func Test_invs07(tst *testing.T) {
//verbose()
chk.PrintTitle("invs07")
smp_a, smp_b, smp_β, smp_ϵ := -1.0, 0.0, 1.0, 1e-3
σ := []float64{-1, -1, 0, 0}
pcam, qcam, _ := M_pqw(σ)
poct, qoct := pcam*SQ3, qcam*SQ2by3
N := make([]float64, 3)
n := make([]float64, 3)
m := SmpDirector(N, σ, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n, m, N)
psmp1, qsmp1, err := GenInvs(σ, n, smp_a)
if err != nil {
chk.Panic("M_GenInvs failed:\n%v", err)
}
psmp2, qsmp2, err := M_pq_smp(σ, smp_a, smp_b, smp_β, smp_ϵ)
if err != nil {
chk.Panic("M_pq_smp failed:\n%v", err)
}
io.Pforan("pcam, qcam = %v, %v\n", pcam, qcam)
io.Pforan("poct, qoct = %v, %v\n", poct, qoct)
io.Pforan("psmp1, qsmp1 = %v, %v\n", psmp1, qsmp1)
io.Pforan("psmp2, qsmp2 = %v, %v\n", psmp2, qsmp2)
chk.Scalar(tst, "p", 1e-15, psmp1, psmp2)
chk.Scalar(tst, "q", 1e-15, qsmp1, qsmp2)
}
// ReadMsh reads .msh file
func ReadMsh(fnk string) (nurbss []*Nurbs) {
// read file
fn := fnk + ".msh"
buf, err := io.ReadFile(fn)
if err != nil {
chk.Panic("ReadMsh cannot read file = '%s', %v'", fn, err)
}
// decode
var dat Data
err = json.Unmarshal(buf, &dat)
if err != nil {
chk.Panic("ReadMsh cannot unmarshal file = '%s', %v'", fn, err)
}
// list of vertices
verts := make([][]float64, len(dat.Verts))
for i, _ := range dat.Verts {
verts[i] = make([]float64, 4)
for j := 0; j < 4; j++ {
verts[i][j] = dat.Verts[i].C[j]
}
}
// allocate NURBSs
nurbss = make([]*Nurbs, len(dat.Nurbss))
for i, v := range dat.Nurbss {
nurbss[i] = new(Nurbs)
nurbss[i].Init(v.Gnd, v.Ords, v.Knots)
nurbss[i].SetControl(verts, v.Ctrls)
}
return
}
// HashPoint returns a unique id of a point
func HashPoint(x, xmin, xdel []float64, tol float64) int {
if tol < 1e-15 {
chk.Panic("HashPoint: minimum tolerance must be 1e-15. %v is invalid", tol)
}
coefs := []float64{11, 101, 1001}
n := utl.Imin(len(x), 3)
var hash, xbar float64
for i := 0; i < n; i++ {
if x[i] < xmin[i] {
chk.Panic("HashPoint: coordinate is outside range: %v < %v", x[i], xmin[i])
}
if x[i] > xmin[i]+xdel[i] {
chk.Panic("HashPoint: coordinate is outside range: %v > %v", x[i], xmin[i]+xdel[i])
}
if xdel[i] > 0 {
xbar = (x[i] - xmin[i]) / xdel[i]
if xbar < 0 {
xbar = 0
}
if xbar > 1 {
xbar = 1
}
hash += (xbar / tol) * coefs[i]
}
}
return int(hash)
}
func Test_up01b(tst *testing.T) {
// capture errors and flush log
defer End()
//verbose()
chk.PrintTitle("up01b")
// start simulation
if !Start("data/up01.sim", true, chk.Verbose) {
chk.Panic("cannot start simulation")
}
// for debugging Kb
if true {
defer up_DebugKb(&testKb{
tst: tst, eid: 3, tol: 1e-8, verb: chk.Verbose,
ni: 1, nj: 1, itmin: 1, itmax: -1, tmin: 800, tmax: 1000,
})()
}
// run simulation
if !Run() {
chk.Panic("cannot run simulation\n")
}
}
func Test_brent03(tst *testing.T) {
//verbose()
chk.PrintTitle("brent03. minimum finding")
ffcn := func(x float64) (res float64, err error) {
return x*x*x - 2.0*x - 5.0, nil
}
var o Brent
o.Init(ffcn)
xa, xb := 0.0, 1.0
x, err := o.Min(xa, xb, false)
if err != nil {
chk.Panic("%v", err)
}
y, err := ffcn(x)
if err != nil {
chk.Panic("%v", err)
}
xcor := math.Sqrt(2.0 / 3.0)
io.Pforan("x = %v (correct=%g)\n", x, xcor)
io.Pforan("f(x) = %v\n", y)
io.Pforan("nfeval = %v\n", o.NFeval)
io.Pforan("nit = %v\n", o.It)
//save := true
save := false
PlotYxe(ffcn, "results", "brent03.png", x, -1, 3, 101, "Brent", "'b-'", save, false, nil)
chk.Scalar(tst, "xcorrect", 1e-8, x, xcor)
}
func ltqnorm(p float64) float64 {
LOW := 0.02425
HIGH := 0.97575
var q, r float64
if p < 0 || p > 1 {
chk.Panic("input value (%g) is outside allowed range [0, 1]", p)
} else if p == 0 {
chk.Panic("p==0 => -infinity")
} else if p == 1 {
chk.Panic("p==1 => infinity")
} else if p < LOW {
/* Rational approximation for lower region */
q = math.Sqrt(-2 * math.Log(p))
return (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q + c[5]) /
((((d[0]*q+d[1])*q+d[2])*q+d[3])*q + 1)
} else if p > HIGH {
/* Rational approximation for upper region */
q = math.Sqrt(-2 * math.Log(1-p))
return -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q + c[5]) /
((((d[0]*q+d[1])*q+d[2])*q+d[3])*q + 1)
} else {
/* Rational approximation for central region */
q = p - 0.5
r = q * q
return (((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r + a[5]) * q /
(((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r + 1)
}
return 0
}
// Init initialises this structure
func (o *DynCoefs) Init(dat *inp.SolverData) {
// hmin
o.hmin = dat.DtMin
// HHT
o.HHT = dat.HHT
// θ-method
o.θ = dat.Theta
if o.θ < 1e-5 || o.θ > 1.0 {
chk.Panic("θ-method requires 1e-5 <= θ <= 1.0 (θ = %v is incorrect)", o.θ)
}
// HHT method
if dat.HHT {
o.α = dat.HHTalp
if o.α < -1.0/3.0 || o.α > 0.0 {
chk.Panic("HHT method requires: -1/3 <= α <= 0 (α = %v is incorrect)", o.α)
}
o.θ1 = (1.0 - 2.0*o.α) / 2.0
o.θ2 = (1.0 - o.α) * (1.0 - o.α) / 2.0
// Newmark's method
} else {
o.θ1, o.θ2 = dat.Theta1, dat.Theta2
if o.θ1 < 0.0001 || o.θ1 > 1.0 {
chk.Panic("θ1 must be between 0.0001 and 1.0 (θ1 = %v is incorrect)", o.θ1)
}
if o.θ2 < 0.0001 || o.θ2 > 1.0 {
chk.Panic("θ2 must be between 0.0001 and 1.0 (θ2 = %v is incorrect)", o.θ2)
}
}
}
func Test_basicgeom05(tst *testing.T) {
//verbose()
chk.PrintTitle("basicgeom05")
zero := 1e-1
told := 1e-9
tolin := 1e-3
o := &Point{0, 0, 0}
a := &Point{0.5, 0.5, 0.5}
b := &Point{0.1, 0.5, 0.8}
c := &Point{1, 1, 1}
cmin, cmax := PointsLims([]*Point{o, a, b, c})
chk.Vector(tst, "cmin", 1e-17, cmin, []float64{0, 0, 0})
chk.Vector(tst, "cmax", 1e-17, cmax, []float64{1, 1, 1})
if !IsPointIn(a, cmin, cmax, zero) {
chk.Panic("a=%v must be in box")
}
if !IsPointIn(b, cmin, cmax, zero) {
chk.Panic("b=%v must be in box")
}
if !IsPointIn(c, cmin, cmax, zero) {
chk.Panic("c=%v must be in box")
}
p := &Point{0.5, 0.5, 0.5}
q := &Point{1.5, 1.5, 1.5}
if !IsPointInLine(p, o, c, zero, told, tolin) {
chk.Panic("p=%v must be in line")
}
if IsPointInLine(q, o, c, zero, told, tolin) {
chk.Panic("q=%v must not be in line")
}
}
// ReadLines reads lines from a file and calls ReadLinesCallback to process each line being read
func ReadLines(fn string, cb ReadLinesCallback) {
fil, err := os.Open(os.ExpandEnv(fn))
if err != nil {
chk.Panic(_fileio_err05, fn)
}
defer fil.Close()
r := bufio.NewReader(fil)
idx := 0
for {
lin, prefix, errl := r.ReadLine()
if prefix {
chk.Panic(_fileio_err06, fn)
}
if errl == io.EOF {
break
}
if errl != nil {
chk.Panic(_fileio_err07, fn)
}
stop := cb(idx, string(lin))
if stop {
break
}
idx++
}
}
func Test_smpinvs01(tst *testing.T) {
//verbose()
chk.PrintTitle("smpinvs01")
a, b, β, ϵ := -1.0, 0.5, 1e-3, 1e-3
L := []float64{-8.0, -8.0, -8.0}
N := make([]float64, 3)
n := make([]float64, 3)
m := SmpDirector(N, L, a, b, β, ϵ)
SmpUnitDirector(n, m, N)
io.Pforan("L = %v\n", L)
io.Pforan("N = %v\n", N)
io.Pforan("m = %v\n", m)
io.Pforan("n = %v\n", n)
chk.Vector(tst, "n", 1e-15, n, []float64{a / SQ3, a / SQ3, a / SQ3})
p, q, err := GenInvs(L, n, a)
if err != nil {
chk.Panic("GenInvs failed:\n%v", err.Error())
}
io.Pforan("p = %v\n", p)
io.Pforan("q = %v\n", q)
if q < 0.0 || q > GENINVSQEPS {
chk.Panic("q=%g is incorrect", q)
}
if math.Abs(p-a*L[0]) > 1e-14 {
chk.Panic("p=%g is incorrect. err = %g", p, math.Abs(p-a*L[0]))
}
}
// IntegOnPlane integrates the results of nodes located on a plane perpedicular to either {x,y,z}
// The mesh on the plane must be structured and with rectangle elements in order to build
// an {u,v} coordinates system
// Input:
// key -- node variable; e.g. "uz", "ex_sz"
// alias -- alias of plane; e.g. "surf"
// Output:
// res -- the result of the integration res = ∫_u ∫_v f(u,v) du dv for all output times
func IntegOnPlane(key, alias string) (res []float64) {
// get plane
plane, ok := Planes[alias]
if !ok {
chk.Panic("cannot get plane with alias=%q", alias)
}
// compute integral
res = make([]float64, len(TimeInds))
u := make([]float64, 2)
for idxI, k := range TimeInds {
for j := 0; j < plane.Nu[1]; j++ {
u[1] = plane.Umin[1] + float64(j)*plane.Du[1]
for i := 0; i < plane.Nu[0]; i++ {
u[0] = plane.Umin[0] + float64(i)*plane.Du[0]
id := plane.Ubins.Find(u)
if id < 0 {
chk.Panic("IntegOnPlane with key=%q and alias=%q\nError: cannot find {u,v} coordinate in any bin. u=%v vid/ipid=%d", key, alias, u, id)
}
vals, ok := plane.id2pt[id].Vals[key]
if !ok {
chk.Panic("cannot find results with key=%q for plane with alias=%q", key, alias)
}
plane.F[i][j] = vals[idxI]
}
}
res[k] = num.Simps2D(plane.Du[0], plane.Du[1], plane.F)
}
return
}
// Define defines aliases
// alias -- an alias to a group of points, an individual point, or to a set of points.
// Example: "A", "left-column" or "a b c". If the number of points found is different
// than the number of aliases, a group is created.
// Note:
// To use spaces in aliases, prefix the alias with an exclamation mark; e.g "!right column"
func Define(alias string, loc Locator) {
// check
if len(alias) < 1 {
chk.Panic("alias must have at least one character. %q is invalid", alias)
}
// set planes map
if plane, ok := loc.(*PlaneData); ok {
Planes[alias] = plane
defer func() {
plane.ConnectResults(alias)
}()
}
// locate points
pts := loc.Locate()
if len(pts) < 1 {
chk.Panic("cannot define entities with alias=%q and locator=%v", alias, loc)
}
// set results map
if alias[0] == '!' {
Results[alias[1:]] = pts
return
}
lbls := strings.Fields(alias)
if len(lbls) == len(pts) {
for i, l := range lbls {
Results[l] = []*Point{pts[i]}
}
return
}
Results[alias] = pts
}
func Test_matinvSmall01(tst *testing.T) {
//verbose()
chk.PrintTitle("matinvSmall01")
noise := 0.0
tol := 1.0e-16
// 1 x 1 matrix
res := MatAlloc(1, 1)
det, err := MatInv(res, [][]float64{{2.0}}, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "1 x 1 matrix: det ", tol, det, 2.0)
chk.Matrix(tst, "1 x 1 matrix: ", tol, res, [][]float64{{0.5}})
// matrix: inverse
A := [][]float64{{1.0, 2.0}, {3.0, 2.0}}
Aicorr := [][]float64{{-0.5, 0.5}, {0.75, -0.25 + noise}}
Ai := MatAlloc(2, 2)
detA, err := MatInv(Ai, A, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "matrix: inv (det) ", tol, detA, -4.0+noise)
chk.Matrix(tst, "matrix: inv (A) ", tol, Ai, Aicorr)
// using MatInvG
Ai_ := MatAlloc(2, 2)
err = MatInvG(Ai_, A, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Matrix(tst, "matrix: inv with MatInvG", tol, Ai_, Aicorr)
// another test
B := [][]float64{{9.0, 3.0, 5.0}, {-6.0, -9.0, 7.0}, {-1.0, -8.0, 1.0}}
Bicorr := [][]float64{
{7.642276422764227e-02, -6.991869918699187e-02, 1.073170731707317e-01},
{-1.626016260162601e-03, 2.276422764227642e-02, -1.512195121951219e-01},
{6.341463414634146e-02, 1.121951219512195e-01, -1.024390243902439e-01 + noise},
}
Bi := MatAlloc(3, 3)
detB, err := MatInv(Bi, B, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "matrix: det ", tol, detB, 615.0+noise)
chk.Matrix(tst, "matrix: inv ", tol, Bi, Bicorr)
// using MatInvG
Bi_ := MatAlloc(3, 3)
err = MatInvG(Bi_, B, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Matrix(tst, "matrix: inv with MatInvG", tol, Bi_, Bicorr)
}
func Test_frees01a(tst *testing.T) {
// finalise analysis process and catch errors
defer End()
//verbose()
chk.PrintTitle("frees01a")
// start simulation
if !Start("data/frees01.sim", true, chk.Verbose) {
chk.Panic("cannot start FE simulation")
}
// domain
distr := false
dom := NewDomain(Global.Sim.Regions[0], distr)
if dom == nil {
chk.Panic("cannot run FE simulation")
}
// set stage
if !dom.SetStage(0, Global.Sim.Stages[0], distr) {
chk.Panic("cannot set stage\n")
}
// nodes and elements
chk.IntAssert(len(dom.Nodes), 62)
chk.IntAssert(len(dom.Elems), 15)
// vertices with "fl"
seepverts := map[int]bool{3: true, 45: true, 7: true, 49: true, 11: true, 53: true, 15: true, 57: true, 19: true, 61: true, 23: true}
// check dofs
var seepeqs []int
for _, nod := range dom.Nodes {
if seepverts[nod.Vert.Id] {
chk.IntAssert(len(nod.Dofs), 2)
seepeqs = append(seepeqs, nod.Dofs[1].Eq)
} else {
chk.IntAssert(len(nod.Dofs), 1)
}
}
sort.Ints(seepeqs)
io.Pforan("seepeqs = %v\n", seepeqs)
chk.Ints(tst, "seepeqs", seepeqs, []int{14, 16, 19, 30, 32, 43, 45, 56, 58, 69, 71})
// check Fmap
e2 := dom.Elems[2].(*ElemP)
chk.Ints(tst, "e2.Fmap", e2.Fmap, []int{14, 16, 19})
e5 := dom.Elems[5].(*ElemP)
chk.Ints(tst, "e5.Fmap", e5.Fmap, []int{16, 30, 32})
e8 := dom.Elems[8].(*ElemP)
chk.Ints(tst, "e8.Fmap", e8.Fmap, []int{30, 43, 45})
e11 := dom.Elems[11].(*ElemP)
chk.Ints(tst, "e11.Fmap", e11.Fmap, []int{43, 56, 58})
e14 := dom.Elems[14].(*ElemP)
chk.Ints(tst, "e14.Fmap", e14.Fmap, []int{56, 69, 71})
}
// SetDefault sets default options for report
func NewTexReport(opts []*Optimiser) (o *TexReport) {
// new struct
o = new(TexReport)
// options
o.DirOut = "/tmp/goga"
o.Fnkey = "texreport"
o.Title = "Goga Report"
o.RefLabel = ""
o.TextSize = `\scriptsize \setlength{\tabcolsep}{0.5em}`
o.MiniPageSz = "4.1cm"
o.HistTextSize = `\fontsize{5pt}{6pt}`
o.Type = 4
o.NRowPerTab = -1
o.UseGeom = true
o.RunPDF = true
o.ShowNsol = false
o.ShowNcpu = false
o.ShowTmax = false
o.ShowDtExc = false
o.ShowDEC = false
o.ShowX01 = true
// constants
o.DroundCte = 0.001e9 // 0.0001e9
// input
o.Opts = opts
// buffers
o.buf = new(bytes.Buffer)
o.binp = new(bytes.Buffer)
o.bxres = new(bytes.Buffer)
// check
if len(o.Opts) < 1 {
chk.Panic("slice Opts must be set with at least one item")
}
if o.Type < 1 || o.Type > 4 {
chk.Panic("type of table must be in [1,4]")
}
// number of samples
o.nsamples = o.Opts[0].Nsamples
// symbol for f
o.symbF = o.Opts[0].RptWordF
if o.symbF == "" {
o.symbF = "f"
}
// flag
o.singleObj = o.Opts[0].Nova == 1
return
}
func Test_out02(tst *testing.T) {
// finalise analysis process and catch errors
defer func() {
if err := recover(); err != nil {
tst.Fail()
io.PfRed("ERROR: %v\n", err)
} else {
fem.End()
}
}()
// test title
//verbose()
chk.PrintTitle("out02")
// run FE simulation
if !fem.Start("data/twoqua4.sim", true, chk.Verbose) {
chk.Panic("cannot start FE simulation")
}
if !fem.Run() {
chk.Panic("cannot run FE simulation")
}
// start analysis process
Start("data/twoqua4.sim", 0, 0)
// get second ip coordinates
xip := Ipoints[1].X
io.Pfcyan("xip = %v\n", xip)
// define points
Define("A", N{-1})
Define("ips", Along{{xip[0], 0}, {xip[0], 1}})
// load results
LoadResults(nil)
// 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
x := GetCoords("A")
ux := GetRes("ux", "A", 0)
uy := GetRes("uy", "A", 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)
}
}
// WriteBytesToFile writes bytes to a new file
func WriteBytesToFile(fn string, b []byte) {
fil, err := os.Create(os.ExpandEnv(fn))
if err != nil {
chk.Panic(_fileio_err03, fn)
}
defer fil.Close()
if _, err = fil.Write(b); err != nil {
chk.Panic(_fileio_err04, err.Error())
}
}
func Test_bins02(tst *testing.T) {
//verbose()
chk.PrintTitle("bins02. find along line (2D)")
// bins
var bins Bins
bins.Init([]float64{-0.2, -0.2}, []float64{0.8, 1.8}, 5)
// fill bins structure
maxit := 5 // number of entries
ID := make([]int, maxit)
for k := 0; k < maxit; k++ {
x := float64(k) / float64(maxit)
ID[k] = k
err := bins.Append([]float64{x, 2*x + 0.2}, ID[k])
if err != nil {
chk.Panic(err.Error())
}
}
// add more points to bins
for i := 0; i < 5; i++ {
err := bins.Append([]float64{float64(i) * 0.1, 1.8}, 100+i)
if err != nil {
chk.Panic(err.Error())
}
}
// message
for _, bin := range bins.All {
if bin != nil {
io.Pf("%v\n", bin)
}
}
// find points along diagonal
ids := bins.FindAlongSegment([]float64{0.0, 0.2}, []float64{0.8, 1.8}, 1e-8)
io.Pforan("ids = %v\n", ids)
chk.Ints(tst, "ids", ids, ID)
// find additional points
ids = bins.FindAlongSegment([]float64{-0.2, 1.8}, []float64{0.8, 1.8}, 1e-8)
io.Pfcyan("ids = %v\n", ids)
chk.Ints(tst, "ids", ids, []int{100, 101, 102, 103, 104, 4})
// draw
if chk.Verbose {
plt.SetForPng(1, 500, 150)
bins.Draw2d(true, true, true, true, map[int]bool{8: true, 9: true, 10: true})
plt.SetXnticks(15)
plt.SetYnticks(15)
plt.SaveD("/tmp/gosl/gm", "test_bins02.png")
}
}
func RunMumpsTestC(t *TripletC, tol_cmp float64, b, x_correct []complex128, sum_b_to_root bool) {
// info
symmetric := false
verbose := false
timing := false
// allocate solver
lis := GetSolver("mumps")
defer lis.Clean()
// initialise solver
err := lis.InitC(t, symmetric, verbose, timing)
if err != nil {
chk.Panic("%v", err.Error())
}
// factorise
err = lis.Fact()
if err != nil {
chk.Panic("%v", err.Error())
}
// solve
bR, bC := ComplexToRC(b)
xR := make([]float64, len(b))
xC := make([]float64, len(b))
err = lis.SolveC(xR, xC, bR, bC, sum_b_to_root) // x := inv(A) * b
if err != nil {
chk.Panic("%v", err.Error())
}
x := RCtoComplex(xR, xC)
if mpi.Rank() == 0 {
// output
A := t.ToMatrix(nil)
io.Pforan("A.x = b\n")
PrintMatC("A", A.ToDense(), "(%g+", "%gi) ", false)
PrintVecC("x", x, "(%g+", "%gi) ", false)
PrintVecC("b", b, "(%g+", "%gi) ", false)
// check
xR_correct, xC_correct := ComplexToRC(x_correct)
errR := VecMaxDiff(xR, xR_correct)
if errR > tol_cmp {
chk.Panic("test failed: errR = %g", errR)
}
errC := VecMaxDiff(xC, xC_correct)
if errC > tol_cmp {
chk.Panic("test failed: errC = %g", errC)
}
io.Pf("err(xR) = %g [1;32mOK[0m\n", errR)
io.Pf("err(xC) = %g [1;32mOK[0m\n", errC)
}
}
// Read reads configuration parameters from JSON file
func (o *Parameters) Read(filenamepath string) {
o.Default()
b, err := io.ReadFile(filenamepath)
if err != nil {
chk.Panic("cannot read parameters file %q", filenamepath)
}
err = json.Unmarshal(b, o)
if err != nil {
chk.Panic("cannot unmarshal parameters file %q", filenamepath)
}
return
}
func Test_plot01(tst *testing.T) {
// test title
//verbose()
chk.PrintTitle("plot01")
// constants
datadir := "$GOPATH/src/github.com/cpmech/gofem/fem/data/"
simfn := "p02.sim"
// run FE simulation
defer fem.End()
if !fem.Start(datadir+simfn, true, chk.Verbose) {
chk.Panic("cannot start FE simulation")
}
if !fem.Run() {
chk.Panic("cannot run FE simulation")
}
// start post-processing
Start(datadir+simfn, 0, 0)
// define entities
Define("A", N{1})
Define("B", At{0, 1})
//Define("left", Along{{0, 0}, {0, 10}})
Define("left", AlongY{0}) // 0 => x_cte
// load results
LoadResults(nil)
plA := GetRes("pl", "A", 0)
Splot("liquid pressure")
Plot("t", "pl", "B", plt.Fmt{C: "b", M: "."}, -1)
Plot("t", plA, "A", plt.Fmt{C: "r", M: "."}, -1)
Splot("")
Plot("pl", "pl", "A", plt.Fmt{C: "k", M: "o"}, -1)
Splot("")
Plot("pl", "y", "left", plt.Fmt{C: "b", M: "o"}, 0)
Plot("pl", "y", "left", plt.Fmt{C: "g", M: "o"}, -1)
Splot("")
io.Pforan("T = %v\n", Times)
last := len(Times) - 1
Plot("y", "pl", "left", plt.Fmt{C: "b", M: "o", L: io.Sf("t=%g", Times[0])}, 0)
Plot("y", "pl", "left", plt.Fmt{C: "m", M: "*", Lw: 2, L: io.Sf("t=%g", Times[last])}, -1)
//Draw("", "", true, nil)
Draw("", "", false, nil)
}
// Krefine returns a new Nurbs with knots refined
// Note: X[gnd][numNewKnots]
func (o *Nurbs) Krefine(X [][]float64) (O *Nurbs) {
// check
if len(X) != o.gnd {
chk.Panic("size of new knots array X must be [gnd==%d][numNewKnots]. len==%d of first dimension is incorrect", o.gnd, len(X))
}
// number of new knots and first and last knots
nk, a, b := make([]int, 3), make([]int, 3), make([]int, 3)
for d := 0; d < o.gnd; d++ {
nk[d] = len(X[d])
a[d] = o.b[d].find_span(X[d][0])
b[d] = o.b[d].find_span(X[d][nk[d]-1])
}
// new knots array
Unew := make([][]float64, o.gnd)
Unew[0] = make([]float64, o.b[0].m+nk[0])
if o.gnd > 1 {
Unew[1] = make([]float64, o.b[1].m+nk[1])
}
if o.gnd > 2 {
Unew[2] = make([]float64, o.b[2].m+nk[2])
}
// refine
var Qnew [][][][]float64
switch o.gnd {
case 1:
Qnew = utl.Deep4alloc(o.n[0]+nk[0], o.n[1], o.n[2], 4)
krefine(Unew, Qnew, o.Q, 0, X[0], o.b[0].T, o.n, o.p, a[0], b[0])
case 2:
// along 0
Qtmp := utl.Deep4alloc(o.n[0]+nk[0], o.n[1], o.n[2], 4)
krefine(Unew, Qtmp, o.Q, 0, X[0], o.b[0].T, o.n, o.p, a[0], b[0])
// along 1
nn := make([]int, 3)
copy(nn, o.n)
nn[0] += nk[0]
Qnew = utl.Deep4alloc(nn[0], o.n[1]+nk[1], o.n[2], 4)
krefine(Unew, Qnew, Qtmp, 1, X[1], o.b[1].T, nn, o.p, a[1], b[1])
case 3:
chk.Panic("nurbs.go: Krefine: gnd=3 not implemented yet")
}
// initialize new nurbs
O = new(Nurbs)
O.Init(o.gnd, o.p, Unew)
O.Q = Qnew
return
}
// SpTriMatTrVecMul returns the matrix-vector multiplication with transposed matrix a in
// triplet format and two dense vectors x and y
// y := transpose(a) * x or y_I := a_JI * x_J or y_j := a_ij * x_i
func SpTriMatTrVecMul(y []float64, a *Triplet, x []float64) {
if len(y) != a.n {
chk.Panic("length of vector y must be equal to %d. y_(%d × 1). a_(%d × %d)", a.n, len(y), a.m, a.n)
}
if len(x) != a.m {
chk.Panic("length of vector x must be equal to %d. x_(%d × 1). a_(%d × %d)", a.m, len(x), a.m, a.n)
}
for j := 0; j < len(y); j++ {
y[j] = 0
}
for k := 0; k < a.pos; k++ {
y[a.j[k]] += a.x[k] * x[a.i[k]]
}
}
// Set sets column-compressed matrix directly
func (o *CCMatrix) Set(m, n int, Ap, Ai []int, Ax []float64) {
if len(Ap)-1 != n {
chk.Panic("len(Ap) must be equal to n. %d != %d", len(Ap), n)
}
nnz := len(Ai)
if len(Ax) != nnz {
chk.Panic("len(Ax) must be equal to len(Ai) == nnz. %d != %d", len(Ax), nnz)
}
if Ap[n] != nnz {
chk.Panic("last item in Ap must be equal to nnz. %d != %d", Ap[n], nnz)
}
o.m, o.n, o.nnz = m, n, nnz
o.p, o.i, o.x = Ap, Ai, Ax
}
// CheckEigenprojsDerivs checks the derivatives of eigen projectors w.r.t defining tensor
func CheckEigenprojsDerivs(a []float64, tol float64, ver bool, zero float64) {
// compute eigenvalues and eigenprojectors
ncp := len(a)
λ := make([]float64, 3)
P := la.MatAlloc(3, ncp)
docalc := func() {
err := M_EigenValsProjsNum(P, λ, a)
if err != nil {
chk.Panic("eigenprojs.go: CheckEigenprojsDerivs failed:\n %v", err.Error())
}
}
// compute derivatives of eigenprojectors
docalc()
dPda := utl.Deep3alloc(3, ncp, ncp)
err := M_EigenProjsDerivAuto(dPda, a, λ, P)
if err != nil {
chk.Panic("%v", err)
}
// check
var tmp float64
has_error := false
for k := 0; k < 3; k++ {
for i := 0; i < ncp; i++ {
for j := 0; j < ncp; j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
docalc()
a[j] = tmp
return P[k][i]
}, a[j], 1e-6)
err := chk.PrintAnaNum(io.Sf("dP%d[%d]/da[%d]", k, i, j), tol, dPda[k][i][j], dnum, ver)
if err != nil {
has_error = true
}
}
}
if ver {
io.Pf("\n")
}
}
if has_error {
chk.Panic(_eigenprojs_err8)
}
return
}
// NewData allocates and initialises a new FEM data structure
func NewData(fnkey string, cpu int) *FemData {
// load data
var o FemData
buf, err := io.ReadFile("od-" + fnkey + ".json")
if err != nil {
chk.Panic("cannot load data:\n%v", err)
}
err = json.Unmarshal(buf, &o)
if err != nil {
chk.Panic("cannot unmarshal data:\n%v", err)
}
// load FEM data
o.Analysis = fem.NewMain(fnkey+".sim", io.Sf("cpu%d", cpu), false, false, false, false, false, cpu)
o.Dom = o.Analysis.Domains[0]
o.Sim = o.Dom.Sim
o.Vars = o.Dom.Sim.AdjRandom
// backup dependent variables
for _, prm := range o.Sim.AdjDependent {
prm.S = prm.V // copy V into S
}
// set stage
err = o.Analysis.SetStage(0)
if err != nil {
chk.Panic("cannot set stage:\n%v", err)
}
// equations to track U
verts := o.Dom.Msh.Verts
if o.VtagU < 0 {
verts = o.Dom.Msh.VertTag2verts[o.VtagU]
if len(verts) < 1 {
chk.Panic("cannot find vertices with tag = %d\n", o.VtagU)
}
}
o.EqsU = make([]int, len(verts))
for i, vert := range verts {
eq := o.Dom.Vid2node[vert.Id].GetEq(o.Ukey)
if eq < 0 {
chk.Panic("cannot find equation corresponding to vertex id=%d and ukey=%q", vert.Id, o.Ukey)
}
o.EqsU[i] = eq
}
return &o
}
// GenerateCxEnds randomly computes the end positions of cuts in chromosomes
// Input:
// size -- size of chromosome
// ncuts -- number of cuts to be used, unless cuts != nil
// cuts -- cut positions. can be nil => use ncuts instead
// Output:
// ends -- end positions where the last one equals size
// Example:
// 0 1 2 3 4 5 6 7
// A = a b c d e f g h size = 8
// ↑ ↑ ↑ cuts = [1, 5]
// 1 5 8 ends = [1, 5, 8]
func GenerateCxEnds(size, ncuts int, cuts []int) (ends []int) {
// handle small slices
if size < 2 {
return
}
if size == 2 {
return []int{1, size}
}
// cuts slice is given
if len(cuts) > 0 {
ncuts = len(cuts)
ends = make([]int, ncuts+1)
ends[ncuts] = size
for i, cut := range cuts {
if cut < 1 || cut >= size {
chk.Panic("cut=%d is outside the allowed range: 1 ≤ cut ≤ size-1", cut)
}
if i > 0 {
if cut == cuts[i-1] {
chk.Panic("repeated cut values are not allowed: cuts=%v", cuts)
}
}
ends[i] = cut
}
sort.Ints(ends)
return
}
// randomly generate cuts
if ncuts < 1 {
ncuts = 1
}
if ncuts >= size {
ncuts = size - 1
}
ends = make([]int, ncuts+1)
ends[ncuts] = size
// pool of values for selections
pool := rnd.IntGetUniqueN(1, size, ncuts)
sort.Ints(pool)
for i := 0; i < ncuts; i++ {
ends[i] = pool[i]
}
return
}
func check_repeated(v []int) {
for i := 1; i < len(v); i++ {
if v[i] == v[i-1] {
chk.Panic("there are repeated entries in v = %v", v)
}
}
}
// Put inserts an element to a pre-allocated (with Init) triplet matrix
func (t *Triplet) Put(i, j int, x float64) {
if t.pos >= t.max {
chk.Panic("cannot put item because max number of items has been exceeded (pos = %d, max = %d)", t.pos, t.max)
}
t.i[t.pos], t.j[t.pos], t.x[t.pos] = i, j, x
t.pos++
}
// Locate finds nodes
func (o N) Locate() (res Points) {
var A []float64 // reference point
for _, idortag := range o {
if idortag < 0 {
tag := idortag
verts := Dom.Msh.VertTag2verts[tag]
for _, v := range verts {
q := get_nod_point(v.Id, A)
if q != nil {
res = append(res, q)
if A == nil {
A = q.X
}
}
}
} else {
vid := idortag
q := get_nod_point(vid, A)
if q != nil {
res = append(res, q)
if A == nil {
A = q.X
}
}
}
}
if len(res) < len(o) {
chk.Panic("cannot locate all nodes in %v", o)
}
return
}
