29 lines
687 B
Julia
29 lines
687 B
Julia
# approximate \int_a^b f using Gauss-Legendre quadratures
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function integrate_legendre(f,a,b,weights)
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out=0
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for i in 1:length(weights[1])
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out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)
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end
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return out
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end
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# \int f*g where g is sampled at the Legendre nodes
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function integrate_legendre_sampled(f,g,a,b,weights)
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out=0
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for i in 1:length(weights[1])
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out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)*g[i]
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end
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return out
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end
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# approximate \int_a^b f/sqrt((b-x)(x-a)) using Gauss-Chebyshev quadratures
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function integrate_chebyshev(f,a,b,N)
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out=0
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for i in 1:N
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out=out+pi/N*f((b-a)/2*cos((2*i-1)/(2*N)*pi)+(b+a)/2)
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end
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return out
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end
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