// 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 (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)
}
}
}
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 (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)
}
}
}
// Draw draws grid
// r -- radius of circles
// W -- width of paths
// dwt -- δwt for positioning text (w = W/2)
// arrow_scale -- scale for arrows. use 0 for default value
func (o *Graph) Draw(dirout, fname string, r, W, dwt, arrow_scale float64,
verts_lbls map[int]string, verts_fsz float64, verts_clr string,
edges_lbls map[int]string, edges_fsz float64, edges_clr string) {
if len(o.Verts) < 1 {
return
}
xmin, ymin := o.Verts[0][0], o.Verts[0][1]
xmax, ymax := xmin, ymin
var lbl string
for i, v := range o.Verts {
if verts_lbls == nil {
lbl = io.Sf("%d", i)
} else {
lbl = verts_lbls[i]
}
plt.Text(v[0], v[1], lbl, io.Sf("clip_on=0, color='%s', fontsize=%g, ha='center', va='center'", verts_clr, verts_fsz))
plt.Circle(v[0], v[1], r, "clip_on=0, ec='k', lw=0.8")
xmin, ymin = utl.Min(xmin, v[0]), utl.Min(ymin, v[1])
xmax, ymax = utl.Max(xmax, v[0]), utl.Max(ymax, v[1])
}
if W > 2*r {
W = 1.8 * r
}
w := W / 2.0
xa, xb := make([]float64, 2), make([]float64, 2)
xc, dx := make([]float64, 2), make([]float64, 2)
mu, nu := make([]float64, 2), make([]float64, 2)
xi, xj := make([]float64, 2), make([]float64, 2)
l := math.Sqrt(r*r - w*w)
var L float64
if arrow_scale <= 0 {
arrow_scale = 20
}
for k, e := range o.Edges {
L = 0.0
for i := 0; i < 2; i++ {
xa[i] = o.Verts[e[0]][i]
xb[i] = o.Verts[e[1]][i]
xc[i] = (xa[i] + xb[i]) / 2.0
dx[i] = xb[i] - xa[i]
L += dx[i] * dx[i]
}
L = math.Sqrt(L)
mu[0], mu[1] = dx[0]/L, dx[1]/L
nu[0], nu[1] = -dx[1]/L, dx[0]/L
for i := 0; i < 2; i++ {
xi[i] = xa[i] + l*mu[i] - w*nu[i]
xj[i] = xb[i] - l*mu[i] - w*nu[i]
xc[i] = (xi[i]+xj[i])/2.0 - dwt*nu[i]
}
plt.Arrow(xi[0], xi[1], xj[0], xj[1], io.Sf("st='->', sc=%g", arrow_scale))
if edges_lbls == nil {
lbl = io.Sf("%d", k)
} else {
lbl = edges_lbls[k]
}
plt.Text(xc[0], xc[1], lbl, io.Sf("clip_on=0, color='%s', fontsize=%g, ha='center', va='center'", edges_clr, edges_fsz))
}
xmin -= r
xmax += r
ymin -= r
ymax += r
plt.AxisOff()
plt.Equal()
plt.AxisRange(xmin, xmax, ymin, ymax)
plt.SaveD(dirout, fname)
}
// 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
}
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")
}