Exemple #1
0
// Init initialises simple flot problem structure
func NewSimpleFltProb(fcn SimpleFltFcn_t, nf, ng, nh int, C *ConfParams) (o *SimpleFltProb) {

	// data
	o = new(SimpleFltProb)
	o.Fcn = fcn
	o.C = C
	o.C.Nova = nf
	o.C.Noor = ng + nh

	// sandbox
	o.nf, o.ng, o.nh = nf, ng, nh
	o.ff = utl.DblsAlloc(o.C.Nisl, o.nf)
	o.gg = utl.DblsAlloc(o.C.Nisl, o.ng)
	o.hh = utl.DblsAlloc(o.C.Nisl, o.nh)

	// objective function
	o.C.OvaOor = func(ind *Individual, isl, time int, report *bytes.Buffer) {
		x := ind.GetFloats()
		o.Fcn(o.ff[isl], o.gg[isl], o.hh[isl], x)
		for i, f := range o.ff[isl] {
			ind.Ovas[i] = f
		}
		for i, g := range o.gg[isl] {
			ind.Oors[i] = utl.GtePenalty(g, 0.0, 1) // g[i] ≥ 0
		}
		for i, h := range o.hh[isl] {
			h = math.Abs(h)
			ind.Ovas[0] += h
			ind.Oors[ng+i] = utl.GtePenalty(o.C.Eps1, h, 1) // ϵ ≥ |h[i]|
		}
	}

	// evolver
	o.Evo = NewEvolver(o.C)

	// auxiliary
	o.NumfmtX = "%8.5f"
	o.NumfmtF = "%8.5f"

	// results and stat
	nx := len(o.C.RangeFlt)
	o.Xbest = utl.DblsAlloc(o.C.Ntrials, nx)

	// plotting
	if o.C.DoPlot {
		o.PopsIni = o.Evo.GetPopulations()
		o.PltDirout = "/tmp/goga"
		o.PltNpts = 41
		o.PltLwg = 1.5
		o.PltLwh = 1.5
	}
	return
}
Exemple #2
0
// HaltonPoints generates randomly spaced points
//   x -- [dim][n] points
func HaltonPoints(dim, n int) (x [][]float64) {
	x = utl.DblsAlloc(dim, n)
	for j := 0; j < dim; j++ {
		for i := 0; i < n; i++ {
			x[j][i] = halton(i, j)
		}
	}
	return
}
Exemple #3
0
func CTPplotter(θ, a, b, c, d, e, f1max float64) func() {
	return func() {
		np := 401
		X, Y := utl.MeshGrid2D(0, 1, 0, f1max, np, np)
		Z1 := utl.DblsAlloc(np, np)
		Z2 := utl.DblsAlloc(np, np)
		sθ, cθ := math.Sin(θ), math.Cos(θ)
		for j := 0; j < np; j++ {
			for i := 0; i < np; i++ {
				f0, f1 := X[i][j], Y[i][j]
				Z1[i][j] = cθ*(f1-e) - sθ*f0
				Z2[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
			}
		}
		plt.Contour(X, Y, Z2, "levels=[0,2],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
		plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['b'], levels=[0]")
	}
}
Exemple #4
0
// GetResults returns all ovas and oors
//  Output:
//   ova -- [nsol][nova] objective values
//   oor -- [nsol][noor] out-of-range values
func GetResults(sols []*Solution, ovaOnly bool) (ova, oor [][]float64) {
	nsol := len(sols)
	nova := len(sols[0].Ova)
	noor := len(sols[0].Oor)
	ova = utl.DblsAlloc(nsol, nova)
	if !ovaOnly {
		oor = utl.DblsAlloc(nsol, noor)
	}
	for i, sol := range sols {
		for j := 0; j < nova; j++ {
			ova[i][j] = sol.Ova[j]
		}
		if !ovaOnly {
			for j := 0; j < noor; j++ {
				oor[i][j] = sol.Oor[j]
			}
		}
	}
	return
}
Exemple #5
0
func get_nurbs_xmat(nurbs *gm.Nurbs, ibasis []int) (xmat [][]float64) {
	nd := nurbs.Gnd()
	xmat = utl.DblsAlloc(nd, len(ibasis))
	for k, l := range ibasis {
		q := nurbs.GetQl(l)
		for j := 0; j < nd; j++ {
			xmat[j][k] = q[j]
		}
	}
	return
}
Exemple #6
0
// Plot plot results
func Plot(dirout, fn string, res *Results, yfcn Cb_ycorr, xa, xb float64, argsAna, argsNum string, extra func()) {

	// data
	if res == nil {
		return
	}
	ndim := len(res.Y)
	if ndim < 1 {
		return
	}

	// closed-form solution
	var xc []float64
	var Yc [][]float64
	if yfcn != nil {
		np := 101
		dx := (xb - xa) / float64(np-1)
		xc = make([]float64, np)
		Yc = utl.DblsAlloc(np, ndim)
		for i := 0; i < np; i++ {
			xc[i] = xa + dx*float64(i)
			yfcn(Yc[i], xc[i])
		}
	}

	// plot
	if argsAna == "" {
		argsAna = "'y-', lw=6, label='analytical', clip_on=0"
	}
	if argsNum == "" {
		argsNum = "'b-', marker='.', lw=1, clip_on=0"
	}
	for j := 0; j < ndim; j++ {
		plt.Subplot(ndim+1, 1, j+1)
		if yfcn != nil {
			plt.Plot(xc, Yc[j], argsAna)
		}
		plt.Plot(res.X, res.Y[j], argsNum+","+io.Sf("label='%s'", res.Method))
		plt.Gll("$x$", "$y$", "")
	}
	plt.Subplot(ndim+1, 1, ndim+1)
	plt.Plot(res.X, res.Dx, io.Sf("'b-', marker='.', lw=1, clip_on=0, label='%s'", res.Method))
	plt.SetYlog()
	plt.Gll("$x$", "$\\log(\\delta x)$", "")

	// write file
	if extra != nil {
		extra()
	}
	plt.SaveD(dirout, fn)
}
Exemple #7
0
// checkShape checks that shape functions result in 1.0 @ nodes
func checkShape(tst *testing.T, shape string, tol float64, verbose bool) {

	// information
	fcn := Functions[shape]
	ndim := GeomNdim[shape]
	nverts := NumVerts[shape]
	coords := NatCoords[shape]

	// allocate slices
	S := make([]float64, nverts)
	dSdR := utl.DblsAlloc(nverts, ndim)

	// loop over all vertices
	errS := 0.0
	r := []float64{0, 0, 0}
	for n := 0; n < nverts; n++ {

		// natural coordinates @ vertex
		for i := 0; i < ndim; i++ {
			r[i] = coords[i][n]
		}

		// compute function
		fcn(S, dSdR, r, false)

		// check
		if verbose {
			for _, val := range S {
				if math.Abs(val) < 1e-15 {
					val = 0
				}
				io.Pf("%3v", val)
			}
			io.Pf("\n")
		}
		for m := 0; m < nverts; m++ {
			if n == m {
				errS += math.Abs(S[m] - 1.0)
			} else {
				errS += math.Abs(S[m])
			}
		}
	}

	// error
	if errS > tol {
		tst.Errorf("%s failed with err = %g\n", shape, errS)
		return
	}
}
Exemple #8
0
// SimpleOutput implements a simple output function
func SimpleOutput(first bool, dx, x float64, y []float64, args ...interface{}) (err error) {
	chk.IntAssert(len(args), 1)
	res := args[0].(*Results)
	res.Dx = append(res.Dx, dx)
	res.X = append(res.X, x)
	ndim := len(y)
	if len(res.Y) == 0 {
		res.Y = utl.DblsAlloc(ndim, 0)
	}
	for j := 0; j < ndim; j++ {
		res.Y[j] = append(res.Y[j], y[j])
	}
	return
}
Exemple #9
0
// Init initialises Munkres' structure
func (o *Munkres) Init(nrow, ncol int) {
	chk.IntAssertLessThan(0, nrow) // nrow > 1
	chk.IntAssertLessThan(0, ncol) // ncol > 1
	o.nrow, o.ncol = nrow, ncol
	o.C = utl.DblsAlloc(o.nrow, o.ncol)
	o.M = make([][]Mask_t, o.nrow)
	for i := 0; i < o.nrow; i++ {
		o.M[i] = make([]Mask_t, o.ncol)
	}
	o.Links = make([]int, o.nrow)
	npath := 2*o.nrow + 1 // TODO: check this
	o.path = utl.IntsAlloc(npath, 2)
	o.row_covered = make([]bool, o.nrow)
	o.col_covered = make([]bool, o.ncol)
}
Exemple #10
0
// Init initialises graph
//  Input:
//    edges    -- [nedges][2] edges (connectivity)
//    weightsE -- [nedges] weights of edges. can be <nil>
//    verts    -- [nverts][ndim] vertices. can be <nil>
//    weightsV -- [nverts] weights of vertices. can be <nil>
func (o *Graph) Init(edges [][]int, weightsE []float64, verts [][]float64, weightsV []float64) {
	o.Edges, o.WeightsE = edges, weightsE
	o.Verts, o.WeightsV = verts, weightsV
	o.Shares = make(map[int][]int)
	o.Key2edge = make(map[int]int)
	for k, edge := range o.Edges {
		i, j := edge[0], edge[1]
		utl.IntIntsMapAppend(&o.Shares, i, k)
		utl.IntIntsMapAppend(&o.Shares, j, k)
		o.Key2edge[o.HashEdgeKey(i, j)] = k
	}
	if o.Verts != nil {
		chk.IntAssert(len(o.Verts), len(o.Shares))
	}
	nv := len(o.Shares)
	o.Dist = utl.DblsAlloc(nv, nv)
	o.Next = utl.IntsAlloc(nv, nv)
}
Exemple #11
0
// PlotHc2d plots 2D hypercube
func PlotHc2d(dirout, fnkey string, x [][]int, xrange [][]float64) {
	m := len(x)
	n := len(x[0])
	dx := make([]float64, m)
	for i := 0; i < m; i++ {
		dx[i] = (xrange[i][1] - xrange[i][0]) / float64(n-1)
	}
	X := utl.DblsAlloc(m, n)
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			X[i][j] = xrange[i][0] + float64(x[i][j]-1)*dx[i]
		}
	}
	plt.SetForEps(0.8, 300)
	plt.Plot(X[0], X[1], "'r.', clip_on=0, zorder=10")
	plt.Equal()
	plt.Gll("$x$", "$y$", "")
	plt.SaveD(dirout, fnkey+".eps")
}
Exemple #12
0
// Delaunay computes 2D Delaunay triangulation using Triangle
//  Input:
//    X = { x0, x1, x2, ... Npoints }
//    Y = { y0, y1, y2, ... Npoints }
//  Ouptut:
//    V = { { x0, y0 }, { x0, y0 }, { x0, y0 } ... Nvertices }
//    C = { { id0, id1, id2 }, { id0, id1, id2 } ... Ncellls }
func Delaunay(X, Y []float64, verbose bool) (V [][]float64, C [][]int, err error) {

	// input
	chk.IntAssert(len(X), len(Y))
	n := len(X)
	verb := 0
	if verbose {
		verb = 1
	}

	// perform triangulation
	var T C.triangulateio
	defer func() { C.trifree(&T) }()
	res := C.delaunay2d(
		&T,
		(C.long)(n),
		(*C.double)(unsafe.Pointer(&X[0])),
		(*C.double)(unsafe.Pointer(&Y[0])),
		(C.long)(verb),
	)
	if res != 0 {
		chk.Err("Delaunay2d failed: Triangle returned %d code\n", res)
	}

	// output
	nverts := int(T.numberofpoints)
	ncells := int(T.numberoftriangles)
	V = utl.DblsAlloc(nverts, 2)
	C = utl.IntsAlloc(ncells, 3)
	for i := 0; i < nverts; i++ {
		V[i][0] = float64(C.getpoint((C.long)(i), 0, &T))
		V[i][1] = float64(C.getpoint((C.long)(i), 1, &T))
	}
	for i := 0; i < ncells; i++ {
		C[i][0] = int(C.getcorner((C.long)(i), 0, &T))
		C[i][1] = int(C.getcorner((C.long)(i), 1, &T))
		C[i][2] = int(C.getcorner((C.long)(i), 2, &T))
	}
	return
}
Exemple #13
0
// checkDerivs checks dSdR derivatives of shape structures
func checkDerivs(tst *testing.T, shape string, r []float64, tol float64, verbose bool) {

	// information
	fcn := Functions[shape]
	ndim := GeomNdim[shape]
	nverts := NumVerts[shape]

	// allocate slices
	S := make([]float64, nverts)
	dSdR := utl.DblsAlloc(nverts, ndim)

	// auxiliary
	r_tmp := make([]float64, len(r))
	S_tmp := make([]float64, nverts)

	// analytical
	fcn(S, dSdR, r, true)

	// numerical
	for n := 0; n < nverts; n++ {
		for i := 0; i < ndim; i++ {
			dSndRi, _ := num.DerivCentral(func(t float64, args ...interface{}) (Sn float64) {
				copy(r_tmp, r)
				r_tmp[i] = t
				fcn(S_tmp, nil, r_tmp, false)
				Sn = S_tmp[n]
				return
			}, r[i], 1e-1)
			if verbose {
				io.Pfgrey2("  dS%ddR%d @ %5.2f = %v (num: %v)\n", n, i, r, dSdR[n][i], dSndRi)
			}
			if math.Abs(dSdR[n][i]-dSndRi) > tol {
				tst.Errorf("nurbs dS%ddR%d failed with err = %g\n", n, i, math.Abs(dSdR[n][i]-dSndRi))
				return
			}
		}
	}
}
Exemple #14
0
// PlotHc3d plots 3D hypercube
func PlotHc3d(dirout, fnkey string, x [][]int, xrange [][]float64, show bool) {
	m := len(x)
	n := len(x[0])
	dx := make([]float64, m)
	for i := 0; i < m; i++ {
		dx[i] = (xrange[i][1] - xrange[i][0]) / float64(n-1)
	}
	X := utl.DblsAlloc(m, n)
	for i := 0; i < m; i++ {
		for j := 0; j < n; j++ {
			X[i][j] = xrange[i][0] + float64(x[i][j]-1)*dx[i]
		}
	}
	if !show {
		plt.SetForEps(0.8, 455)
	}
	plt.Plot3dPoints(X[0], X[1], X[2], "clip_on=0, zorder=10")
	if show {
		plt.Show()
	} else {
		plt.SaveD(dirout, fnkey+".eps")
	}
}
Exemple #15
0
// Plot plots contour
func (o *SimpleFltProb) Plot(fnkey string) {

	// check
	if !o.C.DoPlot {
		return
	}

	// limits and meshgrid
	xmin, xmax := o.C.RangeFlt[0][0], o.C.RangeFlt[0][1]
	ymin, ymax := o.C.RangeFlt[1][0], o.C.RangeFlt[1][1]

	// auxiliary variables
	X, Y := utl.MeshGrid2D(xmin, xmax, ymin, ymax, o.PltNpts, o.PltNpts)
	Zf := utl.DblsAlloc(o.PltNpts, o.PltNpts)
	var Zg [][][]float64
	var Zh [][][]float64
	if o.ng > 0 {
		Zg = utl.Deep3alloc(o.ng, o.PltNpts, o.PltNpts)
	}
	if o.nh > 0 {
		Zh = utl.Deep3alloc(o.nh, o.PltNpts, o.PltNpts)
	}

	// compute values
	x := make([]float64, 2)
	for i := 0; i < o.PltNpts; i++ {
		for j := 0; j < o.PltNpts; j++ {
			x[0], x[1] = X[i][j], Y[i][j]
			o.Fcn(o.ff[0], o.gg[0], o.hh[0], x)
			Zf[i][j] = o.ff[0][o.PltIdxF]
			for k, g := range o.gg[0] {
				Zg[k][i][j] = g
			}
			for k, h := range o.hh[0] {
				Zh[k][i][j] = h
			}
		}
	}

	// prepare plot area
	plt.Reset()
	plt.SetForEps(0.8, 350)

	// plot f
	if o.PltArgs != "" {
		o.PltArgs = "," + o.PltArgs
	}
	if o.PltCsimple {
		plt.ContourSimple(X, Y, Zf, true, 7, "colors=['k'], fsz=7"+o.PltArgs)
	} else {
		plt.Contour(X, Y, Zf, io.Sf("fsz=7, cmapidx=%d"+o.PltArgs, o.PltCmapIdx))
	}

	// plot g
	clr := "yellow"
	if o.PltCsimple {
		clr = "blue"
	}
	for _, g := range Zg {
		plt.ContourSimple(X, Y, g, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", clr, o.PltLwg))
	}

	// plot h
	clr = "yellow"
	if o.PltCsimple {
		clr = "blue"
	}
	for _, h := range Zh {
		plt.ContourSimple(X, Y, h, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", clr, o.PltLwh))
	}

	// initial populations
	l := "initial population"
	for _, pop := range o.PopsIni {
		for _, ind := range pop {
			x := ind.GetFloats()
			plt.PlotOne(x[0], x[1], io.Sf("'k.', zorder=20, clip_on=0, label='%s'", l))
			l = ""
		}
	}

	// final populations
	l = "final population"
	for _, pop := range o.PopsBest {
		for _, ind := range pop {
			x := ind.GetFloats()
			plt.PlotOne(x[0], x[1], io.Sf("'ko', ms=6, zorder=30, clip_on=0, label='%s', markerfacecolor='none'", l))
			l = ""
		}
	}

	// extra
	if o.PltExtra != nil {
		o.PltExtra()
	}

	// best result
	if o.Nfeasible > 0 {
		x, _, _, _ := o.find_best()
		plt.PlotOne(x[0], x[1], "'m*', zorder=50, clip_on=0, label='best', markeredgecolor='m'")
	}

	// save figure
	plt.Cross("clr='grey'")
	if o.PltAxEqual {
		plt.Equal()
	}
	plt.AxisRange(xmin, xmax, ymin, ymax)
	plt.Gll("$x_0$", "$x_1$", "leg_out=1, leg_ncol=4, leg_hlen=1.5")
	plt.SaveD(o.PltDirout, fnkey+".eps")
}
Exemple #16
0
func test_rwstep01(tst *testing.T) {

	verbose()
	chk.PrintTitle("rwstep01")

	buf, err := io.ReadFile("rw/data/beadpanel.step")
	if err != nil {
		tst.Errorf("cannot read file:\n%v", err)
		return
	}
	dat := string(buf)

	var stp rw.STEP
	err = stp.ParseDATA(dat)
	if err != nil {
		tst.Errorf("Parse filed:\n%v", err)
		return
	}

	var bsplines []*Bspline

	for _, scurve := range stp.Scurves {
		curve := stp.BScurves[scurve.Curve_3d]
		if curve == nil {
			continue
		}

		// collect vertices
		nv := len(curve.Control_points_list)
		verts := utl.DblsAlloc(nv, 4)
		for i, key := range curve.Control_points_list {
			if p, ok := stp.Points[key]; ok {
				for j := 0; j < 3; j++ {
					verts[i][j] = p.Coordinates[j]
				}
				verts[i][3] = 1.0
			} else {
				chk.Panic("cannot find point %q", key)
			}
		}

		// collect knots
		nk := 0
		for _, m := range curve.Knot_multiplicities {
			nk += m
		}
		knots := make([]float64, nk)
		k := 0
		for i, u := range curve.Knots {
			m := curve.Knot_multiplicities[i]
			for j := 0; j < m; j++ {
				knots[k] = u
				k++
			}
		}

		// create B-spline
		bsp := new(Bspline)
		bsp.Init(knots, curve.Degree)
		bsp.SetControl(verts)
		bsplines = append(bsplines, bsp)
	}

	if true {
		io.Pforan("n = %v\n", len(bsplines))
		for i, bsp := range bsplines {
			bsp.Draw3d("", "", 21, i == 0)
		}
		//plt.Show()
	}
}
Exemple #17
0
// PlotContour plots contour
func (o *Optimiser) PlotContour(iFlt, jFlt, iOva int, pp *PlotParams) {

	// check
	var x []float64
	if pp.Refx == nil {
		if iFlt > 1 || jFlt > 1 {
			chk.Panic("Refx vector must be given to PlotContour when iFlt or jFlt > 1")
		}
		x = make([]float64, 2)
	} else {
		x = make([]float64, len(pp.Refx))
		copy(x, pp.Refx)
	}

	// limits and meshgrid
	xmin, xmax := o.FltMin[iFlt], o.FltMax[iFlt]
	ymin, ymax := o.FltMin[jFlt], o.FltMax[jFlt]
	if pp.Xrange != nil {
		xmin, xmax = pp.Xrange[0], pp.Xrange[1]
	}
	if pp.Yrange != nil {
		ymin, ymax = pp.Yrange[0], pp.Yrange[1]
	}

	// check objective function
	var sol *Solution // copy of solution for objective function
	if o.MinProb == nil {
		pp.NoG = true
		pp.NoH = true
		sol = NewSolution(o.Nsol, 0, &o.Parameters)
		o.Solutions[0].CopyInto(sol)
		if pp.Refx != nil {
			copy(sol.Flt, pp.Refx)
		}
	}

	// auxiliary variables
	X, Y := utl.MeshGrid2D(xmin, xmax, ymin, ymax, pp.Npts, pp.Npts)
	var Zf [][]float64
	var Zg [][][]float64
	var Zh [][][]float64
	var Za [][]float64
	if !pp.NoF {
		Zf = utl.DblsAlloc(pp.Npts, pp.Npts)
	}
	if o.Ng > 0 && !pp.NoG {
		Zg = utl.Deep3alloc(o.Ng, pp.Npts, pp.Npts)
	}
	if o.Nh > 0 && !pp.NoH {
		Zh = utl.Deep3alloc(o.Nh, pp.Npts, pp.Npts)
	}
	if pp.WithAux {
		Za = utl.DblsAlloc(pp.Npts, pp.Npts)
	}

	// compute values
	grp := 0
	for i := 0; i < pp.Npts; i++ {
		for j := 0; j < pp.Npts; j++ {
			x[iFlt], x[jFlt] = X[i][j], Y[i][j]
			if o.MinProb == nil {
				copy(sol.Flt, x)
				o.ObjFunc(sol, grp)
				if !pp.NoF {
					Zf[i][j] = sol.Ova[iOva]
				}
				if pp.WithAux {
					Za[i][j] = sol.Aux
				}
			} else {
				o.MinProb(o.F[grp], o.G[grp], o.H[grp], x, nil, grp)
				if !pp.NoF {
					Zf[i][j] = o.F[grp][iOva]
				}
				if !pp.NoG {
					for k, g := range o.G[grp] {
						Zg[k][i][j] = g
					}
				}
				if !pp.NoH {
					for k, h := range o.H[grp] {
						Zh[k][i][j] = h
					}
				}
			}
		}
	}

	// plot f
	if !pp.NoF && !pp.OnlyAux {
		txt := "cbar=0"
		if pp.Cbar {
			txt = ""
		}
		if pp.Simple {
			plt.ContourSimple(X, Y, Zf, true, 7, io.Sf("colors=['%s'], fsz=7, %s", pp.FmtF.C, txt))
		} else {
			plt.Contour(X, Y, Zf, io.Sf("fsz=7, cmapidx=%d, %s", pp.CmapIdx, txt))
		}
	}

	// plot g
	if !pp.NoG && !pp.OnlyAux {
		for _, g := range Zg {
			plt.ContourSimple(X, Y, g, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtG.C, pp.FmtG.Lw))
		}
	}

	// plot h
	if !pp.NoH && !pp.OnlyAux {
		for i, h := range Zh {
			if i == pp.IdxH || pp.IdxH < 0 {
				plt.ContourSimple(X, Y, h, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtH.C, pp.FmtH.Lw))
			}
		}
	}

	// plot aux
	if pp.WithAux {
		if pp.OnlyAux {
			txt := "cbar=0"
			if pp.Cbar {
				txt = ""
			}
			if pp.Simple {
				plt.ContourSimple(X, Y, Za, true, 7, io.Sf("colors=['%s'], fsz=7, %s", pp.FmtF.C, txt))
			} else {
				plt.Contour(X, Y, Za, io.Sf("fsz=7, markZero='red', cmapidx=%d, %s", pp.CmapIdx, txt))
			}
		} else {
			plt.ContourSimple(X, Y, Za, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtA.C, pp.FmtA.Lw))
		}
	}

	// limits
	if pp.Limits {
		plt.Plot(
			[]float64{o.FltMin[iFlt], o.FltMax[iFlt], o.FltMax[iFlt], o.FltMin[iFlt], o.FltMin[iFlt]},
			[]float64{o.FltMin[jFlt], o.FltMin[jFlt], o.FltMax[jFlt], o.FltMax[jFlt], o.FltMin[jFlt]},
			"'y--', color='yellow', zorder=10",
		)
	}
}
Exemple #18
0
func solve_problem(problem int) (opt *goga.Optimiser) {

	io.Pf("\n\n------------------------------------- problem = %d ---------------------------------------\n", problem)

	// parameters
	opt = new(goga.Optimiser)
	opt.Default()
	opt.Ncpu = 3
	opt.Tf = 500
	opt.Verbose = false
	opt.Nsamples = 1000
	opt.GenType = "latin"
	opt.DEC = 0.1

	// options for report
	opt.HistNsta = 6
	opt.HistLen = 13
	opt.RptFmtE = "%.4e"
	opt.RptFmtL = "%.4e"
	opt.RptFmtEdev = "%.3e"
	opt.RptFmtLdev = "%.3e"

	// problem variables
	nx := 10
	opt.RptName = io.Sf("CTP%d", problem)
	opt.Nsol = 120
	opt.FltMin = make([]float64, nx)
	opt.FltMax = make([]float64, nx)
	for i := 0; i < nx; i++ {
		opt.FltMin[i] = 0
		opt.FltMax[i] = 1
	}
	nf, ng, nh := 2, 1, 0

	// extra problem variables
	var f1max float64
	var fcn goga.MinProb_t
	var extraplot func()

	// problems
	switch problem {

	// problem # 0 -- TNK
	case 0:
		ng = 2
		f1max = 1.21
		opt.RptName = "TNK"
		opt.FltMin = []float64{0, 0}
		opt.FltMax = []float64{PI, PI}
		fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
			f[0] = x[0]
			f[1] = x[1]
			g[0] = x[0]*x[0] + x[1]*x[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(x[0], x[1]))
			g[1] = 0.5 - math.Pow(x[0]-0.5, 2.0) - math.Pow(x[1]-0.5, 2.0)
		}
		extraplot = func() {
			np := 301
			X, Y := utl.MeshGrid2D(0, 1.3, 0, 1.3, np, np)
			Z1, Z2, Z3 := utl.DblsAlloc(np, np), utl.DblsAlloc(np, np), utl.DblsAlloc(np, np)
			for j := 0; j < np; j++ {
				for i := 0; i < np; i++ {
					g1 := 0.5 - math.Pow(X[i][j]-0.5, 2.0) - math.Pow(Y[i][j]-0.5, 2.0)
					if g1 >= 0 {
						Z1[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
					} else {
						Z1[i][j] = -1
					}
					Z2[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
					Z3[i][j] = g1
				}
			}
			plt.Contour(X, Y, Z1, "levels=[0,2],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
			plt.Text(0.3, 0.95, "0.000", "size=5,rotation=10")
			plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['-'], linewidths=[0.7], colors=['k'], levels=[0]")
			plt.ContourSimple(X, Y, Z3, false, 7, "linestyles=['-'], linewidths=[1.0], colors=['k'], levels=[0]")
		}
		opt.Multi_fcnErr = func(f []float64) float64 {
			return f[0]*f[0] + f[1]*f[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(f[0], f[1]))
		}

	// problem # 1 -- CTP1, Deb 2001, p367, fig 225
	case 1:
		ng = 2
		f1max = 1.0
		a0, b0 := 0.858, 0.541
		a1, b1 := 0.728, 0.295
		fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
			c0 := 1.0
			for i := 1; i < len(x); i++ {
				c0 += x[i]
			}
			f[0] = x[0]
			f[1] = c0 * math.Exp(-x[0]/c0)
			if true {
				g[0] = f[1] - a0*math.Exp(-b0*f[0])
				g[1] = f[1] - a1*math.Exp(-b1*f[0])
			}
		}
		f0a := math.Log(a0) / (b0 - 1.0)
		f1a := math.Exp(-f0a)
		f0b := math.Log(a0/a1) / (b0 - b1)
		f1b := a0 * math.Exp(-b0*f0b)
		opt.Multi_fcnErr = func(f []float64) float64 {
			if f[0] < f0a {
				return f[1] - math.Exp(-f[0])
			}
			if f[0] < f0b {
				return f[1] - a0*math.Exp(-b0*f[0])
			}
			return f[1] - a1*math.Exp(-b1*f[0])
		}
		extraplot = func() {
			np := 201
			X, Y := utl.MeshGrid2D(0, 1, 0, 1, np, np)
			Z := utl.DblsAlloc(np, np)
			for j := 0; j < np; j++ {
				for i := 0; i < np; i++ {
					Z[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
				}
			}
			plt.Contour(X, Y, Z, "levels=[0,0.6],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
			F0 := utl.LinSpace(0, 1, 21)
			F1r := make([]float64, len(F0))
			F1s := make([]float64, len(F0))
			F1t := make([]float64, len(F0))
			for i, f0 := range F0 {
				F1r[i] = math.Exp(-f0)
				F1s[i] = a0 * math.Exp(-b0*f0)
				F1t[i] = a1 * math.Exp(-b1*f0)
			}
			plt.Plot(F0, F1r, "'k--',color='blue'")
			plt.Plot(F0, F1s, "'k--',color='green'")
			plt.Plot(F0, F1t, "'k--',color='gray'")
			plt.PlotOne(f0a, f1a, "'k|', ms=20")
			plt.PlotOne(f0b, f1b, "'k|', ms=20")
		}

	// problem # 2 -- CTP2, Deb 2001, p368/369, fig 226
	case 2:
		f1max = 1.2
		θ, a, b := -0.2*PI, 0.2, 10.0
		c, d, e := 1.0, 6.0, 1.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
		opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)

	// problem # 3 -- CTP3, Deb 2001, p368/370, fig 227
	case 3:
		f1max = 1.2
		θ, a, b := -0.2*PI, 0.1, 10.0
		c, d, e := 1.0, 0.5, 1.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
		opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)

	// problem # 4 -- CTP4, Deb 2001, p368/370, fig 228
	case 4:
		f1max = 2.0
		θ, a, b := -0.2*PI, 0.75, 10.0
		c, d, e := 1.0, 0.5, 1.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
		opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)

	// problem # 5 -- CTP5, Deb 2001, p368/371, fig 229
	case 5:
		f1max = 1.2
		θ, a, b := -0.2*PI, 0.1, 10.0
		c, d, e := 2.0, 0.5, 1.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
		opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)

	// problem # 6 -- CTP6, Deb 2001, p368/372, fig 230
	case 6:
		f1max = 5.0
		θ, a, b := 0.1*PI, 40.0, 0.5
		c, d, e := 1.0, 2.0, -2.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		extraplot = func() {
			np := 201
			X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
			Z := utl.DblsAlloc(np, np)
			for j := 0; j < np; j++ {
				for i := 0; i < np; i++ {
					Z[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
				}
			}
			plt.Contour(X, Y, Z, "levels=[-30,-15,0,15,30],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
		}
		opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)

	// problem # 7 -- CTP7, Deb 2001, p368/373, fig 231
	case 7:
		f1max = 1.2
		θ, a, b := -0.05*PI, 40.0, 5.0
		c, d, e := 1.0, 6.0, 0.0
		fcn = CTPgenerator(θ, a, b, c, d, e)
		opt.Multi_fcnErr = func(f []float64) float64 { return f[1] - (1.0 - f[0]) }
		extraplot = func() {
			np := 201
			X, Y := utl.MeshGrid2D(0, 1, 0, f1max, np, np)
			Z1 := utl.DblsAlloc(np, np)
			Z2 := utl.DblsAlloc(np, np)
			for j := 0; j < np; j++ {
				for i := 0; i < np; i++ {
					Z1[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
					Z2[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
				}
			}
			plt.Contour(X, Y, Z2, "levels=[0,3],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
			plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['b'], levels=[0]")
		}

	// problem # 8 -- CTP8, Deb 2001, p368/373, fig 232
	case 8:
		ng = 2
		f1max = 5.0
		θ1, a, b := 0.1*PI, 40.0, 0.5
		c, d, e := 1.0, 2.0, -2.0
		θ2, A, B := -0.05*PI, 40.0, 2.0
		C, D, E := 1.0, 6.0, 0.0
		sin1, cos1 := math.Sin(θ1), math.Cos(θ1)
		sin2, cos2 := math.Sin(θ2), math.Cos(θ2)
		fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
			c0 := 1.0
			for i := 1; i < len(x); i++ {
				c0 += x[i]
			}
			f[0] = x[0]
			f[1] = c0 * (1.0 - f[0]/c0)
			if true {
				c1 := cos1*(f[1]-e) - sin1*f[0]
				c2 := sin1*(f[1]-e) + cos1*f[0]
				c3 := math.Sin(b * PI * math.Pow(c2, c))
				g[0] = c1 - a*math.Pow(math.Abs(c3), d)
				d1 := cos2*(f[1]-E) - sin2*f[0]
				d2 := sin2*(f[1]-E) + cos2*f[0]
				d3 := math.Sin(B * PI * math.Pow(d2, C))
				g[1] = d1 - A*math.Pow(math.Abs(d3), D)
			}
		}
		extraplot = func() {
			np := 401
			X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
			Z1 := utl.DblsAlloc(np, np)
			Z2 := utl.DblsAlloc(np, np)
			Z3 := utl.DblsAlloc(np, np)
			for j := 0; j < np; j++ {
				for i := 0; i < np; i++ {
					c1 := cos1*(Y[i][j]-e) - sin1*X[i][j]
					c2 := sin1*(Y[i][j]-e) + cos1*X[i][j]
					c3 := math.Sin(b * PI * math.Pow(c2, c))
					d1 := cos2*(Y[i][j]-E) - sin2*X[i][j]
					d2 := sin2*(Y[i][j]-E) + cos2*X[i][j]
					d3 := math.Sin(B * PI * math.Pow(d2, C))
					Z1[i][j] = c1 - a*math.Pow(math.Abs(c3), d)
					Z2[i][j] = d1 - A*math.Pow(math.Abs(d3), D)
					if Z1[i][j] >= 0 && Z2[i][j] >= 0 {
						Z3[i][j] = 1
					} else {
						Z3[i][j] = -1
					}
				}
			}
			plt.Contour(X, Y, Z3, "colors=['white','gray'],clabels=0,cbar=0,lwd=0.5,fsz=5")
			plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
			plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
		}
		opt.Multi_fcnErr = CTPerror1(θ1, a, b, c, d, e)

	default:
		chk.Panic("problem %d is not available", problem)
	}

	// initialise optimiser
	opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)

	// initial solutions
	var sols0 []*goga.Solution
	if false {
		sols0 = opt.GetSolutionsCopy()
	}

	// solve
	opt.RunMany("", "")
	goga.StatMulti(opt, true)
	io.PfYel("Tsys = %v\n", opt.SysTime)

	// check
	goga.CheckFront0(opt, true)

	// plot
	if true {
		feasibleOnly := false
		plt.SetForEps(0.8, 300)
		fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
		fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
		goga.PlotOvaOvaPareto(opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
		extraplot()
		//plt.AxisYrange(0, f1max)
		if problem > 0 && problem < 6 {
			plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
			plt.Text(0.95, f1max-0.05, "feasible", "color='white', ha='right',va='top'")
		}
		if opt.RptName == "CTP6" {
			plt.Text(0.02, 0.15, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
			plt.Text(0.02, 6.50, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
			plt.Text(0.02, 13.0, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
			plt.Text(0.50, 2.40, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
			plt.Text(0.50, 8.80, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
			plt.Text(0.50, 15.30, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
		}
		if opt.RptName == "TNK" {
			plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
			plt.Text(0.80, 0.85, "feasible", "color='white', ha='left',va='top'")
			plt.Equal()
			plt.AxisRange(0, 1.22, 0, 1.22)
		}
		plt.SaveD("/tmp/goga", io.Sf("%s.eps", opt.RptName))
	}
	return
}
Exemple #19
0
// PlotDiagMoment plots bending moment diagram
//  Input:
//   M        -- moment along stations
//   withtext -- show bending moment values
//   numfmt   -- number format for values. use "" to chose default one
//   tolM     -- tolerance to clip absolute values of M
//   sf       -- scaling factor
func (o *Beam) PlotDiagMoment(M []float64, withtext bool, numfmt string, tolM, sf float64) {

	// number of stations
	nstations := len(M)
	ds := 1.0 / float64(nstations-1)

	// nodes
	var xa, xb []float64
	var u []float64 // out-of-pane vector
	if o.Ndim == 2 {
		xa = []float64{o.X[0][0], o.X[1][0], 0}
		xb = []float64{o.X[0][1], o.X[1][1], 0}
		u = []float64{0, 0, 1}
	} else {
		chk.Panic("TODO: 3D beam diagram")
	}

	// unit vector along beam
	v := make([]float64, 3)
	sum := 0.0
	for j := 0; j < o.Ndim; j++ {
		v[j] = xb[j] - xa[j]
		sum += v[j] * v[j]
	}
	sum = math.Sqrt(sum)
	for j := 0; j < o.Ndim; j++ {
		v[j] /= sum
	}

	// unit normal
	n := make([]float64, 3)     // normal
	utl.CrossProduct3d(n, u, v) // n := u cross v

	// auxiliary vectors
	x := make([]float64, o.Ndim) // station
	m := make([]float64, o.Ndim) // vector pointing to other side
	c := make([]float64, o.Ndim) // centre
	imin, imax := utl.DblArgMinMax(M)

	// draw text function
	draw_text := func(mom float64) {
		if math.Abs(mom) > tolM {
			α := math.Atan2(-n[1], -n[0]) * 180.0 / math.Pi
			str := io.Sf("%g", mom)
			if numfmt != "" {
				str = io.Sf(numfmt, mom)
			} else {
				if len(str) > 10 {
					str = io.Sf("%.10f", mom) // truncate number
					str = io.Sf("%g", io.Atof(str))
				}
			}
			plt.Text(c[0], c[1], str, io.Sf("ha='center', size=7, rotation=%g, clip_on=0", α))
		}
	}

	// draw
	pts := utl.DblsAlloc(nstations, 2)
	xx, yy := make([]float64, 2), make([]float64, 2)
	for i := 0; i < nstations; i++ {

		// station
		s := float64(i) * ds
		for j := 0; j < o.Ndim; j++ {
			x[j] = (1.0-s)*o.X[j][0] + s*o.X[j][1]
		}

		// auxiliary vectors
		for j := 0; j < o.Ndim; j++ {
			m[j] = x[j] - sf*M[i]*n[j]
			c[j] = (x[j] + m[j]) / 2.0
		}

		// points on diagram
		pts[i][0], pts[i][1] = m[0], m[1]
		xx[0], xx[1] = x[0], m[0]
		yy[0], yy[1] = x[1], m[1]

		// draw
		clr, lw := "#919191", 1.0
		if i == imin || i == imax {
			lw = 2
			if M[i] < 0 {
				clr = "#9f0000"
			} else {
				clr = "#109f24"
			}
		}
		plt.Plot(xx, yy, io.Sf("'-', color='%s', lw=%g, clip_on=0", clr, lw))
		if withtext {
			if i == imin || i == imax { // draw text @ min/max
				draw_text(M[i])
			} else {
				if i == 0 || i == nstations-1 { // draw text @ extremities
					draw_text(M[i])
				}
			}
		}
	}

	// draw polyline
	plt.DrawPolyline(pts, &plt.Sty{Ec: "k", Fc: "none", Lw: 1}, "")
}