PETSc version 3.16.5
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# 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 `^{-1} = (1 - phi)*BFGS^{-1} + phi*DFP^{-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)

The provided local and global sizes must match the solution and function vectors used with MatLMVMUpdate() and MatSolve(). The resulting L-SymBrdn matrix will have storage vectors allocated with VecCreateSeq() in serial and VecCreateMPI() in parallel. 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, set to PETSC_COMM_SELF
| n | - number of local rows for storage vectors
| N | - global size of the storage vectors

### Output Parameter

| B | - the matrix

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

### Options Database Keys

| -mat_lmvm_num_vecs | - maximum number of correction vectors (i.e.: updates) stored
| -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

### See Also

MatCreate(), MATLMVM, MATLMVMSYMBROYDEN, MatCreateLMVMDFP(), MatCreateLMVMSR1(),
MatCreateLMVMBFGS(), MatCreateLMVMBrdn(), MatCreateLMVMBadBrdn()

### Level

intermediate

### Location

src/ksp/ksp/utils/lmvm/symbrdn/symbadbrdn.c
Index of all KSP routines
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Index of all manual pages