:orphan:
# TSSetIJacobian
Set the function to compute the matrix dF/dU + a*dF/dU_t where F(t,U,U_t) is the function provided with `TSSetIFunction()`. 
## Synopsis
```
#include "petscts.h"  
PetscErrorCode TSSetIJacobian(TS ts, Mat Amat, Mat Pmat, TSIJacobian f, void *ctx)
```
Logically Collective


## Input Parameters

- ***ts  -*** the `TS` context obtained from `TSCreate()`
- ***Amat -*** (approximate) matrix to store Jacobian entries computed by `f`
- ***Pmat -*** matrix used to compute preconditioner (usually the same as `Amat`)
- ***f   -*** the Jacobian evaluation routine
- ***ctx -*** user-defined context for private data for the Jacobian evaluation routine (may be `NULL`)



## Calling sequence of `f`
```none
PetscErrorCode f(TS ts, PetscReal t, Vec U, Vec U_t, PetscReal a, Mat Amat, Mat Pmat, void *ctx)
```

- ***ts  -*** the `TS` context obtained from `TSCreate()`
- ***t    -*** time at step/stage being solved
- ***U    -*** state vector
- ***U_t  -*** time derivative of state vector
- ***a    -*** shift
- ***Amat -*** (approximate) Jacobian of F(t,U,W+a*U), equivalent to dF/dU + a*dF/dU_t
- ***Pmat -*** matrix used for constructing preconditioner, usually the same as `Amat`
- ***ctx  -*** [optional] user-defined context for matrix evaluation routine





## Notes
The matrices `Amat` and `Pmat` are exactly the matrices that are used by `SNES` for the nonlinear solve.

If you know the operator Amat has a null space you can use `MatSetNullSpace()` and `MatSetTransposeNullSpace()` to supply the null
space to `Amat` and the `KSP` solvers will automatically use that null space as needed during the solution process.

The matrix dF/dU + a*dF/dU_t you provide turns out to be
the Jacobian of F(t,U,W+a*U) where F(t,U,U_t) = 0 is the DAE to be solved.
The time integrator internally approximates U_t by W+a*U where the positive "shift"
a and vector W depend on the integration method, step size, and past states. For example with
the backward Euler method a = 1/dt and W = -a*U(previous timestep) so
W + a*U = a*(U - U(previous timestep)) = (U - U(previous timestep))/dt

You must set all the diagonal entries of the matrices, if they are zero you must still set them with a zero value

The TS solver may modify the nonzero structure and the entries of the matrices `Amat` and `Pmat` between the calls to `f`
You should not assume the values are the same in the next call to `f` as you set them in the previous call.


## See Also
 [](ch_ts), `TS`, `TSSetIFunction()`, `TSSetRHSJacobian()`, `SNESComputeJacobianDefaultColor()`, `SNESComputeJacobianDefault()`, `TSSetRHSFunction()`

## Level
beginner

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

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex10.c.html">src/ts/tutorials/ex10.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex14.c.html">src/ts/tutorials/ex14.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex15.c.html">src/ts/tutorials/ex15.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex16.c.html">src/ts/tutorials/ex16.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex17.c.html">src/ts/tutorials/ex17.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex19.c.html">src/ts/tutorials/ex19.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20.c.html">src/ts/tutorials/ex20.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20adj.c.html">src/ts/tutorials/ex20adj.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20fwd.c.html">src/ts/tutorials/ex20fwd.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20opt_ic.c.html">src/ts/tutorials/ex20opt_ic.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20opt_p.c.html">src/ts/tutorials/ex20opt_p.c</A><BR>


---
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[Index of all TS routines](index.md)  
[Table of Contents for all manual pages](/manualpages/index.md)  
[Index of all manual pages](/manualpages/singleindex.md)