func Test_dist_frechet_02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("dist_frechet_02")

	doplot := chk.Verbose
	if doplot {
		plt.SetForEps(1.5, 300)
		l := 0.0                // location
		C := []float64{1, 2.0}  // scale
		A := []float64{1, 2, 3} // shape
		for _, c := range C {
			for _, a := range A {
				plot_frechet(l, c, a, 0, 4)
			}
		}
		plt.SaveD("/tmp/gosl", "rnd_dist_frechet_02a.eps")
		plt.SetForEps(1.5, 300)
		l = 0.5                // location
		C = []float64{1, 2.0}  // scale
		A = []float64{1, 2, 3} // shape
		for _, c := range C {
			for _, a := range A {
				plot_frechet(l, c, a, 0, 4)
			}
		}
		plt.SaveD("/tmp/gosl", "rnd_dist_frechet_02b.eps")
	}
}

// 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)
}

// PlotTwoNurbs plots two NURBS for comparison
func PlotTwoNurbs(dirout, fn string, b, c *Nurbs, npts int, ids bool, extra func()) {
	plt.Reset()
	if io.FnExt(fn) == ".eps" {
		plt.SetForEps(1.5, 500)
	} else {
		plt.SetForPng(1.5, 500, 150)
	}

	plt.Subplot(3, 1, 1)
	b.DrawCtrl2d(ids, "", "")
	b.DrawElems2d(npts, ids, "", "")
	if extra != nil {
		extra()
	}
	plt.Equal()

	plt.Subplot(3, 1, 2)
	c.DrawCtrl2d(ids, "", "")
	c.DrawElems2d(npts, ids, "", "")
	plt.Equal()

	plt.Subplot(3, 1, 3)
	b.DrawElems2d(npts, ids, ", lw=3", "")
	c.DrawElems2d(npts, ids, ", color='red', marker='+', markevery=10", "color='green', size=7, va='bottom'")
	plt.Equal()

	plt.SaveD(dirout, fn)
}

func Test_tri01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("tri01")

	V := [][]float64{
		{0.0, 0.0},
		{1.0, 0.0},
		{1.0, 1.0},
		{0.0, 1.0},
		{0.5, 0.5},
	}

	C := [][]int{
		{0, 1, 4},
		{1, 2, 4},
		{2, 3, 4},
		{3, 0, 4},
	}

	if chk.Verbose {
		plt.SetForPng(1, 300, 150)
		Draw(V, C, nil)
		plt.Equal()
		plt.AxisRange(-0.1, 1.1, -0.1, 1.1)
		plt.Gll("x", "y", "")
		plt.SaveD("/tmp/gosl/tri", "tri01.png")
	}
}

func Test_data3d(tst *testing.T) {

	// data
	prob := "CF9"
	dat := PFdata(prob)
	X := utl.DblsGetColumn(0, dat)
	Y := utl.DblsGetColumn(1, dat)
	Z := utl.DblsGetColumn(2, dat)

	// figure
	plt.SetForEps(1.0, 400)
	plt.Plot3dPoints(X, Y, Z, "s=0.05, color='r', facecolor='r', edgecolor='r', xlbl='$f_1$', ylbl='$f_2$', zlbl='$f_3$'")
	plt.AxisRange3d(0, 1, 0, 1, 0, 1)
	plt.Camera(10, -135, "")
	//plt.Camera(10, 45, "")
	plt.SaveD("/tmp/goga", io.Sf("cec09-%s.eps", prob))

	// interactive
	if false {
		r := 0.005
		scn := vtk.NewScene()
		P := vtk.Spheres{X: X, Y: Y, Z: Z, R: utl.DblVals(len(X), r), Color: []float64{1, 0, 0, 1}}
		P.AddTo(scn)
		scn.Run()
	}
}

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")
}

// PlotTwoVarsContour plots contour for two variables problem. len(x) == 2
//  Input
//   dirout  -- directory to save files
//   fnkey   -- file name key for eps figure
//   x       -- solution. can be <nil>
//   np      -- number of points for contour
//   extra   -- called just before saving figure
//   axequal -- axis.equal
//   vmin    -- min 0 values
//   vmax    -- max 1 values
//   f       -- function to plot filled contour. can be <nil>
//   gs      -- functions to plot contour @ level 0. can be <nil>
func PlotTwoVarsContour(dirout, fnkey string, x []float64, np int, extra func(), axequal bool,
	vmin, vmax []float64, f TwoVarsFunc_t, gs ...TwoVarsFunc_t) {
	if fnkey == "" {
		return
	}
	chk.IntAssert(len(vmin), 2)
	chk.IntAssert(len(vmax), 2)
	V0, V1 := utl.MeshGrid2D(vmin[0], vmax[0], vmin[1], vmax[1], np, np)
	var Zf [][]float64
	var Zg [][][]float64
	if f != nil {
		Zf = la.MatAlloc(np, np)
	}
	if len(gs) > 0 {
		Zg = utl.Deep3alloc(len(gs), np, np)
	}
	xtmp := make([]float64, 2)
	for i := 0; i < np; i++ {
		for j := 0; j < np; j++ {
			xtmp[0], xtmp[1] = V0[i][j], V1[i][j]
			if f != nil {
				Zf[i][j] = f(xtmp)
			}
			for k, g := range gs {
				Zg[k][i][j] = g(xtmp)
			}
		}
	}
	plt.Reset()
	plt.SetForEps(0.8, 350)
	if f != nil {
		cmapidx := 0
		plt.Contour(V0, V1, Zf, io.Sf("fsz=7, cmapidx=%d", cmapidx))
	}
	for k, _ := range gs {
		plt.ContourSimple(V0, V1, Zg[k], false, 8, "zorder=5, levels=[0], colors=['yellow'], linewidths=[2], clip_on=0")
	}
	if x != nil {
		plt.PlotOne(x[0], x[1], "'r*', label='optimum', zorder=10")
	}
	if extra != nil {
		extra()
	}
	if dirout == "" {
		dirout = "."
	}
	plt.Cross("clr='grey'")
	plt.SetXnticks(11)
	plt.SetYnticks(11)
	if axequal {
		plt.Equal()
	}
	plt.AxisRange(vmin[0], vmax[0], vmin[1], vmax[1])
	args := "leg_out='1', leg_ncol=4, leg_hlen=1.5"
	plt.Gll("$x_0$", "$x_1$", args)
	plt.SaveD(dirout, fnkey+".eps")
}

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")
	}
}

func main() {
	Nf := []float64{5, 7, 10, 13, 15, 20}
	Eave := []float64{3.5998e-12, 2.9629e-10, 6.0300e-8, 3.3686e-6, 2.5914e-5, 1.1966e-3}
	plt.SetForEps(0.75, 200)
	plt.Plot(Nf, Eave, "'b-', marker='.', clip_on=0")
	plt.SetYlog()
	plt.Gll("$N_f$", "$E_{ave}$", "")
	plt.SaveD("/tmp/goga", "multierror.eps")
}

func Test_igd01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("igd. igd metric with star equal to trial => igd=0")

	// load star values
	prob := "UF1"
	fStar, err := io.ReadMatrix(io.Sf("./examples/mulobj-cec09/cec09/pf_data/%s.dat", prob))
	if err != nil {
		tst.Errorf("cannot read fStar matrix:\n%v", err)
		return
	}
	npts := len(fStar)

	// optimiser
	var opt Optimiser
	opt.Default()
	opt.Nsol = npts
	opt.Ncpu = 1
	opt.FltMin = []float64{0, 0} // used to store fStar
	opt.FltMax = []float64{1, 1} // used to store fStar
	nf, ng, nh := 2, 0, 0

	// generator (store fStar into Flt)
	gen := func(sols []*Solution, prms *Parameters) {
		for i, sol := range sols {
			sol.Flt[0], sol.Flt[1] = fStar[i][0], fStar[i][1]
		}
	}

	// objective function (copy fStar from Flt into Ova)
	obj := func(f, g, h, x []float64, ξ []int, cpu int) {
		f[0], f[1] = x[0], x[1]
	}

	// initialise optimiser
	opt.Init(gen, nil, obj, nf, ng, nh)

	// compute igd
	igd := StatIgd(&opt, fStar)
	io.Pforan("igd = %v\n", igd)
	chk.Scalar(tst, "igd", 1e-15, igd, 0)

	// plot
	if chk.Verbose {
		fmt := &plt.Fmt{C: "red", M: ".", Ms: 1, Ls: "None", L: "solutions"}
		fS0 := utl.DblsGetColumn(0, fStar)
		fS1 := utl.DblsGetColumn(1, fStar)
		io.Pforan("len(fS0) = %v\n", len(fS0))
		plt.SetForEps(0.75, 300)
		opt.PlotAddOvaOva(0, 1, opt.Solutions, true, fmt)
		plt.Plot(fS0, fS1, io.Sf("'b.', ms=2, label='star(%s)', clip_on=0", prob))
		plt.Gll("$f_0$", "$f_1$", "")
		plt.SaveD("/tmp/goga", "igd01.eps")
	}
}

func Test_bspline01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("bspline01")

	var s1 Bspline
	T1 := []float64{0, 0, 0, 1, 1, 1}
	s1.Init(T1, 2)
	s1.SetControl([][]float64{{0, 0}, {0.5, 1}, {1, 0}})

	var s2 Bspline
	T2 := []float64{0, 0, 0, 0.5, 1, 1, 1}
	s2.Init(T2, 2)
	s2.SetControl([][]float64{{0, 0}, {0.25, 0.5}, {0.75, 0.5}, {1, 0}})

	if chk.Verbose {
		npts := 201
		plt.SetForPng(1.5, 600, 150)
		plt.SplotGap(0.2, 0.4)

		str0 := ",lw=2"
		str1 := ",ls='none',marker='+',color='cyan',markevery=10"
		str2 := ",ls='none',marker='x',markevery=10"
		str3 := ",ls='none',marker='+',markevery=10"
		str4 := ",ls='none',marker='4',markevery=10"

		plt.Subplot(3, 2, 1)
		s1.Draw2d(str0, "", npts, 0) // 0 => CalcBasis
		s1.Draw2d(str1, "", npts, 1) // 1 => RecursiveBasis

		plt.Subplot(3, 2, 2)
		plt.SetAxis(0, 1, 0, 1)
		s2.Draw2d(str0, "", npts, 0) // 0 => CalcBasis
		s2.Draw2d(str1, "", npts, 1) // 1 => RecursiveBasis

		plt.Subplot(3, 2, 3)
		s1.PlotBasis("", npts, 0)   // 0 => CalcBasis
		s1.PlotBasis(str2, npts, 1) // 1 => CalcBasisAndDerivs
		s1.PlotBasis(str3, npts, 2) // 2 => RecursiveBasis

		plt.Subplot(3, 2, 4)
		s2.PlotBasis("", npts, 0)   // 0 => CalcBasis
		s2.PlotBasis(str2, npts, 1) // 1 => CalcBasisAndDerivs
		s2.PlotBasis(str3, npts, 2) // 2 => RecursiveBasis

		plt.Subplot(3, 2, 5)
		s1.PlotDerivs("", npts, 0)   // 0 => CalcBasisAndDerivs
		s1.PlotDerivs(str4, npts, 1) // 1 => NumericalDeriv

		plt.Subplot(3, 2, 6)
		s2.PlotDerivs("", npts, 0)   // 0 => CalcBasisAndDerivs
		s2.PlotDerivs(str4, npts, 1) // 1 => NumericalDeriv

		plt.SaveD("/tmp/gosl/gm", "bspline01.png")
	}
}

func Test_data2d(tst *testing.T) {
	prob := "CF4"
	dat := PFdata(prob)
	X := utl.DblsGetColumn(0, dat)
	Y := utl.DblsGetColumn(1, dat)
	plt.SetForEps(1.0, 250)
	plt.Plot(X, Y, "'r.'")
	plt.Gll("$f_1$", "$f_2$", "")
	plt.SaveD("/tmp/goga", io.Sf("cec09-%s.eps", prob))
}

func Test_bins02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("bins02. find along line (2D)")

	// bins
	var bins Bins
	bins.Init([]float64{-0.2, -0.2}, []float64{0.8, 1.8}, 5)

	// fill bins structure
	maxit := 5 // number of entries
	ID := make([]int, maxit)
	for k := 0; k < maxit; k++ {
		x := float64(k) / float64(maxit)
		ID[k] = k
		err := bins.Append([]float64{x, 2*x + 0.2}, ID[k])
		if err != nil {
			chk.Panic(err.Error())
		}
	}

	// add more points to bins
	for i := 0; i < 5; i++ {
		err := bins.Append([]float64{float64(i) * 0.1, 1.8}, 100+i)
		if err != nil {
			chk.Panic(err.Error())
		}
	}

	// message
	for _, bin := range bins.All {
		if bin != nil {
			io.Pf("%v\n", bin)
		}
	}

	// find points along diagonal
	ids := bins.FindAlongSegment([]float64{0.0, 0.2}, []float64{0.8, 1.8}, 1e-8)
	io.Pforan("ids = %v\n", ids)
	chk.Ints(tst, "ids", ids, ID)

	// find additional points
	ids = bins.FindAlongSegment([]float64{-0.2, 1.8}, []float64{0.8, 1.8}, 1e-8)
	io.Pfcyan("ids = %v\n", ids)
	chk.Ints(tst, "ids", ids, []int{100, 101, 102, 103, 104, 4})

	// draw
	if chk.Verbose {
		plt.SetForPng(1, 500, 150)
		bins.Draw2d(true, true, true, true, map[int]bool{8: true, 9: true, 10: true})
		plt.SetXnticks(15)
		plt.SetYnticks(15)
		plt.SaveD("/tmp/gosl/gm", "test_bins02.png")
	}
}

func savefig(dirout, fnk, ext string, idx int) {
	fn := fnk + ext
	if idx >= 0 {
		fn = io.Sf("%s_%d%s", fnk, idx, ext)
	}
	if dirout == "" {
		plt.Save(fn)
	} else {
		plt.SaveD(dirout, fn)
	}
}

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")
}

// PlotFltFlt plots flt-flt contour
// use iFlt==-1 || jFlt==-1 to plot all combinations
func (o *Optimiser) PlotFltFltContour(sols0 []*Solution, iFlt, jFlt, iOva int, pp *PlotParams) {
	best, _ := GetBestFeasible(o, iOva)
	plotAll := iFlt < 0 || jFlt < 0
	plotCommands := func(i, j int) {
		o.PlotContour(i, j, iOva, pp)
		if sols0 != nil {
			o.PlotAddFltFlt(i, j, sols0, &pp.FmtSols0)
		}
		o.PlotAddFltFlt(i, j, o.Solutions, &pp.FmtSols)
		if best != nil {
			plt.PlotOne(best.Flt[i], best.Flt[j], pp.FmtBest.GetArgs(""))
		}
		if pp.Extra != nil {
			pp.Extra()
		}
		if pp.AxEqual {
			plt.Equal()
		}
	}
	if plotAll {
		idx := 1
		ncol := o.Nflt - 1
		for row := 0; row < o.Nflt; row++ {
			idx += row
			for col := row + 1; col < o.Nflt; col++ {
				plt.Subplot(ncol, ncol, idx)
				plt.SplotGap(0.0, 0.0)
				plotCommands(col, row)
				if col > row+1 {
					plt.SetXnticks(0)
					plt.SetYnticks(0)
				} else {
					plt.Gll(io.Sf("$x_{%d}$", col), io.Sf("$x_{%d}$", row), "leg=0")
				}
				idx++
			}
		}
		idx = ncol*(ncol-1) + 1
		plt.Subplot(ncol, ncol, idx)
		plt.AxisOff()
		// TODO: fix formatting of open marker, add star to legend
		plt.DrawLegend([]plt.Fmt{pp.FmtSols0, pp.FmtSols, pp.FmtBest}, 8, "center", false, "")
	} else {
		plotCommands(iFlt, jFlt)
		if pp.Xlabel == "" {
			plt.Gll(io.Sf("$x_{%d}$", iFlt), io.Sf("$x_{%d}$", jFlt), pp.LegPrms)
		} else {
			plt.Gll(pp.Xlabel, pp.Ylabel, pp.LegPrms)
		}
	}
	plt.SaveD(pp.DirOut, pp.FnKey+pp.FnExt)
}

func plot2(opt *goga.Optimiser, onlyFront0 bool) {

	// plot reference values
	f0 := utl.DblsGetColumn(0, opt.Multi_fStar)
	f1 := utl.DblsGetColumn(1, opt.Multi_fStar)
	plt.Plot(f0, f1, "'b-', label='reference'")

	// plot goga values
	fmt := &plt.Fmt{C: "r", M: "o", Ms: 3, L: "goga", Ls: "None"}
	opt.PlotAddOvaOva(0, 1, opt.Solutions, true, fmt)
	plt.Gll("$f_0$", "$f_1$", "")
	plt.SaveD("/tmp/goga", io.Sf("m2_%s.eps", opt.RptName))
}

func Test_nurbs02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("nurbs02")

	b := get_nurbs_A()
	do_check_derivs(tst, b, 11, 1e-5, false)

	if T_NURBS_SAVE {
		do_plot_nurbs_derivs(b, 0, 7)
		plt.SaveD("/tmp/gosl", "t_nurbs02.eps")
	}
}

// PlotNurbsBasis plots basis functions la and lb
func PlotNurbsBasis(dirout, fn string, b *Nurbs, la, lb int) {
	npts := 41
	plt.Reset()
	if io.FnExt(fn) == ".eps" {
		plt.SetForEps(1.5, 500)
	} else {
		plt.SetForPng(1.5, 600, 150)
	}

	plt.Subplot(3, 2, 1)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	t0 := time.Now()
	b.PlotBasis(la, "", 11, 0) // 0 => CalcBasis
	io.Pfcyan("time elapsed (calcbasis) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(3, 2, 2)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	b.PlotBasis(lb, "", 11, 0) // 0 => CalcBasis
	plt.Equal()

	plt.Subplot(3, 2, 3)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	b.PlotBasis(la, "", 11, 1) // 1 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(3, 2, 4)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	b.PlotBasis(lb, "", 11, 1) // 1 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(3, 2, 5)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	t0 = time.Now()
	b.PlotBasis(la, "", 11, 2) // 2 => RecursiveBasis
	io.Pfcyan("time elapsed (recursive) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(3, 2, 6)
	b.DrawCtrl2d(false, "", "")
	b.DrawElems2d(npts, false, "", "")
	b.PlotBasis(lb, "", 11, 2) // 2 => RecursiveBasis
	plt.Equal()

	plt.SaveD(dirout, fn)
}

func Test_invs05(tst *testing.T) {

	//verbose()
	chk.PrintTitle("invs05")

	if SAVEPLOT {
		plt.Reset()
		plt.SetForPng(1, 500, 125)
		PlotRosette(1.1, true, true, true, 7)
	}

	addtoplot := func(σa, σb float64, σ []float64) {
		plt.PlotOne(σa, σb, "'ro', ms=5")
		plt.Text(σa, σb, io.Sf("$\\sigma_{123}=(%g,%g,%g)$", σ[0], σ[1], σ[2]), "size=8")
	}

	dotest := func(σ []float64, σacor, σbcor, σccor, θcor, tolσ float64) {
		w := M_w(σ)
		θ2 := math.Asin(w) * 180.0 / (3.0 * math.Pi)
		θ3 := M_θ(σ)
		σa, σb, σc := L2O(σ[0], σ[1], σ[2])
		σ0, σ1, σ2 := O2L(σa, σb, σc)
		σI, σA := make([]float64, 3), []float64{σa, σb, σc}
		la.MatVecMul(σI, 1, O2Lmat(), σA) // σI := L * σA
		io.Pf("σa σb σc = %v %v %v\n", σa, σb, σc)
		io.Pf("w        = %v\n", w)
		io.Pf("θ2, θ3   = %v, %v\n", θ2, θ3)
		chk.Scalar(tst, "σa", 1e-17, σa, σacor)
		chk.Scalar(tst, "σb", 1e-17, σb, σbcor)
		chk.Scalar(tst, "σc", 1e-17, σc, σccor)
		chk.Scalar(tst, "σ0", tolσ, σ0, σ[0])
		chk.Scalar(tst, "σ1", tolσ, σ1, σ[1])
		chk.Scalar(tst, "σ2", tolσ, σ2, σ[2])
		chk.Scalar(tst, "σI0", tolσ, σI[0], σ[0])
		chk.Scalar(tst, "σI1", tolσ, σI[1], σ[1])
		chk.Scalar(tst, "σI2", tolσ, σI[2], σ[2])
		chk.Scalar(tst, "θ2", 1e-6, θ2, θcor)
		chk.Scalar(tst, "θ3", 1e-17, θ3, θ2)
		addtoplot(σa, σb, σ)
	}

	dotest([]float64{-1, 0, 0, 0}, 0, 2.0/SQ6, 1.0/SQ3, 30, 1e-15)
	dotest([]float64{0, -1, 0, 0}, 1.0/SQ2, -1.0/SQ6, 1.0/SQ3, 30, 1e-15)
	dotest([]float64{0, 0, -1, 0}, -1.0/SQ2, -1.0/SQ6, 1.0/SQ3, 30, 1e-15)

	if SAVEPLOT {
		plt.Gll("$\\sigma_a$", "$\\sigma_b$", "")
		plt.Equal()
		plt.SaveD("/tmp/gosl", "fig_invs05.png")
	}
}