// Calculate the integral of y from 0 to ymax of: F(y) / (4*pi^2*a*sqrt(b)).
// a, b are parameters in pair spectrum: omega_+(k) = a*(kx^2 + ky^2) + b*(kz^2).
// mu_relative = 0 for omega_+ poles; = omegaCoeffs[3] for omega_- poles.
func omegaIntegralYHelper(env *tempAll.Environment, a, b, mu_relative float64, F func(float64) float64) (float64, error) {
if a == 0.0 || b == 0.0 {
return 0.0, nil
}
ymax := env.Beta * (-2.0*env.Mu_h + env.Mu_b + mu_relative)
if ymax <= 0.0 {
return 0.0, nil
}
upper_a := math.Sqrt(ymax / (2.0 * env.Beta * a))
if upper_a > math.Pi {
ymax = 2.0 * env.Beta * a * math.Pow(math.Pi, 2.0)
}
upper_b := math.Sqrt(ymax / (env.Beta * b))
if upper_b > math.Pi {
ymax = env.Beta * b * math.Pow(math.Pi, 2.0)
}
t := 1e-7
integral, abserr, err := integrate.Qags(F, 0.0, ymax, t, t)
if err != nil {
fmt.Printf("err conditions: ymax = %f; upper_a = %f; upper_b = %f\n", ymax, upper_a, upper_b)
return 0.0, err
}
if math.Abs(abserr) > t*10 {
err = fmt.Errorf("nu integral too innaccurate (abserr = %e)", abserr)
}
val := integral / (4.0 * math.Pow(math.Pi, 2.0) * a * math.Sqrt(b))
return val, err
}
// Calculate the integral of y from 0 to ymax of: F(y) / (8*pi^2*a).
// a, b are parameters in pair spectrum: omega_+(k) = a*(kx^2 + ky^2) + 2b*(1 - cos(kz))
func OmegaIntegralCos(env *tempAll.Environment, a, b float64, F func(float64, float64) float64) (float64, error) {
if a == 0.0 || b == 0.0 {
return 0.0, nil
}
// define the inner integral
t := 1e-7
integral_inner := func(kz float64) float64 {
bterm := 2.0 * b * (1.0 - math.Cos(kz))
ymax := env.Beta * (-2.0*env.Mu_h + env.Mu_b - bterm)
if ymax <= 0.0 {
return 0.0
}
if ymax/env.Beta > a*math.Pow(math.Pi, 2.0) {
fmt.Println("ymax = %f is too large, replacing with (beta*a*pi^2)", ymax)
ymax = env.Beta * a * math.Pow(math.Pi, 2.0)
}
innerF := func(y float64) float64 {
return F(y, kz)
}
integral, abserr, err := integrate.Qags(innerF, 1e-10, ymax, t, t)
if err != nil {
fmt.Printf("inner integral error\n")
panic(err)
}
if math.Abs(abserr) > t*100 {
err = fmt.Errorf("inner integral too innaccurate (abserr = %e)", abserr)
panic(err)
}
return integral
}
// calculate the full integral
integral, abserr, err := integrate.Qags(integral_inner, -math.Pi, math.Pi, t, t)
if err != nil {
fmt.Printf("outer integral error\n")
return 0.0, err
}
if math.Abs(abserr) > t*1000 {
err = fmt.Errorf("outer integral too innaccurate (abserr = %e)", abserr)
return 0.0, err
}
val := integral / (8.0 * math.Pow(math.Pi, 2.0) * env.Beta * a)
return val, nil
}