// CheckDerivT checks derivatives w.r.t to t for fixed coordinates x
func CheckDerivT(tst *testing.T, o Func, t0, tf float64, xcte []float64, np int, tskip []float64, sktol, dtol, dtol2 float64, ver bool) {
t := utl.LinSpace(t0, tf, np)
for i := 0; i < np; i++ {
g := o.G(t[i], xcte)
h := o.H(t[i], xcte)
skip := false
for _, val := range tskip {
if math.Abs(val-t[i]) < sktol {
skip = true
break
}
}
if skip {
continue
}
dnum := num.DerivCen(func(t float64, args ...interface{}) (res float64) {
return o.F(t, xcte)
}, t[i])
chk.AnaNum(tst, io.Sf("G(%10f)", t[i]), dtol, g, dnum, ver)
dnum2 := num.DerivCen(func(t float64, args ...interface{}) (res float64) {
return o.G(t, xcte)
}, t[i])
chk.AnaNum(tst, io.Sf("H(%10f)", t[i]), dtol2, h, dnum2, ver)
}
}
// CheckDerivs compares analytical with numerical derivatives
func (o *Nurbs) CheckDerivs(tst *testing.T, nn int, tol float64, ver bool) {
dana := make([]float64, 2)
dnum := make([]float64, 2)
for _, u := range utl.LinSpace(o.b[0].tmin, o.b[0].tmax, nn) {
for _, v := range utl.LinSpace(o.b[1].tmin, o.b[1].tmax, nn) {
uu := []float64{u, v}
o.CalcBasisAndDerivs(uu)
for i := 0; i < o.n[0]; i++ {
for j := 0; j < o.n[1]; j++ {
l := i + j*o.n[0]
o.GetDerivL(dana, l)
o.NumericalDeriv(dnum, uu, l)
chk.AnaNum(tst, io.Sf("dR[%d][%d][0](%g,%g)", i, j, uu[0], uu[1]), tol, dana[0], dnum[0], ver)
chk.AnaNum(tst, io.Sf("dR[%d][%d][1](%g,%g)", i, j, uu[0], uu[1]), tol, dana[1], dnum[1], ver)
}
}
}
}
}
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)
}
}
}
// CheckDerivX checks derivatives w.r.t to x for fixed t
func CheckDerivX(tst *testing.T, o Func, tcte float64, xmin, xmax []float64, np int, xskip [][]float64, sktol, dtol float64, ver bool) {
ndim := len(xmin)
dx := make([]float64, ndim)
for i := 0; i < ndim; i++ {
dx[i] = (xmax[i] - xmin[i]) / float64(np-1)
}
x := make([]float64, ndim)
g := make([]float64, ndim)
nz := 1
if ndim == 3 {
nz = np
}
xtmp := make([]float64, ndim)
for k := 0; k < nz; k++ {
if ndim == 3 {
x[2] = xmin[2] + float64(k)*dx[2]
}
for j := 0; j < np; j++ {
x[1] = xmin[1] + float64(j)*dx[1]
for i := 0; i < np; i++ {
x[0] = xmin[0] + float64(i)*dx[0]
o.Grad(g, tcte, x)
for l := 0; l < ndim; l++ {
skip := false
for _, val := range xskip {
if math.Abs(val[l]-x[l]) < sktol {
skip = true
break
}
}
if skip {
continue
}
dnum := num.DerivCen(func(s float64, args ...interface{}) (res float64) {
copy(xtmp, x)
xtmp[l] = s
return o.F(tcte, xtmp)
}, x[l])
chk.AnaNum(tst, io.Sf("dFdX(t,%10v)[%d]", x, l), dtol, g[l], dnum, ver)
}
}
}
}
}
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)
}
}
}
// check performs the checking of Kb using numerical derivatives
func (o *testKb) check(label string, d *Domain, e Elem, Imap, Jmap []int, Kana [][]float64, restore func()) {
var imap, jmap []int
if o.ni < 0 {
imap = Imap
} else {
if o.ni <= len(Imap) {
imap = Imap[:o.ni]
}
}
if o.nj < 0 {
jmap = Jmap
} else {
if o.nj <= len(Jmap) {
jmap = Jmap[:o.nj]
}
}
step := 1e-6
//derivfcn := num.DerivForward
//derivfcn := num.DerivBackward
derivfcn := num.DerivCentral
var tmp float64
for i, I := range imap {
for j, J := range jmap {
dnum, _ := derivfcn(func(x float64, args ...interface{}) (res float64) {
tmp, d.Sol.Y[J] = d.Sol.Y[J], x
for k := 0; k < d.Ny; k++ {
o.Fbtmp[k] = 0
d.Sol.ΔY[k] = d.Sol.Y[k] - o.Yold[k]
}
restore()
e.Update(d.Sol)
e.AddToRhs(o.Fbtmp, d.Sol)
res = -o.Fbtmp[I]
d.Sol.Y[J] = tmp
return res
}, d.Sol.Y[J], step)
chk.AnaNum(o.tst, io.Sf(label+"%3d%3d", i, j), o.tol, Kana[i][j], dnum, o.verb)
}
}
}
// testing_compare_results_u compares results with u-formulation
func TestingCompareResultsU(tst *testing.T, simfname, cmpfname string, tolK, tolu, tols float64, skipK, verbose bool) {
// only root can run this test
if !Global.Root {
return
}
// read summary
sum := ReadSum(Global.Dirout, Global.Fnkey)
if sum == nil {
tst.Error("cannot read summary file for simulation=%q\n", simfname)
return
}
// allocate domain
distr := false
d := NewDomain(Global.Sim.Regions[0], distr)
if !d.SetStage(0, Global.Sim.Stages[0], distr) {
tst.Errorf("TestingCompareResultsU: SetStage failed\n")
return
}
// read file
buf, err := io.ReadFile(cmpfname)
if err != nil {
tst.Errorf("TestingCompareResultsU: ReadFile failed\n")
return
}
// unmarshal json
var cmp_set T_results_set
err = json.Unmarshal(buf, &cmp_set)
if err != nil {
tst.Errorf("TestingCompareResultsU: Unmarshal failed\n")
return
}
// run comparisons
dmult := 1.0
for idx, cmp := range cmp_set {
// displacements multiplier
if idx == 0 && math.Abs(cmp.DispMult) > 1e-10 {
dmult = cmp.DispMult
}
// time index
tidx := idx + 1
if verbose {
io.PfYel("\n\ntidx = %d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", tidx)
}
// load gofem results
if !d.In(sum, tidx, true) {
tst.Errorf("TestingCompareResultsU: reading of results failed\n")
return
}
if verbose {
io.Pfyel("time = %v\n", d.Sol.T)
}
// check K matrices
if !skipK {
if verbose {
io.Pfgreen(". . . checking K matrices . . .\n")
}
for eid, Ksg := range cmp.Kmats {
if e, ok := d.Elems[eid].(*ElemU); ok {
if !e.AddToKb(d.Kb, d.Sol, true) {
tst.Errorf("TestingCompareResultsU: AddToKb failed\n")
return
}
chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
}
}
}
// check displacements
if verbose {
io.Pfgreen(". . . checking displacements . . .\n")
}
for nid, usg := range cmp.Disp {
ix := d.Vid2node[nid].Dofs[0].Eq
iy := d.Vid2node[nid].Dofs[1].Eq
chk.AnaNum(tst, "ux", tolu, d.Sol.Y[ix], usg[0]*dmult, verbose)
chk.AnaNum(tst, "uy", tolu, d.Sol.Y[iy], usg[1]*dmult, verbose)
if len(usg) == 3 {
iz := d.Vid2node[nid].Dofs[2].Eq
chk.AnaNum(tst, "uz", tolu, d.Sol.Y[iz], usg[2]*dmult, verbose)
}
}
// check stresses
if true {
if verbose {
io.Pfgreen(". . . checking stresses . . .\n")
}
for eid, sig := range cmp.Sigmas {
if verbose {
io.Pforan("eid = %d\n", eid)
}
if e, ok := d.Cid2elem[eid].(*ElemU); ok {
for ip, val := range sig {
if verbose {
io.Pfgrey2("ip = %d\n", ip)
}
σ := e.States[ip].Sig
if len(val) == 6 {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
} else {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
chk.AnaNum(tst, "sxy", tols, σ[3]/SQ2, val[2], verbose)
if len(val) > 3 { // sx, sy, sxy, sz
chk.AnaNum(tst, "sz ", tols, σ[2], val[3], verbose)
}
}
}
}
}
}
}
}
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_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_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)
}
}
}
}
}
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_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_noncteM01(tst *testing.T) {
//verbose()
chk.PrintTitle("noncteM01")
prms := []string{"φ", "Mfix"}
vals := []float64{32, 0}
var o NcteM
o.Init(prms, vals)
// check
if math.Abs(o.M(1)-o.Mcs) > 1e-17 {
chk.Panic("M(+1) failed. err = %v", o.M(1)-o.Mcs)
}
if o.Mfix {
if math.Abs(o.M(-1)-o.Mcs) > 1e-17 {
chk.Panic("M(-1) failed. err = %v", o.M(-1)-o.Mcs)
}
} else {
Mext := 6.0 * math.Sin(32*math.Pi/180) / (3 + math.Sin(32*math.Pi/180))
if math.Abs(o.M(-1)-Mext) > 1e-15 {
chk.Panic("M(-1) failed. err = %v", o.M(-1)-Mext)
}
}
ver, tol := chk.Verbose, 1e-9
var tmp float64
for _, w := range utl.LinSpace(-1, 1, 11) {
dMdw := o.DMdw(w)
d2Mdw2 := o.D2Mdw2(w)
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, w = w, x
res, w = o.M(w), tmp
return
}, w, 1e-6)
chk.AnaNum(tst, "dM/dw ", tol, dMdw, dnum, ver)
dnum, _ = num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, w = w, x
res, w = o.DMdw(w), tmp
return
}, w, 1e-6)
chk.AnaNum(tst, "d²M/dw²", tol, d2Mdw2, dnum, ver)
}
ver, tol = chk.Verbose, 1e-9
nd := test_nd
for m := 0; m < len(test_nd)-3; m++ {
//for m := 0; m < 3; m++ {
A := test_AA[m]
σ := M_Alloc2(nd[m])
Ten2Man(σ, A)
s := M_Alloc2(nd[m])
dMdσ := M_Alloc2(nd[m])
d2Mdσdσ := M_Alloc4(nd[m])
p, q, w := M_pqws(s, σ)
o.Deriv2(d2Mdσdσ, dMdσ, σ, s, p, q, w)
io.Pforan("σ = %v\n", σ)
io.Pforan("tr(dMdσ) = %v\n", M_Tr(dMdσ))
if math.Abs(M_Tr(dMdσ)) > 1e-16 {
chk.Panic("tr(dMdσ)=%v failed", M_Tr(dMdσ))
}
I_dc_d2Mdσdσ := M_Alloc2(nd[m]) // I:d²M/dσdσ
for j := 0; j < len(σ); j++ {
for k := 0; k < len(σ); k++ {
I_dc_d2Mdσdσ[j] += Im[k] * d2Mdσdσ[k][j]
}
}
//io.Pfblue2("I_dc_d2Mdσdσ = %v\n", I_dc_d2Mdσdσ)
chk.Vector(tst, "I_dc_d2Mdσdσ", 1e-15, I_dc_d2Mdσdσ, nil)
// dMdσ
for j := 0; j < len(σ); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, σ[j] = σ[j], x
w := M_w(σ)
σ[j] = tmp
return o.M(w)
}, σ[j], 1e-6)
chk.AnaNum(tst, io.Sf("dM/dσ[%d]", j), tol, dMdσ[j], dnum, ver)
}
// d²Mdσdσ
s_tmp := M_Alloc2(nd[m])
dMdσ_tmp := M_Alloc2(nd[m])
for i := 0; i < len(σ); i++ {
for j := 0; j < len(σ); j++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, σ[j] = σ[j], x
p_tmp, q_tmp, w_tmp := M_pqws(s_tmp, σ)
o.Deriv1(dMdσ_tmp, σ, s_tmp, p_tmp, q_tmp, w_tmp)
σ[j] = tmp
return dMdσ_tmp[i]
}, σ[j], 1e-6)
chk.AnaNum(tst, io.Sf("d²M/dσdσ[%d][%d]", i, j), tol, d2Mdσdσ[i][j], dnum, ver)
}
}
}
}
// Check checks derivatives
func Check(tst *testing.T, mdl Model, pc0, sl0, pcf float64, npts int, tolCc, tolD1a, tolD1b, tolD2a, tolD2b float64, verbose bool, pcSkip []float64, tolSkip float64, doplot bool) {
// nonrate model
nr_mdl, is_nonrate := mdl.(Nonrate)
io.Pforan("is_nonrate = %v\n", is_nonrate)
// for all pc stations
Pc := utl.LinSpace(pc0, pcf, npts)
Sl := make([]float64, npts)
Sl[0] = sl0
var err error
for i := 1; i < npts; i++ {
// update and plot
Sl[i], err = Update(mdl, Pc[i-1], Sl[i-1], Pc[i]-Pc[i-1])
if err != nil {
tst.Errorf("Update failed: %v\n", err)
return
}
if doplot {
plt.PlotOne(Pc[i], Sl[i], "'ko', clip_on=0")
}
// skip point on checking of derivatives
if doskip(Pc[i], pcSkip, tolSkip) {
continue
}
// wetting flag
wet := Pc[i]-Pc[i-1] < 0
// check Cc = dsl/dpc
io.Pforan("\npc=%g, sl=%g, wetting=%v\n", Pc[i], Sl[i], wet)
if is_nonrate {
// analytical Cc
Cc_ana, err := mdl.Cc(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("Cc failed: %v\n", err)
return
}
// numerical Cc
Cc_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
return nr_mdl.Sl(x)
}, Pc[i], 1e-3)
chk.AnaNum(tst, "Cc = ∂sl/∂pc ", tolCc, Cc_ana, Cc_num, verbose)
}
// compute all derivatives
L, Lx, J, Jx, Jy, err := mdl.Derivs(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("Derivs failed: %v\n", err)
return
}
L_ana_A := L
L_ana_B, err := mdl.L(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("L failed: %v\n", err)
return
}
Lx_ana := Lx
Jx_ana := Jx
Jy_ana := Jy
J_ana_A := J
J_ana_B, err := mdl.J(Pc[i], Sl[i], wet)
if err != nil {
tst.Errorf("J failed: %v\n", err)
return
}
// numerical L = ∂Cc/∂pc
L_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Cctmp, _ := mdl.Cc(x, Sl[i], wet)
return Cctmp
}, Pc[i], 1e-3)
chk.AnaNum(tst, "L = ∂Cc/∂pc ", tolD1a, L_ana_A, L_num, verbose)
// numerical Lx := ∂²Cc/∂pc²
Lx_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ltmp, _, _, _, _, _ := mdl.Derivs(x, Sl[i], wet)
return Ltmp
}, Pc[i], 1e-3)
chk.AnaNum(tst, "Lx = ∂²Cc/∂pc² ", tolD2a, Lx_ana, Lx_num, verbose)
// numerical J := ∂Cc/∂sl (version A)
J_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ccval, _ := mdl.Cc(Pc[i], x, wet)
return Ccval
}, Sl[i], 1e-3)
chk.AnaNum(tst, "J = ∂Cc/∂sl ", tolD1b, J_ana_A, J_num, verbose)
// numerical Jx := ∂²Cc/(∂pc ∂sl)
Jx_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Ltmp, _, _, _, _, _ := mdl.Derivs(Pc[i], x, wet)
return Ltmp
}, Sl[i], 1e-3)
chk.AnaNum(tst, "Jx = ∂²Cc/∂pc∂sl", tolD2b, Jx_ana, Jx_num, verbose)
// numerical Jy := ∂²Cc/∂sl²
Jy_num, _ := num.DerivCentral(func(x float64, args ...interface{}) float64 {
Jtmp, _ := mdl.J(Pc[i], x, wet)
return Jtmp
}, Sl[i], 1e-3)
chk.AnaNum(tst, "Jy = ∂²Cc/∂sl² ", tolD2b, Jy_ana, Jy_num, verbose)
// check A and B derivatives
chk.Scalar(tst, "L_A == L_B", 1e-17, L_ana_A, L_ana_B)
chk.Scalar(tst, "J_A == J_B", 1e-17, J_ana_A, J_ana_B)
}
}
func Test_smpinvs02(tst *testing.T) {
//verbose()
chk.PrintTitle("smpinvs02")
// 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-9
dtol2 := 1e-8
// run tests
nd := test_nd
for idxA := 0; idxA < len(test_nd); idxA++ {
//for idxA := 0; idxA < 1; 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 director
N := make([]float64, 3)
n := make([]float64, 3)
m := SmpDirector(N, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpUnitDirector(n, m, N)
// output
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pforan("L = %v\n", L)
io.Pforan("N = %v\n", N)
io.Pforan("m = %v\n", m)
io.Pfpink("n = %v\n", n)
chk.Vector(tst, "L", 1e-12, L, test_λ[idxA])
chk.Scalar(tst, "norm(n)==1", 1e-15, la.VecNorm(n), 1)
chk.Scalar(tst, "m=norm(N)", 1e-14, m, la.VecNorm(N))
// dN/dL
var tmp float64
N_tmp := make([]float64, 3)
dNdL := make([]float64, 3)
SmpDirectorDeriv1(dNdL, L, smp_a, smp_b, smp_β, smp_ϵ)
io.Pfpink("\ndNdL = %v\n", dNdL)
for i := 0; i < 3; i++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[i] = L[i], x
SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
L[i] = tmp
return N_tmp[i]
}, L[i], 1e-6)
chk.AnaNum(tst, io.Sf("dN/dL[%d][%d]", i, i), dtol, dNdL[i], dnum, dver)
}
// dm/dL
n_tmp := make([]float64, 3)
dmdL := make([]float64, 3)
SmpNormDirectorDeriv1(dmdL, m, N, dNdL)
io.Pfpink("\ndmdL = %v\n", dmdL)
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)
L[j] = tmp
return m_tmp
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("dm/dL[%d]", j), dtol, dmdL[j], dnum, dver)
}
// dn/dL
dndL := la.MatAlloc(3, 3)
SmpUnitDirectorDeriv1(dndL, m, N, dNdL, dmdL)
io.Pfpink("\ndndL = %v\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)
L[j] = tmp
return n_tmp[i]
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("dn/dL[%d][%d]", i, j), dtol, dndL[i][j], dnum, dver)
}
}
// change tolerance
dtol2_tmp := dtol2
if idxA == 10 || idxA == 11 {
dtol2 = 1e-6
}
// d²m/dLdL
dNdL_tmp := make([]float64, 3)
dmdL_tmp := make([]float64, 3)
d2NdL2 := make([]float64, 3)
d2mdLdL := la.MatAlloc(3, 3)
SmpDirectorDeriv2(d2NdL2, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpNormDirectorDeriv2(d2mdLdL, L, smp_a, smp_b, smp_β, smp_ϵ, m, N, dNdL, d2NdL2, dmdL)
io.Pfpink("\nd2mdLdL = %v\n", d2mdLdL)
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)
SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpNormDirectorDeriv1(dmdL_tmp, m_tmp, N_tmp, dNdL_tmp)
L[j] = tmp
return dmdL_tmp[i]
}, L[j], 1e-6)
chk.AnaNum(tst, io.Sf("d2m/dL[%d]dL[%d]", i, j), dtol2, d2mdLdL[i][j], dnum, dver)
}
}
// d²N/dLdL
io.Pfpink("\nd²N/dLdL\n")
for i := 0; i < 3; i++ {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, L[i] = L[i], x
SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
L[i] = tmp
return dNdL_tmp[i]
}, L[i], 1e-6)
chk.AnaNum(tst, io.Sf("d²N[%d]/dL[%d]dL[%d]", i, i, i), dtol2, d2NdL2[i], dnum, dver)
}
// d²n/dLdL
io.Pfpink("\nd²n/dLdL\n")
dndL_tmp := la.MatAlloc(3, 3)
d2ndLdL := utl.Deep3alloc(3, 3, 3)
SmpUnitDirectorDeriv2(d2ndLdL, m, N, dNdL, d2NdL2, dmdL, n, d2mdLdL, dndL)
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 := SmpDirector(N_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpDirectorDeriv1(dNdL_tmp, L, smp_a, smp_b, smp_β, smp_ϵ)
SmpNormDirectorDeriv1(dmdL_tmp, m_tmp, N_tmp, dNdL_tmp)
SmpUnitDirectorDeriv1(dndL_tmp, m_tmp, N_tmp, dNdL_tmp, dmdL_tmp)
L[k] = tmp
return dndL_tmp[i][j]
}, L[k], 1e-6)
chk.AnaNum(tst, io.Sf("d²n[%d]/dL[%d]dL[%d]", i, j, k), dtol2, d2ndLdL[i][j][k], dnum, dver)
}
}
}
// recover tolerance
dtol2 = dtol2_tmp
// SMP derivs
//if false {
if true {
io.Pfpink("\nSMP derivs\n")
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_)
chk.Scalar(tst, "m_", 1e-14, m_, m)
chk.Vector(tst, "N_", 1e-15, N_, N)
chk.Vector(tst, "dNdL_", 1e-15, dNdL_, dNdL)
chk.Matrix(tst, "dndL_", 1e-13, dndL_, dndL)
chk.Deep3(tst, "d2ndLdL_", 1e-11, d2ndLdL_, d2ndLdL)
}
}
}
// testing_compare_results_u compares results with u-formulation
func TestingCompareResultsU(tst *testing.T, simfilepath, cmpfname, alias string, tolK, tolu, tols float64, skipK, verbose bool) {
// FEM structure
fem := NewFEM(simfilepath, alias, false, false, true, false, verbose, 0)
// set stage
err := fem.SetStage(0)
if err != nil {
chk.Panic("cannot set stage:\n%v", err)
}
// zero solution
err = fem.ZeroStage(0, true)
if err != nil {
chk.Panic("cannot zero stage data:\n%v", err)
}
// read file with comparison results
buf, err := io.ReadFile(cmpfname)
if err != nil {
tst.Errorf("TestingCompareResultsU: ReadFile failed\n")
return
}
// unmarshal json
var cmp_set T_results_set
err = json.Unmarshal(buf, &cmp_set)
if err != nil {
tst.Errorf("TestingCompareResultsU: Unmarshal failed\n")
return
}
// run comparisons
dom := fem.Domains[0]
dmult := 1.0
for idx, cmp := range cmp_set {
// displacements multiplier
if idx == 0 && math.Abs(cmp.DispMult) > 1e-10 {
dmult = cmp.DispMult
}
// time index
tidx := idx + 1
if verbose {
io.PfYel("\n\ntidx = %d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", tidx)
}
// load gofem results
err = dom.Read(fem.Summary, tidx, 0, true)
if err != nil {
chk.Panic("cannot read 'gofem' results:\n%v", err)
}
if verbose {
io.Pfyel("time = %v\n", dom.Sol.T)
}
// check K matrices
if !skipK {
if verbose {
io.Pfgreen(". . . checking K matrices . . .\n")
}
for eid, Ksg := range cmp.Kmats {
if e, ok := dom.Elems[eid].(*ElemU); ok {
err = e.AddToKb(dom.Kb, dom.Sol, true)
if err != nil {
chk.Panic("TestingCompareResultsU: AddToKb failed\n")
}
chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
}
if e, ok := dom.Elems[eid].(*Rod); ok {
err = e.AddToKb(dom.Kb, dom.Sol, true)
if err != nil {
chk.Panic("TestingCompareResultsU: AddToKb failed\n")
}
chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
}
if e, ok := dom.Elems[eid].(*ElastRod); ok {
err = e.AddToKb(dom.Kb, dom.Sol, true)
if err != nil {
chk.Panic("TestingCompareResultsU: AddToKb failed\n")
}
chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
}
}
}
// check displacements
if verbose {
io.Pfgreen(". . . checking displacements . . .\n")
}
for nid, usg := range cmp.Disp {
ix := dom.Vid2node[nid].Dofs[0].Eq
iy := dom.Vid2node[nid].Dofs[1].Eq
chk.AnaNum(tst, "ux", tolu, dom.Sol.Y[ix], usg[0]*dmult, verbose)
chk.AnaNum(tst, "uy", tolu, dom.Sol.Y[iy], usg[1]*dmult, verbose)
if len(usg) == 3 {
iz := dom.Vid2node[nid].Dofs[2].Eq
chk.AnaNum(tst, "uz", tolu, dom.Sol.Y[iz], usg[2]*dmult, verbose)
}
}
// check stresses
if true {
if verbose {
io.Pfgreen(". . . checking stresses . . .\n")
}
for eid, sig := range cmp.Sigmas {
if verbose {
io.Pforan("eid = %d\n", eid)
}
if e, ok := dom.Cid2elem[eid].(*ElemU); ok {
for ip, val := range sig {
if verbose {
io.Pfgrey2("ip = %d\n", ip)
}
σ := e.States[ip].Sig
if len(val) == 6 {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
} else {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
chk.AnaNum(tst, "sxy", tols, σ[3]/SQ2, val[2], verbose)
if len(val) > 3 { // sx, sy, sxy, sz
chk.AnaNum(tst, "sz ", tols, σ[2], val[3], verbose)
}
}
}
}
if e, ok := dom.Cid2elem[eid].(*Rod); ok {
for ip, val := range sig {
if verbose {
io.Pfgrey2("ip = %d\n", ip)
}
σ := e.States[ip].Sig
chk.AnaNum(tst, "sig", tols, σ, val[0], verbose)
}
}
if e, ok := dom.Cid2elem[eid].(*ElastRod); ok {
dat := e.OutIpsData()
for ip, val := range sig {
if verbose {
io.Pfgrey2("ip = %d\n", ip)
}
res := dat[ip].Calc(dom.Sol)
σ := res["sig"]
chk.AnaNum(tst, "sig", tols, σ, val[0], verbose)
}
}
}
}
}
}