// Random gamma variable when shape<1
// See Kundu and Gupta 2007
// "A convenient way of generating gamma random variables using generalized exponential distribution"
func (rg RandGen) rgamma2(shape float64) float64 {
if shape <= 0.0 || shape >= 1.0 {
panic("Illegal parameter. Shape must be positive and no greater than one")
}
d := 1.0334 - 0.0766*math.Exp(2.2942*shape) // Constants from paper
a := math.Exp2(shape) * math.Pow(-math.Expm1(-d/2), shape)
pdsh := math.Pow(d, shape-1.0)
b := shape * pdsh * math.Exp(-d)
c := a + b
start:
u := rg.Float64()
var x float64
if u <= a/c {
x = -2.0 * math.Log1p(-math.Pow(c*u, 1.0/shape)/2.0)
} else {
x = -math.Log(c * (1.0 - u) / (shape * pdsh))
}
v := rg.Float64()
if x <= d {
p := math.Pow(x, shape-1.0) * math.Exp(-x/2.0) / (math.Exp2(shape-1.0) * math.Pow(-math.Expm1(-x/2.0), shape-1.0))
if v > p {
goto start
}
} else {
if v > math.Pow(d/x, 1.0-shape) {
goto start
}
}
return x
}
// Rescore recalculates the scores based on the current guests.
func (t *Table) Rescore(p Prefs) {
var left, right int
for _, g := range t.Left {
if g.Name != "" {
left++
}
}
for _, g := range t.Right {
if g.Name != "" {
right++
}
}
t.TableScore = 0
t.TableScore += CapacityPref * math.Expm1(math.Abs(float64(
(len(t.Left)+len(t.Right)-2)-(left+right))))
t.TableScore += ImbalancePref * math.Expm1(math.Abs(float64(left-right)))
t.scoreSide(t.Left, t.Right, t.LeftScores, p)
t.scoreSide(t.Right, t.Left, t.RightScores, p)
t.Score = t.TableScore
for _, s := range t.LeftScores {
if s != 0 {
t.Score += s
}
}
for _, s := range t.RightScores {
if s != 0 {
t.Score += s
}
}
}
func main() {
for true {
r := bufio.NewReader(os.Stdin)
s, err := r.ReadString('\n')
if err == os.EOF {
break
}
s = strings.TrimRight(s, "\n")
a := strings.Split(s, " ")
f := a[0]
x, err := strconv.Atof64(a[1])
switch f {
case "erf":
fmt.Println(math.Erf(x))
case "expm1":
fmt.Println(math.Expm1(x))
case "phi":
fmt.Println(phi.Phi(x))
case "NormalCDFInverse":
fmt.Println(normal_cdf_inverse.NormalCDFInverse(x))
case "Gamma":
fmt.Println(math.Gamma(x))
case "LogGamma":
r, _ := math.Lgamma(x)
fmt.Println(r)
case "LogFactorial":
fmt.Println(log_factorial.LogFactorial(int(x)))
default:
fmt.Println("Unknown function: " + f)
return
}
}
}
// Calculate U_{2}/N = 1/N \sum_k (\omega_+(k) + \mu_b) n_b(\omega_+(k))
func PairEnergy(env *tempAll.Environment) (float64, error) {
// find omega_+ coefficients
a, b := env.A, env.B
if !env.FixedPairCoeffs || !env.PairCoeffsReady {
plusCoeffs, err := OmegaFit(env, OmegaPlus)
if err != nil {
fmt.Println("suppressing error in PairEnergy - cannot find pair spectrum")
return 0.0, nil
}
a, b = plusCoeffs[0], plusCoeffs[2]
}
// kz^2 version - incompatible with finite magnetic field
if env.PairKzSquaredSpectrum && math.Abs(env.Be_field) < 1e-9 {
integrand := func(y float64) float64 {
num := math.Pow(y, 1.5)
denom := math.Exp(y-env.Beta*env.Mu_b) - 1.0
return num / denom
}
integral, err := OmegaIntegralY(env, a, b, integrand)
if err != nil {
return 0.0, err
}
return integral / math.Pow(env.Beta, 2.5), nil
}
// cos(kz) version
if math.Abs(env.Be_field) < 1e-9 {
integrand := func(y, kz float64) float64 {
bterm := 2.0 * b * (1.0 - math.Cos(kz))
num := y/env.Beta + bterm
denom := math.Exp(y+env.Beta*(bterm-env.Mu_b)) - 1.0
return num / denom
}
integral, err := OmegaIntegralCos(env, a, b, integrand)
if err != nil {
return 0.0, err
}
return integral, nil
}
// if we get here, math.Abs(env.Be_field) >= 1e-9
//fmt.Printf("about to calculate E2 B sum for env = %s\n", env.String())
E2BSumTerm := func(ri int) float64 {
r := float64(ri)
I0 := bessel.ModifiedBesselFirstKindZeroth(2.0 * b * env.Beta * r)
I1 := bessel.ModifiedBesselFirstKindFirst(2.0 * b * env.Beta * r)
omega_c := 4.0 * env.Be_field * a
mu_tilde := env.Mu_b - omega_c/2.0
expL := math.Exp(r * env.Beta * (mu_tilde - 2.0*b))
expR := math.Exp(-env.Beta * omega_c * r)
expm1 := -math.Expm1(-env.Beta * omega_c * r)
return expL * ((I0*(0.5+2.0*b)-2.0*b*I1)*expm1 + (I0 * omega_c * expR * expm1 * expm1))
}
sum, _ := seriesaccel.Levin_u(E2BSumTerm, 1, 20)
// reporting of absErr:
// (dropped this since absErr is always very small compared to sum)
//sum, absErr := seriesaccel.Levin_u(E2BSumTerm, 1, 20)
//fmt.Printf("env=%s; E2 B sum %e, absErr %e\n", env.String(), sum, absErr)
return 2.0 * env.Be_field * sum / math.Pi, nil
}
// Magnetization per unit area divided by e
func Magnetization(env *tempAll.Environment) (float64, error) {
if math.Abs(env.Be_field) < 1e-9 {
return 0.0, nil
}
if -env.Mu_b > -2.0*env.Mu_h {
return 0.0, nil
}
// find omega_+ coefficients
a, b := env.A, env.B
if !env.FixedPairCoeffs || !env.PairCoeffsReady {
plusCoeffs, err := OmegaFit(env, OmegaPlus)
//fmt.Printf("plusCoeffs in Magnetization: %v\n", plusCoeffs)
if err != nil {
fmt.Println("suppressing error in magnetization - cannot find pair spectrum")
return 0.0, nil
}
a, b = plusCoeffs[0], plusCoeffs[2]
}
MSumTerm := func(ri int) float64 {
r := float64(ri)
I0 := bessel.ModifiedBesselFirstKindZeroth(2.0 * b * env.Beta * r)
omega_c := 4.0 * env.Be_field * a
mu_tilde := env.Mu_b - omega_c/2.0
exp := -math.Expm1(-r * env.Beta * omega_c)
bracket := 1.0/(env.Beta*r*exp) - omega_c*math.Exp(-r*env.Beta*omega_c)/(exp*exp)
return I0 * math.Exp(r*env.Beta*(mu_tilde-2.0*b)) * bracket
/*
bracket_num_term := func(ni int) float64 {
n := float64(ni)
nm1_fact := math.Gamma(n)
return -math.Pow(-r * env.Beta * omega_c, n + 1.0) / ((n + 1.0) * nm1_fact)
}
bracket_denom_term := func(ni int) float64 {
n := float64(ni)
n_fact := math.Gamma(n + 1.0)
return math.Pow(-r * env.Beta * omega_c, n) * (math.Pow(2.0, n - 1.0) - 1.0) / n_fact
}
bracket_num, _ := seriesaccel.Levin_u(bracket_num_term, 1, 20)
bracket_denom, _ := seriesaccel.Levin_u(bracket_denom_term, 2, 20)
return I0 * math.Exp(r*env.Beta*(mu_tilde-2.0*b)) * bracket_num / (2.0 * bracket_denom)
*/
}
//sum, absErr := seriesaccel.Levin_u(MSumTerm, 1, 20)
//fmt.Printf("Magnetization sum %e, absErr %e\n", sum, absErr)
sum, _ := seriesaccel.Levin_u(MSumTerm, 1, 20)
x2, err := X2(env)
if err != nil {
return 0.0, err
}
return -a*x2 + sum/math.Pi, nil
//return -a*x2 - sum/math.Pi, nil
}
func TestScoring(t *testing.T) {
table := saseat.NewTable(8)
table.Left[0] = saseat.Guest{"Abe", "male"}
table.Left[1] = saseat.Guest{"Mary", "female"}
table.Left[2] = saseat.Guest{"Jane", "female"}
table.Right[0] = saseat.Guest{"Alexander", "male"}
table.Right[1] = saseat.Guest{"Kang", ""}
expectedTableScore := saseat.CapacityPref*math.Expm1(1) + saseat.ImbalancePref*math.Expm1(1)
prefs := saseat.Prefs{}
prefs.Set("Abe", "Mary", 1000)
prefs.Set("Kang", "Jane", -80)
prefs.Set("Alexander", "Jane", 50)
expectedLeft := []float64{
1000 * saseat.AdjacentWeight,
1000*saseat.AdjacentWeight + saseat.SameGenderPref,
-80*saseat.DiagonalWeight + 50*saseat.SameTableWeight + saseat.SameGenderPref,
0,
}
expectedRight := []float64{
50 * saseat.SameTableWeight,
-80 * saseat.DiagonalWeight,
0,
0,
}
table.Rescore(prefs)
if table.TableScore != expectedTableScore {
t.Errorf("got table score %v, want %v", table.TableScore, expectedTableScore)
}
if !reflect.DeepEqual(table.LeftScores, expectedLeft) {
t.Errorf("got left prefs %v, want %v", table.LeftScores, expectedLeft)
}
if !reflect.DeepEqual(table.RightScores, expectedRight) {
t.Errorf("got right prefs %v, want %v", table.RightScores, expectedRight)
}
}
func leaving(matrix [][]float64, coeff []float64, basic []int, enter int) int {
leave := -2
currentConstraint := math.Expm1(64)
for i, v := range matrix {
if v[enter] < 0 {
if q := coeff[i] / -(v[enter]); leave >= 0 && q == currentConstraint {
if basic[i] < basic[leave] {
leave = i
}
} else if q < currentConstraint {
currentConstraint = q
leave = i
}
}
}
return leave
}
// Concentration of paired holons
func X2(env *tempAll.Environment) (float64, error) {
// kz^2 version - incompatible with finite magnetic field
if env.PairKzSquaredSpectrum && math.Abs(env.Be_field) < 1e-9 {
nu, err := nu(env)
if err != nil {
return 0.0, err
}
x2 := nu / math.Pow(env.Beta, 3.0/2.0)
return x2, nil
}
// cos(kz) version
if -env.Mu_b > -2.0*env.Mu_h {
return 0.0, nil
}
// find omega_+ coefficients
a, b := env.A, env.B
if !env.FixedPairCoeffs || !env.PairCoeffsReady {
plusCoeffs, err := OmegaFit(env, OmegaPlus)
//fmt.Printf("plusCoeffs in X2: %v\n", plusCoeffs)
if err != nil {
fmt.Println("suppressing error in x2 - cannot find pair spectrum")
return 0.0, nil
}
a, b = plusCoeffs[0], plusCoeffs[2]
}
// zero magnetic field with cos(kz) spectrum
if math.Abs(env.Be_field) < 1e-9 {
integrand := func(y, kz float64) float64 {
bterm := 2.0 * b * (1.0 - math.Cos(kz))
return 2.0 / (math.Exp(y+env.Beta*(bterm-env.Mu_b)) - 1.0)
}
plus, err := OmegaIntegralCos(env, a, b, integrand)
if err != nil {
return 0.0, err
}
return plus, nil
}
// if we get here, math.Abs(env.Be_field) >= 1e-9
//fmt.Printf("about to calculate x2 sum for env = %s\n", env.String())
x2BSumTerm := func(ri int) float64 {
r := float64(ri)
I0 := bessel.ModifiedBesselFirstKindZeroth(2.0 * b * env.Beta * r)
omega_c := 4.0 * env.Be_field * a
mu_tilde := env.Mu_b - omega_c/2.0
return I0 * math.Exp(env.Beta*r*(mu_tilde-2.0*b)) / (-math.Expm1(-env.Beta * omega_c * r))
/*
sum_n_term := func(ni int) float64 {
n := float64(ni)
np1_fact := math.Gamma(n + 2.0)
return math.Pow(-r * env.Beta * omega_c, n) / np1_fact
}
sum_n, _ := seriesaccel.Levin_u(sum_n_term, 1, 20)
return I0 * math.Exp(env.Beta*r*(mu_tilde-2.0*b)) / (r * (1.0 + sum_n))
*/
}
sum, _ := seriesaccel.Levin_u(x2BSumTerm, 1, 20)
//fmt.Printf("%v\n", sum)
// reporting of absErr:
// (dropped this since absErr is always very small relative to sum)
//sum, absErr := seriesaccel.Levin_u(x2BSumTerm, 1, 20)
//fmt.Printf("for env=%s; x2 B sum %e, absErr %e\n", env.String(), sum, absErr)
return 2.0 * env.Be_field * sum / math.Pi, nil
//return sum / (2.0 * math.Pi * env.Beta * a), nil
}
func ext۰math۰Expm1(fr *Frame, args []Value) Value {
return math.Expm1(args[0].(float64))
}
// float32 version of math.Expm1f
func Expm1(x float32) float32 {
return float32(math.Expm1(float64(x)))
}