civil 0.1.7

//! Calculus utility to be used in other parts of the library.
//! # THERE IS ZERO ERROR HANDLING HERE #
//! # Everything is going to be heavily refactored before 1.0 #

/// These constants are used for Gauss-Legendre Quadrature calculations. We
/// have the option of solving for equations up to the order of 127, which is
/// probably never necessary. So far, these solutions seem to produce very
/// adequate results. At some point these methods should be refactored for
/// either:
/// - symbolic integration
/// - more robust methodology
/// I suspect this will be 'good enough' precision for almost all practical
/// situations.
pub const ABSCISSA: [f64; 224] = [
    -0.5773502691896257,
    0.5773502691896257,
    -0.7745966692414834,
    0.0,
    0.7745966692414834,
    -0.8611363115940526,
    -0.33998104358485626,
    0.33998104358485626,
    0.8611363115940526,
    -0.906179845938664,
    -0.5384693101056831,
    0.0,
    0.5384693101056831,
    0.906179845938664,
    -0.932469514203152,
    -0.6612093864662645,
    -0.2386191860831969,
    0.2386191860831969,
    0.6612093864662645,
    0.932469514203152,
    -0.9491079123427585,
    -0.7415311855993945,
    -0.4058451513773972,
    0.0,
    0.4058451513773972,
    0.7415311855993945,
    0.9491079123427585,
    -0.9602898564975363,
    -0.7966664774136267,
    -0.525532409916329,
    -0.1834346424956498,
    0.1834346424956498,
    0.525532409916329,
    0.7966664774136267,
    0.9602898564975363,
    -0.9681602395076261,
    -0.8360311073266358,
    -0.6133714327005904,
    -0.3242534234038089,
    0.0,
    0.3242534234038089,
    0.6133714327005904,
    0.8360311073266358,
    0.9681602395076261,
    -0.14887433898163122,
    0.0,
    -0.1252334085114689,
    0.0,
    -0.10805494870734367,
    0.0,
    -0.09501250983763744,
    0.0,
    -0.0847750130417353,
    0.0,
    -0.07652652113349734,
    0.07652652113349734,
    -0.1455618541608951,
    0.0,
    -0.06973927331972223,
    0.06973927331972223,
    -0.1332568242984661,
    0.0,
    -0.06405689286260563,
    0.06405689286260563,
    -0.1228646926107104,
    0.0,
    -0.05923009342931321,
    0.05923009342931321,
    -0.11397258560952997,
    0.0,
    -0.05507928988403427,
    0.05507928988403427,
    -0.10627823013267923,
    0.0,
    -0.15386991360858354,
    -0.0514718425553177,
    0.0514718425553177,
    -0.09955531215234152,
    0.0,
    0.09955531215234152,
    -0.1444719615827965,
    -0.04830766568773832,
    0.04830766568773832,
    -0.09363106585473338,
    0.0,
    0.09363106585473338,
    -0.13615235725918298,
    -0.04550982195310254,
    0.04550982195310254,
    -0.08837134327565926,
    0.0,
    0.08837134327565926,
    -0.1287361038093848,
    -0.04301819847370861,
    0.04301819847370861,
    -0.0836704089547699,
    0.0,
    0.0836704089547699,
    -0.12208402533786741,
    -0.04078514790457824,
    0.04078514790457824,
    -0.07944380460875548,
    0.0,
    0.07944380460875548,
    -0.11608407067525521,
    -0.03877241750605082,
    0.03877241750605082,
    0.11608407067525521,
    -0.15081335486399217,
    -0.075623258989163,
    0.0,
    0.075623258989163,
    -0.11064502720851987,
    -0.03694894316535178,
    0.03694894316535178,
    0.11064502720851987,
    -0.14392980951071332,
    -0.07215299087458624,
    0.0,
    0.07215299087458624,
    -0.10569190170865325,
    -0.035289236964135356,
    0.035289236964135356,
    0.10569190170865325,
    -0.13764520598325303,
    -0.06898698016314417,
    0.0,
    0.06898698016314417,
    -0.10116247530558424,
    -0.03377219001605204,
    0.03377219001605204,
    0.10116247530558424,
    -0.1318848665545149,
    -0.06608692391635568,
    0.0,
    0.06608692391635568,
    -0.0970046992094627,
    -0.03238017096286936,
    0.03238017096286936,
    0.0970046992094627,
    -0.12658599726967204,
    -0.06342068498268678,
    0.0,
    0.06342068498268678,
    -0.1548905899981459,
    -0.09317470156008614,
    -0.031098338327188876,
    0.031098338327188876,
    0.09317470156008614,
    -0.12169542101888876,
    -0.06096110015057873,
    0.0,
    0.06096110015057873,
    0.12169542101888876,
    -0.14903550860694917,
    -0.08963524464890056,
    -0.029914109797338766,
    0.029914109797338766,
    0.08963524464890056,
    -0.11716780907195515,
    -0.058685054300259464,
    0.0,
    0.058685054300259464,
    0.11716780907195515,
    -0.14360542731625614,
    -0.08635451826324822,
    -0.02881674819934178,
    0.02881674819934178,
    0.08635451826324822,
    -0.11296428805932926,
    -0.05657275381833678,
    0.0,
    0.05657275381833678,
    0.11296428805932926,
    -0.13855584681037625,
    -0.08330518682243537,
    -0.027797035287275437,
    0.027797035287275437,
    0.08330518682243537,
    -0.1090513328087878,
    -0.05460715100164682,
    0.0,
    0.05460715100164682,
    0.1090513328087878,
    -0.13384825059546684,
    -0.08046363021414273,
    -0.026847012365942356,
    0.026847012365942356,
    0.08046363021414273,
    -0.10539987901634415,
    -0.05277348408831,
    0.0,
    0.05277348408831,
    0.10539987901634415,
    -0.129449135396945,
    -0.07780933394953657,
    -0.0259597723012478,
    0.0259597723012478,
    0.07780933394953657,
    0.129449135396945,
    -0.1526442402308153,
    -0.10198460656227407,
    -0.05105890670797435,
    0.0,
    0.05105890670797435,
    0.10198460656227407,
    -0.1253292236158968,
    -0.07532439549623433,
    -0.025129291421820615,
    0.025129291421820615,
    0.07532439549623433,
    0.1253292236158968,
    -0.14787278635787196,
    -0.09878335644694528,
    -0.049452187116159625,
    0.0,
    0.049452187116159625,
    0.09878335644694528,
    -0.12146281929612056,
    -0.07299312178779904,
    -0.024350292663424433,
    0.024350292663424433,
    0.07299312178779904,
    0.12146281929612056,
];

pub const WEIGHTS: [f64; 224] = [
    1.0,
    1.0,
    0.5555555555555556,
    0.5555555555555556,
    0.8888888888888888,
    0.34785484513745385,
    0.34785484513745385,
    0.6521451548625461,
    0.6521451548625461,
    0.23692688505618908,
    0.23692688505618908,
    0.47862867049936647,
    0.47862867049936647,
    0.5688888888888889,
    0.17132449237917036,
    0.17132449237917036,
    0.3607615730481386,
    0.3607615730481386,
    0.46791393457269104,
    0.46791393457269104,
    0.1294849661688697,
    0.1294849661688697,
    0.27970539148927664,
    0.27970539148927664,
    0.3818300505051189,
    0.3818300505051189,
    0.4179591836734694,
    0.10122853629037626,
    0.10122853629037626,
    0.22238103445337448,
    0.22238103445337448,
    0.31370664587788727,
    0.31370664587788727,
    0.362683783378362,
    0.362683783378362,
    0.08127438836157441,
    0.08127438836157441,
    0.1806481606948574,
    0.1806481606948574,
    0.26061069640293544,
    0.26061069640293544,
    0.31234707704000286,
    0.31234707704000286,
    0.3302393550012598,
    0.29552422471475287,
    0.2729250867779006,
    0.24914704581340277,
    0.2325515532308739,
    0.2152638534631578,
    0.2025782419255613,
    0.1894506104550685,
    0.17944647035620653,
    0.1691423829631436,
    0.1610544498487837,
    0.15275338713072584,
    0.15275338713072584,
    0.14452440398997005,
    0.14608113364969041,
    0.13925187285563198,
    0.13925187285563198,
    0.1324620394046966,
    0.13365457218610619,
    0.12793819534675216,
    0.12793819534675216,
    0.12224244299031004,
    0.12317605372671545,
    0.11832141527926228,
    0.11832141527926228,
    0.11347634610896515,
    0.114220867378957,
    0.1100470130164752,
    0.1100470130164752,
    0.10587615509732094,
    0.10647938171831424,
    0.1017623897484055,
    0.10285265289355884,
    0.10285265289355884,
    0.09922501122667231,
    0.09922501122667231,
    0.09972054479342646,
    0.09563872007927486,
    0.0965400885147278,
    0.0965400885147278,
    0.09335642606559612,
    0.09335642606559612,
    0.09376844616021,
    0.09020304437064074,
    0.09095674033025987,
    0.09095674033025987,
    0.08814053043027546,
    0.08814053043027546,
    0.08848679490710429,
    0.08534668573933862,
    0.08598327567039475,
    0.08598327567039475,
    0.08347457362586279,
    0.08347457362586279,
    0.0837683609931389,
    0.0809824937705971,
    0.08152502928038578,
    0.08152502928038578,
    0.07927622256836847,
    0.07927622256836847,
    0.07952762213944285,
    0.07703981816424797,
    0.07703981816424797,
    0.0775059479784248,
    0.0775059479784248,
    0.07482962317622155,
    0.07547874709271582,
    0.07547874709271582,
    0.07569553564729838,
    0.07346081345346753,
    0.07346081345346753,
    0.07386423423217288,
    0.07386423423217288,
    0.07146373425251414,
    0.07202750197142198,
    0.07202750197142198,
    0.07221575169379899,
    0.07019768547355822,
    0.07019768547355822,
    0.07054915778935407,
    0.07054915778935407,
    0.06838457737866968,
    0.06887731697766132,
    0.06887731697766132,
    0.06904182482923202,
    0.06721061360067818,
    0.06721061360067818,
    0.06751868584903646,
    0.06751868584903646,
    0.06555737776654974,
    0.06599053358881048,
    0.06599053358881048,
    0.06613512962365548,
    0.06446616443595009,
    0.06446616443595009,
    0.06473769681268392,
    0.06473769681268392,
    0.0629527074651957,
    0.06333550929649175,
    0.06333550929649175,
    0.0634632814047906,
    0.061455899590316665,
    0.06193606742068324,
    0.06193606742068324,
    0.06217661665534726,
    0.06217661665534726,
    0.06054550693473779,
    0.06054550693473779,
    0.060885464844856345,
    0.060885464844856345,
    0.06099892484120588,
    0.05916881546604297,
    0.05959626017124816,
    0.05959626017124816,
    0.05981036574529186,
    0.05981036574529186,
    0.05831431136225601,
    0.05831431136225601,
    0.058617586232720266,
    0.058617586232720266,
    0.058718794151164364,
    0.0570439735587946,
    0.05742613705411211,
    0.05742613705411211,
    0.057617536707147025,
    0.057617536707147025,
    0.056240634071084365,
    0.056240634071084365,
    0.056512318249772,
    0.056512318249772,
    0.05660297644456042,
    0.055064895901762424,
    0.05540795250324512,
    0.05540795250324512,
    0.055579746306514397,
    0.055579746306514397,
    0.05430847145249864,
    0.05430847145249864,
    0.05455280360476188,
    0.05455280360476188,
    0.05463432875658403,
    0.05321723644657901,
    0.053526343304058255,
    0.053526343304058255,
    0.05368111986333485,
    0.05368111986333485,
    0.05250390264782874,
    0.05250390264782874,
    0.05272443385912793,
    0.05272443385912793,
    0.05279801262199042,
    0.051488451500980935,
    0.051488451500980935,
    0.05176794317491019,
    0.05176794317491019,
    0.051907877631220636,
    0.051907877631220636,
    0.05048247038679741,
    0.05081476366881834,
    0.05081476366881834,
    0.051014487038697265,
    0.051014487038697265,
    0.05108111944078622,
    0.049867528594952394,
    0.049867528594952394,
    0.05012106956904329,
    0.05012106956904329,
    0.05024800037525628,
    0.05024800037525628,
    0.04892845282051199,
    0.04923038042374756,
    0.04923038042374756,
    0.04941183303991818,
    0.04941183303991818,
    0.04947236662393102,
    0.048344762234802954,
    0.048344762234802954,
    0.04857546744150343,
    0.04857546744150343,
    0.048690957009139724,
    0.048690957009139724,
];

/// define where in our constants is the index of the first abscissa or weight
/// we want based on our order number
fn find_index(m: i32) -> usize {
    ((m + 1) * m / 2 - 1) as usize
}

/// Gauss-Legendre quadrature
/// f - polynomial function
/// n - order of function
/// a - start point of the integral
/// b - end point of the integral
/// There is currently no error handling, so edge cases will panic.
/// Expect a patch in the near future returning Result<f64,SomeError>
/// types instead of just f64s.
pub fn integrate(f: fn(f64) -> f64, n: i32, a: f64, b: f64) -> f64 {
    match n {
        0 => f(0.0_f64) * (b - a),
        1 => (b - a) * f((b + a) / 2.0),
        2...64 => {
            let mut result = 0.0;
            let legendre_number = (&n + 1) / 2 + 1;
            let start_index = find_index(legendre_number);
            for k in 0..legendre_number {
                let const_index = (start_index as i32 + k) as usize;
                let transformed_function = f((b - a) / 2.0 * ABSCISSA[const_index] + (b + a / 2.0));
                result += (b - a) / 2.0 * WEIGHTS[const_index] * transformed_function;
            }
            return result;
        }
        _ => 0.0,
    }
}