Golang plt.Plot函数代码示例

// Plot plots retention model
//  args1 -- arguments for model computed by solving differential equation; e.g. "'b*-'"
//           if args1 == "", plot is skiped
//  args2 -- arguments for model computed by directly calling sl(pc), if available
//           if args2 == "", plot is skiped
func Plot(mdl Model, pc0, sl0, pcf float64, npts int, args1, args2, label string) (err error) {

	// plot using Update
	Pc := utl.LinSpace(pc0, pcf, npts)
	Sl := make([]float64, npts)
	if args1 != "" {
		Sl[0] = sl0
		for i := 1; i < npts; i++ {
			Sl[i], err = Update(mdl, Pc[i-1], Sl[i-1], Pc[i]-Pc[i-1])
			if err != nil {
				return
			}
		}
		plt.Plot(Pc, Sl, io.Sf("%s, label='%s', clip_on=0", args1, label))
	}

	// plot using Sl function
	if args2 != "" {
		if m, ok := mdl.(Nonrate); ok {
			Pc = utl.LinSpace(pc0, pcf, 101)
			Sl = make([]float64, 101)
			for i, pc := range Pc {
				Sl[i] = m.Sl(pc)
			}
			plt.Plot(Pc, Sl, io.Sf("%s, label='%s_direct', clip_on=0", args2, label))
		}
	}
	return
}

func Test_functions03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("functions03")

	eps := 1e-2
	f := func(x float64) float64 { return Sabs(x, eps) }
	ff := func(x float64) float64 { return SabsD1(x, eps) }

	np := 401
	//x  := utl.LinSpace(-5e5, 5e5, np)
	//x  := utl.LinSpace(-5e2, 5e2, np)
	x := utl.LinSpace(-5e1, 5e1, np)
	Y := make([]float64, np)
	y := make([]float64, np)
	g := make([]float64, np)
	h := make([]float64, np)
	tolg, tolh := 1e-6, 1e-5
	with_err := false
	for i := 0; i < np; i++ {
		Y[i] = math.Abs(x[i])
		y[i] = Sabs(x[i], eps)
		g[i] = SabsD1(x[i], eps)
		h[i] = SabsD2(x[i], eps)
		gnum := numderiv(f, x[i])
		hnum := numderiv(ff, x[i])
		errg := math.Abs(g[i] - gnum)
		errh := math.Abs(h[i] - hnum)
		clrg, clrh := "[1;32m", "[1;32m"
		if errg > tolg {
			clrg, with_err = "[1;31m", true
		}
		if errh > tolh {
			clrh, with_err = "[1;31m", true
		}
		io.Pf("errg = %s%23.15e   errh = %s%23.15e[0m\n", clrg, errg, clrh, errh)
	}

	if with_err {
		chk.Panic("errors found")
	}

	if false {
		//if true {
		plt.Subplot(3, 1, 1)
		plt.Plot(x, y, "'k--', label='abs'")
		plt.Plot(x, y, "'b-', label='sabs'")
		plt.Gll("x", "y", "")

		plt.Subplot(3, 1, 2)
		plt.Plot(x, g, "'b-', label='sabs'")
		plt.Gll("x", "dy/dx", "")

		plt.Subplot(3, 1, 3)
		plt.Plot(x, h, "'b-', label='sabs'")
		plt.Gll("x", "d2y/dx2", "")

		plt.Show()
	}
}

func (o *Plotter) Plot_i_f(x, y []float64, res []*State, sts [][]float64, last bool) {
	if o.m == nil {
		o.set_empty()
		return
	}
	nr := len(res)
	var y2 []float64
	if o.nsurf > 1 {
		y2 = make([]float64, nr)
	}
	for i := 0; i < nr; i++ {
		ys := o.m.YieldFuncs(res[i])
		y[i] = ys[0]
		if o.nsurf > 1 {
			y2[i] = ys[1]
		}
		x[i] = float64(i)
	}
	lbl := "f " + o.Lbl
	plt.Plot(x, y, io.Sf("'r.', ls='-', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Clr, o.Mrk, lbl))
	if o.nsurf > 1 {
		lbl = "F " + o.Lbl
		plt.Plot(x, y2, io.Sf("'b+', ls=':', lw=2, clip_on=0, color='%s', marker='%s', label=r'%s'", o.Clr, o.Mrk, lbl))
	}
	if last {
		plt.Gll("$i$", "$f,\\;F$", "leg_out=1, leg_ncol=4, leg_hlen=2")
		if lims, ok := o.Lims["i,f"]; ok {
			plt.AxisLims(lims)
		}
	}
}

func main() {

	// filename
	filename, fnkey := io.ArgToFilename(0, "sg111", ".sim", true)

	// fem
	if !fem.Start(filename, false, false, false) {
		io.PfRed("Start failed\n")
		return
	}
	dom, sum, ok := fem.AllocSetAndInit(0, true, true)
	if !ok {
		io.PfRed("AllocSetAndInit failed\n")
		return
	}

	// selected node and dof index
	nidx := 1
	didx := 1

	// gofem
	ntout := len(sum.OutTimes)
	uy := make([]float64, ntout)
	for tidx, _ := range sum.OutTimes {

		// read results from file
		if !dom.In(sum, tidx, true) {
			io.PfRed("plot_spo751: cannot read solution\n")
			return
		}

		// collect results for load versus time plot
		nod := dom.Nodes[nidx]
		eq := nod.Dofs[didx].Eq
		uy[tidx] = dom.Sol.Y[eq]

		// check
		if math.Abs(dom.Sol.T-sum.OutTimes[tidx]) > 1e-14 {
			io.PfRed("output times do not match time in solution array\n")
			return
		}
	}

	// plot fem results
	plt.SetForPng(0.8, 400, 200)
	plt.Plot(sum.OutTimes, uy, "'ro-', clip_on=0, label='gofem'")

	// analytical solution
	tAna := utl.LinSpace(0, 5, 101)
	uyAna := make([]float64, len(tAna))
	for i, t := range tAna {
		uyAna[i] = solution_uy(t, 1.0)
	}
	plt.Plot(tAna, uyAna, "'g-', clip_on=0, label='analytical'")

	// save
	plt.Gll("$t$", "$u_y$", "")
	plt.SaveD("/tmp", fnkey+".png")
}

func main() {

	// GA parameters
	C := goga.ReadConfParams("tsp-simple.json")
	rnd.Init(C.Seed)

	// location / coordinates of stations
	locations := [][]float64{
		{60, 200}, {180, 200}, {80, 180}, {140, 180}, {20, 160}, {100, 160}, {200, 160},
		{140, 140}, {40, 120}, {100, 120}, {180, 100}, {60, 80}, {120, 80}, {180, 60},
		{20, 40}, {100, 40}, {200, 40}, {20, 20}, {60, 20}, {160, 20},
	}
	nstations := len(locations)
	C.SetIntOrd(nstations)
	C.CalcDerived()

	// objective value function
	C.OvaOor = func(ind *goga.Individual, idIsland, time int, report *bytes.Buffer) {
		L := locations
		ids := ind.Ints
		dist := 0.0
		for i := 1; i < nstations; i++ {
			a, b := ids[i-1], ids[i]
			dist += math.Sqrt(math.Pow(L[b][0]-L[a][0], 2.0) + math.Pow(L[b][1]-L[a][1], 2.0))
		}
		a, b := ids[nstations-1], ids[0]
		dist += math.Sqrt(math.Pow(L[b][0]-L[a][0], 2.0) + math.Pow(L[b][1]-L[a][1], 2.0))
		ind.Ovas[0] = dist
		return
	}

	// evolver
	nova, noor := 1, 0
	evo := goga.NewEvolver(nova, noor, C)
	evo.Run()

	// results
	io.Pfgreen("best = %v\n", evo.Best.Ints)
	io.Pfgreen("best OVA = %v  (871.117353844847)\n\n", evo.Best.Ovas[0])

	// plot travelling salesman path
	if C.DoPlot {
		plt.SetForEps(1, 300)
		X, Y := make([]float64, nstations), make([]float64, nstations)
		for k, id := range evo.Best.Ints {
			X[k], Y[k] = locations[id][0], locations[id][1]
			plt.PlotOne(X[k], Y[k], "'r.', ms=5, clip_on=0, zorder=20")
			plt.Text(X[k], Y[k], io.Sf("%d", id), "fontsize=7, clip_on=0, zorder=30")
		}
		plt.Plot(X, Y, "'b-', clip_on=0, zorder=10")
		plt.Plot([]float64{X[0], X[nstations-1]}, []float64{Y[0], Y[nstations-1]}, "'b-', clip_on=0, zorder=10")
		plt.Equal()
		plt.AxisRange(10, 210, 10, 210)
		plt.Gll("$x$", "$y$", "")
		plt.SaveD("/tmp/goga", "test_evo04.eps")
	}
}

// DrawCtrl2d draws control net
func (o *Nurbs) DrawCtrl2d(ids bool, args, idargs string) {
	if len(idargs) == 0 {
		idargs = "color='r', size=7"
	}
	switch o.gnd {
	// curve
	case 1:
		xa := make([]float64, o.n[0])
		ya := make([]float64, o.n[0])
		j, k := 0, 0
		for i := 0; i < o.n[0]; i++ {
			xa[i] = o.Q[i][j][k][0] / o.Q[i][j][k][3]
			ya[i] = o.Q[i][j][k][1] / o.Q[i][j][k][3]
		}
		plt.Plot(xa, ya, "'k.--', clip_on=0"+args)
		if ids {
			for i := 0; i < o.n[0]; i++ {
				x := o.Q[i][j][k][0] / o.Q[i][j][k][3]
				y := o.Q[i][j][k][1] / o.Q[i][j][k][3]
				plt.Text(x, y, io.Sf("%d", i), idargs)
			}
		}
	// surface
	case 2:
		xa := make([]float64, o.n[1])
		ya := make([]float64, o.n[1])
		k := 0
		for i := 0; i < o.n[0]; i++ {
			for j := 0; j < o.n[1]; j++ {
				xa[j] = o.Q[i][j][k][0] / o.Q[i][j][k][3]
				ya[j] = o.Q[i][j][k][1] / o.Q[i][j][k][3]
			}
			plt.Plot(xa, ya, "'k.--', clip_on=0"+args)
		}
		xb := make([]float64, o.n[0])
		yb := make([]float64, o.n[0])
		for j := 0; j < o.n[1]; j++ {
			for i := 0; i < o.n[0]; i++ {
				xb[i] = o.Q[i][j][k][0] / o.Q[i][j][k][3]
				yb[i] = o.Q[i][j][k][1] / o.Q[i][j][k][3]
			}
			plt.Plot(xb, yb, "'k.--', clip_on=0"+args)
		}
		if ids {
			for i := 0; i < o.n[0]; i++ {
				for j := 0; j < o.n[1]; j++ {
					x := o.Q[i][j][k][0] / o.Q[i][j][k][3]
					y := o.Q[i][j][k][1] / o.Q[i][j][k][3]
					l := i + j*o.n[0]
					plt.Text(x, y, io.Sf("%d", l), idargs)
				}
			}
		}
	}
}

func main() {

	// filename
	filename, fnkey := io.ArgToFilename(0, "rjoint01", ".sim", true)

	// fem
	if !fem.Start(filename, false, false, false) {
		io.PfRed("Start failed\n")
		return
	}
	dom, sum, ok := fem.AllocSetAndInit(0, true, true)
	if !ok {
		io.PfRed("AllocSetAndInit failed\n")
		return
	}

	// rjoint element
	eid := 2
	ele := dom.Elems[eid].(*fem.Rjoint)
	ipd := ele.OutIpsData()

	// load results from file
	n := len(sum.OutTimes)
	mtau0 := make([]float64, n)
	mtau1 := make([]float64, n)
	mtau2 := make([]float64, n)
	ompb0 := make([]float64, n)
	ompb1 := make([]float64, n)
	ompb2 := make([]float64, n)
	for i, _ := range sum.OutTimes {
		if !dom.In(sum, i, true) {
			io.PfRed("cannot read solution\n")
			return
		}
		res0 := ipd[0].Calc(dom.Sol)
		res1 := ipd[1].Calc(dom.Sol)
		res2 := ipd[2].Calc(dom.Sol)
		mtau0[i] = -res0["tau"]
		mtau1[i] = -res1["tau"]
		mtau2[i] = -res2["tau"]
		ompb0[i] = res0["ompb"]
		ompb1[i] = res1["ompb"]
		ompb2[i] = res2["ompb"]
	}

	// plot
	plt.SetForPng(0.8, 400, 200)
	plt.Plot(ompb0, mtau0, "'r-', marker='.', label='p0', clip_on=0")
	plt.Plot(ompb1, mtau1, "'g-', marker='.', label='p1', clip_on=0")
	plt.Plot(ompb2, mtau2, "'b-', marker='.', label='p2', clip_on=0")
	plt.Gll("$\\bar{\\omega}_p$", "$-\\tau$", "")
	plt.SaveD("/tmp", fnkey+".png")
}

// PlotStar plots star with normalised OVAs
func (o *Optimiser) PlotStar() {
	nf := o.Nf
	dθ := 2.0 * math.Pi / float64(nf)
	θ0 := 0.0
	if nf == 3 {
		θ0 = -math.Pi / 6.0
	}
	for _, ρ := range []float64{0.25, 0.5, 0.75, 1.0} {
		plt.Circle(0, 0, ρ, "ec='gray',lw=0.5,zorder=5")
	}
	arrowM, textM := 1.1, 1.15
	for i := 0; i < nf; i++ {
		θ := θ0 + float64(i)*dθ
		xi, yi := 0.0, 0.0
		xf, yf := arrowM*math.Cos(θ), arrowM*math.Sin(θ)
		plt.Arrow(xi, yi, xf, yf, "sc=10,st='->',lw=0.7,zorder=10,clip_on=0")
		plt.PlotOne(xf, yf, "'k+', ms=0")
		xf, yf = textM*math.Cos(θ), textM*math.Sin(θ)
		plt.Text(xf, yf, io.Sf("%d", i), "size=6,zorder=10,clip_on=0")
	}
	X, Y := make([]float64, nf+1), make([]float64, nf+1)
	clr := false
	neg := false
	step := 1
	count := 0
	colors := []string{"m", "orange", "g", "r", "b", "k"}
	var ρ float64
	for i, sol := range o.Solutions {
		if sol.Feasible() && sol.FrontId == 0 && i%step == 0 {
			for j := 0; j < nf; j++ {
				if neg {
					ρ = 1.0 - sol.Ova[j]/(o.RptFmax[j]-o.RptFmin[j])
				} else {
					ρ = sol.Ova[j] / (o.RptFmax[j] - o.RptFmin[j])
				}
				θ := θ0 + float64(j)*dθ
				X[j], Y[j] = ρ*math.Cos(θ), ρ*math.Sin(θ)
			}
			X[nf], Y[nf] = X[0], Y[0]
			if clr {
				j := count % len(colors)
				plt.Plot(X, Y, io.Sf("'k-',color='%s',markersize=3,clip_on=0", colors[j]))
			} else {
				plt.Plot(X, Y, "'r-',marker='.',markersize=3,clip_on=0")
			}
			count++
		}
	}
	plt.Equal()
	plt.AxisOff()
}

// 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)
}

// PlotT plots F, G and H for varying t and fixed coordinates x
func PlotT(o Func, dirout, fname string, t0, tf float64, xcte []float64, np int, args string, withG, withH, save, show bool, extra func()) {
	t := utl.LinSpace(t0, tf, np)
	y := make([]float64, np)
	for i := 0; i < np; i++ {
		y[i] = o.F(t[i], xcte)
	}
	var g, h []float64
	nrow := 1
	if withG {
		g = make([]float64, np)
		for i := 0; i < np; i++ {
			g[i] = o.G(t[i], xcte)
		}
		nrow += 1
	}
	if withH {
		h = make([]float64, np)
		for i := 0; i < np; i++ {
			h[i] = o.H(t[i], xcte)
		}
		nrow += 1
	}
	os.MkdirAll(dirout, 0777)
	if withG || withH {
		plt.Subplot(nrow, 1, 1)
	}
	plt.Plot(t, y, args)
	if extra != nil {
		extra()
	}
	plt.Gll("t", "y", "")
	pidx := 2
	if withG {
		plt.Subplot(nrow, 1, pidx)
		plt.Plot(t, g, args)
		plt.Gll("t", "dy/dt", "")
		pidx += 1
	}
	if withH {
		plt.Subplot(nrow, 1, pidx)
		plt.Plot(t, h, args)
		plt.Gll("t", "d2y/dt2", "")
	}
	if save {
		plt.Save(dirout + "/" + fname)
	}
	if show {
		plt.Show()
	}
}

func Test_Mw02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("Mw02")

	prms := []string{"φ", "Mfix"}
	vals := []float64{32, 0}
	var o NcteM
	o.Init(prms, vals)

	if SAVE_FIG {
		// rosette
		full, ref := false, true
		r := 1.1 * SQ2 * o.M(1) / 3.0
		PlotRosette(r, full, ref, true, 7)

		// NcteM
		npts := 201
		X := make([]float64, npts)
		Y := make([]float64, npts)
		W := utl.LinSpace(-1, 1, npts)
		for i, w := range W {
			θ := math.Asin(w) / 3.0
			r := SQ2 * o.M(w) / 3.0
			X[i] = -r * math.Sin(math.Pi/6.0-θ)
			Y[i] = r * math.Cos(math.Pi/6.0-θ)
			//plt.Text(X[i], Y[i], io.Sf("$\\\\theta=%.2f$", θ*180.0/math.Pi), "size=8, ha='center', color='red'")
			//plt.Text(X[i], Y[i], io.Sf("$w=%.2f$", w), "size=8, ha='center', color='red'")
		}
		plt.Plot(X, Y, "'b-'")

		// MC
		g := func(θ float64) float64 {
			return SQ2 * o.Sinφ / (SQ3*math.Cos(θ) - o.Sinφ*math.Sin(θ))
		}
		io.Pforan("M( 1) = %v\n", SQ2*o.M(1)/3.0)
		io.Pforan("g(30) = %v\n", g(math.Pi/6.0))
		for i, w := range W {
			θ := math.Asin(w) / 3.0
			r := g(θ)
			X[i] = -r * math.Sin(math.Pi/6.0-θ)
			Y[i] = r * math.Cos(math.Pi/6.0-θ)
		}
		plt.Plot(X, Y, "'k-'")

		// save
		plt.Equal()
		plt.SaveD("/tmp/gosl", "mw02.eps")
	}
}

// PlotDerivs plots derivatives of basis functions in I
// option =  0 : use CalcBasisAndDerivs
//           1 : use NumericalDeriv
func (o *Bspline) PlotDerivs(args string, npts, option int) {
	nmks := 10
	tt := utl.LinSpace(o.tmin, o.tmax, npts)
	I := utl.IntRange(o.NumBasis())
	f := make([]float64, len(tt))
	lbls := []string{"N\\&dN", "numD"}
	var cmd string
	for _, i := range I {
		for j, t := range tt {
			switch option {
			case 0:
				o.CalcBasisAndDerivs(t)
				f[j] = o.GetDeriv(i)
			case 1:
				f[j] = o.NumericalDeriv(t, i)
			}
		}
		if strings.Contains(args, "marker") {
			cmd = io.Sf("label=r'%s:%d', color=GetClr(%d, 2) %s", lbls[option], i, i, args)
		} else {
			cmd = io.Sf("label=r'%s:%d', marker=(None if %d %%2 == 0 else GetMrk(%d/2,1)), markevery=(%d-1)/%d, clip_on=0, color=GetClr(%d, 2) %s", lbls[option], i, i, i, npts, nmks, i, args)
		}
		plt.Plot(tt, f, cmd)
	}
	plt.Gll("$t$", io.Sf(`$\frac{\mathrm{d}N_{i,%d}}{\mathrm{d}t}$`, o.p), io.Sf("leg=1, leg_out=1, leg_ncol=%d, leg_hlen=1.5, leg_fsz=7", o.NumBasis()))
	o.plt_ticks_spans()
}

func (o *Plotter) Plot_Dgam_f(x, y []float64, res []*State, sts [][]float64, last bool) {
	if o.m == nil {
		o.set_empty()
		return
	}
	nr := len(res)
	k := nr - 1
	ys := o.m.YieldFuncs(res[0])
	fc0 := ys[0]
	xmi, xma, ymi, yma := res[0].Dgam, res[0].Dgam, fc0, fc0
	for i := 0; i < nr; i++ {
		x[i] = res[i].Dgam
		ys = o.m.YieldFuncs(res[i])
		y[i] = ys[0]
		xmi = min(xmi, x[i])
		xma = max(xma, x[i])
		ymi = min(ymi, y[i])
		yma = max(yma, y[i])
	}
	//o.DrawRamp(xmi, xma, ymi, yma)
	plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
	plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
	plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
	if last {
		plt.Gll("$\\Delta\\gamma$", "$f$", "")
		if lims, ok := o.Lims["Dgam,f"]; ok {
			plt.AxisLims(lims)
		}
	}
}

// PlotFltOva plots flt-ova points
func (o *Optimiser) PlotFltOva(sols0 []*Solution, iFlt, iOva int, ovaMult float64, pp *PlotParams) {
	if pp.YfuncX != nil {
		X := utl.LinSpace(o.FltMin[iFlt], o.FltMax[iFlt], pp.NptsYfX)
		Y := make([]float64, pp.NptsYfX)
		for i := 0; i < pp.NptsYfX; i++ {
			Y[i] = pp.YfuncX(X[i])
		}
		plt.Plot(X, Y, pp.FmtYfX.GetArgs(""))
	}
	if sols0 != nil {
		o.PlotAddFltOva(iFlt, iOva, sols0, ovaMult, &pp.FmtSols0)
	}
	o.PlotAddFltOva(iFlt, iOva, o.Solutions, ovaMult, &pp.FmtSols)
	best, _ := GetBestFeasible(o, iOva)
	if best != nil {
		plt.PlotOne(best.Flt[iFlt], best.Ova[iOva]*ovaMult, pp.FmtBest.GetArgs(""))
	}
	if pp.Extra != nil {
		pp.Extra()
	}
	if pp.AxEqual {
		plt.Equal()
	}
	plt.Gll(io.Sf("$x_{%d}$", iFlt), io.Sf("$f_{%d}$", iOva), "leg_out=1, leg_ncol=4, leg_hlen=1.5")
	plt.SaveD(pp.DirOut, pp.FnKey+pp.FnExt)
}

func main() {

	// filename
	filename, fnkey := io.ArgToFilename(0, "sg111", ".sim", true)

	// results
	out.Start(filename, 0, 0)
	out.Define("tip", out.N{1})
	out.LoadResults(nil)

	// plot FEM results
	out.Plot("t", "uy", "tip", plt.Fmt{C: "r", Ls: "None", M: ".", L: "gofem"}, -1)

	// analytical solution
	tAna := utl.LinSpace(0, 5, 101)
	uyAna := make([]float64, len(tAna))
	for i, t := range tAna {
		uyAna[i] = solution_uy(t, 1.0)
	}

	// save
	plt.SetForPng(0.8, 400, 200)
	out.Draw("/tmp", fnkey+".png", false, func(i, j, n int) {
		plt.Plot(tAna, uyAna, "'g-', clip_on=0, label='analytical'")
	})
}