// 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 Test_bins02(tst *testing.T) {
//verbose()
chk.PrintTitle("bins02. find along line (2D)")
// bins
var bins Bins
bins.Init([]float64{-0.2, -0.2}, []float64{0.8, 1.8}, 5)
// fill bins structure
maxit := 5 // number of entries
ID := make([]int, maxit)
for k := 0; k < maxit; k++ {
x := float64(k) / float64(maxit)
ID[k] = k
err := bins.Append([]float64{x, 2*x + 0.2}, ID[k])
if err != nil {
chk.Panic(err.Error())
}
}
// add more points to bins
for i := 0; i < 5; i++ {
err := bins.Append([]float64{float64(i) * 0.1, 1.8}, 100+i)
if err != nil {
chk.Panic(err.Error())
}
}
// message
for _, bin := range bins.All {
if bin != nil {
io.Pf("%v\n", bin)
}
}
// find points along diagonal
ids := bins.FindAlongSegment([]float64{0.0, 0.2}, []float64{0.8, 1.8}, 1e-8)
io.Pforan("ids = %v\n", ids)
chk.Ints(tst, "ids", ids, ID)
// find additional points
ids = bins.FindAlongSegment([]float64{-0.2, 1.8}, []float64{0.8, 1.8}, 1e-8)
io.Pfcyan("ids = %v\n", ids)
chk.Ints(tst, "ids", ids, []int{100, 101, 102, 103, 104, 4})
// draw
if chk.Verbose {
plt.SetForPng(1, 500, 150)
bins.Draw2d(true, true, true, true, map[int]bool{8: true, 9: true, 10: true})
plt.SetXnticks(15)
plt.SetYnticks(15)
plt.SaveD("/tmp/gosl/gm", "test_bins02.png")
}
}
// 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 solve_problem(fnkey string, problem int) (opt *goga.Optimiser) {
// GA parameters
opt = new(goga.Optimiser)
opt.Default()
// options for report
opt.RptFmtF = "%.4f"
opt.RptFmtX = "%.3f"
opt.RptFmtFdev = "%.1e"
opt.RptWordF = "\\beta"
opt.HistFmt = "%.2f"
opt.HistNdig = 3
opt.HistDelFmin = 0.005
opt.HistDelFmax = 0.005
// FORM data
var lsft LSF_T
var vars rnd.Variables
// simple problem or FEM sim
if fnkey == "simple" {
opt.Read("ga-simple.json")
opt.ProbNum = problem
lsft, vars = get_simple_data(opt)
fnkey += io.Sf("-%d", opt.ProbNum)
io.Pf("\n----------------------------------- simple problem %d --------------------------------\n", opt.ProbNum)
} else {
opt.Read("ga-" + fnkey + ".json")
lsft, vars = get_femsim_data(opt, fnkey)
io.Pf("\n----------------------------------- femsim %s --------------------------------\n", fnkey)
}
// set limits
nx := len(vars)
opt.FltMin = make([]float64, nx)
opt.FltMax = make([]float64, nx)
for i, dat := range vars {
opt.FltMin[i] = dat.Min
opt.FltMax[i] = dat.Max
}
// log input
var buf bytes.Buffer
io.Ff(&buf, "%s", opt.LogParams())
io.WriteFileVD("/tmp/gosl", fnkey+".log", &buf)
// initialise distributions
err := vars.Init()
if err != nil {
chk.Panic("cannot initialise distributions:\n%v", err)
}
// plot distributions
if opt.PlotSet1 {
io.Pf(". . . . . . . . plot distributions . . . . . . . .\n")
np := 201
for i, dat := range vars {
plt.SetForEps(0.75, 250)
dat.PlotPdf(np, "'b-',lw=2,zorder=1000")
//plt.AxisXrange(dat.Min, dat.Max)
plt.SetXnticks(15)
plt.SaveD("/tmp/sims", io.Sf("distr-%s-%d.eps", fnkey, i))
}
return
}
// objective function
nf := 1
var ng, nh int
var fcn goga.MinProb_t
var obj goga.ObjFunc_t
switch opt.Strategy {
// argmin_x{ β(y(x)) | lsf(x) ≤ 0 }
// f ← sqrt(y dot y)
// g ← -lsf(x) ≥ 0
// h ← out-of-range in case Transform fails
case 0:
ng, nh = 1, 1
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
// original and normalised variables
h[0] = 0
y, invalid := vars.Transform(x)
if invalid {
h[0] = 1
return
}
// objective value
f[0] = math.Sqrt(la.VecDot(y, y)) // β
// inequality constraint
lsf, failed := lsft(x, cpu)
g[0] = -lsf
h[0] = failed
}
// argmin_x{ β(y(x)) | lsf(x) = 0 }
// f ← sqrt(y dot y)
// h0 ← lsf(x)
// h1 ← out-of-range in case Transform fails
case 1:
ng, nh = 0, 2
fcn = func(f, g, h, x []float64, ξ []int, cpu int) {
// original and normalised variables
h[0], h[1] = 0, 0
y, invalid := vars.Transform(x)
if invalid {
h[0], h[1] = 1, 1
return
}
// objective value
f[0] = math.Sqrt(la.VecDot(y, y)) // β
// equality constraint
lsf, failed := lsft(x, cpu)
h[0] = lsf
h[1] = failed
// induce minmisation of h0
//f[0] += math.Abs(lsf)
}
case 2:
opt.Nova = 1
opt.Noor = 2
obj = func(sol *goga.Solution, cpu int) {
// clear out-of-range values
sol.Oor[0] = 0 // invalid transformation or FEM failed
sol.Oor[1] = 0 // g(x) ≤ 0 was violated
// original and normalised variables
x := sol.Flt
y, invalid := vars.Transform(x)
if invalid {
sol.Oor[0] = goga.INF
sol.Oor[1] = goga.INF
return
}
// objective value
sol.Ova[0] = math.Sqrt(la.VecDot(y, y)) // β
// inequality constraint
lsf, failed := lsft(x, cpu)
sol.Oor[0] = failed
sol.Oor[1] = fun.Ramp(lsf)
}
default:
chk.Panic("strategy %d is not available", opt.Strategy)
}
// initialise optimiser
opt.Init(goga.GenTrialSolutions, obj, fcn, nf, ng, nh)
// solve
io.Pf(". . . . . . . . running . . . . . . . .\n")
opt.RunMany("", "")
goga.StatF(opt, 0, true)
io.Pfblue2("Tsys = %v\n", opt.SysTimeAve)
// check
goga.CheckFront0(opt, true)
// results
sols := goga.GetFeasible(opt.Solutions)
if len(sols) > 0 {
goga.SortByOva(sols, 0)
best := sols[0]
io.Pforan("x = %.6f\n", best.Flt)
io.Pforan("xref = %.6f\n", opt.RptXref)
io.Pforan("β = %v (%v)\n", best.Ova[0], opt.RptFref[0])
}
return
}
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")
}