Golang math.Abs函数代码示例

// 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 (sp *SmoothFollow) LateUpdate() {
	camera := engine.CurrentCamera()
	if camera != nil {
		myPos := sp.Target.Transform().Position()
		camPos := camera.Transform().Position()

		if sp.Speed > 0 {
			camPos = engine.Lerp(camPos, myPos, float32(engine.DeltaTime())*sp.Speed)
			disX := camPos.X - myPos.X
			disY := camPos.Y - myPos.Y
			if float32(math.Abs(float64(disX))) > sp.MaxDis {
				if disX < 0 {
					camPos.X = myPos.X - sp.MaxDis
				} else {
					camPos.X = myPos.X + sp.MaxDis
				}
			}
			if float32(math.Abs(float64(disY))) > sp.MaxDis {
				if disY < 0 {
					camPos.Y = myPos.Y - sp.MaxDis
				} else {
					camPos.Y = myPos.Y + sp.MaxDis
				}
			}
		} else {
			camPos = myPos
		}
		camera.Transform().SetPosition(camPos)
	}
}

func nearEqual(a, b, closeEnough, maxError float64) bool {
	absDiff := math.Abs(a - b)
	if absDiff < closeEnough { // Necessary when one value is zero and one value is close to zero.
		return true
	}
	return absDiff/max(math.Abs(a), math.Abs(b)) < maxError
}

func bestScaleAndPrefix(unit *pb.TelemetryDatumSchema_Unit,
	values ...float64) (scale float64, prefix string) {
	// Heuristic (can be improved):
	// Use the smallest value.

	m := math.Abs(values[0])
	for _, v := range values {
		v = math.Abs(v)
		if v > m {
			m = v
		}
	}

	prefixes := []struct {
		string
		float64
	}{
		{"T", 1e12},
		{"G", 1e9},
		{"M", 1e6},
		{"k", 1e3},
		{"", 1e0},
		{"m", 1e-3},
		{"μ", 1e-6},
		{"n", 1e-9},
		{"p", 1e-12}}

	for _, s := range prefixes {
		if m >= s.float64 {
			return s.float64, s.string
		}
	}
	return 1.0, ""
}

// 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]")
}

// Determine the symbol that exists at each sample of the signal.
func (p Parser) Quantize() {
	// 0 0011, 3 1100
	// 1 0101, 4 1010
	// 2 0110, 5 1001

	for idx, vec := range p.filtered {
		argmax := byte(0)
		max := math.Abs(vec[0])

		// If v1 is larger than v0, update max and argmax.
		if v1 := math.Abs(vec[1]); v1 > max {
			max = v1
			argmax = 1
		}

		// If v2 is larger than the greater of v1 or v0, update max and argmax.
		if v2 := math.Abs(vec[2]); v2 > max {
			max = v2
			argmax = 2
		}

		// Set the output symbol index.
		p.quantized[idx] = argmax

		// If the sign is negative, jump to the index of the inverted symbol.
		if vec[argmax] > 0 {
			p.quantized[idx] += 3
		}
	}
}

func debug_print_up_results(d *Domain) {
	io.Pf("\ntime = %23.10f\n", d.Sol.T)
	for _, v := range d.Msh.Verts {
		n := d.Vid2node[v.Id]
		eqpl := n.GetEq("pl")
		equx := n.GetEq("ux")
		equy := n.GetEq("uy")
		var pl, ux, uy float64
		if eqpl >= 0 {
			pl = d.Sol.Y[eqpl]
		}
		if equx >= 0 {
			ux = d.Sol.Y[equx]
		}
		if equy >= 0 {
			uy = d.Sol.Y[equy]
		}
		if math.Abs(pl) < 1e-13 {
			pl = 0
		}
		if math.Abs(ux) < 1e-13 {
			ux = 0
		}
		if math.Abs(uy) < 1e-13 {
			uy = 0
		}
		io.Pf("%3d : pl=%23.10v ux=%23.10f uy=%23.10f\n", v.Id, pl, ux, uy)
	}
}

// Horizontal computes data for a horizontal sundial.
//
// Argument φ is geographic latitude at which the sundial will be located,
// a is the length of a straight stylus perpendicular to the plane of the
// sundial.
//
// Results consist of a set of lines, a center point, and u, the length of a
// polar stylus.  They are in units of a, the stylus length.
func Horizontal(φ, a float64) (lines []Line, center Point, u float64) {
	sφ, cφ := math.Sincos(φ)
	tφ := sφ / cφ
	for i := 0; i < 24; i++ {
		l := Line{Hour: i}
		H := float64(i-12) * 15 * math.Pi / 180
		aH := math.Abs(H)
		sH, cH := math.Sincos(H)
		for _, d := range m {
			tδ := math.Tan(d * math.Pi / 180)
			H0 := math.Acos(-tφ * tδ)
			if aH > H0 {
				continue // sun below horizon
			}
			Q := cφ*cH + sφ*tδ
			x := a * sH / Q
			y := a * (sφ*cH - cφ*tδ) / Q
			l.Points = append(l.Points, Point{x, y})
		}
		if len(l.Points) > 0 {
			lines = append(lines, l)
		}
	}
	center.Y = -a / tφ
	u = a / math.Abs(sφ)
	return
}

// Vertical computes data for a vertical sundial.
//
// Argument φ is geographic latitude at which the sundial will be located.
// D is gnomonic declination, the azimuth of the perpendicular to the plane
// of the sundial, measured from the southern meridian towards the west.
// Argument a is the length of a straight stylus perpendicular to the plane
// of the sundial.
//
// Results consist of a set of lines, a center point, and u, the length of a
// polar stylus.  They are in units of a, the stylus length.
func Vertical(φ, D, a float64) (lines []Line, center Point, u float64) {
	sφ, cφ := math.Sincos(φ)
	tφ := sφ / cφ
	sD, cD := math.Sincos(D)
	for i := 0; i < 24; i++ {
		l := Line{Hour: i}
		H := float64(i-12) * 15 * math.Pi / 180
		aH := math.Abs(H)
		sH, cH := math.Sincos(H)
		for _, d := range m {
			tδ := math.Tan(d * math.Pi / 180)
			H0 := math.Acos(-tφ * tδ)
			if aH > H0 {
				continue // sun below horizon
			}
			Q := sD*sH + sφ*cD*cH - cφ*cD*tδ
			if Q < 0 {
				continue // sun below plane of sundial
			}
			x := a * (cD*sH - sφ*sD*cH + cφ*sD*tδ) / Q
			y := -a * (cφ*cH + sφ*tδ) / Q
			l.Points = append(l.Points, Point{x, y})
		}
		if len(l.Points) > 0 {
			lines = append(lines, l)
		}
	}
	center.X = -a * sD / cD
	center.Y = a * tφ / cD
	u = a / math.Abs(cφ*cD)
	return
}

func (hm HMACMiddleware) checkClockSkew(dateHeaderValue string) bool {
	// Reference layout for parsing time: "Mon Jan 2 15:04:05 MST 2006"

	refDate := "Mon, 02 Jan 2006 15:04:05 MST"

	tim, err := time.Parse(refDate, dateHeaderValue)

	if err != nil {
		log.Error("Date parsing failed")
		return false
	}

	inSec := tim.UnixNano()
	now := time.Now().UnixNano()

	diff := now - inSec

	in_ms := diff / 1000000
	if math.Abs(float64(in_ms)) > HMACClockSkewLimitInMs {
		log.Debug("Difference is: ", math.Abs(float64(in_ms)))
		return false
	}

	return true
}

func TestGauss(t *testing.T) {
	src := rand.NewSource(time.Now().Unix())
	gen := rand.New(src)

	// gaussian
	gaussian := NewDist(128)
	for i := 0; i < 1000; i++ {
		v := gen.Intn(200)
		gaussian.Add(v)
	}

	fmt.Println("N-samples:", gaussian.N, ", σ:", gaussian.Sigma)

	// testing
	fmt.Println("range [0,200]")
	sigma := gaussian.Sigma
	mean := gaussian.Mean
	for i := 0; i < 10; i++ {
		v := gen.Intn(200)
		fmt.Printf("X:%4d: P(v)=%0.4f, deriv:%.2fσ\n", v, gaussian.P(v), math.Abs(float64(v)-mean)/sigma)
	}

	fmt.Println("range [0,400]")
	for i := 0; i < 10; i++ {
		v := gen.Intn(400)
		fmt.Printf("X:%4d: P(v)=%0.4f, deriv:%.2fσ\n", v, gaussian.P(v), math.Abs(float64(v)-mean)/sigma)
	}
}

func assertLatLon(t *testing.T, pos Position, doc SampleDoc) {
	slat, haslat := doc.Result["latitude"].(float64)
	slon, haslon := doc.Result["longitude"].(float64)
	if !(haslat && haslon) {
		return
	}
	if math.Abs(pos.Lat-slat) > 0.001 || math.Abs(pos.Lon-slon) > 0.001 {
		t.Fatalf("Error parsing lat/lon from %v, got %v; expected %v,%v",
			doc.Src, pos, slat, slon)
	}
	tbl := doc.Result["symboltable"].(string)[0]
	if pos.Symbol.Table != tbl {
		t.Fatalf("Expected symbol table %v, got %v for %v",
			tbl, pos.Symbol.Table, doc.Src)
	}
	symbol := doc.Result["symbolcode"].(string)[0]
	if pos.Symbol.Symbol != symbol {
		t.Fatalf("Expected symbol %v, got %v for %v",
			symbol, pos.Symbol.Symbol, doc.Src)
	}
	course, _ := doc.Result["course"].(float64)
	assertEpsilon(t, "course of "+doc.Src, course, pos.Velocity.Course)
	speed, _ := doc.Result["speed"].(float64)
	assertEpsilon(t, "speed of "+doc.Src, speed, pos.Velocity.Speed)
}

// Norm returns the L norm of the slice S, defined as
// (sum_{i=1}^N s[i]^L)^{1/L}
// Special cases:
// L = math.Inf(1) gives the maximum absolute value.
// Does not correctly compute the zero norm (use Count).
func Norm(s []float64, L float64) float64 {
	// Should this complain if L is not positive?
	// Should this be done in log space for better numerical stability?
	//	would be more cost
	//	maybe only if L is high?
	if len(s) == 0 {
		return 0
	}
	if L == 2 {
		twoNorm := math.Abs(s[0])
		for i := 1; i < len(s); i++ {
			twoNorm = math.Hypot(twoNorm, s[i])
		}
		return twoNorm
	}
	var norm float64
	if L == 1 {
		for _, val := range s {
			norm += math.Abs(val)
		}
		return norm
	}
	if math.IsInf(L, 1) {
		for _, val := range s {
			norm = math.Max(norm, math.Abs(val))
		}
		return norm
	}
	for _, val := range s {
		norm += math.Pow(math.Abs(val), L)
	}
	return math.Pow(norm, 1/L)
}

// Distance computes the L-norm of s - t. See Norm for special cases.
// A panic will occur if the lengths of s and t do not match.
func Distance(s, t []float64, L float64) float64 {
	if len(s) != len(t) {
		panic("floats: slice lengths do not match")
	}
	if len(s) == 0 {
		return 0
	}
	var norm float64
	if L == 2 {
		for i, v := range s {
			diff := t[i] - v
			norm = math.Hypot(norm, diff)
		}
		return norm
	}
	if L == 1 {
		for i, v := range s {
			norm += math.Abs(t[i] - v)
		}
		return norm
	}
	if math.IsInf(L, 1) {
		for i, v := range s {
			absDiff := math.Abs(t[i] - v)
			if absDiff > norm {
				norm = absDiff
			}
		}
		return norm
	}
	for i, v := range s {
		norm += math.Pow(math.Abs(t[i]-v), L)
	}
	return math.Pow(norm, 1/L)
}

func TestIntensityMeasuredV1(t *testing.T) {
	setup()
	defer teardown()

	b, err := wt.Request{Accept: V1GeoJSON, URL: "/intensity?type=measured"}.Do(ts.URL)
	if err != nil {
		t.Fatal(err)
	}

	var i intensityMeasuredV1Features

	err = json.Unmarshal(b, &i)
	if err != nil {
		t.Fatal(err)
	}

	if len(i.Features) != 1 {
		t.Error("found wrong number of intensities.")
	}
	if math.Abs(i.Features[0].Geometry.Longitude()-175.49) > tolerance {
		t.Error("incorrect Longitude")
	}
	if math.Abs(i.Features[0].Geometry.Latitude()+40.2) > tolerance {
		t.Error("incorrect Latitude")
	}
	if i.Features[0].Properties.MMI != 4 {
		t.Error("incorrect MMI")
	}
}