// Calculate x - (x_1 + x_2) with Mu_h fixed.
func AbsErrorX(env *tempAll.Environment, variables []string) solve.Diffable {
F := func(v vec.Vector) (float64, error) {
if v.ContainsNaN() {
fmt.Printf("got NaN in AbsErrorX (v=%v)\n", v)
return 0.0, errors.New("NaN in input")
}
env.Set(v, variables)
// Before we evaluate error in X, Mu_b and D1 should have
// appropriate values.
system, start := D1Mu_bSystem(env)
eps := 1e-9
_, err := solve.MultiDim(system, start, eps, eps)
if err != nil {
return 0.0, err
}
if env.Mu_b > 0.0 {
fmt.Println("Warning: got Mu_b > 0 in AbsErrorX")
env.Mu_b = 0.0
}
// evaluate X error
x1 := tempPair.X1(env)
x2, err := tempCrit.X2(env)
if err != nil {
fmt.Printf("error from X2(): %v\n", err)
return 0.0, err
}
lhs := env.X
rhs := x1 + x2
return lhs - rhs, nil
}
h := 1e-5
epsabs := 1e-4
return solve.SimpleDiffable(F, len(variables), h, epsabs)
}
// Solve the (D1, Mu_h, Beta) system with x and Mu_b fixed.
func FlucTempSolve(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
// fix pair coefficients
if env.A == 0.0 && env.B == 0.0 && env.FixedPairCoeffs {
D1, Mu_h, Mu_b, Beta := env.D1, env.Mu_h, env.Mu_b, env.Beta
env.Mu_b = 0.0 // Mu_b is 0 at T_c
_, err := tempCrit.CritTempSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
omegaFit, err := tempCrit.OmegaFit(env, tempCrit.OmegaPlus)
if err != nil {
return nil, err
}
env.A, env.B = omegaFit[0], omegaFit[2]
env.PairCoeffsReady = true
// uncache env
env.D1, env.Mu_h, env.Mu_b, env.Beta = D1, Mu_h, Mu_b, Beta
}
// our guess for beta should be a bit above Beta_p
pairSystem, pairStart := tempPair.PairTempSystem(env)
_, err := solve.MultiDim(pairSystem, pairStart, epsAbs, epsRel)
if err != nil {
return nil, err
}
env.Beta += 0.1
// solve fluc temp system for reasonable values of Mu_h and D1 first
system, start := FlucTempD1MuSystem(env)
_, err = solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
// solve the full fluc temp system
system, start = FlucTempFullSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
// Solve the (D1, Mu_h, Mu_b) system with Beta and x fixed.
func SolveD1Mu_hMu_b(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
/*
// fix pair coefficients
if env.A == 0.0 && env.B == 0.0 && env.FixedPairCoeffs {
D1, Mu_h, Mu_b, Beta, Be_field := env.D1, env.Mu_h, env.Mu_b, env.Beta, env.Be_field
env.Mu_b = 0.0 // Mu_b is 0 at T_c
env.Be_field = 0.0
_, err := tempCrit.CritTempSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
omegaFit, err := tempCrit.OmegaFit(env, tempCrit.OmegaPlus)
if err != nil {
return nil, err
}
env.A, env.B = omegaFit[0], omegaFit[2]
env.PairCoeffsReady = true
// uncache env
env.D1, env.Mu_h, env.Mu_b, env.Beta, env.Be_field = D1, Mu_h, Mu_b, Beta, Be_field
}
*/
maxIters := 1000
oldMu_b := env.Mu_b
for i := 0; i < maxIters; i++ {
// iterate D1/Mu_h
solution, err := SolveD1Mu_h(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
// iterate Mu_b
Be_field := env.Be_field
env.Be_field = 0.0
zv := vec.ZeroVector(3)
omega0, err := tempCrit.OmegaPlus(env, zv)
//omegaFit, err := tempCrit.OmegaFit(env, tempCrit.OmegaPlus)
if err != nil {
return nil, err
}
env.Mu_b = -omega0
env.Be_field = Be_field
//A, Mub_eff := omegaFit[0], omegaFit[3]
//env.Mu_b = -omega0 + 2.0 * env.Be_field * env.A
//Mub_eff := omegaFit[3]
//env.Mu_b = Mub_eff
//fmt.Printf("iterating Mu_b: now %f, before %f\n", env.Mu_b, oldMu_b)
// check if done
if math.Abs(env.Mu_b-oldMu_b) < epsAbs || !env.IterateD1Mu_hMu_b {
return []float64{solution[0], solution[1], env.Mu_b}, nil
}
oldMu_b = env.Mu_b
}
return []float64{0.0, 0.0, 0.0}, fmt.Errorf("failed to find D1/Mu_h/Mu_b solution for env=%s\n", env.String())
/*
system, start := D1Mu_hMu_bSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
*/
}
