Beispiel #1
0
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)
	}
}
Beispiel #2
0
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)
}