// Init initialises simple flot problem structure
func NewSimpleFltProb(fcn SimpleFltFcn_t, nf, ng, nh int, C *ConfParams) (o *SimpleFltProb) {
// data
o = new(SimpleFltProb)
o.Fcn = fcn
o.C = C
o.C.Nova = nf
o.C.Noor = ng + nh
// sandbox
o.nf, o.ng, o.nh = nf, ng, nh
o.ff = utl.DblsAlloc(o.C.Nisl, o.nf)
o.gg = utl.DblsAlloc(o.C.Nisl, o.ng)
o.hh = utl.DblsAlloc(o.C.Nisl, o.nh)
// objective function
o.C.OvaOor = func(ind *Individual, isl, time int, report *bytes.Buffer) {
x := ind.GetFloats()
o.Fcn(o.ff[isl], o.gg[isl], o.hh[isl], x)
for i, f := range o.ff[isl] {
ind.Ovas[i] = f
}
for i, g := range o.gg[isl] {
ind.Oors[i] = utl.GtePenalty(g, 0.0, 1) // g[i] ≥ 0
}
for i, h := range o.hh[isl] {
h = math.Abs(h)
ind.Ovas[0] += h
ind.Oors[ng+i] = utl.GtePenalty(o.C.Eps1, h, 1) // ϵ ≥ |h[i]|
}
}
// evolver
o.Evo = NewEvolver(o.C)
// auxiliary
o.NumfmtX = "%8.5f"
o.NumfmtF = "%8.5f"
// results and stat
nx := len(o.C.RangeFlt)
o.Xbest = utl.DblsAlloc(o.C.Ntrials, nx)
// plotting
if o.C.DoPlot {
o.PopsIni = o.Evo.GetPopulations()
o.PltDirout = "/tmp/goga"
o.PltNpts = 41
o.PltLwg = 1.5
o.PltLwh = 1.5
}
return
}
// HaltonPoints generates randomly spaced points
// x -- [dim][n] points
func HaltonPoints(dim, n int) (x [][]float64) {
x = utl.DblsAlloc(dim, n)
for j := 0; j < dim; j++ {
for i := 0; i < n; i++ {
x[j][i] = halton(i, j)
}
}
return
}
func CTPplotter(θ, a, b, c, d, e, f1max float64) func() {
return func() {
np := 401
X, Y := utl.MeshGrid2D(0, 1, 0, f1max, np, np)
Z1 := utl.DblsAlloc(np, np)
Z2 := utl.DblsAlloc(np, np)
sθ, cθ := math.Sin(θ), math.Cos(θ)
for j := 0; j < np; j++ {
for i := 0; i < np; i++ {
f0, f1 := X[i][j], Y[i][j]
Z1[i][j] = cθ*(f1-e) - sθ*f0
Z2[i][j] = CTPconstraint(θ, a, b, c, d, e, X[i][j], Y[i][j])
}
}
plt.Contour(X, Y, Z2, "levels=[0,2],cbar=0,lwd=0.5,fsz=5,cmapidx=6")
plt.ContourSimple(X, Y, Z1, false, 7, "linestyles=['--'], linewidths=[0.7], colors=['b'], levels=[0]")
}
}
// GetResults returns all ovas and oors
// Output:
// ova -- [nsol][nova] objective values
// oor -- [nsol][noor] out-of-range values
func GetResults(sols []*Solution, ovaOnly bool) (ova, oor [][]float64) {
nsol := len(sols)
nova := len(sols[0].Ova)
noor := len(sols[0].Oor)
ova = utl.DblsAlloc(nsol, nova)
if !ovaOnly {
oor = utl.DblsAlloc(nsol, noor)
}
for i, sol := range sols {
for j := 0; j < nova; j++ {
ova[i][j] = sol.Ova[j]
}
if !ovaOnly {
for j := 0; j < noor; j++ {
oor[i][j] = sol.Oor[j]
}
}
}
return
}
func get_nurbs_xmat(nurbs *gm.Nurbs, ibasis []int) (xmat [][]float64) {
nd := nurbs.Gnd()
xmat = utl.DblsAlloc(nd, len(ibasis))
for k, l := range ibasis {
q := nurbs.GetQl(l)
for j := 0; j < nd; j++ {
xmat[j][k] = q[j]
}
}
return
}
// 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)
}
// checkShape checks that shape functions result in 1.0 @ nodes
func checkShape(tst *testing.T, shape string, tol float64, verbose bool) {
// information
fcn := Functions[shape]
ndim := GeomNdim[shape]
nverts := NumVerts[shape]
coords := NatCoords[shape]
// allocate slices
S := make([]float64, nverts)
dSdR := utl.DblsAlloc(nverts, ndim)
// loop over all vertices
errS := 0.0
r := []float64{0, 0, 0}
for n := 0; n < nverts; n++ {
// natural coordinates @ vertex
for i := 0; i < ndim; i++ {
r[i] = coords[i][n]
}
// compute function
fcn(S, dSdR, r, false)
// check
if verbose {
for _, val := range S {
if math.Abs(val) < 1e-15 {
val = 0
}
io.Pf("%3v", val)
}
io.Pf("\n")
}
for m := 0; m < nverts; m++ {
if n == m {
errS += math.Abs(S[m] - 1.0)
} else {
errS += math.Abs(S[m])
}
}
}
// error
if errS > tol {
tst.Errorf("%s failed with err = %g\n", shape, errS)
return
}
}
// SimpleOutput implements a simple output function
func SimpleOutput(first bool, dx, x float64, y []float64, args ...interface{}) (err error) {
chk.IntAssert(len(args), 1)
res := args[0].(*Results)
res.Dx = append(res.Dx, dx)
res.X = append(res.X, x)
ndim := len(y)
if len(res.Y) == 0 {
res.Y = utl.DblsAlloc(ndim, 0)
}
for j := 0; j < ndim; j++ {
res.Y[j] = append(res.Y[j], y[j])
}
return
}
// Init initialises Munkres' structure
func (o *Munkres) Init(nrow, ncol int) {
chk.IntAssertLessThan(0, nrow) // nrow > 1
chk.IntAssertLessThan(0, ncol) // ncol > 1
o.nrow, o.ncol = nrow, ncol
o.C = utl.DblsAlloc(o.nrow, o.ncol)
o.M = make([][]Mask_t, o.nrow)
for i := 0; i < o.nrow; i++ {
o.M[i] = make([]Mask_t, o.ncol)
}
o.Links = make([]int, o.nrow)
npath := 2*o.nrow + 1 // TODO: check this
o.path = utl.IntsAlloc(npath, 2)
o.row_covered = make([]bool, o.nrow)
o.col_covered = make([]bool, o.ncol)
}
// Init initialises graph
// Input:
// edges -- [nedges][2] edges (connectivity)
// weightsE -- [nedges] weights of edges. can be <nil>
// verts -- [nverts][ndim] vertices. can be <nil>
// weightsV -- [nverts] weights of vertices. can be <nil>
func (o *Graph) Init(edges [][]int, weightsE []float64, verts [][]float64, weightsV []float64) {
o.Edges, o.WeightsE = edges, weightsE
o.Verts, o.WeightsV = verts, weightsV
o.Shares = make(map[int][]int)
o.Key2edge = make(map[int]int)
for k, edge := range o.Edges {
i, j := edge[0], edge[1]
utl.IntIntsMapAppend(&o.Shares, i, k)
utl.IntIntsMapAppend(&o.Shares, j, k)
o.Key2edge[o.HashEdgeKey(i, j)] = k
}
if o.Verts != nil {
chk.IntAssert(len(o.Verts), len(o.Shares))
}
nv := len(o.Shares)
o.Dist = utl.DblsAlloc(nv, nv)
o.Next = utl.IntsAlloc(nv, nv)
}
// PlotHc2d plots 2D hypercube
func PlotHc2d(dirout, fnkey string, x [][]int, xrange [][]float64) {
m := len(x)
n := len(x[0])
dx := make([]float64, m)
for i := 0; i < m; i++ {
dx[i] = (xrange[i][1] - xrange[i][0]) / float64(n-1)
}
X := utl.DblsAlloc(m, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
X[i][j] = xrange[i][0] + float64(x[i][j]-1)*dx[i]
}
}
plt.SetForEps(0.8, 300)
plt.Plot(X[0], X[1], "'r.', clip_on=0, zorder=10")
plt.Equal()
plt.Gll("$x$", "$y$", "")
plt.SaveD(dirout, fnkey+".eps")
}
// Delaunay computes 2D Delaunay triangulation using Triangle
// Input:
// X = { x0, x1, x2, ... Npoints }
// Y = { y0, y1, y2, ... Npoints }
// Ouptut:
// V = { { x0, y0 }, { x0, y0 }, { x0, y0 } ... Nvertices }
// C = { { id0, id1, id2 }, { id0, id1, id2 } ... Ncellls }
func Delaunay(X, Y []float64, verbose bool) (V [][]float64, C [][]int, err error) {
// input
chk.IntAssert(len(X), len(Y))
n := len(X)
verb := 0
if verbose {
verb = 1
}
// perform triangulation
var T C.triangulateio
defer func() { C.trifree(&T) }()
res := C.delaunay2d(
&T,
(C.long)(n),
(*C.double)(unsafe.Pointer(&X[0])),
(*C.double)(unsafe.Pointer(&Y[0])),
(C.long)(verb),
)
if res != 0 {
chk.Err("Delaunay2d failed: Triangle returned %d code\n", res)
}
// output
nverts := int(T.numberofpoints)
ncells := int(T.numberoftriangles)
V = utl.DblsAlloc(nverts, 2)
C = utl.IntsAlloc(ncells, 3)
for i := 0; i < nverts; i++ {
V[i][0] = float64(C.getpoint((C.long)(i), 0, &T))
V[i][1] = float64(C.getpoint((C.long)(i), 1, &T))
}
for i := 0; i < ncells; i++ {
C[i][0] = int(C.getcorner((C.long)(i), 0, &T))
C[i][1] = int(C.getcorner((C.long)(i), 1, &T))
C[i][2] = int(C.getcorner((C.long)(i), 2, &T))
}
return
}
// checkDerivs checks dSdR derivatives of shape structures
func checkDerivs(tst *testing.T, shape string, r []float64, tol float64, verbose bool) {
// information
fcn := Functions[shape]
ndim := GeomNdim[shape]
nverts := NumVerts[shape]
// allocate slices
S := make([]float64, nverts)
dSdR := utl.DblsAlloc(nverts, ndim)
// auxiliary
r_tmp := make([]float64, len(r))
S_tmp := make([]float64, nverts)
// analytical
fcn(S, dSdR, r, true)
// numerical
for n := 0; n < nverts; n++ {
for i := 0; i < ndim; i++ {
dSndRi, _ := num.DerivCentral(func(t float64, args ...interface{}) (Sn float64) {
copy(r_tmp, r)
r_tmp[i] = t
fcn(S_tmp, nil, r_tmp, false)
Sn = S_tmp[n]
return
}, r[i], 1e-1)
if verbose {
io.Pfgrey2(" dS%ddR%d @ %5.2f = %v (num: %v)\n", n, i, r, dSdR[n][i], dSndRi)
}
if math.Abs(dSdR[n][i]-dSndRi) > tol {
tst.Errorf("nurbs dS%ddR%d failed with err = %g\n", n, i, math.Abs(dSdR[n][i]-dSndRi))
return
}
}
}
}
// PlotHc3d plots 3D hypercube
func PlotHc3d(dirout, fnkey string, x [][]int, xrange [][]float64, show bool) {
m := len(x)
n := len(x[0])
dx := make([]float64, m)
for i := 0; i < m; i++ {
dx[i] = (xrange[i][1] - xrange[i][0]) / float64(n-1)
}
X := utl.DblsAlloc(m, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
X[i][j] = xrange[i][0] + float64(x[i][j]-1)*dx[i]
}
}
if !show {
plt.SetForEps(0.8, 455)
}
plt.Plot3dPoints(X[0], X[1], X[2], "clip_on=0, zorder=10")
if show {
plt.Show()
} else {
plt.SaveD(dirout, fnkey+".eps")
}
}
// 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")
}
func test_rwstep01(tst *testing.T) {
verbose()
chk.PrintTitle("rwstep01")
buf, err := io.ReadFile("rw/data/beadpanel.step")
if err != nil {
tst.Errorf("cannot read file:\n%v", err)
return
}
dat := string(buf)
var stp rw.STEP
err = stp.ParseDATA(dat)
if err != nil {
tst.Errorf("Parse filed:\n%v", err)
return
}
var bsplines []*Bspline
for _, scurve := range stp.Scurves {
curve := stp.BScurves[scurve.Curve_3d]
if curve == nil {
continue
}
// collect vertices
nv := len(curve.Control_points_list)
verts := utl.DblsAlloc(nv, 4)
for i, key := range curve.Control_points_list {
if p, ok := stp.Points[key]; ok {
for j := 0; j < 3; j++ {
verts[i][j] = p.Coordinates[j]
}
verts[i][3] = 1.0
} else {
chk.Panic("cannot find point %q", key)
}
}
// collect knots
nk := 0
for _, m := range curve.Knot_multiplicities {
nk += m
}
knots := make([]float64, nk)
k := 0
for i, u := range curve.Knots {
m := curve.Knot_multiplicities[i]
for j := 0; j < m; j++ {
knots[k] = u
k++
}
}
// create B-spline
bsp := new(Bspline)
bsp.Init(knots, curve.Degree)
bsp.SetControl(verts)
bsplines = append(bsplines, bsp)
}
if true {
io.Pforan("n = %v\n", len(bsplines))
for i, bsp := range bsplines {
bsp.Draw3d("", "", 21, i == 0)
}
//plt.Show()
}
}
// PlotContour plots contour
func (o *Optimiser) PlotContour(iFlt, jFlt, iOva int, pp *PlotParams) {
// check
var x []float64
if pp.Refx == nil {
if iFlt > 1 || jFlt > 1 {
chk.Panic("Refx vector must be given to PlotContour when iFlt or jFlt > 1")
}
x = make([]float64, 2)
} else {
x = make([]float64, len(pp.Refx))
copy(x, pp.Refx)
}
// limits and meshgrid
xmin, xmax := o.FltMin[iFlt], o.FltMax[iFlt]
ymin, ymax := o.FltMin[jFlt], o.FltMax[jFlt]
if pp.Xrange != nil {
xmin, xmax = pp.Xrange[0], pp.Xrange[1]
}
if pp.Yrange != nil {
ymin, ymax = pp.Yrange[0], pp.Yrange[1]
}
// check objective function
var sol *Solution // copy of solution for objective function
if o.MinProb == nil {
pp.NoG = true
pp.NoH = true
sol = NewSolution(o.Nsol, 0, &o.Parameters)
o.Solutions[0].CopyInto(sol)
if pp.Refx != nil {
copy(sol.Flt, pp.Refx)
}
}
// auxiliary variables
X, Y := utl.MeshGrid2D(xmin, xmax, ymin, ymax, pp.Npts, pp.Npts)
var Zf [][]float64
var Zg [][][]float64
var Zh [][][]float64
var Za [][]float64
if !pp.NoF {
Zf = utl.DblsAlloc(pp.Npts, pp.Npts)
}
if o.Ng > 0 && !pp.NoG {
Zg = utl.Deep3alloc(o.Ng, pp.Npts, pp.Npts)
}
if o.Nh > 0 && !pp.NoH {
Zh = utl.Deep3alloc(o.Nh, pp.Npts, pp.Npts)
}
if pp.WithAux {
Za = utl.DblsAlloc(pp.Npts, pp.Npts)
}
// compute values
grp := 0
for i := 0; i < pp.Npts; i++ {
for j := 0; j < pp.Npts; j++ {
x[iFlt], x[jFlt] = X[i][j], Y[i][j]
if o.MinProb == nil {
copy(sol.Flt, x)
o.ObjFunc(sol, grp)
if !pp.NoF {
Zf[i][j] = sol.Ova[iOva]
}
if pp.WithAux {
Za[i][j] = sol.Aux
}
} else {
o.MinProb(o.F[grp], o.G[grp], o.H[grp], x, nil, grp)
if !pp.NoF {
Zf[i][j] = o.F[grp][iOva]
}
if !pp.NoG {
for k, g := range o.G[grp] {
Zg[k][i][j] = g
}
}
if !pp.NoH {
for k, h := range o.H[grp] {
Zh[k][i][j] = h
}
}
}
}
}
// plot f
if !pp.NoF && !pp.OnlyAux {
txt := "cbar=0"
if pp.Cbar {
txt = ""
}
if pp.Simple {
plt.ContourSimple(X, Y, Zf, true, 7, io.Sf("colors=['%s'], fsz=7, %s", pp.FmtF.C, txt))
} else {
plt.Contour(X, Y, Zf, io.Sf("fsz=7, cmapidx=%d, %s", pp.CmapIdx, txt))
}
}
// plot g
if !pp.NoG && !pp.OnlyAux {
for _, g := range Zg {
plt.ContourSimple(X, Y, g, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtG.C, pp.FmtG.Lw))
}
}
// plot h
if !pp.NoH && !pp.OnlyAux {
for i, h := range Zh {
if i == pp.IdxH || pp.IdxH < 0 {
plt.ContourSimple(X, Y, h, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtH.C, pp.FmtH.Lw))
}
}
}
// plot aux
if pp.WithAux {
if pp.OnlyAux {
txt := "cbar=0"
if pp.Cbar {
txt = ""
}
if pp.Simple {
plt.ContourSimple(X, Y, Za, true, 7, io.Sf("colors=['%s'], fsz=7, %s", pp.FmtF.C, txt))
} else {
plt.Contour(X, Y, Za, io.Sf("fsz=7, markZero='red', cmapidx=%d, %s", pp.CmapIdx, txt))
}
} else {
plt.ContourSimple(X, Y, Za, false, 7, io.Sf("zorder=5, levels=[0], colors=['%s'], linewidths=[%g], clip_on=0", pp.FmtA.C, pp.FmtA.Lw))
}
}
// limits
if pp.Limits {
plt.Plot(
[]float64{o.FltMin[iFlt], o.FltMax[iFlt], o.FltMax[iFlt], o.FltMin[iFlt], o.FltMin[iFlt]},
[]float64{o.FltMin[jFlt], o.FltMin[jFlt], o.FltMax[jFlt], o.FltMax[jFlt], o.FltMin[jFlt]},
"'y--', color='yellow', zorder=10",
)
}
}
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
}
// PlotDiagMoment plots bending moment diagram
// Input:
// M -- moment along stations
// withtext -- show bending moment values
// numfmt -- number format for values. use "" to chose default one
// tolM -- tolerance to clip absolute values of M
// sf -- scaling factor
func (o *Beam) PlotDiagMoment(M []float64, withtext bool, numfmt string, tolM, sf float64) {
// number of stations
nstations := len(M)
ds := 1.0 / float64(nstations-1)
// nodes
var xa, xb []float64
var u []float64 // out-of-pane vector
if o.Ndim == 2 {
xa = []float64{o.X[0][0], o.X[1][0], 0}
xb = []float64{o.X[0][1], o.X[1][1], 0}
u = []float64{0, 0, 1}
} else {
chk.Panic("TODO: 3D beam diagram")
}
// unit vector along beam
v := make([]float64, 3)
sum := 0.0
for j := 0; j < o.Ndim; j++ {
v[j] = xb[j] - xa[j]
sum += v[j] * v[j]
}
sum = math.Sqrt(sum)
for j := 0; j < o.Ndim; j++ {
v[j] /= sum
}
// unit normal
n := make([]float64, 3) // normal
utl.CrossProduct3d(n, u, v) // n := u cross v
// auxiliary vectors
x := make([]float64, o.Ndim) // station
m := make([]float64, o.Ndim) // vector pointing to other side
c := make([]float64, o.Ndim) // centre
imin, imax := utl.DblArgMinMax(M)
// draw text function
draw_text := func(mom float64) {
if math.Abs(mom) > tolM {
α := math.Atan2(-n[1], -n[0]) * 180.0 / math.Pi
str := io.Sf("%g", mom)
if numfmt != "" {
str = io.Sf(numfmt, mom)
} else {
if len(str) > 10 {
str = io.Sf("%.10f", mom) // truncate number
str = io.Sf("%g", io.Atof(str))
}
}
plt.Text(c[0], c[1], str, io.Sf("ha='center', size=7, rotation=%g, clip_on=0", α))
}
}
// draw
pts := utl.DblsAlloc(nstations, 2)
xx, yy := make([]float64, 2), make([]float64, 2)
for i := 0; i < nstations; i++ {
// station
s := float64(i) * ds
for j := 0; j < o.Ndim; j++ {
x[j] = (1.0-s)*o.X[j][0] + s*o.X[j][1]
}
// auxiliary vectors
for j := 0; j < o.Ndim; j++ {
m[j] = x[j] - sf*M[i]*n[j]
c[j] = (x[j] + m[j]) / 2.0
}
// points on diagram
pts[i][0], pts[i][1] = m[0], m[1]
xx[0], xx[1] = x[0], m[0]
yy[0], yy[1] = x[1], m[1]
// draw
clr, lw := "#919191", 1.0
if i == imin || i == imax {
lw = 2
if M[i] < 0 {
clr = "#9f0000"
} else {
clr = "#109f24"
}
}
plt.Plot(xx, yy, io.Sf("'-', color='%s', lw=%g, clip_on=0", clr, lw))
if withtext {
if i == imin || i == imax { // draw text @ min/max
draw_text(M[i])
} else {
if i == 0 || i == nstations-1 { // draw text @ extremities
draw_text(M[i])
}
}
}
}
// draw polyline
plt.DrawPolyline(pts, &plt.Sty{Ec: "k", Fc: "none", Lw: 1}, "")
}