// 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", "$y$", "")
}
// 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 := "[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()
}
}
// 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)
}
// 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 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()
}
// 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")
}
// 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()
}
}
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")
}
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")
}
// 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)
}
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")
}
}
// 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 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()
}
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)
}
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()
}
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")
}
}
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")
}
}
// 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)
}
}
// 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()
}
}
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()
}
// 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)
}
// 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")
})
}
}
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
}
}
}
// 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")
})
}
}
