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src/fft.jl

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@@ -1085,6 +1085,7 @@ function _mul(p::AdjointPlan{T}, x::AbstractArray, PS::R2RProjectionStyle) where
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dims = fftdims(p)
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N = 1
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# Ref: https://www.fftw.org/fftw3_doc/1d-Real_002deven-DFTs-_0028DCTs_0029.html
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# Normalization: P \ P * u = K * u
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# 0, 1 , 2 : NoProjectionStyle() type: K = prod(size(N))
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# 3, 6 : DCTs: K = 2 * (N - 1)

test/runtests.jl

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@@ -583,6 +583,8 @@ end
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y = randn(size(x))
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N = ndims(x)
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for dims in unique((1, 1:N, N))
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# DCT/ IDCT
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for P in (plan_dct(x, dims), plan_idct(x, dims))
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@test (P')' * x == P * x
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@test size(P') == AbstractFFTs.output_size(P)

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