Weight Solver

Classes related to solving for orbital weights. WeightSolver is a generic parent class, specific implementations are sub-classes of this.

API

Classes:

CvxoptNonNegSolver([P, q])	Solver for NNLS problem using CVXOPT
LegacyWeightSolver(config, directory_with_ml)	Use legacy AKA Fortran weight solving.
NNLS(config, directory_with_ml[, CRcut, ...])	Python implementations of NNLS weight solving
WeightSolver()	Generic WeightSolver class

class weight_solvers.CvxoptNonNegSolver(P=None, q=None)

Solver for NNLS problem using CVXOPT

Solves the QP problem:

argmin (1/2 beta^T P beta + q beta T) subject to (component-wise) beta > 0

Parameters:

Parray (p, p)

quadratic part of objective function

qarray (p,)

linear part of objective function

Attributes:

successbool

whether solver was successful

betaarray (p,)

solution

class weight_solvers.LegacyWeightSolver(config, directory_with_ml, CRcut=False)

Use legacy AKA Fortran weight solving.

Uses the legcay_fortran program triaxnnls_CRcut.f90 or `triaxnnls_noCRcut.f90. Uses Lawson and Hanson non-negative least-squares algorithm.

Parameters:

configa dyn.config_reader.Configuration object

directory_with_mlstring

model directory with the ml extension

CRcutBool, default False

whether to use the CRcut solution for the counter-rotating orbit problem. See Zhu et al. 2018 for more.

Methods:

chi2_kinmap()	Returns the chi2 directly calculated from the kinematic maps.
copy_kinematic_data()	Copy kin data to infil/ direc
create_fortran_input_nnls(path, ml)	create fortran input file nn.in
get_weights_and_chi2_from_orbmat_file()	Get weights and chi2 from nn_orbmat.out
read_chi2()	Read chi2 values from nn_kinem.out
read_nnls_orbmat_rhs_and_solution()	Read nn_orbmat.out
read_weights()	Read nn_orb.out to astropy table
solve([orblib])	Main method to solve NNLS problem.
write_executable_for_weight_solver(ml)	write executable bash script file

chi2_kinmap()

Returns the chi2 directly calculated from the kinematic maps.

Returns:

chi2_kinmapfloat

chi2 directly calculated from the kinematic maps.

copy_kinematic_data()

Copy kin data to infil/ direc

create_fortran_input_nnls(path, ml)

create fortran input file nn.in

Parameters:

pathstring

model directory path

mlfloat

the mass-scaling parameter ml

Returns:

None

get_weights_and_chi2_from_orbmat_file()

Get weights and chi2 from nn_orbmat.out

Note: Chi2 values returned differ from read_chi2 method. See that docstring for more.

Returns:

tuple

(weights, chi2_all, chi2_gh), where:

• weights : array of orbit weights

• chi2_all : sum of squared residuals for intrinsic masses, projected_masses and GH coefficients h_1 to h_n

• chi2_kin : sum of squared residuals for GH coefficients h_1 to h_n

read_chi2()

Read chi2 values from nn_kinem.out

Taken from old schwpy code, lines 181-212 of schw_domoditer.py

Note: This is a legacy method for reading legacy output and it not used by default. Instead we use self.get_chi2_from_orbmat get chi2 values. The chi2 value definitions of this method are NOT the same chi2 values given by self.get_chi2_from_orbmat. They differ in (i) including intrinsic/projected mass constraints, and (ii) using h1/h2 vs V/sigma, and (iii) if CRcut==True, whether the ‘cut’ orbits - with artificially large h1 - are included (here they aren’t)

Returns:

tuple

(chi2, kinchi2) where:

• chi2 = sum of sq. residuals of observed GH coefficients h_1 to h_N

• kinchi2 = sum of sq. residuals of V, sigma, and GH coefficients from h_3 to h_N

read_nnls_orbmat_rhs_and_solution()

Read nn_orbmat.out

This contains the matrix and right-hand-side for the NNLS problem, and the solution

Returns:

tuple

(orbmat, rhs, solution)

read_weights()

Read nn_orb.out to astropy table

this contains oribtal weights, orbit type, and other columns

Returns:

None

sets self.weights which is an astropy table containing the orbital weights

solve(orblib=None)

Main method to solve NNLS problem.

Parameters:

orblibdyn.OrbitLibrary

This parameter is not used in this Legacy implementation (as all orbit library information is read from files). It is included here for consistency with later WeightSolver implementations

Returns:

tuple

(weights, chi2_all, chi2_kin) where:

• weights : array, of orbit weights

• chi2_all : float, sum of squared residuals for intrinsic masses, projected_masses and GH coefficients from h_1 to h_n

• chi2_kin : float sum of squared residuals for GH coefficients h_1 to h_n

• chi2_kinmap : directly calculates the chi2 from the kinematic maps

write_executable_for_weight_solver(ml)

write executable bash script file

Parameters:

mlfloat

the mass-scaling parameter ml

Returns:

string

the name of the bash script file to execute

class weight_solvers.NNLS(config, directory_with_ml, CRcut=False, nnls_solver=None)

Python implementations of NNLS weight solving

Uses either scipy.optimize.nnls or cvxopt as backends. This constructs the NNLS matrix and rhs, solves, and saves the result.

Parameters:

configa dyn.config_reader.Configuration object

directory_with_mlstring

model directory with the ml extension

CRcutBool, default False

whether to use the CRcut solution for the counter-rotating orbit problem. See Zhu et al. 2018 for more.

nnls_solverstring

either scipy or cvxopt

Methods:

apply_CR_cut(kins, orb_losvd, orb_gh)	apply CRcut
construct_nnls_matrix_and_rhs(orblib)	construct nnls matrix_and rhs
get_observed_mass_constraints()	Get aperture+intrinsic mass constraits from MGE
solve(orblib)	Solve for orbit weights

apply_CR_cut(kins, orb_losvd, orb_gh)

apply CRcut

to solve the counter rotating orbit problem. This cuts orbits which have \(|V - V_\mathrm{obs}|> 3\sigma_\mathrm{obs}\). See Zhu+2018 MNRAS 2018 473 3000 for details

Parameters:

kinsa dyn.kinematics.Kinematic object

orb_losvddyn.kinematics.Histogram

historgram of orblib losvds

orb_gharray

array of input gh expansion coefficients, before the CRcut

Returns:

array

array of input gh expansion coefficients, after the CRcut

construct_nnls_matrix_and_rhs(orblib)

construct nnls matrix_and rhs

Parameters:

orblibdyn.orblib.OrbitLibrary

an orbit library

Returns:

tuple

(orbmat, rhs)

get_observed_mass_constraints()

Get aperture+intrinsic mass constraits from MGE

Returns:

None

sets attributes:

• self.intrinsic_masses

• self.intrinsic_mass_error

• self.projected_masses

• self.projected_mass_error

• constraint counts self.n_intrinsic, self.n_apertures and self.n_mass_constraints

solve(orblib)

Solve for orbit weights

Note: the returned chi2 values are not the same as LegacyWeightSolver.read_chi2 - see the docstring for more info

Parameters:

orblibdyn.OrbitLibrary

must have attributes losvd_histograms, intrinsic_masses, and projected_masses

Returns:

tuple

(weights, chi2_all, chi2_kin) where:

• weights : array, of orbit weights

• chi2_all : float, sum of squared residuals for intrinsic masses, projected_masses and GH coefficients from h_1 to h_n

• chi2_kin : float sum of squared residuals for GH coefficients h_1 to h_n

• chi2_kinmap : directly calculates the chi2 from the kinematic maps NOT CURRENTLY IMPLEMENTED, RETURNS nan!

class weight_solvers.WeightSolver

Generic WeightSolver class

Specific implementations are defined as sub-classes. Each one should have a main method solve

Methods:

chi2_kinmap()	Template chi2_kinmap method
solve(orblib)	Template solve method

chi2_kinmap()

Template chi2_kinmap method

Returns the chi2 directly calculated from the kinematic maps. Specific implementations should override this.

Returns:

chi2_kinmapfloat

chi2 directly calculated from the kinematic maps.

solve(orblib)

Template solve method

Specific implementations should override this.

Parameters:

orblibdyn.OrbitLibrary object

Returns:

weightsarray

orbit weights

chi2_allfloat

a total chi2 value

chi2_kinfloat

a chi2 value purely for kinematics

chi2_kinmapfloat

directly calculates the chi2 from the kinematic maps

Inheritance Diagram