Chebyshev coefficients: Difference between revisions
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Calculate coefficients: cosine function, '''10''' coefficients, interval '''0 1''' |
Calculate coefficients: cosine function, '''10''' coefficients, interval '''0 1''' |
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<br><br> |
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=={{header|11l}}== |
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{{trans|Python}} |
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<lang 11l>F test_func(Float x) |
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R cos(x) |
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F mapper(x, min_x, max_x, min_to, max_to) |
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R (x - min_x) / (max_x - min_x) * (max_to - min_to) + min_to |
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F cheb_coef(func, n, min, max) |
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V coef = [0.0] * n |
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L(i) 0 .< n |
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V f = func(mapper(cos(math:pi * (i + 0.5) / n), -1, 1, min, max)) * 2 / n |
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L(j) 0 .< n |
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coef[j] += f * cos(math:pi * j * (i + 0.5) / n) |
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R coef |
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F cheb_approx(=x, n, min, max, coef) |
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V a = 1.0 |
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V b = mapper(x, min, max, -1, 1) |
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V res = coef[0] / 2 + coef[1] * b |
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x = 2 * b |
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V i = 2 |
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L i < n |
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V c = x * b - a |
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res = res + coef[i] * c |
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(a, b) = (b, c) |
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i++ |
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R res |
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V n = 10 |
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V minv = 0 |
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V maxv = 1 |
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V c = cheb_coef(test_func, n, minv, maxv) |
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print(‘Coefficients:’) |
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L(i) 0 .< n |
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print(c[i]) |
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print("\n\nApproximation:\n x func(x) approx diff") |
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L(i) 20 |
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V x = mapper(i, 0.0, 20.0, minv, maxv) |
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V f = test_func(x) |
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V approx = cheb_approx(x, n, minv, maxv, c) |
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print(‘#.3 #.10 #.10 #.’.format(x, f, approx, format_float_exp(approx - f, 2, 9)))</lang> |
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{{out}} |
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<pre> |
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Coefficients: |
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1.64717 |
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-0.232299 |
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-0.0537151 |
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0.00245824 |
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0.000282119 |
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-7.72223e-06 |
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-5.89856e-07 |
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1.15214e-08 |
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6.5963e-10 |
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-1.00219e-11 |
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Approximation: |
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x func(x) approx diff |
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0.000 1.0000000000 1.0000000000 4.68e-13 |
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0.050 0.9987502604 0.9987502604 -9.36e-14 |
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0.100 0.9950041653 0.9950041653 4.62e-13 |
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0.150 0.9887710779 0.9887710779 -4.73e-14 |
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0.200 0.9800665778 0.9800665778 -4.60e-13 |
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0.250 0.9689124217 0.9689124217 -2.32e-13 |
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0.300 0.9553364891 0.9553364891 2.62e-13 |
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0.350 0.9393727128 0.9393727128 4.61e-13 |
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0.400 0.9210609940 0.9210609940 1.98e-13 |
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0.450 0.9004471024 0.9004471024 -2.47e-13 |
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0.500 0.8775825619 0.8775825619 -4.58e-13 |
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0.550 0.8525245221 0.8525245221 -2.46e-13 |
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0.600 0.8253356149 0.8253356149 1.96e-13 |
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0.650 0.7960837985 0.7960837985 4.53e-13 |
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0.700 0.7648421873 0.7648421873 2.54e-13 |
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0.750 0.7316888689 0.7316888689 -2.28e-13 |
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0.800 0.6967067093 0.6967067093 -4.47e-13 |
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0.850 0.6599831459 0.6599831459 -4.37e-14 |
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0.900 0.6216099683 0.6216099683 4.46e-13 |
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0.950 0.5816830895 0.5816830895 -8.98e-14 |
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</pre> |
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=={{header|C}}== |
=={{header|C}}== |
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