levmar package

Python binding to the levmar library using Cython.

levmar.levmar(func, p0, y, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_bc(func, p0, y, bc, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function, y = func(p, *args).

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

bc: sequence of 2-tuples

(min, max) pairs for each element of the parameters, specifying the (inclusive) upper and lower bounds. Use None for one of min or max for specifying no bound in that direction.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_blec(func, p0, y, bc, lec, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

bc: sequence of 2-tuples

(min, max) pairs for each element of the parameters, specifying the (inclusive) upper and lower bounds. Use None for one of min or max for specifying no bound in that direction.

lec: 2-tuple of ndarray

(A, b) pair specifying a linear equation constraint, where A and b are a matrix of shape (k1, m) and a vector of shape (k1,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_bleic(func, p0, y, bc, lec, lic, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

bc: sequence of 2-tuples

(min, max) pairs for each element of the parameters, specifying the (inclusive) upper and lower bounds. Use None for one of min or max for specifying no bound in that direction.

lec: 2-tuple of ndarray

(A, b) pair specifying a linear equation constraint, where A and b are a matrix of shape (k1, m) and a vector of shape (k1,) respectively.

lic: 2-tuple of ndarray

(C, d) pair specifying a linear inequality constraint, where C and d are a matrix of shape (k2, m) and a vector of shape (k2,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_blic(func, p0, y, bc, lic, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

bc: sequence of 2-tuples

(min, max) pairs for each element of the parameters, specifying the (inclusive) upper and lower bounds. Use None for one of min or max for specifying no bound in that direction.

lic: 2-tuple of ndarray

(C, d) pair specifying a linear inequality constraint, where C and d are a matrix of shape (k2, m) and a vector of shape (k2,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_lec(func, p0, y, lec, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

lec: 2-tuple of ndarray

(A, b) pair specifying a linear equation constraint, where A and b are a matrix of shape (k1, m) and a vector of shape (k1,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_leic(func, p0, y, lec, lic, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

lec: 2-tuple of ndarray

(A, b) pair specifying a linear equation constraint, where A and b are a matrix of shape (k1, m) and a vector of shape (k1,) respectively.

lic: 2-tuple of ndarray

(C, d) pair specifying a linear inequality constraint, where C and d are a matrix of shape (k2, m) and a vector of shape (k2,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved

levmar.levmar_lic(func, p0, y, lic, args=(), jacf=None, mu=0.001, eps1=1.5e-08, eps2=1.5e-08, eps3=1.5e-08, maxit=1000, cdiff=False)

Parameters

func: callable

Function or method computing the model function.

p0: array_like, shape (m,)

Initial estimate of the parameters.

y: array_like, shape (n,)

Dependent data, or the observation.

lic: 2-tuple of ndarray

(C, d) pair specifying a linear inequality constraint, where C and d are a matrix of shape (k2, m) and a vector of shape (k2,) respectively.

args: tuple, optional

Extra arguments passed to func (and jacf).

jacf: callable, optional

Function or method computing the Jacobian of func. If it is None, the Jacobian will be approximated.

mu: float, optional

Scale factor for initial mu.

eps1: float, optional

Stopping threshold for ||J^T e||_inf.

eps2: float, optional

Stopping threshold for ||Dp||_2.

eps3: float, optional

Stopping threshold for ||e||_2.

maxit: int, optional

The maximum number of iterations.

cdiff: {True, False}, optional

If this is True, the Jacobian is approximated with central differentiation.

Returns

p: ndarray, shape=(m,)

Best-fit parameters.

pcov: ndarray, shape=(m,m)

Covariance of the best-fit parameters.

info: tuple

Information regarding minimization.

0: ||e||_2 at p0 1:

0: 2-norm of e 1: infinity-norm of J^T.e 2: 2-norm of Dp 3: mu / max{(J^T.J)_ii}

2: The number of iterations 3: The reason for termination 4: The number of func evaluations 5: The number of jacf evaluations 6: The number of the linear system solved