def run():
if not np.SPMD_MODE:
print "[rank %d] Warning - ignored in non-SPMD mode\n"%(np.RANK),
return
try:#This test requires the pyHPC module
import pyHPC
except:
print "[rank %d] Warning - ignored pyHPC not found\n"%(np.RANK),
return
#Non-view test - identical to the one in test_dot.py
niter = 6
for m in range(2,niter+2):
for n in range(2,niter+2):
for k in range(2,niter+2):
Asrc = dnumpytest.random_list([k,m])
Bsrc = dnumpytest.random_list([n,k])
Ad = np.array(Asrc, dtype=float, dist=True)
Af = np.array(Asrc, dtype=float, dist=False)
Bd = np.array(Bsrc, dtype=float, dist=True)
Bf = np.array(Bsrc, dtype=float, dist=False)
Cd = pyHPC.summa(Ad,Bd)
Cf = np.dot(Af,Bf)
if not dnumpytest.array_equal(Cd,Cf):
raise Exception("Uncorrect result matrix\n")
niter *= 2
Asrc = dnumpytest.random_list([niter,niter])
Bsrc = dnumpytest.random_list([niter,niter])
Ad = np.array(Asrc, dtype=float, dist=True)
Af = np.array(Asrc, dtype=float, dist=False)
Bd = np.array(Bsrc, dtype=float, dist=True)
Bf = np.array(Bsrc, dtype=float, dist=False)
Cd = np.zeros((niter,niter),dtype=float, dist=True)
BS = np.BLOCKSIZE
for m in xrange(0,niter-BS, BS):
for n in xrange(0,niter-BS,BS):
for k in xrange(0,niter-BS,BS):
tAd = Ad[m:,k:]
tAf = Af[m:,k:]
tBd = Bd[k:,n:]
tBf = Bf[k:,n:]
tCd = Cd[m:,n:]
tCd = pyHPC.matmul(tAd,tBd)
tCf = np.dot(tAf,tBf)
if not dnumpytest.array_equal(tCd,tCf):
raise Exception("Uncorrect result matrix\n")
for m in xrange(BS,niter+BS, BS):
for n in xrange(BS,niter+BS,BS):
for k in xrange(BS,niter+BS,BS):
tAd = Ad[:m,:k]
tAf = Af[:m,:k]
tBd = Bd[:k,:n]
tBf = Bf[:k,:n]
tCd = Cd[:m,:n]
tCd = pyHPC.matmul(tAd,tBd)
tCf = np.dot(tAf,tBf)
if not dnumpytest.array_equal(tCd,tCf):
raise Exception("Uncorrect result matrix\n")
def run():
if not np.SPMD_MODE:
print "[rank %d] Warning - ignored in non-SPMD mode\n" % (np.RANK),
return
try: #This test requires the pyHPC module
import pyHPC
except:
print "[rank %d] Warning - ignored pyHPC not found\n" % (np.RANK),
return
#Non-view test - identical to the one in test_dot.py
niter = 6
for m in range(2, niter + 2):
for n in range(2, niter + 2):
for k in range(2, niter + 2):
Asrc = dnumpytest.random_list([k, m])
Bsrc = dnumpytest.random_list([n, k])
Ad = np.array(Asrc, dtype=float, dist=True)
Af = np.array(Asrc, dtype=float, dist=False)
Bd = np.array(Bsrc, dtype=float, dist=True)
Bf = np.array(Bsrc, dtype=float, dist=False)
Cd = pyHPC.summa(Ad, Bd)
Cf = np.dot(Af, Bf)
if not dnumpytest.array_equal(Cd, Cf):
raise Exception("Uncorrect result matrix\n")
niter *= 2
Asrc = dnumpytest.random_list([niter, niter])
Bsrc = dnumpytest.random_list([niter, niter])
Ad = np.array(Asrc, dtype=float, dist=True)
Af = np.array(Asrc, dtype=float, dist=False)
Bd = np.array(Bsrc, dtype=float, dist=True)
Bf = np.array(Bsrc, dtype=float, dist=False)
Cd = np.zeros((niter, niter), dtype=float, dist=True)
BS = np.BLOCKSIZE
for m in xrange(0, niter - BS, BS):
for n in xrange(0, niter - BS, BS):
for k in xrange(0, niter - BS, BS):
tAd = Ad[m:, k:]
tAf = Af[m:, k:]
tBd = Bd[k:, n:]
tBf = Bf[k:, n:]
tCd = Cd[m:, n:]
tCd = pyHPC.matmul(tAd, tBd)
tCf = np.dot(tAf, tBf)
if not dnumpytest.array_equal(tCd, tCf):
raise Exception("Uncorrect result matrix\n")
for m in xrange(BS, niter + BS, BS):
for n in xrange(BS, niter + BS, BS):
for k in xrange(BS, niter + BS, BS):
tAd = Ad[:m, :k]
tAf = Af[:m, :k]
tBd = Bd[:k, :n]
tBf = Bf[:k, :n]
tCd = Cd[:m, :n]
tCd = pyHPC.matmul(tAd, tBd)
tCf = np.dot(tAf, tBf)
if not dnumpytest.array_equal(tCd, tCf):
raise Exception("Uncorrect result matrix\n")
def lu(matrix):
"""
Compute LU decompostion of a matrix.
Parameters
----------
a : array, shape (M, M)
Array to decompose
Returns
-------
p : array, shape (M, M)
Permutation matrix
l : array, shape (M, M)
Lower triangular or trapezoidal matrix with unit diagonal.
u : array, shape (M, M)
Upper triangular or trapezoidal matrix
"""
SIZE = matrix.shape[0]
BS = np.BLOCKSIZE
if matrix.shape[0] != matrix.shape[0]:
raise Exception("LU only supports squared matricis")
if not matrix.dist():
raise Exception("The matrix is not distributed")
if (SIZE % np.BLOCKSIZE != 0):
raise Exception("The matrix dimensions must be divisible "\
"with np.BLOCKSIZE(%d)"%np.BLOCKSIZE)
(prow, pcol) = matrix.pgrid()
A = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
A += matrix
L = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
U = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
tmpL = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
tmpU = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
for k in xrange(0, SIZE, BS):
bs = min(BS, SIZE - k) #Current block size
kb = k / BS # k as block index
#Compute vertical multiplier
slice = ((kb, kb + 1), (kb, kb + 1))
for a, l, u in zip(A.blocks(slice), L.blocks(slice), U.blocks(slice)):
(p, tl, tu) = linalg.lu(a)
if not (np.diag(p) == 1).all(): #We do not support pivoting
raise Exception("Pivoting was needed!")
#There seems to be a transpose bug in SciPy's LU
l[:] = tl.T
u[:] = tu.T
#Replicate diagonal block horizontal and vertical
for tk in xrange(k + bs, SIZE, BS):
tbs = min(BS, SIZE - tk) #Current block size
L[tk:tk + tbs, k:k + bs] = U[k:k + tbs, k:k + bs]
U[k:k + bs, tk:tk + tbs] = L[k:k + bs, k:k + tbs]
if k + bs < SIZE:
#Compute horizontal multiplier
slice = ((kb, kb + 1), (kb + 1, SIZE / BS))
for a, u in zip(A.blocks(slice), U.blocks(slice)):
u[:] = np.linalg.solve(u.T, a.T).T
#Compute vertical multiplier
slice = ((kb + 1, SIZE / BS), (kb, kb + 1))
for a, l in zip(A.blocks(slice), L.blocks(slice)):
l[:] = np.linalg.solve(l, a)
#Apply to remaining submatrix
A -= pyHPC.summa(L[:, :k + bs],
U[:k + bs, :],
ao=(k + bs, k),
bo=(k, k + bs),
co=(k + bs, k + bs))
return (L, U)
def lu(matrix):
"""
Compute LU decompostion of a matrix.
Parameters
----------
a : array, shape (M, M)
Array to decompose
Returns
-------
p : array, shape (M, M)
Permutation matrix
l : array, shape (M, M)
Lower triangular or trapezoidal matrix with unit diagonal.
u : array, shape (M, M)
Upper triangular or trapezoidal matrix
"""
SIZE = matrix.shape[0]
BS = np.BLOCKSIZE
if matrix.shape[0] != matrix.shape[0]:
raise Exception("LU only supports squared matricis")
if not matrix.dist():
raise Exception("The matrix is not distributed")
if SIZE % np.BLOCKSIZE != 0:
raise Exception("The matrix dimensions must be divisible " "with np.BLOCKSIZE(%d)" % np.BLOCKSIZE)
(prow, pcol) = matrix.pgrid()
A = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
A += matrix
L = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
U = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
tmpL = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
tmpU = np.zeros((SIZE, SIZE), dtype=matrix.dtype, dist=True)
for k in xrange(0, SIZE, BS):
bs = min(BS, SIZE - k) # Current block size
kb = k / BS # k as block index
# Compute vertical multiplier
slice = ((kb, kb + 1), (kb, kb + 1))
for a, l, u in zip(A.blocks(slice), L.blocks(slice), U.blocks(slice)):
(p, tl, tu) = linalg.lu(a)
if not (np.diag(p) == 1).all(): # We do not support pivoting
raise Exception("Pivoting was needed!")
# There seems to be a transpose bug in SciPy's LU
l[:] = tl.T
u[:] = tu.T
# Replicate diagonal block horizontal and vertical
for tk in xrange(k + bs, SIZE, BS):
tbs = min(BS, SIZE - tk) # Current block size
L[tk : tk + tbs, k : k + bs] = U[k : k + tbs, k : k + bs]
U[k : k + bs, tk : tk + tbs] = L[k : k + bs, k : k + tbs]
if k + bs < SIZE:
# Compute horizontal multiplier
slice = ((kb, kb + 1), (kb + 1, SIZE / BS))
for a, u in zip(A.blocks(slice), U.blocks(slice)):
u[:] = np.linalg.solve(u.T, a.T).T
# Compute vertical multiplier
slice = ((kb + 1, SIZE / BS), (kb, kb + 1))
for a, l in zip(A.blocks(slice), L.blocks(slice)):
l[:] = np.linalg.solve(l, a)
# Apply to remaining submatrix
A -= pyHPC.summa(L[:, : k + bs], U[: k + bs, :], ao=(k + bs, k), bo=(k, k + bs), co=(k + bs, k + bs))
return (L, U)