func Test_groups01(tst *testing.T) {
//verbose()
chk.PrintTitle("groups01")
Init(0)
ng := 3 // number of groups
nints := 12 // number of integers
size := nints / ng // groups size
ints := utl.IntRange(nints)
groups := utl.IntsAlloc(ng, size)
hists := make([]*IntHistogram, ng)
for i := 0; i < ng; i++ {
hists[i] = &IntHistogram{Stations: utl.IntRange(nints + 1)}
}
IntGetGroups(groups, ints)
io.Pfcyan("groups = %v\n", groups)
for i := 0; i < NSAMPLES; i++ {
IntGetGroups(groups, ints)
for j := 0; j < ng; j++ {
check_repeated(groups[j])
hists[j].Count(groups[j], false)
}
}
for i := 0; i < ng; i++ {
io.Pf("\n")
io.Pf(TextHist(hists[i].GenLabels("%d"), hists[i].Counts, 60))
}
}
// PlotDerivs plots derivatives of basis functions in I
// option = 0 : use CalcBasisAndDerivs
// 1 : use NumericalDeriv
func (o *Bspline) PlotDerivs(args string, npts, option int) {
nmks := 10
tt := utl.LinSpace(o.tmin, o.tmax, npts)
I := utl.IntRange(o.NumBasis())
f := make([]float64, len(tt))
lbls := []string{"N\\&dN", "numD"}
var cmd string
for _, i := range I {
for j, t := range tt {
switch option {
case 0:
o.CalcBasisAndDerivs(t)
f[j] = o.GetDeriv(i)
case 1:
f[j] = o.NumericalDeriv(t, i)
}
}
if strings.Contains(args, "marker") {
cmd = io.Sf("label=r'%s:%d', color=GetClr(%d, 2) %s", lbls[option], i, i, args)
} else {
cmd = io.Sf("label=r'%s:%d', marker=(None if %d %%2 == 0 else GetMrk(%d/2,1)), markevery=(%d-1)/%d, clip_on=0, color=GetClr(%d, 2) %s", lbls[option], i, i, i, npts, nmks, i, args)
}
plt.Plot(tt, f, cmd)
}
plt.Gll("$t$", io.Sf(`$\frac{\mathrm{d}N_{i,%d}}{\mathrm{d}t}$`, o.p), io.Sf("leg=1, leg_out=1, leg_ncol=%d, leg_hlen=1.5, leg_fsz=7", o.NumBasis()))
o.plt_ticks_spans()
}
func Test_MTint01(tst *testing.T) {
//verbose()
chk.PrintTitle("MTint01. integers (Mersenne Twister)")
Init(1234)
nints := 10
vals := make([]int, NSAMPLES)
// using MTint
t0 := time.Now()
for i := 0; i < NSAMPLES; i++ {
vals[i] = MTint(0, nints-1)
}
io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))
hist := IntHistogram{Stations: utl.IntRange(nints + 1)}
hist.Count(vals, true)
io.Pfyel(TextHist(hist.GenLabels("%d"), hist.Counts, 60))
// using MTints
t0 = time.Now()
MTints(vals, 0, nints-1)
io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))
hist.Count(vals, true)
io.Pfcyan(TextHist(hist.GenLabels("%d"), hist.Counts, 60))
}
func Test_MTshuffleInts01(tst *testing.T) {
//verbose()
chk.PrintTitle("MTshuffleInts01. Mersenne Twister")
Init(0)
n := 10
nums := utl.IntRange(n)
io.Pfgreen("before = %v\n", nums)
MTintShuffle(nums)
io.Pfcyan("after = %v\n", nums)
sort.Ints(nums)
io.Pforan("sorted = %v\n", nums)
chk.Ints(tst, "nums", nums, utl.IntRange(n))
}
func (g *Grid2D) Init(lx, ly float64, nx, ny int) {
g.Lx, g.Ly = lx, ly
g.Nx, g.Ny, g.N = nx, ny, nx*ny
g.Dx, g.Dy = g.Lx/float64(nx-1), g.Ly/float64(ny-1)
g.Dxx, g.Dyy = g.Dx*g.Dx, g.Dy*g.Dy
g.L = utl.IntRange3(0, g.N, g.Nx)
g.R = utl.IntAddScalar(g.L, g.Nx-1)
g.B = utl.IntRange(g.Nx)
g.T = utl.IntAddScalar(g.B, (g.Ny-1)*g.Nx)
}
func Test_GOshuffleInts01(tst *testing.T) {
//verbose()
chk.PrintTitle("GOshuffleInts01")
Init(0)
n := 10
nums := utl.IntRange(n)
io.Pfgreen("before = %v\n", nums)
IntShuffle(nums)
io.Pfcyan("after = %v\n", nums)
sort.Ints(nums)
io.Pforan("sorted = %v\n", nums)
chk.Ints(tst, "nums", nums, utl.IntRange(n))
shufled := IntGetShuffled(nums)
io.Pfyel("shufled = %v\n", shufled)
sort.Ints(shufled)
chk.Ints(tst, "shufled", shufled, utl.IntRange(n))
}
func Test_getunique01(tst *testing.T) {
//verbose()
chk.PrintTitle("getunique01")
Init(0)
nsel := 5 // number of selections
size := 10
nums := utl.IntRange(size)
hist := IntHistogram{Stations: utl.IntRange(size + 5)}
sel := IntGetUnique(nums, nsel)
io.Pfgreen("nums = %v\n", nums)
io.Pfcyan("sel = %v\n", sel)
for i := 0; i < NSAMPLES; i++ {
sel := IntGetUnique(nums, nsel)
check_repeated(sel)
hist.Count(sel, false)
//io.Pfgrey("sel = %v\n", sel)
}
io.Pf(TextHist(hist.GenLabels("%d"), hist.Counts, 60))
}
// FactoryNurbs1dCurveA generates a NURBS 1D curve
func FactoryNurbs1dCurveA() (b *Nurbs) {
verts := [][]float64{
{0.0, 0.0, 0, 1},
{1.0, 0.2, 0, 1},
{0.5, 1.5, 0, 1},
{2.5, 2.0, 0, 1},
{2.0, 0.4, 0, 1},
{3.0, 0.0, 0, 1},
}
knots := [][]float64{
{0, 0, 0, 0, 0.3, 0.7, 1, 1, 1, 1},
}
b = new(Nurbs)
b.Init(1, []int{3}, knots)
b.SetControl(verts, utl.IntRange(len(verts)))
return
}
func Test_ends02(tst *testing.T) {
//verbose()
chk.PrintTitle("ends02")
rnd.Init(0)
size := 20
ncuts := 10
nsamples := 100
hist := rnd.IntHistogram{Stations: utl.IntRange(size + 3)}
for i := 0; i < nsamples; i++ {
ends := GenerateCxEnds(size, ncuts, nil)
hist.Count(ends, false)
}
io.Pf("%s\n", rnd.TextHist(hist.GenLabels("%d"), hist.Counts, 60))
}
// ElemBryLocalInds returns the local (element) indices of control points @ boundaries
// (if element would have all surfaces @ boundaries)
func (o *Nurbs) ElemBryLocalInds() (I [][]int) {
switch o.gnd {
case 1:
return
case 2:
I = make([][]int, 2*o.gnd)
nx, ny := o.p[0]+1, o.p[1]+1
I[3] = utl.IntRange3(0, nx*ny, nx)
I[1] = utl.IntAddScalar(I[3], nx-1)
I[0] = utl.IntRange(nx)
I[2] = utl.IntAddScalar(I[0], (ny-1)*nx)
case 3:
I = make([][]int, 2*o.gnd)
chk.Panic("3D NURBS: ElemBryLocalInds: TODO") // TODO
}
return
}
func Test_mwicz01(tst *testing.T) {
//verbose()
chk.PrintTitle("mwicz01. Michalewicz mutation")
var ops OpsData
ops.SetDefault()
ops.Pm = 1.0
ops.Tmax = 10
rnd.Init(0)
ops.Xrange = [][]float64{{0, 2}, {1, 3}, {2, 4}, {3, 5}, {4, 6}}
T := utl.IntRange(int(ops.Tmax))
for _, t := range T {
io.Pf("t=%v Δ=%v\n", t, ops.MwiczDelta(float64(t), 1))
}
for _, t := range T {
A := []float64{0, 1, 2, 3, 4}
FltMutationMwicz(A, t, &ops)
io.Pforan("A = %.8f\n", A)
}
if chk.Verbose {
b := 2.0
f := func(r, tb float64) float64 {
return math.Pow(r, math.Pow(1.0-tb, b))
}
np := 21
r, tb := utl.MeshGrid2D(0, 1, 0, 1, np, np) // tb = t/tmax
z := la.MatAlloc(np, np)
for i := 0; i < np; i++ {
for j := 0; j < np; j++ {
z[i][j] = f(r[i][j], tb[i][j])
}
}
plt.Surface(tb, r, z, "linewidth=0.8")
plt.Gll("tb", "r", "")
plt.SaveD("/tmp/goga", "test_mwicz01.eps")
//plt.Show()
}
}
func Test_getunique02(tst *testing.T) {
//verbose()
chk.PrintTitle("getunique02")
Init(0)
nsel := 5 // number of selections
start := 2
endp1 := 10
hist := IntHistogram{Stations: utl.IntRange(endp1 + 3)}
sel := IntGetUniqueN(start, endp1, nsel)
io.Pfcyan("sel = %v\n", sel)
for i := 0; i < NSAMPLES; i++ {
sel := IntGetUniqueN(start, endp1, nsel)
check_repeated(sel)
hist.Count(sel, false)
//io.Pfgrey("sel = %v\n", sel)
}
io.Pf(TextHist(hist.GenLabels("%d"), hist.Counts, 60))
}
// FactoryNurbs2dStrip generates a NURBS of a 2D strip (x-quadratic, y-linear)
func FactoryNurbs2dStrip() (b *Nurbs) {
verts := [][]float64{
{0.00, 0.00, 0, 0.80}, // 0
{0.25, 0.15, 0, 1.00}, // 1
{0.50, 0.00, 0, 0.70}, // 2
{0.75, 0.00, 0, 1.20}, // 3
{1.00, 0.10, 0, 1.10}, // 4
{0.00, 0.40, 0, 0.90}, // 5
{0.25, 0.55, 0, 0.60}, // 6
{0.50, 0.40, 0, 1.50}, // 7
{0.75, 0.40, 0, 1.40}, // 8
{1.00, 0.50, 0, 0.50}, // 9
}
knots := [][]float64{
{0, 0, 0, 1, 2, 3, 3, 3},
{0, 0, 1, 1},
}
b = new(Nurbs)
b.Init(2, []int{2, 1}, knots)
b.SetControl(verts, utl.IntRange(len(verts)))
return
}
func Test_p01a(tst *testing.T) {
/* this tests simulates seepage flow along a column
* by reducing the initial hydrostatic pressure at
* at the bottom of the column
*
* Nodes / Tags Equations
*
* 8 o----o----o 9 (-5) 22 o----o----o 21
* | 14 | | 24 |
* | | | |
* 21 o o o 22 (-6) 25 o o o 23
* | 26 | | 26 |
* | | | |
* 6 o----o----o 7 (-4) 16 o----o----o 15
* | 13 | | 18 |
* | | | |
* 19 | o o 20 (-6) 19 | o o 17
* | 25 | | 20 |
* | | | |
* 4 o----o----o 5 (-3) 10 o----o----o 9
* | 12 | | 12 |
* | | | |
* 17 o o o 18 (-6) 13 o o o 11
* | 24 | | 14 |
* | | | |
* 2 o----o----o 3 (-2) 3 o----o----o 2
* | 11 | | 6 |
* | | | |
* 15 o o o 16 (-6) 7 o o o 5
* | 23 | | 8 |
* | | | |
* 0 o----o----o 1 (-1) 0 o----o----o 1
* 10 4
*/
//verbose()
chk.PrintTitle("p01a")
// start simulation
analysis := NewFEM("data/p01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 27)
chk.IntAssert(len(dom.Elems), 4)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 1)
chk.StrAssert(nod.Dofs[0].Key, "pl")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{
0, 1, 3, 2, 10, 16, 11, 15, 23,
5, 4, 18, 12, 17, 24,
7, 6, 20, 13, 19, 25,
9, 8, 22, 14, 21, 26,
})
chk.Ints(tst, "eqs", eqs, utl.IntRange(27))
// check pmap
pmaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8},
{3, 2, 9, 10, 6, 11, 12, 13, 14},
{10, 9, 15, 16, 12, 17, 18, 19, 20},
{16, 15, 21, 22, 18, 23, 24, 25, 26},
}
for i, ele := range dom.Elems {
e := ele.(*ElemP)
io.Pforan("e%d.pmap = %v\n", e.Id(), e.Pmap)
chk.Ints(tst, "pmap", e.Pmap, pmaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 3)
var ct_pl_eqs []int // equations with pl prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pforan("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "pl":
ct_pl_eqs = append(ct_pl_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_pl_eqs)
chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{0, 1, 4})
// initial values @ nodes
io.Pforan("initial values @ nodes\n")
for _, nod := range dom.Nodes {
z := nod.Vert.C[1]
eq := nod.Dofs[0].Eq
pl := dom.Sol.Y[eq]
plC, _, _ := dom.HydSta.Calc(z)
chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, pl), 1e-17, pl, plC)
}
// intial values @ integration points
io.Pforan("initial values @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemP)
for idx, ip := range e.IpsElem {
s := e.States[idx]
z := e.Cell.Shp.IpRealCoords(e.X, ip)[1]
_, ρLC, _ := dom.HydSta.Calc(z)
chk.Scalar(tst, io.Sf("sl(@ %18g)= %18g", z, s.A_sl), 1e-17, s.A_sl, 1)
chk.Scalar(tst, io.Sf("ρL(@ %18g)= %18g", z, s.A_ρL), 1e-13, s.A_ρL, ρLC)
}
}
}
func Test_out01(tst *testing.T) {
// finalise analysis process and catch errors
defer func() {
if err := recover(); err != nil {
tst.Fail()
io.PfRed("ERROR: %v\n", err)
}
}()
// test title
//verbose()
chk.PrintTitle("out01")
// start simulation
processing := fem.NewFEM("data/onequa4.sim", "", true, true, false, false, chk.Verbose, 0)
// run simulation
err := processing.Run()
if err != nil {
tst.Errorf("Run failed:\n%v", err)
return
}
// start post-processing
Start("data/onequa4.sim", 0, 0)
// define points
Define("A B C D", N{0, 1, 2, 3})
Define("a b c d", P{{0, 0}, {0, 1}, {-1, 2}, {-1, 3}})
Define("!right side", Along{{1, 0}, {1, 1}})
io.Pfcyan("Entities = %v\n", Results)
// check slices
nnod := 4
nele := 1
nip := 4
chk.IntAssert(len(Dom.Nodes), nnod)
chk.IntAssert(len(Ipoints), nele*nip)
chk.IntAssert(len(Cid2ips), 1)
chk.IntAssert(len(Ipkey2ips), 4)
chk.IntAssert(len(Ipkeys), 4)
for key, ips := range Ipkey2ips {
chk.Ints(tst, io.Sf("%s : ips", key), ips, utl.IntRange(4))
}
// load results
LoadResults(nil)
// check points
nlabels := []string{"A", "B", "C", "D"}
for _, l := range nlabels {
if _, ok := Results[l]; !ok {
chk.Panic("1: %q alias in Entities is not available", l)
}
}
plabels := []string{"a", "b", "c", "d"}
for _, l := range plabels {
if _, ok := Results[l]; !ok {
chk.Panic("2: %q alias in Entities is not available", l)
}
}
if _, ok := Results["right side"]; !ok {
chk.Panic("3: %q alias in Entities is not available", "right side")
}
// check u-keys
ukeys := []string{"ux", "uy"}
for _, l := range nlabels {
for _, p := range Results[l] {
//io.Pfyel("p = %v\n", p)
if p == nil {
chk.Panic("1: p is nil")
}
for _, key := range ukeys {
if _, ok := p.Vals[key]; !ok {
chk.Panic("%s is not available in point", key)
}
}
}
}
// check s-keys
skeys := fem.StressKeys(Dom.Sim.Ndim)
for _, l := range plabels {
for _, p := range Results[l] {
//io.Pfgreen("q = %v\n", p)
if p == nil {
chk.Panic("2: p is nil")
}
for _, key := range skeys {
if _, ok := p.Vals[key]; !ok {
chk.Panic("%s is not available in point", key)
}
}
}
}
// check GetRes
uxC := GetRes("ux", "C", 0)
uxR := GetRes("ux", "right side", -1)
io.Pforan("uxC = %v\n", uxC)
io.Pforan("uxR = %v\n", uxR)
chk.IntAssert(len(uxC), 2)
idx := len(uxC) - 1
chk.Vector(tst, "uxR", 1e-17, uxR, []float64{uxC[idx], uxC[idx]})
// solution
var sol ana.CteStressPstrain
sol.Init(fun.Prms{
&fun.Prm{N: "qnH", V: -50},
&fun.Prm{N: "qnV", V: -100},
})
// check displacements
tolu := 1e-15
for _, l := range nlabels {
x := GetCoords(l)
ux := GetRes("ux", l, 0)
uy := GetRes("uy", l, 0)
io.Pforan("ux=%v uy=%v\n", ux, uy)
for j, t := range Times {
io.Pfyel("t=%g\n", t)
sol.CheckDispl(tst, t, []float64{ux[j], uy[j]}, x, tolu)
}
}
// check stresses
tolσ := 1e-14
for _, l := range plabels {
x := GetCoords(l)
sx := GetRes("sx", l, 0)
sy := GetRes("sy", l, 0)
sz := GetRes("sz", l, 0)
sxy := GetRes("sxy", l, 0)
for j, t := range Times {
io.Pfyel("t=%g\n", t)
sol.CheckStress(tst, t, []float64{sx[j], sy[j], sz[j], sxy[j]}, x, tolσ)
}
}
}
func test_contact01a(tst *testing.T) {
/* Nodes Equations:
* 7 33,34
* 6 o-----o-----o-----o-----o 8 35 o-----o-----o-----o-----o 45,46,47
* | 13 | 14 | 36 | 39,40 | 51,52 |
* | | | | 37| | 48
* 18 o [2] o19 [3] o 20 41 o o 38o o o 49
* | 23 | 24 | 42 | 43,44 | 53,54 | 50
* | | | | 4| |
* 3 o-----o-----o-----o-----o 5 6 o-----o-----o-----o-----o 21,22,23
* | 11 4| 12 | 7 | 12,13 5| 29,30 |
* | | | | | | 26
* 15 o [0] o16 [1] o 17 14,15 o o 10o o o 27
* | 21 | 22 | | 16,17 11| 31,32 | 28
* | | | | | |
* 0 o-----o-----o-----o-----o 2 0 o-----o-----o-----o-----o 18
* 9 1 10 1 8 2 24,25 19
* 9 3 20
*/
//verbose()
chk.PrintTitle("contact01a")
// start simulation
analysis := NewFEM("data/contact01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 25)
chk.IntAssert(len(dom.Elems), 4)
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{0, 1, 4, 3, 9, 16, 11, 15, 21, 2, 5, 10, 17, 12, 22, 7, 6, 19, 13, 18, 23, 8, 20, 14, 24})
chk.Ints(tst, "eqs", eqs, utl.IntRange(55))
// vertices with "qbn"
contactverts := map[int]bool{2: true, 17: true, 5: true, 20: true, 8: true}
// check dofs
var contacteqs []int
for _, nod := range dom.Nodes {
if contactverts[nod.Vert.Id] {
chk.IntAssert(len(nod.Dofs), 3)
contacteqs = append(contacteqs, nod.Dofs[2].Eq)
} else {
chk.IntAssert(len(nod.Dofs), 2)
}
}
sort.Ints(contacteqs)
io.Pforan("contacteqs = %v\n", contacteqs)
chk.Ints(tst, "contacteqs", contacteqs, []int{20, 23, 28, 47, 50})
// check Qmap
e1 := dom.Elems[1].(*ElemU)
chk.Ints(tst, "e1.Qmap", e1.Qmap, []int{20, 23, 28})
e3 := dom.Elems[3].(*ElemU)
chk.Ints(tst, "e3.Qmap", e3.Qmap, []int{23, 47, 50})
}
// 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_spo751a(tst *testing.T) {
/* de Souza Neto, Perić and Owen, ex 7.5.1 p244
*
* 22
* .
* 19 ,' `.
* ,' '.
* 17 ,' \
* .' \
* 14 ,' `. \ 21
* 12 ,' \ '
* 9 .' \ '
* 7 ,' `. \ 16 '
* 4 .' \ . `
* 2 ' `. \ 11 . |
* `. \ 6 . | |
* 1. . | | |
* | | | | |
* -----------------------------
* 0 3 5 8 10 13 15 18 20
*/
//verbose()
chk.PrintTitle("spo751a")
// start simulation
analysis := NewFEM("data/spo751.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectros
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// nodes and elements
chk.IntAssert(len(dom.Nodes), 23)
chk.IntAssert(len(dom.Elems), 4)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 2)
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "nids", nids, []int{0, 5, 7, 2, 3, 6, 4, 1, 10, 12, 8, 11, 9, 15, 17, 13, 16, 14, 20, 22, 18, 21, 19})
chk.Ints(tst, "eqs", eqs, utl.IntRange(23*2))
// check solution arrays
ny := 23 * 2
nλ := 9 + 9
nyb := ny + nλ
chk.IntAssert(len(dom.Sol.Y), ny)
chk.IntAssert(len(dom.Sol.Dydt), 0)
chk.IntAssert(len(dom.Sol.D2ydt2), 0)
chk.IntAssert(len(dom.Sol.Psi), 0)
chk.IntAssert(len(dom.Sol.Zet), 0)
chk.IntAssert(len(dom.Sol.Chi), 0)
chk.IntAssert(len(dom.Sol.L), nλ)
chk.IntAssert(len(dom.Sol.ΔY), ny)
// check linear solver arrays
chk.IntAssert(len(dom.Fb), nyb)
chk.IntAssert(len(dom.Wb), nyb)
// check umap
umaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{2, 3, 16, 17, 18, 19, 4, 5, 20, 21, 22, 23, 24, 25, 10, 11},
{16, 17, 26, 27, 28, 29, 18, 19, 30, 31, 32, 33, 34, 35, 22, 23},
{26, 27, 36, 37, 38, 39, 28, 29, 40, 41, 42, 43, 44, 45, 32, 33},
}
for i, ele := range dom.Elems {
e := ele.(*ElemU)
io.Pforan("e%d.umap = %v\n", e.Id(), e.Umap)
chk.Ints(tst, "umap", e.Umap, umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), nλ)
var ct_uy_eqs []int // constrained uy equations [sorted]
var ct_incsup_xeqs []int
var ct_incsup_yeqs []int
αrad := 120.0 * math.Pi / 180.0
cα, sα := math.Cos(αrad), math.Sin(αrad)
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssertLessThanOrEqualTo(1, len(c.Eqs)) // 1 ≤ neqs
io.Pforan("c.Key=%s c.Eqs=%v\n", c.Key, c.Eqs)
if len(c.Eqs) == 1 {
if c.Key == "uy" {
ct_uy_eqs = append(ct_uy_eqs, c.Eqs[0])
continue
}
} else {
if c.Key == "incsup" {
ct_incsup_xeqs = append(ct_incsup_xeqs, c.Eqs[0])
ct_incsup_yeqs = append(ct_incsup_yeqs, c.Eqs[1])
chk.AnaNum(tst, "cos(α)", 1e-15, c.ValsA[0], cα, false)
chk.AnaNum(tst, "sin(α)", 1e-15, c.ValsA[1], sα, false)
continue
}
}
tst.Errorf("key %s is incorrect", c.Key)
}
sort.Ints(ct_uy_eqs)
sort.Ints(ct_incsup_xeqs)
sort.Ints(ct_incsup_yeqs)
chk.Ints(tst, "constrained uy equations", ct_uy_eqs, []int{1, 3, 9, 17, 21, 27, 31, 37, 41})
chk.Ints(tst, "incsup x equations", ct_incsup_xeqs, []int{4, 6, 12, 18, 24, 28, 34, 38, 44})
chk.Ints(tst, "incsup y equations", ct_incsup_yeqs, []int{5, 7, 13, 19, 25, 29, 35, 39, 45})
}
func Test_nurbs01(tst *testing.T) {
/* 4 (1,2) (2,2) 6
5 2@o--------------o@3 7
| |
| | @ -- control point
| | o -- node
| | (a,b) -- span
| |
| |
0 0@o--------------o@1 2
1 (1,1) (2,1) 3
*/
//verbose()
chk.PrintTitle("nurb01. square with initial stress")
// fem
analysis := NewFEM("data/nurbs01.sim", "", true, false, false, false, chk.Verbose, 0)
// set stage
err := analysis.SetStage(0)
if err != nil {
tst.Errorf("SetStage failed:\n%v", err)
return
}
// initialise solution vectors
err = analysis.ZeroStage(0, true)
if err != nil {
tst.Errorf("ZeroStage failed:\n%v", err)
return
}
// domain
dom := analysis.Domains[0]
// draw NURBS
if false {
nurbs := dom.Msh.Cells[0].Shp.Nurbs
gm.PlotNurbs("/tmp/gofem", "test_nurbs01", nurbs, 21, false, nil)
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 4)
chk.IntAssert(len(dom.Elems), 1)
// check dofs
for _, nod := range dom.Nodes {
chk.IntAssert(len(nod.Dofs), 2)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "eqs", eqs, utl.IntRange(4*2))
chk.Ints(tst, "nids", nids, []int{0, 1, 2, 3})
// check Umap
Umaps := [][]int{
{0, 1, 2, 3, 4, 5, 6, 7},
}
for i, ele := range dom.Elems {
e := ele.(*ElemU)
io.Pfpink("%2d : Umap = %v\n", e.Id(), e.Umap)
chk.Ints(tst, "Umap", e.Umap, Umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 4)
var ct_ux_eqs []int // equations with ux prescribed [sorted]
var ct_uy_eqs []int // equations with uy prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pfgrey("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "ux":
ct_ux_eqs = append(ct_ux_eqs, eq)
case "uy":
ct_uy_eqs = append(ct_uy_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_ux_eqs)
sort.Ints(ct_uy_eqs)
chk.Ints(tst, "equations with ux prescribed", ct_ux_eqs, []int{0, 4})
chk.Ints(tst, "equations with uy prescribed", ct_uy_eqs, []int{1, 3})
// check displacements
tolu := 1e-16
for _, n := range dom.Nodes {
eqx := n.GetEq("ux")
eqy := n.GetEq("uy")
u := []float64{dom.Sol.Y[eqx], dom.Sol.Y[eqy]}
chk.Vector(tst, "u", tolu, u, nil)
}
// analytical solution
qnV, qnH := -100.0, -50.0
ν := 0.25
σx, σy := qnH, qnV
σz := ν * (σx + σy)
σref := []float64{σx, σy, σz, 0}
// check stresses
e := dom.Elems[0].(*ElemU)
tols := 1e-13
for idx, _ := range e.IpsElem {
σ := e.States[idx].Sig
io.Pforan("σ = %v\n", σ)
chk.Vector(tst, "σ", tols, σ, σref)
}
}
func Test_up01a(tst *testing.T) {
/* this tests simulates seepage flow along a column
* by reducing the initial hydrostatic pressure at
* at the bottom of the column
*
* using mesh from col104elay.msh
*
* Nodes / Tags Equations
* ux uy pl ux uy pl
* 8 o----o----o 9 (-5) 53 54 55 o----o----o 50 51 52
* | 14 | . . . | 58 59 | . . .
* | (-1) | . . . | | . . .
* 21 o o o 22 (-6) 60 61 . o o o 56 57 .
* | 26 | . . . | 62 63 | . . .
* | | . . . | | . . .
* 6 o----o----o 7 (-4) 39 40 41 o----o----o 36 37 38
* | 13 | . . . | 44 45 | . . .
* | (-1) | . . . | | . . .
* 19 | o o 20 (-6) 46 47 . | o o 42 43 .
* | 25 | . . . | 48 49 | . . .
* | | . . . | | . . .
* 4 o----o----o 5 (-3) 25 26 27 o----o----o 22 23 24
* | 12 | . . . | 30 31 | . . .
* | (-2) | . . . | | . . .
* 17 o o o 18 (-6) 32 33 . o o o 28 29 .
* | 24 | . . . | 34 35 | . . .
* | | . . . | | . . .
* 2 o----o----o 3 (-2) 9 10 11 o----o----o 6 7 8
* | 11 | . . . | 16 17 | . . .
* | (-2) | . . . | | . . .
* 15 o o o 16 (-6) 18 19 o o o 14 15
* | 23 | . . . | 20 21 | . . .
* | | . . . | | . . .
* 0 o----o----o 1 (-1) 0 1 2 o----o----o 3 4 5
* 10 12 13
*/
// capture errors and flush log
defer End()
//verbose()
chk.PrintTitle("up01a")
// start simulation
if !Start("data/up01.sim", true, chk.Verbose) {
chk.Panic("cannot start simulation")
}
// domain
distr := false
dom := NewDomain(Global.Sim.Regions[0], distr)
if dom == nil {
chk.Panic("cannot allocate new domain")
}
// set stage
if !dom.SetStage(0, Global.Sim.Stages[0], distr) {
chk.Panic("cannot set stage")
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 27)
chk.IntAssert(len(dom.Elems), 4)
if true {
// nodes with pl
nods_with_pl := map[int]bool{0: true, 2: true, 4: true, 6: true, 8: true, 1: true, 3: true, 5: true, 7: true, 9: true}
// check dofs
for _, nod := range dom.Nodes {
if nods_with_pl[nod.Vert.Id] {
chk.IntAssert(len(nod.Dofs), 3)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
chk.StrAssert(nod.Dofs[2].Key, "pl")
} else {
chk.IntAssert(len(nod.Dofs), 2)
chk.StrAssert(nod.Dofs[0].Key, "ux")
chk.StrAssert(nod.Dofs[1].Key, "uy")
}
}
// check equations
nids, eqs := get_nids_eqs(dom)
chk.Ints(tst, "eqs", eqs, utl.IntRange(10*3+17*2))
chk.Ints(tst, "nids", nids, []int{
0, 1, 3, 2, 10, 16, 11, 15, 23,
5, 4, 18, 12, 17, 24,
7, 6, 20, 13, 19, 25,
9, 8, 22, 14, 21, 26,
})
// check pmap
Pmaps := [][]int{
{2, 5, 8, 11},
{11, 8, 24, 27},
{27, 24, 38, 41},
{41, 38, 52, 55},
}
Umaps := [][]int{
{0, 1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21},
{9, 10, 6, 7, 22, 23, 25, 26, 16, 17, 28, 29, 30, 31, 32, 33, 34, 35},
{25, 26, 22, 23, 36, 37, 39, 40, 30, 31, 42, 43, 44, 45, 46, 47, 48, 49},
{39, 40, 36, 37, 50, 51, 53, 54, 44, 45, 56, 57, 58, 59, 60, 61, 62, 63},
}
for i, ele := range dom.Elems {
e := ele.(*ElemUP)
io.Pfpink("%2d : Pmap = %v\n", e.Id(), e.P.Pmap)
io.Pfpink("%2d : Umap = %v\n", e.Id(), e.U.Umap)
chk.Ints(tst, "Pmap", e.P.Pmap, Pmaps[i])
chk.Ints(tst, "Umap", e.U.Umap, Umaps[i])
}
// constraints
chk.IntAssert(len(dom.EssenBcs.Bcs), 9*2+2+3)
var ct_ux_eqs []int // equations with ux prescribed [sorted]
var ct_uy_eqs []int // equations with uy prescribed [sorted]
var ct_pl_eqs []int // equations with pl prescribed [sorted]
for _, c := range dom.EssenBcs.Bcs {
chk.IntAssert(len(c.Eqs), 1)
eq := c.Eqs[0]
io.Pfgrey("key=%v eq=%v\n", c.Key, eq)
switch c.Key {
case "ux":
ct_ux_eqs = append(ct_ux_eqs, eq)
case "uy":
ct_uy_eqs = append(ct_uy_eqs, eq)
case "pl":
ct_pl_eqs = append(ct_pl_eqs, eq)
default:
tst.Errorf("key %s is incorrect", c.Key)
}
}
sort.Ints(ct_ux_eqs)
sort.Ints(ct_uy_eqs)
sort.Ints(ct_pl_eqs)
chk.Ints(tst, "equations with ux prescribed", ct_ux_eqs, []int{0, 3, 6, 9, 14, 18, 22, 25, 28, 32, 36, 39, 42, 46, 50, 53, 56, 60})
chk.Ints(tst, "equations with uy prescribed", ct_uy_eqs, []int{1, 4, 13})
chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{2, 5})
}
// initial values @ nodes
io.Pforan("initial values @ nodes\n")
for _, nod := range dom.Nodes {
z := nod.Vert.C[1]
for _, dof := range nod.Dofs {
u := dom.Sol.Y[dof.Eq]
switch dof.Key {
case "ux":
chk.Scalar(tst, io.Sf("nod %3d : ux(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
case "uy":
chk.Scalar(tst, io.Sf("nod %3d : uy(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
case "pl":
plC, _, _ := Global.HydroSt.Calc(z)
chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-13, u, plC)
}
}
}
// intial values @ integration points
io.Pforan("initial values @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemUP)
for idx, ip := range e.P.IpsElem {
s := e.P.States[idx]
z := e.P.Shp.IpRealCoords(e.P.X, ip)[1]
chk.AnaNum(tst, io.Sf("sl(z=%11.8f)", z), 1e-17, s.A_sl, 1, chk.Verbose)
}
}
// parameters
ν := 0.2 // Poisson's coefficient
K0 := ν / (1.0 - ν) // earth pressure at rest
nf := 0.3 // porosity
sl := 1.0 // saturation
ρL := 1.0 // intrinsic (real) density of liquid
ρS_top := 2.0 // intrinsic (real) density of solids in top layer
ρS_bot := 3.0 // intrinsic (real) density of solids in bottom layer
h := 5.0 // height of each layer
g := 10.0 // gravity
// densities
nl := nf * sl // volume fraction of luqid
ns := 1.0 - nf // volume fraction of solid
ρl := nl * ρL // partial density of liquid
ρs_top := ns * ρS_top // partial density of solids in top layer
ρs_bot := ns * ρS_bot // partial density of solids in bottom layer
ρ_top := ρl + ρs_top // density of mixture in top layer
ρ_bot := ρl + ρs_bot // density of mixture in bottom layer
// absolute values of stresses
σV_z5 := ρ_top * g * h // total vertical stress @ elevation z = 5 m (absolute value)
σV_z0 := σV_z5 + ρ_bot*g*h // total vertical stress @ elevation z = 0 m (absolute value)
io.Pfyel("ρ_top = %g\n", ρ_top)
io.Pfyel("ρ_bot = %g\n", ρ_bot)
io.Pfyel("|ΔσV_top| = %g\n", ρ_top*g*h)
io.Pfyel("|ΔσV_bot| = %g\n", ρ_bot*g*h)
io.PfYel("|σV|(@ z=0) = %g\n", σV_z0)
io.PfYel("|σV|(@ z=5) = %g\n", σV_z5)
// stress functions
var sig fun.Pts
var pres fun.Pts
sig.Init(fun.Prms{
&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: -σV_z0},
&fun.Prm{N: "t1", V: 5.00}, {N: "y1", V: -σV_z5},
&fun.Prm{N: "t2", V: 10.00}, {N: "y2", V: 0.0},
})
pres.Init(fun.Prms{
&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: 100},
&fun.Prm{N: "t1", V: 10.00}, {N: "y1", V: 0},
})
// check stresses
io.Pforan("initial stresses @ integration points\n")
for _, ele := range dom.Elems {
e := ele.(*ElemUP)
for idx, ip := range e.U.IpsElem {
z := e.U.Shp.IpRealCoords(e.U.X, ip)[1]
σe := e.U.States[idx].Sig
sv := sig.F(z, nil)
sve := sv + pres.F(z, nil)
she := sve * K0
if math.Abs(σe[2]-σe[0]) > 1e-17 {
tst.Errorf("[1;31mσx is not equal to σz: %g != %g[0m\n", σe[2], σe[0])
return
}
if math.Abs(σe[3]) > 1e-17 {
tst.Errorf("[1;31mσxy is not equal to zero: %g != 0[0m\n", σe[3])
return
}
chk.AnaNum(tst, io.Sf("sx(z=%11.8f)", z), 0.0003792, σe[0], she, chk.Verbose)
chk.AnaNum(tst, io.Sf("sy(z=%11.8f)", z), 0.001517, σe[1], sve, chk.Verbose)
}
}
return
}
func Test_int02(tst *testing.T) {
//verbose()
chk.PrintTitle("int02. TSP")
// location / coordinates of stations
locations := [][]float64{
{60, 200}, {180, 200}, {80, 180}, {140, 180}, {20, 160}, {100, 160}, {200, 160},
{140, 140}, {40, 120}, {100, 120}, {180, 100}, {60, 80}, {120, 80}, {180, 60},
{20, 40}, {100, 40}, {200, 40}, {20, 20}, {60, 20}, {160, 20},
}
nstations := len(locations)
// parameters
C := NewConfParams()
C.Nova = 1
C.Noor = 0
C.Nisl = 4
C.Ninds = 24
C.RegTol = 0.3
C.RegPct = 0.2
//C.Dtmig = 30
C.GAtype = "crowd"
C.ParetoPhi = 0.1
C.Elite = false
C.DoPlot = false //chk.Verbose
//C.Rws = true
C.SetIntOrd(nstations)
C.CalcDerived()
// initialise random numbers generator
rnd.Init(0)
// objective value function
C.OvaOor = func(ind *Individual, idIsland, t int, report *bytes.Buffer) {
L := locations
ids := ind.Ints
//io.Pforan("ids = %v\n", ids)
dist := 0.0
for i := 1; i < nstations; i++ {
a, b := ids[i-1], ids[i]
dist += math.Sqrt(math.Pow(L[b][0]-L[a][0], 2.0) + math.Pow(L[b][1]-L[a][1], 2.0))
}
a, b := ids[nstations-1], ids[0]
dist += math.Sqrt(math.Pow(L[b][0]-L[a][0], 2.0) + math.Pow(L[b][1]-L[a][1], 2.0))
ind.Ovas[0] = dist
return
}
// evolver
evo := NewEvolver(C)
// print initial population
pop := evo.Islands[0].Pop
//io.Pf("\n%v\n", pop.Output(nil, false))
// 0,4,8,11,14,17,18,15,12,19,13,16,10,6,1,3,7,9,5,2 894.363
if false {
for i, x := range []int{0, 4, 8, 11, 14, 17, 18, 15, 12, 19, 13, 16, 10, 6, 1, 3, 7, 9, 5, 2} {
pop[0].Ints[i] = x
}
evo.Islands[0].CalcOvs(pop, 0)
evo.Islands[0].CalcDemeritsAndSort(pop)
}
// check initial population
ints := make([]int, nstations)
if false {
for i := 0; i < C.Ninds; i++ {
for j := 0; j < nstations; j++ {
ints[j] = pop[i].Ints[j]
}
sort.Ints(ints)
chk.Ints(tst, "ints", ints, utl.IntRange(nstations))
}
}
// run
evo.Run()
//io.Pf("%v\n", pop.Output(nil, false))
io.Pfgreen("best = %v\n", evo.Best.Ints)
io.Pfgreen("best OVA = %v (871.117353844847)\n\n", evo.Best.Ovas[0])
// best = [18 17 14 11 8 4 0 2 5 9 12 7 6 1 3 10 16 13 19 15]
// best OVA = 953.4643474956656
// best = [8 11 14 17 18 15 12 19 16 13 10 6 1 3 7 9 5 2 0 4]
// best OVA = 871.117353844847
// best = [5 2 0 4 8 11 14 17 18 15 12 19 16 13 10 6 1 3 7 9]
// best OVA = 871.1173538448469
// best = [6 10 13 16 19 15 18 17 14 11 8 4 0 2 5 9 12 7 3 1]
// best OVA = 880.7760751923065
// check final population
if false {
for i := 0; i < C.Ninds; i++ {
for j := 0; j < nstations; j++ {
ints[j] = pop[i].Ints[j]
}
sort.Ints(ints)
chk.Ints(tst, "ints", ints, utl.IntRange(nstations))
}
}
// plot travelling salesman path
if C.DoPlot {
plt.SetForEps(1, 300)
X, Y := make([]float64, nstations), make([]float64, nstations)
for k, id := range evo.Best.Ints {
X[k], Y[k] = locations[id][0], locations[id][1]
plt.PlotOne(X[k], Y[k], "'r.', ms=5, clip_on=0, zorder=20")
plt.Text(X[k], Y[k], io.Sf("%d", id), "fontsize=7, clip_on=0, zorder=30")
}
plt.Plot(X, Y, "'b-', clip_on=0, zorder=10")
plt.Plot([]float64{X[0], X[nstations-1]}, []float64{Y[0], Y[nstations-1]}, "'b-', clip_on=0, zorder=10")
plt.Equal()
plt.AxisRange(10, 210, 10, 210)
plt.Gll("$x$", "$y$", "")
plt.SaveD("/tmp/goga", "test_evo04.eps")
}
}