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added complex sum to the function _linear_expansion #1492

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added complex sum to the function _linear_expansion #1492

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d90aa89
added complex sum to the function _linear_expansion
Bumblebee00 Mar 21, 2025
1da6587
added tests for linear_expansion for input with complex numbers
Bumblebee00 Mar 22, 2025
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13 changes: 13 additions & 0 deletions src/linear_algebra.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -262,6 +262,13 @@ function _linear_expansion(t::Equation, x)
# t.rhs - t.lhs = 0
return (a₂ - a₁, b₂ - b₁, islinear)
end

"""
works with t of two types:
x (variable, type Num)
or
b (constant)
"""
trivial_linear_expansion(t, x) = isequal(t, x) ? (1, 0, true) : (0, t, true)

is_expansion_leaf(t) = !iscall(t) || (operation(t) isa Operator)
Expand Down Expand Up @@ -294,6 +301,12 @@ function _linear_expansion(t, x)
b₁ += b₂
end
return (a₁, b₁, true)
elseif op === Complex{Real}
# x+2im is interpreted as Complex{Real}(x, 2)
real_part, im_part = arguments(t)
a_real, b_real, islinear_real = linear_expansion(real_part, x)
a_im, b_im, islinear_im = linear_expansion(im_part, x)
return (a_real + a_im * im, b_real + b_im * im, islinear_real && islinear_im)
elseif op === (-)
@assert length(args) == 1
a, b, islinear = linear_expansion(args[1], x)
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19 changes: 19 additions & 0 deletions test/linear_solver.jl
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Expand Up @@ -85,3 +85,22 @@ a, b, islinear = Symbolics.linear_expansion(D(x) - x, x)
@variables x y
@test !Symbolics.linear_expansion(x + z([x, y]), y)[3]
end

@testset "linear_expansion with imaginary numbers" begin
@variables x y

a, b, islin = Symbolics.linear_expansion(1im*x^2 + 1im*x, x)
@test !islin
a, b, islin = Symbolics.linear_expansion(2im*x + 1im, x)
@test islin && isequal(a, 2im) && isequal(b, 1im)
a, b, islin = Symbolics.linear_expansion(1im*x + 1im*y, x)
@test islin && isequal(a, 1im) #&& isequal(b, 1im*y)
a, b, islin = Symbolics.linear_expansion(1im*x - y,x)
@test islin && isequal(a, 1im) && isequal(b, -y)

@variables xx[1:2] yy[1:2] zz(..)
a, b, islin = Symbolics.linear_expansion(zz(1im * xx[2]) + 1im*xx[1], xx[1])
@test islin && isequal(a, im) && isequal(b, zz(1im * xx[2]))
a, b, islin = Symbolics.linear_expansion(1im * yy[1], xx[1])
@test islin && isequal(a, 0) # && isequal(b, yy[1])
end
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