pyMOTO Reference

Core

`pymoto.Signal`	Manages the state data, sensitivities, and connects module in- and outputs
`pymoto.Module`	Main class: Module Transforms input signal to output signal and output signal sensitivity to input signal sensitivity
`pymoto.Network`	Binds multiple Modules together as one Module

`pymoto.EinSum`	General linear algebra module which uses the Numpy function `einsum`
`pymoto.MathGeneral`	General mathematical expression module
`pymoto.Inverse`	Calculate the inverse of a matrix \(\mathbf{B} = \mathbf{A}^{-1}\)
`pymoto.LinSolve`	Solves linear system of equations \(\mathbf{A}\mathbf{x}=\mathbf{b}\)
`pymoto.SystemOfEquations`	Solve a partitioned linear system of equations
`pymoto.StaticCondensation`	Static condensation of a linear system of equations
`pymoto.EigenSolve`	Solves the (generalized) eigenvalue problem \(\mathbf{A}\mathbf{q}_i = \lambda_i \mathbf{B} \mathbf{q}_i\)
`pymoto.Scaling`	Scales (scalar) input for different response functions in optimization (objective / constraints).

`pymoto.AssembleGeneral`	Assembles a sparse matrix according to element scaling \(\mathbf{A} = \sum_e x_e \mathbf{A}_e\)
`pymoto.AssembleStiffness`	Stiffness matrix assembly by scaling elements in 2D or 3D \(\mathbf{K} = \sum_e x_e \mathbf{K}_e\)
`pymoto.AssembleMass`	Consistent mass matrix or equivalents assembly by scaling elements \(\mathbf{M} = \sum_e x_e \mathbf{M}_e\)
`pymoto.AssemblePoisson`	Assembly of matrix to solve Poisson equation (e.g. Thermal conductivity, Electric permittivity) \(\mathbf{P} = \sum_e x_e \mathbf{P}_e\).

`pymoto.DensityFilter`	Standard density filter for a structured mesh in topology optimization
`pymoto.OverhangFilter`	Implementation of overhang filter by Langelaar (2016, 2017)

`pymoto.PlotDomain`	Plots the densities of a domain (2D or 3D)
`pymoto.PlotGraph`	Plot an X-Y graph
`pymoto.PlotIter`	Plot iteration history of one or more variables
`pymoto.WriteToVTI`	Writes vectors to a Paraview VTI file

`pymoto.MakeComplex`	Makes a complex variable from two real inputs \(z(x,y) = x + iy\)
`pymoto.RealPart`	Takes the real part of a complex value \(x = \text{Re}(z)\)
`pymoto.ImagPart`	Takes the imaginary part of a complex value \(y = \text{Im}(z)\)
`pymoto.ComplexNorm`	Takes the complex norm \(A = z z^*\)

`pymoto.DomainDefinition`	Definition for a structured domain Nodal numbering used in the domain is given below.
`pymoto.DyadCarrier`	Efficient storage for dyadic or rank-N matrix
`pymoto.finite_difference`	Performs a finite difference check on the given Module or Network
`pymoto.minimize_oc`	Execute minimization using the OC-method
`pymoto.minimize_mma`	Execute minimization using the MMA-method Svanberg (1987), The method of moving asymptotes - a new method for structural optimization

`pymoto.LDAWrapper`	Linear dependency aware solver (LDAS)
`pymoto.SolverDiagonal`	Solver for diagonal matrices
`pymoto.SolverDenseQR`	Solver for dense (square) matrices using a QR decomposition
`pymoto.SolverDenseLU`	Solver for dense (square) matrices using an LU decomposition
`pymoto.SolverDenseCholesky`	Solver for Hermitian positive-definite matrices using a Cholesky factorization.
`pymoto.SolverDenseLDL`	Solver for Hermitian or symmetric matrices using an LDL factorization.
`pymoto.SolverSparseLU`	Solver for sparse (square) matrices using an LU decomposition.
`pymoto.SolverSparsePardiso`	Solver wrapper Intel MKL Pardiso solver, which is a very fast and flexible multi-threaded solver
`pymoto.SolverSparseCholeskyScikit`	Solver for positive-definite Hermitian matrices using a Cholesky factorization.
`pymoto.SolverSparseCholeskyCVXOPT`	Solver for positive-definite Hermitian matrices using a Cholesky factorization.