func Test_dist_lognormal_01(tst *testing.T) {
//verbose()
chk.PrintTitle("dist_lognormal_01")
_, dat, err := io.ReadTable("data/lognormal.dat")
if err != nil {
tst.Errorf("cannot read comparison results:\n%v\n", err)
return
}
X, ok := dat["x"]
if !ok {
tst.Errorf("cannot get x values\n")
return
}
N, ok := dat["n"]
if !ok {
tst.Errorf("cannot get n values\n")
return
}
Z, ok := dat["z"]
if !ok {
tst.Errorf("cannot get z values\n")
return
}
YpdfCmp, ok := dat["ypdf"]
if !ok {
tst.Errorf("cannot get ypdf values\n")
return
}
YcdfCmp, ok := dat["ycdf"]
if !ok {
tst.Errorf("cannot get ycdf values\n")
return
}
var dist DistLogNormal
nx := len(X)
for i := 0; i < nx; i++ {
w := Z[i] * Z[i]
μ := math.Exp(N[i] + w/2.0)
σ := μ * math.Sqrt(math.Exp(w)-1.0)
dist.Init(&VarData{M: μ, S: σ})
Ypdf := dist.Pdf(X[i])
Ycdf := dist.Cdf(X[i])
err := chk.PrintAnaNum("ypdf", 1e-14, YpdfCmp[i], Ypdf, chk.Verbose)
if err != nil {
tst.Errorf("pdf failed: %v\n", err)
return
}
err = chk.PrintAnaNum("ycdf", 1e-15, YcdfCmp[i], Ycdf, chk.Verbose)
if err != nil {
tst.Errorf("cdf failed: %v\n", err)
return
}
}
}
func Test_dist_gumbel_01(tst *testing.T) {
//verbose()
chk.PrintTitle("dist_gumbel_01")
_, dat, err := io.ReadTable("data/gumbel.dat")
if err != nil {
tst.Errorf("cannot read comparison results:\n%v\n", err)
return
}
X, ok := dat["x"]
if !ok {
tst.Errorf("cannot get x values\n")
return
}
U, ok := dat["u"]
if !ok {
tst.Errorf("cannot get u values\n")
return
}
B, ok := dat["b"]
if !ok {
tst.Errorf("cannot get b values\n")
return
}
YpdfCmp, ok := dat["ypdf"]
if !ok {
tst.Errorf("cannot get ypdf values\n")
return
}
YcdfCmp, ok := dat["ycdf"]
if !ok {
tst.Errorf("cannot get ycdf values\n")
return
}
var dist DistGumbel
nx := len(X)
for i := 0; i < nx; i++ {
dist.U = U[i]
dist.B = B[i]
Ypdf := dist.Pdf(X[i])
Ycdf := dist.Cdf(X[i])
err := chk.PrintAnaNum("ypdf", 1e-14, YpdfCmp[i], Ypdf, chk.Verbose)
if err != nil {
tst.Errorf("pdf failed: %v\n", err)
return
}
err = chk.PrintAnaNum("ycdf", 1e-15, YcdfCmp[i], Ycdf, chk.Verbose)
if err != nil {
tst.Errorf("cdf failed: %v\n", err)
return
}
}
}
func Test_dist_uniform_01(tst *testing.T) {
//verbose()
chk.PrintTitle("dist_uniform_01")
_, dat, err := io.ReadTable("data/uniform.dat")
if err != nil {
tst.Errorf("cannot read comparison results:\n%v\n", err)
return
}
X, ok := dat["x"]
if !ok {
tst.Errorf("cannot get x values\n")
return
}
A, ok := dat["a"] // min
if !ok {
tst.Errorf("cannot get a values\n")
return
}
B, ok := dat["b"] // max
if !ok {
tst.Errorf("cannot get b values\n")
return
}
YpdfCmp, ok := dat["ypdf"]
if !ok {
tst.Errorf("cannot get ypdf values\n")
return
}
YcdfCmp, ok := dat["ycdf"]
if !ok {
tst.Errorf("cannot get ycdf values\n")
return
}
var dist DistUniform
nx := len(X)
for i := 0; i < nx; i++ {
dist.Init(&VarData{Min: A[i], Max: B[i]})
Ypdf := dist.Pdf(X[i])
Ycdf := dist.Cdf(X[i])
err := chk.PrintAnaNum("ypdf", 1e-14, YpdfCmp[i], Ypdf, chk.Verbose)
if err != nil {
tst.Errorf("pdf failed: %v\n", err)
return
}
err = chk.PrintAnaNum("ycdf", 1e-15, YcdfCmp[i], Ycdf, chk.Verbose)
if err != nil {
tst.Errorf("cdf failed: %v\n", err)
return
}
}
}
func Test_norm01(tst *testing.T) {
//verbose()
chk.PrintTitle("norm01")
_, dat, err := io.ReadTable("data/normal.dat")
if err != nil {
tst.Errorf("cannot read comparison results:\n%v\n", err)
return
}
X, ok := dat["x"]
if !ok {
tst.Errorf("cannot get x values\n")
return
}
Mu, ok := dat["mu"]
if !ok {
tst.Errorf("cannot get mu values\n")
return
}
Sig, ok := dat["sig"]
if !ok {
tst.Errorf("cannot get sig values\n")
return
}
YpdfCmp, ok := dat["ypdf"]
if !ok {
tst.Errorf("cannot get ypdf values\n")
return
}
YcdfCmp, ok := dat["ycdf"]
if !ok {
tst.Errorf("cannot get ycdf values\n")
return
}
var dist DistNormal
n := len(X)
for i := 0; i < n; i++ {
dist.Init(&VarData{M: Mu[i], S: Sig[i]})
Ypdf := dist.Pdf(X[i])
Ycdf := dist.Cdf(X[i])
err := chk.PrintAnaNum("ypdf", 1e-15, YpdfCmp[i], Ypdf, chk.Verbose)
if err != nil {
tst.Errorf("pdf failed: %v\n", err)
return
}
err = chk.PrintAnaNum("ycdf", 1e-15, YcdfCmp[i], Ycdf, chk.Verbose)
if err != nil {
tst.Errorf("cdf failed: %v\n", err)
return
}
}
}
// ReadGraphTable reads data and allocate graph
func ReadGraphTable(fname string, bargera bool) *Graph {
// data
var ne int
var edges [][]int
var weights []float64
// Bar-Gera format files from: http://www.bgu.ac.il/~bargera/tntp/
if bargera {
k := 0
reading_meta := true
io.ReadLines(fname, func(idx int, line string) (stop bool) {
if len(line) < 1 {
return false
}
line = strings.TrimSpace(line)
if line[0] == '~' {
return false
}
if reading_meta {
switch {
case strings.HasPrefix(line, "<NUMBER OF LINKS>"):
res := strings.Split(line, "<NUMBER OF LINKS>")
ne = io.Atoi(strings.TrimSpace(res[1]))
edges = make([][]int, ne)
weights = make([]float64, ne)
case strings.HasPrefix(line, "<END OF METADATA>"):
reading_meta = false
}
return false
}
l := strings.Fields(line)
edges[k] = []int{io.Atoi(l[0]) - 1, io.Atoi(l[1]) - 1}
weights[k] = io.Atof(l[4])
k++
return false
})
} else {
_, dat, err := io.ReadTable(fname)
if err != nil {
chk.Panic("cannot read datafile\n%v", err)
}
ne = len(dat["from"]) // number of edges
edges = make([][]int, ne)
weights = make([]float64, ne)
for i := 0; i < ne; i++ {
edges[i] = []int{int(dat["from"][i]) - 1, int(dat["to"][i]) - 1}
weights[i] = dat["cost"][i]
}
}
// graph
var G Graph
G.Init(edges, weights, nil, nil)
return &G
}
// ReadTable loads path from datafile in table format
// Note: n -- number of lines to read. use -1 to read all lines
func (o *Path) ReadTable(ndim, nincs, niout int, fname string, n int, mσ, mε float64, stresspath bool) (err error) {
// constants
o.Nincs, o.Niout = nincs, niout
// read data table
keys, d, err := io.ReadTable(fname)
if err != nil {
return
}
if n < 0 {
n = len(d[keys[0]])
}
// find x-y-z keys
ex, ey, ez := "ex", "ey", "ez"
sx, sy, sz := "sx", "sy", "sz"
for _, key := range keys {
switch key {
case "Ex":
ex, ey, ez = "Ex", "Ey", "Ez"
case "Ea":
ex, ey, ez = "Et", "Er", "Ea"
case "ea":
ex, ey, ez = "et", "er", "ea"
case "Sx":
sx, sy, sz = "Sx", "Sy", "Sz"
case "Sa":
sx, sy, sz = "St", "Sr", "Sa"
case "sa":
sx, sy, sz = "st", "sr", "sa"
}
}
// set stress path
if stresspath {
o.Sx, o.Sy, o.Sz = make([]float64, n), make([]float64, n), make([]float64, n)
for i := 0; i < n; i++ {
o.Sx[i], o.Sy[i], o.Sz[i] = mσ*d[sx][i], mσ*d[sy][i], mσ*d[sz][i]
}
o.UseS = utl.IntVals(n, 1)
// set strain path
} else {
o.Ex, o.Ey, o.Ez = make([]float64, n), make([]float64, n), make([]float64, n)
for i := 0; i < n; i++ {
o.Ex[i], o.Ey[i], o.Ez[i] = mε*d[ex][i], mε*d[ey][i], mε*d[ez][i]
}
o.Sx, o.Sy, o.Sz = []float64{mσ * d[sx][0]}, []float64{mσ * d[sy][0]}, []float64{mσ * d[sz][0]}
o.UseE = utl.IntVals(n, 1)
}
// set additional information
return o.Init(ndim)
}
func Test_flt04(tst *testing.T) {
//verbose()
chk.PrintTitle("flt04. two-bar truss. Pareto-optimal")
// data. from Coelho (2007) page 19
ρ := 0.283 // lb/in³
H := 100.0 // in
P := 1e4 // lb
E := 3e7 // lb/in²
σ0 := 2e4 // lb/in²
// parameters
var opt Optimiser
opt.Default()
opt.Nsol = 30
opt.Ncpu = 1
opt.Tf = 100
opt.LatinDup = 5
opt.FltMin = []float64{0.1, 0.5}
opt.FltMax = []float64{2.25, 2.5}
nf, ng, nh := 2, 2, 0
// initialise optimiser
TSQ2 := 2.0 * math.Sqrt2
opt.Init(GenTrialSolutions, nil, func(f, g, h, x []float64, ξ []int, cpu int) {
f[0] = 2.0 * ρ * H * x[1] * math.Sqrt(1.0+x[0]*x[0])
f[1] = P * H * math.Pow(1.0+x[0]*x[0], 1.5) * math.Sqrt(1.0+math.Pow(x[0], 4.0)) / (TSQ2 * E * x[0] * x[0] * x[1])
g[0] = σ0 - P*(1.0+x[0])*math.Sqrt(1.0+x[0]*x[0])/(TSQ2*x[0]*x[1])
g[1] = σ0 - P*(1.0-x[0])*math.Sqrt(1.0+x[0]*x[0])/(TSQ2*x[0]*x[1])
}, nf, ng, nh)
// initial solutions
sols0 := opt.GetSolutionsCopy()
// solve
opt.Solve()
// plot
if chk.Verbose {
_, dat, _ := io.ReadTable("data/coelho-fig1.6.dat")
pp := NewPlotParams(false)
pp.FnKey = "fig-flt04"
pp.FmtSols.C = "gray"
pp.WithAll = true
pp.Extra = func() {
plt.Plot(dat["f1"], dat["f2"], "'b-',ms=3,markeredgecolor='b'")
plt.AxisRange(0, 250, 0, 0.15)
}
opt.PlotOvaOvaPareto(sols0, 0, 1, pp)
}
}
// NewSpheresFromFile add spheres (e.g. particles) by reading a file in the following format
// x y z r
// 0.0 0.0 0.0 0.1
// 1.0 0.0 0.0 0.1
// ...
func NewSpheresFromFile(filename string) *Spheres {
_, dat, err := io.ReadTable(filename)
if err != nil {
chk.Panic("NewSpheresFromFile failed:\n%v", err)
}
return &Spheres{
X: dat["x"],
Y: dat["y"],
Z: dat["z"],
R: dat["r"],
Color: []float64{1, 0, 0, 1},
}
}
func main() {
// finalise analysis process and catch errors
defer out.End()
// input data
simfn := "a-coarse-elast-d2-q9"
flag.Parse()
if len(flag.Args()) > 0 {
simfn = flag.Arg(0)
}
if io.FnExt(simfn) == "" {
simfn += ".sim"
}
// start analysis process
out.Start(simfn, 0, 0)
// define entities
out.Define("a", out.P{{18, 8}})
// load results
out.LoadResults(nil)
nf_a := out.GetRes("nf", "a", -1)
pl_a := out.GetRes("pl", "a", -1)
pc_a := make([]float64, len(pl_a))
for i, _ := range pl_a {
pc_a[i] = -pl_a[i]
}
out.Splot("LRM")
_, d, _ := io.ReadTable("lrm.dat")
plt.Plot(d["pc"], d["sl"], "'c-',lw=2")
out.Plot(pc_a, "sl", "a", plt.Fmt{M: "o"}, -1)
out.Csplot.Xlbl = "$p_c$"
out.Splot("porosity")
out.Plot("t", nf_a, "a", plt.Fmt{M: "+"}, -1)
out.Csplot.Ylbl = "$n_f$"
// show
out.Draw("", "", true, nil)
}
func main() {
// filename
filename, fnkey := io.ArgToFilename(0, "sg1121", ".sim", true)
// results
out.Start(filename, 0, 0)
out.Define("A", out.N{30})
out.LoadResults(nil)
// plot FEM results
out.Plot("t", "uy", "A", plt.Fmt{C: "k", Ls: "-", L: "gofem"}, -1)
// old results
b, err := io.ReadFile("cmp/sg1121gofemold.json")
if err != nil {
io.PfRed("cannot read comparison file\n")
return
}
var gofemold struct {
Time, Uy30 []float64
}
err = json.Unmarshal(b, &gofemold)
if err != nil {
io.PfRed("cannot unmarshal comparison file\n")
return
}
// mechsys results
_, res, err := io.ReadTable("cmp/sg1121mechsysN30.cmp")
if err != nil {
io.PfRed("cannot read mechsys comparison file\n")
return
}
// save
plt.SetForPng(0.8, 400, 200)
out.Draw("/tmp", fnkey+".png", false, func(i, j, n int) {
plt.Plot(gofemold.Time, gofemold.Uy30, "'r-', lw=2, label='gofemOld'")
plt.Plot(res["Time"], res["uy"], "'b-', label='mechsys'")
})
}
func main() {
// filename
filename, fnkey := io.ArgToFilename(0, "a-coarse-elast-d2-q9", ".sim", true)
// start analysis process
out.Start(filename, 0, 0)
// define entities
out.Define("a", out.P{{18, 8}})
// load results
out.LoadResults(nil)
nf_a := out.GetRes("nf", "a", -1)
pl_a := out.GetRes("pl", "a", -1)
pc_a := make([]float64, len(pl_a))
for i, _ := range pl_a {
pc_a[i] = -pl_a[i]
}
out.Splot("LRM")
_, d, _ := io.ReadTable("lrm.dat")
plt.Plot(d["pc"], d["sl"], "'c-',lw=2")
out.Plot(pc_a, "sl", "a", plt.Fmt{M: "o"}, -1)
out.Csplot.Xlbl = "$p_c$"
out.Splot("porosity")
out.Plot("t", nf_a, "a", plt.Fmt{M: "+"}, -1)
out.Csplot.Ylbl = "$n_f$"
// show
plt.SetForPng(1.2, 500, 200)
out.Draw("/tmp", "up_indentation2d_unsat_lrm_"+fnkey+".png", false, nil)
}
func runone(ncpu int) (nsol, tf int, elaspsedTime time.Duration) {
// input filename
fn, fnkey := io.ArgToFilename(0, "ground10", ".sim", true)
// GA parameters
var opt goga.Optimiser
opt.Read("ga-" + fnkey + ".json")
opt.GenType = "rnd"
nsol, tf = opt.Nsol, opt.Tf
postproc := true
if ncpu > 0 {
opt.Ncpu = ncpu
postproc = false
}
// FEM
data := make([]*FemData, opt.Ncpu)
for i := 0; i < opt.Ncpu; i++ {
data[i] = NewData(fn, fnkey, i)
}
io.Pforan("MaxWeight = %v\n", data[0].MaxWeight)
// set integers
if data[0].Opt.BinInt {
opt.CxInt = goga.CxInt
opt.MtInt = goga.MtIntBin
opt.BinInt = data[0].Ncells
}
// set floats
opt.FltMin = make([]float64, data[0].Nareas)
opt.FltMax = make([]float64, data[0].Nareas)
for i := 0; i < data[0].Nareas; i++ {
opt.FltMin[i] = data[0].Opt.Amin
opt.FltMax[i] = data[0].Opt.Amax
}
// initialise optimiser
opt.Nova = 2 // weight and deflection
opt.Noor = 4 // mobility, feasibility, maxdeflection, stress
opt.Init(goga.GenTrialSolutions, func(sol *goga.Solution, cpu int) {
mob, fail, weight, umax, _, errU, errS := data[cpu].RunFEM(sol.Int, sol.Flt, 0, false)
sol.Ova[0] = weight
sol.Ova[1] = umax
sol.Oor[0] = mob
sol.Oor[1] = fail
sol.Oor[2] = errU
sol.Oor[3] = errS
}, nil, 0, 0, 0)
// initial solutions
var sols0 []*goga.Solution
if false {
sols0 = opt.GetSolutionsCopy()
}
// benchmark
initialTime := time.Now()
defer func() {
elaspsedTime = time.Now().Sub(initialTime)
}()
// solve
opt.Verbose = true
opt.Solve()
goga.SortByOva(opt.Solutions, 0)
// post processing
if !postproc {
return
}
// check
nfailed, front0 := goga.CheckFront0(&opt, true)
// save results
var log, res bytes.Buffer
io.Ff(&log, opt.LogParams())
io.Ff(&res, PrintSolutions(data[0], opt.Solutions))
io.Ff(&res, io.Sf("\n\nnfailed = %d\n", nfailed))
io.WriteFileVD("/tmp/goga", fnkey+".log", &log)
io.WriteFileVD("/tmp/goga", fnkey+".res", &res)
// plot Pareto-optimal front
feasibleOnly := true
plt.SetForEps(0.8, 350)
if strings.HasPrefix(fnkey, "ground10") {
_, ref, _ := io.ReadTable("p460_fig300.dat")
plt.Plot(ref["w"], ref["u"], "'b-', label='reference'")
}
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)
plt.Gll("weight ($f_0$)", "deflection ($f_1)$", "") //, "leg_out=1, leg_ncol=4, leg_hlen=1.5")
if strings.HasPrefix(fnkey, "ground10") {
plt.AxisRange(1800, 14000, 1, 6)
}
// plot selected results
ia, ib, ic, id, ie := 0, 0, 0, 0, 0
nfront0 := len(front0)
io.Pforan("nfront0 = %v\n", nfront0)
if nfront0 > 4 {
ib = nfront0 / 10
ic = nfront0 / 5
id = nfront0 / 2
ie = nfront0 - 1
}
A := front0[ia]
B := front0[ib]
C := front0[ic]
D := front0[id]
E := front0[ie]
wid, hei := 0.20, 0.10
draw_truss(data[0], "A", A, 0.17, 0.75, wid, hei)
draw_truss(data[0], "B", B, 0.20, 0.55, wid, hei)
draw_truss(data[0], "C", C, 0.28, 0.33, wid, hei)
draw_truss(data[0], "D", D, 0.47, 0.22, wid, hei)
draw_truss(data[0], "E", E, 0.70, 0.18, wid, hei)
// save figure
plt.SaveD("/tmp/goga", fnkey+".eps")
// tex file
title := "Shape and topology optimisation. Results."
label := "topoFront"
document := true
compact := true
tex_results("/tmp/goga", "tmp_"+fnkey, title, label, data[0], A, B, C, D, E, document, compact)
document = false
tex_results("/tmp/goga", fnkey, title, label, data[0], A, B, C, D, E, document, compact)
return
}
// Hairer-Wanner VII-p3 Eq.(1.4) Robertson's Equation
func Test_ode03(tst *testing.T) {
//verbose()
chk.PrintTitle("ode03: Hairer-Wanner VII-p3 Eq.(1.4) Robertson's Equation")
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
f[0] = -0.04*y[0] + 1.0e4*y[1]*y[2]
f[1] = 0.04*y[0] - 1.0e4*y[1]*y[2] - 3.0e7*y[1]*y[1]
f[2] = 3.0e7 * y[1] * y[1]
return nil
}
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
if dfdy.Max() == 0 {
dfdy.Init(3, 3, 9)
}
dfdy.Start()
dfdy.Put(0, 0, -0.04)
dfdy.Put(0, 1, 1.0e4*y[2])
dfdy.Put(0, 2, 1.0e4*y[1])
dfdy.Put(1, 0, 0.04)
dfdy.Put(1, 1, -1.0e4*y[2]-6.0e7*y[1])
dfdy.Put(1, 2, -1.0e4*y[1])
dfdy.Put(2, 0, 0.0)
dfdy.Put(2, 1, 6.0e7*y[1])
dfdy.Put(2, 2, 0.0)
return nil
}
// data
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
xa, xb := 0.0, 0.3
ya := []float64{1.0, 0.0, 0.0}
ndim := len(ya)
// structure to hold numerical results
res := Results{Method: method}
// allocate ODE object
var o Solver
o.Init(method, ndim, fcn, jac, nil, SimpleOutput, silent)
// tolerances and initial step size
rtol := 1e-2
atol := rtol * 1e-6
o.SetTol(atol, rtol)
o.IniH = 1.0e-6
// solve problem
y := make([]float64, ndim)
copy(y, ya)
if fixstp {
o.Solve(y, xa, xb, 0.01, fixstp, &res)
} else {
o.Solve(y, xa, xb, xb-xa, fixstp, &res)
}
// plot
if chk.Verbose {
plt.SetForEps(1.5, 400)
args := "'b-', marker='.', lw=1, clip_on=0"
Plot("/tmp/gosl/ode", "rober.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/rober_radau5_cpp.dat")
if err != nil {
chk.Panic("%v", err)
}
plt.Subplot(4, 1, 1)
plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=10")
plt.Subplot(4, 1, 2)
plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=10")
plt.Subplot(4, 1, 3)
plt.Plot(T["x"], T["y2"], "'k+',label='reference',ms=10")
})
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")
}
if mpi.Size() != 2 {
chk.Panic(">> error: this test requires 2 MPI processors\n")
return
}
eps := 1.0e-6
w := make([]float64, 2) // workspace
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
f[0], f[1] = 0, 0
switch mpi.Rank() {
case 0:
f[0] = y[1]
case 1:
f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
}
// join all f
mpi.AllReduceSum(f, w)
return nil
}
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
if dfdy.Max() == 0 {
dfdy.Init(2, 2, 4)
}
dfdy.Start()
if false { // per column
switch mpi.Rank() {
case 0:
dfdy.Put(0, 0, 0.0)
dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
case 1:
dfdy.Put(0, 1, 1.0)
dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
}
} else { // per row
switch mpi.Rank() {
case 0:
dfdy.Put(0, 0, 0.0)
dfdy.Put(0, 1, 1.0)
case 1:
dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
}
}
return nil
}
// method and flags
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
numjac := false
xa, xb := 0.0, 2.0
ya := []float64{2.0, -0.6}
ndim := len(ya)
// structure to hold numerical results
res := ode.Results{Method: method}
// allocate ODE object
var o ode.Solver
o.Distr = true
if numjac {
o.Init(method, ndim, fcn, nil, nil, ode.SimpleOutput, silent)
} else {
o.Init(method, ndim, fcn, jac, nil, ode.SimpleOutput, silent)
}
// tolerances and initial step size
rtol := 1e-4
atol := rtol
o.IniH = 1.0e-4
o.SetTol(atol, rtol)
//o.NmaxSS = 2
// solve problem
y := make([]float64, ndim)
copy(y, ya)
t0 := time.Now()
if fixstp {
o.Solve(y, xa, xb, 0.05, fixstp, &res)
} else {
o.Solve(y, xa, xb, xb-xa, fixstp, &res)
}
// plot
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
plt.SetForEps(1.5, 400)
args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
ode.Plot("/tmp/gosl/ode", "vdpolA_mpi.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/vdpol_radau5_for.dat")
if err != nil {
chk.Panic("%v", err)
}
plt.Subplot(3, 1, 1)
plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=7")
plt.Subplot(3, 1, 2)
plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=7")
})
}
}
func Test_sg1121(tst *testing.T) {
//verbose()
chk.PrintTitle("sg1121")
// run simulation
if !Start("data/sg1121.sim", true, chk.Verbose) {
tst.Errorf("test failed\n")
return
}
// make sure to flush log
defer End()
// run simulation
if !Run() {
tst.Errorf("test failed\n")
return
}
// plot
doplot := false
if doplot {
// 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) {
tst.Errorf("SetStage failed\n")
return
}
// selected node and dof index
nidx := 30
didx := 1
// new results
ntout := len(sum.OutTimes)
uy := make([]float64, ntout)
for tidx := 0; tidx < ntout; tidx++ {
if !d.ReadSol(sum.Dirout, sum.Fnkey, tidx) {
tst.Errorf("test failed:\n")
return
}
nod := d.Nodes[nidx]
eq := nod.Dofs[didx].Eq
uy[tidx] = d.Sol.Y[eq]
// check
if math.Abs(d.Sol.T-sum.OutTimes[tidx]) > 1e-14 {
tst.Errorf("output times do not match time in solution array")
return
}
}
plt.Plot(sum.OutTimes, uy, "'k*-', clip_on=0, label='gofem'")
// old results
b, err := io.ReadFile("cmp/sg1121gofemold.json")
if err != nil {
tst.Errorf("cannot read comparison file\n")
return
}
var gofemold struct {
Time, Uy30 []float64
}
err = json.Unmarshal(b, &gofemold)
if err != nil {
tst.Errorf("cannot unmarshal comparison file\n")
return
}
plt.Plot(gofemold.Time, gofemold.Uy30, "'ro-', label='gofemOld'")
// mechsys results
_, res, err := io.ReadTable("cmp/sg1121mechsysN30.cmp")
if err != nil {
tst.Errorf("cannot read mechsys comparison file\n")
return
}
plt.Plot(res["Time"], res["uy"], "'b+-', label='mechsys'")
// show figure
plt.Gll("$t$", "$u_y$", "")
plt.Show()
}
}
func Test_dist_frechet_01(tst *testing.T) {
//verbose()
chk.PrintTitle("dist_frechet_01")
_, dat, err := io.ReadTable("data/frechet.dat")
if err != nil {
tst.Errorf("cannot read comparison results:\n%v\n", err)
return
}
X, ok := dat["x"]
if !ok {
tst.Errorf("cannot get x values\n")
return
}
L, ok := dat["l"] // location
if !ok {
tst.Errorf("cannot get l values\n")
return
}
C, ok := dat["c"] // scale
if !ok {
tst.Errorf("cannot get c values\n")
return
}
A, ok := dat["a"] // shape
if !ok {
tst.Errorf("cannot get a values\n")
return
}
YpdfCmp, ok := dat["ypdf"]
if !ok {
tst.Errorf("cannot get ypdf values\n")
return
}
YcdfCmp, ok := dat["ycdf"]
if !ok {
tst.Errorf("cannot get ycdf values\n")
return
}
var dist DistFrechet
nx := len(X)
for i := 0; i < nx; i++ {
dist.Init(&VarData{L: L[i], C: C[i], A: A[i]})
Ypdf := dist.Pdf(X[i])
Ycdf := dist.Cdf(X[i])
err := chk.PrintAnaNum("ypdf", 1e-14, YpdfCmp[i], Ypdf, chk.Verbose)
if err != nil {
tst.Errorf("pdf failed: %v\n", err)
return
}
err = chk.PrintAnaNum("ycdf", 1e-15, YcdfCmp[i], Ycdf, chk.Verbose)
if err != nil {
tst.Errorf("cdf failed: %v\n", err)
return
}
}
}
// Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation
func Test_ode02(tst *testing.T) {
//verbose()
chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")
// problem definition
eps := 1.0e-6
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
f[0] = y[1]
f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
return nil
}
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
if dfdy.Max() == 0 {
dfdy.Init(2, 2, 4)
}
dfdy.Start()
dfdy.Put(0, 0, 0.0)
dfdy.Put(0, 1, 1.0)
dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
return nil
}
// method and flags
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
numjac := false
xa, xb := 0.0, 2.0
ya := []float64{2.0, -0.6}
ndim := len(ya)
// structure to hold numerical results
res := Results{Method: method}
// allocate ODE object
var o Solver
if numjac {
o.Init(method, ndim, fcn, nil, nil, SimpleOutput, silent)
} else {
o.Init(method, ndim, fcn, jac, nil, SimpleOutput, silent)
}
// tolerances and initial step size
rtol := 1e-4
atol := rtol
o.IniH = 1.0e-4
o.SetTol(atol, rtol)
//o.NmaxSS = 2
// solve problem
y := make([]float64, ndim)
copy(y, ya)
t0 := time.Now()
if fixstp {
o.Solve(y, xa, xb, 0.05, fixstp, &res)
} else {
o.Solve(y, xa, xb, xb-xa, fixstp, &res)
}
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
// plot
if chk.Verbose {
plt.SetForEps(1.5, 400)
args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
Plot("/tmp/gosl/ode", "vdpolA.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/vdpol_radau5_for.dat")
if err != nil {
chk.Panic("%v", err)
}
plt.Subplot(3, 1, 1)
plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=7")
plt.Subplot(3, 1, 2)
plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=7")
})
}
}
func Test_flt04(tst *testing.T) {
//verbose()
chk.PrintTitle("flt04. two-bar truss. Pareto-optimal")
// configuration
C := NewConfParams()
C.Nisl = 4
C.Ninds = 24
C.GAtype = "crowd"
C.DiffEvol = true
C.CrowdSize = 3
C.ParetoPhi = 0.05
C.Tf = 100
C.Dtmig = 25
C.RangeFlt = [][]float64{{0.1, 2.25}, {0.5, 2.5}}
C.PopFltGen = PopFltGen
C.CalcDerived()
rnd.Init(C.Seed)
// data
// from Coelho (2007) page 19
ρ := 0.283 // lb/in³
H := 100.0 // in
P := 1e4 // lb
E := 3e7 // lb/in²
σ0 := 2e4 // lb/in²
// functions
TSQ2 := 2.0 * math.Sqrt2
fcn := func(f, g, h []float64, x []float64) {
f[0] = 2.0 * ρ * H * x[1] * math.Sqrt(1.0+x[0]*x[0])
f[1] = P * H * math.Pow(1.0+x[0]*x[0], 1.5) * math.Sqrt(1.0+math.Pow(x[0], 4.0)) / (TSQ2 * E * x[0] * x[0] * x[1])
g[0] = σ0 - P*(1.0+x[0])*math.Sqrt(1.0+x[0]*x[0])/(TSQ2*x[0]*x[1])
g[1] = σ0 - P*(1.0-x[0])*math.Sqrt(1.0+x[0]*x[0])/(TSQ2*x[0]*x[1])
}
// objective value function
C.OvaOor = func(ind *Individual, idIsland, t int, report *bytes.Buffer) {
x := ind.GetFloats()
f := make([]float64, 2)
g := make([]float64, 2)
fcn(f, g, nil, x)
ind.Ovas[0] = f[0]
ind.Ovas[1] = f[1]
ind.Oors[0] = utl.GtePenalty(g[0], 0, 1)
ind.Oors[1] = utl.GtePenalty(g[1], 0, 1)
}
// simple problem
sim := NewSimpleFltProb(fcn, 2, 2, 0, C)
sim.Run(chk.Verbose)
// results
if chk.Verbose {
// reference data
_, dat, _ := io.ReadTable("data/coelho-fig1.6.dat")
// Pareto-front
feasible := sim.Evo.GetFeasible()
ovas, _ := sim.Evo.GetResults(feasible)
ovafront, _ := sim.Evo.GetParetoFront(feasible, ovas, nil)
xova, yova := sim.Evo.GetFrontOvas(0, 1, ovafront)
// plot
plt.SetForEps(0.75, 355)
plt.Plot(dat["f1"], dat["f2"], "'k+',ms=3")
x := utl.DblsGetColumn(0, ovas)
y := utl.DblsGetColumn(1, ovas)
plt.Plot(x, y, "'r.'")
plt.Plot(xova, yova, "'ko',markerfacecolor='none',ms=6")
plt.Gll("$f_1$", "$f_2$", "")
plt.SaveD("/tmp/goga", "test_flt04.eps")
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("ode04: Hairer-Wanner VII-p376 Transistor Amplifier\n")
}
if mpi.Size() != 3 {
chk.Panic(">> error: this test requires 3 MPI processors\n")
return
}
// data
UE, UB, UF, ALPHA, BETA := 0.1, 6.0, 0.026, 0.99, 1.0e-6
R0, R1, R2, R3, R4, R5 := 1000.0, 9000.0, 9000.0, 9000.0, 9000.0, 9000.0
R6, R7, R8, R9 := 9000.0, 9000.0, 9000.0, 9000.0
W := 2.0 * 3.141592654 * 100.0
// initial values
xa := 0.0
ya := []float64{0.0,
UB,
UB / (R6/R5 + 1.0),
UB / (R6/R5 + 1.0),
UB,
UB / (R2/R1 + 1.0),
UB / (R2/R1 + 1.0),
0.0}
// endpoint of integration
xb := 0.05
//xb = 0.0123 // OK
//xb = 0.01235 // !OK
// right-hand side of the amplifier problem
w := make([]float64, 8) // workspace
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
UET := UE * math.Sin(W*x)
FAC1 := BETA * (math.Exp((y[3]-y[2])/UF) - 1.0)
FAC2 := BETA * (math.Exp((y[6]-y[5])/UF) - 1.0)
la.VecFill(f, 0)
switch mpi.Rank() {
case 0:
f[0] = y[0] / R9
case 1:
f[1] = (y[1]-UB)/R8 + ALPHA*FAC1
f[2] = y[2]/R7 - FAC1
case 2:
f[3] = y[3]/R5 + (y[3]-UB)/R6 + (1.0-ALPHA)*FAC1
f[4] = (y[4]-UB)/R4 + ALPHA*FAC2
f[5] = y[5]/R3 - FAC2
f[6] = y[6]/R1 + (y[6]-UB)/R2 + (1.0-ALPHA)*FAC2
f[7] = (y[7] - UET) / R0
}
mpi.AllReduceSum(f, w)
return nil
}
// Jacobian of the amplifier problem
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
FAC14 := BETA * math.Exp((y[3]-y[2])/UF) / UF
FAC27 := BETA * math.Exp((y[6]-y[5])/UF) / UF
if dfdy.Max() == 0 {
dfdy.Init(8, 8, 16)
}
NU := 2
dfdy.Start()
switch mpi.Rank() {
case 0:
dfdy.Put(2+0-NU, 0, 1.0/R9)
dfdy.Put(2+1-NU, 1, 1.0/R8)
dfdy.Put(1+2-NU, 2, -ALPHA*FAC14)
dfdy.Put(0+3-NU, 3, ALPHA*FAC14)
dfdy.Put(2+2-NU, 2, 1.0/R7+FAC14)
case 1:
dfdy.Put(1+3-NU, 3, -FAC14)
dfdy.Put(2+3-NU, 3, 1.0/R5+1.0/R6+(1.0-ALPHA)*FAC14)
dfdy.Put(3+2-NU, 2, -(1.0-ALPHA)*FAC14)
dfdy.Put(2+4-NU, 4, 1.0/R4)
dfdy.Put(1+5-NU, 5, -ALPHA*FAC27)
case 2:
dfdy.Put(0+6-NU, 6, ALPHA*FAC27)
dfdy.Put(2+5-NU, 5, 1.0/R3+FAC27)
dfdy.Put(1+6-NU, 6, -FAC27)
dfdy.Put(2+6-NU, 6, 1.0/R1+1.0/R2+(1.0-ALPHA)*FAC27)
dfdy.Put(3+5-NU, 5, -(1.0-ALPHA)*FAC27)
dfdy.Put(2+7-NU, 7, 1.0/R0)
}
return nil
}
// matrix "M"
c1, c2, c3, c4, c5 := 1.0e-6, 2.0e-6, 3.0e-6, 4.0e-6, 5.0e-6
var M la.Triplet
M.Init(8, 8, 14)
M.Start()
NU := 1
switch mpi.Rank() {
case 0:
M.Put(1+0-NU, 0, -c5)
M.Put(0+1-NU, 1, c5)
M.Put(2+0-NU, 0, c5)
M.Put(1+1-NU, 1, -c5)
M.Put(1+2-NU, 2, -c4)
M.Put(1+3-NU, 3, -c3)
case 1:
M.Put(0+4-NU, 4, c3)
M.Put(2+3-NU, 3, c3)
M.Put(1+4-NU, 4, -c3)
case 2:
M.Put(1+5-NU, 5, -c2)
M.Put(1+6-NU, 6, -c1)
M.Put(0+7-NU, 7, c1)
M.Put(2+6-NU, 6, c1)
M.Put(1+7-NU, 7, -c1)
}
// flags
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
ndim := len(ya)
numjac := false
// structure to hold numerical results
res := ode.Results{Method: method}
// ODE solver
var osol ode.Solver
osol.Pll = true
// solve problem
if numjac {
osol.Init(method, ndim, fcn, nil, &M, ode.SimpleOutput, silent)
} else {
osol.Init(method, ndim, fcn, jac, &M, ode.SimpleOutput, silent)
}
osol.IniH = 1.0e-6 // initial step size
// set tolerances
atol, rtol := 1e-11, 1e-5
osol.SetTol(atol, rtol)
// run
t0 := time.Now()
if fixstp {
osol.Solve(ya, xa, xb, 0.01, fixstp, &res)
} else {
osol.Solve(ya, xa, xb, xb-xa, fixstp, &res)
}
// plot
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
plt.SetForEps(2.0, 400)
args := "'b-', marker='.', lw=1, clip_on=0"
ode.Plot("/tmp/gosl/ode", "hwamplifier_mpi.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/radau5_hwamplifier.dat")
if err != nil {
chk.Panic("%v", err)
}
for j := 0; j < ndim; j++ {
plt.Subplot(ndim+1, 1, j+1)
plt.Plot(T["x"], T[io.Sf("y%d", j)], "'k+',label='reference',ms=10")
}
})
}
}