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PETSc and Neuronal Networks Toby Isaac VIGRE Seminar, Wednesday, November 15, 2006.

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Presentation on theme: "PETSc and Neuronal Networks Toby Isaac VIGRE Seminar, Wednesday, November 15, 2006."— Presentation transcript:

1 PETSc and Neuronal Networks Toby Isaac VIGRE Seminar, Wednesday, November 15, 2006

2 Tips for general ODEs

3 Recall: have an input program to convert to PETSc binary format

4 Tips for general ODEs Recall: have an input program to convert to PETSc binary format e.g.: Vec for initial values, Mat for linear ODE, adjacency/connectivity Mat

5 Tips for general ODEs Recall: have an input program to convert to PETSc binary format e.g.: Vec for initial values, Mat for linear ODE, adjacency/connectivity Mat PetscBinaryView for arrays of scalars (see exampleinput.c)

6 Tips for general ODEs To keep scalar parameters organized (end time, dt, # cells, etc.) use a PetscBag:

7 Tips for general ODEs To keep scalar parameters organized (end time, dt, # cells, etc.) use a PetscBag: Allows you to save a struct in binary and read in to all processors

8 Tips for general ODEs To keep scalar parameters organized (end time, dt, # cells, etc.) use a PetscBag: Allows you to save a struct in binary and read in to all processors No need to keep track of order in which scalars are written/read

9 Tips for general ODEs Recall: using “Load” functions, parallel layout is specified at read in…

10 Tips for general ODEs Recall: using “Load” functions, parallel layout is specified at read in… Except for arrays: only go to first processor

11 Tips for general ODEs Recall: using “Load” functions, parallel layout is specified at read in… Except for arrays: only go to first processor Use MPI_Bcast to send those arrays to all processors

12 Tips for general ODEs Recall: using “Load” functions, parallel layout is specified at read in… Except for arrays: only go to first processor Use MPI_Bcast to send those arrays to all processors e.g.: piecewise constant inj. current

13 Tips for general ODEs A TS object keeps track of the settings for time-stepping

14 Tips for general ODEs A TS object keeps track of the settings for time-stepping Same old song: TSCreate and TSDestroy

15 Tips for general ODEs A TS object keeps track of the settings for time-stepping Same old song: TSCreate and TSDestroy TSSetType: forward Euler, backward Euler, “ode45”, (pseudo-timestepping)

16 Tips for general ODEs A TS object keeps track of the settings for time-stepping Same old song: TSCreate and TSDestroy TSSetType: forward Euler, backward Euler, “ode45”, (pseudo-timestepping) TSSetProblemType: linear, nonlinear

17 Tips for general ODEs TSSetSolution: set initial conditions

18 Tips for general ODEs TSSetSolution: set initial conditions TSSetRHSFunction/TSSetRHSMatrix:

19 Tips for general ODEs TSSetSolution: set initial conditions TSSetRHSFunction/TSSetRHSMatrix: Specified functions has format rhsfunc(ts, t, u, du, void *additional arguments)

20 Tips for general ODEs TSSetSolution: set initial conditions TSSetRHSFunction/TSSetRHSMatrix: Specified functions has format rhsfunc(ts, t, u, du, void *additional arguments) Create a struct for passing additional arguments

21 Tips for general ODEs TSSetRHSJacobian, if method calls for it

22 Tips for general ODEs TSSetRHSJacobian, if method calls for it TSSetInitialTimeStep (that is, initial time and initial time step)

23 Tips for general ODEs TSSetRHSJacobian, if method calls for it TSSetInitialTimeStep (that is, initial time and initial time step) TSSetDuration

24 Tips for general ODEs TSSetRHSJacobian, if method calls for it TSSetInitialTimeStep (that is, initial time and initial time step) TSSetDuration TSRKSetTolerance:

25 Tips for general ODEs TSSetRHSJacobian, if method calls for it TSSetInitialTimeStep (that is, initial time and initial time step) TSSetDuration TSRKSetTolerance: Control absolute error over whole time of integration: a bit sketchy

26 Tips for general ODEs If only interested in final state, run TSStep to execute

27 Tips for general ODEs If only interested in final state, run TSStep to execute If interested in progress along the way, you need a monitor function:

28 Tips for general ODEs If only interested in final state, run TSStep to execute If interested in progress along the way, you need a monitor function: Runs after every time step, can output, plot, change parameters, change time- step etc.

29 Tips for general ODEs Multiple monitor functions can run: e.g. one for parameter changes, one for output

30 Tips for general ODEs Multiple monitor functions can run: e.g. one for parameter changes, one for output Attention IAF modelers: you can change the state vector too!

31 Tips for general ODEs Multiple monitor functions can run: e.g. one for parameter changes, one for output Attention IAF modelers: you can change the state vector too! Syntax: TSSetMonitor, monitor(ts, iter#, t, u, void *args)

32 Tips for Homogeneous Nets

33 Most dependency occurs within cell: bad to have one cell divided across processors

34 Tips for Homogeneous Nets Most dependency occurs within cell: bad to have one cell divided across processors No guarantee that PETSC_DECIDE won’t split your vector this way

35 Tips for Homogeneous Nets Have a vector y of length = # cells

36 Tips for Homogeneous Nets Have a vector y of length = # cells PETSc evenly distributes this vector

37 Tips for Homogeneous Nets Have a vector y of length = # cells PETSc evenly distributes this vector nlocal = VecGetLocalSize(y)

38 Tips for Homogeneous Nets Have a vector y of length = # cells PETSc evenly distributes this vector nlocal = VecGetLocalSize(y) VecCreateMPI(…, neqns*nlocalcells, PETSC_DETERMINE,&x);

39 Tips for Homogeneous Nets VecSetBlockSize: set this to the number of equations per cell

40 Tips for Homogeneous Nets VecSetBlockSize: set this to the number of equations per cell VecStrideGather: send value from same index for each block to another vector

41 Tips for Homogeneous Nets VecSetBlockSize: set this to the number of equations per cell VecStrideGather: send value from same index for each block to another vector VecStrideScatter: send values from a vector to the same index for each block

42 Tips for Homogeneous Nets Paradigm for ease/simplicity: gather like indices, make changes, scatter back

43 Tips for Homogeneous Nets Paradigm for ease/simplicity: gather like indices, make changes, scatter back VecStrideGatherAll/VecStrideScatterAll: take the state vector, break it up into an array of vectors, one for each equivalent index

44 Tips for Homogeneous Nets In RHSFunction: Vec U and Vec DU are inputs

45 Tips for Homogeneous Nets In RHSFunction: Vec U and Vec DU are inputs Declare arrays Vec u[neqns], du[neqns]

46 Tips for Homogeneous Nets In RHSFunction: Vec U and Vec DU are inputs Declare arrays Vec u[neqns], du[neqns] VecStrideGatherAll at the start

47 Tips for Homogeneous Nets In RHSFunction: Vec U and Vec DU are inputs Declare arrays Vec u[neqns], du[neqns] VecStrideGatherAll at the start Set du[i] in terms of u[] for each i

48 Tips for Homogeneous Nets In RHSFunction: Vec U and Vec DU are inputs Declare arrays Vec u[neqns], du[neqns] VecStrideGatherAll at the start Set du[i] in terms of u[] for each I VecStrideScatterAll at the end

49 Tips for Homogeneous Nets For very large networks, large number of processors: message passing will take its toll

50 Tips for Homogeneous Nets For very large networks, large number of processors: message passing will take its toll Order cells so that connections occur between close numbers

51 Tips for Homogeneous Nets For very large networks, large number of processors: message passing will take its toll Order cells so that connections occur between close numbers MatGetOrdering, MATORDERING_RCM, MatPermute

52 Tips for Inhomogeneous Nets

53 VecSetBlockSize no longer an option

54 Tips for Inhomogeneous Nets VecSetBlockSize no longer an option Can be reproduced with more generic VecGather/VecScatter

55 Tips for Inhomogeneous Nets VecSetBlockSize no longer an option Can be reproduced with more generic VecGather/VecScatter Requires the creation of arrays of VecScatter objects: one for each state

56 Tips for Inhomogeneous Nets VecSetBlockSize no longer an option Can be reproduced with more generic VecGather/VecScatter Requires the creation of arrays of VecScatter objects: one for each state VecScatter created from two IS index objects: TO Vec and FROM Vec

57 Tips for Inhomogeneous Nets Different types: gathered on separate processors or mixed?

58 Tips for Inhomogeneous Nets Different types: gathered on separate processors or mixed? Gathered is easiest to implement: specify which processor, treat like the homogeneous case

59 Tips for Inhomogeneous Nets Different types: gathered on separate processors or mixed? Gathered is easiest to implement: specify which processor, treat like the homogeneous case Mixed is faster: balance processor load, potentially less message passing

60 Tips for Inhomogeneous Nets If there are ODEs for each connection, then the need for mixed distribution is greater

61 Tips for Inhomogeneous Nets If there are ODEs for each connection, then the need for mixed distribution is greater Ideally (if disparity in # eqns isn’t great):

62 Tips for Inhomogeneous Nets If there are ODEs for each connection, then the need for mixed distribution is greater Ideally (if disparity in # eqns isn’t great): Lump all cells together, RCM permute, equal # cells per processor

63 Tips for Adaptive Time Step

64 PETSc RK45 < ode45

65 Tips for Adaptive Time Step PETSc RK45 < ode45 Will not integrate across discontinuities

66 Tips for Adaptive Time Step PETSc RK45 < ode45 Will not integrate across discontinuities For discontinuities you know of (e.g. time dependent forcing function):

67 Tips for Adaptive Time Step PETSc RK45 < ode45 Will not integrate across discontinuities For discontinuities you know of (e.g. time dependent forcing function): Loop: TSSetDuration to discontinuity, TSStep

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