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merged 2 commits into from
Apr 20, 2025
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feat: improve performance of the nonlinear functions #138

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8bdcf57
feat: improve performance of the nonlinear functions
avik-pal Apr 19, 2025
9b2f0b9
fix: fixup
avik-pal Apr 19, 2025
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2 changes: 1 addition & 1 deletion lib/NonlinearProblemLibrary/Project.toml
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Original file line number Diff line number Diff line change
@@ -1,6 +1,6 @@
name = "NonlinearProblemLibrary"
uuid = "b7050fa9-e91f-4b37-bcee-a89a063da141"
version = "0.1.2"
version = "0.1.3"

[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Expand Down
129 changes: 61 additions & 68 deletions lib/NonlinearProblemLibrary/src/NonlinearProblemLibrary.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -6,10 +6,10 @@ using SciMLBase, LinearAlgebra
# [test_nonlin](https://people.sc.fsu.edu/~jburkardt/m_src/test_nonlin/test_nonlin.html)

# ------------------------------------- Problem 1 ------------------------------------------
function p1_f!(out, x, p = nothing)
@inbounds @views function p1_f!(out, x, p = nothing)
n = length(x)
out[1] = 1.0 - x[1]
out[2:n] .= 10.0 .* (x[2:n] .- x[1:(n - 1)] .* x[1:(n - 1)])
@. out[2:n] = 10.0 * (x[2:n] - x[1:(n - 1)] * x[1:(n - 1)])
nothing
end

Expand All @@ -21,7 +21,7 @@ p1_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Generalized Rosenbrock function")

# ------------------------------------- Problem 2 ------------------------------------------
function p2_f!(out, x, p = nothing)
@inbounds function p2_f!(out, x, p = nothing)
out[1] = x[1] + 10.0 * x[2]
out[2] = sqrt(5.0) * (x[3] - x[4])
out[3] = (x[2] - 2.0 * x[3])^2
Expand All @@ -36,7 +36,7 @@ p2_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Powell singular function")

# ------------------------------------- Problem 3 ------------------------------------------
function p3_f!(out, x, p = nothing)
@inbounds function p3_f!(out, x, p = nothing)
out[1] = 10000.0 * x[1] * x[2] - 1.0
out[2] = exp(-x[1]) + exp(-x[2]) - 1.0001
nothing
Expand All @@ -49,7 +49,7 @@ p3_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Powell badly scaled function")

# ------------------------------------- Problem 4 ------------------------------------------
function p4_f!(out, x, p = nothing)
@inbounds function p4_f!(out, x, p = nothing)
temp1 = x[2] - x[1] * x[1]
temp2 = x[4] - x[3] * x[3]

Expand All @@ -66,15 +66,9 @@ x_start = [-3.0, -1.0, -3.0, -1.0]
p4_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol, "title" => "Wood function")

# ------------------------------------- Problem 5 ------------------------------------------
function p5_f!(out, x, p = nothing)
if 0.0 < x[1]
temp = atan(x[2] / x[1]) / (2.0 * pi)
elseif x[1] < 0.0
temp = atan(x[2] / x[1]) / (2.0 * pi) + 0.5
else
temp = 0.25 * sign(x[2])
end

@inbounds function p5_f!(out, x, p = nothing)
temp1 = atan(x[2] / x[1]) / (2.0 * pi)
temp = ifelse(0.0 < x[1], temp1, ifelse(x[1] < 0.0, temp1 + 0.5, 0.25 * sign(x[2])))
out[1] = 10.0 * (x[3] - 10.0 * temp)
out[2] = 10.0 * (sqrt(x[1] * x[1] + x[2] * x[2]) - 1.0)
out[3] = x[3]
Expand All @@ -88,7 +82,7 @@ p5_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Helical valley function")

# ------------------------------------- Problem 6 ------------------------------------------
function p6_f!(out, x, p = nothing)
@inbounds function p6_f!(out, x, p = nothing)
n = length(x)
out .= 0
for i in 1:29
Expand All @@ -114,8 +108,8 @@ function p6_f!(out, x, p = nothing)
end
end

out[1] = out[1] + 3.0 * x[1] - 2.0 * x[1] * x[2] + 2.0 * x[1]^3
out[2] = out[2] + x[2] - x[2]^2 - 1.0
out[1] += x[1] * (3.0 - 2.0 * x[2] + 2.0 * x[1]^2)
out[2] += x[2] * (1.0 - x[2]) - 1.0
nothing
end

Expand All @@ -125,7 +119,7 @@ x_start = zeros(n)
p6_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol, "title" => "Watson function")

# ------------------------------------- Problem 7 ------------------------------------------
function p7_f!(out, x, p = nothing)
@inbounds function p7_f!(out, x, p = nothing)
n = length(x)
out .= 0.0
for j in 1:n
Expand All @@ -138,13 +132,9 @@ function p7_f!(out, x, p = nothing)
t2 = t3
end
end
out ./= n

for i in 1:n
ip1 = i
if ip1 % 2 == 0
out[i] = out[i] + 1.0 / (ip1 * ip1 - 1)
end
@simd ivdep for i in 1:n
out[i] = out[i] / n + ifelse(i % 2 == 0, 1.0 / (i * i - 1), 0.0)
end
nothing
end
Expand All @@ -160,9 +150,10 @@ p7_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Chebyquad function")

# ------------------------------------- Problem 8 ------------------------------------------
function p8_f!(out, x, p = nothing)
@inbounds @views function p8_f!(out, x, p = nothing)
n = length(x)
out[1:(n - 1)] .= x[1:(n - 1)] .+ sum(x) .- (n + 1)
sum_x = sum(x)
@. out[1:(n - 1)] = x[1:(n - 1)] + sum_x - (n + 1)
out[n] = prod(x) - 1.0
nothing
end
Expand All @@ -174,18 +165,18 @@ p8_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Brown almost linear function")

# ------------------------------------- Problem 9 ------------------------------------------
function p9_f!(out, x, p = nothing)
@inline function discrete_bvf_kernel(xk, k, h)
return 2.0 * xk + 0.5 * h^2 * (xk + k * h + 1.0)^3
end

@inbounds function p9_f!(out, x, p = nothing)
n = length(x)
h = 1.0 / (n + 1)
for k in 1:n
out[k] = 2.0 * x[k] + 0.5 * h^2 * (x[k] + k * h + 1.0)^3
if 1 < k
out[k] = out[k] - x[k - 1]
end
if k < n
out[k] = out[k] - x[k + 1]
end
out[1] = discrete_bvf_kernel(x[1], 1, h) - x[2]
for k in 2:(n - 1)
out[k] = discrete_bvf_kernel(x[k], k, h) - x[k - 1] - x[k + 1]
end
out[n] = discrete_bvf_kernel(x[n], n, h) - x[n - 1]
nothing
end

Expand All @@ -199,7 +190,7 @@ p9_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Discrete boundary value function")

# ------------------------------------- Problem 10 -----------------------------------------
function p10_f!(out, x, p = nothing)
@inbounds function p10_f!(out, x, p = nothing)
n = length(x)
h = 1.0 / (n + 1)
for k in 1:n
Expand Down Expand Up @@ -230,11 +221,12 @@ p10_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Discrete integral equation function")

# ------------------------------------- Problem 11 -----------------------------------------
function p11_f!(out, x, p = nothing)
@inbounds function p11_f!(out, x, p = nothing)
n = length(x)
c_sum = sum(cos.(x))
for k in 1:n
out[k] = n - c_sum + k * (1.0 - cos(x[k])) - sin(x[k])
c_sum = sum(cos, x)
@simd ivdep for k in 1:n
sxk, cxk = sincos(x[k])
out[k] = n - c_sum + k * (1.0 - cxk) - sxk
end
nothing
end
Expand All @@ -246,7 +238,7 @@ p11_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Trigonometric function")

# ------------------------------------- Problem 12 -----------------------------------------
function p12_f!(out, x, p = nothing)
@inbounds function p12_f!(out, x, p = nothing)
n = length(x)
sum1 = 0.0
for j in 1:n
Expand All @@ -268,17 +260,15 @@ p12_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Variably dimensioned function")

# ------------------------------------- Problem 13 -----------------------------------------
function p13_f!(out, x, p = nothing)
@inline broyden_tridiag_kernel(xk) = (3.0 - 2.0 * xk) * xk + 1.0

@inbounds function p13_f!(out, x, p = nothing)
n = length(x)
for k in 1:n
out[k] = (3.0 - 2.0 * x[k]) * x[k] + 1.0
if 1 < k
out[k] -= x[k - 1]
end
if k < n
out[k] -= 2.0 * x[k + 1]
end
out[1] = broyden_tridiag_kernel(x[1]) -2.0 * x[2]
for k in 2:(n - 1)
out[k] = broyden_tridiag_kernel(x[k]) - x[k - 1] - 2.0 * x[k + 1]
end
out[n] = broyden_tridiag_kernel(x[n]) - x[n - 1]
nothing
end

Expand All @@ -289,7 +279,7 @@ p13_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Broyden tridiagonal function")

# ------------------------------------- Problem 14 -----------------------------------------
function p14_f!(out, x, p = nothing)
@inbounds function p14_f!(out, x, p = nothing)
n = length(x)
ml = 5
mu = 1
Expand All @@ -315,7 +305,7 @@ p14_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Broyden banded function")

# ------------------------------------- Problem 15 -----------------------------------------
function p15_f!(out, x, p = nothing)
@inbounds function p15_f!(out, x, p = nothing)
out[1] = (x[1] * x[1] + x[2] * x[3]) - 0.0001
out[2] = (x[1] * x[2] + x[2] * x[4]) - 1.0
out[3] = (x[3] * x[1] + x[4] * x[3]) - 0.0
Expand All @@ -330,7 +320,7 @@ p15_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Hammarling 2 by 2 matrix square root problem")

# ------------------------------------- Problem 16 -----------------------------------------
function p16_f!(out, x, p = nothing)
@inbounds function p16_f!(out, x, p = nothing)
out[1] = (x[1] * x[1] + x[2] * x[4] + x[3] * x[7]) - 0.0001
out[2] = (x[1] * x[2] + x[2] * x[5] + x[3] * x[8]) - 1.0
out[3] = x[1] * x[3] + x[2] * x[6] + x[3] * x[9]
Expand All @@ -350,7 +340,7 @@ p16_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Hammarling 3 by 3 matrix square root problem")

# ------------------------------------- Problem 17 -----------------------------------------
function p17_f!(out, x, p = nothing)
@inbounds function p17_f!(out, x, p = nothing)
out[1] = x[1] + x[2] - 3.0
out[2] = x[1]^2 + x[2]^2 - 9.0
nothing
Expand All @@ -364,16 +354,18 @@ p17_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,

# ------------------------------------- Problem 18 -----------------------------------------
function p18_f!(out, x, p = nothing)
if x[1] != 0.0
out[1] = x[2]^2 * (1.0 - exp(-x[1] * x[1])) / x[1]
else
if iszero(x[1])
out[1] = 0.0
end
if x[2] != 0.0
out[2] = x[1] * (1.0 - exp(-x[2] * x[2])) / x[2]
else
out[1] = x[2]^2 * (1.0 - exp(-x[1] * x[1])) / x[1]
end

if iszero(x[2])
out[2] = 0.0
else
out[2] = x[1] * (1.0 - exp(-x[2] * x[2])) / x[2]
end

nothing
end

Expand All @@ -384,9 +376,10 @@ p18_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Sample problem 18")

# ------------------------------------- Problem 19 -----------------------------------------
function p19_f!(out, x, p = nothing)
out[1] = x[1] * (x[1]^2 + x[2]^2)
out[2] = x[2] * (x[1]^2 + x[2]^2)
@inbounds function p19_f!(out, x, p = nothing)
tmp = x[1]^2 + x[2]^2
out[1] = x[1] * tmp
out[2] = x[2] * tmp
nothing
end

Expand All @@ -397,7 +390,7 @@ p19_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Sample problem 19")

# ------------------------------------- Problem 20 -----------------------------------------
function p20_f!(out, x, p = nothing)
@inbounds function p20_f!(out, x, p = nothing)
out[1] = x[1] * (x[1] - 5.0)^2
nothing
end
Expand All @@ -409,7 +402,7 @@ p20_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Scalar problem f(x) = x(x - 5)^2")

# ------------------------------------- Problem 21 -----------------------------------------
function p21_f!(out, x, p = nothing)
@inbounds function p21_f!(out, x, p = nothing)
out[1] = x[1] - x[2]^3 + 5.0 * x[2]^2 - 2.0 * x[2] - 13.0
out[2] = x[1] + x[2]^3 + x[2]^2 - 14.0 * x[2] - 29.0
nothing
Expand All @@ -422,9 +415,9 @@ p21_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Freudenstein-Roth function")

# ------------------------------------- Problem 22 -----------------------------------------
function p22_f!(out, x, p = nothing)
@inbounds function p22_f!(out, x, p = nothing)
out[1] = x[1] * x[1] - x[2] + 1.0
out[2] = x[1] - cos(0.5 * pi * x[2])
out[2] = x[1] - cospi(0.5 * x[2])
nothing
end

Expand All @@ -435,7 +428,7 @@ p22_dict = Dict("n" => n, "start" => x_start, "sol" => x_sol,
"title" => "Boggs function")

# ------------------------------------- Problem 23 -----------------------------------------
function p23_f!(out, x, p = nothing)
@inbounds function p23_f!(out, x, p = nothing)
c = 0.9
out[1:n] = x[1:n]
μ = zeros(n)
Expand Down
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