예제 #1
0
파일: gp.go 프로젝트: hrautila/cvx
func (gp *gpConvexProg) F1(x *matrix.FloatMatrix) (f, Df *matrix.FloatMatrix, err error) {
	f = nil
	Df = nil
	err = nil
	f = matrix.FloatZeros(gp.mnl+1, 1)
	Df = matrix.FloatZeros(gp.mnl+1, gp.n)
	y := gp.g.Copy()
	blas.GemvFloat(gp.F, x, y, 1.0, 1.0)

	for i, s := range gp.ind {
		start := s[0]
		stop := s[1]
		// yi := exp(yi) = exp(Fi*x+gi)
		ymax := maxvec(y.FloatArray()[start:stop])
		// ynew = exp(y[start:stop] - ymax)
		ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
		y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)

		// fi = log sum yi = log sum exp(Fi*x+gi)
		ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
		f.SetIndex(i, ymax+math.Log(ysum))

		blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
		blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
			&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
			&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})
	}
	return
}
예제 #2
0
파일: testgp.go 프로젝트: hrautila/go.opt
func main() {
	flag.Parse()

	aflr := 1000.0
	awall := 100.0
	alpha := 0.5
	beta := 2.0
	gamma := 0.5
	delta := 2.0

	fdata := [][]float64{
		[]float64{-1.0, 1.0, 1.0, 0.0, -1.0, 1.0, 0.0, 0.0},
		[]float64{-1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0, -1.0},
		[]float64{-1.0, 0.0, 1.0, 1.0, 0.0, 0.0, -1.0, 1.0}}

	gdata := []float64{1.0, 2.0 / awall, 2.0 / awall, 1.0 / aflr, alpha, 1.0 / beta, gamma, 1.0 / delta}

	g := matrix.FloatNew(8, 1, gdata).Log()
	F := matrix.FloatMatrixFromTable(fdata)
	K := []int{1, 2, 1, 1, 1, 1, 1}

	var solopts cvx.SolverOptions
	solopts.MaxIter = 40
	if maxIter > 0 {
		solopts.MaxIter = maxIter
	}
	if len(spPath) > 0 {
		checkpnt.Reset(spPath)
		checkpnt.Activate()
		checkpnt.Verbose(spVerbose)
		checkpnt.Format("%.7f")
	}
	solopts.ShowProgress = true
	if maxIter > 0 {
		solopts.MaxIter = maxIter
	}
	if len(solver) > 0 {
		solopts.KKTSolverName = solver
	}
	sol, err := cvx.Gp(K, F, g, nil, nil, nil, nil, &solopts)
	if sol != nil && sol.Status == cvx.Optimal {
		x := sol.Result.At("x")[0]
		r := matrix.Exp(x)
		h := r.GetIndex(0)
		w := r.GetIndex(1)
		d := r.GetIndex(2)
		fmt.Printf("x=\n%v\n", x.ToString("%.9f"))
		fmt.Printf("\n h = %f,  w = %f, d = %f.\n", h, w, d)
		check(x)
	} else {
		fmt.Printf("status: %v\n", err)
	}
}
예제 #3
0
파일: gp_test.go 프로젝트: hrautila/cvx
// The small GP of section 9.3 (Geometric programming).
func TestGp(t *testing.T) {

	xref := []float64{1.06032641296944741, 1.75347359157296845, 2.44603683900611868}

	aflr := 1000.0
	awall := 100.0
	alpha := 0.5
	beta := 2.0
	gamma := 0.5
	delta := 2.0

	fdata := [][]float64{
		[]float64{-1.0, 1.0, 1.0, 0.0, -1.0, 1.0, 0.0, 0.0},
		[]float64{-1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0, -1.0},
		[]float64{-1.0, 0.0, 1.0, 1.0, 0.0, 0.0, -1.0, 1.0}}

	gdata := []float64{1.0, 2.0 / awall, 2.0 / awall, 1.0 / aflr, alpha, 1.0 / beta, gamma, 1.0 / delta}

	g := matrix.FloatNew(8, 1, gdata).Log()
	F := matrix.FloatMatrixFromTable(fdata)
	K := []int{1, 2, 1, 1, 1, 1, 1}

	var solopts SolverOptions
	solopts.MaxIter = 40
	solopts.ShowProgress = false
	solopts.KKTSolverName = "ldl"
	sol, err := Gp(K, F, g, nil, nil, nil, nil, &solopts)
	if sol != nil && sol.Status == Optimal {
		x := sol.Result.At("x")[0]
		r := matrix.Exp(x)
		h := r.GetIndex(0)
		w := r.GetIndex(1)
		d := r.GetIndex(2)
		t.Logf("x=\n%v\n", x.ToString("%.9f"))
		t.Logf("h = %f,  w = %f, d = %f.\n", h, w, d)
		xe, _ := nrmError(matrix.FloatVector(xref), x)
		if xe > TOL {
			t.Logf("x differs [%.3e] from exepted too much.", xe)
			t.Fail()
		}
	} else {
		t.Logf("status: %v\n", err)
		t.Fail()
	}
}
예제 #4
0
파일: gp.go 프로젝트: hrautila/cvx
func (gp *gpConvexProg) F2(x, z *matrix.FloatMatrix) (f, Df, H *matrix.FloatMatrix, err error) {

	err = nil
	f = matrix.FloatZeros(gp.mnl+1, 1)
	Df = matrix.FloatZeros(gp.mnl+1, gp.n)
	H = matrix.FloatZeros(gp.n, gp.n)
	y := gp.g.Copy()
	Fsc := matrix.FloatZeros(gp.maxK, gp.n)
	blas.GemvFloat(gp.F, x, y, 1.0, 1.0)
	//fmt.Printf("y=\n%v\n", y.ToString("%.3f"))

	for i, s := range gp.ind {
		start := s[0]
		stop := s[1]

		// yi := exp(yi) = exp(Fi*x+gi)
		ymax := maxvec(y.FloatArray()[start:stop])
		ynew := matrix.Exp(matrix.FloatVector(y.FloatArray()[start:stop]).Add(-ymax))
		y.SetIndexesFromArray(ynew.FloatArray(), matrix.Indexes(start, stop)...)

		// fi = log sum yi = log sum exp(Fi*x+gi)
		ysum := blas.AsumFloat(y, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})

		f.SetIndex(i, ymax+math.Log(ysum))
		blas.ScalFloat(y, 1.0/ysum, &la.IOpt{"n", stop - start}, &la.IOpt{"offset", start})
		blas.GemvFloat(gp.F, y, Df, 1.0, 0.0, la.OptTrans, &la.IOpt{"m", stop - start},
			&la.IOpt{"incy", gp.mnl + 1}, &la.IOpt{"offseta", start},
			&la.IOpt{"offsetx", start}, &la.IOpt{"offsety", i})

		Fsc.SetSubMatrix(0, 0, gp.F.GetSubMatrix(start, 0, stop-start))

		for k := start; k < stop; k++ {
			blas.AxpyFloat(Df, Fsc, -1.0, &la.IOpt{"n", gp.n},
				&la.IOpt{"incx", gp.mnl + 1}, &la.IOpt{"incy", Fsc.Rows()},
				&la.IOpt{"offsetx", i}, &la.IOpt{"offsety", k - start})
			blas.ScalFloat(Fsc, math.Sqrt(y.GetIndex(k)),
				&la.IOpt{"inc", Fsc.Rows()}, &la.IOpt{"offset", k - start})
		}
		// H += z[i]*Hi = z[i] *Fisc' * Fisc
		blas.SyrkFloat(Fsc, H, z.GetIndex(i), 1.0, la.OptTrans,
			&la.IOpt{"k", stop - start})
	}
	return
}
예제 #5
0
파일: chernoff.go 프로젝트: hrautila/go.opt
func main() {
	m := 6
	Vdata := [][]float64{
		[]float64{1.0, -1.0, -2.0, -2.0, 0.0, 1.5, 1.0},
		[]float64{1.0, 2.0, 1.0, -1.0, -2.0, -1.0, 1.0}}

	V := matrix.FloatMatrixFromTable(Vdata, matrix.RowOrder)

	// V[1, :m] - V[1,1:]
	a0 := matrix.Minus(V.GetSubMatrix(1, 0, 1, m), V.GetSubMatrix(1, 1, 1))
	// V[0, :m] - V[0,1:]
	a1 := matrix.Minus(V.GetSubMatrix(0, 0, 1, m), V.GetSubMatrix(0, 1, 1))
	A0, _ := matrix.FloatMatrixStacked(matrix.StackDown, a0.Scale(-1.0), a1)
	A0 = A0.Transpose()
	b0 := matrix.Mul(A0, V.GetSubMatrix(0, 0, 2, m).Transpose())
	b0 = matrix.Times(b0, matrix.FloatWithValue(2, 1, 1.0))

	A := make([]*matrix.FloatMatrix, 0)
	b := make([]*matrix.FloatMatrix, 0)
	A = append(A, A0)
	b = append(b, b0)

	// List of symbols
	C := make([]*matrix.FloatMatrix, 0)
	C = append(C, matrix.FloatZeros(2, 1))
	var row *matrix.FloatMatrix = nil
	for k := 0; k < m; k++ {
		row = A0.GetRow(k, row)
		nrm := blas.Nrm2Float(row)
		row.Scale(2.0 * b0.GetIndex(k) / (nrm * nrm))
		C = append(C, row.Transpose())
	}

	// Voronoi set around C[1]
	A1 := matrix.FloatZeros(3, 2)
	A1.SetSubMatrix(0, 0, A0.GetSubMatrix(0, 0, 1).Scale(-1.0))
	A1.SetSubMatrix(1, 0, matrix.Minus(C[m], C[1]).Transpose())
	A1.SetSubMatrix(2, 0, matrix.Minus(C[2], C[1]).Transpose())
	b1 := matrix.FloatZeros(3, 1)
	b1.SetIndex(0, -b0.GetIndex(0))
	v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[m], C[1])).Float() * 0.5
	b1.SetIndex(1, v)
	v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[2], C[1])).Float() * 0.5
	b1.SetIndex(2, v)
	A = append(A, A1)
	b = append(b, b1)

	// Voronoi set around C[2] ... C[5]
	for k := 2; k < 6; k++ {
		A1 = matrix.FloatZeros(3, 2)
		A1.SetSubMatrix(0, 0, A0.GetSubMatrix(k-1, 0, 1).Scale(-1.0))
		A1.SetSubMatrix(1, 0, matrix.Minus(C[k-1], C[k]).Transpose())
		A1.SetSubMatrix(2, 0, matrix.Minus(C[k+1], C[k]).Transpose())
		b1 = matrix.FloatZeros(3, 1)
		b1.SetIndex(0, -b0.GetIndex(k-1))
		v := matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[k-1], C[k])).Float() * 0.5
		b1.SetIndex(1, v)
		v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[k+1], C[k])).Float() * 0.5
		b1.SetIndex(2, v)
		A = append(A, A1)
		b = append(b, b1)
	}

	// Voronoi set around C[6]
	A1 = matrix.FloatZeros(3, 2)
	A1.SetSubMatrix(0, 0, A0.GetSubMatrix(5, 0, 1).Scale(-1.0))
	A1.SetSubMatrix(1, 0, matrix.Minus(C[1], C[6]).Transpose())
	A1.SetSubMatrix(2, 0, matrix.Minus(C[5], C[6]).Transpose())
	b1 = matrix.FloatZeros(3, 1)
	b1.SetIndex(0, -b0.GetIndex(5))
	v = matrix.Times(A1.GetRow(1, nil), matrix.Plus(C[1], C[6])).Float() * 0.5
	b1.SetIndex(1, v)
	v = matrix.Times(A1.GetRow(2, nil), matrix.Plus(C[5], C[6])).Float() * 0.5
	b1.SetIndex(2, v)

	A = append(A, A1)
	b = append(b, b1)

	P := matrix.FloatIdentity(2)
	q := matrix.FloatZeros(2, 1)
	solopts := &cvx.SolverOptions{ShowProgress: false, MaxIter: 30}
	ovals := make([]float64, 0)
	for k := 1; k < 7; k++ {
		sol, err := cvx.Qp(P, q, A[k], b[k], nil, nil, solopts, nil)
		_ = err
		x := sol.Result.At("x")[0]
		ovals = append(ovals, math.Pow(blas.Nrm2Float(x), 2.0))
	}

	optvals := matrix.FloatVector(ovals)
	//fmt.Printf("optvals=\n%v\n", optvals)

	rangeFunc := func(n int) []float64 {
		r := make([]float64, 0)
		for i := 0; i < n; i++ {
			r = append(r, float64(i))
		}
		return r
	}

	nopts := 200
	sigmas := matrix.FloatVector(rangeFunc(nopts))
	sigmas.Scale((0.5 - 0.2) / float64(nopts)).Add(0.2)

	bndsVal := func(sigma float64) float64 {
		// 1.0 - sum(exp( -optvals/(2*sigma**2)))
		return 1.0 - matrix.Exp(matrix.Scale(optvals, -1.0/(2*sigma*sigma))).Sum()
	}
	bnds := matrix.FloatZeros(sigmas.NumElements(), 1)
	for j, v := range sigmas.FloatArray() {
		bnds.SetIndex(j, bndsVal(v))
	}
	plotData("plot.png", sigmas.FloatArray(), bnds.FloatArray())
}