Exemple #1
0
// PlotStress plots stresses along y=0 (horizontal line) and x=0 (vertical line)
func (o *PlateHole) PlotStress(t, L float64, npts int) {

	d := utl.LinSpace(o.r, L, npts)
	Sx := make([]float64, npts)
	Sy := make([]float64, npts)
	Sxy := make([]float64, npts)

	plt.Subplot(2, 1, 1)
	for i := 0; i < npts; i++ {
		Sx[i], Sy[i], _, Sxy[i] = o.Stress(t, []float64{d[i], 0}) // y=0
	}
	plt.Plot(d, Sx, "color='r',label='$\\sigma_x$ @ $y=0$'")
	plt.Plot(d, Sy, "color='g',label='$\\sigma_y$ @ $y=0$'")
	plt.Plot(d, Sxy, "color='b',label='$\\sigma_{xy}$ @ $y=0$'")
	plt.Gll("$x$", "stresses", "")

	plt.Subplot(2, 1, 2)
	for i := 0; i < npts; i++ {
		Sx[i], Sy[i], _, Sxy[i] = o.Stress(t, []float64{0, d[i]}) // x=0
	}
	plt.Plot(Sx, d, "color='r',label='$\\sigma_x$ @ $x=0$'")
	plt.Plot(Sy, d, "color='g',label='$\\sigma_y$ @ $x=0$'")
	plt.Plot(Sxy, d, "color='b',label='$\\sigma_{xy}$ @ $x=0$'")
	plt.Gll("stresses", "$y$", "")
}
Exemple #2
0
// 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_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 := "", ""
		if errg > tolg {
			clrg, with_err = "", true
		}
		if errh > tolh {
			clrh, with_err = "", true
		}
		io.Pf("errg = %s%23.15e   errh = %s%23.15e\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()
	}
}
Exemple #4
0
// 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)
}
Exemple #5
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 #6
0
// 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()
	}
}
Exemple #7
0
func do_plot_nurbs_refined(b, c *Nurbs) {
	plt.SetForEps(1.5, 400)
	plt.Subplot(3, 1, 1)
	b.DrawCtrl2D(true)
	b.DrawElems2D(21, true, "", "")
	plt.Equal()

	plt.Subplot(3, 1, 2)
	c.DrawCtrl2D(true)
	c.DrawElems2D(21, true, "", "")
	plt.Equal()

	plt.Subplot(3, 1, 3)
	b.DrawElems2D(21, true, ", lw=3", "")
	c.DrawElems2D(21, true, ", color='red', marker='+', markevery=10", "color='magenta', size=8, va='bottom'")
	plt.Equal()
}
Exemple #8
0
// subplot sets subplot
func (o *Plotter) Subplot() {
	if o.Split {
		plt.Clf()
		return
	}
	plt.Subplot(o.Nrow, o.Ncol, o.Pidx)
	o.Pidx += 1
}
func plot_normal(μ, σ float64) {

	var dist DistNormal
	dist.Init(&VarData{M: μ, S: σ})

	n := 101
	x := utl.LinSpace(-2, 2, n)
	y := make([]float64, n)
	Y := make([]float64, n)
	for i := 0; i < n; i++ {
		y[i] = dist.Pdf(x[i])
		Y[i] = dist.Cdf(x[i])
	}
	plt.Subplot(2, 1, 1)
	plt.Plot(x, y, io.Sf("clip_on=0,zorder=10,label=r'$\\mu=%g,\\;\\sigma=%g$'", μ, σ))
	plt.Gll("$x$", "$f(x)$", "leg_out=1, leg_ncol=2")
	plt.Subplot(2, 1, 2)
	plt.Plot(x, Y, io.Sf("clip_on=0,zorder=10,label=r'$\\mu=%g,\\;\\sigma=%g$'", μ, σ))
	plt.Gll("$x$", "$F(x)$", "leg_out=1, leg_ncol=2")
}
Exemple #10
0
// Draw draws or save figure with plot
//  dirout -- directory to save figure
//  fname  -- file name; e.g. myplot.eps or myplot.png. Use "" to skip saving
//  show   -- shows figure
//  extra  -- is called just after Subplot command and before any plotting
//  Note: subplots will be split if using 'eps' files
func Draw(dirout, fname string, show bool, extra ExtraPlt) {
	var fnk string // filename key
	var ext string // extension
	var eps bool   // is eps figure
	if fname != "" {
		fnk = io.FnKey(fname)
		ext = io.FnExt(fname)
		eps = ext == ".eps"
	}
	nplots := len(Splots)
	nr, nc := utl.BestSquare(nplots)
	var k int
	for i := 0; i < nr; i++ {
		for j := 0; j < nc; j++ {
			if !eps {
				plt.Subplot(nr, nc, k+1)
			}
			if extra != nil {
				extra(i+1, j+1, nplots)
			}
			if Splots[k].Title != "" {
				plt.Title(Splots[k].Title, Splots[k].Topts)
			}
			data := Splots[k].Data
			for _, d := range data {
				if d.Style.L == "" {
					d.Style.L = d.Alias
				}
				x, y := d.X, d.Y
				if math.Abs(Splots[k].Xscale) > 0 {
					x = make([]float64, len(d.X))
					la.VecCopy(x, Splots[k].Xscale, d.X)
				}
				if math.Abs(Splots[k].Yscale) > 0 {
					y = make([]float64, len(d.Y))
					la.VecCopy(y, Splots[k].Yscale, d.Y)
				}
				plt.Plot(x, y, d.Style.GetArgs("clip_on=0"))
			}
			plt.Gll(Splots[k].Xlbl, Splots[k].Ylbl, Splots[k].GllArgs)
			if eps {
				savefig(dirout, fnk, ext, k)
				plt.Clf()
			}
			k += 1
		}
	}
	if !eps && fname != "" {
		savefig(dirout, fnk, ext, -1)
	}
	if show {
		plt.Show()
	}
}
Exemple #11
0
func plot_frechet(l, c, a float64, xmin, xmax float64) {

	var dist DistFrechet
	dist.Init(&VarData{L: l, C: c, A: a})

	n := 101
	x := utl.LinSpace(xmin, xmax, n)
	y := make([]float64, n)
	Y := make([]float64, n)
	for i := 0; i < n; i++ {
		y[i] = dist.Pdf(x[i])
		Y[i] = dist.Cdf(x[i])
	}
	plt.Subplot(2, 1, 1)
	plt.Plot(x, y, io.Sf("clip_on=0,zorder=10,label=r'$(%g,%g,%g)$'", l, c, a))
	plt.Gll("$x$", "$f(x)$", "leg_out=1, leg_ncol=4, leg_hlen=1")
	plt.SetYnticks(11)
	plt.Subplot(2, 1, 2)
	plt.Plot(x, Y, io.Sf("clip_on=0,zorder=10,label=r'$(%g,%g,%g)$'", l, c, a))
	plt.Gll("$x$", "$F(x)$", "leg_out=1, leg_ncol=4, leg_hlen=1")
}
Exemple #12
0
func plot_uniform(A, B float64, xmin, xmax float64) {

	var dist DistUniform
	dist.Init(&VarData{Min: A, Max: B})

	n := 101
	x := utl.LinSpace(xmin, xmax, n)
	y := make([]float64, n)
	Y := make([]float64, n)
	for i := 0; i < n; i++ {
		y[i] = dist.Pdf(x[i])
		Y[i] = dist.Cdf(x[i])
	}
	plt.Subplot(2, 1, 1)
	plt.Plot(x, y, io.Sf("clip_on=0,zorder=10,label=r'$(%g,%g)$'", A, B))
	plt.Gll("$x$", "$f(x)$", "leg_out=1, leg_ncol=4, leg_hlen=1")
	plt.SetYnticks(11)
	plt.Subplot(2, 1, 2)
	plt.Plot(x, Y, io.Sf("clip_on=0,zorder=10,label=r'$(%g,%g)$'", A, B))
	plt.Gll("$x$", "$F(x)$", "leg_out=1, leg_ncol=4, leg_hlen=1")
}
Exemple #13
0
// PlotNurbsDerivs plots derivatives of basis functions la and lb
func PlotNurbsDerivs(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(4, 2, 1)
	t0 := time.Now()
	b.PlotDeriv(la, 0, "", npts, 0) // 0 => CalcBasisAndDerivs
	io.Pfcyan("time elapsed (calcbasis) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(4, 2, 2)
	t0 = time.Now()
	b.PlotDeriv(la, 0, "", npts, 1) // 1 => NumericalDeriv
	io.Pfcyan("time elapsed (numerical) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(4, 2, 3)
	b.PlotDeriv(la, 1, "", npts, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 4)
	b.PlotDeriv(la, 1, "", npts, 1) // 0 => NumericalDeriv
	plt.Equal()

	plt.Subplot(4, 2, 5)
	b.PlotDeriv(lb, 0, "", npts, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 6)
	b.PlotDeriv(lb, 0, "", npts, 1) // 0 => NumericalDeriv
	plt.Equal()

	plt.Subplot(4, 2, 7)
	b.PlotDeriv(lb, 1, "", npts, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 8)
	b.PlotDeriv(lb, 1, "", npts, 1) // 0 => NumericalDeriv
	plt.Equal()

	plt.SaveD(dirout, fn)
}
Exemple #14
0
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_dist_lognormal_03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("dist_lognormal_03. random numbers")

	μ := 1.0
	σ := 0.25

	nsamples := 1000
	X := make([]float64, nsamples)
	for i := 0; i < nsamples; i++ {
		X[i] = Lognormal(μ, σ)
	}

	nstations := 41
	xmin := 0.0
	xmax := 3.0
	dx := (xmax - xmin) / float64(nstations-1)

	var hist Histogram
	hist.Stations = utl.LinSpace(xmin, xmax, nstations)
	hist.Count(X, true)

	prob := make([]float64, nstations)
	for i := 0; i < nstations-1; i++ {
		prob[i] = float64(hist.Counts[i]) / (float64(nsamples) * dx)
	}

	io.Pf(TextHist(hist.GenLabels("%.3f"), hist.Counts, 60))
	io.Pforan("dx = %v\n", dx)

	area := 0.0
	for i := 0; i < nstations-1; i++ {
		area += dx * prob[i]
	}
	io.Pforan("area = %v\n", area)
	chk.Scalar(tst, "area", 1e-15, area, 1)

	if chk.Verbose {
		plt.SetForEps(1.5, 300)
		plot_lognormal(μ, σ)
		plt.Subplot(2, 1, 1)
		hist.PlotDensity(nil, "")
		plt.SaveD("/tmp/gosl", "rnd_dist_lognormal_03.eps")
	}
}
Exemple #16
0
// 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)
}
Exemple #17
0
func do_plot_nurbs_derivs(b *Nurbs, la, lb int) {
	np := 11
	plt.SetForEps(1.5, 500)

	plt.Subplot(4, 2, 1)
	t0 := time.Now()
	b.PlotDeriv(la, 0, "", np, 0) // 0 => CalcBasisAndDerivs
	io.Pfcyan("time elapsed (calcbasis) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(4, 2, 2)
	t0 = time.Now()
	b.PlotDeriv(la, 0, "", np, 1) // 1 => NumericalDeriv
	io.Pfcyan("time elapsed (numerical) = %v\n", time.Now().Sub(t0))
	plt.Equal()

	plt.Subplot(4, 2, 3)
	b.PlotDeriv(la, 1, "", np, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 4)
	b.PlotDeriv(la, 1, "", np, 1) // 0 => NumericalDeriv
	plt.Equal()

	plt.Subplot(4, 2, 5)
	b.PlotDeriv(lb, 0, "", np, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 6)
	b.PlotDeriv(lb, 0, "", np, 1) // 0 => NumericalDeriv
	plt.Equal()

	plt.Subplot(4, 2, 7)
	b.PlotDeriv(lb, 1, "", np, 0) // 0 => CalcBasisAndDerivs
	plt.Equal()

	plt.Subplot(4, 2, 8)
	b.PlotDeriv(lb, 1, "", np, 1) // 0 => NumericalDeriv
	plt.Equal()
}
Exemple #18
0
func Test_fun01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("fun01. Decreasing Reference Model")

	ya := 1.0
	yb := -0.5
	λ1 := 1.0

	o, err := New("ref-dec-gen", []*Prm{
		&Prm{N: "bet", V: 5.0},
		&Prm{N: "a", V: -λ1},
		&Prm{N: "b", V: -1.0},
		&Prm{N: "c", V: ya},
		&Prm{N: "A", V: 0.0},
		&Prm{N: "B", V: λ1},
		&Prm{N: "xini", V: 0.0},
		&Prm{N: "yini", V: yb},
	})
	if err != nil {
		tst.Errorf("test failed: %v\n", err)
		return
	}

	tmax := 3.0
	xcte := []float64{0, 0, 0}
	if chk.Verbose {
		plt.SetForPng(1.2, 400, 150)
		PlotT(o, "", "", 0.0, tmax, xcte, 201, "", "", "", "", "label='f'", "label='g'", "label='h'")
		plt.Subplot(3, 1, 1)
		plt.Plot([]float64{0, tmax}, []float64{ya, ya - λ1*tmax}, "'k-'")
		plt.Equal()
		plt.SaveD("/tmp/gosl/fun", "ref-dec-gen.png")
	}
	//
	sktol := 1e-10
	dtol := 1e-10
	dtol2 := 1e-10
	ver := chk.Verbose
	CheckDerivT(tst, o, 0.0, tmax, xcte, 11, nil, sktol, dtol, dtol2, ver)
}
Exemple #19
0
func do_plot_nurbs_basis(b *Nurbs, la, lb int) {
	npts := 21
	plt.SetForEps(1.2, 500)

	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()
}
Exemple #20
0
func Test_bspline03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("bspline03")

	//             0 1 2 3 4 5 6 7 8 9 10
	T := []float64{0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5}
	var s Bspline
	s.Init(T, 2)
	s.SetControl([][]float64{{0, 0}, {0.5, 1}, {1, 0}, {1.5, 0}, {2, 1}, {2.5, 1}, {3, 0.5}, {3.5, 0}})

	// analytical derivatives
	s.CalcBasisAndDerivs(3.99)
	io.Pfpink("ana: dNdt(t=3.99, i=5) = %v\n", s.GetDeriv(5))
	io.Pfpink("ana: dNdt(t=3.99, i=6) = %v\n", s.GetDeriv(6))
	io.Pfpink("ana: dNdt(t=3.99, i=7) = %v\n", s.GetDeriv(7))
	s.CalcBasisAndDerivs(4.0)
	io.Pforan("ana: dNdt(t=4.00, i=5) = %v\n", s.GetDeriv(5))
	io.Pforan("ana: dNdt(t=4.00, i=6) = %v\n", s.GetDeriv(6))
	io.Pforan("ana: dNdt(t=4.00, i=7) = %v\n", s.GetDeriv(7))

	// numerical derivatives
	io.Pfcyan("num: dNdt(t=3.99, i=5) = %v\n", s.NumericalDeriv(3.99, 5))
	io.Pfcyan("num: dNdt(t=3.99, i=6) = %v\n", s.NumericalDeriv(3.99, 6))
	io.Pfcyan("num: dNdt(t=3.99, i=7) = %v\n", s.NumericalDeriv(3.99, 7))
	io.Pfblue2("num: dNdt(t=4.00, i=5) = %v\n", s.NumericalDeriv(4.00, 5))
	io.Pfblue2("num: dNdt(t=4.00, i=6) = %v\n", s.NumericalDeriv(4.00, 6))
	io.Pfblue2("num: dNdt(t=4.00, i=7) = %v\n", s.NumericalDeriv(4.00, 7))

	ver := false
	tol := 1e-5
	tt := utl.LinSpace(0, 5, 11)
	numd := make([]float64, s.NumBasis())
	anad := make([]float64, s.NumBasis())
	for _, t := range tt {
		for i := 0; i < s.NumBasis(); i++ {
			s.CalcBasisAndDerivs(t)
			anad[i] = s.GetDeriv(i)
			numd[i] = s.NumericalDeriv(t, i)
			// numerical fails @ 4 [4,5,6]
			if t == 4 {
				numd[4] = anad[4]
				numd[5] = anad[5]
				numd[6] = anad[6]
			}
			chk.PrintAnaNum(io.Sf("i=%d t=%v", i, t), tol, anad[i], numd[i], ver)
		}
		chk.Vector(tst, io.Sf("derivs @ %v", t), tol, numd, anad)
	}

	if chk.Verbose {

		npts := 201
		plt.SetForPng(1.5, 600, 150)
		plt.SplotGap(0, 0.3)

		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, 1, 1)
		s.Draw2d(str0, "", npts, 0) // 0 => CalcBasis
		s.Draw2d(str1, "", npts, 1) // 1 => RecursiveBasis

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

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

		plt.SaveD("/tmp/gosl/gm", "bspline03.png")
	}
}
Exemple #21
0
func main() {

	// GA parameters
	opt := new(goga.Optimiser)
	opt.Default()
	opt.Nsol = 6
	opt.Ncpu = 1
	opt.Tf = 10
	opt.EpsH = 1e-3
	opt.Verbose = true
	opt.GenType = "latin"
	//opt.GenType = "halton"
	//opt.GenType = "rnd"
	opt.NormFlt = false
	opt.UseMesh = true
	opt.Nbry = 3

	// define problem
	opt.RptName = "9"
	opt.RptFref = []float64{0.0539498478}
	opt.RptXref = []float64{-1.717143, 1.595709, 1.827247, -0.7636413, -0.7636450}
	opt.FltMin = []float64{-2.3, -2.3, -3.2, -3.2, -3.2}
	opt.FltMax = []float64{+2.3, +2.3, +3.2, +3.2, +3.2}
	ng, nh := 0, 3
	fcn := func(f, g, h, x []float64, ξ []int, cpu int) {
		f[0] = math.Exp(x[0] * x[1] * x[2] * x[3] * x[4])
		h[0] = x[0]*x[0] + x[1]*x[1] + x[2]*x[2] + x[3]*x[3] + x[4]*x[4] - 10.0
		h[1] = x[1]*x[2] - 5.0*x[3]*x[4]
		h[2] = math.Pow(x[0], 3.0) + math.Pow(x[1], 3.0) + 1.0
	}

	// check
	if false {
		f := make([]float64, 1)
		h := make([]float64, 3)
		fcn(f, nil, h, opt.RptXref, nil, 0)
		io.Pforan("f(xref)  = %g  (%g)\n", f[0], opt.RptFref[0])
		io.Pforan("h0(xref) = %g\n", h[0])
		io.Pforan("h1(xref) = %g\n", h[1])
		io.Pforan("h2(xref) = %g\n", h[2])
	}

	// initialise optimiser
	nf := 1
	opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)

	// output function
	T := make([]float64, opt.Tf+1)                    // [nT]
	X := utl.Deep3alloc(opt.Nflt, opt.Nsol, opt.Tf+1) // [nx][nsol][nT]
	F := utl.Deep3alloc(opt.Nova, opt.Nsol, opt.Tf+1) // [nf][nsol][nT]
	U := utl.Deep3alloc(opt.Noor, opt.Nsol, opt.Tf+1) // [nu][nsol][nT]
	opt.Output = func(time int, sols []*goga.Solution) {
		T[time] = float64(time)
		for j, s := range sols {
			for i := 0; i < opt.Nflt; i++ {
				X[i][j][time] = s.Flt[i]
			}
			for i := 0; i < opt.Nova; i++ {
				F[i][j][time] = s.Ova[i]
			}
			for i := 0; i < opt.Noor; i++ {
				U[i][j][time] = s.Oor[i]
			}
		}
	}

	// initial population
	fnk := "one-obj-prob9-dbg"
	//S0 := opt.GetSolutionsCopy()
	goga.WriteAllValues("/tmp/goga", fnk, opt)

	// solve
	opt.Solve()

	// print
	if false {
		io.Pf("%13s%13s%13s%13s%10s\n", "f0", "u0", "u1", "u2", "feasible")
		for _, s := range opt.Solutions {
			io.Pf("%13.5e%13.5e%13.5e%13.5e%10v\n", s.Ova[0], s.Oor[0], s.Oor[1], s.Oor[2], s.Feasible())
		}
	}

	// plot: time series
	//a, b := 100, len(T)
	a, b := 0, 1 //len(T)
	if false {
		plt.SetForEps(2.0, 400)
		nrow := opt.Nflt + opt.Nova + opt.Noor
		for j := 0; j < opt.Nsol; j++ {
			for i := 0; i < opt.Nflt; i++ {
				plt.Subplot(nrow, 1, 1+i)
				plt.Plot(T[a:b], X[i][j][a:b], "")
				plt.Gll("$t$", io.Sf("$x_%d$", i), "")
			}
		}
		for j := 0; j < opt.Nsol; j++ {
			for i := 0; i < opt.Nova; i++ {
				plt.Subplot(nrow, 1, 1+opt.Nflt+i)
				plt.Plot(T[a:b], F[i][j][a:b], "")
				plt.Gll("$t$", io.Sf("$f_%d$", i), "")
			}
		}
		for j := 0; j < opt.Nsol; j++ {
			for i := 0; i < opt.Noor; i++ {
				plt.Subplot(nrow, 1, 1+opt.Nflt+opt.Nova+i)
				plt.Plot(T[a:b], U[i][j][a:b], "")
				plt.Gll("$t$", io.Sf("$u_%d$", i), "")
			}
		}
		plt.SaveD("/tmp/goga", fnk+"-time.eps")
	}

	// plot: x-relationships
	if true {
		plt.SetForEps(1, 700)
		ncol := opt.Nflt - 1
		for i := 0; i < opt.Nflt-1; i++ {
			for j := i + 1; j < opt.Nflt; j++ {
				plt.Subplot(ncol, ncol, i*ncol+j)
				if opt.UseMesh {
					opt.Meshes[i][j].CalcDerived(0)
					opt.Meshes[i][j].Draw2d(false, false, nil, 0)
				}
				for k := 0; k < opt.Nsol; k++ {
					plt.Plot(X[i][k][a:b], X[j][k][a:b], "ls='none', marker='.'")
				}
				plt.Gll(io.Sf("$x_%d$", i), io.Sf("$x_%d$", j), "")
			}
		}
		plt.SaveD("/tmp/goga", fnk+"-x.eps")
	}
}
Exemple #22
0
// PlotT plots F, G and H for varying t and fixed coordinates x
//  fname       -- filename to safe figure
//  args{F,G,H} -- if any is "", the corresponding plot is not created
func PlotT(o Func, dirout, fname string, t0, tf float64, xcte []float64, np int,
	labelT, labelF, labelG, labelH, argsF, argsG, argsH string) {

	// variables
	t := utl.LinSpace(t0, tf, np)
	var f, g, h []float64
	withF := argsF != ""
	withG := argsG != ""
	withH := argsH != ""
	nrow := 0

	// y-values
	if withF {
		f = make([]float64, np)
		for i := 0; i < np; i++ {
			f[i] = o.F(t[i], xcte)
		}
		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
	}
	if nrow == 0 {
		chk.Panic("one of args{F,G,H} must be provided")
	}

	// labels
	if labelT == "" {
		labelT = "$t$"
	}
	labelX := ""
	for _, x := range xcte {
		labelX += io.Sf(",%g", x)
	}
	if labelF == "" {
		labelF = "$f(t" + labelX + ")$"
	}
	if labelG == "" {
		labelG = "$g(t" + labelX + ")=\\frac{\\mathrm{d}f}{\\mathrm{d}t}$"
	}
	if labelH == "" {
		labelH = "$h(t" + labelX + ")=\\frac{\\mathrm{d}^2f}{\\mathrm{d}t^2}$"
	}

	// plot F
	pidx := 1
	if withF {
		if nrow > 1 {
			plt.Subplot(nrow, 1, pidx)
		}
		plt.Plot(t, f, argsF+",clip_on=0")
		plt.Gll(labelT, labelF, "")
		pidx += 1
	}

	// plot G
	if withG {
		if nrow > 1 {
			plt.Subplot(nrow, 1, pidx)
		}
		plt.Plot(t, g, argsG+",clip_on=0")
		plt.Gll(labelT, labelG, "")
		pidx += 1
	}

	// plot H
	if withH {
		if nrow > 1 {
			plt.Subplot(nrow, 1, pidx)
		}
		plt.Plot(t, h, argsH+",clip_on=0")
		plt.Gll(labelT, labelH, "")
	}

	// save figure
	if fname != "" {
		plt.SaveD(dirout, fname)
	}
}
Exemple #23
0
// PlotX plots F and the gradient of F, Gx and Gy, for varying x and fixed t
//  hlZero  -- highlight F(t,x) = 0
//  axEqual -- use axis['equal']
func PlotX(o Func, dirout, fname string, tcte float64, xmin, xmax []float64, np int, args string, withGrad, hlZero, axEqual, save, show bool, extra func()) {
	if len(xmin) == 3 {
		chk.Panic("PlotX works in 2D only")
	}
	X, Y := utl.MeshGrid2D(xmin[0], xmax[0], xmin[1], xmax[1], np, np)
	F := la.MatAlloc(np, np)
	var Gx, Gy [][]float64
	nrow := 1
	if withGrad {
		Gx = la.MatAlloc(np, np)
		Gy = la.MatAlloc(np, np)
		nrow += 1
	}
	x := make([]float64, 2)
	g := make([]float64, 2)
	for i := 0; i < np; i++ {
		for j := 0; j < np; j++ {
			x[0], x[1] = X[i][j], Y[i][j]
			F[i][j] = o.F(tcte, x)
			if withGrad {
				o.Grad(g, tcte, x)
				Gx[i][j] = g[0]
				Gy[i][j] = g[1]
			}
		}
	}
	prop, wid, dpi := 1.0, 600.0, 200
	os.MkdirAll(dirout, 0777)
	if withGrad {
		prop = 2
		plt.SetForPng(prop, wid, dpi)
		plt.Subplot(nrow, 1, 1)
		plt.Title("F(t,x)", "")
	} else {
		plt.SetForPng(prop, wid, dpi)
	}
	plt.Contour(X, Y, F, args)
	if hlZero {
		plt.ContourSimple(X, Y, F, false, 8, "levels=[0], linewidths=[2], colors=['yellow']")
	}
	if axEqual {
		plt.Equal()
	}
	if extra != nil {
		extra()
	}
	plt.Gll("x", "y", "")
	if withGrad {
		plt.Subplot(2, 1, 2)
		plt.Title("gradient", "")
		plt.Quiver(X, Y, Gx, Gy, args)
		if axEqual {
			plt.Equal()
		}
		plt.Gll("x", "y", "")
	}
	if save {
		plt.Save(dirout + "/" + fname)
	}
	if show {
		plt.Show()
	}
}
Exemple #24
0
func main() {

	mpi.Start(false)
	defer func() {
		mpi.Stop(false)
	}()

	if mpi.Rank() == 0 {
		chk.PrintTitle("ode04: Hairer-Wanner VII-p376 Transistor Amplifier\n")
	}
	if mpi.Size() != 3 {
		chk.Panic(">> error: this test requires 3 MPI processors\n")
		return
	}

	// data
	UE, UB, UF, ALPHA, BETA := 0.1, 6.0, 0.026, 0.99, 1.0e-6
	R0, R1, R2, R3, R4, R5 := 1000.0, 9000.0, 9000.0, 9000.0, 9000.0, 9000.0
	R6, R7, R8, R9 := 9000.0, 9000.0, 9000.0, 9000.0
	W := 2.0 * 3.141592654 * 100.0

	// initial values
	xa := 0.0
	ya := []float64{0.0,
		UB,
		UB / (R6/R5 + 1.0),
		UB / (R6/R5 + 1.0),
		UB,
		UB / (R2/R1 + 1.0),
		UB / (R2/R1 + 1.0),
		0.0}

	// endpoint of integration
	xb := 0.05
	//xb = 0.0123 // OK
	//xb = 0.01235 // !OK

	// right-hand side of the amplifier problem
	w := make([]float64, 8) // workspace
	fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
		UET := UE * math.Sin(W*x)
		FAC1 := BETA * (math.Exp((y[3]-y[2])/UF) - 1.0)
		FAC2 := BETA * (math.Exp((y[6]-y[5])/UF) - 1.0)
		la.VecFill(f, 0)
		switch mpi.Rank() {
		case 0:
			f[0] = y[0] / R9
		case 1:
			f[1] = (y[1]-UB)/R8 + ALPHA*FAC1
			f[2] = y[2]/R7 - FAC1
		case 2:
			f[3] = y[3]/R5 + (y[3]-UB)/R6 + (1.0-ALPHA)*FAC1
			f[4] = (y[4]-UB)/R4 + ALPHA*FAC2
			f[5] = y[5]/R3 - FAC2
			f[6] = y[6]/R1 + (y[6]-UB)/R2 + (1.0-ALPHA)*FAC2
			f[7] = (y[7] - UET) / R0
		}
		mpi.AllReduceSum(f, w)
		return nil
	}

	// Jacobian of the amplifier problem
	jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
		FAC14 := BETA * math.Exp((y[3]-y[2])/UF) / UF
		FAC27 := BETA * math.Exp((y[6]-y[5])/UF) / UF
		if dfdy.Max() == 0 {
			dfdy.Init(8, 8, 16)
		}
		NU := 2
		dfdy.Start()
		switch mpi.Rank() {
		case 0:
			dfdy.Put(2+0-NU, 0, 1.0/R9)
			dfdy.Put(2+1-NU, 1, 1.0/R8)
			dfdy.Put(1+2-NU, 2, -ALPHA*FAC14)
			dfdy.Put(0+3-NU, 3, ALPHA*FAC14)
			dfdy.Put(2+2-NU, 2, 1.0/R7+FAC14)
		case 1:
			dfdy.Put(1+3-NU, 3, -FAC14)
			dfdy.Put(2+3-NU, 3, 1.0/R5+1.0/R6+(1.0-ALPHA)*FAC14)
			dfdy.Put(3+2-NU, 2, -(1.0-ALPHA)*FAC14)
			dfdy.Put(2+4-NU, 4, 1.0/R4)
			dfdy.Put(1+5-NU, 5, -ALPHA*FAC27)
		case 2:
			dfdy.Put(0+6-NU, 6, ALPHA*FAC27)
			dfdy.Put(2+5-NU, 5, 1.0/R3+FAC27)
			dfdy.Put(1+6-NU, 6, -FAC27)
			dfdy.Put(2+6-NU, 6, 1.0/R1+1.0/R2+(1.0-ALPHA)*FAC27)
			dfdy.Put(3+5-NU, 5, -(1.0-ALPHA)*FAC27)
			dfdy.Put(2+7-NU, 7, 1.0/R0)
		}
		return nil
	}

	// matrix "M"
	c1, c2, c3, c4, c5 := 1.0e-6, 2.0e-6, 3.0e-6, 4.0e-6, 5.0e-6
	var M la.Triplet
	M.Init(8, 8, 14)
	M.Start()
	NU := 1
	switch mpi.Rank() {
	case 0:
		M.Put(1+0-NU, 0, -c5)
		M.Put(0+1-NU, 1, c5)
		M.Put(2+0-NU, 0, c5)
		M.Put(1+1-NU, 1, -c5)
		M.Put(1+2-NU, 2, -c4)
		M.Put(1+3-NU, 3, -c3)
	case 1:
		M.Put(0+4-NU, 4, c3)
		M.Put(2+3-NU, 3, c3)
		M.Put(1+4-NU, 4, -c3)
	case 2:
		M.Put(1+5-NU, 5, -c2)
		M.Put(1+6-NU, 6, -c1)
		M.Put(0+7-NU, 7, c1)
		M.Put(2+6-NU, 6, c1)
		M.Put(1+7-NU, 7, -c1)
	}

	// flags
	silent := false
	fixstp := false
	//method := "Dopri5"
	method := "Radau5"
	ndim := len(ya)
	numjac := false

	// structure to hold numerical results
	res := ode.Results{Method: method}

	// ODE solver
	var osol ode.Solver
	osol.Pll = true

	// solve problem
	if numjac {
		osol.Init(method, ndim, fcn, nil, &M, ode.SimpleOutput, silent)
	} else {
		osol.Init(method, ndim, fcn, jac, &M, ode.SimpleOutput, silent)
	}
	osol.IniH = 1.0e-6 // initial step size

	// set tolerances
	atol, rtol := 1e-11, 1e-5
	osol.SetTol(atol, rtol)

	// run
	t0 := time.Now()
	if fixstp {
		osol.Solve(ya, xa, xb, 0.01, fixstp, &res)
	} else {
		osol.Solve(ya, xa, xb, xb-xa, fixstp, &res)
	}

	// plot
	if mpi.Rank() == 0 {
		io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
		plt.SetForEps(2.0, 400)
		args := "'b-', marker='.', lw=1, clip_on=0"
		ode.Plot("/tmp/gosl/ode", "hwamplifier_mpi.eps", &res, nil, xa, xb, "", args, func() {
			_, T, err := io.ReadTable("data/radau5_hwamplifier.dat")
			if err != nil {
				chk.Panic("%v", err)
			}
			for j := 0; j < ndim; j++ {
				plt.Subplot(ndim+1, 1, j+1)
				plt.Plot(T["x"], T[io.Sf("y%d", j)], "'k+',label='reference',ms=10")
			}
		})
	}
}
func Test_hyperelast01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("hyperelast01")

	var m HyperElast1
	m.Init(2, false, []*fun.Prm{
		&fun.Prm{N: "kap", V: 0.05},
		&fun.Prm{N: "kapb", V: 20.0},
		&fun.Prm{N: "G0", V: 10000},
		&fun.Prm{N: "pr", V: 2.0},
		&fun.Prm{N: "pt", V: 10.0},
	})
	io.Pforan("m = %+v\n", m)
	pr := m.pr
	pt := m.pt

	np := 21
	Ev := utl.LinSpace(0, -0.2, np)
	P := make([]float64, np)
	Q := make([]float64, np)
	X := make([]float64, np)

	for j, ed := range []float64{0, 0.05, 0.1, 0.15, 0.2} {
		for i, ev := range Ev {
			P[i], Q[i] = m.Calc_pq(ev, ed)
			X[i] = math.Log(1.0 + (P[i]+pt)/pr)
		}
		slope := (Ev[0] - Ev[np-1]) / (X[np-1] - X[0])
		xm := (X[0] + X[np-1]) / 2.0
		ym := (Ev[0]+Ev[np-1])/2.0 - float64(j)*0.01

		plt.Subplot(3, 2, 1)
		plt.Plot(P, Ev, io.Sf("label='$\\\\varepsilon_d=%g$'", ed))
		plt.PlotOne(P[0], Ev[0], "'ro', clip_on=0")
		plt.Gll("$p$", "$\\varepsilon_v$", "")

		plt.Subplot(3, 2, 3)
		plt.Plot(X, Ev, "")
		plt.PlotOne(X[0], Ev[0], "'ro', clip_on=0")
		plt.Text(xm, ym, io.Sf("slope=%g", slope), "")
		plt.Gll("$x=\\log{[1+(p+p_t)/p_r]}$", "$\\varepsilon_v$", "")

		plt.Subplot(3, 2, 5)
		plt.Plot(Q, Ev, "")
		plt.PlotOne(Q[0], Ev[0], "'ro', clip_on=0")
		plt.Gll("$q$", "$\\varepsilon_v$", "")
	}

	Ed := utl.LinSpace(0, -0.2, np)

	for j, ev := range []float64{0, -0.05, -0.1, -0.15, -0.2} {
		for i, ed := range Ed {
			P[i], Q[i] = m.Calc_pq(ev, ed)
			X[i] = math.Log(1.0 + (P[i]+pt)/pr)
		}
		slope := (Ed[0] - Ed[np-1]) / (Q[np-1] - Q[0])
		xm := (Q[0] + Q[np-1]) / 2.0
		ym := (Ed[0]+Ed[np-1])/2.0 - float64(j)*0.01

		plt.Subplot(3, 2, 2)
		plt.Plot(P, Ed, io.Sf("label='$\\\\varepsilon_v=%g$'", ev))
		plt.PlotOne(P[0], Ed[0], "'ro', clip_on=0")
		plt.Gll("$p$", "$\\varepsilon_d$", "")

		plt.Subplot(3, 2, 4)
		plt.Plot(X, Ed, "")
		plt.PlotOne(X[0], Ed[0], "'ro', clip_on=0")
		plt.Gll("$x=\\log{[1+(p+p_t)/p_r]}$", "$\\varepsilon_d$", "")

		plt.Subplot(3, 2, 6)
		plt.Plot(Q, Ed, "")
		plt.PlotOne(Q[0], Ed[0], "'ro', clip_on=0")
		plt.Text(xm, ym, io.Sf("slope=%g", slope), "")
		plt.Gll("$q$", "$\\varepsilon_d$", "")
	}

	//plt.Show()
}
Exemple #26
0
// PlotNurbsBasis plots basis functions la and lb
func PlotNurbsBasis(dirout, fn string, b *Nurbs, la, lb int) {
	npts := 41
	ndiv := 11
	if b.gnd == 1 {
		ndiv = 101
	}
	plt.Reset()
	if io.FnExt(fn) == ".eps" {
		plt.SetForEps(1.5, 500)
	} else {
		plt.SetForPng(1.5, 600, 150)
	}

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

	plt.Subplot(3, 2, 2)
	if b.gnd == 2 {
		b.DrawCtrl2d(false, "", "")
		b.DrawElems2d(npts, false, "", "")
	}
	b.PlotBasis(lb, "clip_on=0", ndiv, 0) // 0 => CalcBasis
	if b.gnd == 2 {
		plt.Equal()
	}

	plt.Subplot(3, 2, 3)
	if b.gnd == 2 {
		b.DrawCtrl2d(false, "", "")
		b.DrawElems2d(npts, false, "", "")
	}
	b.PlotBasis(la, "clip_on=0", ndiv, 1) // 1 => CalcBasisAndDerivs
	if b.gnd == 2 {
		plt.Equal()
	}

	plt.Subplot(3, 2, 4)
	if b.gnd == 2 {
		b.DrawCtrl2d(false, "", "")
		b.DrawElems2d(npts, false, "", "")
	}
	b.PlotBasis(lb, "clip_on=0", ndiv, 1) // 1 => CalcBasisAndDerivs
	if b.gnd == 2 {
		plt.Equal()
	}

	plt.Subplot(3, 2, 5)
	if b.gnd == 2 {
		b.DrawCtrl2d(false, "", "")
		b.DrawElems2d(npts, false, "", "")
	}
	t0 = time.Now()
	b.PlotBasis(la, "clip_on=0", ndiv, 2) // 2 => RecursiveBasis
	io.Pfcyan("time elapsed (recursive) = %v\n", time.Now().Sub(t0))
	if b.gnd == 2 {
		plt.Equal()
	}

	plt.Subplot(3, 2, 6)
	if b.gnd == 2 {
		b.DrawCtrl2d(false, "", "")
		b.DrawElems2d(npts, false, "", "")
	}
	b.PlotBasis(lb, "clip_on=0", ndiv, 2) // 2 => RecursiveBasis
	if b.gnd == 2 {
		plt.Equal()
	}

	plt.SaveD(dirout, fn)
}
Exemple #27
0
// Hairer-Wanner VII-p3 Eq.(1.4) Robertson's Equation
func Test_ode03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("ode03: Hairer-Wanner VII-p3 Eq.(1.4) Robertson's Equation")

	fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
		f[0] = -0.04*y[0] + 1.0e4*y[1]*y[2]
		f[1] = 0.04*y[0] - 1.0e4*y[1]*y[2] - 3.0e7*y[1]*y[1]
		f[2] = 3.0e7 * y[1] * y[1]
		return nil
	}
	jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
		if dfdy.Max() == 0 {
			dfdy.Init(3, 3, 9)
		}
		dfdy.Start()
		dfdy.Put(0, 0, -0.04)
		dfdy.Put(0, 1, 1.0e4*y[2])
		dfdy.Put(0, 2, 1.0e4*y[1])
		dfdy.Put(1, 0, 0.04)
		dfdy.Put(1, 1, -1.0e4*y[2]-6.0e7*y[1])
		dfdy.Put(1, 2, -1.0e4*y[1])
		dfdy.Put(2, 0, 0.0)
		dfdy.Put(2, 1, 6.0e7*y[1])
		dfdy.Put(2, 2, 0.0)
		return nil
	}

	// data
	silent := false
	fixstp := false
	//method := "Dopri5"
	method := "Radau5"
	xa, xb := 0.0, 0.3
	ya := []float64{1.0, 0.0, 0.0}
	ndim := len(ya)

	// structure to hold numerical results
	res := Results{Method: method}

	// allocate ODE object
	var o Solver
	o.Init(method, ndim, fcn, jac, nil, SimpleOutput, silent)

	// tolerances and initial step size
	rtol := 1e-2
	atol := rtol * 1e-6
	o.SetTol(atol, rtol)
	o.IniH = 1.0e-6

	// solve problem
	y := make([]float64, ndim)
	copy(y, ya)
	if fixstp {
		o.Solve(y, xa, xb, 0.01, fixstp, &res)
	} else {
		o.Solve(y, xa, xb, xb-xa, fixstp, &res)
	}

	// plot
	if chk.Verbose {
		plt.SetForEps(1.5, 400)
		args := "'b-', marker='.', lw=1, clip_on=0"
		Plot("/tmp/gosl/ode", "rober.eps", &res, nil, xa, xb, "", args, func() {
			_, T, err := io.ReadTable("data/rober_radau5_cpp.dat")
			if err != nil {
				chk.Panic("%v", err)
			}
			plt.Subplot(4, 1, 1)
			plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=10")
			plt.Subplot(4, 1, 2)
			plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=10")
			plt.Subplot(4, 1, 3)
			plt.Plot(T["x"], T["y2"], "'k+',label='reference',ms=10")
		})
	}
}
Exemple #28
0
func main() {

	mpi.Start(false)
	defer func() {
		mpi.Stop(false)
	}()

	if mpi.Rank() == 0 {
		chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")
	}
	if mpi.Size() != 2 {
		chk.Panic(">> error: this test requires 2 MPI processors\n")
		return
	}

	eps := 1.0e-6
	w := make([]float64, 2) // workspace
	fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
		f[0], f[1] = 0, 0
		switch mpi.Rank() {
		case 0:
			f[0] = y[1]
		case 1:
			f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
		}
		// join all f
		mpi.AllReduceSum(f, w)
		return nil
	}
	jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
		if dfdy.Max() == 0 {
			dfdy.Init(2, 2, 4)
		}
		dfdy.Start()
		if false { // per column
			switch mpi.Rank() {
			case 0:
				dfdy.Put(0, 0, 0.0)
				dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
			case 1:
				dfdy.Put(0, 1, 1.0)
				dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
			}
		} else { // per row
			switch mpi.Rank() {
			case 0:
				dfdy.Put(0, 0, 0.0)
				dfdy.Put(0, 1, 1.0)
			case 1:
				dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
				dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
			}
		}
		return nil
	}

	// method and flags
	silent := false
	fixstp := false
	//method := "Dopri5"
	method := "Radau5"
	numjac := false
	xa, xb := 0.0, 2.0
	ya := []float64{2.0, -0.6}
	ndim := len(ya)

	// structure to hold numerical results
	res := ode.Results{Method: method}

	// allocate ODE object
	var o ode.Solver
	o.Distr = true
	if numjac {
		o.Init(method, ndim, fcn, nil, nil, ode.SimpleOutput, silent)
	} else {
		o.Init(method, ndim, fcn, jac, nil, ode.SimpleOutput, silent)
	}

	// tolerances and initial step size
	rtol := 1e-4
	atol := rtol
	o.IniH = 1.0e-4
	o.SetTol(atol, rtol)
	//o.NmaxSS = 2

	// solve problem
	y := make([]float64, ndim)
	copy(y, ya)
	t0 := time.Now()
	if fixstp {
		o.Solve(y, xa, xb, 0.05, fixstp, &res)
	} else {
		o.Solve(y, xa, xb, xb-xa, fixstp, &res)
	}

	// plot
	if mpi.Rank() == 0 {
		io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
		plt.SetForEps(1.5, 400)
		args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
		ode.Plot("/tmp/gosl/ode", "vdpolA_mpi.eps", &res, nil, xa, xb, "", args, func() {
			_, T, err := io.ReadTable("data/vdpol_radau5_for.dat")
			if err != nil {
				chk.Panic("%v", err)
			}
			plt.Subplot(3, 1, 1)
			plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=7")
			plt.Subplot(3, 1, 2)
			plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=7")
		})
	}
}
func Test_lognorm03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("lognorm03. Rackwitz-Fiessler conversion")

	dat := &VarData{D: D_Log, M: 10, S: 2}
	var dist DistLogNormal
	dist.Init(dat)
	dat.distr = &dist

	doplot := false
	if doplot {
		plt.SetForEps(1.5, 300)
		n := 101
		x := utl.LinSpace(5, 15, n)
		y := make([]float64, n)
		Y := make([]float64, n)
		for i := 0; i < n; i++ {
			y[i] = dist.Pdf(x[i])
			Y[i] = dist.Cdf(x[i])
		}
		plt.Subplot(2, 1, 1)
		plt.Plot(x, y, io.Sf("clip_on=0,zorder=10,label=r'$m=%.3f,\\;s=%.3f$'", dist.M, dist.S))
		plt.Gll("$x$", "$f(x)$", "leg_out=0, leg_ncol=2")
		plt.Subplot(2, 1, 2)
		plt.Plot(x, Y, io.Sf("clip_on=0,zorder=10,label=r'$m=%.3f,\\;s=%.3f$'", dist.M, dist.S))
		plt.Gll("$x$", "$F(x)$", "leg_out=0, leg_ncol=2")
		plt.SaveD("/tmp/gosl", "test_lognorm03.eps")
	}

	for i, x := range []float64{10, 20, 50} {

		// Rackwitz-Fiessler
		f := dist.Pdf(x)
		F := dist.Cdf(x)
		io.Pforan("\nx=%g  f(x)=%v  F(x)=%v\n", x, f, F)
		var σNrf, μNrf float64
		if F == 0 || F == 1 { // z = Φ⁻¹(F) → -∞ or +∞
			chk.Panic("cannot compute equivalent normal parameters @ %g because F=%g", x, F)
		} else {
			z := StdInvPhi(F)
			σNrf = Stdphi(z) / f
			μNrf = x - σNrf*z
			if μNrf < 0 {
				μNrf = 0
				σNrf = x / z
			}
		}

		// analytical solution for lognormal distribution
		μN, σN, invalid := dat.CalcEquiv(x)
		if invalid {
			tst.Errorf("CalcEquiv failed\n")
			return
		}

		// check
		tol := 1e-10
		if i > 0 {
			tol = 1e-6
		}
		err := chk.PrintAnaNum("μN", tol, μN, μNrf, chk.Verbose)
		if err != nil {
			tst.Errorf("μN values are different: %v\n", err)
			//return
		}
		err = chk.PrintAnaNum("σN", tol, σN, σNrf, chk.Verbose)
		if err != nil {
			tst.Errorf("σN values are different: %v\n", err)
			//return
		}
	}
}
Exemple #30
0
// Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation
func Test_ode02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")

	// problem definition
	eps := 1.0e-6
	fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
		f[0] = y[1]
		f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
		return nil
	}
	jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
		if dfdy.Max() == 0 {
			dfdy.Init(2, 2, 4)
		}
		dfdy.Start()
		dfdy.Put(0, 0, 0.0)
		dfdy.Put(0, 1, 1.0)
		dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
		dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
		return nil
	}

	// method and flags
	silent := false
	fixstp := false
	//method := "Dopri5"
	method := "Radau5"
	numjac := false
	xa, xb := 0.0, 2.0
	ya := []float64{2.0, -0.6}
	ndim := len(ya)

	// structure to hold numerical results
	res := Results{Method: method}

	// allocate ODE object
	var o Solver
	if numjac {
		o.Init(method, ndim, fcn, nil, nil, SimpleOutput, silent)
	} else {
		o.Init(method, ndim, fcn, jac, nil, SimpleOutput, silent)
	}

	// tolerances and initial step size
	rtol := 1e-4
	atol := rtol
	o.IniH = 1.0e-4
	o.SetTol(atol, rtol)
	//o.NmaxSS = 2

	// solve problem
	y := make([]float64, ndim)
	copy(y, ya)
	t0 := time.Now()
	if fixstp {
		o.Solve(y, xa, xb, 0.05, fixstp, &res)
	} else {
		o.Solve(y, xa, xb, xb-xa, fixstp, &res)
	}
	io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))

	// plot
	if chk.Verbose {
		plt.SetForEps(1.5, 400)
		args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
		Plot("/tmp/gosl/ode", "vdpolA.eps", &res, nil, xa, xb, "", args, func() {
			_, T, err := io.ReadTable("data/vdpol_radau5_for.dat")
			if err != nil {
				chk.Panic("%v", err)
			}
			plt.Subplot(3, 1, 1)
			plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=7")
			plt.Subplot(3, 1, 2)
			plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=7")
		})
	}
}