MatCreateLMVMSymBadBroyden#

Creates a limited-memory Symmetric “Bad” Broyden-type matrix used for approximating Jacobians. L-SymBadBrdn is a convex combination of L-DFP and L-BFGS such that SymBadBrdn^{-1} = (1 - phi)BFGS^{-1} + phiDFP^{-1}. The combination factor phi 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.

Synopsis#

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

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.

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_phi - (developer) convex ratio between BFGS and DFP components of the update
-mat_lmvm_scale_type - (developer) type of scaling applied to J0 (none, scalar, diagonal)
-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