func plot_cone(α float64, preservePrev bool) {
nu, nv := 11, 21
l := 1.2
r := math.Tan(α) * l
S, T := utl.MeshGrid2D(0, l, 0, 2.0*PI, nu, nv)
X := la.MatAlloc(nv, nu)
Y := la.MatAlloc(nv, nu)
Z := la.MatAlloc(nv, nu)
u := make([]float64, 3)
v := make([]float64, 3)
L := rot_matrix()
for j := 0; j < nu; j++ {
for i := 0; i < nv; i++ {
u[0] = S[i][j] * r * math.Cos(T[i][j])
u[1] = S[i][j] * r * math.Sin(T[i][j])
u[2] = S[i][j]
la.MatVecMul(v, 1, L, u)
X[i][j], Y[i][j], Z[i][j] = v[0], v[1], v[2]
}
}
pp := 0
if preservePrev {
pp = 1
}
plt.Wireframe(X, Y, Z, io.Sf("color='b', lw=0.5, preservePrev=%d", pp))
}
func Test_invs05(tst *testing.T) {
//verbose()
chk.PrintTitle("invs05")
if SAVEPLOT {
plt.Reset()
plt.SetForPng(1, 500, 125)
PlotRosette(1.1, true, true, true, 7)
}
addtoplot := func(σa, σb float64, σ []float64) {
plt.PlotOne(σa, σb, "'ro', ms=5")
plt.Text(σa, σb, io.Sf("$\\sigma_{123}=(%g,%g,%g)$", σ[0], σ[1], σ[2]), "size=8")
}
dotest := func(σ []float64, σacor, σbcor, σccor, θcor, tolσ float64) {
w := M_w(σ)
θ2 := math.Asin(w) * 180.0 / (3.0 * math.Pi)
θ3 := M_θ(σ)
σa, σb, σc := L2O(σ[0], σ[1], σ[2])
σ0, σ1, σ2 := O2L(σa, σb, σc)
σI, σA := make([]float64, 3), []float64{σa, σb, σc}
la.MatVecMul(σI, 1, O2Lmat(), σA) // σI := L * σA
io.Pf("σa σb σc = %v %v %v\n", σa, σb, σc)
io.Pf("w = %v\n", w)
io.Pf("θ2, θ3 = %v, %v\n", θ2, θ3)
chk.Scalar(tst, "σa", 1e-17, σa, σacor)
chk.Scalar(tst, "σb", 1e-17, σb, σbcor)
chk.Scalar(tst, "σc", 1e-17, σc, σccor)
chk.Scalar(tst, "σ0", tolσ, σ0, σ[0])
chk.Scalar(tst, "σ1", tolσ, σ1, σ[1])
chk.Scalar(tst, "σ2", tolσ, σ2, σ[2])
chk.Scalar(tst, "σI0", tolσ, σI[0], σ[0])
chk.Scalar(tst, "σI1", tolσ, σI[1], σ[1])
chk.Scalar(tst, "σI2", tolσ, σI[2], σ[2])
chk.Scalar(tst, "θ2", 1e-6, θ2, θcor)
chk.Scalar(tst, "θ3", 1e-17, θ3, θ2)
addtoplot(σa, σb, σ)
}
dotest([]float64{-1, 0, 0, 0}, 0, 2.0/SQ6, 1.0/SQ3, 30, 1e-15)
dotest([]float64{0, -1, 0, 0}, 1.0/SQ2, -1.0/SQ6, 1.0/SQ3, 30, 1e-15)
dotest([]float64{0, 0, -1, 0}, -1.0/SQ2, -1.0/SQ6, 1.0/SQ3, 30, 1e-15)
if SAVEPLOT {
plt.Gll("$\\sigma_a$", "$\\sigma_b$", "")
plt.Equal()
plt.SaveD("/tmp/gosl", "fig_invs05.png")
}
}
// adds -R to global residual vector fb
func (o Beam) AddToRhs(fb []float64, sol *Solution) (ok bool) {
// node displacements
for i, I := range o.Umap {
o.ue[i] = sol.Y[I]
}
// steady/dynamics
if Global.Sim.Data.Steady {
la.MatVecMul(o.fi, 1, o.K, o.ue)
} else {
dc := Global.DynCoefs
for i := 0; i < o.Nu; i++ {
o.fi[i] = 0
for j := 0; j < o.Nu; j++ {
o.fi[i] += o.M[i][j]*(dc.α1*o.ue[j]-o.ζe[j]) + o.K[i][j]*o.ue[j]
}
}
}
// distributed loads
if o.Hasq {
dx := o.X[0][1] - o.X[0][0]
dy := o.X[1][1] - o.X[1][0]
l := math.Sqrt(dx*dx + dy*dy)
qnL := o.QnL.F(sol.T, nil)
qnR := o.QnR.F(sol.T, nil)
qt := o.Qt.F(sol.T, nil)
o.fxl[0] = qt * l / 2.0
o.fxl[1] = l * (7.0*qnL + 3.0*qnR) / 20.0
o.fxl[2] = l * l * (3.0*qnL + 2.0*qnR) / 60.0
o.fxl[3] = qt * l / 2.0
o.fxl[4] = l * (3.0*qnL + 7.0*qnR) / 20.0
o.fxl[5] = -l * l * (2.0*qnL + 3.0*qnR) / 60.0
la.MatTrVecMulAdd(o.fi, -1.0, o.T, o.fxl) // Rus -= fx; fx = trans(T) * fxl
}
// add to fb
for i, I := range o.Umap {
fb[I] -= o.fi[i]
}
return true
}
// adds -R to global residual vector fb
func (o *Beam) AddToRhs(fb []float64, sol *Solution) (err error) {
// node displacements
for i, I := range o.Umap {
o.ue[i] = sol.Y[I]
}
// steady/dynamics
if sol.Steady {
la.MatVecMul(o.fi, 1, o.K, o.ue)
} else {
α1 := sol.DynCfs.α1
for i := 0; i < o.Nu; i++ {
o.fi[i] = 0
for j := 0; j < o.Nu; j++ {
o.fi[i] += o.M[i][j]*(α1*o.ue[j]-o.ζe[j]) + o.K[i][j]*o.ue[j]
}
}
}
// distributed loads
if o.Hasq {
dx := o.X[0][1] - o.X[0][0]
dy := o.X[1][1] - o.X[1][0]
l := math.Sqrt(dx*dx + dy*dy)
qnL, qnR, qt := o.calc_loads(sol.T)
o.fxl[0] = qt * l / 2.0
o.fxl[1] = l * (7.0*qnL + 3.0*qnR) / 20.0
o.fxl[2] = l * l * (3.0*qnL + 2.0*qnR) / 60.0
o.fxl[3] = qt * l / 2.0
o.fxl[4] = l * (3.0*qnL + 7.0*qnR) / 20.0
o.fxl[5] = -l * l * (2.0*qnL + 3.0*qnR) / 60.0
la.MatTrVecMulAdd(o.fi, -1.0, o.T, o.fxl) // Rus -= fx; fx = trans(T) * fxl
}
// add to fb
for i, I := range o.Umap {
fb[I] -= o.fi[i]
}
return
}
func Test_invs02(tst *testing.T) {
//verbose()
chk.PrintTitle("invs02")
eps := [][]float64{
{100 / 200.0, 150 / 200.0, 5 / 200.0},
{150 / 200.0, 100 / 200.0, 10 / 200.0},
{5 / 200.0, 10 / 200.0, 100 / 200.0},
}
ε := make([]float64, 6)
e := make([]float64, 6)
e_ := make([]float64, 6)
Ten2Man(ε, eps)
εv := M_εv(ε)
εd := M_εd(ε)
eno, εv_, εd_ := M_devε(e, ε)
Lε := make([]float64, 3)
err := M_EigenValsNum(Lε, ε)
if err != nil {
tst.Errorf("test failed: %v\n", err)
return
}
Lεv, Lεd := L_strains(Lε)
la.MatVecMul(e_, 1, Psd, ε)
la.PrintMat("eps", eps, "%8g", false)
io.Pf("ε = %v\n", ε)
io.Pf("e = %v\n", e)
io.Pf("e_ = %v\n", e_)
io.Pf("eno = %v\n", eno)
io.Pf("εv = %v Lεv=%v\n", εv, Lεv)
io.Pf("εd = %v Lεd=%v\n", εd, Lεd)
io.Pf("εd_ = %v\n", εd_)
chk.Scalar(tst, "Lεv", 1e-17, Lεv, εv)
chk.Scalar(tst, "Lεd", 1e-15, Lεd, εd)
chk.Scalar(tst, "εv", 1e-17, εv, εv_)
chk.Scalar(tst, "εv", 1e-17, εv, eps[0][0]+eps[1][1]+eps[2][2])
chk.Scalar(tst, "εd", 1e-13, εd, εd_)
chk.Vector(tst, "e", 1e-17, e, e_)
}
func Test_invs03(tst *testing.T) {
//verbose()
chk.PrintTitle("invs03")
// square with vertical stress only under plane-strain
E, ν := 210000.0, 0.49999
qY := 240.0
σx := 0.0
σy := -qY / math.Sqrt(ν*ν-ν+1.0)
σz := ν * (σx + σy)
εx := -(ν*σz + ν*σy - σx) / E
εy := -(ν*σz - σy + ν*σx) / E
εz := 0.0
// check
c := E / ((1.0 + ν) * (1.0 - 2.0*ν))
De := [][]float64{
{c * (1.0 - ν), c * ν, c * ν, 0.0},
{c * ν, c * (1.0 - ν), c * ν, 0.0},
{c * ν, c * ν, c * (1.0 - ν), 0.0},
{0.0, 0.0, 0.0, c * (1.0 - 2.0*ν)},
}
ε := [][]float64{
{εx, 0, 0},
{0, εy, 0},
{0, 0, εz},
}
εm := make([]float64, 4)
σm := make([]float64, 4)
Ten2Man(εm, ε)
la.MatVecMul(σm, 1, De, εm)
q := M_q(σm)
θ := M_θ(σm)
io.Pfcyan("σm = %v\n", σm)
io.Pfcyan("q = %v\n", q)
io.Pfcyan("θ = %v\n", θ)
chk.Scalar(tst, "q", 1e-10, q, qY)
chk.Scalar(tst, "θ", 1e-3, θ, 0)
}
func Test_linipm03(tst *testing.T) {
//verbose()
chk.PrintTitle("linipm03")
t0 := time.Now()
defer func() { io.Pfblue2("\ntime elapsed = %v\n", time.Now().Sub(t0)) }()
// read LP
A, b, c, l, u := ReadLPfortran("data/afiro.dat")
//A, b, c, l, u := ReadLPfortran("data/adlittle.dat")
//A, b, c, l, u := ReadLPfortran("data/share1b.dat")
// check for unbounded variables
nx := len(c)
for i := 0; i < nx; i++ {
if math.Abs(l[i]) > 1e-15 {
chk.Panic("cannot handle l != 0 yet")
}
if math.Abs(u[i]-1e20) > 1e-15 {
chk.Panic("cannot handle u != ∞ yet")
}
}
// solve LP
var ipm LinIpm
defer ipm.Clean()
ipm.Init(A, b, c, nil)
err := ipm.Solve(chk.Verbose)
if err != nil {
tst.Errorf("ipm failed:\n%v", err)
return
}
// check
io.Pf("\n")
bres := make([]float64, len(b))
la.MatVecMul(bres, 1, A.ToDense(), ipm.X)
chk.Vector(tst, "A*x=b", 1e-13, bres, b)
}
func Test_invs01(tst *testing.T) {
//verbose()
chk.PrintTitle("invs01")
sig := [][]float64{
{100, 150, 5},
{150, 100, 10},
{5, 10, 100},
}
σ := make([]float64, 6)
s := make([]float64, 6)
s_ := make([]float64, 6)
Ten2Man(σ, sig) // σ := sig
p := M_p(σ)
q := M_q(σ)
θ := M_θ(σ)
sno, p_, q_ := M_devσ(s, σ)
p1, q1, θ1 := M_pqθ(σ)
la.MatVecMul(s_, 1, Psd, σ)
la.PrintMat("sig", sig, "%8g", false)
io.Pf("σ = %v\n", σ)
io.Pf("s = %v\n", s)
io.Pf("s_ = %v\n", s_)
io.Pf("sno = %v\n", sno)
io.Pf("p = %v\n", p)
io.Pf("q = %v\n", q)
io.Pf("q_ = %v\n", q_)
io.Pf("θ = %v\n", θ)
chk.Scalar(tst, "p", 1e-17, p, p_)
chk.Scalar(tst, "p", 1e-17, p, -100)
chk.Scalar(tst, "q", 1e-17, q, 260.52830940226056)
chk.Scalar(tst, "q", 1e-13, q, q_)
chk.Vector(tst, "s", 1e-17, s, s_)
chk.Scalar(tst, "p1", 1e-17, p, p1)
chk.Scalar(tst, "q1", 1e-13, q, q1)
chk.Scalar(tst, "θ1", 1e-17, θ, θ1)
}
func Test_extrapapolation(tst *testing.T) {
//verbose()
chk.PrintTitle("Test extrapolation")
GetIpNums := func(name string) []int {
var nums []int
for key, _ := range ipsfactory {
name_n := strings.Split(key, "_")
if name_n[0] == name {
nip := io.Atoi(name_n[1])
nums = append(nums, nip)
}
}
return nums
}
for name, shape := range factory {
gndim := shape.Gndim
if gndim == 1 {
continue
}
io.Pfyel("--------------------------------- %-6s---------------------------------\n", name)
for _, nip := range GetIpNums(shape.Type) {
if nip <= 1 {
continue
}
io.Pfblue("nip = %v\n", nip)
tol := 1.0e-13
// create a N vector with nodal values
nverts := shape.Nverts
X := shape.NatCoords
delta := rand.Float64()
N := make([]float64, shape.Nverts)
for i := 0; i < shape.Nverts; i++ {
var x, y, z float64
x = X[0][i]
y = X[1][i]
if shape.Gndim == 3 {
z = X[2][i]
}
N[i] = x + y + z + delta
}
io.Pfblue("N = %v\n", N)
// calculate P vector with corresponding values at ips
key := name + "_" + strconv.Itoa(nip)
ips := ipsfactory[key]
P := make([]float64, nip)
Xip := la.MatAlloc(nip, 4) // ips local coordinates
for i := 0; i < nip; i++ {
var x, y, z float64
x = ips[i][0]
y = ips[i][1]
z = ips[i][2]
Xip[i][0] = x
Xip[i][1] = y
Xip[i][2] = z
P[i] = x + y + z + delta
}
// Allocate E matrix
E := la.MatAlloc(nverts, nip)
// Calculate extrapolator matrix
shape.Extrapolator(E, ips)
// Recalculate nodal values NN = E*P
NN := make([]float64, shape.Nverts)
la.MatVecMul(NN, 1.0, E, P)
io.Pfblue("N ext= %v\n", NN)
// Compare vectors N and NN
msg := name + "_" + strconv.Itoa(nip)
chk.Vector(tst, msg, tol, NN, N)
}
}
}
func Test_linipm02(tst *testing.T) {
//verbose()
chk.PrintTitle("linipm02")
// linear program
// min 2*x0 + x1
// s.t. -x0 + x1 ≤ 1
// x0 + x1 ≥ 2 → -x0 - x1 ≤ -2
// x0 - 2*x1 ≤ 4
// x1 ≥ 0
// standard (step 1) add slack
// s.t. -x0 + x1 + x2 = 1
// -x0 - x1 + x3 = -2
// x0 - 2*x1 + x4 = 4
// standard (step 2)
// replace x0 := x0_ - x5
// because it's unbounded
// min 2*x0_ + x1 - 2*x5
// s.t. -x0_ + x1 + x2 + x5 = 1
// -x0_ - x1 + x3 + x5 = -2
// x0_ - 2*x1 + x4 - x5 = 4
// x0_,x1,x2,x3,x4,x5 ≥ 0
var T la.Triplet
T.Init(3, 6, 12)
T.Put(0, 0, -1)
T.Put(0, 1, 1)
T.Put(0, 2, 1)
T.Put(0, 5, 1)
T.Put(1, 0, -1)
T.Put(1, 1, -1)
T.Put(1, 3, 1)
T.Put(1, 5, 1)
T.Put(2, 0, 1)
T.Put(2, 1, -2)
T.Put(2, 4, 1)
T.Put(2, 5, -1)
Am := T.ToMatrix(nil)
A := Am.ToDense()
c := []float64{2, 1, 0, 0, 0, -2}
b := []float64{1, -2, 4}
// print LP
la.PrintMat("A", A, "%6g", false)
la.PrintVec("b", b, "%6g", false)
la.PrintVec("c", c, "%6g", false)
io.Pf("\n")
// solve LP
var ipm LinIpm
defer ipm.Clean()
ipm.Init(Am, b, c, nil)
err := ipm.Solve(chk.Verbose)
if err != nil {
tst.Errorf("ipm failed:\n%v", err)
return
}
// check
io.Pf("\n")
bres := make([]float64, len(b))
la.MatVecMul(bres, 1, A, ipm.X)
io.Pforan("bres = %v\n", bres)
chk.Vector(tst, "A*x=b", 1e-8, bres, b)
// fix and check x
x := ipm.X[:2]
x[0] -= ipm.X[5]
io.Pforan("x = %v\n", x)
chk.Vector(tst, "x", 1e-8, x, []float64{0.5, 1.5})
// plot
if true && chk.Verbose {
f := func(x []float64) float64 {
return c[0]*x[0] + c[1]*x[1]
}
g := func(x []float64, i int) float64 {
return A[i][0]*x[0] + A[i][1]*x[1] - b[i]
}
np := 41
vmin, vmax := []float64{-2.0, -2.0}, []float64{2.0, 2.0}
PlotTwoVarsContour("/tmp/gosl", "test_linipm02", x, np, nil, true, vmin, vmax, f,
func(x []float64) float64 { return g(x, 0) },
func(x []float64) float64 { return g(x, 1) },
)
}
}
func Test_linipm01(tst *testing.T) {
//verbose()
chk.PrintTitle("linipm01")
// linear programming problem
// min -4*x0 - 5*x1
// s.t. 2*x0 + x1 ≤ 3
// x0 + 2*x1 ≤ 3
// x0,x1 ≥ 0
// standard:
// 2*x0 + x1 + x2 = 3
// x0 + 2*x1 + x3 = 3
// x0,x1,x2,x3 ≥ 0
var T la.Triplet
T.Init(2, 4, 6)
T.Put(0, 0, 2.0)
T.Put(0, 1, 1.0)
T.Put(0, 2, 1.0)
T.Put(1, 0, 1.0)
T.Put(1, 1, 2.0)
T.Put(1, 3, 1.0)
Am := T.ToMatrix(nil)
A := Am.ToDense()
c := []float64{-4, -5, 0, 0}
b := []float64{3, 3}
// print LP
la.PrintMat("A", A, "%6g", false)
la.PrintVec("b", b, "%6g", false)
la.PrintVec("c", c, "%6g", false)
io.Pf("\n")
// solve LP
var ipm LinIpm
defer ipm.Clean()
ipm.Init(Am, b, c, nil)
err := ipm.Solve(chk.Verbose)
if err != nil {
tst.Errorf("ipm failed:\n%v", err)
return
}
// check
io.Pf("\n")
io.Pforan("x = %v\n", ipm.X)
io.Pfcyan("λ = %v\n", ipm.L)
io.Pforan("s = %v\n", ipm.S)
x := ipm.X[:2]
bres := make([]float64, 2)
la.MatVecMul(bres, 1, A, x)
io.Pforan("bres = %v\n", bres)
chk.Vector(tst, "x", 1e-9, x, []float64{1, 1})
chk.Vector(tst, "A*x=b", 1e-8, bres, b)
// plot
if true && chk.Verbose {
f := func(x []float64) float64 {
return c[0]*x[0] + c[1]*x[1]
}
g := func(x []float64, i int) float64 {
return A[i][0]*x[0] + A[i][1]*x[1] - b[i]
}
np := 41
vmin, vmax := []float64{-2.0, -2.0}, []float64{2.0, 2.0}
PlotTwoVarsContour("/tmp/gosl", "test_linipm01", x, np, nil, true, vmin, vmax, f,
func(x []float64) float64 { return g(x, 0) },
func(x []float64) float64 { return g(x, 1) },
)
}
}
// Connect connects rod/solid elements in this Rjoint
func (o *Rjoint) Connect(cid2elem []Elem, c *inp.Cell) (nnzK int, err error) {
// get rod and solid elements
rodId := c.JlinId
sldId := c.JsldId
o.Rod = cid2elem[rodId].(*Rod)
o.Sld = cid2elem[sldId].(*ElemU)
if o.Rod == nil {
err = chk.Err("cannot find joint's rod cell with id == %d", rodId)
return
}
if o.Sld == nil {
err = chk.Err("cannot find joint's solid cell with id == %d", sldId)
return
}
// total number of dofs
o.Ny = o.Rod.Nu + o.Sld.Nu
// material model name
matdata := o.Sim.MatParams.Get(o.Edat.Mat)
if matdata == nil {
err = chk.Err("materials database failed on getting %q material\n", o.Edat.Mat)
return
}
// initialise model
err = o.Mdl.Init(matdata.Prms)
if err != nil {
err = chk.Err("model initialisation failed:\n%v", err)
return
}
// parameters
for _, p := range matdata.Prms {
switch p.N {
case "h":
o.h = p.V
case "k1":
o.k1 = p.V
case "k2":
o.k2 = p.V
case "mu":
if p.V > 0.0 {
o.Coulomb = true
}
}
}
// auxiliary
nsig := 2 * o.Ndim
// rod data
rodH := o.Rod.Cell.Shp
rodNp := len(o.Rod.IpsElem)
rodNn := rodH.Nverts
rodNu := o.Rod.Nu
// solid data
sldH := o.Sld.Cell.Shp
sldS := sldH.S
sldNp := len(o.Sld.IpsElem)
sldNn := sldH.Nverts
sldNu := o.Sld.Nu
// shape functions of solid @ nodes of rod
o.Nmat = la.MatAlloc(sldNn, rodNn)
rodYn := make([]float64, o.Ndim)
rodRn := make([]float64, 3)
for m := 0; m < rodNn; m++ {
for i := 0; i < o.Ndim; i++ {
rodYn[i] = o.Rod.X[i][m]
}
err = sldH.InvMap(rodRn, rodYn, o.Sld.X)
if err != nil {
return
}
err = sldH.CalcAtR(o.Sld.X, rodRn, false)
if err != nil {
return
}
for n := 0; n < sldNn; n++ {
o.Nmat[n][m] = sldH.S[n]
}
}
// coulomb model => σc depends on p values of solid
if o.Coulomb {
// allocate variables
o.Pmat = la.MatAlloc(sldNn, rodNp)
o.Emat = la.MatAlloc(sldNn, sldNp)
o.rodRp = la.MatAlloc(rodNp, 3)
o.σNo = la.MatAlloc(sldNn, nsig)
o.σIp = make([]float64, nsig)
o.t1 = make([]float64, o.Ndim)
o.t2 = make([]float64, o.Ndim)
// extrapolator matrix
err = sldH.Extrapolator(o.Emat, o.Sld.IpsElem)
if err != nil {
return
}
// shape function of solid @ ips of rod
for idx, ip := range o.Rod.IpsElem {
rodYp := rodH.IpRealCoords(o.Rod.X, ip)
err = sldH.InvMap(o.rodRp[idx], rodYp, o.Sld.X)
if err != nil {
return
}
err = sldH.CalcAtR(o.Sld.X, o.rodRp[idx], false)
if err != nil {
return
}
for n := 0; n < sldNn; n++ {
o.Pmat[n][idx] = sldS[n]
}
}
}
// joint direction @ ip[idx]; corotational system aligned with rod element
o.e0 = la.MatAlloc(rodNp, o.Ndim)
o.e1 = la.MatAlloc(rodNp, o.Ndim)
o.e2 = la.MatAlloc(rodNp, o.Ndim)
π := make([]float64, o.Ndim) // Eq. (27)
Q := la.MatAlloc(o.Ndim, o.Ndim)
α := 666.0
Jvec := rodH.Jvec3d[:o.Ndim]
for idx, ip := range o.Rod.IpsElem {
// auxiliary
e0, e1, e2 := o.e0[idx], o.e1[idx], o.e2[idx]
// interpolation functions and gradients
err = rodH.CalcAtIp(o.Rod.X, ip, true)
if err != nil {
return
}
// compute basis vectors
J := rodH.J
π[0] = Jvec[0] + α
π[1] = Jvec[1]
e0[0] = Jvec[0] / J
e0[1] = Jvec[1] / J
if o.Ndim == 3 {
π[2] = Jvec[2]
e0[2] = Jvec[2] / J
}
la.MatSetDiag(Q, 1)
la.VecOuterAdd(Q, -1, e0, e0) // Q := I - e0 dyad e0
la.MatVecMul(e1, 1, Q, π) // Eq. (29) * norm(E1)
la.VecScale(e1, 0, 1.0/la.VecNorm(e1), e1)
if o.Ndim == 3 {
e2[0] = e0[1]*e1[2] - e0[2]*e1[1]
e2[1] = e0[2]*e1[0] - e0[0]*e1[2]
e2[2] = e0[0]*e1[1] - e0[1]*e1[0]
}
// compute auxiliary tensors
if o.Coulomb {
e1_dy_e1 := tsr.Alloc2()
e2_dy_e2 := tsr.Alloc2()
for i := 0; i < o.Ndim; i++ {
for j := 0; j < o.Ndim; j++ {
e1_dy_e1[i][j] = e1[i] * e1[j]
e2_dy_e2[i][j] = e2[i] * e2[j]
}
}
}
}
// auxiliary variables
o.ΔuC = la.MatAlloc(rodNn, o.Ndim)
o.Δw = make([]float64, o.Ndim)
o.qb = make([]float64, o.Ndim)
o.fC = make([]float64, rodNu)
// temporary Jacobian matrices. see Eq. (57)
o.Krr = la.MatAlloc(rodNu, rodNu)
o.Krs = la.MatAlloc(rodNu, sldNu)
o.Ksr = la.MatAlloc(sldNu, rodNu)
o.Kss = la.MatAlloc(sldNu, sldNu)
// debugging
//if true {
if false {
o.debug_print_init()
}
// success
return o.Ny * o.Ny, nil
}