Laplace Transform #1590
Laplace Transform #1590
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…h no repeated roots)
…ving to do with constant distribution
unable to test on laptop. will test on different computer soon
…dOfFrogs/Symbolics.jl into ToriDell/symbolic-ode-solver
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## master #1590 +/- ##
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Reference to Ds replaced with Differential(s), as Ds was local variable in laplace
| Helper function to unwrap derivatives of `f(t)` in `expr` with respect to the differential operator `Dt = Differential(t)`. Returns a tuple `(n, base_expr)`, where `n` is the order of the derivative and `base_expr` is the expression with the derivatives removed. If `expr` does not contain `f(t)` or its derivatives, returns `(0, expr)`. | ||
| """ | ||
| function unwrap_der(expr, Dt) | ||
| reduce_rule = @rule Dt(~x) => ~x |
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Repeatedly creating @rule in the recursive call and then matching it is pretty expensive. I'd recommend just doing
function reduce_rule(expr, Dt)
iscall(expr) && isequal(operation(expr), Dt) ? arguments(expr)[1] : nothing
end| end | ||
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| # takes into account fractions | ||
| function _true_factors(expr) |
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You can use SymbolicUtils.flatten_fractions to handle nested fractions and then SymbolicUtils.numerators to get the list of factors in the numerator and SymbolicUtils.denominators to get the list of factors in the denominator. Make sure to unwrap everything passed into those functions.
| return isequal(expr, 0) | ||
| end | ||
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| function _parse_trig(expr, t) |
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Same comment about @rule in a function.
| import DomainSets.ClosedInterval | ||
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| # from https://tutorial.math.lamar.edu/Classes/DE/Laplace_Table.aspx | ||
| transform_rules(f, t, F, s) = Symbolics.Chain([ |
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I wonder if SymbolicUtils.@cache will play nicely with this. It could save a lot of time considering that this is called recursively. This also applies to the previous comments about @rule in recursive functions.
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Alternatively, the laplace function could have a keyword rules = nothing. It then does
if rules === nothing
rules = transform_rules(f, t, F, s)
endand passes rules down to recursive calls. Again, this approach works for the similar previous comments and is arguably better than @cache.
| # t-derivative rule ((Dt^n)(f(t)) -> s^n*F(s) - s^(n-1)*f(0) - s^(n-2)*f'(0) - ... - f^(n-1)(0)) | ||
| n, expr = unwrap_der(expr, Dt) | ||
| if n != 0 && isequal(expr, f(t)) | ||
| f0 = Symbolics.variables(:f0, 0:(n-1)) |
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Use some unicode here to avoid name collisions?
| @variables λ # eigenvalue | ||
| v = variables(:v, 1:size(A, 1)) # vector of subscripted variables to represent eigenvector |
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Both of these should use unicode to avoid name collisions
Adds Laplace and inverse Laplace transforms based on linearity and rule tables. Planned use for solving ODEs.