func (o *Plotter) Plot_ed_q(x, y []float64, res []*State, sts [][]float64, last bool) {
nr := len(res)
if len(sts) != nr {
return
}
k := nr - 1
for i := 0; i < nr; i++ {
x[i] = o.Ed[i] * 100.0
if o.QdivP {
y[i] = o.Q[i] / o.P[i]
} else {
y[i] = o.Q[i]
}
if o.Multq {
y[i] *= fun.Sign(o.W[i])
}
}
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
if last {
ylbl := "$q$"
if o.QdivP {
ylbl = "$q/p$"
}
plt.Gll("$\\varepsilon_d\\;[\\%]$", ylbl, "leg_out=1, leg_ncol=4, leg_hlen=1.5")
if lims, ok := o.Lims["ed,q"]; ok {
plt.AxisLims(lims)
}
}
}
func (o *Plotter) Plot_Dgam_f(x, y []float64, res []*State, sts [][]float64, last bool) {
if o.m == nil {
o.set_empty()
return
}
nr := len(res)
k := nr - 1
ys := o.m.YieldFuncs(res[0])
fc0 := ys[0]
xmi, xma, ymi, yma := res[0].Dgam, res[0].Dgam, fc0, fc0
for i := 0; i < nr; i++ {
x[i] = res[i].Dgam
ys = o.m.YieldFuncs(res[i])
y[i] = ys[0]
xmi = min(xmi, x[i])
xma = max(xma, x[i])
ymi = min(ymi, y[i])
yma = max(yma, y[i])
}
//o.DrawRamp(xmi, xma, ymi, yma)
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
if last {
plt.Gll("$\\Delta\\gamma$", "$f$", "")
if lims, ok := o.Lims["Dgam,f"]; ok {
plt.AxisLims(lims)
}
}
}
// PlotYxe plots the function y(x) implemented by Cb_yxe
func PlotYxe(ffcn Cb_yxe, dirout, fname string, xsol, xa, xb float64, np int, xsolLbl, args string, save, show bool, extra func()) (err error) {
if !save && !show {
return
}
x := utl.LinSpace(xa, xb, np)
y := make([]float64, np)
for i := 0; i < np; i++ {
y[i], err = ffcn(x[i])
if err != nil {
return
}
}
var ysol float64
ysol, err = ffcn(xsol)
if err != nil {
return
}
plt.Cross("")
plt.Plot(x, y, args)
plt.PlotOne(xsol, ysol, io.Sf("'ro', label='%s'", xsolLbl))
if extra != nil {
extra()
}
plt.Gll("x", "y(x)", "")
if save {
os.MkdirAll(dirout, 0777)
plt.Save(dirout + "/" + fname)
}
if show {
plt.Show()
}
return
}
// 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)
}
// run_rootsol_test runs root solution test
// Note: xguess is the trial solution for Newton's method (not Brent's)
func run_rootsol_test(tst *testing.T, xa, xb, xguess, tolcmp float64, ffcnA Cb_yxe, ffcnB Cb_f, JfcnB Cb_Jd, fname string, save, show bool) (xbrent float64) {
// Brent
io.Pfcyan("\n - - - - - - - using Brent's method - - -- - - - \n")
var o Brent
o.Init(ffcnA)
var err error
xbrent, err = o.Solve(xa, xb, false)
if err != nil {
chk.Panic("%v", err)
}
var ybrent float64
ybrent, err = ffcnA(xbrent)
if err != nil {
chk.Panic("%v", err)
}
io.Pforan("x = %v\n", xbrent)
io.Pforan("f(x) = %v\n", ybrent)
io.Pforan("nfeval = %v\n", o.NFeval)
io.Pforan("nit = %v\n", o.It)
if math.Abs(ybrent) > 1e-10 {
chk.Panic("Brent failed: f(x) = %g > 1e-10\n", ybrent)
}
// Newton
io.Pfcyan("\n - - - - - - - using Newton's method - - -- - - - \n")
var p NlSolver
p.Init(1, ffcnB, nil, JfcnB, true, false, nil)
xnewt := []float64{xguess}
var cnd float64
cnd, err = p.CheckJ(xnewt, 1e-6, true, !chk.Verbose)
io.Pforan("cond(J) = %v\n", cnd)
if err != nil {
chk.Panic("%v", err.Error())
}
err = p.Solve(xnewt, false)
if err != nil {
chk.Panic("%v", err.Error())
}
var ynewt float64
ynewt, err = ffcnA(xnewt[0])
if err != nil {
chk.Panic("%v", err)
}
io.Pforan("x = %v\n", xnewt[0])
io.Pforan("f(x) = %v\n", ynewt)
io.Pforan("nfeval = %v\n", p.NFeval)
io.Pforan("nJeval = %v\n", p.NJeval)
io.Pforan("nit = %v\n", p.It)
if math.Abs(ynewt) > 1e-9 {
chk.Panic("Newton failed: f(x) = %g > 1e-10\n", ynewt)
}
// compare Brent's and Newton's solutions
PlotYxe(ffcnA, "results", fname, xbrent, xa, xb, 101, "Brent", "'b-'", save, show, func() {
plt.PlotOne(xnewt[0], ynewt, "'g+', ms=15, label='Newton'")
})
chk.Scalar(tst, "xbrent - xnewt", tolcmp, xbrent, xnewt[0])
return
}
func (o *Plotter) Plot_ed_ev(x, y []float64, res []*State, sts [][]float64, last bool) {
nr := len(sts)
k := nr - 1
for i := 0; i < nr; i++ {
x[i], y[i] = o.Ed[i]*100.0, o.Ev[i]*100.0
}
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
if last {
plt.Gll("$\\varepsilon_d\\;[\\%]$", "$\\varepsilon_v\\;[\\%]$", "leg_out=1, leg_ncol=4, leg_hlen=1.5")
if lims, ok := o.Lims["ed,ev"]; ok {
plt.AxisLims(lims)
}
}
}
// 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")
}
}
// 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 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")
}
}
// PlotStar plots star with normalised OVAs
func (o *Optimiser) PlotStar() {
nf := o.Nf
dθ := 2.0 * math.Pi / float64(nf)
θ0 := 0.0
if nf == 3 {
θ0 = -math.Pi / 6.0
}
for _, ρ := range []float64{0.25, 0.5, 0.75, 1.0} {
plt.Circle(0, 0, ρ, "ec='gray',lw=0.5,zorder=5")
}
arrowM, textM := 1.1, 1.15
for i := 0; i < nf; i++ {
θ := θ0 + float64(i)*dθ
xi, yi := 0.0, 0.0
xf, yf := arrowM*math.Cos(θ), arrowM*math.Sin(θ)
plt.Arrow(xi, yi, xf, yf, "sc=10,st='->',lw=0.7,zorder=10,clip_on=0")
plt.PlotOne(xf, yf, "'k+', ms=0")
xf, yf = textM*math.Cos(θ), textM*math.Sin(θ)
plt.Text(xf, yf, io.Sf("%d", i), "size=6,zorder=10,clip_on=0")
}
X, Y := make([]float64, nf+1), make([]float64, nf+1)
clr := false
neg := false
step := 1
count := 0
colors := []string{"m", "orange", "g", "r", "b", "k"}
var ρ float64
for i, sol := range o.Solutions {
if sol.Feasible() && sol.FrontId == 0 && i%step == 0 {
for j := 0; j < nf; j++ {
if neg {
ρ = 1.0 - sol.Ova[j]/(o.RptFmax[j]-o.RptFmin[j])
} else {
ρ = sol.Ova[j] / (o.RptFmax[j] - o.RptFmin[j])
}
θ := θ0 + float64(j)*dθ
X[j], Y[j] = ρ*math.Cos(θ), ρ*math.Sin(θ)
}
X[nf], Y[nf] = X[0], Y[0]
if clr {
j := count % len(colors)
plt.Plot(X, Y, io.Sf("'k-',color='%s',markersize=3,clip_on=0", colors[j]))
} else {
plt.Plot(X, Y, "'r-',marker='.',markersize=3,clip_on=0")
}
count++
}
}
plt.Equal()
plt.AxisOff()
}
func draw_truss(dat *FemData, key string, A *goga.Solution, lef, bot, wid, hei float64) (weight, deflection float64) {
gap := 0.1
plt.PyCmds(io.Sf(`
from pylab import axes, setp, sca
ax_current = gca()
ax_new = axes([%g, %g, %g, %g], axisbg='#dcdcdc')
setp(ax_new, xticks=[0,720], yticks=[0,360])
axis('equal')
axis('off')
`, lef, bot, wid, hei))
_, _, weight, deflection, _, _, _ = dat.RunFEM(A.Int, A.Flt, 1, false)
plt.PyCmds("sca(ax_current)\n")
plt.PlotOne(weight, deflection, "'g*', zorder=1000, clip_on=0")
plt.Text(weight, deflection+gap, key, "")
return
}
// Draw2d draws bins' grid
func (o *Bins) Draw2d(withtxt bool) {
// horizontal lines
x := []float64{o.Xi[0], o.Xi[0] + o.L[0] + o.S}
y := make([]float64, 2)
for j := 0; j < o.N[1]+1; j++ {
y[0] = o.Xi[1] + float64(j)*o.S
y[1] = y[0]
plt.Plot(x, y, "'-', color='#4f3677', clip_on=0")
}
// vertical lines
y[0] = o.Xi[1]
y[1] = o.Xi[1] + o.L[1] + o.S
for i := 0; i < o.N[0]+1; i++ {
x[0] = o.Xi[0] + float64(i)*o.S
x[1] = x[0]
plt.Plot(x, y, "'k-', color='#4f3677', clip_on=0")
}
// plot items
for _, bin := range o.All {
if bin == nil {
continue
}
for _, entry := range bin.Entries {
plt.PlotOne(entry.X[0], entry.X[1], "'r.', clip_on=0")
}
}
// labels
if withtxt {
for j := 0; j < o.N[1]; j++ {
for i := 0; i < o.N[0]; i++ {
idx := i + j*o.N[0]
x := o.Xi[0] + float64(i)*o.S + 0.02*o.S
y := o.Xi[1] + float64(j)*o.S + 0.02*o.S
plt.Text(x, y, io.Sf("%d", idx), "size=7")
}
}
}
// setup
plt.Equal()
plt.AxisRange(o.Xi[0]-0.1, o.Xf[0]+o.S+0.1, o.Xi[1]-0.1, o.Xf[1]+o.S+0.1)
}
func Test_cubiceq03(tst *testing.T) {
//verbose()
chk.PrintTitle("cubiceq03. y(x) = x³ + c")
doplot := false
np := 41
var X, Y []float64
if doplot {
X = utl.LinSpace(-2, 2, np)
Y = make([]float64, np)
plt.SetForPng(0.8, 400, 200)
}
a, b := 0.0, 0.0
colors := []string{"red", "green", "blue"}
for k, c := range []float64{-1, 0, 1} {
x1, x2, x3, nx := EqCubicSolveReal(a, b, c)
io.Pforan("\na=%v b=%v c=%v\n", a, b, c)
io.Pfcyan("nx=%v\n", nx)
io.Pfcyan("x1=%v x2=%v x3=%v\n", x1, x2, x3)
chk.IntAssert(nx, 1)
chk.Scalar(tst, "x1", 1e-17, x1, -c)
if doplot {
for i, x := range X {
Y[i] = x*x*x + a*x*x + b*x + c
}
plt.Plot(X, Y, io.Sf("color='%s', label='c=%g'", colors[k], c))
plt.PlotOne(x1, 0, io.Sf("'ko', color='%s'", colors[k]))
plt.Cross("")
plt.Gll("x", "y", "")
}
}
if doplot {
plt.SaveD("/tmp", "fig_cubiceq03.png")
}
}
func plot_spo751(fnkey string) {
// constants
nidx := 20 // selected node at outer surface
didx := 0 // selected dof index for plot
nels := 4 // number of elements
nips := 4 // number of ips
// selected P values for stress plot
Psel := []float64{100, 140, 180, 190}
tolPsel := 2.0 // tolerance to compare P
GPa2MPa := 1000.0 // conversion factor
// input data
Pcen := 200.0 // [Mpa]
a, b := 100.0, 200.0 // [mm], [mm]
E, ν := 210000.0, 0.3 // [MPa], [-]
σy := 240.0 // [MPa]
// analytical solution
var sol ana.PressCylin
sol.Init([]*fun.Prm{
&fun.Prm{N: "a", V: a}, &fun.Prm{N: "b", V: b},
&fun.Prm{N: "E", V: E}, &fun.Prm{N: "ν", V: ν},
&fun.Prm{N: "σy", V: σy},
})
np := 41
P_ana, Ub_ana := sol.CalcPressDisp(np)
R_ana, Sr_ana, St_ana := sol.CalcStresses(Psel, np)
// read summary
sum := ReadSum(Global.Dirout, Global.Fnkey)
// allocate domain
distr := false
d := NewDomain(Global.Sim.Regions[0], distr)
if !d.SetStage(0, Global.Sim.Stages[0], distr) {
io.PfRed("plot_spo751: SetStage failed\n")
return
}
// gofem results
nto := len(sum.OutTimes)
P := make([]float64, nto)
Ub := make([]float64, nto)
R := utl.Deep3alloc(len(Psel), nels, nips)
Sr := utl.Deep3alloc(len(Psel), nels, nips)
St := utl.Deep3alloc(len(Psel), nels, nips)
i := 0
for tidx, t := range sum.OutTimes {
// read results from file
if !d.In(sum, tidx, true) {
io.PfRed("plot_spo751: cannot read solution\n")
return
}
// collect results for load versus displacement plot
nod := d.Nodes[nidx]
eq := nod.Dofs[didx].Eq
P[tidx] = t * Pcen
Ub[tidx] = d.Sol.Y[eq]
// stresses
if isPsel(Psel, P[tidx], tolPsel) {
for j, ele := range d.ElemIntvars {
e := ele.(*ElemU)
ipsdat := e.OutIpsData()
for k, dat := range ipsdat {
res := dat.Calc(d.Sol)
x, y := dat.X[0], dat.X[1]
sx := res["sx"] * GPa2MPa
sy := res["sy"] * GPa2MPa
sxy := res["sxy"] * GPa2MPa / math.Sqrt2
R[i][j][k], Sr[i][j][k], St[i][j][k], _ = ana.PolarStresses(x, y, sx, sy, sxy)
}
}
i++
}
}
// auxiliary data for plotting stresses
colors := []string{"r", "m", "g", "k", "y", "c", "r", "m"}
markers1 := []string{"o", "s", "x", ".", "^", "*", "o", "s"}
markers2 := []string{"+", "+", "+", "+", "+", "+", "+", "+"}
// plot load displacements
plt.SetForEps(0.8, 300)
if true {
//if false {
plt.Plot(Ub_ana, P_ana, "'b-', ms=2, label='solution', clip_on=0")
plt.Plot(Ub, P, "'r.--', label='fem: outer', clip_on=0")
plt.Gll("$u_x\\;\\mathrm{[mm]}$", "$P\\;\\mathrm{[MPa]}$", "")
plt.SaveD("/tmp", io.Sf("gofem_%s_disp.eps", fnkey))
}
// plot radial stresses
if true {
//if false {
plt.Reset()
for i, Pval := range Psel {
plt.Plot(R_ana, Sr_ana[i], "'b-'")
for k := 0; k < nips; k++ {
for j := 0; j < nels; j++ {
args := io.Sf("'%s%s'", colors[i], markers1[i])
if k > 1 {
args = io.Sf("'k%s', ms=10", markers2[i])
}
if k == 0 && j == 0 {
args += io.Sf(", label='P=%g'", Pval)
}
plt.PlotOne(R[i][j][k], Sr[i][j][k], args)
}
}
}
plt.Gll("$r\\;\\mathrm{[mm]}$", "$\\sigma_r\\;\\mathrm{[MPa]}$", "leg_loc='lower right'")
plt.AxisXrange(a, b)
plt.SaveD("/tmp", io.Sf("gofem_%s_sr.eps", fnkey))
}
// plot tangential stresses
if true {
//if false {
plt.Reset()
for i, Pval := range Psel {
plt.Plot(R_ana, St_ana[i], "'b-'")
for k := 0; k < nips; k++ {
for j := 0; j < nels; j++ {
args := io.Sf("'%s%s'", colors[i], markers1[i])
if k > 1 {
args = io.Sf("'k%s', ms=10", markers2[i])
}
if k == 0 && j == 0 {
args += io.Sf(", label='P=%g'", Pval)
}
plt.PlotOne(R[i][j][k], St[i][j][k], args)
}
}
}
plt.Gll("$r\\;\\mathrm{[mm]}$", "$\\sigma_t\\;\\mathrm{[MPa]}$", "leg_loc='upper left'")
plt.SaveD("/tmp", io.Sf("gofem_%s_st.eps", fnkey))
}
}
func Test_flt02(tst *testing.T) {
//verbose()
chk.PrintTitle("flt02. circle with equality constraint")
// parameters
C := NewConfParams()
C.Eps1 = 1e-3
C.Pll = false
C.Nisl = 4
C.Ninds = 12
C.Ntrials = 1
if chk.Verbose {
C.Ntrials = 40
}
C.Verbose = false
C.Dtmig = 50
C.CrowdSize = 3
C.CompProb = false
C.GAtype = "crowd"
C.DiffEvol = true
C.RangeFlt = [][]float64{
{-1, 3}, // gene # 0: min and max
{-1, 3}, // gene # 1: min and max
}
C.Latin = true
C.PopFltGen = PopFltGen
if chk.Verbose {
C.FnKey = ""
if C.Ntrials == 1 {
C.DoPlot = true
}
}
C.Ops.EnfRange = true
C.NumFmts = map[string][]string{"flt": {"%8.4f", "%8.4f"}}
C.ShowDem = true
C.RegTol = 0.01
C.CalcDerived()
rnd.Init(C.Seed)
// geometry
xe := 1.0 // centre of circle
le := -0.4 // selected level of f(x)
ys := xe - (1.0+le)/math.Sqrt2 // coordinates of minimum point with level=le
y0 := 2.0*ys + xe // vertical axis intersect of straight line defined by c(x)
xc := []float64{xe, xe} // centre
nx := len(xc)
// functions
fcn := func(f, g, h []float64, x []float64) {
res := 0.0
for i := 0; i < nx; i++ {
res += (x[i] - xc[i]) * (x[i] - xc[i])
}
f[0] = math.Sqrt(res) - 1
h[0] = x[0] + x[1] + xe - y0
}
// simple problem
sim := NewSimpleFltProb(fcn, 1, 0, 1, C)
sim.Run(chk.Verbose)
// stat
io.Pf("\n")
sim.Stat(0, 60, -0.4)
// plot
sim.PltExtra = func() {
plt.PlotOne(ys, ys, "'o', markeredgecolor='yellow', markerfacecolor='none', markersize=10")
}
sim.Plot("test_flt02")
}
// Run computes β starting witn an initial guess
func (o *ReliabFORM) Run(βtrial float64, verbose bool, args ...interface{}) (β float64, μ, σ, x []float64) {
// initial random variables
β = βtrial
nx := len(o.μ)
μ = make([]float64, nx) // mean values (equivalent normal value)
σ = make([]float64, nx) // deviation values (equivalent normal value)
x = make([]float64, nx) // current vector of random variables defining min(β)
for i := 0; i < nx; i++ {
μ[i] = o.μ[i]
σ[i] = o.σ[i]
x[i] = o.μ[i]
}
// lognormal distribution structure
var lnd DistLogNormal
// has lognormal random variable?
haslrv := false
for _, found := range o.lrv {
if found {
haslrv = true
break
}
}
// function to compute β with x-constant
// gβ(β) = g(μ - β・A・σ) = 0
var err error
gβfcn := func(fy, y []float64) error {
βtmp := y[0]
for i := 0; i < nx; i++ {
o.xtmp[i] = μ[i] - βtmp*o.α[i]*σ[i]
}
fy[0], err = o.gfcn(o.xtmp, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", o.xtmp, err)
}
return nil
}
// derivative of gβ w.r.t β
hβfcn := func(dfdy [][]float64, y []float64) error {
βtmp := y[0]
for i := 0; i < nx; i++ {
o.xtmp[i] = μ[i] - βtmp*o.α[i]*σ[i]
}
err = o.hfcn(o.dgdx, o.xtmp, args)
if err != nil {
chk.Panic("cannot compute hfcn(%v):\n%v", o.xtmp, err)
}
dfdy[0][0] = 0
for i := 0; i < nx; i++ {
dfdy[0][0] -= o.dgdx[i] * o.α[i] * σ[i]
}
return nil
}
// nonlinear solver with y[0] = β
// solving: gβ(β) = g(μ - β・A・σ) = 0
var nls num.NlSolver
nls.Init(1, gβfcn, nil, hβfcn, true, false, nil)
defer nls.Clean()
// message
if verbose {
io.Pf("\n%s", io.StrThickLine(60))
}
// plotting
plot := o.PlotFnk != ""
if nx != 2 {
plot = false
}
if plot {
if o.PlotNp < 3 {
o.PlotNp = 41
}
var umin, umax, vmin, vmax float64
if o.PlotCf < 1 {
o.PlotCf = 2
}
if len(o.PlotUrange) == 0 {
umin, umax = μ[0]-o.PlotCf*μ[0], μ[0]+o.PlotCf*μ[0]
vmin, vmax = μ[1]-o.PlotCf*μ[1], μ[1]+o.PlotCf*μ[1]
} else {
chk.IntAssert(len(o.PlotUrange), 2)
chk.IntAssert(len(o.PlotVrange), 2)
umin, umax = o.PlotUrange[0], o.PlotUrange[1]
vmin, vmax = o.PlotVrange[0], o.PlotVrange[1]
}
o.PlotU, o.PlotV = utl.MeshGrid2D(umin, umax, vmin, vmax, o.PlotNp, o.PlotNp)
o.PlotZ = la.MatAlloc(o.PlotNp, o.PlotNp)
plt.SetForEps(0.8, 300)
for i := 0; i < o.PlotNp; i++ {
for j := 0; j < o.PlotNp; j++ {
o.xtmp[0] = o.PlotU[i][j]
o.xtmp[1] = o.PlotV[i][j]
o.PlotZ[i][j], err = o.gfcn(o.xtmp, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
}
}
plt.Contour(o.PlotU, o.PlotV, o.PlotZ, "")
plt.ContourSimple(o.PlotU, o.PlotV, o.PlotZ, true, 8, "levels=[0], colors=['yellow']")
plt.PlotOne(x[0], x[1], "'ro', label='initial'")
}
// iterations to find β
var dat VarData
B := []float64{β}
itB := 0
for itB = 0; itB < o.NmaxItB; itB++ {
// message
if verbose {
gx, err := o.gfcn(x, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
io.Pf("%s itB=%d β=%g g=%g\n", io.StrThinLine(60), itB, β, gx)
}
// plot
if plot {
plt.PlotOne(x[0], x[1], "'r.'")
}
// compute direction cosines
itA := 0
for itA = 0; itA < o.NmaxItA; itA++ {
// has lognormal random variable (lrv)
if haslrv {
// find equivalent normal mean and std deviation for lognormal variables
for i := 0; i < nx; i++ {
if o.lrv[i] {
// set distribution
dat.M, dat.S = o.μ[i], o.σ[i]
lnd.Init(&dat)
// update μ and σ
fx := lnd.Pdf(x[i])
Φinvx := (math.Log(x[i]) - lnd.M) / lnd.S
φx := math.Exp(-Φinvx*Φinvx/2.0) / math.Sqrt2 / math.SqrtPi
σ[i] = φx / fx
μ[i] = x[i] - Φinvx*σ[i]
}
}
}
// compute direction cosines
err = o.hfcn(o.dgdx, x, args)
if err != nil {
chk.Panic("cannot compute hfcn(%v):\n%v", x, err)
}
den := 0.0
for i := 0; i < nx; i++ {
den += math.Pow(o.dgdx[i]*σ[i], 2.0)
}
den = math.Sqrt(den)
αerr := 0.0 // difference on α
for i := 0; i < nx; i++ {
αnew := o.dgdx[i] * σ[i] / den
αerr += math.Pow(αnew-o.α[i], 2.0)
o.α[i] = αnew
}
αerr = math.Sqrt(αerr)
// message
if verbose {
io.Pf(" itA=%d\n", itA)
io.Pf("%12s%12s%12s%12s\n", "x", "μ", "σ", "α")
for i := 0; i < nx; i++ {
io.Pf("%12.3f%12.3f%12.3f%12.3f\n", x[i], μ[i], σ[i], o.α[i])
}
}
// update x-star
for i := 0; i < nx; i++ {
x[i] = μ[i] - β*o.α[i]*σ[i]
}
// check convergence on α
if itA > 1 && αerr < o.TolA {
if verbose {
io.Pfgrey(". . . converged on α with αerr=%g . . .\n", αerr)
}
break
}
}
// failed to converge on α
if itA == o.NmaxItA {
chk.Panic("failed to convege on α")
}
// compute new β
B[0] = β
nls.Solve(B, o.NlsSilent)
βerr := math.Abs(B[0] - β)
β = B[0]
if o.NlsCheckJ {
nls.CheckJ(B, o.NlsCheckJtol, true, false)
}
// update x-star
for i := 0; i < nx; i++ {
x[i] = μ[i] - β*o.α[i]*σ[i]
}
// check convergence on β
if βerr < o.TolB {
if verbose {
io.Pfgrey2(". . . converged on β with βerr=%g . . .\n", βerr)
}
break
}
}
// failed to converge on β
if itB == o.NmaxItB {
chk.Panic("failed to converge on β")
}
// message
if verbose {
gx, err := o.gfcn(x, args)
if err != nil {
chk.Panic("cannot compute gfcn(%v):\n%v", x, err)
}
io.Pfgreen("x = %v\n", x)
io.Pfgreen("g = %v\n", gx)
io.PfGreen("β = %v\n", β)
}
// plot
if plot {
plt.Gll("$x_0$", "$x_1$", "")
plt.Cross("")
plt.SaveD("/tmp/gosl", "fig_form_"+o.PlotFnk+".eps")
}
return
}
// Plot plots contour
func (o *SimpleFltProb) Plot(fnkey string) {
// check
if !o.C.DoPlot {
return
}
// limits and meshgrid
xmin, xmax := o.C.RangeFlt[0][0], o.C.RangeFlt[0][1]
ymin, ymax := o.C.RangeFlt[1][0], o.C.RangeFlt[1][1]
// auxiliary variables
X, Y := utl.MeshGrid2D(xmin, xmax, ymin, ymax, o.PltNpts, o.PltNpts)
Zf := utl.DblsAlloc(o.PltNpts, o.PltNpts)
var Zg [][][]float64
var Zh [][][]float64
if o.ng > 0 {
Zg = utl.Deep3alloc(o.ng, o.PltNpts, o.PltNpts)
}
if o.nh > 0 {
Zh = utl.Deep3alloc(o.nh, o.PltNpts, o.PltNpts)
}
// compute values
x := make([]float64, 2)
for i := 0; i < o.PltNpts; i++ {
for j := 0; j < o.PltNpts; j++ {
x[0], x[1] = X[i][j], Y[i][j]
o.Fcn(o.ff[0], o.gg[0], o.hh[0], x)
Zf[i][j] = o.ff[0][o.PltIdxF]
for k, g := range o.gg[0] {
Zg[k][i][j] = g
}
for k, h := range o.hh[0] {
Zh[k][i][j] = h
}
}
}
// prepare plot area
plt.Reset()
plt.SetForEps(0.8, 350)
// plot f
if o.PltArgs != "" {
o.PltArgs = "," + o.PltArgs
}
if o.PltCsimple {
plt.ContourSimple(X, Y, Zf, true, 7, "colors=['k'], fsz=7"+o.PltArgs)
} else {
plt.Contour(X, Y, Zf, io.Sf("fsz=7, cmapidx=%d"+o.PltArgs, o.PltCmapIdx))
}
// plot g
clr := "yellow"
if o.PltCsimple {
clr = "blue"
}
for _, g := range Zg {
plt.ContourSimple(X, Y, g, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", clr, o.PltLwg))
}
// plot h
clr = "yellow"
if o.PltCsimple {
clr = "blue"
}
for _, h := range Zh {
plt.ContourSimple(X, Y, h, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", clr, o.PltLwh))
}
// initial populations
l := "initial population"
for _, pop := range o.PopsIni {
for _, ind := range pop {
x := ind.GetFloats()
plt.PlotOne(x[0], x[1], io.Sf("'k.', zorder=20, clip_on=0, label='%s'", l))
l = ""
}
}
// final populations
l = "final population"
for _, pop := range o.PopsBest {
for _, ind := range pop {
x := ind.GetFloats()
plt.PlotOne(x[0], x[1], io.Sf("'ko', ms=6, zorder=30, clip_on=0, label='%s', markerfacecolor='none'", l))
l = ""
}
}
// extra
if o.PltExtra != nil {
o.PltExtra()
}
// best result
if o.Nfeasible > 0 {
x, _, _, _ := o.find_best()
plt.PlotOne(x[0], x[1], "'m*', zorder=50, clip_on=0, label='best', markeredgecolor='m'")
}
// save figure
plt.Cross("clr='grey'")
if o.PltAxEqual {
plt.Equal()
}
plt.AxisRange(xmin, xmax, ymin, ymax)
plt.Gll("$x_0$", "$x_1$", "leg_out=1, leg_ncol=4, leg_hlen=1.5")
plt.SaveD(o.PltDirout, fnkey+".eps")
}
// Check checks derivatives
func Check(tst *testing.T, mdl Model, pc0, sl0, pcf float64, npts int, tolCc, tolD1a, tolD1b, tolD2a, tolD2b float64, verbose bool, pcSkip []float64, tolSkip float64, doplot bool) {
// nonrate model
nr_mdl, is_nonrate := mdl.(Nonrate)
io.Pforan("is_nonrate = %v\n", is_nonrate)
// for all pc stations
Pc := utl.LinSpace(pc0, pcf, npts)
Sl := make([]float64, npts)
Sl[0] = sl0
var err error
for i := 1; i < npts; i++ {
// update and plot
Sl[i], err = Update(mdl, Pc[i-1], Sl[i-1], Pc[i]-Pc[i-1])
if err != nil {
tst.Errorf("Update failed: %v\n", err)
return
}
if doplot {
plt.PlotOne(Pc[i], Sl[i], "'ko', clip_on=0")
}
// skip point on checking of derivatives
if doskip(Pc[i], pcSkip, tolSkip) {
continue
}
// wetting flag
wet := Pc[i]-Pc[i-1] < 0
// check Cc = dsl/dpc
io.Pforan("\npc=%g, sl=%g, wetting=%v\n", Pc[i], Sl[i], wet)
if is_nonrate {
// analytical Cc
Cc_ana, err := mdl.Cc(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("Cc failed: %v\n", err)
return
}
// numerical Cc
Cc_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
return nr_mdl.Sl(x)
}, Pc[i], 1e-3)
chk.AnaNum(tst, "Cc = ∂sl/∂pc ", tolCc, Cc_ana, Cc_num, verbose)
}
// compute all derivatives
L, Lx, J, Jx, Jy, err := mdl.Derivs(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("Derivs failed: %v\n", err)
return
}
L_ana_A := L
L_ana_B, err := mdl.L(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("L failed: %v\n", err)
return
}
Lx_ana := Lx
Jx_ana := Jx
Jy_ana := Jy
J_ana_A := J
J_ana_B, err := mdl.J(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("J failed: %v\n", err)
return
}
// numerical L = ∂Cc/∂pc
L_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Cctmp, _ := mdl.Cc(x, Sl[i], wet)
return Cctmp
}, Pc[i], 1e-3)
chk.AnaNum(tst, "L = ∂Cc/∂pc ", tolD1a, L_ana_A, L_num, verbose)
// numerical Lx := ∂²Cc/∂pc²
Lx_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ltmp, _, _, _, _, _ := mdl.Derivs(x, Sl[i], wet)
return Ltmp
}, Pc[i], 1e-3)
chk.AnaNum(tst, "Lx = ∂²Cc/∂pc² ", tolD2a, Lx_ana, Lx_num, verbose)
// numerical J := ∂Cc/∂sl (version A)
J_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ccval, _ := mdl.Cc(Pc[i], x, wet)
return Ccval
}, Sl[i], 1e-3)
chk.AnaNum(tst, "J = ∂Cc/∂sl ", tolD1b, J_ana_A, J_num, verbose)
// numerical Jx := ∂²Cc/(∂pc ∂sl)
Jx_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ltmp, _, _, _, _, _ := mdl.Derivs(Pc[i], x, wet)
return Ltmp
}, Sl[i], 1e-3)
chk.AnaNum(tst, "Jx = ∂²Cc/∂pc∂sl", tolD2b, Jx_ana, Jx_num, verbose)
// numerical Jy := ∂²Cc/∂sl²
Jy_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Jtmp, _ := mdl.J(Pc[i], x, wet)
return Jtmp
}, Sl[i], 1e-3)
chk.AnaNum(tst, "Jy = ∂²Cc/∂sl² ", tolD2b, Jy_ana, Jy_num, verbose)
// check A and B derivatives
chk.Scalar(tst, "L_A == L_B", 1e-17, L_ana_A, L_ana_B)
chk.Scalar(tst, "J_A == J_B", 1e-17, J_ana_A, J_ana_B)
}
}
func solve_problem(problem int) (opt *goga.Optimiser) {
io.Pf("\n\n------------------------------------- problem = %d ---------------------------------------\n", problem)
// parameters
opt = new(goga.Optimiser)
opt.Default()
opt.Ncpu = 3
opt.Tf = 500
opt.Verbose = false
opt.Nsamples = 1000
opt.GenType = "latin"
opt.DEC = 0.1
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtE = "%.4e"
opt.RptFmtL = "%.4e"
opt.RptFmtEdev = "%.3e"
opt.RptFmtLdev = "%.3e"
// problem variables
nx := 10
opt.RptName = io.Sf("CTP%d", problem)
opt.Nsol = 120
opt.FltMin = make([]float64, nx)
opt.FltMax = make([]float64, nx)
for i := 0; i < nx; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh := 2, 1, 0
// extra problem variables
var f1max float64
var fcn goga.MinProb_t
var extraplot func()
// problems
switch problem {
// problem # 0 -- TNK
case 0:
ng = 2
f1max = 1.21
opt.RptName = "TNK"
opt.FltMin = []float64{0, 0}
opt.FltMax = []float64{PI, PI}
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
f[1] = x[1]
g[0] = x[0]*x[0] + x[1]*x[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(x[0], x[1]))
g[1] = 0.5 - math.Pow(x[0]-0.5, 2.0) - math.Pow(x[1]-0.5, 2.0)
}
extraplot = func() {
np := 301
X, Y := utl.MeshGrid2D(0, 1.3, 0, 1.3, np, np)
Z1, Z2, Z3 := utl.DblsAlloc(np, np), utl.DblsAlloc(np, np), utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
g1 := 0.5 - math.Pow(X[i][j]-0.5, 2.0) - math.Pow(Y[i][j]-0.5, 2.0)
if g1 >= 0 {
Z1[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
} else {
Z1[i][j] = -1
}
Z2[i][j] = X[i][j]*X[i][j] + Y[i][j]*Y[i][j] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(Y[i][j], X[i][j]))
Z3[i][j] = g1
}
}
plt.Contour(X, Y, Z1, "levels=[0,2],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
plt.Text(0.3, 0.95, "0.000", "size=5,rotation=10")
plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['-'], linewidths=[0.7], colors=['k'], levels=[0]")
plt.ContourSimple(X, Y, Z3, false, 7, "linestyles=['-'], linewidths=[1.0], colors=['k'], levels=[0]")
}
opt.Multi_fcnErr = func(f []float64) float64 {
return f[0]*f[0] + f[1]*f[1] - 1.0 - 0.1*math.Cos(16.0*math.Atan2(f[0], f[1]))
}
// problem # 1 -- CTP1, Deb 2001, p367, fig 225
case 1:
ng = 2
f1max = 1.0
a0, b0 := 0.858, 0.541
a1, b1 := 0.728, 0.295
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c0 := 1.0
for i := 1; i < len(x); i++ {
c0 += x[i]
}
f[0] = x[0]
f[1] = c0 * math.Exp(-x[0]/c0)
if true {
g[0] = f[1] - a0*math.Exp(-b0*f[0])
g[1] = f[1] - a1*math.Exp(-b1*f[0])
}
}
f0a := math.Log(a0) / (b0 - 1.0)
f1a := math.Exp(-f0a)
f0b := math.Log(a0/a1) / (b0 - b1)
f1b := a0 * math.Exp(-b0*f0b)
opt.Multi_fcnErr = func(f []float64) float64 {
if f[0] < f0a {
return f[1] - math.Exp(-f[0])
}
if f[0] < f0b {
return f[1] - a0*math.Exp(-b0*f[0])
}
return f[1] - a1*math.Exp(-b1*f[0])
}
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, 1, np, np)
Z := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
}
}
plt.Contour(X, Y, Z, "levels=[0,0.6],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
F0 := utl.LinSpace(0, 1, 21)
F1r := make([]float64, len(F0))
F1s := make([]float64, len(F0))
F1t := make([]float64, len(F0))
for i, f0 := range F0 {
F1r[i] = math.Exp(-f0)
F1s[i] = a0 * math.Exp(-b0*f0)
F1t[i] = a1 * math.Exp(-b1*f0)
}
plt.Plot(F0, F1r, "'k--',color='blue'")
plt.Plot(F0, F1s, "'k--',color='green'")
plt.Plot(F0, F1t, "'k--',color='gray'")
plt.PlotOne(f0a, f1a, "'k|', ms=20")
plt.PlotOne(f0b, f1b, "'k|', ms=20")
}
// problem # 2 -- CTP2, Deb 2001, p368/369, fig 226
case 2:
f1max = 1.2
θ, a, b := -0.2*PI, 0.2, 10.0
c, d, e := 1.0, 6.0, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 3 -- CTP3, Deb 2001, p368/370, fig 227
case 3:
f1max = 1.2
θ, a, b := -0.2*PI, 0.1, 10.0
c, d, e := 1.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 4 -- CTP4, Deb 2001, p368/370, fig 228
case 4:
f1max = 2.0
θ, a, b := -0.2*PI, 0.75, 10.0
c, d, e := 1.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 5 -- CTP5, Deb 2001, p368/371, fig 229
case 5:
f1max = 1.2
θ, a, b := -0.2*PI, 0.1, 10.0
c, d, e := 2.0, 0.5, 1.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = CTPplotter(θ, a, b, c, d, e, f1max)
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 6 -- CTP6, Deb 2001, p368/372, fig 230
case 6:
f1max = 5.0
θ, a, b := 0.1*PI, 40.0, 0.5
c, d, e := 1.0, 2.0, -2.0
fcn = CTPgenerator(θ, a, b, c, d, e)
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
Z := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
}
}
plt.Contour(X, Y, Z, "levels=[-30,-15,0,15,30],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
}
opt.Multi_fcnErr = CTPerror1(θ, a, b, c, d, e)
// problem # 7 -- CTP7, Deb 2001, p368/373, fig 231
case 7:
f1max = 1.2
θ, a, b := -0.05*PI, 40.0, 5.0
c, d, e := 1.0, 6.0, 0.0
fcn = CTPgenerator(θ, a, b, c, d, e)
opt.Multi_fcnErr = func(f []float64) float64 { return f[1] - (1.0 - f[0]) }
extraplot = func() {
np := 201
X, Y := utl.MeshGrid2D(0, 1, 0, f1max, np, np)
Z1 := utl.DblsAlloc(np, np)
Z2 := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
Z1[i][j] = opt.Multi_fcnErr([]float64{X[i][j], Y[i][j]})
Z2[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
}
}
plt.Contour(X, Y, Z2, "levels=[0,3],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['b'], levels=[0]")
}
// problem # 8 -- CTP8, Deb 2001, p368/373, fig 232
case 8:
ng = 2
f1max = 5.0
θ1, a, b := 0.1*PI, 40.0, 0.5
c, d, e := 1.0, 2.0, -2.0
θ2, A, B := -0.05*PI, 40.0, 2.0
C, D, E := 1.0, 6.0, 0.0
sin1, cos1 := math.Sin(θ1), math.Cos(θ1)
sin2, cos2 := math.Sin(θ2), math.Cos(θ2)
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
c0 := 1.0
for i := 1; i < len(x); i++ {
c0 += x[i]
}
f[0] = x[0]
f[1] = c0 * (1.0 - f[0]/c0)
if true {
c1 := cos1*(f[1]-e) - sin1*f[0]
c2 := sin1*(f[1]-e) + cos1*f[0]
c3 := math.Sin(b * PI * math.Pow(c2, c))
g[0] = c1 - a*math.Pow(math.Abs(c3), d)
d1 := cos2*(f[1]-E) - sin2*f[0]
d2 := sin2*(f[1]-E) + cos2*f[0]
d3 := math.Sin(B * PI * math.Pow(d2, C))
g[1] = d1 - A*math.Pow(math.Abs(d3), D)
}
}
extraplot = func() {
np := 401
X, Y := utl.MeshGrid2D(0, 1, 0, 20, np, np)
Z1 := utl.DblsAlloc(np, np)
Z2 := utl.DblsAlloc(np, np)
Z3 := utl.DblsAlloc(np, np)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
c1 := cos1*(Y[i][j]-e) - sin1*X[i][j]
c2 := sin1*(Y[i][j]-e) + cos1*X[i][j]
c3 := math.Sin(b * PI * math.Pow(c2, c))
d1 := cos2*(Y[i][j]-E) - sin2*X[i][j]
d2 := sin2*(Y[i][j]-E) + cos2*X[i][j]
d3 := math.Sin(B * PI * math.Pow(d2, C))
Z1[i][j] = c1 - a*math.Pow(math.Abs(c3), d)
Z2[i][j] = d1 - A*math.Pow(math.Abs(d3), D)
if Z1[i][j] >= 0 && Z2[i][j] >= 0 {
Z3[i][j] = 1
} else {
Z3[i][j] = -1
}
}
}
plt.Contour(X, Y, Z3, "colors=['white','gray'],clabels=0,cbar=0,lwd=0.5,fsz=5")
plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
plt.ContourSimple(X, Y, Z2, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['gray'], levels=[0]")
}
opt.Multi_fcnErr = CTPerror1(θ1, a, b, c, d, e)
default:
chk.Panic("problem %d is not available", problem)
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// solve
opt.RunMany("", "")
goga.StatMulti(opt, true)
io.PfYel("Tsys = %v\n", opt.SysTime)
// check
goga.CheckFront0(opt, true)
// plot
if true {
feasibleOnly := false
plt.SetForEps(0.8, 300)
fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
goga.PlotOvaOvaPareto(opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
extraplot()
//plt.AxisYrange(0, f1max)
if problem > 0 && problem < 6 {
plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
plt.Text(0.95, f1max-0.05, "feasible", "color='white', ha='right',va='top'")
}
if opt.RptName == "CTP6" {
plt.Text(0.02, 0.15, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.02, 6.50, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.02, 13.0, "unfeasible", "rotation=-7,color='gray', ha='left',va='bottom'")
plt.Text(0.50, 2.40, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
plt.Text(0.50, 8.80, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
plt.Text(0.50, 15.30, "feasible", "rotation=-7,color='white', ha='center',va='bottom'")
}
if opt.RptName == "TNK" {
plt.Text(0.05, 0.05, "unfeasible", "color='gray', ha='left',va='bottom'")
plt.Text(0.80, 0.85, "feasible", "color='white', ha='left',va='top'")
plt.Equal()
plt.AxisRange(0, 1.22, 0, 1.22)
}
plt.SaveD("/tmp/goga", io.Sf("%s.eps", opt.RptName))
}
return
}
func Test_mdl01(tst *testing.T) {
//verbose()
//doplot := true
doplot := false
chk.PrintTitle("mdl01")
// info
simfnk := "mdl01"
matname := "mat1"
getnew := false
example := true
// conductivity model
cnd := mconduct.GetModel(simfnk, matname, "m1", getnew)
err := cnd.Init(cnd.GetPrms(example))
if err != nil {
tst.Errorf("mconduct.Init failed: %v\n", err)
return
}
// liquid retention model
lrm_name := "ref-m1"
//lrm_name := "vg"
lrm := mreten.GetModel(simfnk, matname, lrm_name, getnew)
err = lrm.Init(lrm.GetPrms(example))
if err != nil {
tst.Errorf("mreten.Init failed: %v\n", err)
return
}
// porous model
mdl := GetModel(simfnk, matname, getnew)
err = mdl.Init(mdl.GetPrms(example), cnd, lrm)
if err != nil {
tst.Errorf("mporous.Init failed: %v\n", err)
return
}
//mdl.MEtrial = false
mdl.ShowR = true
// initial and final values
pc0 := -5.0
sl0 := 1.0
pcf := 20.0
// plot lrm
if doplot {
npts := 41
plt.Reset()
mreten.Plot(mdl.Lrm, pc0, sl0, pcf, npts, "'b.-'", "'r+-'", lrm_name)
}
// state A
pcA := 5.0
A, err := mdl.NewState(mdl.RhoL0, mdl.RhoG0, -pcA, 0)
if err != nil {
tst.Errorf("mporous.NewState failed: %v\n", err)
return
}
// state B
pcB := 10.0
B, err := mdl.NewState(mdl.RhoL0, mdl.RhoG0, -pcB, 0)
if err != nil {
tst.Errorf("mporous.NewState failed: %v\n", err)
return
}
// plot A and B points
if doplot {
plt.PlotOne(pcA, A.A_sl, "'gs', clip_on=0, label='A', ms=10")
plt.PlotOne(pcB, B.A_sl, "'ks', clip_on=0, label='B'")
}
// incremental update
//Δpl := -20.0 // << problems with this one and VG
Δpl := -5.0
n := 23
iwet := 10
Pc := make([]float64, n)
Sl := make([]float64, n)
pl := -pcA
Pc[0] = pcA
Sl[0] = A.A_sl
for i := 1; i < n; i++ {
if i > iwet {
Δpl = -Δpl
iwet = n
}
pl += Δpl
err = mdl.Update(A, Δpl, 0, pl, 0)
if err != nil {
tst.Errorf("test failed: %v\n", err)
return
}
Pc[i] = -pl
Sl[i] = A.A_sl
}
// show graph
if doplot {
plt.Plot(Pc, Sl, "'ro-', clip_on=0, label='update'")
mreten.PlotEnd(true)
}
}
// Draw2d draws bins' grid
func (o *Bins) Draw2d(withtxt, withgrid, withentries, setup bool, selBins map[int]bool) {
if withgrid {
// horizontal lines
x := []float64{o.Xi[0], o.Xi[0] + o.L[0] + o.S[0]}
y := make([]float64, 2)
for j := 0; j < o.N[1]+1; j++ {
y[0] = o.Xi[1] + float64(j)*o.S[1]
y[1] = y[0]
plt.Plot(x, y, "'-', color='#4f3677', clip_on=0")
}
// vertical lines
y[0] = o.Xi[1]
y[1] = o.Xi[1] + o.L[1] + o.S[1]
for i := 0; i < o.N[0]+1; i++ {
x[0] = o.Xi[0] + float64(i)*o.S[0]
x[1] = x[0]
plt.Plot(x, y, "'k-', color='#4f3677', clip_on=0")
}
}
// selected bins
nxy := o.N[0] * o.N[1]
for idx, _ := range selBins {
i := idx % o.N[0] // indices representing bin
j := (idx % nxy) / o.N[0]
x := o.Xi[0] + float64(i)*o.S[0] // coordinates of bin corner
y := o.Xi[1] + float64(j)*o.S[1]
plt.DrawPolyline([][]float64{
{x, y},
{x + o.S[0], y},
{x + o.S[0], y + o.S[1]},
{x, y + o.S[1]},
}, &plt.Sty{Fc: "#fbefdc", Ec: "#8e8371", Lw: 0.5, Closed: true}, "clip_on=0")
}
// plot items
if withentries {
for _, bin := range o.All {
if bin == nil {
continue
}
for _, entry := range bin.Entries {
plt.PlotOne(entry.X[0], entry.X[1], "'r.', clip_on=0")
}
}
}
// labels
if withtxt {
for j := 0; j < o.N[1]; j++ {
for i := 0; i < o.N[0]; i++ {
idx := i + j*o.N[0]
x := o.Xi[0] + float64(i)*o.S[0] + 0.02*o.S[0]
y := o.Xi[1] + float64(j)*o.S[1] + 0.02*o.S[1]
plt.Text(x, y, io.Sf("%d", idx), "size=7")
}
}
}
// setup
if setup {
plt.Equal()
plt.AxisRange(o.Xi[0]-0.1, o.Xf[0]+o.S[0]+0.1, o.Xi[1]-0.1, o.Xf[1]+o.S[1]+0.1)
}
}
func (o *Plotter) Plot_oct(x, y []float64, res []*State, sts [][]float64, last bool) {
// stress path
nr := len(res)
k := nr - 1
var σa, σb, xmi, xma, ymi, yma float64
for i := 0; i < nr; i++ {
σa, σb, _ = tsr.PQW2O(o.P[i], o.Q[i], o.W[i])
x[i], y[i] = σa, σb
o.maxR = max(o.maxR, math.Sqrt(σa*σa+σb*σb))
if i == 0 {
xmi, xma = x[i], x[i]
ymi, yma = y[i], y[i]
} else {
xmi = min(xmi, x[i])
xma = max(xma, x[i])
ymi = min(ymi, y[i])
yma = max(yma, y[i])
}
}
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
// fix range and max radius
xmi, xma, ymi, yma = o.fix_range(0, xmi, xma, ymi, yma)
rr := math.Sqrt((xma-xmi)*(xma-xmi) + (yma-ymi)*(yma-ymi))
if o.maxR < rr {
o.maxR = rr
}
if o.maxR < 1e-10 {
o.maxR = 1
}
if yma > -xmi {
xmi = -yma
}
if o.OctLims != nil {
xmi, xma, ymi, yma = o.OctLims[0], o.OctLims[1], o.OctLims[2], o.OctLims[3]
}
//xmi, xma, ymi, yma = -20000, 20000, -20000, 20000
// yield surface
var σcmax float64
if o.WithYs && o.m != nil {
//io.Pforan("xmi,xma ymi,yma = %v,%v %v,%v\n", xmi,xma, ymi,yma)
dx := (xma - xmi) / float64(o.NptsOct-1)
dy := (yma - ymi) / float64(o.NptsOct-1)
xx := la.MatAlloc(o.NptsOct, o.NptsOct)
yy := la.MatAlloc(o.NptsOct, o.NptsOct)
zz := la.MatAlloc(o.NptsOct, o.NptsOct)
var λ0, λ1, λ2, σc float64
v := NewState(len(res[0].Sig), len(res[0].Alp), false, len(res[0].EpsE) > 0)
for k := 0; k < nr; k++ {
copy(v.Alp, res[k].Alp)
v.Dgam = res[k].Dgam
σc = tsr.M_p(res[k].Sig) * tsr.SQ3
//σc = 30000
σcmax = max(σcmax, σc)
for i := 0; i < o.NptsOct; i++ {
for j := 0; j < o.NptsOct; j++ {
xx[i][j] = xmi + float64(i)*dx
yy[i][j] = ymi + float64(j)*dy
λ0, λ1, λ2 = tsr.O2L(xx[i][j], yy[i][j], σc)
v.Sig[0], v.Sig[1], v.Sig[2] = λ0, λ1, λ2
ys := o.m.YieldFuncs(v)
zz[i][j] = ys[0]
}
}
plt.ContourSimple(xx, yy, zz, io.Sf("colors=['%s'], levels=[0], linestyles=['%s'], linewidths=[%g], clip_on=0", o.YsClr0, o.YsLs0, o.YsLw0)+o.ArgsYs)
}
}
// predictor-corrector
if len(o.PreCor) > 1 {
var σa, σb, σanew, σbnew float64
for i := 1; i < len(o.PreCor); i++ {
σa, σb, _ = tsr.M_oct(o.PreCor[i-1])
σanew, σbnew, _ = tsr.M_oct(o.PreCor[i])
if math.Abs(σanew-σa) > 1e-7 || math.Abs(σbnew-σb) > 1e-7 {
//plt.Plot([]float64{σa,σanew}, []float64{σb,σbnew}, "'k+', ms=3, color='k'")
plt.Arrow(σa, σb, σanew, σbnew, io.Sf("sc=%d, fc='%s', ec='%s'", o.ArrWid, o.ClrPC, o.ClrPC))
}
o.maxR = max(o.maxR, math.Sqrt(σa*σa+σb*σb))
o.maxR = max(o.maxR, math.Sqrt(σanew*σanew+σbnew*σbnew))
}
}
// rosette and settings
if last {
tsr.PlotRefOct(o.Phi, σcmax, true)
tsr.PlotRosette(o.maxR, false, true, true, 6)
if o.OctAxOff {
plt.AxisOff()
}
plt.Gll("$\\sigma_a$", "$\\sigma_b$", "")
if lims, ok := o.Lims["oct"]; ok {
plt.AxisLims(lims)
}
if lims, ok := o.Lims["oct,ys"]; ok {
plt.AxisLims(lims)
}
}
}
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()
}
func (o *Plotter) Plot_p_ev(x, y []float64, res []*State, sts [][]float64, last bool) {
nr := len(res)
if len(sts) != nr {
return
}
k := nr - 1
var x0, x1 []float64
if !o.NoAlp {
x0, x1 = make([]float64, nr), make([]float64, nr)
}
withα := false
if o.LogP {
xmin := o.calc_x(o.P[0])
xmax := xmin
for i := 0; i < nr; i++ {
x[i], y[i] = o.calc_x(o.P[i]), o.Ev[i]*100.0
if !o.NoAlp && len(res[i].Alp) > 0 {
withα = true
x0[i] = o.calc_x(res[i].Alp[0])
if o.nsurf > 1 {
x1[i] = o.calc_x(res[i].Alp[1])
}
}
xmin = min(xmin, x[i])
xmax = max(xmax, x[i])
}
} else {
xmin := o.P[0]
xmax := xmin
for i := 0; i < nr; i++ {
x[i], y[i] = o.P[i], o.Ev[i]*100.0
if !o.NoAlp && len(res[i].Alp) > 0 {
withα = true
x0[i] = res[i].Alp[0]
if o.nsurf > 1 {
x1[i] = res[i].Alp[1]
}
}
xmin = min(xmin, x[i])
xmax = max(xmax, x[i])
}
}
if withα {
plt.Plot(x0, y, io.Sf("'r-', ls='--', lw=3, clip_on=0, color='grey', label=r'%s'", o.Lbl+" $\\alpha_0$"))
if o.nsurf > 1 {
plt.Plot(x1, y, io.Sf("'r-', ls=':', lw=3, clip_on=0, color='grey', label=r'%s'", o.Lbl+" $\\alpha_1$"))
}
}
plt.Plot(x, y, io.Sf("'r.', ls='-', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
if last {
xlbl := "$p$"
if o.LogP {
xlbl = "$\\log{[1+(p+p_t)/p_r]}$"
}
plt.Gll(xlbl, "$\\varepsilon_v\\;[\\%]$", "leg_out=1, leg_ncol=4, leg_hlen=2")
if lims, ok := o.Lims["p,ev"]; ok {
plt.AxisLims(lims)
}
}
}
func solve_problem(problem int) (opt *goga.Optimiser) {
io.Pf("\n\n------------------------------------- problem = %d ---------------------------------------\n", problem)
// parameters
opt = new(goga.Optimiser)
opt.Default()
opt.Ncpu = 1
opt.Tf = 500
opt.Verbose = false
opt.Nsamples = 2
opt.GenType = "latin"
opt.DEC = 0.1
// options for report
opt.HistNsta = 6
opt.HistLen = 13
opt.RptFmtE = "%.4e"
opt.RptFmtL = "%.4e"
opt.RptFmtEdev = "%.3e"
opt.RptFmtLdev = "%.3e"
// problem variables
var fmin, fmax []float64
var nf, ng, nh int
var fcn goga.MinProb_t
// problems
switch problem {
// problem # 1 -- ZDT1, Deb 2001, p356
case 1:
opt.Ncpu = 6
opt.RptName = "ZDT1"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Sqrt(f[0]/c0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 2 -- ZDT2, Deb 2001, p356
case 2:
opt.Ncpu = 6
opt.RptName = "ZDT2"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Pow(f[0]/c0, 2.0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Pow(f0, 2.0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 3 -- ZDT3, Deb 2001, p356
case 3:
opt.Ncpu = 6
opt.RptName = "ZDT3"
n := 30
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
c0 := 1.0 + 9.0*sum/float64(n-1)
c1 := 1.0 - math.Sqrt(f[0]/c0) - math.Sin(10.0*math.Pi*f[0])*f[0]/c0
f[1] = c0 * c1
}
fmin = []float64{0, -1}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0) - math.Sin(10.0*math.Pi*f0)*f0
}
opt.F1F0_f0ranges = [][]float64{
{0.000000100000000, 0.083001534925223},
{0.182228728029413, 0.257762363387862},
{0.409313674808657, 0.453882104088830},
{0.618396794416602, 0.652511703804663},
{0.823331798326633, 0.851832865436414},
}
opt.F1F0_arcLenRef = 1.811
// problem # 4 -- ZDT4, Deb 2001, p358
case 4:
opt.Ncpu = 2
opt.RptName = "ZDT4"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
opt.FltMin[0] = 0
opt.FltMax[0] = 1
for i := 1; i < n; i++ {
opt.FltMin[i] = -5
opt.FltMax[i] = 5
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = x[0]
sum := 0.0
w := 4.0 * math.Pi
for i := 1; i < n; i++ {
sum += x[i]*x[i] - 10.0*math.Cos(w*x[i])
}
c0 := 1.0 + 10.0*float64(n-1) + sum
c1 := 1.0 - math.Sqrt(f[0]/c0)
f[1] = c0 * c1
}
fmin = []float64{0, 0}
fmax = []float64{1, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Sqrt(f0)
}
// arc length = sqrt(5)/2 + log(sqrt(5)+2)/4 ≈ 1.4789428575445975
opt.F1F0_arcLenRef = math.Sqrt(5.0)/2.0 + math.Log(math.Sqrt(5.0)+2.0)/4.0
// problem # 5 -- FON (Fonseca and Fleming 1995), Deb 2001, p339
case 5:
opt.DEC = 0.8
opt.Ncpu = 2
opt.RptName = "FON"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = -4
opt.FltMax[i] = 4
}
nf, ng, nh = 2, 0, 0
coef := 1.0 / math.Sqrt(float64(n))
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
sum0, sum1 := 0.0, 0.0
for i := 0; i < n; i++ {
sum0 += math.Pow(x[i]-coef, 2.0)
sum1 += math.Pow(x[i]+coef, 2.0)
}
f[0] = 1.0 - math.Exp(-sum0)
f[1] = 1.0 - math.Exp(-sum1)
}
fmin = []float64{0, 0}
fmax = []float64{0.98, 1}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Exp(-math.Pow(2.0-math.Sqrt(-math.Log(1.0-f0)), 2.0))
}
opt.F1F0_arcLenRef = 1.45831385
// problem # 6 -- ZDT6, Deb 2001, p360
case 6:
opt.Ncpu = 2
opt.RptName = "ZDT6"
n := 10
opt.FltMin = make([]float64, n)
opt.FltMax = make([]float64, n)
for i := 0; i < n; i++ {
opt.FltMin[i] = 0
opt.FltMax[i] = 1
}
nf, ng, nh = 2, 0, 0
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
w := 6.0 * math.Pi
f[0] = 1.0 - math.Exp(-4.0*x[0])*math.Pow(math.Sin(w*x[0]), 6.0)
sum := 0.0
for i := 1; i < n; i++ {
sum += x[i]
}
w = float64(n - 1)
c0 := 1.0 + 9.0*math.Pow(sum/w, 0.25)
c1 := 1.0 - math.Pow(f[0]/c0, 2.0)
f[1] = c0 * c1
}
opt.F1F0_func = func(f0 float64) float64 {
return 1.0 - math.Pow(f0, 2.0)
}
xs := math.Atan(9.0*math.Pi) / (6.0 * math.Pi)
f0min := 1.0 - math.Exp(-4.0*xs)*math.Pow(math.Sin(6.0*math.Pi*xs), 6.0)
f1max := opt.F1F0_func(f0min)
io.Pforan("xs=%v f0min=%v f1max=%v\n", xs, f0min, f1max)
// xs=0.08145779687998356 f0min=0.2807753188153699 f1max=0.9211652203441274
fmin = []float64{f0min, 0}
fmax = []float64{1, 1}
opt.F1F0_arcLenRef = 1.184
default:
chk.Panic("problem %d is not available", problem)
}
// number of trial solutions and number of groups
opt.Nsol = len(opt.FltMin) * 10
// initialise optimiser
opt.Init(goga.GenTrialSolutions, nil, fcn, nf, ng, nh)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// solve
opt.RunMany("", "")
goga.StatF1F0(opt, true)
// check
goga.CheckFront0(opt, true)
// plot
if true {
feasibleOnly := true
plt.SetForEps(0.8, 300)
fmtAll := &plt.Fmt{L: "final solutions", M: ".", C: "orange", Ls: "none", Ms: 3}
fmtFront := &plt.Fmt{L: "final Pareto front", C: "r", M: "o", Ms: 3, Ls: "none"}
goga.PlotOvaOvaPareto(opt, sols0, 0, 1, feasibleOnly, fmtAll, fmtFront)
np := 201
F0 := utl.LinSpace(fmin[0], fmax[0], np)
F1 := make([]float64, np)
for i := 0; i < np; i++ {
F1[i] = opt.F1F0_func(F0[i])
}
plt.Plot(F0, F1, io.Sf("'b-', label='%s'", opt.RptName))
for _, f0vals := range opt.F1F0_f0ranges {
f0A, f0B := f0vals[0], f0vals[1]
f1A, f1B := opt.F1F0_func(f0A), opt.F1F0_func(f0B)
plt.PlotOne(f0A, f1A, "'g_', mew=1.5, ms=10, clip_on=0")
plt.PlotOne(f0B, f1B, "'g|', mew=1.5, ms=10, clip_on=0")
}
plt.AxisRange(fmin[0], fmax[0], fmin[1], fmax[1])
plt.Gll("$f_0$", "$f_1$", "")
plt.SaveD("/tmp/goga", io.Sf("%s.eps", opt.RptName))
}
return
}
func (o *Plotter) Plot_p_q(x, y []float64, res []*State, sts [][]float64, last bool) {
// stress path
nr := len(res)
k := nr - 1
var xmi, xma, ymi, yma float64
for i := 0; i < nr; i++ {
x[i], y[i] = o.P[i], o.Q[i]
if o.Multq {
mult := fun.Sign(o.W[i])
y[i] *= mult
}
if o.UseOct {
x[i] *= tsr.SQ3
y[i] *= tsr.SQ2by3
}
if i == 0 {
xmi, xma = x[i], x[i]
ymi, yma = y[i], y[i]
} else {
xmi = min(xmi, x[i])
xma = max(xma, x[i])
ymi = min(ymi, y[i])
yma = max(yma, y[i])
}
if o.SMPon {
x[i], y[i], _ = tsr.M_pq_smp(res[i].Sig, o.SMPa, o.SMPb, o.SMPβ, o.SMPϵ)
}
}
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
// yield surface
if o.WithYs && o.m != nil {
mx, my := 1.0, 1.0
if o.UseOct {
mx, my = tsr.SQ3, tsr.SQ2by3
}
if o.UsePmin {
xmi = min(xmi, o.Pmin*mx)
}
if o.UsePmax {
xma = max(xma, o.Pmax*mx)
yma = max(yma, o.Pmax*my)
}
xmi, xma, ymi, yma = o.fix_range(xmi, xmi, xma, ymi, yma)
if o.PqLims != nil {
xmi, xma, ymi, yma = o.PqLims[0], o.PqLims[1], o.PqLims[2], o.PqLims[3]
}
//io.Pforan("xmi,xma ymi,yma = %v,%v %v,%v\n", xmi,xma, ymi,yma)
dx := (xma - xmi) / float64(o.NptsPq-1)
dy := (yma - ymi) / float64(o.NptsPq-1)
xx := la.MatAlloc(o.NptsPq, o.NptsPq)
yy := la.MatAlloc(o.NptsPq, o.NptsPq)
za := la.MatAlloc(o.NptsPq, o.NptsPq)
zb := la.MatAlloc(o.NptsPq, o.NptsPq)
var p, q, σa, σb, σc, λ0, λ1, λ2 float64
v := NewState(len(res[0].Sig), len(res[0].Alp), false, len(res[0].EpsE) > 0)
for k := 0; k < nr; k++ {
copy(v.Alp, res[k].Alp)
v.Dgam = res[k].Dgam
for i := 0; i < o.NptsPq; i++ {
for j := 0; j < o.NptsPq; j++ {
xx[i][j] = xmi + float64(i)*dx
yy[i][j] = ymi + float64(j)*dy
p, q = xx[i][j], yy[i][j]
if o.UseOct {
p /= tsr.SQ3
q /= tsr.SQ2by3
}
σa, σb, σc = tsr.PQW2O(p, q, o.W[k])
λ0, λ1, λ2 = tsr.O2L(σa, σb, σc)
v.Sig[0], v.Sig[1], v.Sig[2] = λ0, λ1, λ2
ys := o.m.YieldFuncs(v)
za[i][j] = ys[0]
if o.nsurf > 1 {
zb[i][j] = ys[1]
}
if o.SMPon {
xx[i][j], yy[i][j], _ = tsr.M_pq_smp(v.Sig, o.SMPa, o.SMPb, o.SMPβ, o.SMPϵ)
}
}
}
plt.ContourSimple(xx, yy, za, io.Sf("colors=['%s'], levels=[0], linestyles=['%s'], linewidths=[%g], clip_on=0", o.YsClr0, o.YsLs0, o.YsLw0)+o.ArgsYs)
if o.nsurf > 1 {
plt.ContourSimple(xx, yy, zb, io.Sf("colors=['%s'], levels=[0], linestyles=['%s'], linewidths=[%g], clip_on=0", o.YsClr1, o.YsLs1, o.YsLw1)+o.ArgsYs)
}
}
}
// predictor-corrector
if len(o.PreCor) > 1 {
var p, q, pnew, qnew float64
for i := 1; i < len(o.PreCor); i++ {
p = tsr.M_p(o.PreCor[i-1])
q = tsr.M_q(o.PreCor[i-1])
pnew = tsr.M_p(o.PreCor[i])
qnew = tsr.M_q(o.PreCor[i])
if o.UseOct {
p *= tsr.SQ3
pnew *= tsr.SQ3
q *= tsr.SQ2by3
qnew *= tsr.SQ2by3
}
if o.SMPon {
p, q, _ = tsr.M_pq_smp(o.PreCor[i-1], o.SMPa, o.SMPb, o.SMPβ, o.SMPϵ)
pnew, qnew, _ = tsr.M_pq_smp(o.PreCor[i], o.SMPa, o.SMPb, o.SMPβ, o.SMPϵ)
}
if math.Abs(pnew-p) > 1e-10 || math.Abs(qnew-q) > 1e-10 {
plt.Arrow(p, q, pnew, qnew, io.Sf("sc=%d, fc='%s', ec='%s'", o.ArrWid, o.ClrPC, o.ClrPC))
}
}
}
// settings
if last {
plt.Equal()
xl, yl := "$p_{cam}$", "$q_{cam}$"
if o.UseOct {
xl, yl = "$p_{oct}$", "$q_{oct}$"
}
if o.SMPon {
xl, yl = "$p_{smp}$", "$q_{smp}$"
}
if o.AxLblX != "" {
xl = o.AxLblX
}
if o.AxLblY != "" {
yl = o.AxLblY
}
plt.Gll(xl, yl, "leg_out=1, leg_ncol=4, leg_hlen=1.5")
if lims, ok := o.Lims["p,q"]; ok {
plt.AxisLims(lims)
}
if lims, ok := o.Lims["p,q,ys"]; ok {
plt.AxisLims(lims)
}
}
}
func main() {
PI := math.Pi
yf := func(x float64) float64 {
return 1.0 - math.Sqrt(x) - math.Sin(10.0*math.Pi*x)*x
}
dydx := func(x float64) float64 {
return -math.Sin(10.0*PI*x) - 10.0*PI*x*math.Cos(10.0*PI*x) - 1.0/(2.0*math.Sqrt(x))
}
var nlsDY num.NlSolver
nlsDY.Init(1, func(fx, x []float64) error {
fx[0] = dydx(x[0])
return nil
}, nil, nil, false, true, nil)
defer nlsDY.Clean()
X := []float64{0.09, 0.25, 0.45, 0.65, 0.85}
Y := make([]float64, len(X))
for i, x := range X {
// find min
xx := []float64{x}
err := nlsDY.Solve(xx, true)
if err != nil {
io.PfRed("dydx nls failed:\n%v", err)
return
}
X[i] = xx[0]
Y[i] = yf(X[i])
}
// find next point along horizontal line
Xnext := []float64{0.2, 0.4, 0.6, 0.8}
Ynext := make([]float64, len(Xnext))
for i, xnext := range Xnext {
var nlsX num.NlSolver
nlsX.Init(1, func(fx, x []float64) error {
fx[0] = Y[i] - yf(x[0])
return nil
}, nil, nil, false, true, nil)
defer nlsX.Clean()
xx := []float64{xnext}
err := nlsX.Solve(xx, true)
if err != nil {
io.PfRed("dydx nls failed:\n%v", err)
return
}
Xnext[i] = xx[0]
Ynext[i] = yf(Xnext[i])
}
// auxiliary points
XX := []float64{
0, X[0],
Xnext[0], X[1],
Xnext[1], X[2],
Xnext[2], X[3],
Xnext[3], X[4],
}
YY := []float64{
1, Y[0],
Ynext[0], Y[1],
Ynext[1], Y[2],
Ynext[2], Y[3],
Ynext[3], Y[4],
}
io.Pforan("XX = %.3f\n", XX)
io.Pforan("YY = %.3f\n", YY)
// find arc-length
arclen := 0.0
for i := 0; i < len(XX); i += 2 {
a := XX[i]
b := XX[i+1]
if i == 0 {
a += 1e-7
}
var quad num.Simp
quad.Init(func(x float64) float64 {
return math.Sqrt(1.0 + math.Pow(dydx(x), 2.0))
}, a, b, 1e-4)
res, err := quad.Integrate()
if err != nil {
io.PfRed("quad failed:\n%v", err)
return
}
arclen += res
io.Pf("int(...) from %.15f to %.15f = %g\n", a, b, res)
}
io.Pforan("arclen = %v\n", arclen)
np := 201
xx := utl.LinSpace(0, 1, np)
yy := make([]float64, np)
for i := 0; i < np; i++ {
yy[i] = yf(xx[i])
}
plt.Plot(xx, yy, "'b-', clip_on=0")
for i, x := range X {
plt.PlotOne(x, Y[i], "'r|', mew=2, ms=30, clip_on=0")
}
for i, x := range Xnext {
plt.PlotOne(x, Ynext[i], "'r_', mew=2, ms=30, clip_on=0")
}
for i := 0; i < len(XX); i += 2 {
x0, y0 := XX[i], YY[i]
x1, y1 := XX[i+1], YY[i+1]
plt.Arrow(x0, y0, x1, y1, "")
}
plt.SetXnticks(11)
plt.Gll("x", "y", "")
plt.SaveD("/tmp/goga", "calcZDT3pts.eps")
}
func (o *Plotter) Plot_s3_s1(x, y []float64, res []*State, sts [][]float64, last bool) {
// stress path
nr := len(res)
k := nr - 1
x2 := make([]float64, nr)
var xmi, xma, ymi, yma float64
for i := 0; i < nr; i++ {
σ1, σ2, σ3, err := tsr.M_PrincValsNum(res[i].Sig)
if err != nil {
chk.Panic("computation of eigenvalues failed", err)
}
x[i], y[i] = -tsr.SQ2*σ3, -σ1
x2[i] = -tsr.SQ2 * σ2
if i == 0 {
xmi, xma = x[i], x[i]
ymi, yma = y[i], y[i]
} else {
xmi = min(min(xmi, x[i]), x2[i])
xma = max(max(xma, x[i]), x2[i])
ymi = min(ymi, y[i])
yma = max(yma, y[i])
}
}
plt.Plot(x, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'$\\sigma_3$ %s'", o.Ls, o.Clr, o.Mrk, o.Lbl))
plt.Plot(x2, y, io.Sf("'r.', ls='%s', clip_on=0, color='%s', marker='%s', label=r'$\\sigma_2$ %s'", o.LsAlt, o.Clr, o.Mrk, o.Lbl))
plt.PlotOne(x[0], y[0], io.Sf("'bo', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.SpMrk, o.SpMs))
plt.PlotOne(x[k], y[k], io.Sf("'bs', clip_on=0, color='%s', marker='%s', ms=%d", o.SpClr, o.EpMrk, o.EpMs))
// yield surface
if o.WithYs && o.m != nil {
if o.UsePmin {
xmi = min(xmi, o.Pmin*tsr.SQ2)
ymi = min(ymi, o.Pmin)
}
if o.UsePmax {
xma = max(xma, o.Pmax*tsr.SQ2)
yma = max(yma, o.Pmax)
}
xmi, xma, ymi, yma = o.fix_range(0, xmi, xma, ymi, yma)
if o.S3s1Lims != nil {
xmi, xma, ymi, yma = o.S3s1Lims[0], o.S3s1Lims[1], o.S3s1Lims[2], o.S3s1Lims[3]
}
//io.Pforan("xmi,xma ymi,yma = %v,%v %v,%v\n", xmi,xma, ymi,yma)
dx := (xma - xmi) / float64(o.NptsSig-1)
dy := (yma - ymi) / float64(o.NptsSig-1)
xx := la.MatAlloc(o.NptsSig, o.NptsSig)
yy := la.MatAlloc(o.NptsSig, o.NptsSig)
zz := la.MatAlloc(o.NptsSig, o.NptsSig)
v := NewState(len(res[0].Sig), len(res[0].Alp), false, len(res[0].EpsE) > 0)
for k := 0; k < nr; k++ {
copy(v.Alp, res[k].Alp)
v.Dgam = res[k].Dgam
for i := 0; i < o.NptsSig; i++ {
for j := 0; j < o.NptsSig; j++ {
xx[i][j] = xmi + float64(i)*dx
yy[i][j] = ymi + float64(j)*dy
v.Sig[0], v.Sig[1], v.Sig[2] = -yy[i][j], -xx[i][j]/tsr.SQ2, -xx[i][j]/tsr.SQ2
ys := o.m.YieldFuncs(v)
zz[i][j] = ys[0]
}
}
plt.ContourSimple(xx, yy, zz, io.Sf("colors=['%s'], levels=[0], linestyles=['%s'], linewidths=[%g], clip_on=0", o.YsClr0, o.YsLs0, o.YsLw0)+o.ArgsYs)
}
}
// predictor-corrector
if len(o.PreCor) > 1 {
var σ3, σ1, σ3new, σ1new float64
for i := 1; i < len(o.PreCor); i++ {
σ1, _, σ3, _ = tsr.M_PrincValsNum(o.PreCor[i-1])
σ1new, _, σ3new, _ = tsr.M_PrincValsNum(o.PreCor[i])
if math.Abs(σ3new-σ3) > 1e-7 || math.Abs(σ1new-σ1) > 1e-7 {
plt.Arrow(-σ3*tsr.SQ2, -σ1, -σ3new*tsr.SQ2, -σ1new, io.Sf("sc=%d, fc='%s', ec='%s'", o.ArrWid, o.ClrPC, o.ClrPC))
}
}
}
// settings
if last {
plt.Equal()
plt.Gll("$-\\sqrt{2}\\sigma_3$", "$-\\sigma_1$", "leg=1, leg_out=1, leg_ncol=4, leg_hlen=2")
if lims, ok := o.Lims["s3,s1"]; ok {
plt.AxisLims(lims)
}
if lims, ok := o.Lims["s3,s1,ys"]; ok {
plt.AxisLims(lims)
}
}
}
// DistPoint returns the distance from a point to this Bezier curve
// It finds the closest projection which is stored in P
func (o *BezierQuad) DistPoint(X []float64, doplot bool) float64 {
// TODO:
// 1) split this into closest projections finding
// 2) finish distance computation
// check
if len(o.Q) != 3 {
chk.Panic("DistPoint: quadratic Bezier must be initialised first (with 3 control points)")
}
ndim := len(o.Q[0])
chk.IntAssert(len(X), ndim)
// solve cubic equation
var A_i, B_i, M_i, a, b, c, d float64
for i := 0; i < ndim; i++ {
A_i = o.Q[2][i] - 2.0*o.Q[1][i] + o.Q[0][i]
B_i = o.Q[1][i] - o.Q[0][i]
M_i = o.Q[0][i] - X[i]
a += A_i * A_i
b += 3.0 * A_i * B_i
c += 2.0*B_i*B_i + M_i*A_i
d += M_i * B_i
}
//io.Pforan("a=%v b=%v c=%v d=%v\n", a, b, c, d)
if math.Abs(a) < 1e-7 {
chk.Panic("DistPoint does not yet work with this type of Bezier (straight line?):\nQ=%v\n", o.Q)
}
x1, x2, x3, nx := num.EqCubicSolveReal(b/a, c/a, d/a)
io.Pfyel("\nx1=%v x2=%v x3=%v nx=%v\n", x1, x2, x3, nx)
// auxiliary
if len(o.P) != ndim {
o.P = make([]float64, ndim)
}
// closest projections
t := x1
if nx == 2 {
chk.Panic("nx=2 => not implemented yet")
}
if nx == 3 {
T := []float64{x1, x2, x3}
D := []float64{-1, -1, -1}
ok := []bool{
!(x1 < 0.0 || x1 > 1.0),
!(x2 < 0.0 || x2 > 1.0),
!(x3 < 0.0 || x3 > 1.0),
}
io.Pforan("ok = %v\n", ok)
for i, t := range T {
if ok[i] {
o.Point(o.P, t)
if doplot {
plt.PlotOne(X[0], X[1], "'ko'")
plt.PlotOne(o.P[0], o.P[1], "'k.'")
plt.Arrow(X[0], X[1], o.P[0], o.P[1], "ec='none'")
}
D[i] = ppdist(X, o.P)
}
}
io.Pforan("D = %v\n", D)
}
o.Point(o.P, t)
io.Pfcyan("P = %v\n", o.P)
return 0
}
