func checkinput(tst *testing.T, m *Mesh, nverts, ncells int, X [][]float64, vtags, ctags, parts []int, types []string, V [][]int, etags, ftags [][]int) {
	if len(m.Verts) != nverts {
		tst.Errorf("nverts is incorrect: %d != %d", len(m.Verts), nverts)
		return
	}
	if len(m.Cells) != ncells {
		tst.Errorf("ncells is incorrect: %d != %d", len(m.Cells), ncells)
		return
	}
	io.Pfyel("\nvertices:\n")
	for i, v := range m.Verts {
		io.Pf("%+v\n", v)
		chk.Vector(tst, io.Sf("vertex %2d: X", v.Id), 1e-15, v.X, X[v.Id])
		if v.Tag != vtags[i] {
			tst.Errorf("vtag is incorrect: %d != %d", v.Tag, vtags[i])
			return
		}
	}
	io.Pfyel("\ncells:\n")
	for i, c := range m.Cells {
		io.Pf("%+v\n", c)
		if c.Tag != ctags[i] {
			tst.Errorf("ctag is incorrect: %d != %d", c.Tag, ctags[i])
			return
		}
		if c.Part != parts[i] {
			tst.Errorf("part is incorrect: %d != %d", c.Part, parts[i])
			return
		}
		chk.String(tst, types[i], c.Type)
		chk.Ints(tst, io.Sf("cell %2d : V", c.Id), c.V, V[c.Id])
		chk.Ints(tst, io.Sf("cell %2d : edgetags", c.Id), c.EdgeTags, etags[c.Id])
	}
}

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_stat02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("stat02")

	x := [][]float64{
		{100, 100, 102, 98, 77, 99, 70, 105, 98},
		{80, 101, 12, 58, 47, 80, 20, 111, 89},
		{50, 130, 72, 38, 71, 15, 10, 12, 55},
	}

	y, z := StatTable(x, true, true)
	la.PrintMat("x", x, "%5g", false)
	la.PrintMat("y", y, "%13.6f", false)
	la.PrintMat("z", z, "%13.6f", false)
	io.Pforan("\nmin\n")
	chk.Scalar(tst, "y00=min(x[0,:])", 1e-17, y[0][0], 70)
	chk.Scalar(tst, "y01=min(x[1,:])", 1e-17, y[0][1], 12)
	chk.Scalar(tst, "y02=min(x[2,:])", 1e-17, y[0][2], 10)
	io.Pforan("\nave\n")
	chk.Scalar(tst, "y10=ave(x[0,:])", 1e-17, y[1][0], 849.0/9.0)
	chk.Scalar(tst, "y11=ave(x[1,:])", 1e-17, y[1][1], 598.0/9.0)
	chk.Scalar(tst, "y12=ave(x[2,:])", 1e-17, y[1][2], 453.0/9.0)
	io.Pforan("\nmax\n")
	chk.Scalar(tst, "y20=max(x[0,:])", 1e-17, y[2][0], 105)
	chk.Scalar(tst, "y21=max(x[1,:])", 1e-17, y[2][1], 111)
	chk.Scalar(tst, "y22=max(x[2,:])", 1e-17, y[2][2], 130)
	io.Pforan("\ndev\n")
	chk.Scalar(tst, "y30=dev(x[0,:])", 1e-17, y[3][0], 12.134661099511597)
	chk.Scalar(tst, "y31=dev(x[1,:])", 1e-17, y[3][1], 34.688294535444918)
	chk.Scalar(tst, "y32=dev(x[2,:])", 1e-17, y[3][2], 38.343839140075687)
	io.Pfyel("\nmin\n")
	chk.Scalar(tst, "z00=min(y[0,:])=min(min)", 1e-17, z[0][0], 10)
	chk.Scalar(tst, "z01=min(y[1,:])=min(ave)", 1e-17, z[0][1], 453.0/9.0)
	chk.Scalar(tst, "z02=min(y[2,:])=min(max)", 1e-17, z[0][2], 105)
	chk.Scalar(tst, "z03=min(y[3,:])=min(dev)", 1e-17, z[0][3], 12.134661099511597)
	io.Pfyel("\nave\n")
	chk.Scalar(tst, "z10=ave(y[0,:])=ave(min)", 1e-17, z[1][0], 92.0/3.0)
	chk.Scalar(tst, "z11=ave(y[1,:])=ave(ave)", 1e-17, z[1][1], ((849.0+598.0+453.0)/9.0)/3.0)
	chk.Scalar(tst, "z12=ave(y[2,:])=ave(max)", 1e-17, z[1][2], 346.0/3.0)
	chk.Scalar(tst, "z13=ave(y[3,:])=ave(dev)", 1e-17, z[1][3], (12.134661099511597+34.688294535444918+38.343839140075687)/3.0)
	io.Pfyel("\nmax\n")
	chk.Scalar(tst, "z20=max(y[0,:])=max(min)", 1e-17, z[2][0], 70)
	chk.Scalar(tst, "z21=max(y[1,:])=max(ave)", 1e-17, z[2][1], 849.0/9.0)
	chk.Scalar(tst, "z22=max(y[2,:])=max(max)", 1e-17, z[2][2], 130)
	chk.Scalar(tst, "z23=max(y[3,:])=max(dev)", 1e-17, z[2][3], 38.343839140075687)
	io.Pfyel("\ndev\n")
	chk.Scalar(tst, "z30=dev(y[0,:])=dev(min)", 1e-17, z[3][0], 34.078341117685483)
	chk.Scalar(tst, "z31=dev(y[1,:])=dev(ave)", 1e-17, z[3][1], 22.261169573539771)
	chk.Scalar(tst, "z32=dev(y[2,:])=dev(max)", 1e-17, z[3][2], 13.051181300301263)
	chk.Scalar(tst, "z33=dev(y[3,:])=dev(dev)", 1e-17, z[3][3], 14.194778389023206)
}

// CalcΔεElast calculates Δε corresponding to an elastic loading with Δp and Δq
func CalcΔεElast(Δε []float64, K, G float64, Δp, Δq float64, axsym bool) (Δεv, Δεd float64, err error) {
	Δεv = -Δp / K
	Δεd = Δq / (3.0 * G)
	var Δεx, Δεy, Δεz float64
	if axsym { // axisymmetric
		compression := true
		if compression {
			Δεx = Δεv/3.0 + Δεd/2.0
			Δεy = Δεx
			Δεz = Δεv/3.0 - Δεd
		} else {
			Δεx = Δεv/3.0 - Δεd/2.0
			Δεy = Δεv/3.0 + Δεd
			Δεz = Δεx
		}
	} else { // plane-strain with Δεy = Δεx / 2
		c := 9.0 * Δεd * Δεd / (4.0 * Δεv * Δεv)
		α := 0.0
		if math.Abs(c-1.0) > 1e-15 {
			d := 3.0 * (4.0*c - 1.0)
			if d < 0.0 {
				return 0, 0, chk.Err("discriminant < 0:  c=%v  d=%v", c, d)
			}
			α1 := (1.0 + 2.0*c + math.Sqrt(d)) / (2.0 - 2.0*c)
			α2 := (1.0 + 2.0*c - math.Sqrt(d)) / (2.0 - 2.0*c)
			α = α1
			io.Pfyel("d, α1, α2 = %v, %v, %v\n", d, α1, α2)
		}
		io.Pfyel("c, α = %v, %v\n", c, α)
		Δεy = Δεv / (1.0 + α)
		Δεx = α * Δεy
		Δεz = 0
	}
	//io.Pfpink("Δp=%v, Δq=%v => Δεv=%v, Δεd=%v => Δεx=%v, Δεy=%v, Δεz=%v\n", Δp, Δq, Δεv, Δεd, Δεx, Δεy, Δεz)
	Δε[0] = Δεx
	Δε[1] = Δεy
	Δε[2] = Δεz
	Δε[3] = 0
	Δεv_ := tsr.M_εv(Δε)
	Δεd_ := tsr.M_εd(Δε)
	if math.Abs(Δεv-Δεv_) > 1e-15 {
		return 0, 0, chk.Err(_path_err09, Δεv, Δεv_)
	}
	if Δεd < 0 {
		Δεd_ = -Δεd_ // allow negative values
	}
	if math.Abs(Δεd-Δεd_) > 1e-15 {
		return 0, 0, chk.Err(_path_err10, Δεd, Δεd_)
	}
	return
}

func Test_shp01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("shp01")

	r := []float64{0, 0, 0}

	verb := true
	for name, _ := range Functions {

		io.Pfyel("--------------------------------- %-6s---------------------------------\n", name)

		// check S
		tol := 1e-17
		if name == "tri10" {
			tol = 1e-14
		}
		checkShape(tst, name, tol, verb)

		// check dSdR
		tol = 1e-14
		if name == "lin5" || name == "lin4" || name == "tri10" || name == "qua12" || name == "qua16" {
			tol = 1e-10
		}
		if name == "tri15" {
			tol = 1e-9
		}
		checkDerivs(tst, name, r, tol, verb)

		io.PfGreen("OK\n")
	}
}

func Test_MTint01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("MTint01. integers (Mersenne Twister)")

	Init(1234)

	nints := 10
	vals := make([]int, NSAMPLES)

	// using MTint
	t0 := time.Now()
	for i := 0; i < NSAMPLES; i++ {
		vals[i] = MTint(0, nints-1)
	}
	io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))

	hist := IntHistogram{Stations: utl.IntRange(nints + 1)}
	hist.Count(vals, true)
	io.Pfyel(TextHist(hist.GenLabels("%d"), hist.Counts, 60))

	// using MTints
	t0 = time.Now()
	MTints(vals, 0, nints-1)
	io.Pforan("time elapsed = %v\n", time.Now().Sub(t0))

	hist.Count(vals, true)
	io.Pfcyan(TextHist(hist.GenLabels("%d"), hist.Counts, 60))
}

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")
	}
}

func Test_out02(tst *testing.T) {

	// finalise analysis process and catch errors
	defer func() {
		if err := recover(); err != nil {
			tst.Fail()
			io.PfRed("ERROR: %v\n", err)
		}
	}()

	// test title
	//verbose()
	chk.PrintTitle("out02")

	// start simulation
	processing := fem.NewFEM("data/twoqua4.sim", "", true, true, false, false, chk.Verbose, 0)

	// run simulation
	err := processing.Run()
	if err != nil {
		tst.Errorf("Run failed:\n%v", err)
		return
	}

	// start post-processing
	Start("data/twoqua4.sim", 0, 0)

	// get second ip coordinates
	xip := Ipoints[1].X
	io.Pfcyan("xip = %v\n", xip)

	// define points
	Define("A", N{-1})
	Define("ips", Along{{xip[0], 0}, {xip[0], 1}})

	// load results
	LoadResults(nil)

	// solution
	var sol ana.CteStressPstrain
	sol.Init(fun.Prms{
		&fun.Prm{N: "qnH", V: -50},
		&fun.Prm{N: "qnV", V: -100},
	})

	// check displacements
	tolu := 1e-15
	x := GetCoords("A")
	ux := GetRes("ux", "A", 0)
	uy := GetRes("uy", "A", 0)
	io.Pforan("ux=%v uy=%v\n", ux, uy)
	for j, t := range Times {
		io.Pfyel("t=%g\n", t)
		sol.CheckDispl(tst, t, []float64{ux[j], uy[j]}, x, tolu)
	}
}

// msg prints information on residuals
func (o *NlSolver) msg(typ string, it int, Ldx, fx_max float64, first, last bool) {
	if first {
		io.Pfpink("\n%4s%23s%23s\n", "it", "Ldx", "fx_max")
		io.Pfpink("%4s%23s%23s\n", "", io.Sf("(%7.1e)", o.fnewt), io.Sf("(%7.1e)", o.ftol))
		return
	}
	io.Pfyel("%4d%23.15e%23.15e\n", it, Ldx, fx_max)
	if last {
		io.Pfgrey(". . . converged with %s. nit=%d, nFeval=%d, nJeval=%d\n", typ, it, o.NFeval, o.NJeval)
	}
}

// PrintConstraints prints violated or not constraints
func (o System) PrintConstraints(P []float64, Pdemand float64, full bool) {
	sumP := 0.0
	for i, g := range o.G {
		if full {
			io.Pfyel("P%d range error = %v\n", i, utl.GtePenalty(P[i], g.Pmin, 1)+utl.GtePenalty(g.Pmax, P[i], 1))
		}
		sumP += P[i]
	}
	Ploss := 0.0
	io.Pf("balance error = %v\n", math.Abs(sumP-Pdemand-Ploss))
}

func Test_nurbs02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("nurbs02. square with initial stress. run")

	// fem
	analysis := NewFEM("data/nurbs02.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]

	e := dom.Elems[0].(*ElemU)
	io.PfYel("fex = %v\n", e.fex)
	io.PfYel("fey = %v\n", e.fey)
	la.PrintMat("K", e.K, "%10.2f", false)

	// solution
	var sol ana.CteStressPstrain
	sol.Init(fun.Prms{
		&fun.Prm{N: "qnH0", V: -20},
		&fun.Prm{N: "qnV0", V: -20},
		&fun.Prm{N: "qnH", V: -50},
		&fun.Prm{N: "qnV", V: -100},
	})

	// check displacements
	t := dom.Sol.T
	tolu := 1e-16
	for _, n := range dom.Nodes {
		eqx := n.GetEq("ux")
		eqy := n.GetEq("uy")
		u := []float64{dom.Sol.Y[eqx], dom.Sol.Y[eqy]}
		io.Pfyel("u = %v\n", u)
		sol.CheckDispl(tst, t, u, n.Vert.C, tolu)
	}

	// check stresses
	tols := 1e-13
	for idx, ip := range e.IpsElem {
		x := e.Cell.Shp.IpRealCoords(e.X, ip)
		σ := e.States[idx].Sig
		io.Pforan("σ = %v\n", σ)
		sol.CheckStress(tst, t, σ, x, tols)
	}
}

// PrintMemStat prints memory statistics
func PrintMemStat(msg string) {
	var mem runtime.MemStats
	runtime.ReadMemStats(&mem)
	io.PfYel("%s\n", msg)
	io.Pfyel("Alloc      = %v [KB]  %v [MB]  %v [GB]\n", mem.Alloc/KBSIZE, mem.Alloc/MBSIZE, mem.Alloc/GBSIZE)
	io.Pfyel("HeapAlloc  = %v [KB]  %v [MB]  %v [GB]\n", mem.HeapAlloc/KBSIZE, mem.HeapAlloc/MBSIZE, mem.HeapAlloc/GBSIZE)
	io.Pfyel("Sys        = %v [KB]  %v [MB]  %v [GB]\n", mem.Sys/KBSIZE, mem.Sys/MBSIZE, mem.Sys/GBSIZE)
	io.Pfyel("HeapSys    = %v [KB]  %v [MB]  %v [GB]\n", mem.HeapSys/KBSIZE, mem.HeapSys/MBSIZE, mem.HeapSys/GBSIZE)
	io.Pfyel("TotalAlloc = %v [KB]  %v [MB]  %v [GB]\n", mem.TotalAlloc/KBSIZE, mem.TotalAlloc/MBSIZE, mem.TotalAlloc/GBSIZE)
	io.Pfyel("Mallocs    = %v\n", mem.Mallocs)
	io.Pfyel("Frees      = %v\n", mem.Frees)
}

func Test_nurbs03(tst *testing.T) {

	//verbose()
	chk.PrintTitle("nurbs03. ini stress free square")

	// fem
	analysis := NewFEM("data/nurbs03.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]

	// element
	e := dom.Elems[0].(*ElemU)
	io.PfYel("fex = %v\n", e.fex)
	io.PfYel("fey = %v\n", e.fey)
	la.PrintMat("K", e.K, "%10.2f", false)

	// solution
	var sol ana.CteStressPstrain
	sol.Init(fun.Prms{
		&fun.Prm{N: "qnH", V: -50},
		&fun.Prm{N: "qnV", V: -100},
	})

	// check displacements
	t := dom.Sol.T
	tolu := 1e-16
	for _, n := range dom.Nodes {
		eqx := n.GetEq("ux")
		eqy := n.GetEq("uy")
		u := []float64{dom.Sol.Y[eqx], dom.Sol.Y[eqy]}
		io.Pfyel("u = %v\n", u)
		sol.CheckDispl(tst, t, u, n.Vert.C, tolu)
	}
}

func Test_eigenp01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("eigenp01")

	// constants
	tolP := 1e-14        // eigenprojectors
	tolS := 1e-13        // spectral decomposition
	toldP := 1e-9        // derivatives of eigenprojectors
	ver := chk.Verbose   // check P verbose
	verdP := chk.Verbose // check dPda verbose

	// run test
	nd := test_nd
	for idxA := 0; idxA < len(test_nd); idxA++ {
		//for idxA := 10; idxA < 11; idxA++ {
		//for idxA := 11; idxA < 12; idxA++ {
		//for idxA := 12; idxA < 13; idxA++ {

		// tensor and eigenvalues
		A := test_AA[idxA]
		a := M_Alloc2(nd[idxA])
		Ten2Man(a, A)
		io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
		io.Pfblue2("a = %v\n", a)
		io.Pfblue2("λ = %v\n", test_λ[idxA])

		// check eigenprojectors
		io.Pforan("\neigenprojectors\n")
		λsorted := CheckEigenprojs(a, tolP, tolS, ver)
		io.Pfyel("λsorted = %v\n", λsorted)
		λchk := utl.DblGetSorted(test_λ[idxA])
		chk.Vector(tst, "λchk", 1e-12, λsorted, λchk)

		// check derivatives of eigenprojectors
		io.Pforan("\nderivatives\n")
		CheckEigenprojsDerivs(a, toldP, verdP, EV_ZERO)

	}
}

func Test_GOshuffleInts01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("GOshuffleInts01")

	Init(0)

	n := 10
	nums := utl.IntRange(n)
	io.Pfgreen("before = %v\n", nums)
	IntShuffle(nums)
	io.Pfcyan("after  = %v\n", nums)

	sort.Ints(nums)
	io.Pforan("sorted = %v\n", nums)
	chk.Ints(tst, "nums", nums, utl.IntRange(n))

	shufled := IntGetShuffled(nums)
	io.Pfyel("shufled = %v\n", shufled)
	sort.Ints(shufled)
	chk.Ints(tst, "shufled", shufled, utl.IntRange(n))
}

func Test_shape01(tst *testing.T) {

	//verbose()
	chk.PrintTitle("shape01")

	r := []float64{0, 0, 0}

	verb := true
	for name, shape := range factory {

		io.Pfyel("--------------------------------- %-6s---------------------------------\n", name)

		// check S
		tol := 1e-17
		if name == "tri10" {
			tol = 1e-14
		}
		CheckShape(tst, shape, tol, verb)

		// check Sf
		tol = 1e-18
		CheckShapeFace(tst, shape, tol, verb)

		// check dSdR
		tol = 1e-14
		if name == "lin5" || name == "lin4" || name == "tri10" || name == "qua12" || name == "qua16" {
			tol = 1e-10
		}
		if name == "tri15" {
			tol = 1e-9
		}
		CheckDSdR(tst, shape, r, tol, verb)

		io.PfGreen("OK\n")
	}
}

func Test_sim02(tst *testing.T) {

	//verbose()
	chk.PrintTitle("sim01")

	sim := ReadSim("data", "frees01.sim", "", true)
	if sim == nil {
		tst.Errorf("test failed: check error log\n")
		return
	}
	if chk.Verbose {
		sim.GetInfo(os.Stdout)
		io.Pf("\n")
	}

	io.Pfyel("ndim    = %v\n", sim.Ndim)
	io.Pfyel("maxElev = %v\n", sim.MaxElev)
	io.Pfyel("grav    = %v\n", sim.Gfcn.F(0, nil))
	io.Pfyel("Wrho0   = %v\n", sim.WaterRho0)
	io.Pfyel("Wbulk   = %v\n", sim.WaterBulk)
	io.Pfyel("Wlevel  = %v\n", sim.WaterLevel)
}

// testing_compare_results_u compares results with u-formulation
func TestingCompareResultsU(tst *testing.T, simfname, cmpfname string, tolK, tolu, tols float64, skipK, verbose bool) {

	// only root can run this test
	if !Global.Root {
		return
	}

	// read summary
	sum := ReadSum(Global.Dirout, Global.Fnkey)
	if sum == nil {
		tst.Error("cannot read summary file for simulation=%q\n", simfname)
		return
	}

	// allocate domain
	distr := false
	d := NewDomain(Global.Sim.Regions[0], distr)
	if !d.SetStage(0, Global.Sim.Stages[0], distr) {
		tst.Errorf("TestingCompareResultsU: SetStage failed\n")
		return
	}

	// read file
	buf, err := io.ReadFile(cmpfname)
	if err != nil {
		tst.Errorf("TestingCompareResultsU: ReadFile failed\n")
		return
	}

	// unmarshal json
	var cmp_set T_results_set
	err = json.Unmarshal(buf, &cmp_set)
	if err != nil {
		tst.Errorf("TestingCompareResultsU: Unmarshal failed\n")
		return
	}

	// run comparisons
	dmult := 1.0
	for idx, cmp := range cmp_set {

		// displacements multiplier
		if idx == 0 && math.Abs(cmp.DispMult) > 1e-10 {
			dmult = cmp.DispMult
		}

		// time index
		tidx := idx + 1
		if verbose {
			io.PfYel("\n\ntidx = %d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", tidx)
		}

		// load gofem results
		if !d.In(sum, tidx, true) {
			tst.Errorf("TestingCompareResultsU: reading of results failed\n")
			return
		}
		if verbose {
			io.Pfyel("time = %v\n", d.Sol.T)
		}

		// check K matrices
		if !skipK {
			if verbose {
				io.Pfgreen(". . . checking K matrices . . .\n")
			}
			for eid, Ksg := range cmp.Kmats {
				if e, ok := d.Elems[eid].(*ElemU); ok {
					if !e.AddToKb(d.Kb, d.Sol, true) {
						tst.Errorf("TestingCompareResultsU: AddToKb failed\n")
						return
					}
					chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
				}
			}
		}

		// check displacements
		if verbose {
			io.Pfgreen(". . . checking displacements . . .\n")
		}
		for nid, usg := range cmp.Disp {
			ix := d.Vid2node[nid].Dofs[0].Eq
			iy := d.Vid2node[nid].Dofs[1].Eq
			chk.AnaNum(tst, "ux", tolu, d.Sol.Y[ix], usg[0]*dmult, verbose)
			chk.AnaNum(tst, "uy", tolu, d.Sol.Y[iy], usg[1]*dmult, verbose)
			if len(usg) == 3 {
				iz := d.Vid2node[nid].Dofs[2].Eq
				chk.AnaNum(tst, "uz", tolu, d.Sol.Y[iz], usg[2]*dmult, verbose)
			}
		}

		// check stresses
		if true {
			if verbose {
				io.Pfgreen(". . . checking stresses . . .\n")
			}
			for eid, sig := range cmp.Sigmas {
				if verbose {
//.........这里部分代码省略.........

// Solve solves y(x) = 0 for x in [xa, xb] with f(xa) * f(xb) < 0
//
//  Based on ZEROIN C math library: http://www.netlib.org/c/
//  By: Oleg Keselyov <[email protected], [email protected]> May 23, 1991
//
//   G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical
//   computations. M., Mir, 1980, p.180 of the Russian edition
//
//   The function makes use of the bissection procedure combined with
//   the linear or quadric inverse interpolation.
//   At every step program operates on three abscissae - a, b, and c.
//   b - the last and the best approximation to the root
//   a - the last but one approximation
//   c - the last but one or even earlier approximation than a that
//       1) |f(b)| <= |f(c)|
//       2) f(b) and f(c) have opposite signs, i.e. b and c confine
//          the root
//   At every step Zeroin selects one of the two new approximations, the
//   former being obtained by the bissection procedure and the latter
//   resulting in the interpolation (if a,b, and c are all different
//   the quadric interpolation is utilized, otherwise the linear one).
//   If the latter (i.e. obtained by the interpolation) point is
//   reasonable (i.e. lies within the current interval [b,c] not being
//   too close to the boundaries) it is accepted. The bissection result
//   is used in the other case. Therefore, the range of uncertainty is
//   ensured to be reduced at least by the factor 1.6
//
func (o *Brent) Solve(xa, xb float64, silent bool) (res float64, err error) {

	// basic variables and function evaluation
	a := xa // the last but one approximation
	b := xb // the last and the best approximation to the root
	c := a  // the last but one or even earlier approximation than a that
	fa, erra := o.Ffcn(a)
	fb, errb := o.Ffcn(b)
	o.NFeval = 2
	if erra != nil {
		return 0, chk.Err(_brent_err1, "a", xa, erra.Error())
	}
	if errb != nil {
		return 0, chk.Err(_brent_err1, "b", xb, errb.Error())
	}
	fc := fa

	// check input
	if fa*fb >= -EPS {
		return 0, chk.Err(_brent_err2, xa, xb, fa, fb)
	}

	// message
	if !silent {
		io.Pfpink("%4s%23s%23s%23s\n", "it", "x", "f(x)", "err")
		io.Pfpink("%50s%23.1e\n", "", o.Tol)
	}

	// solve
	var prev_step float64  // distance from the last but one to the last approximation
	var tol_act float64    // actual tolerance
	var p, q float64       // interpol. step is calculated in the form p/q (divisions are delayed)
	var new_step float64   // step at this iteration
	var t1, cb, t2 float64 // auxiliary variables
	for o.It = 0; o.It < o.MaxIt; o.It++ {

		// distance
		prev_step = b - a

		// swap data for b to be the best approximation
		if math.Abs(fc) < math.Abs(fb) {
			a = b
			b = c
			c = a
			fa = fb
			fb = fc
			fc = fa
		}
		tol_act = 2.0*EPS*math.Abs(b) + o.Tol/2.0
		new_step = (c - b) / 2.0

		// converged?
		if !silent {
			io.Pfyel("%4d%23.15e%23.15e%23.15e\n", o.It, b, fb, math.Abs(new_step))
		}
		if math.Abs(new_step) <= tol_act || fb == 0.0 {
			return b, nil
		}

		// decide if the interpolation can be tried
		if math.Abs(prev_step) >= tol_act && math.Abs(fa) > math.Abs(fb) {
			// if prev_step was large enough and was in true direction, interpolatiom may be tried
			cb = c - b

			// with two distinct points, linear interpolation must be applied
			if a == c {
				t1 = fb / fa
				p = cb * t1
				q = 1.0 - t1

				// otherwise, quadric inverse interpolation is applied
			} else {
				q = fa / fc
//.........这里部分代码省略.........

//.........这里部分代码省略.........
		chk.Ints(tst, "equations with pl prescribed", ct_pl_eqs, []int{2, 5})

	}

	// initial values @ nodes
	io.Pforan("initial values @ nodes\n")
	for _, nod := range dom.Nodes {
		z := nod.Vert.C[1]
		for _, dof := range nod.Dofs {
			u := dom.Sol.Y[dof.Eq]
			switch dof.Key {
			case "ux":
				chk.Scalar(tst, io.Sf("nod %3d : ux(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
			case "uy":
				chk.Scalar(tst, io.Sf("nod %3d : uy(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-17, u, 0)
			case "pl":
				plC, _, _ := Global.HydroSt.Calc(z)
				chk.Scalar(tst, io.Sf("nod %3d : pl(@ %4g)= %6g", nod.Vert.Id, z, u), 1e-13, u, plC)
			}
		}
	}

	// intial values @ integration points
	io.Pforan("initial values @ integration points\n")
	for _, ele := range dom.Elems {
		e := ele.(*ElemUP)
		for idx, ip := range e.P.IpsElem {
			s := e.P.States[idx]
			z := e.P.Shp.IpRealCoords(e.P.X, ip)[1]
			chk.AnaNum(tst, io.Sf("sl(z=%11.8f)", z), 1e-17, s.A_sl, 1, chk.Verbose)
		}
	}

	// parameters
	ν := 0.2            // Poisson's coefficient
	K0 := ν / (1.0 - ν) // earth pressure at rest
	nf := 0.3           // porosity
	sl := 1.0           // saturation
	ρL := 1.0           // intrinsic (real) density of liquid
	ρS_top := 2.0       // intrinsic (real) density of solids in top layer
	ρS_bot := 3.0       // intrinsic (real) density of solids in bottom layer
	h := 5.0            // height of each layer
	g := 10.0           // gravity

	// densities
	nl := nf * sl         // volume fraction of luqid
	ns := 1.0 - nf        // volume fraction of solid
	ρl := nl * ρL         // partial density of liquid
	ρs_top := ns * ρS_top // partial density of solids in top layer
	ρs_bot := ns * ρS_bot // partial density of solids in bottom layer
	ρ_top := ρl + ρs_top  // density of mixture in top layer
	ρ_bot := ρl + ρs_bot  // density of mixture in bottom layer

	// absolute values of stresses
	σV_z5 := ρ_top * g * h     // total vertical stress @ elevation z = 5 m (absolute value)
	σV_z0 := σV_z5 + ρ_bot*g*h // total vertical stress @ elevation z = 0 m (absolute value)
	io.Pfyel("ρ_top       = %g\n", ρ_top)
	io.Pfyel("ρ_bot       = %g\n", ρ_bot)
	io.Pfyel("|ΔσV_top|   = %g\n", ρ_top*g*h)
	io.Pfyel("|ΔσV_bot|   = %g\n", ρ_bot*g*h)
	io.PfYel("|σV|(@ z=0) = %g\n", σV_z0)
	io.PfYel("|σV|(@ z=5) = %g\n", σV_z5)

	// stress functions
	var sig fun.Pts
	var pres fun.Pts
	sig.Init(fun.Prms{
		&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: -σV_z0},
		&fun.Prm{N: "t1", V: 5.00}, {N: "y1", V: -σV_z5},
		&fun.Prm{N: "t2", V: 10.00}, {N: "y2", V: 0.0},
	})
	pres.Init(fun.Prms{
		&fun.Prm{N: "t0", V: 0.00}, {N: "y0", V: 100},
		&fun.Prm{N: "t1", V: 10.00}, {N: "y1", V: 0},
	})

	// check stresses
	io.Pforan("initial stresses @ integration points\n")
	for _, ele := range dom.Elems {
		e := ele.(*ElemUP)
		for idx, ip := range e.U.IpsElem {
			z := e.U.Shp.IpRealCoords(e.U.X, ip)[1]
			σe := e.U.States[idx].Sig
			sv := sig.F(z, nil)
			sve := sv + pres.F(z, nil)
			she := sve * K0
			if math.Abs(σe[2]-σe[0]) > 1e-17 {
				tst.Errorf("[1;31mσx is not equal to σz: %g != %g[0m\n", σe[2], σe[0])
				return
			}
			if math.Abs(σe[3]) > 1e-17 {
				tst.Errorf("[1;31mσxy is not equal to zero: %g != 0[0m\n", σe[3])
				return
			}
			chk.AnaNum(tst, io.Sf("sx(z=%11.8f)", z), 0.0003792, σe[0], she, chk.Verbose)
			chk.AnaNum(tst, io.Sf("sy(z=%11.8f)", z), 0.001517, σe[1], sve, chk.Verbose)
		}
	}
	return
}