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"""general tests and simple benchmarks for the sparse module"""
import time
import numpy
from numpy import ones, array, asarray, empty
from numpy.testing import *
from scipy import sparse
from scipy.sparse import csr_matrix, coo_matrix, dia_matrix, lil_matrix, \
dok_matrix
def random_sparse(m,n,nnz_per_row):
rows = numpy.arange(m).repeat(nnz_per_row)
cols = numpy.random.random_integers(low=0,high=n-1,size=nnz_per_row*m)
vals = numpy.random.random_sample(m*nnz_per_row)
return coo_matrix((vals,(rows,cols)),(m,n)).tocsr()
#TODO move this to a matrix gallery and add unittests
def poisson2d(N,dtype='d',format=None):
"""
Return a sparse matrix for the 2d poisson problem
with standard 5-point finite difference stencil on a
square N-by-N grid.
"""
if N == 1:
diags = asarray( [[4]],dtype=dtype)
return dia_matrix((diags,[0]), shape=(1,1)).asformat(format)
offsets = array([0,-N,N,-1,1])
diags = empty((5,N**2),dtype=dtype)
diags[0] = 4 #main diagonal
diags[1:] = -1 #all offdiagonals
diags[3,N-1::N] = 0 #first lower diagonal
diags[4,N::N] = 0 #first upper diagonal
return dia_matrix((diags,offsets),shape=(N**2,N**2)).asformat(format)
class BenchmarkSparse(TestCase):
"""Simple benchmarks for sparse matrix module"""
def bench_arithmetic(self):
matrices = []
#matrices.append( ('A','Identity', sparse.identity(500**2,format='csr')) )
matrices.append( ('A','Poisson5pt', poisson2d(250,format='csr')) )
matrices.append( ('B','Poisson5pt^2', poisson2d(250,format='csr')**2) )
print
print ' Sparse Matrix Arithmetic'
print '===================================================================='
print ' var | name | shape | dtype | nnz '
print '--------------------------------------------------------------------'
fmt = ' %1s | %14s | %20s | %9s | %8d '
for var,name,mat in matrices:
name = name.center(14)
shape = ("%s" % (mat.shape,)).center(20)
dtype = mat.dtype.name.center(9)
print fmt % (var,name,shape,dtype,mat.nnz)
space = ' ' * 10
print
print space+' Timings'
print space+'=========================================='
print space+' format | operation | time (msec) '
print space+'------------------------------------------'
fmt = space+' %3s | %17s | %7.1f '
for format in ['csr']:
vars = dict( [(var,mat.asformat(format)) for (var,name,mat) in matrices ] )
for X,Y in [ ('A','A'),('A','B'),('B','A'),('B','B') ]:
x,y = vars[X],vars[Y]
for op in ['__add__','__sub__','multiply','__div__','__mul__']:
fn = getattr(x,op)
fn(y) #warmup
start = time.clock()
iter = 0
while iter < 3 or time.clock() < start + 0.5:
fn(y)
iter += 1
end = time.clock()
msec_per_it = 1000*(end - start)/float(iter)
operation = (X + '.' + op + '(' + Y + ')').center(17)
print fmt % (format,operation,msec_per_it)
def bench_sort(self):
"""sort CSR column indices"""
matrices = []
matrices.append( ('Rand10', 1e4, 10) )
matrices.append( ('Rand25', 1e4, 25) )
matrices.append( ('Rand50', 1e4, 50) )
matrices.append( ('Rand100', 1e4, 100) )
matrices.append( ('Rand200', 1e4, 200) )
print
print ' Sparse Matrix Index Sorting'
print '====================================================================='
print ' type | name | shape | nnz | time (msec) '
print '---------------------------------------------------------------------'
fmt = ' %3s | %12s | %20s | %8d | %6.2f '
for name,N,K in matrices:
N = int(N)
A = random_sparse(N,N,K)
start = time.clock()
iter = 0
while iter < 5 and time.clock() - start < 1:
A.has_sorted_indices = False
A.indices[:2] = 2,1
A.sort_indices()
iter += 1
end = time.clock()
name = name.center(12)
shape = ("%s" % (A.shape,)).center(20)
print fmt % (A.format,name,shape,A.nnz,1e3*(end-start)/float(iter) )
def bench_matvec(self):
matrices = []
matrices.append(('Identity', sparse.identity(10**4,format='dia')))
matrices.append(('Identity', sparse.identity(10**4,format='csr')))
matrices.append(('Poisson5pt', poisson2d(300,format='lil')))
matrices.append(('Poisson5pt', poisson2d(300,format='dok')))
matrices.append(('Poisson5pt', poisson2d(300,format='dia')))
matrices.append(('Poisson5pt', poisson2d(300,format='coo')))
matrices.append(('Poisson5pt', poisson2d(300,format='csr')))
matrices.append(('Poisson5pt', poisson2d(300,format='csc')))
matrices.append(('Poisson5pt', poisson2d(300,format='bsr')))
A = sparse.kron(poisson2d(150),ones((2,2))).tobsr(blocksize=(2,2))
matrices.append( ('Block2x2', A.tocsr()) )
matrices.append( ('Block2x2', A) )
A = sparse.kron(poisson2d(100),ones((3,3))).tobsr(blocksize=(3,3))
matrices.append( ('Block3x3', A.tocsr()) )
matrices.append( ('Block3x3', A) )
print
print ' Sparse Matrix Vector Product'
print '=================================================================='
print ' type | name | shape | nnz | MFLOPs '
print '------------------------------------------------------------------'
fmt = ' %3s | %12s | %20s | %8d | %6.1f '
for name,A in matrices:
x = ones(A.shape[1],dtype=A.dtype)
y = A*x #warmup
start = time.clock()
iter = 0
while iter < 5 or time.clock() < start + 1:
y = A*x
iter += 1
end = time.clock()
del y
name = name.center(12)
shape = ("%s" % (A.shape,)).center(20)
MFLOPs = (2*A.nnz*iter/(end-start))/float(1e6)
print fmt % (A.format,name,shape,A.nnz,MFLOPs)
def bench_matvecs(self):
matrices = []
matrices.append(('Poisson5pt', poisson2d(300,format='dia')))
matrices.append(('Poisson5pt', poisson2d(300,format='coo')))
matrices.append(('Poisson5pt', poisson2d(300,format='csr')))
matrices.append(('Poisson5pt', poisson2d(300,format='csc')))
matrices.append(('Poisson5pt', poisson2d(300,format='bsr')))
n_vecs = 10
print
print ' Sparse Matrix (Block) Vector Product'
print ' Blocksize = %d' % (n_vecs,)
print '=================================================================='
print ' type | name | shape | nnz | MFLOPs '
print '------------------------------------------------------------------'
fmt = ' %3s | %12s | %20s | %8d | %6.1f '
for name,A in matrices:
x = ones((A.shape[1],10),dtype=A.dtype)
y = A*x #warmup
start = time.clock()
iter = 0
while iter < 5 or time.clock() < start + 1:
y = A*x
iter += 1
end = time.clock()
del y
name = name.center(12)
shape = ("%s" % (A.shape,)).center(20)
MFLOPs = (2*n_vecs*A.nnz*iter/(end-start))/float(1e6)
print fmt % (A.format,name,shape,A.nnz,MFLOPs)
def bench_construction(self):
"""build matrices by inserting single values"""
matrices = []
matrices.append( ('Empty',csr_matrix((10000,10000))) )
matrices.append( ('Identity',sparse.identity(10000)) )
matrices.append( ('Poisson5pt', poisson2d(100)) )
print
print ' Sparse Matrix Construction'
print '===================================================================='
print ' type | name | shape | nnz | time (sec) '
print '--------------------------------------------------------------------'
fmt = ' %3s | %12s | %20s | %8d | %6.4f '
for name,A in matrices:
A = A.tocoo()
for format in ['lil','dok']:
start = time.clock()
iter = 0
while time.clock() < start + 0.5:
T = eval(format + '_matrix')(A.shape)
for i,j,v in zip(A.row,A.col,A.data):
T[i,j] = v
iter += 1
end = time.clock()
del T
name = name.center(12)
shape = ("%s" % (A.shape,)).center(20)
print fmt % (format,name,shape,A.nnz,(end-start)/float(iter))
def bench_conversion(self):
A = poisson2d(100)
formats = ['csr','csc','coo','dia','lil','dok']
print
print ' Sparse Matrix Conversion'
print '===================================================================='
print ' format | tocsr() | tocsc() | tocoo() | todia() | tolil() | todok() '
print '--------------------------------------------------------------------'
for fromfmt in formats:
base = getattr(A,'to' + fromfmt)()
times = []
for tofmt in formats:
try:
fn = getattr(base,'to' + tofmt)
except:
times.append(None)
else:
x = fn() #warmup
start = time.clock()
iter = 0
while time.clock() < start + 0.2:
x = fn()
iter += 1
end = time.clock()
del x
times.append( (end - start)/float(iter))
output = " %3s " % fromfmt
for t in times:
if t is None:
output += '| n/a '
else:
output += '| %5.1fms ' % (1000*t)
print output
#class TestLarge(TestCase):
# def bench_large(self):
# # Create a 100x100 matrix with 100 non-zero elements
# # and play around with it
# #TODO move this out of Common since it doesn't use spmatrix
# random.seed(0)
# A = dok_matrix((100,100))
# for k in range(100):
# i = random.randrange(100)
# j = random.randrange(100)
# A[i,j] = 1.
# csr = A.tocsr()
# csc = A.tocsc()
# csc2 = csr.tocsc()
# coo = A.tocoo()
# csr2 = coo.tocsr()
# assert_array_equal(A.transpose().todense(), csr.transpose().todense())
# assert_array_equal(csc.todense(), csr.todense())
# assert_array_equal(csr.todense(), csr2.todense())
# assert_array_equal(csr2.todense().transpose(), coo.transpose().todense())
# assert_array_equal(csr2.todense(), csc2.todense())
# csr_plus_csc = csr + csc
# csc_plus_csr = csc + csr
# assert_array_equal(csr_plus_csc.todense(), (2*A).todense())
# assert_array_equal(csr_plus_csc.todense(), csc_plus_csr.todense())
if __name__ == "__main__":
run_module_suite()
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