MatCreateLMVMSymBadBroyden

Creates a limited-memory Symmetric “Bad” Broyden-type matrix used for approximating Jacobians.

Synopsis

#include "petscksp.h" 
PetscErrorCode MatCreateLMVMSymBadBroyden(MPI_Comm comm, PetscInt n, PetscInt N, Mat *B)

Collective

Input Parameters

• comm - MPI communicator

• n - number of local rows for storage vectors

• N - global size of the storage vectors

Output Parameter

• B - the matrix

Options Database Keys

• -mat_lmvm_hist_size - the number of history vectors to keep

• -mat_lmvm_psi - convex ratio between BFGS and DFP components of the update

• -mat_lmvm_scale_type - type of scaling applied to J0 (none, scalar, diagonal)

• -mat_lmvm_mult_algorithm - the algorithm to use for multiplication (recursive, dense, compact_dense)

• -mat_lmvm_cache_J0_products - whether products between the base Jacobian J0 and history vectors should be cached or recomputed

• -mat_lmvm_eps - (developer) numerical zero tolerance for testing when an update should be skipped

• -mat_lmvm_debug - (developer) perform internal debugging checks

• -mat_lmvm_theta - (developer) convex ratio between BFGS and DFP components of the diagonal J0 scaling

• -mat_lmvm_rho - (developer) update limiter for the J0 scaling

• -mat_lmvm_alpha - (developer) coefficient factor for the quadratic subproblem in J0 scaling

• -mat_lmvm_beta - (developer) exponential factor for the diagonal J0 scaling

• -mat_lmvm_sigma_hist - (developer) number of past updates to use in J0 scaling

Notes

L-SymBadBrdn is a convex combination of L-DFP and L-BFGS such that \(B^{-1} = (1 - \psi)*B_{\text{DFP}}^{-1} + \psi*B_{\text{BFGS}}^{-1}\). The combination factor \(\psi\) is restricted to the range \([0, 1]\), where the L-SymBadBrdn matrix is guaranteed to be symmetric positive-definite. Note that this combination is on the inverses and not on the forwards. For forward convex combinations, use the L-SymBrdn matrix (MATLMVMSYMBROYDEN).

To use the L-SymBrdn matrix with other vector types, the matrix must be created using MatCreate() and MatSetType(), followed by MatLMVMAllocate(). This ensures that the internal storage and work vectors are duplicated from the correct type of vector.

It is recommended that one use the MatCreate(), MatSetType() and/or MatSetFromOptions() paradigm instead of this routine directly.

See Also

KSP: Linear System Solvers, LMVM Matrices, MatCreate(), MATLMVM, MATLMVMSYMBROYDEN, MatCreateLMVMDFP(), MatCreateLMVMSR1(), MatCreateLMVMBFGS(), MatCreateLMVMBroyden(), MatCreateLMVMBadBroyden()

Level

intermediate

Location

src/ksp/ksp/utils/lmvm/symbrdn/symbadbrdn.c

---

Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages