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) }