# 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
- ***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





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


## See Also
 [](chapter_ksp), [LMVM Matrices](sec_matlmvm), `MatCreate()`, `MATLMVM`, `MATLMVMSYMBROYDEN`, `MatCreateLMVMDFP()`, `MatCreateLMVMSR1()`,
`MatCreateLMVMBFGS()`, `MatCreateLMVMBrdn()`, `MatCreateLMVMBadBrdn()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/utils/lmvm/symbrdn/symbadbrdn.c.html#MatCreateLMVMSymBadBroyden">src/ksp/ksp/utils/lmvm/symbrdn/symbadbrdn.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ksp/ksp/utils/lmvm/symbrdn/symbadbrdn.c)


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