[petsc-users] petsc4py sparse matrix construction time

Matthew Knepley knepley at gmail.com
Wed Nov 1 03:34:38 CDT 2017

```On Tue, Oct 31, 2017 at 10:00 PM, Cetinbas, Cankur Firat <ccetinbas at anl.gov>
wrote:

> Hi,
>
> Thanks a lot. Based on both of your suggestions I modified the code using
> Mat.createAIJ() and csr option. The computation time decreased
> significantly after using this method. Still if there is a better option
> please let me know after seeing the modified code below.
>
> At first trial with 1000x1000 matrix with 96019 non-zeros in the matrix,
> the computation time did not scale with the number of cores : Single core
> python @ 0.0035s, single core petsc @ 0.0024s, 2 cores petsc @ 0.0036s, 4
> cores petsc @ 0.0032, 8 cores petsc @ 0.0030s.
>
> Then I tried with larger matrix 181797x181797 with more non-zeros and I
> got the following results: Single core python @ 0.021, single core petsc @
> 0.031, 2 cores petsc @ 0.024s, 4 cores petsc @ 0.014, 8 cores petsc @
> 0.009s, 16 cores petsc @ 0.0087s.
>
> I think the optimum number of nodes is highly dependent on matrix size and
> the number of non-zeros. In the real code matrix size (and so the number of
> non-zero elements) will grow at every iteration starting with very small
> matrices growing to very big ones. Is it possible to set the number process
> from the code dynamically?
>

I am not sure how you are interpreting these measurements. Normally, I
would say

1) Everything timed below is "parallel overhead". This is not intended to
scale with P, instead it will look like a constant, as you observe

2) The time to compute the matrix entires should far outstrip the time
below to figure the nonzero structure. Is this true?

3) Solve time is often larger than matrix calculation. Is it?

Thus, we deciding on parallelism, you need to look at the largest costs,
and how they scale with P.

Thanks,

Matt

Another question is about the data types; mpi4py only let me transfer float
> type data, and petsc4py only lets me use int32 type indices. Besides keep
> converting the data, is there any solution for this?
>
> The modified code for matrix creation part:
>
> comm = MPI.COMM_WORLD
> rank = comm.Get_rank()
> size = comm.Get_size()
>
> if rank==0:
>     m = 1000    # 1000  x 1000 matrix
>     if size>1:
>         rbc = np.bincount(row)*1.0
>         ieq = int(np.floor(m/size))
>         a = [ieq]*size
>         ix = int(np.mod(m,size))
>         if ix>0:
>             for i in range(0,ix):
>                 a[i]= a[i]+1
>         a = np.array([0]+a).cumsum()
>         b = np.zeros(a.shape[0]-1)
>         for i in range(0,a.shape[0]-1):
>             b[i]=rbc[a[i]:a[i+1]].sum()      # b is the send counts for
> Scatterv
>         row = row.astype(dtype=float)
>         col = col.astype(dtype=float)
>         val = val.astype(dtype=float)
> else:
>     row=None
>     col=None
>     val=None
>     indpt=None
>     b=None
>     m=None
>
> if size>1:
>     ml = comm.bcast(m,root=0)
>     bl = comm.bcast(b,root=0)
>     row_lcl = np.zeros(bl[rank])
>     col_lcl = row_lcl.copy()
>     val_lcl = row_lcl.copy()
>
>     comm.Scatterv([row,b],row_lcl)
>     comm.Scatterv([col,b],col_lcl)
>     comm.Scatterv([val,b],val_lcl)
>     comm.Barrier()
>
>     row_lcl = row_lcl.astype(dtype='int32')
>     col_lcl = col_lcl.astype(dtype='int32')
>     val_lcl = val_lcl.astype(dtype='int32')
>
>     indptr = np.bincount(row_lcl)
>     indptr = indptr[indptr>0]
>     indptr = np.insert(indptr,0,0).cumsum()
>     indptr = indptr.astype(dtype='int32')
>     comm.Barrier()
>
>     pA = PETSc.Mat().createAIJ(size=(ml,ml),csr=(indptr, col_lcl,
> val_lcl))     # Matrix generation
>
> else:
>     indptr = np.bincount(row)
>     indptr = np.insert(indptr,0,0).cumsum()
>     indptr = indptr.astype(dtype='int32')
>     st=time.time()
>     pA = PETSc.Mat().createAIJ(size=(m,m),csr=(indptr, col, val))
>     print('dt:',time.time()-st)
>
>
> Regards,
>
> Firat
>
>
> -----Original Message-----
> From: Smith, Barry F.
> Sent: Tuesday, October 31, 2017 10:18 AM
> To: Matthew Knepley
> Cc: Cetinbas, Cankur Firat; petsc-users at mcs.anl.gov; Ahluwalia, Rajesh K.
> Subject: Re: [petsc-users] petsc4py sparse matrix construction time
>
>
>    You also need to make sure that most matrix entries are generated on
> the process that they will belong on.
>
>   Barry
>
> > On Oct 30, 2017, at 8:01 PM, Matthew Knepley <knepley at gmail.com> wrote:
> >
> > On Mon, Oct 30, 2017 at 8:06 PM, Cetinbas, Cankur Firat <
> ccetinbas at anl.gov> wrote:
> > Hello,
> >
> >
> >
> > I am a beginner both in PETSc and mpi4py. I have been working on
> parallelizing our water transport code (where we solve linear system of
> equations) and I started with the toy code below.
> >
> >
> >
> > The toy code reads right hand size (rh), row, column, value vectors to
> construct sparse coefficient matrix and then scatters them to construct
> parallel PETSc coefficient matrix and right hand side vector.
> >
> >
> >
> > The sparse matrix generation time is extremely high in comparison to
> sps.csr_matrix((val, (row, col)), shape=(n,n)) in python. For instance
> python generates 181197x181197 sparse matrix in 0.06 seconds and this code
> with 32 cores:1.19s, 16 cores:6.98s and 8 cores:29.5 s.  I was wondering if
> I am making a mistake in generating sparse matrix? Is there a more
> efficient way?
> >
> >
> > It looks like you do not preallocate the matrix. There is a chapter on
> this in the manual.
> >
> >    Matt
> >
> >
> >
> >
> > Regards,
> >
> >
> >
> > Firat
> >
> >
> >
> > from petsc4py import PETSc
> >
> > from mpi4py import MPI
> >
> > import numpy as np
> >
> > import time
> >
> >
> >
> > comm = MPI.COMM_WORLD
> >
> > rank = comm.Get_rank()
> >
> > size = comm.Get_size()
> >
> >
> >
> > if rank==0:
> >
> >     # proc 0 loads tomo image and does fast calculations to append row,
> col, val, rh lists
> >
> >     # in the real code this vectors will be available on proc 0 no txt
> >
> >     row = np.loadtxt('row.out')  # indices of non-zero rows
> >
> >     col = np.loadtxt('col.out') # indices of non-zero columns
> >
> >     val = np.loadtxt('vs.out')  # values in the sparse matrix
> >
> >     rh = np.loadtxt('RHS.out') # right hand side vector
> >
> >     n = row.shape[0]  #1045699
> >
> >     m = rh.shape[0] #181197 square sparse matrix size
> >
> > else:
> >
> >     n = None
> >
> >     m = None
> >
> >     row = None
> >
> >     col = None
> >
> >     val = None
> >
> >     rh = None
> >
> >     rh_ind = None
> >
> >
> >
> > m_lcl = comm.bcast(m,root=0)
> >
> > n_lcl = comm.bcast(n,root=0)
> >
> > neq = n_lcl//size
> >
> > meq = m_lcl//size
> >
> > nx = np.mod(n_lcl,size)
> >
> > mx = np.mod(m_lcl,size)
> >
> > row_lcl = np.zeros(neq)
> >
> > col_lcl = np.zeros(neq)
> >
> > val_lcl = np.zeros(neq)
> >
> > rh_lcl = np.zeros(meq)
> >
> > a = [neq]*size #send counts for Scatterv
> >
> > am = [meq]*size #send counts for Scatterv
> >
> >
> >
> > if nx>0:
> >
> >     for i in range(0,nx):
> >
> >         if rank==i:
> >
> >             row_lcl = np.zeros(neq+1)
> >
> >             col_lcl = np.zeros(neq+1)
> >
> >             val_lcl = np.zeros(neq+1)
> >
> >         a[i] = a[i]+1
> >
> > if mx>0:
> >
> >     for ii in range(0,mx):
> >
> >         if rank==ii:
> >
> >             rh_lcl = np.zeros(meq+1)
> >
> >         am[ii] = am[ii]+1
> >
> >
> >
> > comm.Scatterv([row,a],row_lcl)
> >
> > comm.Scatterv([col,a],col_lcl)
> >
> > comm.Scatterv([val,a],val_lcl)
> >
> > comm.Scatterv([rh,am],rh_lcl)
> >
> > comm.Barrier()
> >
> >
> >
> > A = PETSc.Mat()
> >
> > A.create()
> >
> > A.setSizes([m_lcl,m_lcl])
> >
> > A.setType('aij')
> >
> > A.setUp()
> >
> > lr = row_lcl.shape[0]
> >
> > for i in range(0,lr):
> >
> >     A[row_lcl[i],col_lcl[i]] = val_lcl[i]
> >
> > A.assemblyBegin()
> >
> > A.assemblyEnd()
> >
> >
> >
> > if size>1: # to get the range for scattered vectors
> >
> >     ami = [0]
> >
> >     ami = np.array([0]+am).cumsum()
> >
> >     for kk in range(0,size):
> >
> >         if rank==kk:
> >
> >             Is = ami[kk]
> >
> >             Ie = ami[kk+1]
> >
> > else:
> >
> >     Is=0; Ie=m_lcl
> >
> >
> >
> > b= PETSc.Vec()
> >
> > b.create()
> >
> > b.setSizes(m_lcl)
> >
> > b.setFromOptions()
> >
> > b.setUp()
> >
> > b.setValues(list(range(Is,Ie)),rh_lcl)
> >
> > b.assemblyBegin()
> >
> > b.assemblyEnd()
> >
> >
> >
> > # solution vector
> >
> > x = b.duplicate()
> >
> > x.assemblyBegin()
> >
> > x.assemblyEnd()
> >
> >
> >
> > # create linear solver
> >
> > ksp = PETSc.KSP()
> >
> > ksp.create()
> >
> > ksp.setOperators(A)
> >
> > ksp.setType('cg')
> >
> > #ksp.getPC().setType('icc') # only sequential
> >
> > ksp.getPC().setType('jacobi')
> >
> > print('solving with:', ksp.getType())
> >
> >
> >
> > #solve
> >
> > st=time.time()
> >
> > ksp.solve(b,x)
> >
> > et=time.time()
> >
> > print(et-st)
> >
> >
> >
> > if size>1:
> >
> >     #gather
> >
> >     if rank==0:
> >
> >         xGthr = np.zeros(m)
> >
> >     else:
> >
> >         xGthr = None
> >
> >     comm.Gatherv(x,[xGthr,am])
> >
> >
> >
> >
> > --
> > What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> > -- Norbert Wiener
> >
> > https://www.cse.buffalo.edu/~knepley/
>
>

--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their