// Solve the (D1, Mu_h, Beta) system with x and F0 fixed.
func D1MuBetaSolve(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
// our guess for beta should be above beta_c
if env.A == 0.0 && env.B == 0.0 {
D1, Mu_h, F0 := env.D1, env.Mu_h, env.F0
env.F0 = 0.0 // F0 is 0 at T_c
_, err := tempCrit.CritTempSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
fmt.Printf("%v; Tc = %f\n", env, 1.0/env.Beta)
omegaFit, err := tempCrit.OmegaFit(env, tempCrit.OmegaPlus)
if err != nil {
return nil, err
}
env.A, env.B = omegaFit[0], omegaFit[2]
env.PairCoeffsReady = true
env.Beta += 0.1
// we are at T < T_c; uncache env
env.D1, env.Mu_h, env.F0 = D1, Mu_h, F0
}
//fmt.Printf("%v; Tc = %f\n", env, 1.0 / env.Beta)
// solve low temp system for reasonable values of D1 and Mu_h first
_, err := D1MuSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
// solve the full low temp system
system, start := D1MuBetaSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
// 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)
}
func AbsErrorBeta(env *tempAll.Environment, variables []string) solve.Diffable {
F := func(v vec.Vector) (float64, error) {
if v.ContainsNaN() {
fmt.Printf("got NaN in AbsErrorBeta (v=%v)\n", v)
return 0.0, errors.New("NaN in input")
}
env.Set(v, variables)
// Before we evaluate error in Beta, Mu_h and D1 should have
// appropriate values.
system, start := CritTempD1MuSystem(env)
eps := 1e-9
_, err := solve.MultiDim(system, start, eps, eps)
if err != nil {
return 0.0, err
}
// Beta equation error = x - x1 - x2
x1 := tempPair.X1(env)
x2, err := 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)
}
func PairTempSolve(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
system, start := PairTempSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
func SolveNoninteracting(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
env.F0 = 0.0
env.Mu_h = 0.3
env.Beta = 50.0
system, start := NoninteractingSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
// Solve the environment under the conditions at T = T_c.
func CritTempSolve(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
// 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 crit temp system for reasonable values of Mu and D1 first
system, start := CritTempD1MuSystem(env)
_, err = solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
// solve the full crit temp system
system, start = CritTempFullSystem(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
// 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, F0) system with x and Beta fixed.
func D1MuF0Solve(env *tempAll.Environment, epsAbs, epsRel float64) (vec.Vector, error) {
if env.A == 0.0 && env.B == 0.0 {
// We must have T < T_c < T_p (Beta > Beta_c > Beta_p).
// Getting Beta_p is fast, so do that first.
D1, Mu_h, F0, Beta := env.F0, env.Mu_h, env.F0, env.Beta // cache env
env.F0 = 0.0 // F0 is 0 at T_c and T_p
_, err := tempPair.PairTempSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
if Beta < env.Beta {
return nil, fmt.Errorf("Beta = %f less than Beta_p in env %s", Beta, env.String())
}
_, err = tempCrit.CritTempSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
if Beta < env.Beta {
return nil, fmt.Errorf("Beta = %f less than Beta_c in env %s", Beta, env.String())
}
fmt.Printf("%v; Tc = %f\n", env, 1.0/env.Beta)
omegaFit, err := tempCrit.OmegaFit(env, tempCrit.OmegaPlus)
if err != nil {
return nil, err
}
env.A, env.B = omegaFit[0], omegaFit[2]
env.PairCoeffsReady = true
// we are at T < T_c; uncache env
env.D1, env.Mu_h, env.F0, env.Beta = D1, Mu_h, F0, Beta
}
// solve low temp system for reasonable values of D1 and Mu_h first
_, err := D1MuSolve(env, epsAbs, epsRel)
if err != nil {
return nil, err
}
// solve the full low temp system
system, start := D1MuF0System(env)
solution, err := solve.MultiDim(system, start, epsAbs, epsRel)
if err != nil {
return nil, err
}
return solution, nil
}
// Regression test: solution for D1 in default environment should stay constant
func TestSolveAbsErrorD1(t *testing.T) {
solution_expected := 0.05139504320378395
env, err := d1DefaultEnv()
if err != nil {
t.Fatal(err)
}
diffD1 := AbsErrorD1(env, []string{"D1"})
system := solve.Combine([]solve.Diffable{diffD1})
start := []float64{env.D1}
epsabs := 1e-8
epsrel := 1e-8
solution, err := solve.MultiDim(system, start, epsabs, epsrel)
if err != nil {
t.Fatal(err)
}
errabs, err := diffD1.F([]float64{env.D1})
if err != nil {
t.Fatal(err)
}
if math.Abs(solution[0]-solution_expected) > epsabs || math.Abs(errabs) > epsabs {
t.Fatalf("incorrect D1 solution (got %v, expected %v); error is %v", solution[0], solution_expected, errabs)
}
}