Module lmdif 

MINPACK routines backing the Levenberg-Marquardt method.

Port of ql/math/optimization/lmdif.{hpp,cpp}, itself the C translation of the MINPACK Fortran (Argonne National Laboratory, Garbow, Hillstrom, More, 1980). Matrices are stored column-major in flat slices, as in the original; the arithmetic constants MACHEP and DWARF keep MINPACK’s values so results match QuantLib’s.

Traits

LmdifCostFunction

The user-supplied functions minimized by lmdif.

Functions

enorm

Computes the Euclidean norm of x.

fdjac2

Computes a forward-difference approximation to the m by n Jacobian at x into the column-major fjac.

lmdif

Minimizes the sum of the squares of m nonlinear functions in n variables by the Levenberg-Marquardt algorithm, approximating the Jacobian by forward differences unless fcn supplies it.

lmpar

Determines the Levenberg-Marquardt parameter par and the corresponding step x such that, with dxnorm = ||D*x||, either par is zero and dxnorm - delta <= 0.1 * delta, or par is positive and |dxnorm - delta| <= 0.1 * delta.

qrfac

Computes the QR factorization A * P = Q * R of the column-major m by n matrix a by Householder transformations with optional column pivoting.

qrsolv

Solves the least-squares system A*x = b, D*x = 0 given the QR factorization of A * P = Q * R.