Index

A

add_constraints() (Irene.program.OptimizationProblem method) add_derivative() (Irene.grouprings.SemigroupAlgebra method) add_relations() (Irene.grouprings.CommutativeSemigroup method) AddConstantBlock() (Irene.sdp.sdp method) AddConstraint() (Irene.relaxations.SDPRelaxations method)

AddConstraintBlock() (Irene.sdp.sdp method) analyse_program() (Irene.program.OptimizationProblem method) AtomicSGElement (class in Irene.grouprings) auto_transform_matrix() (Irene.geometric.GPRelaxations method) aux_rels (Irene.grouprings.CommutativeSemigroup attribute) AvailableSDPSolvers() (Irene.base.base method)

B

base (class in Irene.base)

Basis() (pyProximation.orthsys.OrthSystem method) boxCheck() (pyProximation.measure.Measure method)

C

Calpha() (Irene.relaxations.SDPRelaxations method) Calpha_() (in module Irene.relaxations) Calpha__() (in module Irene.relaxations) check() (pyProximation.measure.Measure method) Commit() (Irene.relaxations.SDPRelaxations method) CommutativeSemigroup (class in Irene.grouprings) compare_diags() (Irene.geometric.GPRelaxations static method) constraint_terms_with_even_exponent (Irene.program.OptimizationProblem attribute) constraint_terms_with_odd_exponent (Irene.program.OptimizationProblem attribute)

constraint_trms_with_negative_coefficient (Irene.program.OptimizationProblem attribute) constraint_trms_with_positive_coefficient (Irene.program.OptimizationProblem attribute) constraints (Irene.program.OptimizationProblem attribute) constraints_degree (Irene.program.OptimizationProblem attribute) constraints_half_degree (Irene.program.OptimizationProblem attribute) content (Irene.grouprings.AtomicSGElement attribute) (Irene.grouprings.SemigroupAlgebraElement attribute) convex_combination() (Irene.program.OptimizationProblem method) csdp() (Irene.sdp.sdp method) CvxOpt() (Irene.sdp.sdp method)

D

Decompose() (Irene.relaxations.SDPRelaxations method) degree() (Irene.grouprings.CommutativeSemigroup method) delta() (Irene.program.OptimizationProblem method) Delta() (pyProximation.interpolation.Interpolation method) delta_vertex() (Irene.program.OptimizationProblem method)

derivative() (Irene.grouprings.SemigroupAlgebra method) derivatives (Irene.grouprings.SemigroupAlgebra attribute) DetSymEnv() (pyProximation.base.Foundation method) diff() (Irene.grouprings.SemigroupAlgebra method) divide() (Irene.grouprings.AtomicSGElement method) (Irene.grouprings.SemigroupAlgebraElement method)

E

edges (Irene.grouprings.CommutativeSemigroup attribute) element_sub_lattice() (Irene.grouprings.CommutativeSemigroup method) ExponentsVec() (Irene.relaxations.SDPRelaxations method)

ExtractSolution() (Irene.relaxations.SDRelaxSol method) ExtractSolutionLH() (Irene.relaxations.SDRelaxSol method) ExtractSolutionScipy() (Irene.relaxations.SDRelaxSol method)

F

FormBasis() (pyProximation.orthsys.OrthSystem method) Foundation (class in pyProximation.base)

FourierBasis() (pyProximation.orthsys.OrthSystem method) from_problem() (Irene.relaxations.SDPRelaxations class method)

G

gens (Irene.grouprings.CommutativeSemigroup attribute) (Irene.grouprings.SemigroupAlgebra attribute) getConstraint() (Irene.relaxations.SDPRelaxations method)

getMomentConstraint() (Irene.relaxations.SDPRelaxations method) getObjective() (Irene.relaxations.SDPRelaxations method) GPRelaxations (class in Irene.geometric)

H

h_plus() (Irene.geometric.GPRelaxations method)

has_symbol() (Irene.program.OptimizationProblem static method)

I

in_newton() (Irene.program.OptimizationProblem method) InitSDP() (Irene.relaxations.SDPRelaxations method) inner() (pyProximation.orthsys.OrthSystem method) integral() (pyProximation.measure.Measure method) Interpolate() (pyProximation.interpolation.Interpolation method) Interpolation (class in pyProximation.interpolation) inverses (Irene.grouprings.CommutativeSemigroup attribute) Irene.base module Irene.geometric module

Irene.grouprings module Irene.program module Irene.relaxations module Irene.sdp module Irene.sonc module is_abelian (Irene.grouprings.CommutativeSemigroup attribute) is_semigroup (Irene.grouprings.CommutativeSemigroup attribute)

L

LaTeX() (in module Irene.base) lattice_edges() (Irene.grouprings.CommutativeSemigroup method) lattice_vertices() (Irene.grouprings.CommutativeSemigroup method) LC() (Irene.grouprings.AtomicSGElement method) (Irene.grouprings.SemigroupAlgebraElement method) linear_combination() (Irene.program.OptimizationProblem method) LM() (Irene.grouprings.AtomicSGElement method) (Irene.grouprings.SemigroupAlgebraElement method)

LocalizedMoment() (Irene.relaxations.SDPRelaxations method) LocalizedMoment_() (Irene.relaxations.SDPRelaxations method) LT() (Irene.grouprings.AtomicSGElement method) (Irene.grouprings.SemigroupAlgebraElement method) lt_divisible_by() (Irene.grouprings.AtomicSGElement method) (Irene.grouprings.SemigroupAlgebraElement method)

M

max_deg (Irene.grouprings.CommutativeSemigroup attribute) Measure (class in pyProximation.measure) measure() (pyProximation.measure.Measure method) Minimize() (Irene.relaxations.SDPRelaxations method) MinNumPoints() (pyProximation.interpolation.Interpolation method) module Irene.base Irene.geometric Irene.grouprings Irene.program Irene.relaxations Irene.sdp Irene.sonc pyProximation.base pyProximation.interpolation pyProximation.measure pyProximation.orthsys pyProximation.rational

Mom (class in Irene.relaxations) MomentConstraint() (Irene.relaxations.SDPRelaxations method) MomentMat() (Irene.relaxations.SDPRelaxations method) MomentsOrd() (Irene.relaxations.SDPRelaxations method) mono2ord_tuple() (Irene.program.OptimizationProblem method) Monomials() (pyProximation.interpolation.Interpolation method)

N

newton() (Irene.program.OptimizationProblem method)

norm() (pyProximation.measure.Measure method) NumericalRank() (Irene.relaxations.SDRelaxSol method)

O

objective (Irene.program.OptimizationProblem attribute) objective_degree (Irene.program.OptimizationProblem attribute) objective_half_degree (Irene.program.OptimizationProblem attribute) objective_terms_with_even_exponent (Irene.program.OptimizationProblem attribute) objective_terms_with_odd_exponent (Irene.program.OptimizationProblem attribute)

objective_trms_with_negative_coefficient (Irene.program.OptimizationProblem attribute) objective_trms_with_positive_coefficient (Irene.program.OptimizationProblem attribute) omega() (Irene.program.OptimizationProblem static method) OptimizationProblem (class in Irene.program) Option() (Irene.sdp.sdp method) OrthSystem (class in pyProximation.orthsys)

P

parse_solution_matrix() (Irene.sdp.sdp static method) pInitSDP() (Irene.relaxations.SDPRelaxations method) Pivot() (Irene.relaxations.SDRelaxSol method) PolyBasis() (pyProximation.orthsys.OrthSystem method) PolyCoefFullVec() (Irene.relaxations.SDPRelaxations method) positive_exp() (Irene.grouprings.CommutativeSemigroup method) program_degree() (Irene.program.OptimizationProblem method) project() (pyProximation.orthsys.OrthSystem method) pyProximation.base module

pyProximation.interpolation module pyProximation.measure module pyProximation.orthsys module pyProximation.rational module

R

RationalApprox (in module pyProximation.rational) RationalAprox (class in pyProximation.rational) RatLSQ() (pyProximation.rational.RationalAprox method) read_csdp_out() (Irene.sdp.sdp method) read_sdpa_out() (Irene.sdp.sdp method)

ReducedMonomialBase() (Irene.relaxations.SDPRelaxations method) ReduceExp() (Irene.relaxations.SDPRelaxations method) relations (Irene.program.OptimizationProblem attribute) RelaxationDeg() (Irene.relaxations.SDPRelaxations method) rels (Irene.grouprings.CommutativeSemigroup attribute) Resume() (Irene.relaxations.SDPRelaxations method)

S

sample() (pyProximation.measure.Measure method) SaveState() (Irene.relaxations.SDPRelaxations method) sdp (class in Irene.sdp) sdpa() (Irene.sdp.sdp method) sdpa_param() (Irene.sdp.sdp method) SDPRelaxations (class in Irene.relaxations) SDRelaxSol (class in Irene.relaxations) semigroup (Irene.grouprings.AtomicSGElement attribute) (Irene.grouprings.SemigroupAlgebra attribute) (Irene.grouprings.SemigroupAlgebraElement attribute) (Irene.program.OptimizationProblem attribute) SemigroupAlgebra (class in Irene.grouprings) SemigroupAlgebraElement (class in Irene.grouprings) Series() (pyProximation.orthsys.OrthSystem method) set_objective() (Irene.program.OptimizationProblem method) SetMeasure() (pyProximation.orthsys.OrthSystem method) SetMonoOrd() (Irene.relaxations.SDPRelaxations method)

SetNumCores() (Irene.relaxations.SDPRelaxations method) SetObjective() (Irene.relaxations.SDPRelaxations method) (Irene.sdp.sdp method) SetOrthBase() (pyProximation.orthsys.OrthSystem method) SetScipySolver() (Irene.relaxations.SDRelaxSol method) SetSDPSolver() (Irene.relaxations.SDPRelaxations method) sga (Irene.program.OptimizationProblem attribute) sInitSDP() (Irene.relaxations.SDPRelaxations method) solve() (Irene.geometric.GPRelaxations method) (Irene.sdp.sdp method) (Irene.sonc.SONCRelaxations method) SONCRelaxations (class in Irene.sonc) square_exponent() (Irene.program.OptimizationProblem static method) State() (Irene.relaxations.SDPRelaxations method) StblRedEch() (Irene.relaxations.SDRelaxSol method) symbol (Irene.grouprings.AtomicSGElement attribute) symbols (Irene.grouprings.CommutativeSemigroup attribute)

T

TensorPrd() (pyProximation.orthsys.OrthSystem method) Term2Mmnt() (Irene.relaxations.SDRelaxSol method) to_sympy() (Irene.program.OptimizationProblem method)

total_degree (Irene.program.OptimizationProblem attribute) transform_program() (Irene.geometric.GPRelaxations method) tuple2mono() (Irene.program.OptimizationProblem method)

V

VEC() (Irene.sdp.sdp static method)

vertices (Irene.grouprings.CommutativeSemigroup attribute)

W

which() (Irene.base.base static method)

write_sdpa_dat() (Irene.sdp.sdp method) write_sdpa_dat_sparse() (Irene.sdp.sdp method)