func Test_ind02(tst *testing.T) {
//verbose()
chk.PrintTitle("ind02. copy into")
rnd.Init(0)
nbases := 1
A := get_individual(0, nbases)
B := get_individual(1, nbases)
fmts := map[string][]string{
"int": {"%2d", "%4d", "%5d"}, // ints
"flt": {"%6g", "%6g", "%5g"}, // floats
"str": {"%4s", "%2s", "%2s"}, // strings
"key": {"%3x", "%3x", "%3x"}, // keys
"byt": {"%4s", "%4s", "%4s"}, // bytes
"fun": {"%3s", "%3s", "%3s"}, // funcs
}
io.Pfpink("A = %v\n", A.Output(fmts, false))
io.Pfcyan("B = %v\n", B.Output(fmts, false))
var ops OpsData
ops.SetDefault()
ops.Pc = 1.0
ops.Cuts = []int{1, 2}
ops.Xrange = [][]float64{{0, 1}, {-20, 20}, {-300, 300}}
a := A.GetCopy()
b := A.GetCopy()
IndCrossover(a, b, A, B, 0, &ops)
io.Pforan("a = %v\n", a.Output(fmts, false))
io.Pfblue2("b = %v\n", b.Output(fmts, false))
chk.Ints(tst, "a.Ints ", a.Ints, []int{1, -20, 300})
chk.Ints(tst, "b.Ints ", b.Ints, []int{-1, 20, -300})
chk.Strings(tst, "a.Strings", a.Strings, []string{"abc", "Y", "c"})
chk.Strings(tst, "b.Strings", b.Strings, []string{"X", "b", "Z"})
// TODO: add other tests here
io.Pf("\n")
x := get_individual(0, nbases)
x.Ovas = []float64{0, 0}
x.Oors = []float64{0, 0, 0}
io.Pfblue2("x = %v\n", x.Output(fmts, false))
B.CopyInto(x)
chk.Scalar(tst, "ova0", 1e-17, x.Ovas[0], 200)
chk.Scalar(tst, "ova1", 1e-17, x.Ovas[1], 100)
chk.Scalar(tst, "oor0", 1e-17, x.Oors[0], 15)
chk.Scalar(tst, "oor1", 1e-17, x.Oors[1], 25)
chk.Scalar(tst, "oor2", 1e-17, x.Oors[2], 35)
io.Pforan("x = %v\n", x.Output(fmts, false))
chk.String(tst, x.Output(fmts, false), B.Output(fmts, false))
}
func Test_pareto01(tst *testing.T) {
//verbose()
chk.PrintTitle("pareto01. compare vectors: Pareto-optimal")
u := []float64{1, 2, 3, 4, 5, 6}
v := []float64{1, 2, 3, 4, 5, 6}
io.Pforan("u = %v\n", u)
io.Pfblue2("v = %v\n", v)
u_dominates, v_dominates := DblsParetoMin(u, v)
io.Pfpink("u_dominates = %v\n", u_dominates)
io.Pfpink("v_dominates = %v\n", v_dominates)
if u_dominates {
tst.Errorf("test failed\n")
return
}
if v_dominates {
tst.Errorf("test failed\n")
return
}
v = []float64{1, 1.8, 3, 4, 5, 6}
io.Pforan("\nu = %v\n", u)
io.Pfblue2("v = %v\n", v)
u_dominates, v_dominates = DblsParetoMin(u, v)
io.Pfpink("u_dominates = %v\n", u_dominates)
io.Pfpink("v_dominates = %v\n", v_dominates)
if u_dominates {
tst.Errorf("test failed\n")
return
}
if !v_dominates {
tst.Errorf("test failed\n")
return
}
v = []float64{1, 2.1, 3, 4, 5, 6}
io.Pforan("\nu = %v\n", u)
io.Pfblue2("v = %v\n", v)
u_dominates, v_dominates = DblsParetoMin(u, v)
io.Pfpink("u_dominates = %v\n", u_dominates)
io.Pfpink("v_dominates = %v\n", v_dominates)
if !u_dominates {
tst.Errorf("test failed\n")
return
}
if v_dominates {
tst.Errorf("test failed\n")
return
}
}
func main() {
// input data
matOld := "matOld.mat"
matNew := "matNew.mat"
convSymb := true
// parse flags
flag.Parse()
if len(flag.Args()) > 0 {
matOld = flag.Arg(0)
}
if len(flag.Args()) > 1 {
matNew = flag.Arg(1)
}
if len(flag.Args()) > 2 {
convSymb = io.Atob(flag.Arg(2))
}
// print input data
io.Pf("\nInput data\n")
io.Pf("==========\n")
io.Pf(" matOld = %30s // old material filename\n", matOld)
io.Pf(" matNew = %30s // new material filename\n", matNew)
io.Pf(" convSymb = %30v // do convert symbols\n", convSymb)
io.Pf("\n")
// convert old => new
inp.MatfileOld2New("", matNew, matOld, convSymb)
io.Pf("conversion successful\n")
io.Pfblue2("file <matNew.mat> created\n")
}
func Test_GOflt01(tst *testing.T) {
//verbose()
chk.PrintTitle("GOflt01. float64")
Init(1234)
xmin := 10.0
xmax := 20.0
vals := make([]float64, NSAMPLES)
// using Float64
t0 := time.Now()
for i := 0; i < NSAMPLES; i++ {
vals[i] = Float64(xmin, xmax)
}
io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))
hist := Histogram{Stations: []float64{10, 12.5, 15, 17.5, 20}}
hist.Count(vals, true)
io.Pfpink(TextHist(hist.GenLabels("%4g"), hist.Counts, 60))
// using Float64s
t0 = time.Now()
Float64s(vals, xmin, xmax)
io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))
hist.Count(vals, true)
io.Pfblue2(TextHist(hist.GenLabels("%4g"), hist.Counts, 60))
}
func main() {
// default input data
fn := "nurbs01.msh"
ctrl := true
ids := true
npts := 41
// parse flags
flag.Parse()
if len(flag.Args()) > 0 {
fn = flag.Arg(0)
}
if len(flag.Args()) > 1 {
ctrl = io.Atob(flag.Arg(1))
}
if len(flag.Args()) > 2 {
ids = io.Atob(flag.Arg(2))
}
if len(flag.Args()) > 3 {
npts = io.Atoi(flag.Arg(3))
}
// print input data
io.Pforan("Input data\n")
io.Pforan("==========\n")
io.Pfblue2(" fn = %v\n", fn)
io.Pfblue2(" ctrl = %v\n", ctrl)
io.Pfblue2(" ids = %v\n", ids)
io.Pfblue2(" npts = %v\n", npts)
// load nurbss
fnk := io.FnKey(fn)
B := gm.ReadMsh(fnk)
// plot
plt.SetForEps(0.75, 500)
for _, b := range B {
if ctrl {
b.DrawCtrl2d(ids, "", "")
}
b.DrawElems2d(npts, ids, "", "")
}
plt.Equal()
plt.Save(fnk + ".eps")
}
func Test_cxint01(tst *testing.T) {
//verbose()
chk.PrintTitle("cxint01")
var ops OpsData
ops.SetDefault()
ops.Pc = 1
ops.Ncuts = 1
A := []int{1, 2}
B := []int{-1, -2}
a := make([]int, len(A))
b := make([]int, len(A))
IntCrossover(a, b, A, B, 0, &ops)
io.Pfred("A = %2d\n", A)
io.PfRed("B = %2d\n", B)
io.Pfcyan("a = %2d\n", a)
io.Pfblue2("b = %2d\n", b)
chk.Ints(tst, "a", a, []int{1, -2})
chk.Ints(tst, "b", b, []int{-1, 2})
io.Pf("\n")
A = []int{1, 2, 3, 4, 5, 6, 7, 8}
B = []int{-1, -2, -3, -4, -5, -6, -7, -8}
a = make([]int, len(A))
b = make([]int, len(A))
ops.Cuts = []int{1, 3}
IntCrossover(a, b, A, B, 0, &ops)
io.Pfred("A = %2v\n", A)
io.PfRed("B = %2v\n", B)
io.Pfcyan("a = %2v\n", a)
io.Pfblue2("b = %2v\n", b)
chk.Ints(tst, "a", a, []int{1, -2, -3, 4, 5, 6, 7, 8})
chk.Ints(tst, "b", b, []int{-1, 2, 3, -4, -5, -6, -7, -8})
ops.Cuts = []int{5, 7}
IntCrossover(a, b, A, B, 0, &ops)
io.Pfred("A = %2v\n", A)
io.PfRed("B = %2v\n", B)
io.Pfcyan("a = %2v\n", a)
io.Pfblue2("b = %2v\n", b)
chk.Ints(tst, "a", a, []int{1, 2, 3, 4, 5, -6, -7, 8})
chk.Ints(tst, "b", b, []int{-1, -2, -3, -4, -5, 6, 7, -8})
}
func Test_split01(tst *testing.T) {
//verbose()
chk.PrintTitle("split01")
r := DblSplit(" 1e4 1 3 8 88 ")
io.Pfblue2("r = %v\n", r)
chk.Vector(tst, "r", 1e-16, r, []float64{1e4, 1, 3, 8, 88})
}
func Test_copy01(tst *testing.T) {
//verbose()
chk.PrintTitle("copy01")
v := []float64{1, 2, 3, 4, 4, 5, 5, 6, 6, 6}
w := DblCopy(v)
io.Pfblue2("v = %v\n", v)
chk.Vector(tst, "w==v", 1e-16, w, v)
}
func Test_fileio01(tst *testing.T) {
chk.PrintTitle("fileio01")
// start
if !Start("data/bh16.sim", true, chk.Verbose) {
tst.Errorf("test failed\n")
}
defer End()
// domain A
distr := false
domA := NewDomain(Global.Sim.Regions[0], distr)
if domA == nil {
tst.Errorf("test failed\n")
}
if !domA.SetStage(0, Global.Sim.Stages[0], distr) {
tst.Errorf("test failed\n")
}
for i, _ := range domA.Sol.Y {
domA.Sol.Y[i] = float64(i)
}
io.Pforan("domA.Sol.Y = %v\n", domA.Sol.Y)
// write file
tidx := 123
if !domA.SaveSol(tidx) {
tst.Errorf("test failed")
return
}
dir, fnk := Global.Dirout, Global.Fnkey
io.Pfblue2("file %v written\n", out_nod_path(dir, fnk, tidx, Global.Rank))
// domain B
domB := NewDomain(Global.Sim.Regions[0], distr)
if domB == nil {
tst.Errorf("test failed\n")
}
if !domB.SetStage(0, Global.Sim.Stages[0], distr) {
tst.Errorf("test failed")
}
io.Pfpink("domB.Sol.Y (before) = %v\n", domB.Sol.Y)
// read file
if !domB.ReadSol(dir, fnk, tidx) {
tst.Errorf("test failed")
return
}
io.Pfgreen("domB.Sol.Y (after) = %v\n", domB.Sol.Y)
// check
chk.Vector(tst, "Y", 1e-17, domA.Sol.Y, domB.Sol.Y)
chk.Vector(tst, "dy/dt", 1e-17, domA.Sol.Dydt, domB.Sol.Dydt)
chk.Vector(tst, "d²y/dt²", 1e-17, domA.Sol.D2ydt2, domB.Sol.D2ydt2)
}
func save_file(filename string, buf *bytes.Buffer, verbose bool) (err error) {
fil, err := os.Create(filename)
if err != nil {
return
}
defer func() { err = fil.Close() }()
_, err = fil.Write(buf.Bytes())
if verbose {
io.Pfblue2("file <%s> written\n", filename)
}
return
}
func Test_eigenp01(tst *testing.T) {
//verbose()
chk.PrintTitle("eigenp01")
// constants
tolP := 1e-14 // eigenprojectors
tolS := 1e-13 // spectral decomposition
toldP := 1e-9 // derivatives of eigenprojectors
ver := chk.Verbose // check P verbose
verdP := chk.Verbose // check dPda verbose
// run test
nd := test_nd
for idxA := 0; idxA < len(test_nd); idxA++ {
//for idxA := 10; idxA < 11; idxA++ {
//for idxA := 11; idxA < 12; idxA++ {
//for idxA := 12; idxA < 13; idxA++ {
// tensor and eigenvalues
A := test_AA[idxA]
a := M_Alloc2(nd[idxA])
Ten2Man(a, A)
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pfblue2("a = %v\n", a)
io.Pfblue2("λ = %v\n", test_λ[idxA])
// check eigenprojectors
io.Pforan("\neigenprojectors\n")
λsorted := CheckEigenprojs(a, tolP, tolS, ver)
io.Pfyel("λsorted = %v\n", λsorted)
λchk := utl.DblGetSorted(test_λ[idxA])
chk.Vector(tst, "λchk", 1e-12, λsorted, λchk)
// check derivatives of eigenprojectors
io.Pforan("\nderivatives\n")
CheckEigenprojsDerivs(a, toldP, verdP, EV_ZERO)
}
}
func Test_mat02(tst *testing.T) {
chk.PrintTitle("mat02 (conversion)")
convertsymbols := true
MatfileOld2New("/tmp/gofem/inp", "new_layers.mat", "data/old_layers.mat", convertsymbols)
mdb := ReadMat("/tmp/gofem/inp/", "new_layers.mat")
if mdb == nil {
tst.Errorf("test failed\n")
return
}
io.Pfblue2("%v\n", mdb)
}
func Test_hyperelast02(tst *testing.T) {
//verbose()
chk.PrintTitle("hyperelast02 (linear)")
E, ν := 1500.0, 0.25
K := Calc_K_from_Enu(E, ν)
G := Calc_G_from_Enu(E, ν)
io.Pforan("K = %v\n", K)
io.Pforan("G = %v\n", G)
var m HyperElast1
m.Init(2, false, []*fun.Prm{
&fun.Prm{N: "K0", V: K},
&fun.Prm{N: "G0", V: G},
&fun.Prm{N: "le", V: 1},
})
io.Pforan("m = %+v\n", m)
ε := []float64{-0.001, -0.002, -0.003}
σ := make([]float64, 3)
m.L_update(σ, ε)
io.Pfblue2("ε = %v\n", ε)
io.Pfcyan("σ = %v\n", σ)
D := la.MatAlloc(3, 3)
m.L_CalcD(D, ε)
la.PrintMat("D", D, "%14.6f", false)
tol := 1e-11
verb := io.Verbose
var tmp float64
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
dnum := num.DerivCen(func(x float64, args ...interface{}) (res float64) {
tmp, ε[j] = ε[j], x
m.L_update(σ, ε)
res = σ[i]
ε[j] = tmp
return
}, ε[j])
chk.AnaNum(tst, io.Sf("D%d%d", i, j), tol, D[i][j], dnum, verb)
}
}
}
func Test_hyperelast03(tst *testing.T) {
//verbose()
chk.PrintTitle("hyperelast03 (nonlinear)")
var m HyperElast1
m.Init(2, false, []*fun.Prm{
&fun.Prm{N: "kap", V: 0.05},
&fun.Prm{N: "kapb", V: 20.0},
&fun.Prm{N: "G0", V: 1500},
&fun.Prm{N: "pr", V: 2.2},
&fun.Prm{N: "pt", V: 11.0},
})
io.Pforan("m = %+v\n", m)
ε := []float64{-0.001, -0.002, -0.003}
σ := make([]float64, 3)
m.L_update(σ, ε)
io.Pfblue2("ε = %v\n", ε)
io.Pfcyan("σ = %v\n", σ)
D := la.MatAlloc(3, 3)
m.L_CalcD(D, ε)
la.PrintMat("D", D, "%14.6f", false)
tol := 1e-7
verb := io.Verbose
var tmp float64
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
dnum := num.DerivCen(func(x float64, args ...interface{}) (res float64) {
tmp, ε[j] = ε[j], x
m.L_update(σ, ε)
res = σ[i]
ε[j] = tmp
return
}, ε[j])
chk.AnaNum(tst, io.Sf("D%d%d", i, j), tol, D[i][j], dnum, verb)
}
}
}
func Test_mat01(tst *testing.T) {
chk.PrintTitle("mat01")
mdb1 := ReadMat("data", "bh.mat")
if mdb1 == nil {
tst.Errorf("test failed\n")
return
}
io.Pforan("bh.mat just read:\n%v\n", mdb1)
fn := "test_bh.mat"
io.WriteFileSD("/tmp/gofem/inp", fn, mdb1.String())
mdb2 := ReadMat("/tmp/gofem/inp/", fn)
if mdb2 == nil {
tst.Errorf("test failed\n")
return
}
io.Pfblue2("\n%v\n", mdb2)
}
func Test_linipm03(tst *testing.T) {
//verbose()
chk.PrintTitle("linipm03")
t0 := time.Now()
defer func() { io.Pfblue2("\ntime elapsed = %v\n", time.Now().Sub(t0)) }()
// read LP
A, b, c, l, u := ReadLPfortran("data/afiro.dat")
//A, b, c, l, u := ReadLPfortran("data/adlittle.dat")
//A, b, c, l, u := ReadLPfortran("data/share1b.dat")
// check for unbounded variables
nx := len(c)
for i := 0; i < nx; i++ {
if math.Abs(l[i]) > 1e-15 {
chk.Panic("cannot handle l != 0 yet")
}
if math.Abs(u[i]-1e20) > 1e-15 {
chk.Panic("cannot handle u != ∞ yet")
}
}
// solve LP
var ipm LinIpm
defer ipm.Clean()
ipm.Init(A, b, c, nil)
err := ipm.Solve(chk.Verbose)
if err != nil {
tst.Errorf("ipm failed:\n%v", err)
return
}
// check
io.Pf("\n")
bres := make([]float64, len(b))
la.MatVecMul(bres, 1, A.ToDense(), ipm.X)
chk.Vector(tst, "A*x=b", 1e-13, bres, b)
}
func main() {
// catch errors
defer func() {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
}()
// input data
matOld := io.ArgToString(0, "matOld.mat")
matNew := io.ArgToString(1, "matNew.mat")
convSymb := io.ArgToBool(2, true)
io.Pf("\n%s\n", io.ArgsTable(
"old material filename", "matOld", matOld,
"new material filenamen", "matNew", matNew,
"do convert symbols", "convSymb", convSymb,
))
// convert old => new
inp.MatfileOld2New("", matNew, matOld, convSymb)
io.Pf("conversion successful\n")
io.Pfblue2("file <matNew.mat> created\n")
}
// Run runs FE simulation
func Run() (runisok bool) {
// plot functions
if Global.Sim.PlotF != nil && Global.Root {
Global.Sim.Functions.PlotAll(Global.Sim.PlotF, Global.Dirout, Global.Fnkey)
}
// alloc domains
var domains []*Domain
for _, reg := range Global.Sim.Regions {
dom := NewDomain(reg, Global.Distr)
if dom == nil {
break
}
domains = append(domains, dom)
}
if Stop() {
return
}
// make sure to call linear solver clean up routines upon exit
defer func() {
for _, d := range domains {
if !d.InitLSol {
d.LinSol.Clean()
}
}
}()
// current time and output time
t := 0.0
tout := 0.0
tidx := 0
// summary of outputs; e.g. with output times
cputime := time.Now()
var sum Summary
sum.OutTimes = []float64{t}
defer func() {
sum.Save()
if Global.Verbose && !Global.Debug {
io.Pf("\nfinal t = %v\n", t)
io.Pfblue2("cpu time = %v\n", time.Now().Sub(cputime))
}
}()
// loop over stages
for stgidx, stg := range Global.Sim.Stages {
// time incrementers
Dt := stg.Control.DtFunc
DtOut := stg.Control.DtoFunc
tf := stg.Control.Tf
tout = t + DtOut.F(t, nil)
// set stage
for _, d := range domains {
if LogErrCond(!d.SetStage(stgidx, Global.Sim.Stages[stgidx], Global.Distr), "SetStage failed") {
break
}
d.Sol.T = t
if !d.Out(tidx) {
break
}
}
if Stop() {
return
}
tidx += 1
// log models
mconduct.LogModels()
mreten.LogModels()
mporous.LogModels()
msolid.LogModels()
// skip stage?
if stg.Skip {
continue
}
// time loop using Richardson's extrapolation
// TODO: works with only one domain for now
if Global.Sim.Solver.RE {
var re RichardsonExtrap
re.Init(domains[0], Dt)
if !re.Run(domains[0], &sum, DtOut, &t, tf, tout, &tidx) {
return
}
continue
}
// time loop
ndiverg := 0 // number of steps diverging
md := 1.0 // time step multiplier if divergence control is on
var Δt, Δtout float64
var lasttimestep bool
for t < tf {
// check for continued divergence
if LogErrCond(ndiverg >= Global.Sim.Solver.NdvgMax, "continuous divergence after %d steps reached", ndiverg) {
return
}
// time increment
Δt = Dt.F(t, nil) * md
if t+Δt >= tf {
Δt = tf - t
lasttimestep = true
}
if Δt < Global.Sim.Solver.DtMin {
if md < 1 {
LogErrCond(true, "Δt increment is too small: %g < %g", Δt, Global.Sim.Solver.DtMin)
return false
}
return true
}
// dynamic coefficients
if LogErr(Global.DynCoefs.CalcBoth(Δt), "cannot compute dynamic coefficients") {
return
}
// time update
t += Δt
for _, d := range domains {
d.Sol.T = t
}
Δtout = DtOut.F(t, nil)
// message
if Global.Verbose {
if !Global.Sim.Data.ShowR && !Global.Debug {
io.PfWhite("%30.15f\r", t)
}
}
// for all domains
docontinue := false
for _, d := range domains {
// backup solution if divergence control is on
if Global.Sim.Solver.DvgCtrl {
d.backup()
}
// run iterations
diverging, ok := run_iterations(t, Δt, d, &sum)
if !ok {
return
}
// restore solution and reduce time step if divergence control is on
if Global.Sim.Solver.DvgCtrl {
if diverging {
if Global.Verbose {
io.Pfred(". . . iterations diverging (%2d) . . .\n", ndiverg+1)
}
d.restore()
t -= Δt
d.Sol.T = t
md *= 0.5
ndiverg += 1
docontinue = true
break
}
ndiverg = 0
md = 1.0
}
}
if docontinue {
continue
}
// perform output
if t >= tout || lasttimestep {
sum.OutTimes = append(sum.OutTimes, t)
for _, d := range domains {
//if true {
if false {
debug_print_p_results(d)
}
if false {
debug_print_up_results(d)
}
if !d.Out(tidx) {
break
}
}
if Stop() {
return
}
tout += Δtout
tidx += 1
}
}
}
return true
}
func Test_ind03(tst *testing.T) {
//verbose()
chk.PrintTitle("ind03. comparing")
nbases := 1
A := get_individual(0, nbases)
B := get_individual(1, nbases)
A_dominates, B_dominates := IndCompareDet(A, B)
io.Pfblue2("A: ovas = %v\n", A.Ovas)
io.Pfblue2("A: oors = %v\n", A.Oors)
io.Pfcyan("B: ovas = %v\n", B.Ovas)
io.Pfcyan("B: oors = %v\n", B.Oors)
io.Pforan("A_dominates = %v\n", A_dominates)
io.Pforan("B_dominates = %v\n", B_dominates)
if !A_dominates {
tst.Errorf("test failed\n")
return
}
if B_dominates {
tst.Errorf("test failed\n")
return
}
A.Oors = []float64{0, 0, 0}
B.Oors = []float64{0, 0, 0}
A_dominates, B_dominates = IndCompareDet(A, B)
io.Pfblue2("\nA: ovas = %v\n", A.Ovas)
io.Pfblue2("A: oors = %v\n", A.Oors)
io.Pfcyan("B: ovas = %v\n", B.Ovas)
io.Pfcyan("B: oors = %v\n", B.Oors)
io.Pforan("A_dominates = %v\n", A_dominates)
io.Pforan("B_dominates = %v\n", B_dominates)
if A_dominates {
tst.Errorf("test failed\n")
return
}
if B_dominates {
tst.Errorf("test failed\n")
return
}
A.Ovas = []float64{200, 100}
A_dominates, B_dominates = IndCompareDet(A, B)
io.Pfblue2("\nA: ovas = %v\n", A.Ovas)
io.Pfblue2("A: oors = %v\n", A.Oors)
io.Pfcyan("B: ovas = %v\n", B.Ovas)
io.Pfcyan("B: oors = %v\n", B.Oors)
io.Pforan("A_dominates = %v\n", A_dominates)
io.Pforan("B_dominates = %v\n", B_dominates)
if A_dominates {
tst.Errorf("test failed\n")
return
}
if B_dominates {
tst.Errorf("test failed\n")
return
}
A.Ovas = []float64{200, 99}
A_dominates, B_dominates = IndCompareDet(A, B)
io.Pfblue2("\nA: ovas = %v\n", A.Ovas)
io.Pfblue2("A: oors = %v\n", A.Oors)
io.Pfcyan("B: ovas = %v\n", B.Ovas)
io.Pfcyan("B: oors = %v\n", B.Oors)
io.Pforan("A_dominates = %v\n", A_dominates)
io.Pforan("B_dominates = %v\n", B_dominates)
if !A_dominates {
tst.Errorf("test failed\n")
return
}
if B_dominates {
tst.Errorf("test failed\n")
return
}
A.Ovas = []float64{200, 100}
B.Ovas = []float64{199, 100}
A_dominates, B_dominates = IndCompareDet(A, B)
io.Pfblue2("\nA: ovas = %v\n", A.Ovas)
io.Pfblue2("A: oors = %v\n", A.Oors)
io.Pfcyan("B: ovas = %v\n", B.Ovas)
io.Pfcyan("B: oors = %v\n", B.Oors)
io.Pforan("A_dominates = %v\n", A_dominates)
io.Pforan("B_dominates = %v\n", B_dominates)
if A_dominates {
tst.Errorf("test failed\n")
return
}
if !B_dominates {
tst.Errorf("test failed\n")
return
}
}
func Test_bspline03(tst *testing.T) {
//verbose()
chk.PrintTitle("bspline03")
// 0 1 2 3 4 5 6 7 8 9 10
T := []float64{0, 0, 0, 1, 2, 3, 4, 4, 5, 5, 5}
var s Bspline
s.Init(T, 2)
s.SetControl([][]float64{{0, 0}, {0.5, 1}, {1, 0}, {1.5, 0}, {2, 1}, {2.5, 1}, {3, 0.5}, {3.5, 0}})
// analytical derivatives
s.CalcBasisAndDerivs(3.99)
io.Pfpink("ana: dNdt(t=3.99, i=5) = %v\n", s.GetDeriv(5))
io.Pfpink("ana: dNdt(t=3.99, i=6) = %v\n", s.GetDeriv(6))
io.Pfpink("ana: dNdt(t=3.99, i=7) = %v\n", s.GetDeriv(7))
s.CalcBasisAndDerivs(4.0)
io.Pforan("ana: dNdt(t=4.00, i=5) = %v\n", s.GetDeriv(5))
io.Pforan("ana: dNdt(t=4.00, i=6) = %v\n", s.GetDeriv(6))
io.Pforan("ana: dNdt(t=4.00, i=7) = %v\n", s.GetDeriv(7))
// numerical derivatives
io.Pfcyan("num: dNdt(t=3.99, i=5) = %v\n", s.NumericalDeriv(3.99, 5))
io.Pfcyan("num: dNdt(t=3.99, i=6) = %v\n", s.NumericalDeriv(3.99, 6))
io.Pfcyan("num: dNdt(t=3.99, i=7) = %v\n", s.NumericalDeriv(3.99, 7))
io.Pfblue2("num: dNdt(t=4.00, i=5) = %v\n", s.NumericalDeriv(4.00, 5))
io.Pfblue2("num: dNdt(t=4.00, i=6) = %v\n", s.NumericalDeriv(4.00, 6))
io.Pfblue2("num: dNdt(t=4.00, i=7) = %v\n", s.NumericalDeriv(4.00, 7))
ver := false
tol := 1e-5
tt := utl.LinSpace(0, 5, 11)
numd := make([]float64, s.NumBasis())
anad := make([]float64, s.NumBasis())
for _, t := range tt {
for i := 0; i < s.NumBasis(); i++ {
s.CalcBasisAndDerivs(t)
anad[i] = s.GetDeriv(i)
numd[i] = s.NumericalDeriv(t, i)
// numerical fails @ 4 [4,5,6]
if t == 4 {
numd[4] = anad[4]
numd[5] = anad[5]
numd[6] = anad[6]
}
chk.PrintAnaNum(io.Sf("i=%d t=%v", i, t), tol, anad[i], numd[i], ver)
}
chk.Vector(tst, io.Sf("derivs @ %v", t), tol, numd, anad)
}
if chk.Verbose {
npts := 201
plt.SetForPng(1.5, 600, 150)
plt.SplotGap(0, 0.3)
str0 := ",lw=2"
str1 := ",ls='none',marker='+',color='cyan',markevery=10"
str2 := ",ls='none',marker='x',markevery=10"
str3 := ",ls='none',marker='+',markevery=10"
str4 := ",ls='none',marker='4',markevery=10"
plt.Subplot(3, 1, 1)
s.Draw2d(str0, "", npts, 0) // 0 => CalcBasis
s.Draw2d(str1, "", npts, 1) // 1 => RecursiveBasis
plt.Subplot(3, 1, 2)
s.PlotBasis("", npts, 0) // 0 => CalcBasis
s.PlotBasis(str2, npts, 1) // 1 => CalcBasisAndDerivs
s.PlotBasis(str3, npts, 2) // 2 => RecursiveBasis
plt.Subplot(3, 1, 3)
s.PlotDerivs("", npts, 0) // 0 => CalcBasisAndDerivs
s.PlotDerivs(str4, npts, 1) // 1 => NumericalDeriv
plt.SaveD("/tmp/gosl/gm", "bspline03.png")
}
}
func Test_geninvs01(tst *testing.T) {
//verbose()
chk.PrintTitle("geninvs01")
// coefficients for smp invariants
smp_a := -1.0
smp_b := 0.5
smp_β := 1e-1 // derivative values become too high with
smp_ϵ := 1e-1 // small β and ϵ @ zero
// constants for checking derivatives
dver := chk.Verbose
dtol := 1e-6
dtol2 := 1e-6
// run tests
nd := test_nd
for idxA := 0; idxA < len(test_nd); idxA++ {
//for idxA := 10; idxA < 11; idxA++ {
// tensor and eigenvalues
A := test_AA[idxA]
a := M_Alloc2(nd[idxA])
Ten2Man(a, A)
L := make([]float64, 3)
M_EigenValsNum(L, a)
// SMP derivs and SMP director
dndL := la.MatAlloc(3, 3)
dNdL := make([]float64, 3)
d2ndLdL := utl.Deep3alloc(3, 3, 3)
N := make([]float64, 3)
F := make([]float64, 3)
G := make([]float64, 3)
m := SmpDerivs1(dndL, dNdL, N, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpDerivs2(d2ndLdL, L, smp_a, smp_b, smp_β, smp_ϵ, m, N, F, G, dNdL, dndL)
n := make([]float64, 3)
SmpUnitDirector(n, m, N)
// SMP invariants
p, q, err := GenInvs(L, n, smp_a)
if err != nil {
chk.Panic("SmpInvs failed:\n%v", err)
}
// output
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pfblue2("L = %v\n", L)
io.Pforan("n = %v\n", n)
io.Pforan("p = %v\n", p)
io.Pforan("q = %v\n", q)
// check invariants
tvec := make([]float64, 3)
GenTvec(tvec, L, n)
proj := make([]float64, 3) // projection of tvec along n
tdn := la.VecDot(tvec, n) // tvec dot n
for i := 0; i < 3; i++ {
proj[i] = tdn * n[i]
}
norm_proj := la.VecNorm(proj)
norm_tvec := la.VecNorm(tvec)
q_ := GENINVSQEPS + math.Sqrt(norm_tvec*norm_tvec-norm_proj*norm_proj)
io.Pforan("proj = %v\n", proj)
io.Pforan("norm(proj) = %v == p\n", norm_proj)
chk.Scalar(tst, "p", 1e-14, math.Abs(p), norm_proj)
chk.Scalar(tst, "q", 1e-13, q, q_)
// dt/dL
var tmp float64
N_tmp := make([]float64, 3)
n_tmp := make([]float64, 3)
tvec_tmp := make([]float64, 3)
dtdL := la.MatAlloc(3, 3)
GenTvecDeriv1(dtdL, L, n, dndL)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[j] = L[j], x
m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
GenTvec(tvec_tmp, L, n_tmp)
L[j] = tmp
return tvec_tmp[i]
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("dt/dL[%d][%d]", i, j), dtol, dtdL[i][j], dnum, dver)
}
}
// d²t/dLdL
io.Pfpink("\nd²t/dLdL\n")
dNdL_tmp := make([]float64, 3)
dndL_tmp := la.MatAlloc(3, 3)
dtdL_tmp := la.MatAlloc(3, 3)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
for k := 0; k < 3; k++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[k] = L[k], x
m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
GenTvecDeriv1(dtdL_tmp, L, n_tmp, dndL_tmp)
L[k] = tmp
return dtdL_tmp[i][j]
}, L[k], 1e-6)
dana := GenTvecDeriv2(i, j, k, L, dndL, d2ndLdL[i][j][k])
chk.AnaNum(tst, io.Sf("d²t[%d]/dL[%d]dL[%d]", i, j, k), dtol2, dana, dnum, dver)
}
}
}
// change tolerance
dtol_tmp := dtol
switch idxA {
case 5, 11:
dtol = 1e-5
case 12:
dtol = 0.0013
}
// first order derivatives
dpdL := make([]float64, 3)
dqdL := make([]float64, 3)
p_, q_, err := GenInvsDeriv1(dpdL, dqdL, L, n, dndL, smp_a)
if err != nil {
chk.Panic("%v", err)
}
chk.Scalar(tst, "p", 1e-17, p, p_)
chk.Scalar(tst, "q", 1e-17, q, q_)
var ptmp, qtmp float64
io.Pfpink("\ndp/dL\n")
for j := 0; j < 3; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[j] = L[j], x
m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
ptmp, _, err = GenInvs(L, n_tmp, smp_a)
if err != nil {
chk.Panic("DerivCentral: SmpInvs failed:\n%v", err)
}
L[j] = tmp
return ptmp
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("dp/dL[%d]", j), dtol, dpdL[j], dnum, dver)
}
io.Pfpink("\ndq/dL\n")
for j := 0; j < 3; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[j] = L[j], x
m_tmp := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
_, qtmp, err = GenInvs(L, n_tmp, smp_a)
if err != nil {
chk.Panic("DerivCentral: SmpInvs failed:\n%v", err)
}
L[j] = tmp
return qtmp
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("dq/dL[%d]", j), dtol, dqdL[j], dnum, dver)
}
// recover tolerance
dtol = dtol_tmp
// change tolerance
io.Pforan("dtol2 = %v\n", dtol2)
dtol2_tmp := dtol2
switch idxA {
case 5:
dtol2 = 1e-5
case 10:
dtol2 = 0.72
case 11:
dtol2 = 1e-5
case 12:
dtol2 = 544
}
// second order derivatives
dpdL_tmp := make([]float64, 3)
dqdL_tmp := make([]float64, 3)
d2pdLdL := la.MatAlloc(3, 3)
d2qdLdL := la.MatAlloc(3, 3)
GenInvsDeriv2(d2pdLdL, d2qdLdL, L, n, dpdL, dqdL, p, q, dndL, d2ndLdL, smp_a)
io.Pfpink("\nd²p/dLdL\n")
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[j] = L[j], x
m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
GenInvsDeriv1(dpdL_tmp, dqdL_tmp, L, n_tmp, dndL_tmp, smp_a)
L[j] = tmp
return dpdL_tmp[i]
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("d²p/dL[%d][%d]", i, j), dtol2, d2pdLdL[i][j], dnum, dver)
}
}
io.Pfpink("\nd²q/dLdL\n")
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[j] = L[j], x
m_tmp := SmpDerivs1(dndL_tmp, dNdL_tmp, N_tmp, F, G, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n_tmp, m_tmp, N_tmp)
GenInvsDeriv1(dpdL_tmp, dqdL_tmp, L, n_tmp, dndL_tmp, smp_a)
L[j] = tmp
return dqdL_tmp[i]
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("d²q/dL[%d][%d]", i, j), dtol2, d2qdLdL[i][j], dnum, dver)
}
}
// recover tolerance
dtol2 = dtol2_tmp
}
}
func Test_ops02(tst *testing.T) {
//verbose()
chk.PrintTitle("ops02")
nd := []int{2, 2, 3, 3, 3}
AA := [][][]float64{
{
{1, 2, 0},
{2, -2, 0},
{0, 0, -2},
},
{
{-100, 33, 0},
{33, -200, 0},
{0, 0, 150},
},
{
{1, 2, 4},
{2, -2, 3},
{4, 3, -2},
},
{
{-100, -10, 20},
{-10, -200, 15},
{20, 15, -300},
},
{
{-100, 0, -10},
{0, -200, 0},
{-10, 0, 100},
},
}
BB := [][][]float64{
{
{0.13, 1.2, 0},
{1.2, -20, 0},
{0, 0, -28},
},
{
{-10, 3.3, 0},
{3.3, -2, 0},
{0, 0, 1.5},
},
{
{0.1, 0.2, 0.8},
{0.2, -1.3, 0.3},
{0.8, 0.3, -0.2},
},
{
{-10, -1, 2},
{-1, -20, 1},
{2, 1, -30},
},
{
{-10, 3, -1},
{3, -20, 1},
{-1, 1, 10},
},
}
nonsymTol := 1e-15
for m := 0; m < len(nd); m++ {
// tensors
A := AA[m]
B := BB[m]
a := M_Alloc2(nd[m])
b := M_Alloc2(nd[m])
Ten2Man(a, A)
Ten2Man(b, B)
io.PfYel("\n\ntst # %d ###################################################################################\n", m)
io.Pfblue2("a = %v\n", a)
io.Pfblue2("b = %v\n", b)
// dyadic
c := M_Dy(a, b)
c_ := M_Alloc4(nd[m])
c__ := M_Alloc4(nd[m])
M_DyAdd(c_, 1, a, b)
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
for k := 0; k < len(a); k++ {
c__[i][j] = a[i] * b[j]
}
}
}
chk.Matrix(tst, "a dy b", 1e-12, c, c_)
chk.Matrix(tst, "a dy b", 1e-12, c, c__)
// dot product
d := M_Alloc2(nd[m])
D := Alloc2()
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
for k := 0; k < 3; k++ {
D[i][j] += A[i][k] * B[k][j]
}
}
}
err := M_Dot(d, a, b, nonsymTol)
for i := 0; i < 3; i++ {
chk.Scalar(tst, io.Sf("a_dot_b[%d][%d]", i, i), 1e-15, D[i][i], d[i])
}
/*
for k := 0; k < 2*nd[m]; k++ {
I, J := M2Ti[k], M2Tj[k]
cf := 1.0
if k > 2 {
cf = 1.0 / SQ2
}
io.Pforan("%v %v\n", D[I][J], d[k] * cf)
chk.Scalar(tst, io.Sf("a_dot_b[%d][%d]",I,J), 1e-15, D[I][J], d[k] * cf)
}
*/
if err == nil {
chk.Panic("dot product failed: error should be non-nil, since the result is expected to be non-symmetric")
}
// dot product (square tensor)
a2 := M_Alloc2(nd[m])
M_Sq(a2, a)
aa := M_Alloc2(nd[m])
tol_tmp := nonsymTol
if m == 3 || m == 4 {
nonsymTol = 1e-12
}
err = M_Dot(aa, a, a, nonsymTol)
io.Pforan("a2 = %v\n", a2)
io.Pforan("aa = %v\n", aa)
if err != nil {
chk.Panic("%v", err)
}
chk.Vector(tst, "a2", 1e-15, a2, aa)
nonsymTol = tol_tmp
}
}
func Test_ops03(tst *testing.T) {
//verbose()
chk.PrintTitle("ops03")
nonsymTol := 1e-15
dtol := 1e-9
dver := chk.Verbose
nd := test_nd
for idxA := 0; idxA < len(test_nd)-3; idxA++ {
//for idxA := 0; idxA < 1; idxA++ {
// tensor and eigenvalues
A := test_AA[idxA]
a := M_Alloc2(nd[idxA])
Ten2Man(a, A)
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pfblue2("a = %v\n", a)
// inverse
Ai := Alloc2()
ai := M_Alloc2(nd[idxA])
detA, err := Inv(Ai, A)
if err != nil {
chk.Panic("%v", err)
}
deta_ := M_Det(a)
deta, err := M_Inv(ai, a, MINDET)
if err != nil {
chk.Panic("%v", err)
}
Ai_ := Alloc2()
Man2Ten(Ai_, ai)
aia := M_Alloc2(nd[idxA])
err = M_Dot(aia, ai, a, nonsymTol)
if err != nil {
chk.Panic("%v", err)
}
chk.Scalar(tst, "detA", 1e-14, detA, deta)
chk.Scalar(tst, "deta", 1e-14, deta, deta_)
chk.Matrix(tst, "Ai", 1e-14, Ai, Ai_)
chk.Vector(tst, "ai*a", 1e-15, aia, Im[:2*nd[idxA]])
io.Pforan("ai*a = %v\n", aia)
// derivative of inverse
dtol_tmp := dtol
if idxA == 5 {
dtol = 1e-8
}
var tmp float64
ai_tmp := M_Alloc2(nd[idxA])
daida := M_Alloc4(nd[idxA])
M_InvDeriv(daida, ai)
io.Pforan("ai = %v\n", ai)
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
//dnum, _ := num.DerivForward(func(x float64, args ...interface{}) (res float64) {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
_, err := M_Inv(ai_tmp, a, MINDET)
a[j] = tmp
if err != nil {
chk.Panic("daida failed:\n%v", err)
}
return ai_tmp[i]
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dai/da[%d][%d]", i, j), dtol, daida[i][j], dnum, dver)
}
}
dtol = dtol_tmp
}
}
func Test_isofun01(tst *testing.T) {
//verbose()
chk.PrintTitle("isofun01. rounded cone")
// SMP director parameters
// Note:
// 1) eps and ϵ have an effect on how close to DP/MC SMP will be
// 2) as eps increases, SMP is closer to DP/MC
// 3) as ϵ increases, SMP is closer to DP/MC
// 4) eps also changes the shape of FC surface
a, b, eps, ϵ := -1.0, 0.5, 1e-3, 1e-3
shift := 1.0
// radius
r := 2.0
// failure crit parameters and number of stress components
φ, ncp := 30.0, 6
// q/p coefficient
μ := SmpCalcμ(φ, a, b, eps, ϵ)
io.Pforan("μ = %v\n", μ)
// isotropic functions
var o IsoFun
o.Init(a, b, eps, ϵ, shift, ncp, rounded_cone_ffcn, rounded_cone_gfcn, rounded_cone_hfcn)
// plot
if false {
//if true {
σcCte := 10.0
M := Phi2M(φ, "oct")
rmin, rmax := 0.0, 1.28*M*σcCte
nr, nα := 31, 81
//nr, nα := 31, 1001
npolarc := true
simplec := true
only0 := true
grads := false
showpts := false
ferr := 10.0
PlotOct("fig_isofun01.png", σcCte, rmin, rmax, nr, nα, φ, o.Fa, o.Ga,
npolarc, simplec, only0, grads, showpts, true, true, ferr, r, μ)
}
// 3D view
if false {
//if true {
grads := true
gftol := 5e-2
o.View(10, nil, grads, gftol, func(e *vtk.IsoSurf) {
e.Nlevels = 7
}, r, μ)
}
// constants
ver := chk.Verbose
tol := 1e-6
tol2 := 1e-6
tolq := tol2
// check gradients
for idxA := 0; idxA < len(test_nd); idxA++ {
//for idxA := 0; idxA < 1; idxA++ {
//for idxA := 2; idxA < 3; idxA++ {
//for idxA := 10; idxA < 11; idxA++ {
//for idxA := 11; idxA < 12; idxA++ {
//for idxA := 12; idxA < 13; idxA++ {
// tensor
AA := test_AA[idxA]
A := M_Alloc2(3)
Ten2Man(A, AA)
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pfblue2("A = %v\n", A)
// function evaluation and shifted eigenvalues
fval, err := o.Fa(A, r, μ)
if err != nil {
chk.Panic("cannot compute F(A):\n%v", err)
}
io.Pfpink("shift = %v\n", shift)
io.Pforan("p, q = %v, %v\n", o.p, o.q)
io.Pforan("f(A) = %v\n", fval)
// change tolerances
tol3 := tol2
tol2_tmp := tol2
switch idxA {
case 7:
tolq = 1e-5
case 10:
tolq = 2508 // TODO
tol3 = 0.772 // TODO: check why test # 10 fails with d2f/dAdA
case 11:
tol2 = 0.0442 // TODO: check this
tol3 = 440 //TODO: check this
case 12:
tol2 = 1e-3
tol3 = 0.082 // TODO: check this
}
// check gradients
err = o.CheckDerivs(A, tol, tol2, tolq, tol3, ver, r, μ)
if err != nil {
// plot
if true {
np := 41
pmin, pmax := -o.p*10, o.p*10
pq_point := []float64{o.p, o.q}
o.PlotFfcn("/tmp", io.Sf("t_isofun01_%d.png", idxA), pmin, pmax, np, pq_point, "", "'ro'", nil, nil, r, μ)
}
// test failed
chk.Panic("CheckDerivs failed:%v\n", err)
}
// recover tolerances
tol2 = tol2_tmp
}
}
func Test_ops01(tst *testing.T) {
//verbose()
chk.PrintTitle("ops01")
// basic derivatives
dver := chk.Verbose
dtol := 1e-5
// invariants derivatives
dveri := false
dtoli1 := []float64{1e-6, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6}
dtoli2 := []float64{1e-6, 1e-5, 1e-6, 1e-4, 1e-5, 1e-6, 1e-6, 1e-6, 1e-6, 1e-6}
dtoli3 := []float64{1e-6, 1e-3, 1e-6, 1e-3, 1e-3, 1e-6, 1e-6, 1e-6, 1e-5, 1e-6}
// lode derivatives
dverw := chk.Verbose
dtolw := 1e-8
nd := test_nd
for m := 0; m < len(test_nd)-3; m++ {
//for m := 0; m < 3; m++ {
A := test_AA[m]
a := M_Alloc2(nd[m])
Ten2Man(a, A)
trA := Tr(A)
tra := M_Tr(a)
detA := Det(A)
deta := M_Det(a)
devA := Dev(A)
deva := M_Dev(a)
devA_ := Alloc2()
a2 := M_Alloc2(nd[m])
A2 := Alloc2()
A2_ := Alloc2()
trDevA := Tr(devA)
deva__ := M_Alloc2(nd[m])
devA__ := Alloc2()
s2 := M_Alloc2(nd[m])
M_Sq(a2, a)
M_Sq(s2, deva)
Man2Ten(A2, a2)
Man2Ten(devA_, deva)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
for k := 0; k < 3; k++ {
A2_[i][j] += A[i][k] * A[k][j]
}
}
}
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
deva__[i] += Psd[i][j] * a[j]
}
}
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
for k := 0; k < 3; k++ {
for l := 0; l < 3; l++ {
devA__[i][j] += M2TT(Psd, i, j, k, l) * A[k][l]
}
}
}
}
// check basic
if math.Abs(trA-tra) > 1e-17 {
chk.Panic("tra failed. diff = %g", trA-tra)
}
if math.Abs(detA-deta) > 1e-14 {
chk.Panic("detA failed. diff = %g", detA-deta)
}
if math.Abs(trDevA) > 1e-13 {
chk.Panic("trDevA failed. error = %g", trDevA)
}
chk.Matrix(tst, "devA", 1e-13, devA, devA_)
chk.Matrix(tst, "devA", 1e-13, devA, devA__)
chk.Vector(tst, "devA", 1e-13, deva, deva__)
chk.Matrix(tst, "A²", 1e-11, A2, A2_)
// check tr(s2)
io.Pfblue2("tr(s²) = %v\n", M_Tr(s2))
if M_Tr(s2) < 1 {
chk.Panic("Tr(s2) failed")
}
// check derivatives
da2da := M_Alloc4(nd[m])
a2tmp := M_Alloc2(nd[m]) // a2tmp == a²
M_SqDeriv(da2da, a)
var tmp float64
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
M_Sq(a2tmp, a)
a[j] = tmp
return a2tmp[i]
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("da²/da[%d][%d]", i, j), dtol, da2da[i][j], dnum, dver)
}
}
// characteristic invariants
I1, I2, I3 := M_CharInvs(a)
I2a := 0.5 * (tra*tra - M_Tr(a2))
I1_, I2_, I3_, dI1da, dI2da, dI3da := M_CharInvsAndDerivs(a)
if math.Abs(I1-tra) > 1e-17 {
chk.Panic("I1 failed (a). error = %v", I1-tra)
}
if math.Abs(I2-I2a) > 1e-12 {
chk.Panic("I2 failed (a). error = %v (I2=%v, I2_=%v)", I2-I2a, I2, I2a)
}
if math.Abs(I3-deta) > 1e-17 {
chk.Panic("I3 failed (a). error = %v", I3-deta)
}
if math.Abs(I1-I1_) > 1e-17 {
chk.Panic("I1 failed (b). error = %v", I1-I1_)
}
if math.Abs(I2-I2_) > 1e-17 {
chk.Panic("I2 failed (b). error = %v", I2-I2_)
}
if math.Abs(I3-I3_) > 1e-17 {
chk.Panic("I3 failed (b). error = %v", I3-I3_)
}
// dI1da
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
i1, _, _ := M_CharInvs(a)
a[j] = tmp
return i1
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dI1/da[%d]", j), dtoli1[m], dI1da[j], dnum, dveri)
}
// dI2da
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
_, i2, _ := M_CharInvs(a)
a[j] = tmp
return i2
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dI2/da[%d]", j), dtoli2[m], dI2da[j], dnum, dveri)
}
// dI3da
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
_, _, i3 := M_CharInvs(a)
a[j] = tmp
return i3
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dI3/da[%d]", j), dtoli3[m], dI3da[j], dnum, dveri)
}
// dDet(a)/da
DdetaDa := make([]float64, len(a))
M_DetDeriv(DdetaDa, a)
for j := 0; j < len(a); j++ {
chk.AnaNum(tst, io.Sf("dDet(a)/da[%d]", j), dtoli3[m], dI3da[j], DdetaDa[j], dveri)
}
// lode angle
if true {
s := M_Alloc2(nd[m])
dwda := M_Alloc2(nd[m])
dwda_ := M_Alloc2(nd[m])
d2wdada := M_Alloc4(nd[m])
p, q, w := M_pqws(s, a)
M_LodeDeriv1(dwda, a, s, p, q, w)
M_LodeDeriv2(d2wdada, dwda_, a, s, p, q, w)
chk.Vector(tst, "s", 1e-13, deva, s)
chk.Vector(tst, "dwda", 1e-13, dwda, dwda_)
// dwda
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
res = M_w(a)
a[j] = tmp
return res
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dw/da[%d]", j), dtolw, dwda[j], dnum, dverw)
}
// d2wdada
s_tmp := M_Alloc2(nd[m])
dwda_tmp := M_Alloc2(nd[m])
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
p_tmp, q_tmp, w_tmp := M_pqws(s_tmp, a)
M_LodeDeriv1(dwda_tmp, a, s_tmp, p_tmp, q_tmp, w_tmp)
a[j] = tmp
return dwda_tmp[i]
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("d2w/dada[%d][%d]", i, j), dtolw, d2wdada[i][j], dnum, dverw)
}
}
}
}
}
// Solve solves optimisation problem
func (o *Optimiser) Solve() {
// benchmark
if o.Verbose {
t0 := gotime.Now()
defer func() {
io.Pf("\nnfeval = %d\n", o.Nfeval)
io.Pfblue2("cpu time = %v\n", gotime.Now().Sub(t0))
}()
}
// output
if o.Output != nil {
o.Output(0, o.Solutions)
}
// perform evolution
done := make(chan int, o.Ncpu)
time := 0
texc := time + o.DtExc
for time < o.Tf {
// run groups in parallel. up to exchange time
for icpu := 0; icpu < o.Ncpu; icpu++ {
go func(cpu int) {
nfeval := 0
for t := time; t < texc; t++ {
if cpu == 0 && o.Verbose {
io.Pf("time = %10d\r", t+1)
}
nfeval += o.EvolveOneGroup(cpu)
}
done <- nfeval
}(icpu)
}
for cpu := 0; cpu < o.Ncpu; cpu++ {
o.Nfeval += <-done
}
// compute metrics with all solutions included
o.Metrics.Compute(o.Solutions)
// exchange via tournament
if o.Ncpu > 1 {
if o.ExcTour {
for i := 0; i < o.Ncpu; i++ {
j := (i + 1) % o.Ncpu
I := rnd.IntGetUnique(o.Groups[i].Indices, 2)
J := rnd.IntGetUnique(o.Groups[j].Indices, 2)
A, B := o.Groups[i].All[I[0]], o.Groups[i].All[I[1]]
a, b := o.Groups[j].All[J[0]], o.Groups[j].All[J[1]]
o.Tournament(A, B, a, b, o.Metrics)
}
}
// exchange one randomly
if o.ExcOne {
rnd.IntGetGroups(o.cpupairs, utl.IntRange(o.Ncpu))
for _, pair := range o.cpupairs {
i, j := pair[0], pair[1]
n := utl.Imin(o.Groups[i].Ncur, o.Groups[j].Ncur)
k := rnd.Int(0, n)
A := o.Groups[i].All[k]
B := o.Groups[j].All[k]
B.CopyInto(o.tmp)
A.CopyInto(B)
o.tmp.CopyInto(A)
}
}
}
// update time variables
time += o.DtExc
texc += o.DtExc
time = utl.Imin(time, o.Tf)
texc = utl.Imin(texc, o.Tf)
// output
if o.Output != nil {
o.Output(time, o.Solutions)
}
}
}
func Test_mylab06(tst *testing.T) {
//verbose()
chk.PrintTitle("mylab06. scaling")
// |dx|>0: increasing
io.Pfblue2("\n|dx|>0: increasing\n")
reverse := false
useinds := true
x := []float64{10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
s := make([]float64, len(x))
Scaling(s, x, -2.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, LinSpace(-2, -1, len(x)))
// |dx|>0: reverse
io.Pfblue2("\n|dx|>0: reverse\n")
reverse = true
Scaling(s, x, -3.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, LinSpace(-2, -3, len(x)))
// |dx|>0: increasing
io.Pfblue2("\n|dx|>0: increasing (shuffled)\n")
reverse = false
x = []float64{11, 10, 12, 19, 15, 20, 17, 16, 18, 13, 14}
Scaling(s, x, 0.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, []float64{0.1, 0.0, 0.2, 0.9, 0.5, 1.0, 0.7, 0.6, 0.8, 0.3, 0.4})
// |dx|=0: increasing (using indices)
io.Pfblue2("\n|dx|=0: increasing (using indices)\n")
reverse = false
x = []float64{123, 123, 123, 123, 123}
s = make([]float64, len(x))
Scaling(s, x, 10.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, []float64{10, 10.25, 10.5, 10.75, 11})
// |dx|=0: reverse (using indices)
io.Pfblue2("\n|dx|=0: reverse (using indices)\n")
reverse = true
Scaling(s, x, 10.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, []float64{11, 10.75, 10.5, 10.25, 10})
// |dx|=0: increasing (not using indices)
io.Pfblue2("\n|dx|=0: increasing (not using indices)\n")
reverse = false
useinds = false
Scaling(s, x, 88.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, DblVals(len(x), 88))
// |dx|=0: reverse (not using indices)
io.Pfblue2("\n|dx|=0: reverse (not using indices)\n")
reverse = true
Scaling(s, x, 88.0, 1e-16, reverse, useinds)
io.Pfpink("x = %v\n", x)
io.Pforan("s = %v\n", s)
chk.Vector(tst, "s", 1e-15, s, DblVals(len(x), 88))
}
// generate_solutions generate solutions
func (o *Optimiser) generate_solutions(itrial int) {
// benchmark
t0 := gotime.Now()
var tgen, tmsh gotime.Time
if o.VerbTime && itrial == 0 {
defer func() {
io.Pfblue2("time spent in generation of solutions = %v\n", tgen.Sub(t0))
io.Pfblue2("time spent in Delaunay triangulations = %v\n", tmsh.Sub(tgen))
io.Pfblue2("total time in generate_solutions = %v\n", gotime.Now().Sub(t0))
}()
}
// generate
if o.GenAll {
o.Generator(o.Solutions, &o.Parameters)
for _, sol := range o.Solutions {
o.ObjFunc(sol, 0)
}
} else {
done := make(chan int, o.Ncpu)
for icpu := 0; icpu < o.Ncpu; icpu++ {
go func(cpu int) {
start, endp1 := (cpu*o.Nsol)/o.Ncpu, ((cpu+1)*o.Nsol)/o.Ncpu
sols := o.Solutions[start:endp1]
o.Generator(sols, &o.Parameters)
for _, sol := range sols {
o.ObjFunc(sol, cpu)
}
done <- 1
}(icpu)
}
for cpu := 0; cpu < o.Ncpu; cpu++ {
<-done
}
}
tgen = gotime.Now()
// metrics
o.iova0 = -1
o.Nfeval = o.Nsol
o.Metrics.Compute(o.Solutions)
// meshes
if o.Nflt > 1 && o.UseMesh {
var err error
Xi, Xj := make([]float64, o.Nsol), make([]float64, o.Nsol)
o.Meshes = make([][]*Mesh, o.Nflt-1)
for i := 0; i < o.Nflt-1; i++ {
o.Meshes[i] = make([]*Mesh, o.Nflt)
for k, s := range o.Solutions {
Xi[k] = s.Flt[i]
}
for j := i + 1; j < o.Nflt; j++ {
for k, s := range o.Solutions {
Xj[k] = s.Flt[j]
}
o.Meshes[i][j].V, o.Meshes[i][j].C, err = tri.Delaunay(Xi, Xj, false)
if err != nil {
chk.Panic("Delaunay2d failed:%v\n", err)
}
}
}
}
tmsh = gotime.Now()
}
// Run runs optimisations
func (o *SimpleFltProb) Run(verbose bool) {
// benchmark
if verbose {
time0 := time.Now()
defer func() {
io.Pfblue2("\ncpu time = %v\n", time.Now().Sub(time0))
}()
}
// run all trials
for itrial := 0; itrial < o.C.Ntrials; itrial++ {
// reset populations
if itrial > 0 {
for id, isl := range o.Evo.Islands {
isl.Pop = o.C.PopFltGen(id, o.C)
isl.CalcOvs(isl.Pop, 0)
isl.CalcDemeritsAndSort(isl.Pop)
}
}
// run evolution
o.Evo.Run()
// results
xbest := o.Evo.Best.GetFloats()
o.Fcn(o.ff[0], o.gg[0], o.hh[0], xbest)
// check if best is unfeasible
unfeasible := false
for _, g := range o.gg[0] {
if g < 0 {
unfeasible = true
break
}
}
for _, h := range o.hh[0] {
if math.Abs(h) > o.C.Eps1 {
unfeasible = true
break
}
}
// feasible results
if !unfeasible {
for i, x := range xbest {
o.Xbest[o.Nfeasible][i] = x
}
o.Nfeasible++
}
// message
if verbose {
io.Pfyel("%3d x*="+o.NumfmtX+" f="+o.NumfmtF, itrial, xbest, o.ff[0])
if unfeasible {
io.Pfred(" unfeasible\n")
} else {
io.Pfgreen(" ok\n")
}
}
// best populations
if o.C.DoPlot {
if o.Nfeasible == 1 {
o.PopsBest = o.Evo.GetPopulations()
} else {
fcur := utl.DblCopy(o.ff[0])
o.Fcn(o.ff[0], o.gg[0], o.hh[0], o.Xbest[o.Nfeasible-1])
cur_dom, _ := utl.DblsParetoMin(fcur, o.ff[0])
if cur_dom {
o.PopsBest = o.Evo.GetPopulations()
}
}
}
}
}
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
}