chrono::modal Namespace Reference

Description

Namespace with classes for the modal module.

Classes
class	callback_Ax
	Generic A*x callback. More...
class	callback_Ax_sparse_complexshiftinvert
	The callback to be used for "A*x" where for shift&invert is: A = (As - sigma Bs)/Bs , with COMPLEX sigma shift, so A*x = (As - sigma Bs)/(Bs*x), just like a linear system with coefficient matrix (As - sigma Bs) and known rhs Bs*x. More...
class	callback_Ax_sparse_shiftinvert
	The callback to be used for "A*x" where for shift&invert is: A = (As - sigma Bs)/Bs , so A*x = (As - sigma Bs)/(Bs*x), just like a linear system with coefficient matrix (As - sigma Bs) and known rhs Bs*x. More...
class	ChEigenvalueSolverSettings
	Class for passing basic settings to the Solve() function of the various solvers. More...
class	ChGeneralizedEigenvalueSolver
	Base interface class for eigensolvers for the undamped constrained generalized problem (-wsquare*M + K)*x = 0 s.t. More...
class	ChGeneralizedEigenvalueSolverKrylovSchur
	Solves the undamped constrained eigenvalue problem with the Krylov-Schur iterative method. More...
class	ChGeneralizedEigenvalueSolverLanczos
	Solves the undamped constrained eigenvalue problem with the Lanczos iterative method. More...
class	ChKrylovSchurEig
	Compute (complex) eigenvalues and eigenvectors using the Krylov-Schur algorithm. More...
class	ChModalAssembly
	Class for assemblies of items, for example ChBody, ChLink, ChMesh, etc. More...
class	ChModalDamping
	Base class for damping models of modal reduced assemblies. More...
class	ChModalDampingCustom
	Class for damping defined with an user-defined matrix that could be obtained via external tools such as Matlab or FEA. More...
class	ChModalDampingFactorAssembly
	Class for setting the damping via N damping factors z_i for all the modes of the subassembly, where assembly n.modes = (boundary coords+internal modes) R^ = V'^-1 * Dd * V^-1 with Dd=diag { 2 z_1 w_1, 2 z_2 w_2, ..., 2 z_i w_i }, and V = eigenvectors of (M^, K^). More...
class	ChModalDampingFactorRayleigh
	Class for setting the damping via N damping factors z_i of the internal mode coordinates and alpha-beta Rayleigh damping for the boundary nodes, assuming R^ = [Rbb Rbm ] [Rmb Rmm ] with Rmm=diag { 2 z_1 w_1, 2 z_2 w_2, ..., 2 z_i w_i }, Rbb= alpha*Mbb + beta*Kbb, Rbm = 0, Rmb = 0. More...
class	ChModalDampingFactorRmm
	Class for setting the damping via N damping factors z_i of the internal mode coordinates. More...
class	ChModalDampingNone
	Class for no damping model. More...
class	ChModalDampingRayleigh
	Class for simple Rayleigh damping model R^ = alpha*M^ + beta*K^ where M^ and K^ are the reduced matrices, both for boundary nodes and modal coords. More...
class	ChModalDampingReductionR
	Class for damping as reduction of the original damping matrix via the eigenvectors of the undamped assembly, i.e. More...
class	ChModalSolveDamped
	Class for computing eigenvalues/eigenvectors for the DAMPED constrained system. More...
class	ChModalSolveUndamped
	Class for computing eigenvalues/eigenvectors for the undamped constrained system. More...
class	ChQuadraticEigenvalueSolver
	Base interface class for eigensolvers for the damped dynamic problem ie. More...
class	ChQuadraticEigenvalueSolverKrylovSchur
	Solves the eigenvalue problem with the Krylov-Schur iterative method. More...
class	ChQuadraticEigenvalueSolverNullspaceDirect
	Solves the eigenvalue problem with a direct method: first does LU factorization of Cq jacobians to find the null space, then solves the problem using the direct Eigen::EigenSolver. More...

Functions
void	sparse_assembly_2x2symm (Eigen::SparseMatrix< double, Eigen::ColMajor, int > &HCQ, const ChSparseMatrix &H, const ChSparseMatrix &Cq)
void	placeMatrix (Eigen::SparseMatrix< double, Eigen::ColMajor, int > &HCQ, const ChSparseMatrix &H, int row_start, int col_start)
void	ordschur (ChMatrixDynamic< std::complex< double >> &U, ChMatrixDynamic< std::complex< double >> &T, ChVectorDynamic< bool > &select)
int	testConverge (ChMatrixDynamic< std::complex< double >> &H, int k, int i, double tol)
void	truncateKrylov (ChMatrixDynamic< std::complex< double >> &Q, ChMatrixDynamic< std::complex< double >> &H, const int k, const int m)
void	sortSchur (ChMatrixDynamic< std::complex< double >> &US, ChMatrixDynamic< std::complex< double >> &TS, bool &isC, const ChMatrixDynamic< std::complex< double >> &A, const int k)
void	expandKrylov (ChMatrixDynamic< std::complex< double >> &Q, ChMatrixDynamic< std::complex< double >> &H, callback_Ax *Ax_function, int sk, int ek)
void	KrylovSchur (ChMatrixDynamic< std::complex< double >> &Q, ChMatrixDynamic< std::complex< double >> &H, bool &isC, bool &flag, int &nc, int &ni, callback_Ax *Ax_function, const ChVectorDynamic< std::complex< double >> &v1, const int n, const int k, const int m, const int maxIt, const double tol)
void	swap (ChModalAssembly &first, ChModalAssembly &second)
void	util_sparse_assembly_2x2symm (Eigen::SparseMatrix< double, Eigen::ColMajor, int > &HCQ, const ChSparseMatrix &H, const ChSparseMatrix &Cq)

Function Documentation

expandKrylov()

void chrono::modal::expandKrylov	(	ChMatrixDynamic< std::complex< double >> &	Q,
		ChMatrixDynamic< std::complex< double >> &	H,
		callback_Ax *	Ax_function,
		int	sk,
		int	ek
	)

Parameters

Q	orthonormal matrix with dimension [n x k+1] or [n x k+2]
H	`Hessenberg' matrix with dimension [k+1 x k] or [k+2 x k+1]
sk	void (*Ax_function)(ChVectorDynamic<std::complex<double>>& A_x, const ChVectorDynamic<std::complex<double>>& x), ///< compute the A*x operation, for standard eigenvalue problem A*v=lambda*v.

KrylovSchur()

void chrono::modal::KrylovSchur	(	ChMatrixDynamic< std::complex< double >> &	Q,
		ChMatrixDynamic< std::complex< double >> &	H,
		bool &	isC,
		bool &	flag,
		int &	nc,
		int &	ni,
		callback_Ax *	Ax_function,
		const ChVectorDynamic< std::complex< double >> &	v1,
		const int	n,
		const int	k,
		const int	m,
		const int	maxIt,
		const double	tol
	)

Parameters

Q	orthonormal matrix with dimension [n x k+1] or [n x k+2]
H	`Hessenberg' matrix with dimension [k+1 x k] or [k+2 x k+1]
isC	0 = k-th eigenvalue is real, 1= k-th and k-th+1 are complex conjugate pairs
flag	0 = has converged, 1 = hasn't converged
nc	number of converged eigenvalues
ni	number of used iterations
v1	void (*Ax_function)(ChVectorDynamic<std::complex<double>>& A_x, const ChVectorDynamic<std::complex<double>>& x), ///< compute the A*x operation, for standard eigenvalue problem A*v=lambda*v. initial approx of eigenvector, or random
n	size of A
k	number of needed eigenvalues
m	Krylov restart threshold (largest dimension of krylov subspace)
maxIt	max iteration number
tol	tolerance

sparse_assembly_2x2symm()

void chrono::modal::sparse_assembly_2x2symm	(	Eigen::SparseMatrix< double, Eigen::ColMajor, int > &	HCQ,
		const ChSparseMatrix &	H,
		const ChSparseMatrix &	Cq
	)

Parameters

HCQ	resulting square sparse matrix (column major)
H	square sparse H matrix, n_v x n_v
Cq	rectangular sparse Cq n_c x n_v

swap()

void chrono::modal::swap	(	ChModalAssembly &	first,
		ChModalAssembly &	second
	)

Implemented as a friend (as opposed to a member function) so classes with a ChModalAssembly member can use ADL when implementing their own swap.

util_sparse_assembly_2x2symm()

void chrono::modal::util_sparse_assembly_2x2symm	(	Eigen::SparseMatrix< double, Eigen::ColMajor, int > &	HCQ,
		const ChSparseMatrix &	H,
		const ChSparseMatrix &	Cq
	)

Parameters

HCQ	resulting square sparse matrix (column major)
H	square sparse H matrix, n_v x n_v
Cq	rectangular sparse Cq n_c x n_v