// contact_init initialises variables need by contact model
func (o *ElemU) contact_init(edat *inp.ElemData) {
// vertices on faces with contact
var contactverts []int
if len(o.Cell.FaceBcs) > 0 {
lverts := o.Cell.FaceBcs.GetVerts("contact")
for _, m := range lverts {
contactverts = append(contactverts, m)
}
}
o.Nq = len(contactverts)
// contact flag
o.HasContact = o.Nq > 0
if !o.HasContact {
return
}
// vertices on contact face; numbering
o.ContactId2vid = contactverts
o.Vid2contactId = utl.IntVals(o.Nu, -1)
o.Qmap = make([]int, o.Nq)
for μ, m := range o.ContactId2vid {
o.Vid2contactId[m] = μ
}
// flags
o.Macaulay, o.βrmp, o.κ = GetContactFaceFlags(edat.Extra)
// allocate coupling matrices
o.Kuq = la.MatAlloc(o.Nu, o.Nq)
o.Kqu = la.MatAlloc(o.Nq, o.Nu)
o.Kqq = la.MatAlloc(o.Nq, o.Nq)
}
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))
}
// StatTable computes the min, ave, max, and dev of values organised in a table
// Input:
// x -- sample
// std -- compute standard deviation (σ) instead of average deviation (adev)
// withZ -- computes z-matrix as well
// Convention of indices:
// 0=min 1=ave 2=max 3=dev
// Output: min ave max dev
// ↓ ↓ ↓ ↓
// x00 x01 x02 x03 x04 x05 → y00=min(x0?) y10=ave(x0?) y20=max(x0?) y30=dev(x0?)
// x10 x11 x12 x13 x14 x15 → y01=min(x1?) y11=ave(x1?) y21=max(x1?) y31=dev(x1?)
// x20 x21 x22 x23 x24 x25 → y02=min(x2?) y12=ave(x2?) y22=max(x2?) y32=dev(x2?)
// ↓ ↓ ↓ ↓
// min → z00=min(y0?) z01=min(y1?) z02=min(y2?) z03=min(y3?)
// ave → z10=ave(y0?) z11=ave(y1?) z12=ave(y2?) z13=ave(y3?)
// max → z20=max(y0?) z21=max(y1?) z22=max(y2?) z23=max(y3?)
// dev → z30=dev(y0?) z31=dev(y1?) z32=dev(y2?) z33=dev(y3?)
// = = = =
// min → z00=min(min) z01=min(ave) z02=min(max) z03=min(dev)
// ave → z10=ave(min) z11=ave(ave) z12=ave(max) z13=ave(dev)
// max → z20=max(min) z21=max(ave) z22=max(max) z23=max(dev)
// dev → z30=dev(min) z31=dev(ave) z32=dev(max) z33=dev(dev)
func StatTable(x [][]float64, std, withZ bool) (y, z [][]float64) {
// dimensions
m := len(x)
if m < 1 {
return
}
n := len(x[0])
if n < 2 {
return
}
// compute y
y = la.MatAlloc(4, m)
for i := 0; i < m; i++ {
y[0][i], y[1][i], y[2][i], y[3][i] = StatBasic(x[i], std)
}
// compute z
if withZ {
z = la.MatAlloc(4, 4)
for i := 0; i < 4; i++ {
z[0][i], z[1][i], z[2][i], z[3][i] = StatBasic(y[i], std)
}
}
return
}
// PlotDeriv plots derivative dR[i][j][k]du[d] (2D only)
// option = 0 : use CalcBasisAndDerivs
// 1 : use NumericalDeriv
func (o *Nurbs) PlotDeriv(l, d int, args string, npts, option int) {
lbls := []string{"N\\&dN", "numD"}
switch o.gnd {
// curve
case 1:
// surface
case 2:
xx := la.MatAlloc(npts, npts)
yy := la.MatAlloc(npts, npts)
zz := la.MatAlloc(npts, npts)
du0 := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
du1 := (o.b[1].tmax - o.b[1].tmin) / float64(npts-1)
drdu := make([]float64, 2)
for m := 0; m < npts; m++ {
u0 := o.b[0].tmin + float64(m)*du0
for n := 0; n < npts; n++ {
u1 := o.b[1].tmin + float64(n)*du1
u := []float64{u0, u1}
x := o.Point(u)
xx[m][n] = x[0]
yy[m][n] = x[1]
switch option {
case 0:
o.CalcBasisAndDerivs(u)
o.GetDerivL(drdu, l)
case 1:
o.NumericalDeriv(drdu, u, l)
}
zz[m][n] = drdu[d]
}
}
plt.Title(io.Sf("%d,%d:%s", l, d, lbls[option]), "size=10")
plt.Contour(xx, yy, zz, "fsz=8")
}
}
// PlotRamp plots the ramp function (contour)
func (o *Plotter) DrawRamp(xmi, xma, ymi, yma float64) {
if o.Rmpf == nil {
o.set_empty()
return
}
if o.NptsRmp < 2 {
o.NptsRmp = 101
}
if math.Abs(xma-xmi) < 1e-5 {
xmi, xma = -0.1, 0.1
}
if math.Abs(yma-ymi) < 1e-5 {
ymi, yma = -0.1, 0.1
}
xx := la.MatAlloc(o.NptsRmp, o.NptsRmp)
yy := la.MatAlloc(o.NptsRmp, o.NptsRmp)
zz := la.MatAlloc(o.NptsRmp, o.NptsRmp)
dx := (xma - xmi) / float64(o.NptsRmp-1)
dy := (yma - ymi) / float64(o.NptsRmp-1)
for i := 0; i < o.NptsRmp; i++ {
for j := 0; j < o.NptsRmp; j++ {
xx[i][j] = xmi + float64(i)*dx
yy[i][j] = ymi + float64(j)*dy
zz[i][j] = xx[i][j] - o.Rmpf(xx[i][j]+yy[i][j])
}
}
plt.ContourSimple(xx, yy, zz, "colors=['blue'], linewidths=[2], levels=[0]")
}
func Test_imap(tst *testing.T) {
//utl.Tsilent = false
chk.PrintTitle("Test imap")
for name, shape := range factory {
gndim := shape.Gndim
if gndim == 1 {
continue
}
io.Pfyel("--------------------------------- %-6s---------------------------------\n", name)
// check inverse mapping
tol := 1e-14
noise := 0.01
if name == "tri10" {
tol = 1e-14
}
if shape.FaceNvertsMax > 2 {
noise = 0.0
}
nverts := shape.Nverts
C := la.MatAlloc(gndim, nverts)
s := []float64{rand.Float64(), rand.Float64(), rand.Float64()} // scale factors
la.MatCopy(C, 1.0, shape.NatCoords)
_ = tol
io.Pf("nverts:%v\n", nverts)
io.Pf("gndim:%v\n", gndim)
for i := 0; i < gndim; i++ {
for j := 0; j < nverts; j++ {
C[i][j] *= s[i]
C[i][j] += noise * rand.Float64() // noise
}
}
r := make([]float64, 3)
x := make([]float64, 3)
R := la.MatAlloc(gndim, nverts)
for j := 0; j < nverts; j++ {
for i := 0; i < gndim; i++ {
x[i] = C[i][j]
}
err := shape.InvMap(r, x, C)
io.Pf("r:%v\n", r)
_ = err
for i := 0; i < gndim; i++ {
R[i][j] = r[i]
}
}
chk.Matrix(tst, "checking", tol, R, shape.NatCoords)
io.PfGreen("OK\n")
}
}
// PlotBasis plots basis function (2D only)
// option = 0 : use CalcBasis
// 1 : use CalcBasisAndDerivs
// 2 : use RecursiveBasis
func (o *Nurbs) PlotBasis(l int, args string, npts, option int) {
lbls := []string{"CalcBasis function", "CalcBasisAndDerivs function", "RecursiveBasis function"}
switch o.gnd {
// curve
case 1:
U := make([]float64, npts)
S := make([]float64, npts)
du := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
uvec := []float64{0}
for m := 0; m < npts; m++ {
U[m] = o.b[0].tmin + float64(m)*du
uvec[0] = U[m]
switch option {
case 0:
o.CalcBasis(uvec)
S[m] = o.GetBasisL(l)
case 1:
o.CalcBasisAndDerivs(uvec)
S[m] = o.GetBasisL(l)
case 2:
S[m] = o.RecursiveBasis(uvec, l)
}
}
plt.Plot(U, S, args)
plt.Gll("$u$", io.Sf("$S_%d$", l), "")
// surface
case 2:
xx := la.MatAlloc(npts, npts)
yy := la.MatAlloc(npts, npts)
zz := la.MatAlloc(npts, npts)
du0 := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
du1 := (o.b[1].tmax - o.b[1].tmin) / float64(npts-1)
for m := 0; m < npts; m++ {
u0 := o.b[0].tmin + float64(m)*du0
for n := 0; n < npts; n++ {
u1 := o.b[1].tmin + float64(n)*du1
u := []float64{u0, u1}
x := o.Point(u)
xx[m][n] = x[0]
yy[m][n] = x[1]
switch option {
case 0:
o.CalcBasis(u)
zz[m][n] = o.GetBasisL(l)
case 1:
o.CalcBasisAndDerivs(u)
zz[m][n] = o.GetBasisL(l)
case 2:
zz[m][n] = o.RecursiveBasis(u, l)
}
}
}
plt.Contour(xx, yy, zz, "fsz=7")
}
plt.Title(io.Sf("%s @ %d", lbls[option], l), "size=7")
}
// PlotBasis plots basis function (2D only)
// option = 0 : use CalcBasis
// 1 : use CalcBasisAndDerivs
// 2 : use RecursiveBasis
func (o *Nurbs) PlotBasis(l int, args string, npts, option int) {
lbls := []string{"Nonly", "N\\&dN", "recN"}
switch o.gnd {
// curve
case 1:
xx := make([]float64, npts)
yy := make([]float64, npts)
du0 := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
for m := 0; m < npts; m++ {
u0 := o.b[0].tmin + float64(m)*du0
u := []float64{u0}
x := o.Point(u)
xx[m] = x[0]
switch option {
case 0:
o.CalcBasis(u)
yy[m] = o.GetBasisL(l)
case 1:
o.CalcBasisAndDerivs(u)
yy[m] = o.GetBasisL(l)
case 2:
yy[m] = o.RecursiveBasis(u, l)
}
}
plt.Plot(xx, yy, "fsz=8")
// surface
case 2:
xx := la.MatAlloc(npts, npts)
yy := la.MatAlloc(npts, npts)
zz := la.MatAlloc(npts, npts)
du0 := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
du1 := (o.b[1].tmax - o.b[1].tmin) / float64(npts-1)
for m := 0; m < npts; m++ {
u0 := o.b[0].tmin + float64(m)*du0
for n := 0; n < npts; n++ {
u1 := o.b[1].tmin + float64(n)*du1
u := []float64{u0, u1}
x := o.Point(u)
xx[m][n] = x[0]
yy[m][n] = x[1]
switch option {
case 0:
o.CalcBasis(u)
zz[m][n] = o.GetBasisL(l)
case 1:
o.CalcBasisAndDerivs(u)
zz[m][n] = o.GetBasisL(l)
case 2:
zz[m][n] = o.RecursiveBasis(u, l)
}
}
}
plt.Contour(xx, yy, zz, "fsz=8")
}
plt.Title(io.Sf("%d:%s", l, lbls[option]), "size=10")
}
// Initialises continues initialisation by generating individuals
// Optional: obj XOR fcn, nf, ng, nh
func (o *Optimiser) Init(gen Generator_t, obj ObjFunc_t, fcn MinProb_t, nf, ng, nh int) {
// generic or minimisation problem
if obj != nil {
o.ObjFunc = obj
} else {
if fcn == nil {
chk.Panic("either ObjFunc or MinProb must be provided")
}
o.Nf, o.Ng, o.Nh, o.MinProb = nf, ng, nh, fcn
o.ObjFunc = func(sol *Solution, cpu int) {
o.MinProb(o.F[cpu], o.G[cpu], o.H[cpu], sol.Flt, sol.Int, cpu)
for i, f := range o.F[cpu] {
sol.Ova[i] = f
}
for i, g := range o.G[cpu] {
sol.Oor[i] = utl.GtePenalty(g, 0.0, 1) // g[i] ≥ 0
}
for i, h := range o.H[cpu] {
h = math.Abs(h)
sol.Ova[0] += h
sol.Oor[o.Ng+i] = utl.GtePenalty(o.EpsH, h, 1) // ϵ ≥ |h[i]|
}
}
o.F = la.MatAlloc(o.Ncpu, o.Nf)
o.G = la.MatAlloc(o.Ncpu, o.Ng)
o.H = la.MatAlloc(o.Ncpu, o.Nh)
o.Nova = o.Nf
o.Noor = o.Ng + o.Nh
}
// calc derived parameters
o.Generator = gen
o.CalcDerived()
// allocate solutions
o.Solutions = NewSolutions(o.Nsol, &o.Parameters)
o.Groups = make([]*Group, o.Ncpu)
for cpu := 0; cpu < o.Ncpu; cpu++ {
o.Groups[cpu] = new(Group)
o.Groups[cpu].Init(cpu, o.Ncpu, o.Solutions, &o.Parameters)
}
// metrics
o.Metrics = new(Metrics)
o.Metrics.Init(o.Nsol, &o.Parameters)
// auxiliary
o.tmp = NewSolution(0, 0, &o.Parameters)
o.cpupairs = utl.IntsAlloc(o.Ncpu/2, 2)
o.iova0 = -1
o.ova0 = make([]float64, o.Tf)
// generate trial solutions
o.generate_solutions(0)
}
// PlotDeriv plots derivative dR[i][j][k]du[d] (2D only)
// option = 0 : use CalcBasisAndDerivs
// 1 : use NumericalDeriv
func (o *Nurbs) PlotDeriv(l, d int, args string, npts, option int) {
lbls := []string{"CalcBasisAndDerivs function", "NumericalDeriv function"}
switch o.gnd {
// curve
case 1:
U := make([]float64, npts)
G := make([]float64, npts)
du := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
uvec := []float64{0}
gvec := []float64{0}
for m := 0; m < npts; m++ {
U[m] = o.b[0].tmin + float64(m)*du
uvec[0] = U[m]
switch option {
case 0:
o.CalcBasisAndDerivs(uvec)
o.GetDerivL(gvec, l)
case 1:
o.NumericalDeriv(gvec, uvec, l)
}
G[m] = gvec[0]
}
plt.Plot(U, G, args)
plt.Gll("$u$", io.Sf("$G_%d$", l), "")
// surface
case 2:
xx := la.MatAlloc(npts, npts)
yy := la.MatAlloc(npts, npts)
zz := la.MatAlloc(npts, npts)
du0 := (o.b[0].tmax - o.b[0].tmin) / float64(npts-1)
du1 := (o.b[1].tmax - o.b[1].tmin) / float64(npts-1)
drdu := make([]float64, 2)
for m := 0; m < npts; m++ {
u0 := o.b[0].tmin + float64(m)*du0
for n := 0; n < npts; n++ {
u1 := o.b[1].tmin + float64(n)*du1
u := []float64{u0, u1}
x := o.Point(u)
xx[m][n] = x[0]
yy[m][n] = x[1]
switch option {
case 0:
o.CalcBasisAndDerivs(u)
o.GetDerivL(drdu, l)
case 1:
o.NumericalDeriv(drdu, u, l)
}
zz[m][n] = drdu[d]
}
}
plt.Contour(xx, yy, zz, "fsz=7")
}
plt.Title(io.Sf("%s @ %d,%d", lbls[option], l, d), "size=7")
}
// register element
func init() {
// information allocator
infogetters["phi"] = func(sim *inp.Simulation, cell *inp.Cell, edat *inp.ElemData) *Info {
// new info
var info Info
nverts := cell.Shp.Nverts
ykeys := []string{"h"}
info.Dofs = make([][]string, nverts)
for m := 0; m < nverts; m++ {
info.Dofs[m] = ykeys
}
info.T1vars = ykeys
// return information
return &info
}
// element allocator
eallocators["phi"] = func(sim *inp.Simulation, cell *inp.Cell, edat *inp.ElemData, x [][]float64) Elem {
// basic data
var o ElemPhi
o.Cell = cell
o.X = x
o.Nu = o.Cell.Shp.Nverts
o.Ndim = sim.Ndim
// integration points
var err error
o.IpsElem, o.IpsFace, err = o.Cell.Shp.GetIps(edat.Nip, edat.Nipf)
if err != nil {
chk.Panic("cannot allocate integration points of solid element with nip=%d and nipf=%d:\n%v", edat.Nip, edat.Nipf, err)
}
// local starred variables
nip := len(o.IpsElem)
o.ψs = make([]float64, nip)
o.PhiSign = make([]float64, nip)
// scratchpad. computed @ each ip
o.K = la.MatAlloc(o.Nu, o.Nu)
o.v_0 = la.MatAlloc(nip, o.Ndim)
o.reinit = false
// return new element
return &o
}
}
func (o PressCylin) CalcStresses(Pvals []float64, nr int) (R []float64, Sr, St [][]float64) {
R = utl.LinSpace(o.a, o.b, nr)
np := len(Pvals)
Sr = la.MatAlloc(np, nr)
St = la.MatAlloc(np, nr)
for i, P := range Pvals {
c := o.Calc_c(P)
for j := 0; j < nr; j++ {
Sr[i][j], St[i][j] = o.Stresses(c, R[j])
}
}
return
}
// Ipoints returns the real coordinates of integration points [nip][ndim]
func (o *ElemUP) Ipoints() (coords [][]float64) {
coords = la.MatAlloc(len(o.U.IpsElem), o.Ndim)
for idx, ip := range o.U.IpsElem {
coords[idx] = o.U.Cell.Shp.IpRealCoords(o.U.X, ip)
}
return
}
func Test_2dinteg02(tst *testing.T) {
//verbose()
chk.PrintTitle("2dinteg02. bidimensional integral")
// Γ(1/4, 1)
gamma_1div4_1 := 0.2462555291934987088744974330686081384629028737277219
x := utl.LinSpace(0, 1, 11)
y := utl.LinSpace(0, 1, 11)
m, n := len(x), len(y)
f := la.MatAlloc(m, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
f[i][j] = 8.0 * math.Exp(-math.Pow(x[i], 2)-math.Pow(y[j], 4))
}
}
dx, dy := x[1]-x[0], y[1]-y[0]
Vt := Trapz2D(dx, dy, f)
Vs := Simps2D(dx, dy, f)
Vc := math.Sqrt(math.Pi) * math.Erf(1) * (math.Gamma(1.0/4.0) - gamma_1div4_1)
io.Pforan("Vt = %v\n", Vt)
io.Pforan("Vs = %v\n", Vs)
io.Pfgreen("Vc = %v\n", Vc)
chk.Scalar(tst, "Vt", 0.0114830435645548, Vt, Vc)
chk.Scalar(tst, "Vs", 1e-4, Vs, Vc)
}
// Ipoints returns the real coordinates of integration points [nip][ndim]
func (o ElemU) Ipoints() (coords [][]float64) {
coords = la.MatAlloc(len(o.IpsElem), Global.Ndim)
for idx, ip := range o.IpsElem {
coords[idx] = o.Shp.IpRealCoords(o.X, ip)
}
return
}
func (o *Plotter) Plot_i_alp(x, y []float64, res []*State, sts [][]float64, last bool) {
nr := len(res)
nα := len(res[0].Alp)
if nα == 0 {
o.set_empty()
return
}
yy := la.MatAlloc(nα, nr)
for i := 0; i < nr; i++ {
x[i] = float64(i)
for j := 0; j < nα; j++ {
yy[j][i] = res[i].Alp[j]
}
}
for j := 0; j < nα; j++ {
lbl := io.Sf("$\\alpha_%d$ "+o.Lbl, j)
plt.Plot(x, yy[j], io.Sf("'r-', ls='-', clip_on=0, color='%s', marker='%s', label=r'%s'", o.Clr, o.Mrk, lbl))
}
if last {
plt.Gll("$i$", "$\\alpha_k$", "leg_out=1, leg_ncol=4, leg_hlen=2")
if lims, ok := o.Lims["i,alp"]; ok {
plt.AxisLims(lims)
}
}
}
func (o *Rjoint) debug_print_K() {
sldNn := o.Sld.Cell.Shp.Nverts
rodNn := o.Rod.Cell.Shp.Nverts
K := la.MatAlloc(o.Ny, o.Ny)
start := o.Sld.Nu
for i := 0; i < o.Ndim; i++ {
for m := 0; m < sldNn; m++ {
r := i + m*o.Ndim
for j := 0; j < o.Ndim; j++ {
for n := 0; n < sldNn; n++ {
c := j + n*o.Ndim
K[r][c] = o.Kss[r][c]
}
for n := 0; n < rodNn; n++ {
c := j + n*o.Ndim
K[r][start+c] = o.Ksr[r][c]
K[start+c][r] = o.Krs[c][r]
}
}
}
}
for i := 0; i < o.Ndim; i++ {
for m := 0; m < rodNn; m++ {
r := i + m*o.Ndim
for j := 0; j < o.Ndim; j++ {
for n := 0; n < rodNn; n++ {
c := j + n*o.Ndim
K[start+r][start+c] = o.Krr[r][c]
}
}
}
}
la.PrintMat("K", K, "%20.10f", false)
}
// Extrapolator computes the extrapolation matrix for this Shape with a combination of integration points 'ips'
// Note: E[nverts][nip] must be pre-allocated
func (o *Shape) Extrapolator(E [][]float64, ips []*Ipoint) (err error) {
la.MatFill(E, 0)
nip := len(ips)
N := o.GetShapeMatAtIps(ips)
if nip < o.Nverts {
ξ := o.GetNodesNatCoordsMat()
ξh := o.GetIpsNatCoordsMat(ips)
ξhi := la.MatAlloc(o.Gndim+1, nip)
Ni := la.MatAlloc(o.Nverts, nip)
err = la.MatInvG(Ni, N, 1e-10)
if err != nil {
return
}
err = la.MatInvG(ξhi, ξh, 1e-10)
if err != nil {
return
}
ξhξhI := la.MatAlloc(nip, nip) // ξh * inv(ξh)
for k := 0; k < o.Gndim+1; k++ {
for j := 0; j < nip; j++ {
for i := 0; i < nip; i++ {
ξhξhI[i][j] += ξh[i][k] * ξhi[k][j]
}
for i := 0; i < o.Nverts; i++ {
E[i][j] += ξ[i][k] * ξhi[k][j] // ξ * inv(ξh)
}
}
}
for i := 0; i < o.Nverts; i++ {
for j := 0; j < nip; j++ {
for k := 0; k < nip; k++ {
I_kj := 0.0
if j == k {
I_kj = 1.0
}
E[i][j] += Ni[i][k] * (I_kj - ξhξhI[k][j])
}
}
}
} else {
err = la.MatInvG(E, N, 1e-10)
if err != nil {
return
}
}
return
}
// CheckJ check Jacobian matrix
// Ouptut: cnd -- condition number (with Frobenius norm)
func (o *NlSolver) CheckJ(x []float64, tol float64, chkJnum, silent bool) (cnd float64, err error) {
// Jacobian matrix
var Jmat [][]float64
if o.useDn {
Jmat = la.MatAlloc(o.neq, o.neq)
err = o.JfcnDn(Jmat, x)
if err != nil {
return 0, chk.Err(_nls_err5, "dense", err.Error())
}
} else {
if o.numJ {
err = Jacobian(&o.Jtri, o.Ffcn, x, o.fx, o.w, false)
if err != nil {
return 0, chk.Err(_nls_err5, "sparse", err.Error())
}
} else {
err = o.JfcnSp(&o.Jtri, x)
if err != nil {
return 0, chk.Err(_nls_err5, "sparse(num)", err.Error())
}
}
Jmat = o.Jtri.ToMatrix(nil).ToDense()
}
//la.PrintMat("J", Jmat, "%23g", false)
// condition number
cnd, err = la.MatCondG(Jmat, "F", 1e-10)
if err != nil {
return cnd, chk.Err(_nls_err6, err.Error())
}
if math.IsInf(cnd, 0) || math.IsNaN(cnd) {
return cnd, chk.Err(_nls_err7, cnd)
}
// numerical Jacobian
if !chkJnum {
return
}
var Jtmp la.Triplet
ws := make([]float64, o.neq)
err = o.Ffcn(o.fx, x)
if err != nil {
return
}
Jtmp.Init(o.neq, o.neq, o.neq*o.neq)
Jacobian(&Jtmp, o.Ffcn, x, o.fx, ws, false)
Jnum := Jtmp.ToMatrix(nil).ToDense()
for i := 0; i < o.neq; i++ {
for j := 0; j < o.neq; j++ {
chk.PrintAnaNum(io.Sf("J[%d][%d]", i, j), tol, Jmat[i][j], Jnum[i][j], !silent)
}
}
maxdiff := la.MatMaxDiff(Jmat, Jnum)
if maxdiff > tol {
err = chk.Err(_nls_err8, maxdiff)
}
return
}
func plot_sphere(preservePrev bool) {
R := 1.0
U, V := utl.MeshGrid2D(0, PI/2.0, 0, PI/2.0, NU, NV)
X, Y, Z := la.MatAlloc(NV, NU), la.MatAlloc(NV, NU), la.MatAlloc(NV, NU)
for j := 0; j < NU; j++ {
for i := 0; i < NV; i++ {
X[i][j] = R * math.Cos(U[i][j]) * math.Sin(V[i][j])
Y[i][j] = R * math.Sin(U[i][j]) * math.Sin(V[i][j])
Z[i][j] = R * math.Cos(V[i][j])
}
}
pp := 0
if preservePrev {
pp = 1
}
plt.Wireframe(X, Y, Z, io.Sf("color='k', lw=0.5, preservePrev=%d", pp))
}
// InitWithModel initialises driver with existent model
func (o *Driver) InitWithModel(ndim int, model Model) (err error) {
o.nsig = 2 * ndim
o.model = model
o.D = la.MatAlloc(o.nsig, o.nsig)
o.TolD = 1e-8
o.VerD = chk.Verbose
return
}
func plot_superquadric(a, b, c float64, preservePrev bool) {
A, B, C := 2.0/a, 2.0/b, 2.0/c
R := 1.0
U, V := utl.MeshGrid2D(0, PI/2.0, 0, PI/2.0, NU, NV)
X, Y, Z := la.MatAlloc(NV, NU), la.MatAlloc(NV, NU), la.MatAlloc(NV, NU)
for j := 0; j < NU; j++ {
for i := 0; i < NV; i++ {
X[i][j] = R * cosX(U[i][j], A) * sinX(V[i][j], A)
Y[i][j] = R * sinX(U[i][j], B) * sinX(V[i][j], B)
Z[i][j] = R * cosX(V[i][j], C)
}
}
pp := 0
if preservePrev {
pp = 1
}
plt.Wireframe(X, Y, Z, io.Sf("color='k', lw=0.5, preservePrev=%d", pp))
}
// PlotTwoVarsContour plots contour for two variables problem. len(x) == 2
// Input
// dirout -- directory to save files
// fnkey -- file name key for eps figure
// x -- solution. can be <nil>
// np -- number of points for contour
// extra -- called just before saving figure
// axequal -- axis.equal
// vmin -- min 0 values
// vmax -- max 1 values
// f -- function to plot filled contour. can be <nil>
// gs -- functions to plot contour @ level 0. can be <nil>
func PlotTwoVarsContour(dirout, fnkey string, x []float64, np int, extra func(), axequal bool,
vmin, vmax []float64, f TwoVarsFunc_t, gs ...TwoVarsFunc_t) {
if fnkey == "" {
return
}
chk.IntAssert(len(vmin), 2)
chk.IntAssert(len(vmax), 2)
V0, V1 := utl.MeshGrid2D(vmin[0], vmax[0], vmin[1], vmax[1], np, np)
var Zf [][]float64
var Zg [][][]float64
if f != nil {
Zf = la.MatAlloc(np, np)
}
if len(gs) > 0 {
Zg = utl.Deep3alloc(len(gs), np, np)
}
xtmp := make([]float64, 2)
for i := 0; i < np; i++ {
for j := 0; j < np; j++ {
xtmp[0], xtmp[1] = V0[i][j], V1[i][j]
if f != nil {
Zf[i][j] = f(xtmp)
}
for k, g := range gs {
Zg[k][i][j] = g(xtmp)
}
}
}
plt.Reset()
plt.SetForEps(0.8, 350)
if f != nil {
cmapidx := 0
plt.Contour(V0, V1, Zf, io.Sf("fsz=7, cmapidx=%d", cmapidx))
}
for k, _ := range gs {
plt.ContourSimple(V0, V1, Zg[k], false, 8, "zorder=5, levels=[0], colors=['yellow'], linewidths=[2], clip_on=0")
}
if x != nil {
plt.PlotOne(x[0], x[1], "'r*', label='optimum', zorder=10")
}
if extra != nil {
extra()
}
if dirout == "" {
dirout = "."
}
plt.Cross("clr='grey'")
plt.SetXnticks(11)
plt.SetYnticks(11)
if axequal {
plt.Equal()
}
plt.AxisRange(vmin[0], vmax[0], vmin[1], vmax[1])
args := "leg_out='1', leg_ncol=4, leg_hlen=1.5"
plt.Gll("$x_0$", "$x_1$", args)
plt.SaveD(dirout, fnkey+".eps")
}
// BuildCoordsMatrix returns the coordinate matrix of a particular Cell
func BuildCoordsMatrix(cell *inp.Cell, msh *inp.Mesh) (x [][]float64) {
x = la.MatAlloc(msh.Ndim, len(cell.Verts))
for i := 0; i < msh.Ndim; i++ {
for j, v := range cell.Verts {
x[i][j] = msh.Verts[v].C[i]
}
}
return
}
// Init initialises B-spline
func (o *Bspline) Init(T []float64, p int) {
// check
if len(T) < 2*(p+1) {
chk.Panic("at least %d knots are required to define clamped B-spline of order p==%d. m==%d is invalid", 2*(p+1), p, len(T))
}
// essential
o.T, o.p, o.m = T, p, len(T)
o.tmin, o.tmax = la.VecMinMax(T)
// auxiliary
o.le = make([]float64, o.p+1)
o.ri = make([]float64, o.p+1)
o.ndu = la.MatAlloc(o.p+1, o.p+1)
o.der = la.MatAlloc(o.p+1, o.p+1)
o.daux = la.MatAlloc(2, o.p+1)
}
// Init initialises B-spline
func (o *Bspline) Init(T []float64, p int) {
// check
if len(T) < 2*(p+1) {
chk.Panic(_bspline_err00, 2*(p+1), p, len(T))
}
// essential
o.T, o.p, o.m = T, p, len(T)
o.tmin, o.tmax = la.VecMinMax(T)
// auxiliary
o.le = make([]float64, o.p+1)
o.ri = make([]float64, o.p+1)
o.ndu = la.MatAlloc(o.p+1, o.p+1)
o.der = la.MatAlloc(o.p+1, o.p+1)
o.daux = la.MatAlloc(2, o.p+1)
}
// GetNodesNatCoordsMat returns the matrix (ξ) with natural coordinates of nodes,
// augmented by one column which is filled with ones [nverts][ndim+1]
func (o *Shape) GetNodesNatCoordsMat() (ξ [][]float64) {
ξ = la.MatAlloc(o.Nverts, o.Gndim+1)
for i := 0; i < o.Nverts; i++ {
for j := 0; j < o.Gndim; j++ {
ξ[i][j] = o.NatCoords[j][i]
}
ξ[i][o.Gndim] = 1.0
}
return
}
// UnitVectors generates random unit vectors in 3D
func UnitVectors(n int) (U [][]float64) {
U = la.MatAlloc(n, 3)
for i := 0; i < n; i++ {
φ := 2.0 * math.Pi * rand.Float64()
θ := math.Acos(1.0 - 2.0*rand.Float64())
U[i][0] = math.Sin(θ) * math.Cos(φ)
U[i][1] = math.Sin(θ) * math.Sin(φ)
U[i][2] = math.Cos(θ)
}
return
}
// GetIpsNatCoordsMat returns the matrix (\hat{ξ}) with natural coordinates of interation
// points, augmented by one column which is filled with ones [nip][ndim+1]
func (o *Shape) GetIpsNatCoordsMat(ips []Ipoint) (ξh [][]float64) {
nip := len(ips)
ξh = la.MatAlloc(nip, o.Gndim+1)
for i := 0; i < nip; i++ {
for j := 0; j < o.Gndim; j++ {
ξh[i][j] = ips[i][j]
}
ξh[i][o.Gndim] = 1.0
}
return
}
// SMPderivs1 computes the 1st order derivatives of SMP invariants
// Note: internal variables are created => not efficient
func SMPderivs1(dpdL, dqdL, L []float64, a, b, β, ϵ float64) (p, q float64, err error) {
dndL := la.MatAlloc(3, 3)
dNdL := make([]float64, 3)
Frmp := make([]float64, 3)
Grmp := make([]float64, 3)
W := make([]float64, 3) // workspace
m := SmpDerivs1(dndL, dNdL, W, Frmp, Grmp, L, a, b, β, ϵ) // W := N
W[0], W[1], W[2] = W[0]/m, W[1]/m, W[2]/m // W := n
p, q, err = GenInvsDeriv1(dpdL, dqdL, L, W, dndL, a)
return
}
