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@mfalt
mfalt committed Sep 8, 2017
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1 change: 0 additions & 1 deletion REQUIRE
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Expand Up @@ -2,4 +2,3 @@ julia 0.6
StaticArrays
QuadGK
IterTools
Interpolations
43 changes: 22 additions & 21 deletions test/discrete_transition_costs.jl
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Expand Up @@ -28,33 +28,34 @@ I1 = [1,10,30,40,50]
Y1 = g[I1]

y1 = interpolate((I1,), Y1, Gridded(Linear()))[1:length(g)]
@testset "Discrete Transition Costs" begin
@test compute_cost(ℓ,I1,Y1) ≈ sum((y1[1:end-1]-g[1:end-1]).^2)

@test compute_cost(ℓ,I1,Y1) ≈ sum((y1[1:end-1]-g[1:end-1]).^2)

## Test 1b
I2 = [1,15,30,36,50]
Y2 = randn(5)

## Test 1b
I2 = [1,15,30,36,50]
Y2 = randn(5)
y2 = interpolate((t[I2],), Y2, Gridded(Linear()))[t]

y2 = interpolate((t[I2],), Y2, Gridded(Linear()))[t]
@test compute_cost(ℓ,I2,Y2) ≈ sum((y2[1:end-1]-g[1:end-1]).^2)

@test compute_cost(ℓ,I2,Y2) ≈ sum((y2[1:end-1]-g[1:end-1]).^2)
#plot(t, sin.(t))
#plot!(t[I1], Y1)
#plot!(t, y1, color="red")

#plot(t, sin.(t))
#plot!(t[I1], Y1)
#plot!(t, y1, color="red")

## Test 2
# Check the transition costs for a simple example
ℓ = dev.compute_discrete_transition_costs([1.0, 2.0, 3.0])

## Test 2
# Check the transition costs for a simple example
ℓ = dev.compute_discrete_transition_costs([1.0, 2.0, 3.0])
# (y - 1)^2
@test ℓ[1,2].P == [1.0 0.0; 0.0 0.0]
@test ℓ[1,2].q == [-2.0, 0]
@test ℓ[1,2].r == 1

# (y - 1)^2
@test ℓ[1,2].P == [1.0 0.0; 0.0 0.0]
@test ℓ[1,2].q == [-2.0, 0]
@test ℓ[1,2].r == 1

# (y - 1)^2 + (y/2 + y'/2 - 2)^2
@test ℓ[1,3].P == [1.25 0.25; 0.25 0.25]
@test ℓ[1,3].q == [-4.0, -2.0]
@test ℓ[1,3].r == 5.0
# (y - 1)^2 + (y/2 + y'/2 - 2)^2
@test ℓ[1,3].P == [1.25 0.25; 0.25 0.25]
@test ℓ[1,3].q == [-4.0, -2.0]
@test ℓ[1,3].r == 5.0
end
29 changes: 16 additions & 13 deletions test/find_optimal_fit.jl
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Expand Up @@ -16,16 +16,19 @@ g = sin
@time I_dp4, _, f_dp4 = dev.recover_solution(Λ[4, 1], 1, N)
@time I_dp5, _, f_dp5 = dev.recover_solution(Λ[5, 1], 1, N)

# Comparisons to solutions found by brute force optimization
@test I_dp3 == [1, 21, 30, 50]
@test I_dp4 ∈ ([1, 8, 19, 30, 50], [1, 21, 32, 43, 50]) # Two symmetric solutions
@test I_dp5 == [1, 8, 19, 32, 43, 50]

@test f_dp3 ≈ 1.7402065022125042
@test f_dp4 ≈ 0.9196880458290417
@test f_dp5 ≈ 0.09174442455649423

## Test of brute force optimization
m = 3
@time I_bf, _, f_bf = dev.brute_force_optimization(ℓ, m-1);
@test I_bf == [1, 21, 30, 50]
@testset "Optimal Fit" begin
# Comparisons to solutions found by brute force optimization
@test I_dp3 == [1, 21, 30, 50]
@test I_dp4 ∈ ([1, 8, 19, 30, 50], [1, 21, 32, 43, 50]) # Two symmetric solutions
@test I_dp5 == [1, 8, 19, 32, 43, 50]

@test f_dp3 ≈ 1.7402065022125042
@test f_dp4 ≈ 0.9196880458290417
@test f_dp5 ≈ 0.09174442455649423

## Test of brute force optimization
m = 3
@time I_bf, _, f_bf = dev.brute_force_optimization(ℓ, m-1);
@test I_bf == [1, 21, 30, 50]

end
141 changes: 73 additions & 68 deletions test/piecewise_quadratics.jl
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Expand Up @@ -2,39 +2,7 @@ using Base.Test

include(joinpath(Pkg.dir("DynamicApproximations"),"src","dev.jl"))

pwq = dev.generate_PiecewiseQuadratic(([2.0, 2, 1], -Inf), ([2.0, -2, 1], 0.0))

@test length(pwq) == 2
dev.add_quadratic(pwq, dev.QuadraticPolynomial([1, 0, 1.0]))

@test length(pwq) == 3

#---
# Tests with (2x^2 + 1) and (x^2 + 2) which have intersections in -1, +1
# and 5/2*x(x-1) + 1 = 2.5x^2 - 2.5x + 1

p1 = dev.QuadraticPolynomial([2.0, 0, 1])
p2 = dev.QuadraticPolynomial([1.0, 0, 2])
p3 = dev.QuadraticPolynomial(2.5, -2.5, 1.0)

pwq1 = dev.create_new_pwq(p1)
dev.add_quadratic(pwq1, p2)
@test length(pwq1) == 3
dev.add_quadratic(pwq1, p3)
@test length(pwq1) == 4

pwq2 = dev.create_new_pwq(p2)
dev.add_quadratic(pwq2, p3)
@test length(pwq2) == 3
dev.add_quadratic(pwq2, p1)
@test length(pwq2) == 4

@test pwq1[1].p === pwq2[1].p == p1
@test pwq1[2].left_endpoint == pwq2[2].left_endpoint == -1
@test pwq1[2].p === pwq2[2].p == p2
@test pwq1[3].left_endpoint == pwq2[3].left_endpoint == 0
@test pwq1[3].p === pwq2[3].p

global const TEST_PRINT_LEVEL = 0
#---

# Given a matrix with coefficients for quadratic polynomials this function
Expand All @@ -55,28 +23,28 @@ function verify_piecewise_quadratic(c_mat, show_plot=false)
# Insert quadratics into piecewise quadfatic
pwq = dev.create_new_pwq()
for p in poly_list
println("Inserting: ", p)
TEST_PRINT_LEVEL > 0 && println("Inserting: ", p)
dev.add_quadratic(pwq, p)

println("After Insertion: ")
println(pwq)
TEST_PRINT_LEVEL > 0 && println("After Insertion: ")
TEST_PRINT_LEVEL > 0 && println(pwq)
end

# Check that the intersections between the quadratics are in increasing order
println("Checking that intersections points are increasing: ")
TEST_PRINT_LEVEL > 0 && println("Checking that intersections points are increasing: ")
for λ in pwq
@test λ.left_endpoint < dev.get_right_endpoint(λ)
end

# Check for continuity of the piecewise quadratic
println("Checking continuity: ")
TEST_PRINT_LEVEL > 0 && println("Checking continuity: ")
for λ in pwq
x = dev.get_right_endpoint(λ)
if x == Inf
break
end

println("Continutiy diff: ", λ.p(x) - λ.next.p(x))
TEST_PRINT_LEVEL > 0 && println("Continutiy diff: ", λ.p(x) - λ.next.p(x))
@test λ.p(x) ≈ λ.next.p(x)
end

Expand All @@ -86,40 +54,77 @@ function verify_piecewise_quadratic(c_mat, show_plot=false)
y_pwq = dev.evalPwq(pwq, x_grid)

for p in poly_list
@printf("suboptimality diff: %2.3f\n", maximum(y_pwq - p.(x_grid)))
TEST_PRINT_LEVEL > 0 && @printf("suboptimality diff: %2.3f\n", maximum(y_pwq - p.(x_grid)))
#println(" ", x_grid[ (y_pwq - p.(x_grid)) .> 0])
@test (y_pwq .<= p.(x_grid)) == trues(length(x_grid))
end

end

#---
c_mat1 = [
2.53106 1.59097 1.60448
2.51349 0.681205 1.60553
2.09364 0.714858 1.08607
]
verify_piecewise_quadratic(c_mat1)

#---
c_mat2 = [
2.01532 1.59269 1.65765
2.50071 1.56421 1.53899
2.02767 0.706143 1.129
]
verify_piecewise_quadratic(c_mat2)

#---
pwq = dev.generate_PiecewiseQuadratic(([2.0, 2, 1], -Inf), ([2.0, -2, 1], 0.0))

c_mat3 = [
2.42298 0.796953 1.02011
2.45055 1.32235 1.4894
2.1762 0.855014 1.0647
]
verify_piecewise_quadratic(c_mat3)
#---
# Random test case
N = 10
c_mat_rand = [2+rand(N) 2*rand(N) 1+rand(N)]
@testset "Piecewise Quadratics" begin
@test length(pwq) == 2
dev.add_quadratic(pwq, dev.QuadraticPolynomial([1, 0, 1.0]))

@test length(pwq) == 3

#---
# Tests with (2x^2 + 1) and (x^2 + 2) which have intersections in -1, +1
# and 5/2*x(x-1) + 1 = 2.5x^2 - 2.5x + 1

p1 = dev.QuadraticPolynomial([2.0, 0, 1])
p2 = dev.QuadraticPolynomial([1.0, 0, 2])
p3 = dev.QuadraticPolynomial(2.5, -2.5, 1.0)

pwq1 = dev.create_new_pwq(p1)
dev.add_quadratic(pwq1, p2)
@test length(pwq1) == 3
dev.add_quadratic(pwq1, p3)
@test length(pwq1) == 4

pwq2 = dev.create_new_pwq(p2)
dev.add_quadratic(pwq2, p3)
@test length(pwq2) == 3
dev.add_quadratic(pwq2, p1)
@test length(pwq2) == 4

@test pwq1[1].p === pwq2[1].p == p1
@test pwq1[2].left_endpoint == pwq2[2].left_endpoint == -1
@test pwq1[2].p === pwq2[2].p == p2
@test pwq1[3].left_endpoint == pwq2[3].left_endpoint == 0
@test pwq1[3].p === pwq2[3].p


#---
c_mat1 = [
2.53106 1.59097 1.60448
2.51349 0.681205 1.60553
2.09364 0.714858 1.08607
]
verify_piecewise_quadratic(c_mat1)

#---
c_mat2 = [
2.01532 1.59269 1.65765
2.50071 1.56421 1.53899
2.02767 0.706143 1.129
]
verify_piecewise_quadratic(c_mat2)

#---

c_mat3 = [
2.42298 0.796953 1.02011
2.45055 1.32235 1.4894
2.1762 0.855014 1.0647
]
verify_piecewise_quadratic(c_mat3)
#---
# Random test case
N = 10
c_mat_rand = [2+rand(N) 2*rand(N) 1+rand(N)]

verify_piecewise_quadratic(c_mat_rand)

verify_piecewise_quadratic(c_mat_rand)
end
45 changes: 23 additions & 22 deletions test/quadratic_forms.jl
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Expand Up @@ -8,34 +8,35 @@ include(joinpath(Pkg.dir("DynamicApproximations"),"src","dev.jl"))
# Addition of quaratic forms
Q = dev.QuadraticForm2(@SMatrix([2.0 0; 0 1]), @SVector([0.0,0]), 1.0) +
dev.QuadraticForm2(@SMatrix([2.0 1; 1 2]), @SVector([1.0,0]), 0.0)
@testset "Quadratic Forms" begin
@test Q == dev.QuadraticForm2(@SMatrix([4.0 1; 1 3]), @SVector([1.0,0]), 1.0)

@test Q == dev.QuadraticForm2(@SMatrix([4.0 1; 1 3]), @SVector([1.0,0]), 1.0)


# Maybe somewhat surprising that the tests pass considering equalities between
# Floats, or is the aritmhetic exact

# Maybe somewhat surprising that the tests pass considering equalities between
# Floats, or is the aritmhetic exact
# x^2 + y^2 + 1
Q1 = dev.QuadraticForm2(@SMatrix([1.0 0; 0 0]), @SVector([0.0, 0]), 0.5)
p1 = dev.QuadraticPolynomial(1.0, 0.0, 0.5)
@test dev.minimize_wrt_x2(Q1, p1) == dev.QuadraticPolynomial(1,0,1)
@test Q1(1, 2) == 1.5

# x^2 + y^2 + 1
Q1 = dev.QuadraticForm2(@SMatrix([1.0 0; 0 0]), @SVector([0.0, 0]), 0.5)
p1 = dev.QuadraticPolynomial(1.0, 0.0, 0.5)
@test dev.minimize_wrt_x2(Q1, p1) == dev.QuadraticPolynomial(1,0,1)
@test Q1(1, 2) == 1.5

# (2x - y + 1)^2 + x^2 - 2x + 4
# = 5x^2 + y^2 + 2 + 2x - 2y - 4xy
Q2 = dev.QuadraticForm2(@SMatrix([5.0 -2; -2 0.5]), @SVector([2.0, -2]), 1.0)
p2 = dev.QuadraticPolynomial(0.5, 0.0, 5.0)
@test dev.minimize_wrt_x2(Q2, p2) == dev.QuadraticPolynomial(1,-2,5)

# (2x - y + 1)^2 + x^2 - 2x + 4
# = 5x^2 + y^2 + 2 + 2x - 2y - 4xy
Q2 = dev.QuadraticForm2(@SMatrix([5.0 -2; -2 0.5]), @SVector([2.0, -2]), 1.0)
p2 = dev.QuadraticPolynomial(0.5, 0.0, 5.0)
@test dev.minimize_wrt_x2(Q2, p2) == dev.QuadraticPolynomial(1,-2,5)
# x^2 + 2x + 2
Q3 = dev.QuadraticForm2(@SMatrix([1.0 0; 0 0]), @SVector([2.0, 0]), 2.0)
p3 = dev.QuadraticPolynomial(0.0, 0.0, 0.0)
@test dev.minimize_wrt_x2(Q3, p3) == dev.QuadraticPolynomial(1.0,2.0,2.0)

# x^2 + 2x + 2
Q3 = dev.QuadraticForm2(@SMatrix([1.0 0; 0 0]), @SVector([2.0, 0]), 2.0)
p3 = dev.QuadraticPolynomial(0.0, 0.0, 0.0)
@test dev.minimize_wrt_x2(Q3, p3) == dev.QuadraticPolynomial(1.0,2.0,2.0)


# y^2 + 2y + 2
Q4 = dev.QuadraticForm2(@SMatrix([0.0 0; 0 1]), @SVector([0.0, 2]),2.0)
p4 = dev.QuadraticPolynomial(0.0, 0.0, 0.0)
@test dev.minimize_wrt_x2(Q4, p4) == dev.QuadraticPolynomial(0,0,1)
# y^2 + 2y + 2
Q4 = dev.QuadraticForm2(@SMatrix([0.0 0; 0 1]), @SVector([0.0, 2]),2.0)
p4 = dev.QuadraticPolynomial(0.0, 0.0, 0.0)
@test dev.minimize_wrt_x2(Q4, p4) == dev.QuadraticPolynomial(0,0,1)
end
32 changes: 17 additions & 15 deletions test/quadratic_polynomials.jl
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Expand Up @@ -2,25 +2,27 @@ using Base.Test

include(joinpath(Pkg.dir("DynamicApproximations"),"src","dev.jl"))

# Subtraction of quadratic polynomials
@test dev.QuadraticPolynomial(4.0, -2.0, 3.0) - dev.QuadraticPolynomial(1.0, 1.0, 2.0) == dev.QuadraticPolynomial(3.0,-3.0,1.0)
@testset "Quadratic Polynomials" begin
# Subtraction of quadratic polynomials
@test dev.QuadraticPolynomial(4.0, -2.0, 3.0) - dev.QuadraticPolynomial(1.0, 1.0, 2.0) == dev.QuadraticPolynomial(3.0,-3.0,1.0)


### Minimization of quadratic polynomials ###
@test dev.find_minimum(dev.QuadraticPolynomial(1 ,0 ,0)) == (0, 0)
@test dev.find_minimum(dev.QuadraticPolynomial(1 ,0 ,1)) == (0, 1)
### Minimization of quadratic polynomials ###
@test dev.find_minimum(dev.QuadraticPolynomial(1 ,0 ,0)) == (0, 0)
@test dev.find_minimum(dev.QuadraticPolynomial(1 ,0 ,1)) == (0, 1)

# 2*x*(x+1) + 1
@test dev.find_minimum(dev.QuadraticPolynomial(2, 2, 1)) == (-0.5, 0.5)
# 2*x*(x+1) + 1
@test dev.find_minimum(dev.QuadraticPolynomial(2, 2, 1)) == (-0.5, 0.5)

# (x+1)^2 + 1
@test dev.find_minimum(dev.QuadraticPolynomial(1, 2, 2)) == (-1, 1)
# (x+1)^2 + 1
@test dev.find_minimum(dev.QuadraticPolynomial(1, 2, 2)) == (-1, 1)

# 2*((x+1)^2 + 1)
@test dev.find_minimum(dev.QuadraticPolynomial(2, 4, 4)) == (-1, 2)
# 2*((x+1)^2 + 1)
@test dev.find_minimum(dev.QuadraticPolynomial(2, 4, 4)) == (-1, 2)

# (3x+1)^2 + 1 = 9x^2 + 6x + 2
@test dev.find_minimum(dev.QuadraticPolynomial(9, 6, 2)) == (-1/3, 1)
# (3x+1)^2 + 1 = 9x^2 + 6x + 2
@test dev.find_minimum(dev.QuadraticPolynomial(9, 6, 2)) == (-1/3, 1)

# (3x+1)^2 + 1 = 9x^2 + 6x + 2
@test dev.unsafe_minimum(dev.QuadraticPolynomial(9.0, 6.0, 2.0)) == 1.0
# (3x+1)^2 + 1 = 9x^2 + 6x + 2
@test dev.unsafe_minimum(dev.QuadraticPolynomial(9.0, 6.0, 2.0)) == 1.0
end
16 changes: 10 additions & 6 deletions test/runtests.jl
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@@ -1,9 +1,13 @@
#using DynamicApproximations
using Base.Test

include("quadratic_polynomials.jl")
include("quadratic_forms.jl")
include("piecewise_quadratics.jl")
include("transition_costs.jl")
include("discrete_transition_costs.jl")
include("find_optimal_fit.jl")
include(joinpath(Pkg.dir("DynamicApproximations"),"src","dev.jl"))

@testset "All Tests" begin
include("quadratic_polynomials.jl")
include("quadratic_forms.jl")
include("piecewise_quadratics.jl")
include("transition_costs.jl")
include("discrete_transition_costs.jl")
include("find_optimal_fit.jl")
end
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