func main() {
blas.PanicOnError(true)
matrix.PanicOnError(true)
var data *matrix.FloatMatrix = nil
flag.Parse()
if len(dataVal) > 0 {
data, _ = matrix.FloatParse(dataVal)
if data == nil {
fmt.Printf("could not parse:\n%s\n", dataVal)
return
}
} else {
data = matrix.FloatNormal(20, 20)
}
if len(spPath) > 0 {
checkpnt.Reset(spPath)
checkpnt.Activate()
checkpnt.Verbose(spVerbose)
checkpnt.Format("%.7f")
}
sol, err := mcsdp(data)
if sol != nil && sol.Status == cvx.Optimal {
x := sol.Result.At("x")[0]
z := sol.Result.At("z")[0]
matrix.Reshape(z, data.Rows(), data.Rows())
fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
//fmt.Printf("z=\n%v\n", z.ToString("%.9f"))
check(x, z)
} else {
fmt.Printf("status: %v\n", err)
}
}
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)
}
