def contribution(self, v):
if self.dxdt is None:
if len(v.shape) == 0:
return pascal.dot(v, v*0)
else:
return pascal.dot(v, v[0]*0)
else:
return pascal.dot(v, self.dxdt) / pascal.dot(self.dxdt, self.dxdt)
def checkpoint(self, V, v):
#Q, R = pascal.qr(V.T)
#b = pascal.dot(Q.T, v)
#V[:] = Q.T
#v -= pascal.dot(Q, b)
Q, R = pascal.qr_transpose(V)
b = pascal.dot(Q, v)
#V[:] = Q
#v -= pascal.dot(b, Q)
V = Q
v = v - pascal.dot(b, Q)
self.Rs.append(R)
self.bs.append(b)
return V, v
def checkpoint(self, V, v):
#Q, R = pascal.qr(V.T)
#b = pascal.dot(Q.T, v)
#V[:] = Q.T
#v -= pascal.dot(Q, b)
Q, R = pascal.qr_transpose(V)
b = pascal.dot(Q, v)
#V[:] = Q
#v -= pascal.dot(b, Q)
V = Q
v = v - pascal.dot(b, Q)
self.Rs.append(R)
self.bs.append(b)
return V, v
def test_linalg():
for mod in list(sys.modules.keys()):
if mod.startswith('pascal_lite'):
del sys.modules[mod]
import pascal_lite as pascal
subspace_dimension = 4
V = pascal.symbolic_array(subspace_dimension)
v = pascal.symbolic_array()
v1 = pascal.dot(V, v)
assert not v1.is_distributed
v2 = pascal.outer(v1, v)
assert v2.is_distributed
v3 = pascal.qr_transpose(V)[0]
assert v3.is_distributed
g = pascal.ComputationalGraph([v1.value, v2.value, v3.value])
n = 16
A = np.random.rand(subspace_dimension, n)
b = np.random.rand(n)
def actual_inputs(x):
if x is V.value:
return A
elif x is v.value:
return b
o1, o2, o3 = g(actual_inputs)
assert np.allclose(o1, np.dot(A, b))
assert np.allclose(o2, np.outer(np.dot(A, b), b))
assert np.allclose(o3, np.linalg.qr(A.T)[0].T)
def project(self, v):
if self.dxdt_normalized is None:
return v
else:
dv = pascal.outer(pascal.dot(v, self.dxdt_normalized), self.dxdt_normalized)
return v - dv.reshape(v.shape)