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

PETSc and Neuronal Networks

Toby IsaacVIGRE Seminar, Wednesday,

November 15, 2006

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)

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

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

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

TSSetSolution: set initial conditions

TSSetSolution: set initial conditions TSSetRHSFunction/

TSSetRHSMatrix:

TSSetSolution: set initial conditions TSSetRHSFunction/

TSSetRHSMatrix: Specified functions has format

rhsfunc(ts, t, u, du, void *additional arguments)

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

TSSetRHSJacobian, if method calls for it

TSSetInitialTimeStep (that is, initial time and initial time step)

TSSetDuration

TSSetDuration TSRKSetTolerance:

TSSetDuration TSRKSetTolerance: Control absolute error over whole

time of integration: a bit sketchy

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.

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)

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

Have a vector y of length = # cells

Have a vector y of length = # cells PETSc evenly distributes this

vector

vector nlocal = VecGetLocalSize(y)

vector nlocal = VecGetLocalSize(y) VecCreateMPI(…,

neqns*nlocalcells, PETSC_DETERMINE,&x);

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

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

In RHSFunction: Vec U and Vec DU are inputs

Declare arrays Vec u[neqns], du[neqns]

VecStrideGatherAll at the start

VecStrideGatherAll at the start Set du[i] in terms of u[] for each i

VecStrideGatherAll at the start Set du[i] in terms of u[] for each I VecStrideScatterAll at the end

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

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

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

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

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

Tips for Adaptive Time Step

PETSc RK45 < ode45

PETSc RK45 < ode45 Will not integrate across

discontinuities

discontinuities For discontinuities you know of

(e.g. time dependent forcing function):

discontinuities For discontinuities you know of (e.g.

time dependent forcing function): Loop: TSSetDuration to

discontinuity, TSStep

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

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

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