# MatCreateLMVMSymBroyden
Creates a limited-memory Symmetric Broyden-type matrix used for approximating Jacobians. L-SymBrdn is a convex combination of L-DFP and L-BFGS such that SymBrdn = (1 - phi)*BFGS + phi*DFP. The combination factor phi is restricted to the range [0, 1], where the L-SymBrdn matrix is guaranteed to be symmetric positive-definite. 
## Synopsis
```
#include "petscksp.h" 
PetscErrorCode MatCreateLMVMSymBroyden(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_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
 [](chapter_ksp), `MatCreate()`, `MATLMVM`, `MATLMVMSYMBROYDEN`, `MatCreateLMVMDFP()`, `MatCreateLMVMSR1()`,
`MatCreateLMVMBFGS()`, `MatCreateLMVMBrdn()`, `MatCreateLMVMBadBrdn()`

## Level
intermediate

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


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


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