Chebyshev coefficients: Difference between revisions
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Line 838:
1.0 0.54030231 0.54030231 -4.477e-13
</pre>
=={{header|Python}}==
{{trans|C++}}
<lang python>import math
def test_func(x):
return math.cos(x)
def mapper(x, min_x, max_x, min_to, max_to):
return (x - min_x) / (max_x - min_x) * (max_to - min_to) + min_to
def cheb_coef(func, n, min, max):
coef = [0.0] * n
for i in xrange(n):
f = func(mapper(math.cos(math.pi * (i + 0.5) / n), -1, 1, min, max)) * 2 / n
for j in xrange(n):
coef[j] += f * math.cos(math.pi * j * (i + 0.5) / n)
return coef
def cheb_approx(x, n, min, max, coef):
a = 1
b = mapper(x, min, max, -1, 1)
c = float('nan')
res = coef[0] / 2 + coef[1] * b
x = 2 * b
i = 2
while i < n:
c = x * b - a
res = res + coef[i] * c
(a, b) = (b, c)
i += 1
return res
def main():
N = 10
min = 0
max = 1
c = cheb_coef(test_func, N, min, max)
print "Coefficients:"
for i in xrange(N):
print " % lg" % c[i]
print "\n\nApproximation:\n x func(x) approx diff"
for i in xrange(20):
x = mapper(i, 0.0, 20.0, min, max)
f = test_func(x)
approx = cheb_approx(x, N, min, max, c)
print "%1.3f %10.10f %10.10f % 4.2e" % (x, f, approx, approx - f)
return None
main()</lang>
{{out}}
<pre>Coefficients:
1.64717
-0.232299
-0.0537151
0.00245824
0.000282119
-7.72223e-06
-5.89856e-07
1.15214e-08
6.5963e-10
-1.00219e-11
Approximation:
x func(x) approx diff
0.000 1.0000000000 1.0000000000 4.68e-13
0.050 0.9987502604 0.9987502604 -9.36e-14
0.100 0.9950041653 0.9950041653 4.62e-13
0.150 0.9887710779 0.9887710779 -4.73e-14
0.200 0.9800665778 0.9800665778 -4.60e-13
0.250 0.9689124217 0.9689124217 -2.32e-13
0.300 0.9553364891 0.9553364891 2.62e-13
0.350 0.9393727128 0.9393727128 4.61e-13
0.400 0.9210609940 0.9210609940 1.98e-13
0.450 0.9004471024 0.9004471024 -2.47e-13
0.500 0.8775825619 0.8775825619 -4.58e-13
0.550 0.8525245221 0.8525245221 -2.46e-13
0.600 0.8253356149 0.8253356149 1.96e-13
0.650 0.7960837985 0.7960837985 4.53e-13
0.700 0.7648421873 0.7648421873 2.54e-13
0.750 0.7316888689 0.7316888689 -2.28e-13
0.800 0.6967067093 0.6967067093 -4.47e-13
0.850 0.6599831459 0.6599831459 -4.37e-14
0.900 0.6216099683 0.6216099683 4.46e-13
0.950 0.5816830895 0.5816830895 -8.99e-14</pre>
=={{header|Racket}}==
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