Numerical integration: Difference between revisions
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(→{{header|R}}: Somewhat more idiomatic R) |
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=={{header|R}}== |
=={{header|R}}== |
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{{needs-review|R|These examples may not be idiomatic}} |
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{{works with|R|2.11.0}} |
{{works with|R|2.11.0}} |
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<lang R> |
<lang R>integrate.rect <- function(f, a, b, n, k=0) { |
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#k = 0 for left, 1 for right, 0.5 for midpoint |
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h = (b-a)/n |
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h <- (b-a)/n |
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x <- seq(a, b, len=n+1) |
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sum(f(x[-1]-h*(1-k)))*h |
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sum1 = sum1 + f(a + h * i + h/2) |
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sum2 = sum2 + f(a + h * i) |
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} |
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(h / 6) * (f(a) + f(b) + (4*sum1) + (2*sum2)) |
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} |
} |
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integrate.trapezoid <- function(f, a, b, n) { |
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h <- (b-a)/n |
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x <- seq(a, b, len=n+1) |
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fx <- f(x) |
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sum(fx[-1] + fx[-length(x)])*h/2 |
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} |
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x |
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} |
} |
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integrate.simpsons <- function(f, a, b, n) { |
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h <- (b-a)/n |
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x <- seq(a, b, len=n+1) |
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x=0 |
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fx <- f(x) |
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sum(fx[-length(x)] + 4*f(x[-1]-h/2) + fx[-1]) * h/6 |
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} |
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(h/2) * (f(a) + f(b)) + (h*x) |
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} |
} |
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f4 <- (function(x) {x}) |
f4 <- (function(x) {x}) |
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integrate.simpsons(f1,0,1,100) #0.25 |
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integrate.simpsons(f2,1,100,1000) # 4.60517 |
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integrate.simpsons(f3,0,5000,5000000) # 12500000 |
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integrate.simpsons(f4,0,6000,6000000) # 1.8e+07 |
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integrate.rect(f1,0,1,100,0) #TopLeft 0.245025 |
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integrate.rect(f1,0,1,100,0.5) #Mid 0.2499875 |
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integrate.rect(f1,0,1,100,1) #TopRight 0.255025 |
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integrate.trapezoid(f1,0,1,100) # 0.250025</lang> |
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=={{header|REXX}}== |
=={{header|REXX}}== |
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