func main() {
flag.Parse()
gdata0 := [][]float64{
[]float64{12., 13., 12.},
[]float64{6., -3., -12.},
[]float64{-5., -5., 6.}}
gdata1 := [][]float64{
[]float64{3., 3., -1., 1.},
[]float64{-6., -6., -9., 19.},
[]float64{10., -2., -2., -3.}}
c := matrix.FloatVector([]float64{-2.0, 1.0, 5.0})
g0 := matrix.FloatMatrixFromTable(gdata0, matrix.ColumnOrder)
g1 := matrix.FloatMatrixFromTable(gdata1, matrix.ColumnOrder)
Ghq := sets.FloatSetNew("Gq", "hq")
Ghq.Append("Gq", g0, g1)
h0 := matrix.FloatVector([]float64{-12.0, -3.0, -2.0})
h1 := matrix.FloatVector([]float64{27.0, 0.0, 3.0, -42.0})
Ghq.Append("hq", h0, h1)
var Gl, hl, A, b *matrix.FloatMatrix = nil, nil, nil, nil
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Socp(c, Gl, hl, A, b, Ghq, &solopts, nil, nil)
fmt.Printf("status: %v\n", err)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
for i, m := range sol.Result.At("sq") {
fmt.Printf("sq[%d]=\n%v\n", i, m.ToString("%.9f"))
}
for i, m := range sol.Result.At("zq") {
fmt.Printf("zq[%d]=\n%v\n", i, m.ToString("%.9f"))
}
sq0 := sol.Result.At("sq")[0]
sq1 := sol.Result.At("sq")[1]
zq0 := sol.Result.At("zq")[0]
zq1 := sol.Result.At("zq")[1]
check(x, sq0, sq1, zq0, zq1)
}
}
func main() {
flag.Parse()
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.17f")
}
gdata0 := [][]float64{
[]float64{-7., -11., -11., 3.},
[]float64{7., -18., -18., 8.},
[]float64{-2., -8., -8., 1.}}
gdata1 := [][]float64{
[]float64{-21., -11., 0., -11., 10., 8., 0., 8., 5.},
[]float64{0., 10., 16., 10., -10., -10., 16., -10., 3.},
[]float64{-5., 2., -17., 2., -6., 8., -17., -7., 6.}}
hdata0 := [][]float64{
[]float64{33., -9.},
[]float64{-9., 26.}}
hdata1 := [][]float64{
[]float64{14., 9., 40.},
[]float64{9., 91., 10.},
[]float64{40., 10., 15.}}
g0 := matrix.FloatMatrixFromTable(gdata0, matrix.ColumnOrder)
g1 := matrix.FloatMatrixFromTable(gdata1, matrix.ColumnOrder)
Ghs := sets.FloatSetNew("Gs", "hs")
Ghs.Append("Gs", g0, g1)
h0 := matrix.FloatMatrixFromTable(hdata0, matrix.ColumnOrder)
h1 := matrix.FloatMatrixFromTable(hdata1, matrix.ColumnOrder)
Ghs.Append("hs", h0, h1)
c := matrix.FloatVector([]float64{1.0, -1.0, 1.0})
var Gs, hs, A, b *matrix.FloatMatrix = nil, nil, nil, nil
var solopts cvx.SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = true
if maxIter > -1 {
solopts.MaxIter = maxIter
}
if len(solver) > 0 {
solopts.KKTSolverName = solver
}
sol, err := cvx.Sdp(c, Gs, hs, A, b, Ghs, &solopts, nil, nil)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
for i, m := range sol.Result.At("zs") {
fmt.Printf("zs[%d]=\n%v\n", i, m.ToString("%.9f"))
}
ss0 := sol.Result.At("ss")[0]
ss1 := sol.Result.At("ss")[1]
zs0 := sol.Result.At("zs")[0]
zs1 := sol.Result.At("zs")[1]
check(x, ss0, ss1, zs0, zs1)
} else {
fmt.Printf("status: %v\n", err)
}
checkpnt.Report()
}
func mcsdp(w *matrix.FloatMatrix) (*Solution, error) {
//
// Returns solution x, z to
//
// (primal) minimize sum(x)
// subject to w + diag(x) >= 0
//
// (dual) maximize -tr(w*z)
// subject to diag(z) = 1
// z >= 0.
//
n := w.Rows()
G := &matrixFs{n}
cngrnc := func(r, x *matrix.FloatMatrix, alpha float64) (err error) {
// Congruence transformation
//
// x := alpha * r'*x*r.
//
// r and x are square matrices.
//
err = nil
// tx = matrix(x, (n,n)) is copying and reshaping
// scale diagonal of x by 1/2, (x is (n,n))
tx := x.Copy()
matrix.Reshape(tx, n, n)
tx.Diag().Scale(0.5)
// a := tril(x)*r
// (python: a = +r is really making a copy of r)
a := r.Copy()
err = blas.TrmmFloat(tx, a, 1.0, linalg.OptLeft)
// x := alpha*(a*r' + r*a')
err = blas.Syr2kFloat(r, a, tx, alpha, 0.0, linalg.OptTrans)
// x[:] = tx[:]
tx.CopyTo(x)
return
}
Fkkt := func(W *sets.FloatMatrixSet) (KKTFunc, error) {
// Solve
// -diag(z) = bx
// -diag(x) - inv(rti*rti') * z * inv(rti*rti') = bs
//
// On entry, x and z contain bx and bs.
// On exit, they contain the solution, with z scaled
// (inv(rti)'*z*inv(rti) is returned instead of z).
//
// We first solve
//
// ((rti*rti') .* (rti*rti')) * x = bx - diag(t*bs*t)
//
// and take z = -rti' * (diag(x) + bs) * rti.
var err error = nil
rti := W.At("rti")[0]
// t = rti*rti' as a nonsymmetric matrix.
t := matrix.FloatZeros(n, n)
err = blas.GemmFloat(rti, rti, t, 1.0, 0.0, linalg.OptTransB)
if err != nil {
return nil, err
}
// Cholesky factorization of tsq = t.*t.
tsq := matrix.Mul(t, t)
err = lapack.Potrf(tsq)
if err != nil {
return nil, err
}
f := func(x, y, z *matrix.FloatMatrix) (err error) {
// tbst := t * zs * t = t * bs * t
tbst := z.Copy()
matrix.Reshape(tbst, n, n)
cngrnc(t, tbst, 1.0)
// x := x - diag(tbst) = bx - diag(rti*rti' * bs * rti*rti')
diag := tbst.Diag().Transpose()
x.Minus(diag)
// x := (t.*t)^{-1} * x = (t.*t)^{-1} * (bx - diag(t*bs*t))
err = lapack.Potrs(tsq, x)
// z := z + diag(x) = bs + diag(x)
// z, x are really column vectors here
z.AddIndexes(matrix.MakeIndexSet(0, n*n, n+1), x.FloatArray())
// z := -rti' * z * rti = -rti' * (diag(x) + bs) * rti
cngrnc(rti, z, -1.0)
return nil
}
return f, nil
}
c := matrix.FloatWithValue(n, 1, 1.0)
// initial feasible x: x = 1.0 - min(lmbda(w))
lmbda := matrix.FloatZeros(n, 1)
wp := w.Copy()
lapack.Syevx(wp, lmbda, nil, 0.0, nil, []int{1, 1}, linalg.OptRangeInt)
x0 := matrix.FloatZeros(n, 1).Add(-lmbda.GetAt(0, 0) + 1.0)
s0 := w.Copy()
s0.Diag().Plus(x0.Transpose())
matrix.Reshape(s0, n*n, 1)
// initial feasible z is identity
z0 := matrix.FloatIdentity(n)
matrix.Reshape(z0, n*n, 1)
dims := sets.DSetNew("l", "q", "s")
dims.Set("s", []int{n})
primalstart := sets.FloatSetNew("x", "s")
dualstart := sets.FloatSetNew("z")
primalstart.Set("x", x0)
primalstart.Set("s", s0)
dualstart.Set("z", z0)
var solopts SolverOptions
solopts.MaxIter = 30
solopts.ShowProgress = false
h := w.Copy()
matrix.Reshape(h, h.NumElements(), 1)
return ConeLpCustomMatrix(c, G, h, nil, nil, dims, Fkkt, &solopts, primalstart, dualstart)
}
