// 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
}
// PlotEnd ends plot and show figure, if show==true
func PlotEnd(show bool) {
plt.AxisYrange(0, 1)
plt.Cross("")
plt.Gll("$p_c$", "$s_{\\ell}$", "")
if show {
plt.Show()
}
}
// 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_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 main() {
// input data
simfn := "elast.sim"
matname := "lrm1"
pcmax := 30.0
npts := 101
// parse flags
flag.Parse()
if len(flag.Args()) > 0 {
simfn = flag.Arg(0)
}
if len(flag.Args()) > 1 {
matname = flag.Arg(1)
}
if len(flag.Args()) > 2 {
pcmax = io.Atof(flag.Arg(2))
}
if len(flag.Args()) > 3 {
npts = io.Atoi(flag.Arg(3))
}
// check extension
if io.FnExt(simfn) == "" {
simfn += ".sim"
}
// print input data
io.Pf("\nInput data\n")
io.Pf("==========\n")
io.Pf(" simfn = %30s // simulation filename\n", simfn)
io.Pf(" matname = %30s // material name\n", matname)
io.Pf(" pcmax = %30v // max pc\n", pcmax)
io.Pf(" npts = %30v // number of points\n", npts)
io.Pf("\n")
// load simulation
sim := inp.ReadSim("", simfn, "lrm_", false)
if sim == nil {
io.PfRed("cannot load simulation\n")
return
}
// get material data
mat := sim.Mdb.Get(matname)
if mat == nil {
io.PfRed("cannot get material\n")
return
}
io.Pforan("mat = %v\n", mat)
// get and initialise model
mdl := mreten.GetModel(simfn, matname, mat.Model, false)
if mdl == nil {
io.PfRed("cannot allocate model\n")
return
}
mdl.Init(mat.Prms)
// plot drying path
d_Pc := utl.LinSpace(0, pcmax, npts)
d_Sl := make([]float64, npts)
d_Sl[0] = 1
var err error
for i := 1; i < npts; i++ {
d_Sl[i], err = mreten.Update(mdl, d_Pc[i-1], d_Sl[i-1], d_Pc[i]-d_Pc[i-1])
if err != nil {
io.PfRed("drying: cannot updated model\n%v\n", err)
return
}
}
plt.Plot(d_Pc, d_Sl, io.Sf("'b-', label='%s (dry)', clip_on=0", matname))
// plot wetting path
w_Pc := utl.LinSpace(pcmax, 0, npts)
w_Sl := make([]float64, npts)
w_Sl[0] = d_Sl[npts-1]
for i := 1; i < npts; i++ {
w_Sl[i], err = mreten.Update(mdl, w_Pc[i-1], w_Sl[i-1], w_Pc[i]-w_Pc[i-1])
if err != nil {
io.PfRed("wetting: cannot updated model\n%v\n", err)
return
}
}
plt.Plot(w_Pc, w_Sl, io.Sf("'c-', label='%s (wet)', clip_on=0", matname))
// save results
type Results struct{ Pc, Sl []float64 }
res := Results{append(d_Pc, w_Pc...), append(d_Sl, w_Sl...)}
var buf bytes.Buffer
enc := json.NewEncoder(&buf)
err = enc.Encode(&res)
if err != nil {
io.PfRed("cannot encode results\n")
return
}
fn := path.Join(sim.Data.DirOut, matname+".dat")
io.WriteFile(fn, &buf)
io.Pf("file <[1;34m%s[0m> written\n", fn)
// show figure
plt.AxisYrange(0, 1)
plt.Cross()
plt.Gll("$p_c$", "$s_{\\ell}$", "")
plt.Show()
}
// 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")
}
func main() {
// catch errors
defer func() {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
}()
// input data
simfn, _ := io.ArgToFilename(0, "elast", ".sim", true)
matname := io.ArgToString(1, "lrm1")
pcmax := io.ArgToFloat(2, 30.0)
npts := io.ArgToInt(3, 101)
// print input table
io.Pf("\n%s\n", io.ArgsTable(
"simulation filename", "simfn", simfn,
"material name", "matname", matname,
"max pc", "pcmax", pcmax,
"number of points", "npts", npts,
))
// load simulation
sim := inp.ReadSim(simfn, "lrm", false, 0)
if sim == nil {
io.PfRed("cannot load simulation\n")
return
}
// get material data
mat := sim.MatParams.Get(matname)
if mat == nil {
io.PfRed("cannot get material\n")
return
}
io.Pforan("mat = %v\n", mat)
// get and initialise model
mdl := mreten.GetModel(simfn, matname, mat.Model, false)
if mdl == nil {
io.PfRed("cannot allocate model\n")
return
}
mdl.Init(mat.Prms)
// plot drying path
d_Pc := utl.LinSpace(0, pcmax, npts)
d_Sl := make([]float64, npts)
d_Sl[0] = 1
var err error
for i := 1; i < npts; i++ {
d_Sl[i], err = mreten.Update(mdl, d_Pc[i-1], d_Sl[i-1], d_Pc[i]-d_Pc[i-1])
if err != nil {
io.PfRed("drying: cannot updated model\n%v\n", err)
return
}
}
plt.Plot(d_Pc, d_Sl, io.Sf("'b-', label='%s (dry)', clip_on=0", matname))
// plot wetting path
w_Pc := utl.LinSpace(pcmax, 0, npts)
w_Sl := make([]float64, npts)
w_Sl[0] = d_Sl[npts-1]
for i := 1; i < npts; i++ {
w_Sl[i], err = mreten.Update(mdl, w_Pc[i-1], w_Sl[i-1], w_Pc[i]-w_Pc[i-1])
if err != nil {
io.PfRed("wetting: cannot updated model\n%v\n", err)
return
}
}
plt.Plot(w_Pc, w_Sl, io.Sf("'c-', label='%s (wet)', clip_on=0", matname))
// save results
type Results struct{ Pc, Sl []float64 }
res := Results{append(d_Pc, w_Pc...), append(d_Sl, w_Sl...)}
var buf bytes.Buffer
enc := json.NewEncoder(&buf)
err = enc.Encode(&res)
if err != nil {
io.PfRed("cannot encode results\n")
return
}
fn := path.Join(sim.Data.DirOut, matname+".dat")
io.WriteFile(fn, &buf)
io.Pf("file <[1;34m%s[0m> written\n", fn)
// show figure
plt.AxisYrange(0, 1)
plt.Cross("")
plt.Gll("$p_c$", "$s_{\\ell}$", "")
plt.Show()
}