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flame.jl
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flame.jl
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module flame
using LinearAlgebra
"""
merge_2x2!(TL::Matrix, TR::Matrix, BL::Matrix, BR::Matrix, A::Matrix)
Modify `A` to contain the values of submatrices/quadrants TL, TR,
BL, and BR.
"""
function merge_2x2!(TL::Matrix, TR::Matrix, BL::Matrix, BR::Matrix, A::Matrix)
if size(TL)[1] > 0 && size(TL)[2] > 0
for i in 1:size(TL)[1], j in 1:size(TL)[2]
A[i, j] = TL[i, j]
end
end
if size(TR)[1] > 0 && size(TR)[2] > 0
for i in 1:size(TR)[1], j in 1:size(TR)[2]
A[i, j + size(TL)[2]] = TR[i, j]
end
end
if size(BL)[1] > 0 && size(BL)[2] > 0
for i in 1:size(BL)[1], j in 1:size(BL)[2]
A[i + size(TL)[1], j] = BL[i, j]
end
end
if size(BR)[1] > 0 && size(BR)[2] > 0
for i in 1:size(BR)[1], j in 1:size(BR)[2]
A[i + size(TL)[1], j + size(TL)[2]] = BR[i, j]
end
end
end
"""
merge_2x1!(T::Vector, B::Vector, x::Vector)
Combine input vectors `T` and `B` to create input/output vector `x`.
"""
function merge_2x1!(T::Vector, B::Vector, x::Vector)
xtemp = vcat(T, B)
for i in 1:length(xtemp)
x[i] = xtemp[i]
end
end
"""
merge_2x1!(T::Matrix, B::Matrix, A::Union{Matrix, LinearAlgebra.Transpose{T, Matrix{T}} where T})
Combine input matrices `T` and `B` vertically to create input/output matrix `A`.
"""
function merge_2x1!(T::Matrix, B::Matrix, A::Union{Matrix, LinearAlgebra.Transpose{T, Matrix{T}} where T})
Atemp = vcat(T, B)
m, n = size(Atemp)
for i in 1:m, j in 1:n
A[i, j] = Atemp[i, j]
end
end
"""
merge_1x2!(L::Matrix, R::Matrix, A::Matrix)
Update matrix `A` to contain the elements of the submatrices
`L` on the left and `R` on the right.
"""
function merge_1x2!(L::Matrix, R::Matrix, A::Matrix)
if size(L)[1] > 0 && size(L)[2] > 0
for i in 1:size(L)[1], j in 1:size(L)[2]
A[i, j] = L[i, j]
end
end
if size(R)[1] > 0 && size(R)[2] > 0
for i in 1:size(R)[1], j in 1:size(R)[2]
A[i, j + size(L)[2]] = R[i, j]
end
end
end
"""
cont_with_1x3_to_1x2(A1::Matrix, A2::Matrix, A3::Matrix, side = "LEFT")
Repartition three matrices (vertical slabs of an original matrix) into two by combining the middle portion, A2, of the original matrix with the `side` input submatrix.
"""
function cont_with_1x3_to_1x2(A1::Matrix, A2::Matrix, A3::Matrix, side = "LEFT")
(side == "LEFT") ? (hcat(A1, A2), A3) : (A1, hcat(A2, A3))
end
"""
cont_with_3x1_to_2x1(A1::Vector, A2::Vector, A3::Vector, side = "TOP")
Repartition three vectors into two by combining the middle portion, A2, of the original vector with the `side` input subvector.
"""
function cont_with_3x1_to_2x1(A1::Vector, A2::Vector, A3::Vector, side = "TOP")
(side == "TOP") ? (vcat(A1, A2), A3) : (A1, vcat(A2, A3))
end
"""
cont_with_3x1_to_2x1(A1::Matrix, A2::Matrix, A3::Matrix, side = "TOP")
Repartition three matrices (horizontal slabs of an original matrix) into two by combining the middle portion, A2, of the original matrix with the `side` input submatrix.
"""
function cont_with_3x1_to_2x1(A1::Matrix, A2::Matrix, A3::Matrix, side = "TOP")
(side == "TOP") ? (vcat(A1, A2), A3) : (A1, vcat(A2, A3))
end
"""
cont_with_3x3_to_2x2(A11::Matrix, A12::Matrix, A13::Matrix,
A21::Matrix, A22::Matrix, A23::Matrix,
A31::Matrix, A32::Matrix, A33::Matrix, quad = "TL")
Concatenate matrices together to repartition the original matrix into 4 quadrants
rather than a 3x3 grid. The middle submatrix `A22` is included in the `quad` output quadrant.
"""
function cont_with_3x3_to_2x2(A11::Matrix, A12::Matrix, A13::Matrix,
A21::Matrix, A22::Matrix, A23::Matrix,
A31::Matrix, A32::Matrix, A33::Matrix, quad = "TL")
if quad == "TL"
TL = hcat(vcat(A11, A21), vcat(A12, A22))
TR = vcat(A13, A23)
BL = hcat(A31, A32)
BR = A33
elseif quad == "TR"
TL = vcat(A11, A21)
TR = hcat(vcat(A12, A22), vcat(A13, A23))
BL = A31
BR = hcat(A32, A33)
elseif quad == "BL"
TL = hcat(A11, A12)
TR = A13
BL = hcat(vcat(A21, A31), vcat(A22, A32))
BR = vcat(A23, A33)
elseif quad == "BR"
TL = A11
TR = hcat(A12, A13)
BL = vcat(A21, A31)
BR = hcat(vcat(A22, A32), vcat(A23, A33))
end
return TL, TR, BL, BR
end
"""
part_1x2(A::Matrix, vpart = 0, side = "LEFT")
Partition a matrix into left and righthand portions, with
`vpart` columns in the `side`hand side.
"""
function part_1x2(A::Matrix, vpart = 0, side = "LEFT")
if vpart < 0
throw(DimensionMismatch("size < 0"))
elseif vpart > size(A)[2]
throw(DimensionMismatch("size > col dimension"))
elseif !(side in ("LEFT", "RIGHT"))
throw(ArgumentError("""side must be "LEFT" or "RIGHT" """))
end
vpart = (side == "LEFT") ? vpart : size(A)[2] - vpart
AL, AR = A[:, 1:vpart], A[:, vpart + 1:end]
end
"""
part_2x1(x::Vector, hpart=0, side="TOP")
Partition a vector into top and bottom portions, with
`hpart` elements in the `side` portion.
"""
function part_2x1(x::Vector, hpart=0, side="TOP")
if hpart < 0
throw(DimensionMismatch("size < 0"))
elseif hpart > size(x)[1]
throw(DimensionMismatch("size > row dimension"))
elseif !(side in ("TOP", "BOTTOM"))
throw(ArgumentError("""side must be "TOP" or "BOTTOM" """))
end
hpart = (side == "TOP") ? hpart : size(x)[1] - hpart
xT, xB = x[1:hpart], x[hpart + 1:end]
end
"""
part_2x1(A::Matrix, hpart = 0, side = "TOP")
Partition a matrix into top and bottom portions, with
`hpart` rows in the `side` portion.
"""
function part_2x1(A::Union{Matrix, LinearAlgebra.Transpose{T, Matrix{T}} where T}, hpart=0, side="TOP")
if hpart < 0
throw(DimensionMismatch("size < 0"))
elseif hpart > size(A)[1]
throw(DimensionMismatch("size > row dimension"))
elseif !(side in ("TOP", "BOTTOM"))
throw(ArgumentError("""side must be "TOP" or "BOTTOM" """))
end
hpart = (side == "TOP") ? hpart : size(A)[1] - hpart
AT, AB = A[1:hpart, :], A[hpart + 1:end, :]
end
"""
part_2x2(A::Matrix, m::Int, n::Int, quad::String)
Break `A` into four quadrants. `quad` specifies the quadrant
that should be `m` x `n`.
"""
function part_2x2(A::Matrix, m::Int, n::Int, quad::String)
if !(quad in ("TL", "TR", "BL", "BR"))
throw(ArgumentError("""quad must be "TL", "TR", "BL", or "BR"."""))
end
hpart = (quad in ("TL", "TR")) ? m : size(A)[1] - m
vpart = (quad in ("TL", "BL")) ? n : size(A)[2] - n
TL, TR = A[1:hpart, 1:vpart], A[1:hpart, (vpart + 1):end]
BL, BR = A[(hpart + 1):end, 1:vpart], A[(hpart + 1):end, (vpart + 1):end]
return TL, TR, BL, BR
end
"""
repart_1x2_to_1x3(AL::Matrix, AR::Matrix, n=1, side = "RIGHT")
Takes two submatrices and breaks the `side`hand portion into two
submatrices. `n` specifies the number of columns in what is ultimately
the middle submatrix.
"""
function repart_1x2_to_1x3(AL::Matrix, AR::Matrix, n=1, side = "RIGHT")
if side == "RIGHT"
vpart = n
A1 = AL
A2 = AR[:, 1:vpart]
A3 = AR[:, (vpart + 1):end]
else
vpart = size(AL)[2] - n
A1 = AL[:, 1:vpart]
A2 = AL[:, (vpart + 1):end]
A3 = AR
end
return A1, A2, A3
end
"""
repart_2x1_to_3x1(xT::Vector, xB::Vector, m=1, side = "BOTTOM")
Repartition a vector already divided into top and bottom portions,
`xT` and `xB`, into three horizontal slabs, `x1`, `x2`, and `x3`.
The middle segment, `x2`, is created from the `m` elements in the `side`
input portion that are closest to the interface between `xT` and `xB`.
For example, if side == "BOTTOM", x1 == xT; x2 is created from the top m
elements from xB, and x2 is what remains of xB after its m elements are excluded.
"""
function repart_2x1_to_3x1(xT::Vector, xB::Vector, m=1, side = "BOTTOM")
top_end = (side == "BOTTOM") ? size(xT)[1] : size(xT)[1] - m
bottom_start = (side == "TOP") ? 1 : m + 1
x1 = xT[1:top_end]
x3 = xB[bottom_start: end]
# What if you're taking from the bottom but the bottom is empty?
# Or taking from the top, but the top is empty?
# If "BOTTOM", x2 == xB[1:m] if length(xB) >= m,
# x2 == xB[1:0] if length(xB) == 0
# x2 == xB[1:length(xB)] if length(xB) <= m
# Generalization:
# x2 == xB[1:min(length(xB), m)]
# What if m > length(xB) > 0?
# If "TOP", x2 == xT[end - m + 1: end] if length(xT) >= m,
# x2 == xT[1:end] if length(xT) == 0
# x2 == xT[1:end] if length(xT) <= m
# Generalization:
# x2 == xT[max(1, end - m + 1):end]
# What if m > length(xT) > 0?
x2 = []
if side == "BOTTOM"
x2 = xB[1:min(bottom_start - 1, length(xB))]
else
x2 = xT[max(top_end + 1, 1): end]
end
# Expressed another way:
# x2 = (side == "BOTTOM") ? xB[1:min(bottom_start - 1, length(xB))] : xT[max(top_end + 1, 1): end]
return x1, x2, x3
end
"""
repart_2x1_to_3x1(AT::Matrix, AB::Matrix, m=1, side = "BOTTOM")
Repartition a matrix already divided into top and bottom portions,
`AT` and `AB`, into three horizontal slabs, `A1`, `A2`, and `A3`.
The middle segment, `A2`, is created from the `m` rows in the `side`
input portion that are closest to the interface between `AT` and `AB`.
For example, if side == "BOTTOM", A1 == AT; A2 is created from the top m
rows from AB, and A3 is what remains of AB after its m rows are excluded.
"""
function repart_2x1_to_3x1(AT::Matrix, AB::Matrix, m=1, side = "BOTTOM")
top_end = (side == "BOTTOM") ? size(AT)[1] : size(AT)[1] - m
bottom_start = (side == "TOP") ? 1 : m + 1
A1 = AT[1:top_end, :]
A3 = AB[bottom_start: end, :]
A2 = []
if side == "BOTTOM"
A2 = AB[1:min(bottom_start - 1, length(AB)), :]
else
A2 = AT[max(top_end + 1, 1): end, :]
end
# Expressed another way:
# A2 = (side == "BOTTOM") ? AB[1:min(bottom_start - 1, length(AB)), :] : AT[max(top_end + 1, 1): end, :]
return A1, A2, A3
end
"""
repart_2x2_to_3x3(ATL::Matrix, ATR::Matrix,
ABL::Matrix, ABR::Matrix, m = 1, n = 1, quad = "BR")
Repartition a 2x2 matrix into a 3x3 matrix. The `quad` quadrant is broken into four
submatrices and the interior matrix returned, `A22`, will be m x n.
"""
function repart_2x2_to_3x3(ATL::Matrix, ATR::Matrix,
ABL::Matrix, ABR::Matrix, m = 1, n = 1, quad = "BR")
hpart = (quad in ("TL", "TR")) ? size(ATL, 1) - m : m
vpart = (quad in ("TL", "BL")) ? size(ATL, 2) - n : n
if quad == "TL"
A11, A12, A13 = ATL[1:hpart, 1:vpart], ATL[1:hpart, (vpart + 1):end], ATR[1:hpart, :]
A21, A22, A23 = ATL[(hpart + 1):end, 1:vpart], ATL[(hpart + 1):end, (vpart + 1):end], ATR[(hpart + 1):end, :]
A31, A32, A33 = ABL[:, 1:vpart], ABL[:, (vpart + 1):end], ABR[:, :]
elseif quad == "TR"
A11, A12, A13 = ATL[1:hpart, :], ATR[1:hpart, 1:vpart], ATR[1:hpart, (vpart + 1):end]
A21, A22, A23 = ATL[(hpart + 1):end, :], ATR[(hpart + 1):end, 1:vpart], ATR[(hpart + 1):end, (vpart + 1):end]
A31, A32, A33 = ABL[:, :], ABR[:, 1:vpart], ABR[:, (vpart + 1):end]
elseif quad == "BL"
A11, A12, A13 = ATL[:, 1:vpart], ATL[:, (vpart + 1):end], ATR[:, :]
A21, A22, A23 = ABL[1:hpart, 1:vpart], ABL[1:hpart, (vpart + 1):end], ABR[1:hpart, :]
A31, A32, A33 = ABL[(hpart + 1):end, 1:vpart], ABL[(hpart + 1):end, (vpart + 1):end], ABR[(hpart + 1):end, :]
elseif quad == "BR"
A11, A12, A13 = ATL[:, :], ATR[:, 1:vpart], ATR[:, (vpart + 1):end]
A21, A22, A23 = ABL[1:hpart, :], ABR[1:hpart, 1:vpart], ABR[1:hpart, (vpart + 1):end]
A31, A32, A33 = ABL[(hpart + 1):end, :], ABR[(hpart + 1):end, 1:vpart], ABR[(hpart + 1):end, (vpart + 1):end]
end
return ( A11, A12, A13,
A21, A22, A23,
A31, A32, A33 )
end
end