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) }
func Test_munkres04(tst *testing.T) { //verbose() chk.PrintTitle("munkres04. row and column matrices") C := [][]float64{ {1.0}, {2.0}, {0.5}, {3.0}, {4.0}, } var mnk Munkres mnk.Init(len(C), len(C[0])) mnk.SetCostMatrix(C) mnk.Run() io.Pforan("links = %v\n", mnk.Links) io.Pforan("cost = %v (13938)\n", mnk.Cost) chk.Ints(tst, "links", mnk.Links, []int{-1, -1, 0, -1, -1}) chk.Scalar(tst, "cost", 1e-17, mnk.Cost, 0.5) C = [][]float64{ {1.0, 2.0, 0.5, 3.0, 4.0}, } mnk.Init(len(C), len(C[0])) mnk.SetCostMatrix(C) mnk.Run() io.Pforan("links = %v\n", mnk.Links) io.Pforan("cost = %v (13938)\n", mnk.Cost) chk.Ints(tst, "links", mnk.Links, []int{2}) chk.Scalar(tst, "cost", 1e-17, mnk.Cost, 0.5) }
func Test_quad01(tst *testing.T) { //verbose() chk.PrintTitle("quad01") y := func(x float64) float64 { return math.Sqrt(1.0 + math.Pow(math.Sin(x), 3.0)) } var err error Acor := 1.08268158558 // trapezoidal rule var T Quadrature T = new(Trap) T.Init(y, 0, 1, 1e-11) A, err := T.Integrate() if err != nil { io.Pforan(err.Error()) } io.Pforan("A = %v\n", A) chk.Scalar(tst, "A", 1e-11, A, Acor) // Simpson's rule var S Quadrature S = new(Simp) S.Init(y, 0, 1, 1e-11) A, err = S.Integrate() if err != nil { io.Pforan(err.Error()) } io.Pforan("A = %v\n", A) chk.Scalar(tst, "A", 1e-11, A, Acor) }
func Test_mylab08(tst *testing.T) { //verbose() chk.PrintTitle("mylab08. dot and cross products") u := []float64{3, -3, 1} v := []float64{4, 9, 2} w := make([]float64, 3) s := Dot3d(u, v) Cross3d(w, u, v) // w := u cross v chk.Scalar(tst, "s = u dot v", 1e-17, s, -13) chk.Vector(tst, "w = u cross v", 1e-17, w, []float64{-15, -2, 39}) u = []float64{3, -3, 1} v = []float64{-12, 12, -4} s = Dot3d(u, v) Cross3d(w, u, v) // w := u cross v chk.Scalar(tst, "s = u dot v", 1e-17, s, -76) chk.Vector(tst, "w = u cross v", 1e-17, w, []float64{0, 0, 0}) u = []float64{3, 2, -2} v = []float64{1, 0, -5} s = Dot3d(u, v) Cross3d(w, u, v) // w := u cross v chk.Scalar(tst, "s = u dot v", 1e-17, s, 13) chk.Vector(tst, "w = u cross v", 1e-17, w, []float64{-10, 13, -2}) }
func Test_invs07(tst *testing.T) { //verbose() chk.PrintTitle("invs07") smp_a, smp_b, smp_β, smp_ϵ := -1.0, 0.0, 1.0, 1e-3 σ := []float64{-1, -1, 0, 0} pcam, qcam, _ := M_pqw(σ) poct, qoct := pcam*SQ3, qcam*SQ2by3 N := make([]float64, 3) n := make([]float64, 3) m := SmpDirector(N, σ, smp_a, smp_b, smp_β, smp_ϵ) SmpUnitDirector(n, m, N) psmp1, qsmp1, err := GenInvs(σ, n, smp_a) if err != nil { chk.Panic("M_GenInvs failed:\n%v", err) } psmp2, qsmp2, err := M_pq_smp(σ, smp_a, smp_b, smp_β, smp_ϵ) if err != nil { chk.Panic("M_pq_smp failed:\n%v", err) } io.Pforan("pcam, qcam = %v, %v\n", pcam, qcam) io.Pforan("poct, qoct = %v, %v\n", poct, qoct) io.Pforan("psmp1, qsmp1 = %v, %v\n", psmp1, qsmp1) io.Pforan("psmp2, qsmp2 = %v, %v\n", psmp2, qsmp2) chk.Scalar(tst, "p", 1e-15, psmp1, psmp2) chk.Scalar(tst, "q", 1e-15, qsmp1, qsmp2) }
func Test_beam01b(tst *testing.T) { //verbose() chk.PrintTitle("beam01b. simply supported") // start simulation analysis := NewFEM("data/beam01.sim", "", true, true, false, false, chk.Verbose, 0) // run simulation err := analysis.Run() if err != nil { tst.Errorf("Run failed:\n%v", err) return } // check dom := analysis.Domains[0] ele := dom.Elems[0].(*Beam) _, M := ele.CalcVandM(dom.Sol, 0.5, 1) qn, L := 15.0, 1.0 Mcentre := qn * L * L / 8.0 io.Pforan("M = %v (%v)\n", M, Mcentre) chk.Scalar(tst, "M @ centre", 1e-17, M[0], Mcentre) // check moment using OutIpsData idx_centre := 5 // considering 11 stations dat := ele.OutIpsData() res := dat[idx_centre].Calc(dom.Sol) io.Pfcyan("M @ centre (OutIpsData) = %v\n", res["M"]) chk.Scalar(tst, "M @ centre (OutIpsData)", 1e-17, res["M"], Mcentre) }
func TestMyLab03b(tst *testing.T) { //verbose() chk.PrintTitle("mylab03b") a := []int{1, 2, 3, -1, -2, 0, 8, -3} b := IntFilter(a, func(i int) bool { if a[i] < 0 { return true } return false }) c := IntNegOut(a) io.Pf("a = %v\n", a) io.Pf("b = %v\n", b) io.Pf("c = %v\n", c) chk.Ints(tst, "b", b, []int{1, 2, 3, 0, 8}) chk.Ints(tst, "c", c, []int{1, 2, 3, 0, 8}) A := []float64{1, 2, 3, -1, -2, 0, 8, -3} s := DblSum(A) mi, ma := DblMinMax(A) io.Pf("A = %v\n", A) io.Pf("sum(A) = %v\n", s) io.Pf("min(A) = %v\n", mi) io.Pf("max(A) = %v\n", ma) chk.Scalar(tst, "sum(A)", 1e-17, s, 8) chk.Scalar(tst, "min(A)", 1e-17, mi, -3) chk.Scalar(tst, "max(A)", 1e-17, ma, 8) }
func Test_prms02(tst *testing.T) { //verbose() chk.PrintTitle("prms02") var prms Prms prms = []*Prm{ &Prm{N: "klx", V: 1.0}, &Prm{N: "kly", V: 2.0}, &Prm{N: "klz", V: 3.0}, } io.Pforan("%v\n", prms) var klx, kly, klz float64 err_msg := prms.ConnectSet([]*float64{&klx, &kly, &klz}, []string{"klx", "kly", "klz"}, "Test_prms02") if err_msg != "" { tst.Error("connect set failed: %v\n", err_msg) return } chk.Scalar(tst, "klx", 1e-15, klx, 1.0) chk.Scalar(tst, "kly", 1e-15, kly, 2.0) chk.Scalar(tst, "klz", 1e-15, klz, 3.0) prms[1].Set(2.2) chk.Scalar(tst, "kly", 1e-15, kly, 2.2) }
func Test_ind01(tst *testing.T) { //verbose() chk.PrintTitle("ind01. representation and copying") rnd.Init(0) nbases := 3 A := get_individual(0, nbases) B := A.GetCopy() chk.Scalar(tst, "ova0", 1e-17, B.Ovas[0], 123) chk.Scalar(tst, "ova1", 1e-17, B.Ovas[1], 345) chk.Scalar(tst, "oor0", 1e-17, B.Oors[0], 10) chk.Scalar(tst, "oor1", 1e-17, B.Oors[1], 20) chk.Scalar(tst, "oor2", 1e-17, B.Oors[2], 30) fmts := map[string][]string{"int": {" %d"}, "flt": {" %.1f"}, "str": {" %q"}, "key": {" %x"}, "byt": {" %q"}, "fun": {" %q"}} oA := A.Output(fmts, false) oB := B.Output(fmts, false) io.Pfyel("\n%v\n", oA) io.Pfyel("%v\n\n", oB) chk.String(tst, oA, " 1 20 300 4.4 5.5 666.0 \"abc\" \"b\" \"c\" 53 47 41 \"ABC\" \"DEF\" \"GHI\" \"f0\" \"f1\" \"f2\"") chk.String(tst, oB, " 1 20 300 4.4 5.5 666.0 \"abc\" \"b\" \"c\" 53 47 41 \"ABC\" \"DEF\" \"GHI\" \"f0\" \"f1\" \"f2\"") A.SetFloat(1, 33) A.SetFloat(2, 88) oA = A.Output(fmts, false) io.Pfyel("\n%v\n", oA) chk.String(tst, oA, " 1 20 300 4.4 33.0 88.0 \"abc\" \"b\" \"c\" 53 47 41 \"ABC\" \"DEF\" \"GHI\" \"f0\" \"f1\" \"f2\"") }
func Test_matinvSmall01(tst *testing.T) { //verbose() chk.PrintTitle("matinvSmall01") noise := 0.0 tol := 1.0e-16 // 1 x 1 matrix res := MatAlloc(1, 1) det, err := MatInv(res, [][]float64{{2.0}}, tol) if err != nil { chk.Panic("%v", err.Error()) } chk.Scalar(tst, "1 x 1 matrix: det ", tol, det, 2.0) chk.Matrix(tst, "1 x 1 matrix: ", tol, res, [][]float64{{0.5}}) // matrix: inverse A := [][]float64{{1.0, 2.0}, {3.0, 2.0}} Aicorr := [][]float64{{-0.5, 0.5}, {0.75, -0.25 + noise}} Ai := MatAlloc(2, 2) detA, err := MatInv(Ai, A, tol) if err != nil { chk.Panic("%v", err.Error()) } chk.Scalar(tst, "matrix: inv (det) ", tol, detA, -4.0+noise) chk.Matrix(tst, "matrix: inv (A) ", tol, Ai, Aicorr) // using MatInvG Ai_ := MatAlloc(2, 2) err = MatInvG(Ai_, A, tol) if err != nil { chk.Panic("%v", err.Error()) } chk.Matrix(tst, "matrix: inv with MatInvG", tol, Ai_, Aicorr) // another test B := [][]float64{{9.0, 3.0, 5.0}, {-6.0, -9.0, 7.0}, {-1.0, -8.0, 1.0}} Bicorr := [][]float64{ {7.642276422764227e-02, -6.991869918699187e-02, 1.073170731707317e-01}, {-1.626016260162601e-03, 2.276422764227642e-02, -1.512195121951219e-01}, {6.341463414634146e-02, 1.121951219512195e-01, -1.024390243902439e-01 + noise}, } Bi := MatAlloc(3, 3) detB, err := MatInv(Bi, B, tol) if err != nil { chk.Panic("%v", err.Error()) } chk.Scalar(tst, "matrix: det ", tol, detB, 615.0+noise) chk.Matrix(tst, "matrix: inv ", tol, Bi, Bicorr) // using MatInvG Bi_ := MatAlloc(3, 3) err = MatInvG(Bi_, B, tol) if err != nil { chk.Panic("%v", err.Error()) } chk.Matrix(tst, "matrix: inv with MatInvG", tol, Bi_, Bicorr) }
func Test_ind02(tst *testing.T) { //verbose() chk.PrintTitle("ind02. copy into") rnd.Init(0) nbases := 1 A := get_individual(0, nbases) B := get_individual(1, nbases) fmts := map[string][]string{ "int": {"%2d", "%4d", "%5d"}, // ints "flt": {"%6g", "%6g", "%5g"}, // floats "str": {"%4s", "%2s", "%2s"}, // strings "key": {"%3x", "%3x", "%3x"}, // keys "byt": {"%4s", "%4s", "%4s"}, // bytes "fun": {"%3s", "%3s", "%3s"}, // funcs } io.Pfpink("A = %v\n", A.Output(fmts, false)) io.Pfcyan("B = %v\n", B.Output(fmts, false)) var ops OpsData ops.SetDefault() ops.Pc = 1.0 ops.Cuts = []int{1, 2} ops.Xrange = [][]float64{{0, 1}, {-20, 20}, {-300, 300}} a := A.GetCopy() b := A.GetCopy() IndCrossover(a, b, A, B, 0, &ops) io.Pforan("a = %v\n", a.Output(fmts, false)) io.Pfblue2("b = %v\n", b.Output(fmts, false)) chk.Ints(tst, "a.Ints ", a.Ints, []int{1, -20, 300}) chk.Ints(tst, "b.Ints ", b.Ints, []int{-1, 20, -300}) chk.Strings(tst, "a.Strings", a.Strings, []string{"abc", "Y", "c"}) chk.Strings(tst, "b.Strings", b.Strings, []string{"X", "b", "Z"}) // TODO: add other tests here io.Pf("\n") x := get_individual(0, nbases) x.Ovas = []float64{0, 0} x.Oors = []float64{0, 0, 0} io.Pfblue2("x = %v\n", x.Output(fmts, false)) B.CopyInto(x) chk.Scalar(tst, "ova0", 1e-17, x.Ovas[0], 200) chk.Scalar(tst, "ova1", 1e-17, x.Ovas[1], 100) chk.Scalar(tst, "oor0", 1e-17, x.Oors[0], 15) chk.Scalar(tst, "oor1", 1e-17, x.Oors[1], 25) chk.Scalar(tst, "oor2", 1e-17, x.Oors[2], 35) io.Pforan("x = %v\n", x.Output(fmts, false)) chk.String(tst, x.Output(fmts, false), B.Output(fmts, false)) }
func Test_fun05(tst *testing.T) { //verbose() chk.PrintTitle("fun05. zero and one") io.Pforan("Zero(666,nil) = %v\n", Zero.F(666, nil)) io.Pforan("One(666,nil) = %v\n", One.F(666, nil)) chk.Scalar(tst, "zero", 1e-17, Zero.F(666, nil), 0) chk.Scalar(tst, "one ", 1e-17, One.F(666, nil), 1) }
func check_constants(tst *testing.T, E, ν, Kcor, Gcor, lcor float64) { K, G := Calc_K_from_Enu(E, ν), Calc_G_from_Enu(E, ν) l := Calc_l_from_Enu(E, ν) io.Pf("E = %v\n", E) io.Pf("ν = %v\n", ν) io.Pf("K = %v\n", K) io.Pf("G = %v\n", G) io.Pf("l = %v\n", l) chk.Scalar(tst, "KfromEν", 1e-17, K, Kcor) chk.Scalar(tst, "GfromEν", 1e-17, G, Gcor) chk.Scalar(tst, "lfromEν", 1e-17, l, lcor) EfromKG, νfromKG := Calc_E_from_KG(K, G), Calc_nu_from_KG(K, G) chk.Scalar(tst, "EfromKG", 1e-17, EfromKG, E) chk.Scalar(tst, "νfromKG", 1e-17, νfromKG, ν) EfromlG, νfromlG := Calc_E_from_lG(l, G), Calc_nu_from_lG(l, G) chk.Scalar(tst, "EfromlG", 1e-17, EfromlG, E) chk.Scalar(tst, "νfromlG", 1e-17, νfromlG, ν) EfromKν, GfromKν := Calc_E_from_Knu(K, ν), Calc_G_from_Knu(K, ν) chk.Scalar(tst, "EfromKν", 1e-17, EfromKν, E) chk.Scalar(tst, "GfromKν", 1e-17, GfromKν, G) }
func Test_gumbel_03(tst *testing.T) { //verbose() chk.PrintTitle("dist_gumbel_03") var dist DistGumbel dist.Init(&VarData{M: 61.3, S: 7.52}) // from Haldar & Mahadevan page 90 io.Pforan("dist = %+#v\n", dist) chk.Scalar(tst, "u", 0.00011, dist.U, 57.9157) chk.Scalar(tst, "β", 1e-4, dist.B, 1.0/0.17055) }
func Test_cubiceq02(tst *testing.T) { //verbose() chk.PrintTitle("cubiceq02. y(x) = x³ + x²") a, b, c := 1.0, 0.0, 0.0 x1, x2, x3, nx := EqCubicSolveReal(a, b, c) io.Pforan("\na=%v b=%v c=%v\n", a, b, c) io.Pfcyan("nx=%v\n", nx) io.Pfcyan("x1=%v x2=%v x3=%v\n", x1, x2, x3) chk.IntAssert(nx, 2) chk.Scalar(tst, "x1", 1e-17, x1, -1) chk.Scalar(tst, "x2", 1e-17, x2, 0) }
func Test_cubiceq01(tst *testing.T) { //verbose() chk.PrintTitle("cubiceq01. y(x) = x³ - 3x² - 144x + 432") a, b, c := -3.0, -144.0, 432.0 x1, x2, x3, nx := EqCubicSolveReal(a, b, c) io.Pforan("\na=%v b=%v c=%v\n", a, b, c) io.Pfcyan("nx=%v\n", nx) io.Pfcyan("x1=%v x2=%v x3=%v\n", x1, x2, x3) chk.IntAssert(nx, 3) chk.Scalar(tst, "x1", 1e-17, x1, -12) chk.Scalar(tst, "x2", 1e-17, x2, 12) chk.Scalar(tst, "x3", 1e-14, x3, 3) }
func Test_simplechromo01(tst *testing.T) { //verbose() chk.PrintTitle("simplechromo01") rnd.Init(0) nbases := 2 for i := 0; i < 10; i++ { chromo := SimpleChromo([]float64{1, 10, 100}, nbases) io.Pforan("chromo = %v\n", chromo) chk.IntAssert(len(chromo), 3*nbases) chk.Scalar(tst, "gene0", 1e-14, chromo[0]+chromo[1], 1) chk.Scalar(tst, "gene1", 1e-14, chromo[2]+chromo[3], 10) chk.Scalar(tst, "gene2", 1e-13, chromo[4]+chromo[5], 100) } }
func Test_phi03(tst *testing.T) { // verbose() chk.PrintTitle("phi03 - Reinitialisation") // run simulation analysis := NewFEM("data/phi03.sim", "", true, false, false, false, chk.Verbose, 0) // run simulation err := analysis.Run() if err != nil { tst.Errorf("Run failed:\n%v", err) return } // domain dom := analysis.Domains[0] eq := []int{ 0, 20, 54, } node := []int{ 0, 10, 27, } // check results for i, v := range eq { // chk.PrintTitle(io.Sf("%25.10e%25.10e", dom.Sol.Y[v], dom.Msh.Verts[node[i]].C[0])) chk.Scalar(tst, "h @ nod "+string(i), 5e-2, dom.Sol.Y[v], dom.Msh.Verts[node[i]].C[0]) } }
func Test_msh01(tst *testing.T) { chk.PrintTitle("msh01") msh := ReadMsh("data", "bh16.msh") if msh == nil { tst.Errorf("test failed\n") return } io.Pforan("%v\n", msh) io.Pfcyan("lims = [%g, %g, %g, %g, %g, %g]\n", msh.Xmin, msh.Xmax, msh.Ymin, msh.Ymax, msh.Zmin, msh.Zmax) chk.Scalar(tst, "xmin", 1e-17, msh.Xmin, 10) chk.Scalar(tst, "xmax", 1e-17, msh.Xmax, 14) chk.Scalar(tst, "ymin", 1e-17, msh.Ymin, -1) chk.Scalar(tst, "ymax", 1e-17, msh.Ymax, 1) }
func Test_brent03(tst *testing.T) { //verbose() chk.PrintTitle("brent03. minimum finding") ffcn := func(x float64) (res float64, err error) { return x*x*x - 2.0*x - 5.0, nil } var o Brent o.Init(ffcn) xa, xb := 0.0, 1.0 x, err := o.Min(xa, xb, false) if err != nil { chk.Panic("%v", err) } y, err := ffcn(x) if err != nil { chk.Panic("%v", err) } xcor := math.Sqrt(2.0 / 3.0) io.Pforan("x = %v (correct=%g)\n", x, xcor) io.Pforan("f(x) = %v\n", y) io.Pforan("nfeval = %v\n", o.NFeval) io.Pforan("nit = %v\n", o.It) //save := true save := false PlotYxe(ffcn, "results", "brent03.png", x, -1, 3, 101, "Brent", "'b-'", save, false, nil) chk.Scalar(tst, "xcorrect", 1e-8, x, xcor) }
// run_rootsol_test runs root solution test // Note: xguess is the trial solution for Newton's method (not Brent's) func run_rootsol_test(tst *testing.T, xa, xb, xguess, tolcmp float64, ffcnA Cb_yxe, ffcnB Cb_f, JfcnB Cb_Jd, fname string, save, show bool) (xbrent float64) { // Brent io.Pfcyan("\n - - - - - - - using Brent's method - - -- - - - \n") var o Brent o.Init(ffcnA) var err error xbrent, err = o.Solve(xa, xb, false) if err != nil { chk.Panic("%v", err) } var ybrent float64 ybrent, err = ffcnA(xbrent) if err != nil { chk.Panic("%v", err) } io.Pforan("x = %v\n", xbrent) io.Pforan("f(x) = %v\n", ybrent) io.Pforan("nfeval = %v\n", o.NFeval) io.Pforan("nit = %v\n", o.It) if math.Abs(ybrent) > 1e-10 { chk.Panic("Brent failed: f(x) = %g > 1e-10\n", ybrent) } // Newton io.Pfcyan("\n - - - - - - - using Newton's method - - -- - - - \n") var p NlSolver p.Init(1, ffcnB, nil, JfcnB, true, false, nil) xnewt := []float64{xguess} var cnd float64 cnd, err = p.CheckJ(xnewt, 1e-6, true, !chk.Verbose) io.Pforan("cond(J) = %v\n", cnd) if err != nil { chk.Panic("%v", err.Error()) } err = p.Solve(xnewt, false) if err != nil { chk.Panic("%v", err.Error()) } var ynewt float64 ynewt, err = ffcnA(xnewt[0]) if err != nil { chk.Panic("%v", err) } io.Pforan("x = %v\n", xnewt[0]) io.Pforan("f(x) = %v\n", ynewt) io.Pforan("nfeval = %v\n", p.NFeval) io.Pforan("nJeval = %v\n", p.NJeval) io.Pforan("nit = %v\n", p.It) if math.Abs(ynewt) > 1e-9 { chk.Panic("Newton failed: f(x) = %g > 1e-10\n", ynewt) } // compare Brent's and Newton's solutions PlotYxe(ffcnA, "results", fname, xbrent, xa, xb, 101, "Brent", "'b-'", save, show, func() { plt.PlotOne(xnewt[0], ynewt, "'g+', ms=15, label='Newton'") }) chk.Scalar(tst, "xbrent - xnewt", tolcmp, xbrent, xnewt[0]) return }
func Test_brent02(tst *testing.T) { //verbose() chk.PrintTitle("brent02. root finding") ffcnA := func(x float64) (res float64, err error) { return x*x*x - 2.0*x - 5.0, nil } ffcnB := func(fx, x []float64) (err error) { fx[0], err = ffcnA(x[0]) return } JfcnB := func(dfdx [][]float64, x []float64) (err error) { dfdx[0][0] = 3.0*x[0]*x[0] - 2.0 return } xa, xb := 2.0, 3.0 xguess := 2.1 //save := true save := false xbrent := run_rootsol_test(tst, xa, xb, xguess, 1e-7, ffcnA, ffcnB, JfcnB, "brent02.png", save, false) chk.Scalar(tst, "xsol", 1e-14, xbrent, 2.09455148154233) }
func Test_pop02(tst *testing.T) { //verbose() chk.PrintTitle("pop02") rnd.Init(0) genes := [][]float64{ {1, 5}, // 0 {1, 3}, // 1 {5, 7}, // 2 {1, 2}, // 3 {2, 4}, // 4 {3, 6}, // 5 {4, 8}, // 6 {4, 6}, // 7 {1, 3}, // 8 {0, 0}, // 9 } // objective values, oor and demerits // 0 1 2 3 4 5 6 7 8 9 ovs := []float64{11, 21, 10, 12, 13, 31, 41, 11.1, 31.5, 11.5} dem := []float64{0.2, 0.7, 0.1, 0.5, 0.6, 0.8, 1.0, 0.3, 0.9, 0.4} // init population ninds := len(genes) nova := 1 noor := 0 nbases := 2 var pop Population pop = make([]*Individual, ninds) for i := 0; i < ninds; i++ { pop[i] = NewIndividual(nova, noor, nbases, genes[i]) pop[i].Ovas[0] = ovs[i] pop[i].Demerit = dem[i] } pop.Sort() genes_sorted := [][]float64{ {5, 7}, // 2 {1, 5}, // 0 {4, 6}, // 7 {0, 0}, // 9 {1, 2}, // 3 {2, 4}, // 4 {1, 3}, // 1 {3, 6}, // 5 {1, 3}, // 8 {4, 8}, // 6 } for i, ind := range pop { for j := 0; j < ind.Nfltgenes; j++ { chk.Scalar(tst, io.Sf("i%dg%d", i, j), 1e-14, ind.GetFloat(j), genes_sorted[i][j]) } } }
func Test_reliab01(tst *testing.T) { //verbose() chk.PrintTitle("reliab01. simply supported beam") // Simply supported beam // Analyse the max deflection at mid-span of simply supported beam // with uniform distributed load q and concentrated load at midspan // Data: // L -- span // EI -- Young's modulus times cross-sectional moment of inertia // p -- x[0] concentrated load at mid-span // q -- x[1] distributed load // δlim -- max deflection (vertical displacement) at mid-span // Reference // Haldar A, Reliability-Based Structura Design, 2005 // constants δlim := 0.0381 // [m] max allowed deflection L := 9.144 // [m] span EI := 182262.0 // [kN m²] flexural rigidity L3 := math.Pow(L, 3.0) // statistics of p=x[0] and q=x[1] μ := []float64{111.2, 35.03} // mean values σ := []float64{11.12, 5.25} // deviation values lrv := []bool{true, false} // is lognormal random variable? // limit state function gfcn := func(x []float64, args ...interface{}) (g float64, err error) { p, q := x[0], x[1] g = δlim - (p*L3/EI/48.0 + 5.0*q*L3*L/EI/384.0) return } // derivative of limit state function hfcn := func(dgdx, x []float64, args ...interface{}) (err error) { dgdx[0] = -L3 / EI / 48.0 // dg/dp dgdx[1] = -5.0 * L3 * L / EI / 384.0 // dg/dq return } // first order reliability method var form ReliabFORM form.Init(μ, σ, lrv, gfcn, hfcn) form.NlsSilent = !chk.Verbose form.NlsCheckJ = chk.Verbose form.TolA = 0.005 form.TolB = 0.005 if chk.Verbose { form.PlotFnk = "beam" } // run FORM verbose := chk.Verbose // show messages βtrial := 3.0 β, _, _, _ := form.Run(βtrial, verbose) chk.Scalar(tst, "β", 0.0015, β, 3.8754) }
func Test_tsr03(tst *testing.T) { //verbose() chk.PrintTitle("tsr03") a := [][]float64{ {4.0, 1.0 / SQ2, 0}, {1.0 / SQ2, 5.0, 0}, {0, 0, 6.0}, } am := make([]float64, 4) aa := Alloc2() Ten2Man(am, a) Man2Ten(aa, am) io.Pf("a = %v\n", a) io.Pf("am = %v\n", am) io.Pf("aa = %v\n", aa) chk.Matrix(tst, "aa", 1.0e-15, aa, a) for i := 0; i < 3; i++ { for j := 0; j < 3; j++ { chk.Scalar(tst, fmt.Sprintf("am[%d][%d]", i, j), 1.0e-15, M2T(am, i, j), a[i][j]) } } b := [][]float64{ {4.0, 1.0 / SQ2, 3.0 / SQ2}, {1.0 / SQ2, 5.0, 2.0 / SQ2}, {3.0 / SQ2, 2.0 / SQ2, 6.0}, } bm := make([]float64, 6) bb := Alloc2() Ten2Man(bm, b) Man2Ten(bb, bm) io.Pf("b = %v\n", b) io.Pf("bm = %v\n", bm) io.Pf("bb = %v\n", bb) chk.Matrix(tst, "bb", 1.0e-15, bb, b) for i := 0; i < 3; i++ { for j := 0; j < 3; j++ { chk.Scalar(tst, fmt.Sprintf("bm[%d][%d]", i, j), 1.0e-15, M2T(bm, i, j), b[i][j]) } } }
func Test_nurbs01(tst *testing.T) { //verbose() chk.PrintTitle("nurbs01") nurbs := get_nurbs_A() faces := nurbs.ExtractSurfaces() spans := nurbs.Elements() ibasis0 := nurbs.IndBasis(spans[0]) ibasis1 := nurbs.IndBasis(spans[1]) io.Pforan("spans = %v\n", spans) chk.Ints(tst, "span0", spans[0], []int{2, 3, 1, 2}) chk.Ints(tst, "span1", spans[1], []int{3, 4, 1, 2}) chk.Ints(tst, "ibasis0", ibasis0, []int{0, 1, 2, 4, 5, 6}) chk.Ints(tst, "ibasis1", ibasis1, []int{1, 2, 3, 5, 6, 7}) shape0 := GetShapeNurbs(nurbs, faces, spans[0]) shape1 := GetShapeNurbs(nurbs, faces, spans[1]) dux := 0.5 duy := 1.0 drx := 2.0 dry := 2.0 r := []float64{0.75, 0.75, 0} shape0.NurbsFunc(shape0.S, shape0.DSdR, r, true, -1) io.Pforan("0: u = %v\n", shape0.U) chk.Scalar(tst, "0: ux", 1e-17, shape0.U[0], (1.0+r[0])*dux/drx) chk.Scalar(tst, "0: uy", 1e-17, shape0.U[1], (1.0+r[1])*duy/dry) chk.Ints(tst, "0: ibasis", shape0.Ibasis, []int{0, 1, 2, 4, 5, 6}) io.Pforan("S(u(r)) = %v\n", shape0.S) shape1.NurbsFunc(shape1.S, shape1.DSdR, r, true, -1) io.Pfpink("\n1: u = %v\n", shape1.U) chk.Scalar(tst, "1: ux", 1e-17, shape1.U[0], 0.5+(1.0+r[0])*dux/drx) chk.Scalar(tst, "1: uy", 1e-17, shape1.U[1], (1.0+r[1])*duy/dry) chk.Ints(tst, "1: ibasis", shape1.Ibasis, []int{1, 2, 3, 5, 6, 7}) if chk.Verbose { gm.PlotNurbs("/tmp/gofem", "tst_nurbs01", nurbs, 21, false, nil) } }
func Test_igd01(tst *testing.T) { //verbose() chk.PrintTitle("igd. igd metric with star equal to trial => igd=0") // load star values prob := "UF1" fStar, err := io.ReadMatrix(io.Sf("./examples/mulobj-cec09/cec09/pf_data/%s.dat", prob)) if err != nil { tst.Errorf("cannot read fStar matrix:\n%v", err) return } npts := len(fStar) // optimiser var opt Optimiser opt.Default() opt.Nsol = npts opt.Ncpu = 1 opt.FltMin = []float64{0, 0} // used to store fStar opt.FltMax = []float64{1, 1} // used to store fStar nf, ng, nh := 2, 0, 0 // generator (store fStar into Flt) gen := func(sols []*Solution, prms *Parameters) { for i, sol := range sols { sol.Flt[0], sol.Flt[1] = fStar[i][0], fStar[i][1] } } // objective function (copy fStar from Flt into Ova) obj := func(f, g, h, x []float64, ξ []int, cpu int) { f[0], f[1] = x[0], x[1] } // initialise optimiser opt.Init(gen, nil, obj, nf, ng, nh) // compute igd igd := StatIgd(&opt, fStar) io.Pforan("igd = %v\n", igd) chk.Scalar(tst, "igd", 1e-15, igd, 0) // plot if chk.Verbose { fmt := &plt.Fmt{C: "red", M: ".", Ms: 1, Ls: "None", L: "solutions"} fS0 := utl.DblsGetColumn(0, fStar) fS1 := utl.DblsGetColumn(1, fStar) io.Pforan("len(fS0) = %v\n", len(fS0)) plt.SetForEps(0.75, 300) opt.PlotAddOvaOva(0, 1, opt.Solutions, true, fmt) plt.Plot(fS0, fS1, io.Sf("'b.', ms=2, label='star(%s)', clip_on=0", prob)) plt.Gll("$f_0$", "$f_1$", "") plt.SaveD("/tmp/goga", "igd01.eps") } }
func Test_trapz01(tst *testing.T) { //verbose() chk.PrintTitle("trapz01") x := []float64{4, 6, 8} y := []float64{1, 2, 3} A := Trapz(x, y) chk.Scalar(tst, "A", 1e-17, A, 8) }
func Test_trapz02(tst *testing.T) { //verbose() chk.PrintTitle("trapz02") y := func(x float64) float64 { return math.Sqrt(1.0 + math.Pow(math.Sin(x), 3.0)) } n := 11 x := utl.LinSpace(0, 1, n) A := TrapzF(x, y) A_ := TrapzRange(0, 1, n, y) io.Pforan("A = %v\n", A) io.Pforan("A_ = %v\n", A_) Acor := 1.08306090851465 // right value is Acor := 1.08268158558 chk.Scalar(tst, "A", 1e-15, A, Acor) chk.Scalar(tst, "A_", 1e-15, A_, Acor) }
func Test_basicgeom02(tst *testing.T) { //verbose() chk.PrintTitle("basicgeom02. Vector") u := []float64{1, 2, 3} v := []float64{4, 5, 6} s := VecDot(u, v) r := VecNew(2, u) w := VecNewAdd(2, u, -3, v) io.Pforan("u = %v norm = %g\n", u, VecNorm(u)) io.Pforan("v = %v norm = %g\n", v, VecNorm(v)) io.Pforan("w = %v norm = %g\n", w, VecNorm(w)) io.Pforan("u.v = %v\n", s) chk.Scalar(tst, "u.v", 1e-17, s, 32.0) chk.Scalar(tst, "norm(u)", 1e-17, VecNorm(u), math.Sqrt(14.0)) chk.Scalar(tst, "norm(v)", 1e-17, VecNorm(v), math.Sqrt(77.0)) chk.Vector(tst, "r", 1e-17, r, []float64{2, 4, 6}) chk.Vector(tst, "w", 1e-17, w, []float64{-10, -11, -12}) }