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Remove solve_triu and solve_triu_left for RingElem #1661

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Apr 13, 2024
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Remove solve_triu and solve_triu_left for RingElem #1661

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72 changes: 0 additions & 72 deletions src/Matrix.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -3306,78 +3306,6 @@ function _solve_triu(U::MatElem{T}, b::MatElem{T}, unit::Bool = false) where {T
return X
end

@doc raw"""
_solve_triu(U::MatElem{T}, b::MatElem{T}) where {T <: RingElement}

Given a non-singular $n\times n$ matrix $U$ over a field which is upper
triangular, and an $n\times m$ matrix $b$ over the same ring, return an
$n\times m$ matrix $x$ such that $Ux = b$. If this is not possible, an error
will be raised.

See also [`_solve_triu_left`](@ref).
"""
function _solve_triu(U::MatElem{T}, b::MatElem{T}) where {T <: RingElement}
n = nrows(U)
m = ncols(b)
R = base_ring(U)
X = zero(b)
tmp = Vector{elem_type(R)}(undef, n)
t = R()
for i = 1:m
for j = 1:n
tmp[j] = X[j, i]
end
for j = n:-1:1
s = R(0)
for k = j + 1:n
s = addmul!(s, U[j, k], tmp[k], t)
end
s = b[j, i] - s
tmp[j] = divexact(s, U[j,j])
end
for j = 1:n
X[j, i] = tmp[j]
end
end
return X
end

@doc raw"""
_solve_triu_left(b::MatElem{T}, U::MatElem{T}) where {T <: RingElement}

Given a non-singular $n\times n$ matrix $U$ over a field which is upper
triangular, and an $m\times n$ matrix $b$ over the same ring, return an
$m\times n$ matrix $x$ such that $xU = b$. If this is not possible, an error
will be raised.

See also [`_solve_triu`](@ref).
"""
function _solve_triu_left(b::MatElem{T}, U::MatElem{T}) where {T <: RingElement}
n = ncols(U)
m = nrows(b)
R = base_ring(U)
X = zero(b)
tmp = Vector{elem_type(R)}(undef, n)
t = R()
for i = 1:m
for j = 1:n
tmp[j] = X[i, j]
end
for j = 1:n
s = R()
for k = 1:j-1
s = addmul!(s, U[k, j], tmp[k], t)
end
s = b[i, j] - s
tmp[j] = divexact(s, U[j,j])
end
for j = 1:n
X[i, j] = tmp[j]
end
end
return X
end

#solves A x = B for A intended to be lower triangular
#only the lower part is used. if f is true, then the diagonal is assumed to be 1
#used to use lu!
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23 changes: 0 additions & 23 deletions test/generic/Matrix-test.jl
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Expand Up @@ -2637,29 +2637,6 @@ end

@test M*x == b
end

for dim = 0:10
S = matrix_space(R, dim, dim)
U = matrix_space(R, dim, rand(1:5))

M = randmat_triu(S, 3, -10:10)
b = rand(U, 3, -10:10)
c = M*b

x = AbstractAlgebra._solve_triu(M, c)

@test M*x == c

V = matrix_space(R, rand(1:5), dim)

M = randmat_triu(S, 3, -10:10)
b = rand(V, 3, -10:10)
c = b*M

x = AbstractAlgebra._solve_triu_left(c, M)

@test x*M == c
end
end

@testset "Generic.Mat.rref" begin
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