func (p *acenterProg) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
f, Df, err = p.F1(x)
u := matrix.Pow(x, 2.0).Scale(-1.0).Add(1.0)
z0 := z.GetIndex(0)
u2 := matrix.Pow(u, 2.0)
hd := matrix.Div(matrix.Add(u2, 1.0), u2).Scale(2 * z0)
H = matrix.FloatDiagonal(hd.NumElements(), hd.FloatArray()...)
return
}
func TestInvLower(t *testing.T) {
N := 36
nb := 12
A := matrix.FloatUniformSymmetric(N, matrix.Lower)
I := matrix.FloatDiagonal(N, 1.0)
I0 := matrix.FloatZeros(N, N)
A0 := A.Copy()
// A0 = A.-1
InverseTrm(A0, LOWER, 0)
Mult(I0, A, A0, 1.0, 0.0, NOTRANS)
I0.Minus(I)
nrm := NormP(I0, NORM_ONE)
t.Logf("unblk: ||I - A*A.-1||_1 : %e\n", nrm)
A0 = A.Copy()
// A0 = A.-1
InverseTrm(A0, LOWER, nb)
Mult(I0, A, A0, 1.0, 0.0, NOTRANS)
I0.Minus(I)
nrm = NormP(I0, NORM_ONE)
t.Logf("blk: ||I - A*A.-1||_1 : %e\n", nrm)
}
func TestConeQp(t *testing.T) {
adata := [][]float64{
[]float64{0.3, -0.4, -0.2, -0.4, 1.3},
[]float64{0.6, 1.2, -1.7, 0.3, -0.3},
[]float64{-0.3, 0.0, 0.6, -1.2, -2.0}}
// reference values from cvxopt coneqp.py
xref := []float64{0.72558318685981904, 0.61806264311119252, 0.30253527966423444}
sref := []float64{
0.72558318685981904, 0.61806264311119263,
0.30253527966423449, 1.00000000000041678,
-0.72558318686012169, -0.61806264311145032,
-0.30253527966436067}
zref := []float64{
0.00000003332583626, 0.00000005116586239,
0.00000009993673262, 0.56869648433154019,
0.41264857754144563, 0.35149286573190930,
0.17201618570052318}
A := matrix.FloatMatrixFromTable(adata, matrix.ColumnOrder)
b := matrix.FloatVector([]float64{1.5, 0.0, -1.2, -0.7, 0.0})
_, n := A.Size()
N := n + 1 + n
h := matrix.FloatZeros(N, 1)
h.SetIndex(n, 1.0)
I0 := matrix.FloatDiagonal(n, -1.0)
I1 := matrix.FloatIdentity(n)
G, _ := matrix.FloatMatrixStacked(matrix.StackDown, I0, matrix.FloatZeros(1, n), I1)
At := A.Transpose()
P := matrix.Times(At, A)
q := matrix.Times(At, b).Scale(-1.0)
dims := sets.DSetNew("l", "q", "s")
dims.Set("l", []int{n})
dims.Set("q", []int{n + 1})
var solopts SolverOptions
solopts.MaxIter = 10
solopts.ShowProgress = false
sol, err := ConeQp(P, q, G, h, nil, nil, dims, &solopts, nil)
if err == nil {
fail := false
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
t.Logf("Optimal\n")
t.Logf("x=\n%v\n", x.ToString("%.9f"))
t.Logf("s=\n%v\n", s.ToString("%.9f"))
t.Logf("z=\n%v\n", z.ToString("%.9f"))
xe, _ := nrmError(matrix.FloatVector(xref), x)
if xe > TOL {
t.Logf("x differs [%.3e] from exepted too much.", xe)
fail = true
}
se, _ := nrmError(matrix.FloatVector(sref), s)
if se > TOL {
t.Logf("s differs [%.3e] from exepted too much.", se)
fail = true
}
ze, _ := nrmError(matrix.FloatVector(zref), z)
if ze > TOL {
t.Logf("z differs [%.3e] from exepted too much.", ze)
fail = true
}
if fail {
t.Fail()
}
}
}