152 lines
3.9 KiB
Julia
152 lines
3.9 KiB
Julia
|
#!/usr/bin/env julia
|
|||
|
|
|
|||
|
|
# Jacek Poziemski 272389
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
sumvectorsforwards(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
|
|||
|
|
Calculate the scalar sum of `x` and `y`,
|
|||
|
|
going from the first element to the last.
|
|||
|
|
|
|||
|
|
# Arguments
|
|||
|
|
- `x::Vector{T}`: first of the 2 vectors
|
|||
|
|
- `y::Vector{T}`: second of the 2 vectors
|
|||
|
|
"""
|
|||
|
|
function sumvectorsforwards(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
s::T = zero(T)
|
|||
|
|
|
|||
|
|
for i::Int in 1:(length(x))
|
|||
|
|
s += x[i] * y[i]
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
return s
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
sumvectorsbackwards(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
|
|||
|
|
Calculate the scalar sum of `x` and `y`,
|
|||
|
|
going from the last element to the first.
|
|||
|
|
|
|||
|
|
# Arguments
|
|||
|
|
- `x::Vector{T}`: first of the 2 vectors
|
|||
|
|
- `y::Vector{T}`: second of the 2 vectors
|
|||
|
|
"""
|
|||
|
|
function sumvectorsbackwards(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
s::T = zero(T)
|
|||
|
|
|
|||
|
|
for i::Int in (length(x)):-1:1
|
|||
|
|
s += x[i] * y[i]
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
return s
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
sumvectorsdecreasing(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
|
|||
|
|
Calculate the scalar sum of `x` and `y` by calculating
|
|||
|
|
the partial sums of positive and negative numbers,
|
|||
|
|
summing up the partial sums using a decreasing order
|
|||
|
|
according to their absolute values.
|
|||
|
|
|
|||
|
|
# Arguments
|
|||
|
|
- `x::Vector{T}`: first of the 2 vectors
|
|||
|
|
- `y::Vector{T}`: second of the 2 vectors
|
|||
|
|
"""
|
|||
|
|
function sumvectorsdecreasing(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
s::Vector{T} = zeros(T, length(x))
|
|||
|
|
|
|||
|
|
for i::Int in 1:(length(x))
|
|||
|
|
s[i] = x[i] * y[i]
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
spos::Vector{T} = s[s .> 0]
|
|||
|
|
sort!(spos, rev = true)
|
|||
|
|
|
|||
|
|
sneg::Vector{T} = s[s .<= 0]
|
|||
|
|
sort!(sneg)
|
|||
|
|
|
|||
|
|
neg::T = zero(T)
|
|||
|
|
for x::T in sneg
|
|||
|
|
neg += x
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
pos::T = zero(T)
|
|||
|
|
for x::T in spos
|
|||
|
|
pos += x
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
return pos + neg
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
"""
|
|||
|
|
sumvectorsincreasing(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
|
|||
|
|
Calculate the scalar sum of `x` and `y` by calculating
|
|||
|
|
the partial sums of positive and negative numbers,
|
|||
|
|
summing up the partial sums using an increasing order
|
|||
|
|
according to their absolute values.
|
|||
|
|
|
|||
|
|
# Arguments
|
|||
|
|
- `x::Vector{T}`: first of the 2 vectors
|
|||
|
|
- `y::Vector{T}`: second of the 2 vectors
|
|||
|
|
"""
|
|||
|
|
function sumvectorsincreasing(x::Vector{T}, y::Vector{T})::T where T <: AbstractFloat
|
|||
|
|
s::Vector{T} = zeros(T, length(x))
|
|||
|
|
|
|||
|
|
for i::Int in 1:(length(x))
|
|||
|
|
s[i] = x[i] * y[i]
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
spos::Vector{T} = s[s .> 0]
|
|||
|
|
sort!(spos)
|
|||
|
|
|
|||
|
|
sneg::Vector{T} = s[s .<= 0]
|
|||
|
|
sort!(sneg, rev = true)
|
|||
|
|
|
|||
|
|
neg::T = zero(T)
|
|||
|
|
for x::T in sneg
|
|||
|
|
neg += x
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
pos::T = zero(T)
|
|||
|
|
for x::T in spos
|
|||
|
|
pos += x
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
return pos + neg
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
x32::Vector{Float32} = [2.718281828, −3.141592654, 1.414213562, 0.577215664, 0.301029995]
|
|||
|
|
y32::Vector{Float32} = [1486.2497, 878366.9879, −22.37492, 4773714.647, 0.000185049]
|
|||
|
|
|
|||
|
|
x64::Vector{Float64} = [2.718281828, −3.141592654, 1.414213562, 0.577215664, 0.301029995]
|
|||
|
|
y64::Vector{Float64} = [1486.2497, 878366.9879, −22.37492, 4773714.647, 0.000185049]
|
|||
|
|
|
|||
|
|
expected::Float64 = −1.00657107000000 * 10^(−11)
|
|||
|
|
|
|||
|
|
res::Float64 = sumvectorsforwards(x32, y32)
|
|||
|
|
println("summing x32 and y32 forwards: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsbackwards(x32, y32)
|
|||
|
|
println("summing x32 and y32 backwards: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsdecreasing(x32, y32)
|
|||
|
|
println("summing x32 and y32 decreasing: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsincreasing(x32, y32)
|
|||
|
|
println("summing x32 and y32 increasing: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsforwards(x64, y64)
|
|||
|
|
println("summing x64 and y64 forwards: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsbackwards(x64, y64)
|
|||
|
|
println("summing x64 and y64 backwards: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsdecreasing(x64, y64)
|
|||
|
|
println("summing x64 and y64 decreasing: $res; correct: $(res == expected)")
|
|||
|
|
|
|||
|
|
res = sumvectorsincreasing(x64, y64)
|
|||
|
|
println("summing x64 and y64 increasing: $res; correct: $(res == expected)")
|