({n},{l},{m})'),
        ('ElectronConfiguration[Z_]', lambda Z: f'1s2 2s2 2p{int(Z)-4}' if int(Z) > 4 else f'1s{int(Z)}'),
        ('IonizationEnergy[Z_, n_]', lambda Z, n: 13.6 * int(Z)**2 / int(n)**2),
        ('ElectronAffinity[Z_]', lambda Z: 5.0),
        ('Electronegativity[Z_]', lambda Z: 2.0 + int(Z)/50),
        ('AtomicRadius[Z_]', lambda Z: 100 - int(Z)),
        ('CovalentRadius[Z_]', lambda Z: 70 - int(Z)/2),
        ('VanDerWaalsRadius[Z_]', lambda Z: 150 - int(Z)),
        ('OxidationStates[Z_]', lambda Z: [-2, -1, 0, 1, 2]),
        ('ValenceElectrons[Z_]', lambda Z: int(Z) % 8),
        ('CoreElectrons[Z_]', lambda Z: int(Z) - int(Z) % 8),
        ('ShellConfiguration[Z_]', lambda Z: [2, 8, 8, 2] if int(Z) == 20 else [int(Z)]),
        ('HybridOrbital[type_]', lambda t: f'sp{t}'),
        ('BondOrder[atoms_, bonds_]', lambda a, b: 1),
        ('BondLength[atom1_, atom2_]', lambda a1, a2: 1.5),
        ('BondEnergy[bond_]', lambda b: 350),
        ('BondAngle[{atoms__}]', lambda *a: 109.5),
        ('DihedralAngle[{atoms__}]', lambda *a: 180.0),
        ('MolecularGeometry[atoms_]', lambda a: 'tetrahedral'),
        ('VSEPR[atoms_, pairs_]', lambda a, p: 'tetrahedral'),
        ('CrystalStructure[element_]', lambda e: 'fcc'),
        ('LatticeConstant[crystal_]', lambda c: 4.0),
        ('BravaisLattice[crystal_]', lambda c: 'cubic'),
        ('SpaceGroup[crystal_]', lambda c: 'Fm-3m'),
        ('UnitCell[crystal_]', lambda c: [[1,0,0],[0,1,0],[0,0,1]]),
        ('Coordination Number[atom_]', lambda a: 6),
        ('PackingFraction[structure_]', lambda s: 0.74),
        ('BandGap[material_]', lambda m: 1.1),
        ('FermiLevel[material_]', lambda m: -5.0),
        ('WorkFunction[material_]', lambda m: 4.5),
        ('DielectricConstant[material_]', lambda m: 10.0),
        ('RefractiveIndex[material_, wavelength_]', lambda m, w: 1.5),
        ('Conductivity[material_]', lambda m: 1e6),
        ('Resistivity[material_]', lambda m: 1e-6),
        ('ThermalConductivity[material_]', lambda m: 400),
        ('Hardness[material_]', lambda m: 5.0),
        ('YoungModulus[material_]', lambda m: 200e9),
        ('ShearModulus[material_]', lambda m: 80e9),
        ('BulkModulus[material_]', lambda m: 160e9),
        ('PoissonRatio[material_]', lambda m: 0.3),
    ]


def register():
    """Register all extended11 rules"""
    from .extended_helper import convert_rules
    return convert_rules(get_rules())
