diff --git a/dist/generate.py b/dist/generate.py index 7484354..5aa6cfc 100755 --- a/dist/generate.py +++ b/dist/generate.py @@ -163,13 +163,14 @@ def generate_test_cases(): def main(): parser = argparse.ArgumentParser() - parser.add_argument('-o', '--output', type=str, help="Output file") + parser.add_argument('-o', '--output', type=str, help='Output file') args = parser.parse_args() + output = generate_test_cases() if not args.output: - print(generate_test_cases(), end='') + print(output, end='') else: with open(args.output, 'w') as file: - file.write(generate_test_cases()) + file.write(output) if __name__ == '__main__': diff --git a/poly/generate.py b/poly/generate.py new file mode 100755 index 0000000..5a80de9 --- /dev/null +++ b/poly/generate.py @@ -0,0 +1,107 @@ +#!/usr/bin/env python3 +import argparse +from concurrent.futures import ProcessPoolExecutor +from mpmath import mp +import sympy as sp + +mp.dps = 50 + +precision = 17 +zero_threshold = mp.mpf('1e-40') + +nn = 23 + +def exp(x): + return mp.exp(x) +def sin(x): + return mp.sin(x) +def cos(x): + return mp.cos(x) +def f1(x): + return mp.fabs(x) + x/2 - x*x +def f2(x): + return -3*mp.sin(10*x) + 10*mp.sin(mp.fabs(x) + x/2) + +def uniform(n): + return [0] if n == 1 else [2 * mp.mpf(k) / (n-1) - 1 for k in range(n)] +def chebyshev(n): + return [-mp.cos((2*k - 1) * mp.pi / (2*n)) for k in range(1, n + 1)] +def chebyshev_2(n): + return [mp.sin(mp.pi / 2 * x) for x in uniform(n)] + +test_cases = [] + +functions = [exp, sin, cos, f1, f2] +distributions = [uniform, chebyshev, chebyshev_2] +point_counts = [7, 15, 25] +intervals = [(-2, 2), (-10, 10)] + +for func in functions: + for dist in distributions: + for n in point_counts: + for a, b in intervals: + test_cases.append((func, dist, n, a, b)) + + +def stretched(points, a, b): + if not points: + return [] + if len(points) == 1 or min(points) == max(points): + return [(a+b)/2] * len(points) + return [a + (p-min(points)) * (b-a) / (max(points)-min(points)) for p in points] + + +def format_number(number): + return '0' if abs(number) < zero_threshold else mp.nstr(number, n=precision).removesuffix('.0') + + +def format_array(array): + return '[' + ', '.join(format_number(x) for x in array) + ']' + + +def format_test_case(func, dist, X, Y, coeffs, xx, yy): + return '\n'.join([ + '[[test_cases]]', + f'func = "{func.__name__}"', + f'dist = "{dist.__name__}"', + f'X = {format_array(X)}', + f'Y = {format_array(Y)}', + f'coeffs = {format_array(coeffs)}', + f'xx = {format_array(xx)}', + f'yy = {format_array(yy)}', + ]) + + +def generate_test_case(params): + func, dist, n, a, b = params + X = stretched(dist(n), a, b) + Y = [func(x) for x in X] + x_sym = sp.symbols('x') + polynomial = sp.interpolate(list(zip(X, Y)), x_sym) + coeffs = [polynomial.coeff(x_sym, i) for i in reversed(range(n))] + f = sp.lambdify(x_sym, polynomial, modules='mpmath') + xx = stretched(uniform(nn), a, b) + yy = [f(x) for x in xx] + return format_test_case(func, dist, X, Y, coeffs, xx, yy) + + +def generate_test_cases(): + with ProcessPoolExecutor() as executor: + results = list(executor.map(generate_test_case, test_cases)) + return '\n\n'.join(results) + + +def main(): + parser = argparse.ArgumentParser() + parser.add_argument('-o', '--output', type=str, help='Output file') + args = parser.parse_args() + output = generate_test_cases() + if not args.output: + print(output, end='') + else: + with open(args.output, 'w') as file: + file.write(output) + + +if __name__ == '__main__': + main() \ No newline at end of file diff --git a/poly/imp_lagrange.toml b/poly/imp_lagrange.toml deleted file mode 100644 index e69de29..0000000 diff --git a/poly/lagrange.toml b/poly/lagrange.toml deleted file mode 100644 index e69de29..0000000 diff --git a/poly/newton.toml b/poly/newton.toml deleted file mode 100644 index e69de29..0000000 diff --git a/poly/poly.toml b/poly/poly.toml new file mode 100644 index 0000000..5f1d979 --- /dev/null +++ b/poly/poly.toml @@ -0,0 +1,809 @@ +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-2, -1.3333333333333333, -0.66666666666666667, 0, 0.66666666666666667, 1.3333333333333333, 2] +Y = [0.13533528323661269, 0.26359713811572677, 0.51341711903259203, 1, 1.9477340410546759, 3.7936678946831777, 7.3890560989306502] +coeffs = [0.0015514756877560909, 0.0096510993602761245, 0.041410327781817552, 0.16458224417989315, 0.5000840006395402, 1.0006836374395188, 1] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [0.13533528323661269, 0.16134860038300697, 0.19390603646698013, 0.23322316413979598, 0.28017173941758792, 0.33616679585401101, 0.40309409408292756, 0.48327792673112609, 0.57948927870107378, 0.69499434282370228, 0.83364339088122704, 1, 1.1995106344133958, 1.4387145825947312, 1.7254942497602185, 2.0693658057419515, 2.4818101882309258, 2.9766444613900916, 3.5704335298374414, 4.2829422079991292, 5.1376276448326245, 6.1621721039198998, 7.3890560989306502] + +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-10, -6.6666666666666667, -3.3333333333333333, 0, 3.3333333333333333, 6.6666666666666667, 10] +Y = [4.5399929762484852e-5, 0.0012726338013398083, 0.035673993347252398, 1, 28.031624894526134, 785.7719942274173, 22026.465794806717] +coeffs = [0.017934246168886903, 0.19261154650257445, -0.76701438531557351, -9.0586391278349163, 7.4813060437215509, 81.071735228086464, 1] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [4.5399929762484852e-5, -386.89503422520326, -319.25324873048223, -119.25842004158702, 45.5817109710898, 114.8317822122234, 94.813966461939686, 25.581985856800749, -44.81601524860711, -78.785739039482888, -60.346144618017852, 1, 73.684424269183988, 114.78051987914932, 87.999363899716156, -11.025399693284769, -122.16382011160407, -80.927041467563059, 428.68415389355935, 1928.6196604417423, 5208.5092228910413, 11394.680468009009, 22026.465794806717] + +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-2, -1.7142857142857143, -1.4285714285714286, -1.1428571428571429, -0.85714285714285714, -0.57142857142857143, -0.28571428571428571, 0, 0.28571428571428571, 0.57142857142857143, 0.85714285714285714, 1.1428571428571429, 1.4285714285714286, 1.7142857142857143, 2] +Y = [0.13533528323661269, 0.18009231214795238, 0.23965103644177579, 0.31890655732397042, 0.42437284567694995, 0.56471812200775921, 0.75147729307528595, 1, 1.33071219744735, 1.770794952435155, 2.3564184423836606, 3.1357147635698227, 4.1727338835980962, 5.5527078756058373, 7.3890560989306502] +coeffs = [1.2029796680557142e-11, 1.6956129270466279e-10, 2.0852253535708776e-9, 2.5012752978365164e-8, 2.7557834625664201e-7, 2.7558147365757053e-6, 2.4801581856524759e-5, 0.00019841261090270871, 0.0013888888916373175, 0.0083333333775098371, 0.041666666666102949, 0.16666666665760528, 0.50000000000003044, 1.0000000000004894, 1] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [0.13533528323661269, 0.16232061116112651, 0.19468670833574423, 0.23350647909141589, 0.28006676082096242, 0.3359109812393346, 0.40289032152922453, 0.48322508118972385, 0.57957827878482932, 0.69514392839891958, 0.8337529180751383, 1, 1.1993961020354291, 1.4385510095776351, 1.7253924734665147, 2.0694290071570674, 2.4820650846229095, 2.9769791874947735, 3.5705772333227427, 4.282536415662023, 5.1364574837651535, 6.1606470843306387, 7.3890560989306502] + +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-10, -8.5714285714285714, -7.1428571428571429, -5.7142857142857143, -4.2857142857142857, -2.8571428571428571, -1.4285714285714286, 0, 1.4285714285714286, 2.8571428571428571, 4.2857142857142857, 5.7142857142857143, 7.1428571428571429, 8.5714285714285714, 10] +Y = [4.5399929762484852e-5, 0.00018944182523289421, 0.00079049032311996648, 0.0032985057559390917, 0.0137637867330504, 0.05743261926761735, 0.23965103644177579, 1, 4.1727338835980962, 17.411708063327651, 72.654424207165474, 303.16757768254912, 1265.0376238043307, 5278.6653568747525, 22026.465794806717] +coeffs = [3.6990520567293841e-11, 6.0308278642448932e-10, -1.1743347874518634e-9, -3.2411026350043697e-8, 4.5936916429739258e-7, 6.0157807243862106e-6, 1.9767965750814212e-5, 0.00010880946297413942, 0.0014536701452400646, 0.0094887377972518206, 0.041331183140520883, 0.16067733141618522, 0.50045456125182033, 1.0081180193897818, 1] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [4.5399929762484852e-5, -1.2618457556017294, 0.26458147528301699, 0.032881629870073028, -0.04344988136210698, 0.015936052757760672, 0.016998060894809184, 0.019039293290465244, 0.066869824265743636, 0.16546416494606542, 0.39951820254718108, 1, 2.4857988428670419, 6.1567915788187687, 15.289125046040962, 37.96460227466951, 94.192528001277743, 233.79677043241624, 580.44722904214413, 1440.3983448208477, 3574.6537229358509, 8878.0023766525758, 22026.465794806717] + +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-2, -1.8333333333333333, -1.6666666666666667, -1.5, -1.3333333333333333, -1.1666666666666667, -1, -0.83333333333333333, -0.66666666666666667, -0.5, -0.33333333333333333, -0.16666666666666667, 0, 0.16666666666666667, 0.33333333333333333, 0.5, 0.66666666666666667, 0.83333333333333333, 1, 1.1666666666666667, 1.3333333333333333, 1.5, 1.6666666666666667, 1.8333333333333333, 2] +Y = [0.13533528323661269, 0.15987974607969391, 0.18887560283756184, 0.22313016014842983, 0.26359713811572677, 0.31140322391459768, 0.36787944117144232, 0.43459820850707822, 0.51341711903259203, 0.60653065971263342, 0.71653131057378925, 0.84648172489061407, 1, 1.181360412865646, 1.3956124250860895, 1.6487212707001281, 1.9477340410546759, 2.3009758908928249, 2.7182818284590452, 3.2112705431535607, 3.7936678946831777, 4.4816890703380648, 5.2944900504700294, 6.2547009519363287, 7.3890560989306502] +coeffs = [1.6571250185236175e-24, 3.9863020352236935e-23, 8.8932669758788965e-22, 1.956376477072559e-20, 4.1103329647234379e-19, 8.2206751967050357e-18, 1.561920655489157e-16, 2.8114571466062492e-15, 4.7794773331076708e-14, 7.6471637336957836e-13, 1.1470745597721536e-11, 1.6059043836800285e-10, 2.0876756987868159e-9, 2.5052108385441876e-8, 2.755731922398589e-7, 2.755731922398589e-6, 2.4801587301587302e-5, 0.00019841269841269841, 0.0013888888888888889, 0.0083333333333333333, 0.041666666666666667, 0.16666666666666667, 0.5, 1, 1] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [0.13533528323661269, 0.16232061118184817, 0.19468670833151017, 0.23350647909091339, 0.28006676082164886, 0.33591098123916238, 0.402890321529133, 0.48322508118982544, 0.57957827878480951, 0.69514392839887873, 0.83375291807518055, 1, 1.1993961020353859, 1.4385510095776778, 1.7253924734665359, 2.0694290071569562, 2.482065084623012, 2.9769791874949708, 3.5705772333219383, 4.2825364156626254, 5.1364574837703461, 6.1606470843046396, 7.3890560989306502] + +[[test_cases]] +func = "exp" +dist = "uniform" +X = [-10, -9.1666666666666667, -8.3333333333333333, -7.5, -6.6666666666666667, -5.8333333333333333, -5, -4.1666666666666667, -3.3333333333333333, -2.5, -1.6666666666666667, -0.83333333333333333, 0, 0.83333333333333333, 1.6666666666666667, 2.5, 3.3333333333333333, 4.1666666666666667, 5, 5.8333333333333333, 6.6666666666666667, 7.5, 8.3333333333333333, 9.1666666666666667, 10] +Y = [4.5399929762484852e-5, 0.00010446414383170526, 0.00024036947641951421, 0.00055308437014783358, 0.0012726338013398083, 0.0029282996948181878, 0.0067379469990854671, 0.015503853599009319, 0.035673993347252398, 0.082084998623898795, 0.18887560283756184, 0.43459820850707822, 1, 2.3009758908928249, 5.2944900504700294, 12.182493960703473, 28.031624894526134, 64.500093064855761, 148.4131591025766, 341.49510098626977, 785.7719942274173, 1808.0424144560632, 4160.2620053750542, 9572.6625741654358, 22026.465794806717] +coeffs = [3.2148549251872901e-24, 8.1570755269557383e-23, 5.4570879373258774e-22, 1.0303862905484372e-20, 4.503016882344763e-19, 9.2824521861617214e-18, 1.5347042582768439e-16, 2.7377229449286457e-15, 4.7915337200606879e-14, 7.6798672493541506e-13, 1.1467278385480334e-11, 1.6049631050703459e-10, 2.0877399020577587e-9, 2.5053852367973411e-8, 2.7557244959899874e-7, 2.7557117418044744e-6, 2.480159236512001e-5, 0.0001984128360460157, 0.0013888888705179452, 0.008333332833902971, 0.041666666695918219, 0.16666666746197206, 0.49999999998701282, 0.9999999996468853, 1] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [4.5399929762484852e-5, 0.00011442463605394606, 0.00027943550030833041, 0.00069426209697622207, 0.0017230792289782999, 0.0042768231778198049, 0.010615345532336164, 0.026347981170109867, 0.065397403076885737, 0.16232061125142676, 0.40289032150104624, 1, 2.4820650846530417, 6.1606470842250916, 15.291127026824168, 37.953572496885916, 94.203237133685847, 233.81856574050797, 580.35289818823914, 1440.4736652323078, 3575.3493904663069, 8874.249882753377, 22026.465794806717] + +[[test_cases]] +func = "exp" +dist = "chebyshev" +X = [-2, -1.6038754716096765, -0.89008373582525762, 0, 0.89008373582525762, 1.6038754716096765, 2] +Y = [0.13533528323661269, 0.20111558798453324, 0.41062136759364689, 1, 2.4353335674182581, 4.9722650045251829, 7.3890560989306502] +coeffs = [0.0015826039662564989, 0.0099059589059432607, 0.041251964105920946, 0.1632859522388786, 0.5002194028871201, 1.0017910524729028, 1] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [0.13533528323661269, 0.16190410673644546, 0.19460835425301005, 0.23381461891498232, 0.2805197601229765, 0.33623719218577269, 0.40292433800294409, 0.48295124779388402, 0.57911038287323283, 0.69466756447270454, 0.83345408760931336, 1, 1.1997085460226578, 1.4390717757235585, 1.7259273188711784, 2.0697563240564235, 2.4820225628392548, 2.9765526989417142, 3.5699577224873485, 4.2820955492870351, 5.1365747851712061, 6.1612996553684728, 7.3890560989306502] + +[[test_cases]] +func = "exp" +dist = "chebyshev" +X = [-10, -8.0193773580483825, -4.4504186791262881, 0, 4.4504186791262881, 8.0193773580483825, 10] +Y = [4.5399929762484852e-5, 0.000329024823706973, 0.011673678421618059, 1, 85.66280172221778, 3039.2843577376775, 22026.465794806717] +coeffs = [0.024200863546475373, 0.26818922522722499, -1.5525514470164589, -18.5174568389918, 23.368838437925391, 271.17671909726949, 1] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, 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-0.58316419173546813, 0.93125436439215166, 0.37240482229609585, -0.75389822715038677, -0.99046914354729024, -0.83907152907645245] +coeffs = [-2.1736003378137106e-12, 0, 1.0228835709597638e-9, 0, -2.0444633300337449e-7, 0, 2.2094719675872036e-5, 0, -0.0013341915105404803, 0, 0.041168693868397011, 0, -0.49866674404417661, 0, 1] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [-0.83907152907645245, -0.95033431449512946, -0.31642631170546931, 0.54684343067564351, 0.99312884257527111, 0.67904459142614806, -0.16361121818387267, -0.88213420798227417, -0.91735018718929209, -0.24422490698821115, 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[-0.41614683654714239, -0.16055653857469063, 0.54030230586813972, 1, 0.54030230586813972, -0.16055653857469063, -0.41614683654714239] +coeffs = [-0.0012024289717901414, 0, 0.041232473190642269, 0, -0.49972773835071241, 0, 1] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [-0.41614683654714239, -0.24483452734669982, -0.065562477113750199, 0.11590209264028777, 0.29360148992937613, 0.46165340110058753, 0.61448546331151395, 0.7470385606773543, 0.85493884408768076, 0.93463847469288407, 0.98352509106029754, 1, 0.98352509106029754, 0.93463847469288407, 0.85493884408768076, 0.7470385606773543, 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0.85489155786239455, 0.74699036415028168, 0.61446322644851387, 0.46167915140916075, 0.29367495376883011, 0.11598920826689764, -0.065520339901016386, -0.24486988668511491, -0.41614683654714239] + +[[test_cases]] +func = "cos" +dist = "chebyshev_2" +X = [-10, -9.7492791218182361, -9.0096886790241913, -7.8183148246802981, -6.2348980185873353, -4.3388373911755812, -2.225209339563144, 0, 2.225209339563144, 4.3388373911755812, 6.2348980185873353, 7.8183148246802981, 9.0096886790241913, 9.7492791218182361, 10] +Y = [-0.83907152907645245, -0.94780989216119485, -0.91508031934675098, 0.035659247690618328, 0.99883439538963222, -0.36492438807633473, -0.60869362940405637, 1, -0.60869362940405637, -0.36492438807633473, 0.99883439538963222, 0.035659247690618328, -0.91508031934675098, -0.94780989216119485, -0.83907152907645245] +coeffs = [-1.9590616251537127e-12, 0, 9.5165356652276242e-10, 0, -1.9533662745596665e-7, 0, 2.1534346276935001e-5, 0, -0.0013173867160430981, 0, 0.040951806246976181, 0, 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-7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [-11.108339669960661, -8.2698186037444918, -5.019011243579333, -5.3859738215045746, 0.51756949210403691, 4.5505294920192566, 4.3780149232396233, 7.5914703118556836, 8.7042675607497238, 8.4995813836633405, 3.2114150673629438, 0, 7.6539470278729818, 6.2920573668162263, -8.2889337257444612, -5.5060924991126906, 9.3728294813832249, 7.76985792157006, -1.073308338187914, -10.249695790996673, -5.2155050399247269, 7.2904846548673782, 8.021975324900445] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-2, -1.7320508075688773, -1, 0, 1, 1.7320508075688773, 2] +Y = [11.153545600261848, 4.6202138379486744, 3.1621920533739206, 0, 11.607013198708654, 8.1688748735587091, -1.3276356715842107] +coeffs = [0.57442262540950079, -0.84856844491899121, -4.9242344220330315, 1.795273594385329, 11.734414422664818, 3.2757054232010288, 0] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [11.153545600261848, 5.8444036566831911, 3.8721406538216044, 3.4601169625814259, 3.4922483612407351, 3.3657723895121098, 2.8589559857874615, 2.0137444075669503, 1.0333514350719779, 0.19479085804225977, -0.2236507542830242, 0, 0.98875869180920891, 2.7389796806098687, 5.1075940171321012, 7.8142886292724287, 10.458626791179397, 12.552109875523279, 13.565180388949854, 12.989166290718268, 10.413166594522975, 5.6158782534997501, -1.3276356715842107] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-10, -8.6602540378443865, -5, 0, 5, 8.6602540378443865, 10] +Y = [-11.108339669960661, -12.213109425752846, 5.1975968799277786, 0, 10.167124328859175, 7.0490674454996312, 8.021975324900445] +coeffs = [0.00010125643208805365, -0.00024701937497586401, -0.016960070623020575, 0.037004928603315211, 0.66801091969621992, -0.27378336082982562, 0] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [-11.108339669960661, -13.450885415144513, -9.8798386407815253, -4.349521748550516, 0.746923591505253, 4.2093323983988484, 5.7034651012584916, 5.4751090240244417, 4.1053326337839351, 2.3068925527441812, 0.76179333384341387, 0, 0.31930334699960396, 1.7463380100204083, 4.0387532937963907, 6.7285367664186577, 9.2064906167748337, 10.847860775626508, 11.179118800324734, 10.085896523163594, 8.062073463371806, 6.5000170027424003, 8.021975324900445] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-2, -1.9498558243636472, -1.8019377358048383, -1.5636629649360596, -1.2469796037174671, -0.86776747823511624, -0.44504186791262881, 0, 0.44504186791262881, 0.86776747823511624, 1.2469796037174671, 1.5636629649360596, 1.8019377358048383, 1.9498558243636472, 2] +Y = [11.153545600261848, 10.089789934752748, 5.6251323956807042, 7.2596220582964286, 5.5494453290181119, 6.2425273473799533, -0.69075372899936143, 0, 9.0883828887827549, 7.6014367108316098, 9.8436040819140162, 6.9325029017168936, 6.4616585942403921, 0.33796786693535095, -1.3276356715842107] +coeffs = [0.083092060895087581, 0.60999908125529595, -1.3392811324911351, -8.4452275461398672, 8.7211533847940901, 45.599203422846198, -29.363977572015792, -121.26234548546407, 54.476373271301042, 164.45281147262365, -55.738209482674677, -106.00502631094213, 30.317200677333981, 26.405631610434531, 0] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [11.153545600261848, 5.8217179563900596, 6.612417140014488, 7.2492373597665755, 5.7237802291367239, 5.3716219494081724, 6.1924151094667492, 5.3495160721243782, 1.7273300625970656, -2.3018928422986682, -3.252525127353311, 0, 5.1390109285540214, 8.605127694996354, 8.8929905391603341, 7.7256684015585155, 7.7977801283934476, 9.3335924843578698, 9.7395242882115538, 7.8647477741056263, 6.8604570174188405, 6.1323993501159564, -1.3276356715842107] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-10, -9.7492791218182361, -9.0096886790241913, -7.8183148246802981, -6.2348980185873353, -4.3388373911755812, -2.225209339563144, 0, 2.225209339563144, 4.3388373911755812, 6.2348980185873353, 7.8183148246802981, 9.0096886790241913, 9.7492791218182361, 10] +Y = [-11.108339669960661, -10.178366358832497, -7.2460198338280356, -5.8963870177715176, -1.1515635174018261, 6.5822768717070804, 8.1945579181885944, 0, -1.1756654773726404, 3.9106037049034072, 2.1166526830927951, -8.4865356482876383, 5.5840740704649093, 9.1482732647095771, 8.021975324900445] +coeffs = [5.6752940495346989e-11, 3.1711677625097062e-10, -1.940921176655011e-8, -1.0821350810424571e-7, 2.5389996557563058e-6, 1.3698559622637907e-5, -0.00016041278645229158, -0.00077088210782291668, 0.005279636402740603, 0.017132846143913085, -0.10054991990174544, -0.01985969361090038, 1.0951941878583337, -2.3415259776853406, 0] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [-11.108339669960661, -7.4100172640232926, -6.4408566133481893, -4.5697497127877015, -1.6100296785438475, 1.8559149431577542, 5.7420440201328151, 8.8173243965961693, 9.2805613211731081, 6.7782027202777521, 2.9726810960674852, 0, -1.2939839533152598, -1.3898042419801445, -0.64171873738233763, 1.442621198732132, 4.6173947473711373, 5.8063072078220504, 1.0600802731861, -7.0466677095050791, -6.3180152585542261, 6.6835038876198212, 8.021975324900445] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-2, -1.9828897227476208, -1.9318516525781366, -1.8477590650225735, -1.7320508075688773, -1.5867066805824703, -1.414213562373095, -1.2175228580174413, -1, -0.76536686473017954, -0.51763809020504152, -0.26105238444010318, 0, 0.26105238444010318, 0.51763809020504152, 0.76536686473017954, 1, 1.2175228580174413, 1.414213562373095, 1.5867066805824703, 1.7320508075688773, 1.8477590650225735, 1.9318516525781366, 1.9828897227476208, 2] +Y = [11.153545600261848, 10.858569713285883, 9.5816354972064003, 6.889118233403459, 4.6202138379486744, 6.651795676768162, 9.4963323591669857, 4.574784952774907, 3.1621920533739206, 6.6741244439432281, -0.12342837093486593, 2.8209244532503581, 0, 2.297114121532859, 9.6903828726191867, 6.1796447205629193, 11.607013198708654, 10.819134281813649, 5.5225421131585318, 7.3756148218843456, 8.1688748735587091, 4.7060669937999592, 1.0581890699671111, -0.82559773354361185, -1.3276356715842107] +coeffs = [-0.027591504382583162, 0.084802569859771468, 0.71837110677792773, -2.2764178316173782, -8.24820989062449, 27.00532911007815, 54.93073818108252, -185.93802386631627, -234.77208369416783, 819.74163577050252, 672.86398217787235, -2405.2657124877435, -1312.3445117484266, 4723.2286006157105, 1731.9324115284206, -6075.4847594940381, -1509.2183475353288, 4857.7658455558445, 830.18628315550104, -2186.1034216724685, -271.25967232849158, 454.71639763874732, 52.623233177808633, -23.251865335891707, 0] +xx = [-2, -1.8181818181818182, -1.6363636363636364, -1.4545454545454545, -1.2727272727272727, -1.0909090909090909, -0.90909090909090909, -0.72727272727272727, -0.54545454545454545, -0.36363636363636364, -0.18181818181818182, 0, 0.18181818181818182, 0.36363636363636364, 0.54545454545454545, 0.72727272727272727, 0.90909090909090909, 1.0909090909090909, 1.2727272727272727, 1.4545454545454545, 1.6363636363636364, 1.8181818181818182, 2] +yy = [11.153545600261848, 5.9897181560933596, 5.5406071803607382, 9.3302332558770246, 6.5290564679942522, 2.0335579394867216, 5.5713788802675911, 5.9450176723274606, 0.37832170673417849, 0.75353362874180091, 3.3697045319202033, 0, -0.42684756423938235, 6.7203327175746872, 9.4937356812746819, 6.3558348888402893, 8.8023222343975277, 12.974964697230519, 8.9450735996830444, 5.4431318678623714, 8.1657095939757683, 5.8865824209213032, -1.3276356715842107] + +[[test_cases]] +func = "f2" +dist = "chebyshev_2" +X = [-10, -9.9144486137381041, -9.6592582628906829, -9.2387953251128676, -8.6602540378443865, -7.9335334029123516, -7.0710678118654752, -6.0876142900872064, -5, -3.8268343236508977, -2.5881904510252076, -1.3052619222005159, 0, 1.3052619222005159, 2.5881904510252076, 3.8268343236508977, 5, 6.0876142900872064, 7.0710678118654752, 7.9335334029123516, 8.6602540378443865, 9.2387953251128676, 9.6592582628906829, 9.9144486137381041, 10] +Y = [-11.108339669960661, -12.650957212708364, -7.7860052803520979, -12.832356591769076, -12.213109425752846, -9.4893368428608686, -0.83923327379164615, -1.8041949032021551, 5.1975968799277786, 11.035728537268166, 11.66269767671793, 7.4747255658646066, 0, 7.8581523310930924, -8.791074164909253, -6.7834557936021352, 10.167124328859175, 5.6721621415381328, -12.252066141749254, -4.0363336950148384, 7.0490674454996312, 12.488947230763426, 7.2424666924806242, 10.370804135474245, 8.021975324900445] +coeffs = [-3.2888943938788561e-18, -6.4463412582356561e-17, 2.1480843309762829e-15, 3.702050470399911e-14, -6.193794404447818e-13, -9.2389739559124241e-12, 1.0374490308611482e-10, 1.3133582356812083e-9, -1.117579880305663e-8, -1.1714818916490641e-7, 8.0963762290281259e-7, 6.8138076812456714e-6, -4.0052735672141463e-5, -0.00026070652791916419, 0.001344130524484338, 0.0064954074819156873, -0.029676728678278642, -0.10292700687486431, 0.4028894142419455, 0.99422367229223322, -2.9315979019979684, -5.0965446345198455, 8.4609948624132892, 6.4019001815054196, 0] +xx = [-10, -9.0909090909090909, -8.1818181818181818, -7.2727272727272727, -6.3636363636363636, -5.4545454545454545, -4.5454545454545455, -3.6363636363636364, -2.7272727272727273, -1.8181818181818182, -0.90909090909090909, 0, 0.90909090909090909, 1.8181818181818182, 2.7272727272727273, 3.6363636363636364, 4.5454545454545455, 5.4545454545454545, 6.3636363636363636, 7.2727272727272727, 8.1818181818181818, 9.0909090909090909, 10] +yy = [-11.108339669960661, -13.962768942455835, -10.391296433936761, -2.8430362828243747, -0.51277936073700816, -0.19655501386108818, 10.054744126468004, 10.469260569690673, 11.058326405310546, 12.186052523688824, 2.6463368079651776, 0, 7.7623006962138799, 2.665083057344796, -10.17526278064467, -8.9756050001953858, 3.9991246937625152, 12.617716504876042, -0.42152974042089865, -12.319793503061603, -0.18533161094333639, 12.603857447843778, 8.021975324900445] \ No newline at end of file diff --git a/requirements.txt b/requirements.txt index 64d3e72..ffc7f10 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1 +1,2 @@ -mpmath \ No newline at end of file +mpmath +sympy \ No newline at end of file diff --git a/verify_data.py b/verify_data.py index 3581f1d..1adecca 100755 --- a/verify_data.py +++ b/verify_data.py @@ -11,4 +11,5 @@ def check_data(original, generator): execute_command([generator, '-o', tmpfile.name]) execute_command(['diff', original, tmpfile.name]) -check_data('dist/dist.toml', 'dist/generate.py') \ No newline at end of file +check_data('dist/dist.toml', 'dist/generate.py') +check_data('poly/poly.toml', 'poly/generate.py') \ No newline at end of file