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Add mul! for matrices #330

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May 16, 2024
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50 changes: 50 additions & 0 deletions src/adjtrans.jl
Original file line number Diff line number Diff line change
Expand Up @@ -141,6 +141,25 @@ function mul!(
conj!(res)
end

function mul!(
res::AbstractMatrix,
op::AdjointLinearOperator{T, S},
m::AbstractMatrix,
α,
β,
) where {T, S}
p = op.parent
(size(m, 1) == size(p, 1) && size(res, 1) == size(p, 2) && size(m, 2) == size(res, 2)) ||
throw(LinearOperatorException("shape mismatch"))
if ishermitian(p)
return mul!(res, p, m, α, β)
elseif p.ctprod! !== nothing
return p.ctprod!(res, m, α, β)
else
error("Not implemented")
end
end

function mul!(
res::AbstractVector,
op::TransposeLinearOperator{T, S},
Expand Down Expand Up @@ -188,6 +207,25 @@ function mul!(
conj!(res)
end

function mul!(
res::AbstractMatrix,
op::TransposeLinearOperator{T, S},
m::AbstractMatrix,
α,
β,
) where {T, S}
p = op.parent
(size(m, 1) == size(p, 1) && size(res, 1) == size(p, 2) && size(m, 2) == size(res, 2)) ||
throw(LinearOperatorException("shape mismatch"))
if issymmetric(p)
return mul!(res, p, m, α, β)
elseif p.tprod! !== nothing
return p.tprod!(res, m, α, β)
else
error("Not implemented")
end
end

function mul!(
res::AbstractVector,
op::ConjugateLinearOperator{T, S},
Expand All @@ -200,6 +238,18 @@ function mul!(
conj!(res)
end

function mul!(
res::AbstractMatrix,
op::ConjugateLinearOperator{T, S},
v::AbstractMatrix,
α,
β,
) where {T, S}
p = op.parent
mul!(res, p, conj.(v), α, β)
conj!(res)
end

-(op::AdjointLinearOperator) = adjoint(-op.parent)
-(op::TransposeLinearOperator) = transpose(-op.parent)
-(op::ConjugateLinearOperator) = conj(-op.parent)
Expand Down
2 changes: 2 additions & 0 deletions src/constructors.jl
Original file line number Diff line number Diff line change
Expand Up @@ -102,6 +102,8 @@ op = LinearOperator(Float64, 2, 2, false, false,
(res, v) -> mul!(res, A, v),
(res, w) -> mul!(res, A', w))
```

The 3-args `mul!` also works when applying the operator on a matrix.
"""
function LinearOperator(
::Type{T},
Expand Down
36 changes: 30 additions & 6 deletions src/operations.jl
Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,11 @@ function mul!(res::AbstractVector, op::AbstractLinearOperator{T}, v::AbstractVec
end
end

function mul!(res::AbstractVector, op::AbstractLinearOperator, v::AbstractVector{T}) where {T}
function mul!(res::AbstractMatrix, op::AbstractLinearOperator, m::AbstractMatrix{T}, α, β) where {T}
op.prod!(res, m, α, β)
end

function mul!(res::AbstractVecOrMat, op::AbstractLinearOperator, v::AbstractVecOrMat{T}) where {T}
mul!(res, op, v, one(T), zero(T))
end

Expand Down Expand Up @@ -73,6 +77,26 @@ function *(
return v_wrapper(res)
end

# Apply an operator to a matrix (only in-place, since operator * matrix is a matrix).

function mul!(
res::Adjoint{S1, M1},
m::Adjoint{S2, M2},
op::AbstractLinearOperator{T},
) where {T, S1, S2, M1 <: AbstractMatrix{S1}, M2 <: AbstractMatrix{S2}}
mul!(adjoint(res), adjoint(op), adjoint(m))
return res
end

function mul!(
res::Transpose{S1, M1},
m::Transpose{S2, M2},
op::AbstractLinearOperator{T},
) where {T, S1, S2, M1 <: AbstractMatrix{S1}, M2 <: AbstractMatrix{S2}}
mul!(transpose(res), transpose(op), transpose(m))
return res
end

# Unary operations.
+(op::AbstractLinearOperator) = op

Expand All @@ -95,11 +119,11 @@ function -(op::AbstractLinearOperator{T}) where {T}
end

function prod_op!(
res::AbstractVector,
res::AbstractVecOrMat,
op1::AbstractLinearOperator,
op2::AbstractLinearOperator,
vtmp::AbstractVector,
v::AbstractVector,
vtmp::AbstractVecOrMat,
v::AbstractVecOrMat,
α,
β,
)
Expand Down Expand Up @@ -162,10 +186,10 @@ end
# Operator + operator.

function sum_prod!(
res::AbstractVector,
res::AbstractVecOrMat,
op1::AbstractLinearOperator,
op2::AbstractLinearOperator{T},
v::AbstractVector,
v::AbstractVecOrMat,
α,
β,
) where {T}
Expand Down
12 changes: 12 additions & 0 deletions test/test_linop.jl
Original file line number Diff line number Diff line change
Expand Up @@ -61,6 +61,18 @@ function test_linop()
@test(norm(transpose(u) * A - transpose(u) * op) <= rtol * norm(u))
@test(typeof(u' * op * v) <: Number)
@test(norm(u' * A * v - u' * op * v) <= rtol * norm(u))

mv = hcat(v, -2v)
mu = hcat(u, -2u)
res_mat = similar(mu)
res_trans = similar(mv)
res_adj = similar(mv)
mul!(res_mat, op, mv)
mul!(res_trans, transpose(op), mu)
mul!(res_adj, op', mu)
@test(norm(A * mv - res_mat) <= rtol * norm(mv))
@test(norm(transpose(A) * mu - res_trans) <= rtol * norm(mu))
@test(norm(A' * mu - res_adj) <= rtol * norm(mu))
end

A3 = Hermitian(A2' * A2)
Expand Down
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