def solve(A, b, factor, r, regParam):
n = A.shape[0]
L = ctf.cholesky(A + regParam * ctf.eye(n))
factor = ctf.solve_tri(L, b.reshape((n, 1)), True, True, False)
factor = ctf.solve_tri(L, factor, True, True, True).reshape((n, ))
return factor
def run_bench(num_iter, s, k):
wrld = ctf.comm()
M = ctf.random.random((s,s))
X = ctf.random.random((k,s))
[U,S,VT] = ctf.svd(M)
S = np.arange(0,s)+1
M = ctf.dot(U*S,U.T())
te = ctf.timer_epoch("BENCHMARK: SPD SOLVE")
te.begin()
times = []
for i in range(num_iter):
t0 = time.time()
X = ctf.solve_spd(M,X)
times.append(time.time()-t0)
te.end()
if ctf.comm().rank() == 0:
print("ctf.solve_spd average time:",np.sum(times)/num_iter,"sec")
print("ctf.solve_spd iteration timings:",times)
te = ctf.timer_epoch("BENCHMARK: Manual Cholesky+TRSM SPD SOLVE")
te.begin()
times = []
for i in range(num_iter):
t0 = time.time()
L = ctf.cholesky(M)
X = ctf.solve_tri(M,X,from_left=False)
times.append(time.time()-t0)
te.end()
if ctf.comm().rank() == 0:
print("ctf.cholesky+solve_tri average time:",np.sum(times)/num_iter,"sec")
print("ctf.cholesky+solve_tri iteration timings:",times)
def test_solve_tri(self):
n = 4
m = 7
for dt in [numpy.float32, numpy.float64]:
B = ctf.random.random((n,m))
B = ctf.astensor(B,dtype=dt)
L = ctf.random.random((n,n))
L = ctf.astensor(L,dtype=dt)
L = ctf.tril(L)
D = L.T() * L
D.i("ii") << -1.0*L.i("ii")*L.i("ii")
self.assertTrue(abs(ctf.vecnorm(D))<= 1.e-6)
X = ctf.solve_tri(L,B)
self.assertTrue(allclose(B, ctf.dot(L,X)))
U = ctf.random.random((n,n))
U = ctf.astensor(U,dtype=dt)
U = ctf.triu(U)
D = U.T() * U
D.i("ii") << -1.0*U.i("ii")*U.i("ii")
self.assertTrue(abs(ctf.vecnorm(D))<= 1.e-6)
X = ctf.solve_tri(U,B,False)
self.assertTrue(allclose(B, ctf.dot(U,X)))
U = ctf.random.random((m,m))
U = ctf.astensor(U,dtype=dt)
U = ctf.triu(U)
D = U.T() * U
D.i("ii") << -1.0*U.i("ii")*U.i("ii")
self.assertTrue(abs(ctf.vecnorm(D))<= 1.e-6)
X = ctf.solve_tri(U,B,False,False)
self.assertTrue(allclose(B, ctf.dot(X,U)))
U = ctf.random.random((m,m))
U = ctf.astensor(U,dtype=dt)
U = ctf.triu(U)
D = U.T() * U
D.i("ii") << -1.0*U.i("ii")*U.i("ii")
self.assertTrue(abs(ctf.vecnorm(D))<= 1.e-6)
X = ctf.solve_tri(U,B,False,False,True)
self.assertTrue(allclose(B, ctf.dot(X,U.T())))
def solve_tri(A, B, lower=True, from_left=False, transp_L=False):
return ctf.solve_tri(A, B, lower, from_left, transp_L)