# TSComputeIJacobianDefaultColor
Computes the Jacobian using finite differences and coloring to exploit matrix sparsity. 
## Synopsis
```
#include "petscts.h"  
PetscErrorCode TSComputeIJacobianDefaultColor(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal shift, Mat J, Mat B, void *ctx)
```
Collective on ts


## Input Parameters

- ***ts -*** the `TS` context
- ***t -*** current timestep
- ***U -*** state vector
- ***Udot -*** time derivative of state vector
- ***shift -*** shift to apply, see note below
- ***ctx -*** an optional user context



## Output Parameters

- ***J -*** Jacobian matrix (not altered in this routine)
- ***B -*** newly computed Jacobian matrix to use with preconditioner (generally the same as J)





## Notes
If F(t,U,Udot)=0 is the DAE, the required Jacobian is

dF/dU + shift*dF/dUdot

Most users should not need to explicitly call this routine, as it
is used internally within the nonlinear solvers.

This will first try to get the coloring from the `DM`.  If the `DM` type has no coloring
routine, then it will try to get the coloring from the matrix.  This requires that the
matrix have nonzero entries precomputed.


## See Also
 [](chapter_ts), `TS`, `TSSetIJacobian()`, `MatFDColoringCreate()`, `MatFDColoringSetFunction()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/interface/ts.c.html#TSComputeIJacobianDefaultColor">src/ts/interface/ts.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/ts/interface/ts.c)


[Index of all TS routines](index.md)  
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[Index of all manual pages](/docs/manualpages/singleindex.md)  
