Package lm solves non-linear least squares problems using the Levenberg-Marquardt method.
- Define a function:
func biggsEXP6Func(dst, x []float64) {
for i := 0; i < 13; i++ {
z := float64(i) / 10
y := math.Exp(-z) - 5*math.Exp(-10*z) + 3*math.Exp(-4*z)
dst[i] = x[2]*math.Exp(-x[0]*z) - x[3]*math.Exp(-x[1]*z) + x[5]*math.Exp(-x[4]*z) - y
}
}- Define the jacobian. In this case the jacobian will be evaluated by finite differences:
biggsNumJac := lm.NumJac{Func: biggsEXP6Func}- Call the solver:
biggsProb := lm.LMProblem{
Dim: 6,
Size: 13,
Func: biggsEXP6Func,
Jac: biggsNumJac.Jac,
InitParams: []float64{1, 2, 1, 1, 1, 1},
Tau: 1e-6,
Eps1: 1e-8,
Eps2: 1e-8,
}
biggsResults, biggsErr := lm.LM(biggsProb, &lm.Settings{Iterations: 100, ObjectiveTol: 1e-16})
fmt.Println(biggsResults)
fmt.Println(biggsErr)- Madsen, Kaj, Hans Bruun Nielsen, and Ole Tingleff. "Methods for non-linear least squares problems.", 2nd edition, 2004.
- Lourakis, Manolis. "A Brief Description of the Levenberg-Marquardt Algorithm Implemened by levmar", 2005.
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