func MakeData(M, N, P int, randomData, diagonal bool) (A, B, C *matrix.FloatMatrix) {
if diagonal && M != N {
diagonal = false
fmt.Printf("cannot make diagonal if B.rows != B.cols\n")
}
if randomData {
A = matrix.FloatNormal(M, P)
if diagonal {
d := matrix.FloatNormal(P, 1)
B := matrix.FloatDiagonal(P, 0.0)
B.SetIndexesFromArray(d.FloatArray(), matrix.DiagonalIndexes(B)...)
} else {
B = matrix.FloatNormal(P, N)
}
} else {
A = matrix.FloatWithValue(M, P, 1.0)
if diagonal {
B = matrix.FloatDiagonal(P, 1.0)
} else {
B = matrix.FloatWithValue(P, N, 1.0)
}
}
C = matrix.FloatZeros(M, N)
return
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
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}}
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 := At.Times(A)
q := At.Times(b).Scale(-1.0)
dims := sets.NewDimensionSet("l", "q", "s")
dims.Set("l", []int{n})
dims.Set("q", []int{n + 1})
var solopts cvx.SolverOptions
solopts.MaxIter = 20
solopts.ShowProgress = true
if maxIter > 0 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.ConeQp(P, q, G, h, nil, nil, dims, &solopts, nil)
if err == nil {
x := sol.Result.At("x")[0]
s := sol.Result.At("s")[0]
z := sol.Result.At("z")[0]
fmt.Printf("Optimal\n")
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
fmt.Printf("s=\n%v\n", s.ToString("%.9f"))
fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, s, z)
}
}
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 (p *floorPlan) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {
f, Df, err = p.F1(x)
x17 := matrix.FloatVector(x.FloatArray()[17:])
tmp := matrix.Div(p.Amin, matrix.Pow(x17, 3.0))
tmp = matrix.Mul(z, tmp).Scale(2.0)
diag := matrix.FloatDiagonal(5, tmp.FloatArray()...)
H = matrix.FloatZeros(22, 22)
H.SetSubMatrix(17, 17, diag)
return
}
func (p *floorPlan) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
err = nil
mn := x.Min(-1, -2, -3, -4, -5)
if mn <= 0.0 {
f, Df = nil, nil
return
}
zeros := matrix.FloatZeros(5, 12)
dk1 := matrix.FloatDiagonal(5, -1.0)
dk2 := matrix.FloatZeros(5, 5)
x17 := matrix.FloatVector(x.FloatArray()[17:])
// -( Amin ./ (x17 .* x17) )
diag := matrix.Div(p.Amin, matrix.Mul(x17, x17)).Scale(-1.0)
dk2.SetIndexesFromArray(diag.FloatArray(), matrix.MakeDiagonalSet(5)...)
Df, _ = matrix.FloatMatrixStacked(matrix.StackRight, zeros, dk1, dk2)
x12 := matrix.FloatVector(x.FloatArray()[12:17])
// f = -x[12:17] + div(Amin, x[17:]) == div(Amin, x[17:]) - x[12:17]
f = matrix.Minus(matrix.Div(p.Amin, x17), x12)
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 main() {
Sdata := [][]float64{
[]float64{4e-2, 6e-3, -4e-3, 0.0},
[]float64{6e-3, 1e-2, 0.0, 0.0},
[]float64{-4e-3, 0.0, 2.5e-3, 0.0},
[]float64{0.0, 0.0, 0.0, 0.0}}
pbar := matrix.FloatVector([]float64{.12, .10, .07, .03})
S := matrix.FloatMatrixFromTable(Sdata)
n := pbar.Rows()
G := matrix.FloatDiagonal(n, -1.0)
h := matrix.FloatZeros(n, 1)
A := matrix.FloatWithValue(1, n, 1.0)
b := matrix.FloatNew(1, 1, []float64{1.0})
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
mu := 1.0
Smu := matrix.Scale(S, mu)
pbarNeg := matrix.Scale(pbar, -1.0)
fmt.Printf("Smu=\n%v\n", Smu.String())
fmt.Printf("-pbar=\n%v\n", pbarNeg.String())
sol, err := cvx.Qp(Smu, pbarNeg, G, h, A, b, &solopts, nil)
fmt.Printf("status: %v\n", err)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
ret := blas.DotFloat(x, pbar)
risk := math.Sqrt(blas.DotFloat(x, S.Times(x)))
fmt.Printf("ret=%.3f, risk=%.3f\n", ret, risk)
fmt.Printf("x=\n%v\n", x)
}
}
func main() {
flag.Parse()
m := len(udata)
nvars := 2 * m
u := matrix.FloatVector(udata[:m])
y := matrix.FloatVector(ydata[:m])
// minimize (1/2) * || yhat - y ||_2^2
// subject to yhat[j] >= yhat[i] + g[i]' * (u[j] - u[i]), j, i = 0,...,m-1
//
// Variables yhat (m), g (m).
P := matrix.FloatZeros(nvars, nvars)
// set m first diagonal indexes to 1.0
//P.SetIndexes(1.0, matrix.DiagonalIndexes(P)[:m]...)
P.Diag().SubMatrix(0, 0, 1, m).SetIndexes(1.0)
q := matrix.FloatZeros(nvars, 1)
q.SubMatrix(0, 0, y.NumElements(), 1).Plus(matrix.Scale(y, -1.0))
// m blocks (i = 0,...,m-1) of linear inequalities
//
// yhat[i] + g[i]' * (u[j] - u[i]) <= yhat[j], j = 0,...,m-1.
G := matrix.FloatZeros(m*m, nvars)
I := matrix.FloatDiagonal(m, 1.0)
for i := 0; i < m; i++ {
// coefficients of yhat[i] (column i)
//G.Set(1.0, matrix.ColumnIndexes(G, i)[i*m:(i+1)*m]...)
column(G, i).SetIndexes(1.0)
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
//rows := matrix.Indexes(i*m, (i+1)*m)
//G.SetAtColumnArray(m+i, rows, matrix.Add(u, -u.GetIndex(i)).FloatArray())
// coefficients of gi[i] (column i, rows i*m ... (i+1)*m)
// from column m+i staring at row i*m select m rows and one column
G.SubMatrix(i*m, m+i, m, 1).Plus(matrix.Add(u, -u.GetIndex(i)))
// coeffients of yhat[i]) from rows i*m ... (i+1)*m, cols 0 ... m
//G.SetSubMatrix(i*m, 0, matrix.Minus(G.GetSubMatrix(i*m, 0, m, m), I))
G.SubMatrix(i*m, 0, m, m).Minus(I)
}
h := matrix.FloatZeros(m*m, 1)
var A, b *matrix.FloatMatrix = nil, nil
var solopts cvx.SolverOptions
solopts.ShowProgress = true
solopts.KKTSolverName = solver
sol, err := cvx.Qp(P, q, G, h, A, b, &solopts, nil)
if err != nil {
fmt.Printf("error: %v\n", err)
return
}
if sol != nil && sol.Status != cvx.Optimal {
fmt.Printf("status not optimal\n")
return
}
x := sol.Result.At("x")[0]
//yhat := matrix.FloatVector(x.FloatArray()[:m])
//g := matrix.FloatVector(x.FloatArray()[m:])
yhat := x.SubMatrix(0, 0, m, 1).Copy()
g := x.SubMatrix(m, 0).Copy()
rangeFunc := func(n int) []float64 {
r := make([]float64, 0)
for i := 0; i < n; i++ {
r = append(r, float64(i)*2.2/float64(n))
}
return r
}
ts := rangeFunc(1000)
fitFunc := func(points []float64) []float64 {
res := make([]float64, len(points))
for k, t := range points {
res[k] = matrix.Plus(yhat, matrix.Mul(g, matrix.Scale(u, -1.0).Add(t))).Max()
}
return res
}
fs := fitFunc(ts)
plotData("cvxfit.png", u.FloatArray(), y.FloatArray(), ts, fs)
}
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()
}
}
}