func TestJacobian03(tst *testing.T) {
//verbose()
chk.PrintTitle("TestJacobian 03")
// grid
var g fdm.Grid2D
//g.Init(1.0, 1.0, 4, 4)
g.Init(1.0, 1.0, 6, 6)
//g.Init(1.0, 1.0, 11, 11)
// equations numbering
var e fdm.Equations
peq := utl.IntUnique(g.L, g.R, g.B, g.T)
e.Init(g.N, peq)
// K11 and K12
var K11, K12 la.Triplet
fdm.InitK11andK12(&K11, &K12, &e)
// assembly
F1 := make([]float64, e.N1)
fdm.Assemble(&K11, &K12, F1, nil, &g, &e)
// prescribed values
U2 := make([]float64, e.N2)
for _, eq := range g.L {
U2[e.FR2[eq]] = 50.0
}
for _, eq := range g.R {
U2[e.FR2[eq]] = 0.0
}
for _, eq := range g.B {
U2[e.FR2[eq]] = 0.0
}
for _, eq := range g.T {
U2[e.FR2[eq]] = 50.0
}
// functions
k11 := K11.ToMatrix(nil)
k12 := K12.ToMatrix(nil)
ffcn := func(fU1, U1 []float64) error { // K11*U1 + K12*U2 - F1
la.VecCopy(fU1, -1, F1) // fU1 := (-F1)
la.SpMatVecMulAdd(fU1, 1, k11, U1) // fU1 += K11*U1
la.SpMatVecMulAdd(fU1, 1, k12, U2) // fU1 += K12*U2
return nil
}
Jfcn := func(dfU1dU1 *la.Triplet, U1 []float64) error {
fdm.Assemble(dfU1dU1, &K12, F1, nil, &g, &e)
return nil
}
U1 := make([]float64, e.N1)
CompareJac(tst, ffcn, Jfcn, U1, 0.0075)
print_jac := false
if print_jac {
W1 := make([]float64, e.N1)
fU1 := make([]float64, e.N1)
ffcn(fU1, U1)
var Jnum la.Triplet
Jnum.Init(e.N1, e.N1, e.N1*e.N1)
Jacobian(&Jnum, ffcn, U1, fU1, W1)
la.PrintMat("K11 ", K11.ToMatrix(nil).ToDense(), "%g ", false)
la.PrintMat("Jnum", Jnum.ToMatrix(nil).ToDense(), "%g ", false)
}
test_ffcn := false
if test_ffcn {
Uc := []float64{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 50.0, 25.0, 325.0 / 22.0, 100.0 / 11.0, 50.0 / 11.0,
0.0, 50.0, 775.0 / 22.0, 25.0, 375.0 / 22.0, 100.0 / 11.0, 0.0, 50.0, 450.0 / 11.0, 725.0 / 22.0,
25.0, 325.0 / 22.0, 0.0, 50.0, 500.0 / 11.0, 450.0 / 11.0, 775.0 / 22.0, 25.0, 0.0, 50.0, 50.0,
50.0, 50.0, 50.0, 50.0,
}
for i := 0; i < e.N1; i++ {
U1[i] = Uc[e.RF1[i]]
}
fU1 := make([]float64, e.N1)
min, max := la.VecMinMax(fU1)
io.Pf("min/max fU1 = %v\n", min, max)
}
}
func Test_nls04(tst *testing.T) {
//verbose()
chk.PrintTitle("nls04. finite differences problem")
// grid
var g fdm.Grid2D
g.Init(1.0, 1.0, 6, 6)
// equations numbering
var e fdm.Equations
peq := utl.IntUnique(g.L, g.R, g.B, g.T)
e.Init(g.N, peq)
// K11 and K12
var K11, K12 la.Triplet
fdm.InitK11andK12(&K11, &K12, &e)
// assembly
F1 := make([]float64, e.N1)
fdm.Assemble(&K11, &K12, F1, nil, &g, &e)
// prescribed values
U2 := make([]float64, e.N2)
for _, eq := range g.L {
U2[e.FR2[eq]] = 50.0
}
for _, eq := range g.R {
U2[e.FR2[eq]] = 0.0
}
for _, eq := range g.B {
U2[e.FR2[eq]] = 0.0
}
for _, eq := range g.T {
U2[e.FR2[eq]] = 50.0
}
// functions
k11 := K11.ToMatrix(nil)
k12 := K12.ToMatrix(nil)
ffcn := func(fU1, U1 []float64) error { // K11*U1 + K12*U2 - F1
la.VecCopy(fU1, -1, F1) // fU1 := (-F1)
la.SpMatVecMulAdd(fU1, 1, k11, U1) // fU1 += K11*U1
la.SpMatVecMulAdd(fU1, 1, k12, U2) // fU1 += K12*U2
return nil
}
Jfcn := func(dfU1dU1 *la.Triplet, U1 []float64) error {
fdm.Assemble(dfU1dU1, &K12, F1, nil, &g, &e)
return nil
}
JfcnD := func(dfU1dU1 [][]float64, U1 []float64) error {
la.MatCopy(dfU1dU1, 1, K11.ToMatrix(nil).ToDense())
return nil
}
prms := map[string]float64{
"atol": 1e-8,
"rtol": 1e-8,
"ftol": 1e-12,
"lSearch": 0.0,
}
// init
var nls_sps NlSolver // sparse analytical
var nls_num NlSolver // sparse numerical
var nls_den NlSolver // dense analytical
nls_sps.Init(e.N1, ffcn, Jfcn, nil, false, false, prms)
nls_num.Init(e.N1, ffcn, nil, nil, false, true, prms)
nls_den.Init(e.N1, ffcn, nil, JfcnD, true, false, prms)
defer nls_sps.Clean()
defer nls_num.Clean()
defer nls_den.Clean()
// results
U1sps := make([]float64, e.N1)
U1num := make([]float64, e.N1)
U1den := make([]float64, e.N1)
Usps := make([]float64, e.N)
Unum := make([]float64, e.N)
Uden := make([]float64, e.N)
// solution
Uc := []float64{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 50.0, 25.0, 325.0 / 22.0, 100.0 / 11.0, 50.0 / 11.0,
0.0, 50.0, 775.0 / 22.0, 25.0, 375.0 / 22.0, 100.0 / 11.0, 0.0, 50.0, 450.0 / 11.0, 725.0 / 22.0,
25.0, 325.0 / 22.0, 0.0, 50.0, 500.0 / 11.0, 450.0 / 11.0, 775.0 / 22.0, 25.0, 0.0, 50.0, 50.0,
50.0, 50.0, 50.0, 50.0,
}
io.PfYel("\n---- sparse -------- Analytical Jacobian -------------------\n")
// solve
err := nls_sps.Solve(U1sps, false)
if err != nil {
chk.Panic(err.Error())
}
// check
fdm.JoinVecs(Usps, U1sps, U2, &e)
chk.Vector(tst, "Usps", 1e-14, Usps, Uc)
// plot
if false {
g.Contour("results", "fig_t_heat_square", nil, Usps, 11, false)
}
io.PfYel("\n---- dense -------- Analytical Jacobian -------------------\n")
// solve
err = nls_den.Solve(U1den, false)
if err != nil {
chk.Panic(err.Error())
}
// check
fdm.JoinVecs(Uden, U1den, U2, &e)
chk.Vector(tst, "Uden", 1e-14, Uden, Uc)
io.PfYel("\n---- sparse -------- Numerical Jacobian -------------------\n")
// solve
err = nls_num.Solve(U1num, false)
if err != nil {
chk.Panic(err.Error())
}
// check
fdm.JoinVecs(Unum, U1num, U2, &e)
chk.Vector(tst, "Unum", 1e-14, Unum, Uc)
}