func TestExampleModel(t *testing.T) {
//badly conditioned Hessian leads to zig-zagging of the steepest descent
//algorithm
condNo := 100.0
optSol := mat.Vec{1, 2}
A := mat.NewFromArray([]float64{condNo, 0, 0, 1}, true, 2, 2)
b := mat.Vec{-2 * optSol[0] * condNo, -2 * optSol[1]}
c := -0.5 * mat.Dot(b, optSol)
//define objective function
fun := opt.NewQuadratic(A, b, c)
//set inital solution estimate
sol := NewSolution(mat.NewVec(2))
//set termination parameters
p := NewParams()
p.IterMax = 5
//Use steepest descent solver to solve the model
result := NewSteepestDescent().Solve(fun, sol, p, NewDisplay(1))
fmt.Println("x =", result.X)
//should be [1,2], but because of the bad conditioning we made little
//progress in the second dimension
//Use a BFGS solver to refine the result:
result = NewLBFGS().Solve(fun, result.Solution, p, NewDisplay(1))
fmt.Println("x =", result.X)
}
func TestQuadratic(t *testing.T) {
mat.Register(cops)
n := 10
xStar := mat.NewVec(n)
xStar.AddSc(1)
A := mat.RandN(n)
At := A.TrView()
AtA := mat.New(n)
AtA.Mul(At, A)
bTmp := mat.NewVec(n)
bTmp.Apply(A, xStar)
b := mat.NewVec(n)
b.Apply(At, bTmp)
b.Scal(-2)
c := bTmp.Nrm2Sq()
//Define input arguments
obj := opt.NewQuadratic(AtA, b, c)
p := NewParams()
sol := NewSolution(mat.NewVec(n))
//Steepest descent with armijo
stDesc := NewSteepestDescent()
res1 := stDesc.Solve(obj, sol, p, NewDisplay(100))
t.Log(res1.ObjX, res1.FunEvals, res1.GradEvals, res1.Status)
//Steepest descent with Quadratic
stDesc.LineSearch = uni.DerivWrapper{uni.NewQuadratic()}
res2 := stDesc.Solve(obj, sol, p, NewDisplay(100))
t.Log(res2.ObjX, res2.FunEvals, res2.GradEvals, res2.Status)
//LBFGS with armijo
lbfgs := NewLBFGS()
res3 := lbfgs.Solve(obj, sol, p, NewDisplay(10))
t.Log(res3.ObjX, res3.FunEvals, res3.GradEvals, res3.Status)
//constrained problems (constraints described as projection)
projGrad := NewProjGrad()
res4 := projGrad.Solve(obj, opt.RealPlus{}, sol, p, NewDisplay(100))
t.Log(res4.ObjX, res4.FunEvals, res4.GradEvals, res4.Status)
if math.Abs(res1.ObjX) > 0.01 {
t.Fail()
}
if math.Abs(res2.ObjX) > 0.01 {
t.Fail()
}
if math.Abs(res3.ObjX) > 0.01 {
t.Fail()
}
if math.Abs(res4.ObjX) > 0.01 {
t.Fail()
}
}