diff --git a/src/TestFunctions.jl b/src/TestFunctions.jl
index 6e444a769eb44973ba1642b1461cf7c50e9824b9..120542cadd252cdd557f87f5cd0e00694072f0f0 100644
--- a/src/TestFunctions.jl
+++ b/src/TestFunctions.jl
@@ -49,8 +49,8 @@ end
Evaluates the Rosenbrock function.
"""
function rosenbrock!(fval::Vector{Float64}, x::Vector{Float64})
- fval[1] = ONE-x[1]
- fval[2] = TEN*(x[2]-fval[1]*fval[1])
+ @inbounds fval[1] = ONE-x[1]
+ @inbounds fval[2] = TEN*(x[2]-fval[1]*fval[1])
end
"""
@@ -59,10 +59,10 @@ end
Evaluates the jacobian matrix of the Rosenbrock function.
"""
function rosenbrock!(fjac::Matrix{Float64}, x::Vector{Float64})
- fjac[1,1] = -ONE
- fjac[1,2] = ZERO
- fjac[2,1] = -TWENTY*x[1]
- fjac[2,2] = TEN
+ @inbounds fjac[1,1] = -ONE
+ @inbounds fjac[1,2] = ZERO
+ @inbounds fjac[2,1] = -TWENTY*x[1]
+ @inbounds fjac[2,2] = TEN
end
"""
@@ -75,24 +75,24 @@ function rosenbrock()
end
function powell1!(fval::Vector{Float64}, x::Vector{Float64})
- fval[1] = x[1]+TEN*x[2]
- fval[2] = sqrt(FIVE)*(x[3]-x[4])
- tmp = x[2]-TWO*x[3]
- fval[3] = tmp*tmp
- tmp = x[1]-x[4]
- fval[4] = sqrt(TEN)*tmp*tmp
+ @inbounds fval[1] = x[1]+TEN*x[2]
+ @inbounds fval[2] = sqrt(FIVE)*(x[3]-x[4])
+ @inbounds tmp = x[2]-TWO*x[3]
+ @inbounds fval[3] = tmp*tmp
+ @inbounds tmp = x[1]-x[4]
+ @inbounds fval[4] = sqrt(TEN)*tmp*tmp
end
function powell1!(fjac::Matrix{Float64}, x::Vector{Float64})
fill!(fjac, 0.0)
- fjac[1,1] = ONE
- fjac[1,2] = TEN
- fjac[2,3] = sqrt(FIVE)
- fjac[2,4] = -fjac[2,3]
- fjac[3,2] = TWO*(x[2]-TWO*x[3])
- fjac[3,3] = -TWO*fjac[3,2]
- fjac[4,1] = TWO*sqrt(TEN)*(x[1]-x[4])
- fjac[4,4] = -fjac[4,1]
+ @inbounds fjac[1,1] = ONE
+ @inbounds fjac[1,2] = TEN
+ @inbounds fjac[2,3] = sqrt(FIVE)
+ @inbounds fjac[2,4] = -fjac[2,3]
+ @inbounds fjac[3,2] = TWO*(x[2]-TWO*x[3])
+ @inbounds fjac[3,3] = -TWO*fjac[3,2]
+ @inbounds fjac[4,1] = TWO*sqrt(TEN)*(x[1]-x[4])
+ @inbounds fjac[4,4] = -fjac[4,1]
end
function powell1()
@@ -100,15 +100,15 @@ function powell1()
end
function powell2!(fval::Vector{Float64}, x::Vector{Float64})
- fval[1] = C1*x[1]*x[2]-ONE
- fval[2] = exp(-x[1])+exp(-x[2])-C2
+ @inbounds fval[1] = C1*x[1]*x[2]-ONE
+ @inbounds fval[2] = exp(-x[1])+exp(-x[2])-C2
end
function powell2!(fjac::Matrix{Float64}, x::Vector{Float64})
- fjac[1,1] = C1*x[2]
- fjac[1,2] = C1*x[1]
- fjac[2,1] = -exp(-x[1])
- fjac[2,2] = -exp(-x[2])
+ @inbounds fjac[1,1] = C1*x[2]
+ @inbounds fjac[1,2] = C1*x[1]
+ @inbounds fjac[2,1] = -exp(-x[1])
+ @inbounds fjac[2,2] = -exp(-x[2])
end
function powell2()
@@ -116,28 +116,28 @@ function powell2()
end
function wood!(fval::Vector{Float64}, x::Vector{Float64})
- tmp1 = x[2]-x[1]*x[1]
- tmp2 = x[4]-x[3]*x[3]
- fval[1] = -C3*x[1]*tmp1-(ONE-x[1])
- fval[2] = C3*tmp1+C4*(x[2]-1.0)+C5*(x[4]-ONE)
- fval[3] = -C6*x[3]*tmp2-(ONE-x[3])
- fval[4] = C6*tmp2+C4*(x[4]-ONE)+C5*(x[2]-ONE)
+ @inbounds tmp1 = x[2]-x[1]*x[1]
+ @inbounds tmp2 = x[4]-x[3]*x[3]
+ @inbounds fval[1] = -C3*x[1]*tmp1-(ONE-x[1])
+ @inbounds fval[2] = C3*tmp1+C4*(x[2]-1.0)+C5*(x[4]-ONE)
+ @inbounds fval[3] = -C6*x[3]*tmp2-(ONE-x[3])
+ @inbounds fval[4] = C6*tmp2+C4*(x[4]-ONE)+C5*(x[2]-ONE)
end
function wood!(fjac::Matrix{Float64}, x::Vector{Float64})
fill!(fjac, ZERO)
- tmp1 = x[2]-THREE*x[1]*x[1]
- tmp2 = x[4]-THREE*x[3]*x[3]
- fjac[1,1] = -C3*tmp1+ONE
- fjac[1,2] = -C3*x[1]
- fjac[2,1] = -TWO*C3*x[1]
- fjac[2,2] = C3+C4
- fjac[2,4] = C5
- fjac[3,3] = -C6*tmp2+ONE
- fjac[3,4] = -C6*x[3]
- fjac[4,2] = C5
- fjac[4,3] = -TWO*C6*x[3]
- fjac[4,4] = C6+C4
+ @inbounds tmp1 = x[2]-THREE*x[1]*x[1]
+ @inbounds tmp2 = x[4]-THREE*x[3]*x[3]
+ @inbounds fjac[1,1] = -C3*tmp1+ONE
+ @inbounds fjac[1,2] = -C3*x[1]
+ @inbounds fjac[2,1] = -TWO*C3*x[1]
+ @inbounds fjac[2,2] = C3+C4
+ @inbounds fjac[2,4] = C5
+ @inbounds fjac[3,3] = -C6*tmp2+ONE
+ @inbounds fjac[3,4] = -C6*x[3]
+ @inbounds fjac[4,2] = C5
+ @inbounds fjac[4,3] = -TWO*C6*x[3]
+ @inbounds fjac[4,4] = C6+C4
end
function wood()
@@ -145,32 +145,32 @@ function wood()
end
function helicalvalley!(fval::Vector{Float64}, x::Vector{Float64})
- tmp1 = sign(C7, x[2])
+ @inbounds tmp1 = sign(C7, x[2])
if x[1]>ZERO
- tmp1 = atan(x[2]/x[1])/TPI
+ @inbounds tmp1 = atan(x[2]/x[1])/TPI
end
if x[1]<ZERO
- tmp1 = atan(x[2]/x[1])/TPI+C8
+ @inbounds tmp1 = atan(x[2]/x[1])/TPI+C8
end
- tmp2 = sqrt(x[1]*x[1]+x[2]*x[2])
- fval[1] = TEN*(x[3]-TEN*tmp1)
- fval[2] = TEN*(tmp2-ONE)
- fval[3] = x[3]
+ @inbounds tmp2 = sqrt(x[1]*x[1]+x[2]*x[2])
+ @inbounds fval[1] = TEN*(x[3]-TEN*tmp1)
+ @inbounds fval[2] = TEN*(tmp2-ONE)
+ @inbounds fval[3] = x[3]
end
function helicalvalley!(fjac::Matrix{Float64}, x::Vector{Float64})
- tmp = x[1]*x[1]+x[2]*x[2]
+ @inbounds tmp = x[1]*x[1]+x[2]*x[2]
tmp1 = TPI*tmp
tmp2 = sqrt(tmp)
- fjac[1,1] = HUNDRD*x[2]/tmp1
- fjac[1,2] = -HUNDRD*x[1]/tmp1
- fjac[1,3] = TEN
- fjac[2,1] = TEN*x[1]/tmp2
- fjac[2,2] = TEN*x[2]/tmp2
- fjac[2,3] = ZERO
- fjac[3,1] = ZERO
- fjac[3,2] = ZERO
- fjac[3,3] = ONE
+ @inbounds fjac[1,1] = HUNDRD*x[2]/tmp1
+ @inbounds fjac[1,2] = -HUNDRD*x[1]/tmp1
+ @inbounds fjac[1,3] = TEN
+ @inbounds fjac[2,1] = TEN*x[1]/tmp2
+ @inbounds fjac[2,2] = TEN*x[2]/tmp2
+ @inbounds fjac[2,3] = ZERO
+ @inbounds fjac[3,1] = ZERO
+ @inbounds fjac[3,2] = ZERO
+ @inbounds fjac[3,3] = ONE
end
function helicalvalley()
@@ -185,26 +185,26 @@ function watson!(fval::Vector{Float64}, x::Vector{Float64})
sum1 = ZERO
tmp = ONE
for j=2:n
- sum1 += Float64(j-1)*tmp*x[j]
+ @inbounds sum1 += Float64(j-1)*tmp*x[j]
tmp *= ti
end
sum2 = ZERO
tmp = ONE
for j=1:n
- sum2 += tmp*x[j]
+ @inbounds sum2 += tmp*x[j]
tmp *= ti
end
tmp1 = sum1-sum2*sum2-ONE
tmp2 = TWO*ti*sum2
tmp = ONE/ti
for k=1:n
- fval[k] += tmp*(Float64(k-1)-tmp2)*tmp1
+ @inbounds fval[k] += tmp*(Float64(k-1)-tmp2)*tmp1
tmp *= ti
end
end
- tmp = x[2]-x[1]*x[1]-ONE
- fval[1] += x[1]*(ONE-TWO*tmp)
- fval[2] += tmp
+ @inbounds tmp = x[2]-x[1]*x[1]-ONE
+ @inbounds fval[1] += x[1]*(ONE-TWO*tmp)
+ @inbounds fval[2] += tmp
end
function watson!(fjac::Matrix{Float64}, x::Vector{Float64})
@@ -215,13 +215,13 @@ function watson!(fjac::Matrix{Float64}, x::Vector{Float64})
sum1 = ZERO
tmp = ONE
for j=2:n
- sum1 += Float64(j-1)*tmp*x[j]
+ @inbounds sum1 += Float64(j-1)*tmp*x[j]
tmp *= ti
end
sum2 = ZERO
tmp = ONE
for j=1:n
- sum2 += tmp*x[j]
+ @inbounds sum2 += tmp*x[j]
tmp *= ti
end
tmp1 = TWO*(sum1-sum2*sum2-ONE)
@@ -231,18 +231,18 @@ function watson!(fjac::Matrix{Float64}, x::Vector{Float64})
for k=1:n
tj = tk
for j=k:n
- fjac[k,j] += tj*((Float64(k-1)/ti-tmp2)*(Float64(j-1)/ti-tmp2)-tmp1)
+ @inbounds fjac[k,j] += tj*((Float64(k-1)/ti-tmp2)*(Float64(j-1)/ti-tmp2)-tmp1)
tj *= ti
end
tk *= tmp
end
end
- fjac[1,1] = fjac[1,1]+SIX*x[1]*x[1]-TWO*x[2]+THREE
- fjac[1,2] = fjac[1,2]-TWO*x[1]
- fjac[2,2] = fjac[2,2]+ONE
+ @inbounds fjac[1,1] = fjac[1,1]+SIX*x[1]*x[1]-TWO*x[2]+THREE
+ @inbounds fjac[1,2] = fjac[1,2]-TWO*x[1]
+ @inbounds fjac[2,2] = fjac[2,2]+ONE
for k=1:n
for j=k:n
- fjac[j,k] = fjac[k,j]
+ @inbounds fjac[j,k] = fjac[k,j]
end
end
end
@@ -256,10 +256,10 @@ function chebyquad!(fval::Vector{Float64}, x::Vector{Float64})
fill!(fval, ZERO)
for j=1:n
tmp1 = ONE
- tmp2 = TWO*x[j]-ONE
+ @inbounds tmp2 = TWO*x[j]-ONE
tmp = TWO*tmp2
for i=1:n
- fval[i] += tmp2
+ @inbounds fval[i] += tmp2
ti = tmp*tmp2-tmp1
tmp1 = tmp2
tmp2 = ti
@@ -268,9 +268,9 @@ function chebyquad!(fval::Vector{Float64}, x::Vector{Float64})
tk = ONE/Float64(n)
iev = -1
for k=1:n
- fval[k] *= tk
+ @inbounds fval[k] *= tk
if iev>0
- fval[k] += ONE/(Float64(k)^2-ONE)
+ @inbounds fval[k] += ONE/(Float64(k)^2-ONE)
end
iev = -iev
end
@@ -281,12 +281,12 @@ function chebyquad!(fjac::Matrix{Float64}, x::Vector{Float64})
tk = ONE/Float64(n)
for j=1:n
tmp1 = ONE
- tmp2 = TWO*x[j]-ONE
+ @inbounds tmp2 = TWO*x[j]-ONE
tmp = TWO*tmp2
tmp3 = ZERO
tmp4 = TWO
for k=1:n
- fjac[k,j] = tk*tmp4
+ @inbounds fjac[k,j] = tk*tmp4
ti = FOUR*tmp2+tmp*tmp4-tmp3
tmp3 = tmp4
tmp4 = ti
@@ -301,7 +301,7 @@ function chebyquad(n::Int)
h = ONE/Float64(n+1)
x = Vector{Float64}(undef,n)
for j=1:n
- x[j] = Float64(j)*h
+ @inbounds x[j] = Float64(j)*h
end
return x
end
@@ -310,38 +310,38 @@ function brown!(fval::Vector{Float64}, x::Vector{Float64})
n = length(fval)
sum = -Float64(n+1)
prod = ONE
- for j=1:n
+ @inbounds for j=1:n
sum += x[j]
prod *= x[j]
end
for k=1:n-1
- fval[k]=x[k]+sum
+ @inbounds fval[k]=x[k]+sum
end
- fval[n] = prod-ONE
+ @inbounds fval[n] = prod-ONE
end
function brown!(fjac::Matrix{Float64}, x::Vector{Float64})
n = length(x)
prod = ONE
for j=1:n
- prod *= x[j]
+ @inbounds prod *= x[j]
for k=1:n
- fjac[k,j] = ONE
+ @inbounds fjac[k,j] = ONE
end
- fjac[j,j] = TWO
+ @inbounds fjac[j,j] = TWO
end
for j=1:n
- tmp = x[j]
+ @inbounds tmp = x[j]
if abs(tmp)<eps(Float64)
tmp = ONE
prod = ONE
for k=1:n
if k!=j
- prod *= x[k]
+ @inbounds prod *= x[k]
end
end
end
- fjac[n,j] = prod/tmp
+ @inbounds fjac[n,j] = prod/tmp
end
end
@@ -359,13 +359,13 @@ function discreteboundaryvalue!(fval::Vector{Float64}, x::Vector{Float64})
tmp = (x[k]+Float64(k)*h+ONE)^3
tmp1 = ZERO
if k!=1
- tmp1 = x[k-1]
+ @inbounds tmp1 = x[k-1]
end
tmp2 = ZERO
if k!=n
- tmp2 = x[k+1]
+ @inbounds tmp2 = x[k+1]
end
- fval[k] = TWO*x[k]-tmp1-tmp2+tmp*hh/TWO
+ @inbounds fval[k] = TWO*x[k]-tmp1-tmp2+tmp*hh/TWO
end
end
@@ -375,13 +375,13 @@ function discreteboundaryvalue!(fjac::Matrix{Float64}, x::Vector{Float64})
hh = h*h
fill!(fjac, ZERO)
for k=1:n
- tmp = THREE*(x[k]+Float64(k)*h+ONE)^2
- fjac[k,k] = TWO+tmp*hh/TWO
+ @inbounds tmp = THREE*(x[k]+Float64(k)*h+ONE)^2
+ @inbounds fjac[k,k] = TWO+tmp*hh/TWO
if k!=1
- fjac[k,k-1] = -ONE
+ @inbounds fjac[k,k-1] = -ONE
end
if k!=n
- fjac[k,k+1] = -ONE
+ @inbounds fjac[k,k+1] = -ONE
end
end
end
@@ -391,7 +391,7 @@ function discreteboundaryvalue(n::Int)
x = Vector{Float64}(undef,n)
for j=1:n
tj = Float64(j)*h
- x[j] = tj*(tj-ONE)
+ @inbounds x[j] = tj*(tj-ONE)
end
return x
end
@@ -404,7 +404,7 @@ function discreteintegralequation!(fval::Vector{Float64}, x::Vector{Float64})
sum1 = ZERO
for j=1:k
tj = Float64(j)*h
- tmp = (x[j]+tj+ONE)^3
+ @inbounds tmp = (x[j]+tj+ONE)^3
sum1 += tj*tmp
end
sum2 = ZERO
@@ -412,11 +412,11 @@ function discreteintegralequation!(fval::Vector{Float64}, x::Vector{Float64})
if n>=kp1
for j=kp1:n
tj = Float64(j)*h
- tmp = (x[j]+tj+ONE)^3
+ @inbounds tmp = (x[j]+tj+ONE)^3
sum2 += (ONE-tj)*tmp
end
end
- fval[k] = x[k] + h*((ONE-tk)*sum1+tk*sum2)/TWO
+ @inbounds fval[k] = x[k] + h*((ONE-tk)*sum1+tk*sum2)/TWO
end
end
@@ -427,10 +427,10 @@ function discreteintegralequation!(fjac::Matrix{Float64}, x::Vector{Float64})
tk = Float64(k)*h
for j=1:n
tj = Float64(j)*h
- tmp = THREE*(x[j]+tj+ONE)^2
- fjac[k,j] = h*min(tj*(ONE-tk),tk*(ONE-tj))*tmp/TWO
+ @inbounds tmp = THREE*(x[j]+tj+ONE)^2
+ @inbounds fjac[k,j] = h*min(tj*(ONE-tk),tk*(ONE-tj))*tmp/TWO
end
- fjac[k,k] += ONE
+ @inbounds fjac[k,k] += ONE
end
end
@@ -440,22 +440,22 @@ function trigonometric!(fval::Vector{Float64}, x::Vector{Float64})
n = length(fval)
sum = ZERO
for j=1:n
- fval[j] = cos(x[j])
- sum += fval[j]
+ @inbounds fval[j] = cos(x[j])
+ @inbounds sum += fval[j]
end
for k=1:n
- fval[k] = Float64(n+k)-sin(x[k])-sum-Float64(k)*fval[k]
+ @inbounds fval[k] = Float64(n+k)-sin(x[k])-sum-Float64(k)*fval[k]
end
end
function trigonometric!(fjac::Matrix{Float64}, x::Vector{Float64})
n = length(x)
for j=1:n
- tmp = sin(x[j])
+ @inbounds tmp = sin(x[j])
for k=1:n
- fjac[k,j] = tmp
+ @inbounds fjac[k,j] = tmp
end
- fjac[j,j] = Float64(j+1)*tmp-cos(x[j])
+ @inbounds fjac[j,j] = Float64(j+1)*tmp-cos(x[j])
end
end
@@ -469,11 +469,11 @@ function variablydimensioned!(fval::Vector{Float64}, x::Vector{Float64})
n = length(fval)
sum = ZERO
for j=1:n
- sum += Float64(j)*(x[j]-ONE)
+ @inbounds sum += Float64(j)*(x[j]-ONE)
end
tmp = sum*(ONE+TWO*sum*sum)
for k=1:n
- fval[k] = x[k]-ONE+Float64(k)*tmp
+ @inbounds fval[k] = x[k]-ONE+Float64(k)*tmp
end
end
@@ -481,15 +481,15 @@ function variablydimensioned!(fjac::Matrix{Float64}, x::Vector{Float64})
n = length(x)
sum = ZERO
for j=1:n
- sum += Float64(j)*(x[j]-ONE)
+ @inbounds sum += Float64(j)*(x[j]-ONE)
end
tmp = ONE+SIX*sum*sum
for k=1:n
for j=1:n
- fjac[k,j] = Float64(k*j)*tmp
- fjac[j,k] = fjac[k,j]
+ @inbounds fjac[k,j] = Float64(k*j)*tmp
+ @inbounds fjac[j,k] = fjac[k,j]
end
- fjac[k,k] += ONE
+ @inbounds fjac[k,k] += ONE
end
end
@@ -497,7 +497,7 @@ function variablydimensioned(n::Int)
h = ONE/Float64(n)
x = Vector{Float64}(undef,n)
for j=1:n
- x[j] = ONE-Float64(j)*h
+ @inbounds x[j] = ONE-Float64(j)*h
end
return x
end
@@ -505,16 +505,16 @@ end
function broydentridiagonal!(fval::Vector{Float64}, x::Vector{Float64})
n = length(fval)
for k=1:n
- tmp = (THREE-TWO*x[k])*x[k]
+ @inbounds tmp = (THREE-TWO*x[k])*x[k]
tmp1 = ZERO
if k!=1
- tmp1 = x[k-1]
+ @inbounds tmp1 = x[k-1]
end
tmp2 = ZERO
if k!=n
- tmp2 = x[k+1]
+ @inbounds tmp2 = x[k+1]
end
- fval[k] = tmp-tmp1-TWO*tmp2+ONE
+ @inbounds fval[k] = tmp-tmp1-TWO*tmp2+ONE
end
end
@@ -522,12 +522,12 @@ function broydentridiagonal!(fjac::Matrix{Float64}, x::Vector{Float64})
n = length(x)
fill!(fjac, ZERO)
for k=1:n
- fjac[k,k] = THREE-FOUR*x[k]
+ @inbounds fjac[k,k] = THREE-FOUR*x[k]
if k!=1
- fjac[k,k-1] = -ONE
+ @inbounds fjac[k,k-1] = -ONE
end
if k!=n
- fjac[k,k+1] = -TWO
+ @inbounds fjac[k,k+1] = -TWO
end
end
end
@@ -548,10 +548,10 @@ function broydenbanded!(fval::Vector{Float64}, x::Vector{Float64})
tmp = ZERO
for j=k1:k2
if j!=k
- tmp += x[j]*(ONE+x[j])
+ @inbounds tmp += x[j]*(ONE+x[j])
end
end
- fval[k] = x[k]*(TWO+FIVE*x[k]*x[k])+ONE-tmp
+ @inbounds fval[k] = x[k]*(TWO+FIVE*x[k]*x[k])+ONE-tmp
end
end
@@ -565,10 +565,10 @@ function broydenbanded!(fjac::Matrix{Float64}, x::Vector{Float64})
k2 = min(k+mu,n)
for j=k1:k2
if j!=k
- fjac[k,j] = -(ONE+TWO*x[j])
+ @inbounds fjac[k,j] = -(ONE+TWO*x[j])
end
end
- fjac[k,k] = TWO+FIFTN*x[k]*x[k]
+ @inbounds fjac[k,k] = TWO+FIFTN*x[k]*x[k]
end
end