Symbolic Differentiation in Julia
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differentiate(x::Number, target::Symbol) = 0 | |
function differentiate(s::Symbol, target::Symbol) | |
if s == target | |
return 1 | |
else | |
return 0 | |
end | |
end | |
function differentiate_sum(ex::Expr, target::Symbol) | |
n = length(ex.args) | |
new_args = Array(Any, n) | |
new_args[1] = :+ | |
for i in 2:n | |
new_args[i] = differentiate(ex.args[i], target) | |
end | |
return Expr(:call, new_args, Any) | |
end | |
function differentiate_subtraction(ex::Expr, target::Symbol) | |
n = length(ex.args) | |
new_args = Array(Any, n) | |
new_args[1] = :- | |
for i in 2:n | |
new_args[i] = differentiate(ex.args[i], target) | |
end | |
return Expr(:call, new_args, Any) | |
end | |
function differentiate_product(ex::Expr, target::Symbol) | |
n = length(ex.args) | |
res_args = Array(Any, n) | |
res_args[1] = :+ | |
for i in 2:n | |
new_args = Array(Any, n) | |
new_args[1] = :* | |
for j in 2:n | |
if j == i | |
new_args[j] = differentiate(ex.args[j], target) | |
else | |
new_args[j] = ex.args[j] | |
end | |
end | |
res_args[i] = Expr(:call, new_args, Any) | |
end | |
return Expr(:call, res_args, Any) | |
end | |
function differentiate_quotient(ex::Expr, target::Symbol) | |
return Expr(:call, | |
{ | |
:/, | |
Expr(:call, | |
{ | |
:-, | |
Expr(:call, | |
{ | |
:*, | |
differentiate(ex.args[2], target), | |
ex.args[3] | |
}, | |
Any), | |
Expr(:call, | |
{ | |
:*, | |
ex.args[2], | |
differentiate(ex.args[3], target) | |
}, | |
Any) | |
}, | |
Any), | |
Expr(:call, | |
{ | |
:^, | |
ex.args[3], | |
2 | |
}, | |
Any) | |
}, | |
Any) | |
end | |
differentiate_lookup = { | |
:+ => differentiate_sum, | |
:- => differentiate_subtraction, | |
:* => differentiate_product, | |
:/ => differentiate_quotient | |
} | |
function differentiate(ex::Expr, target::Symbol) | |
if ex.head == :call | |
if has(differentiate_lookup, ex.args[1]) | |
return differentiate_lookup[ex.args[1]](ex, target) | |
else | |
error("Don't know how to differentiate $(ex.args[1])") | |
end | |
else | |
return differentiate(ex.head) | |
end | |
end |
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