def test_eigh(self):
n = 11
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((n, n))
A += A.conj().T()
[D, X] = ctf.eigh(A)
self.assertTrue(allclose(ctf.dot(A, X), X * D))
self.assertTrue(allclose(ctf.eye(n), ctf.dot(X.conj().T(), X)))
def test_dot_1d(self):
a1 = numpy.ones(4)
self.assertTrue(
allclose(ctf.dot(ctf.astensor(a1), a1), numpy.dot(a1, a1)))
self.assertTrue(
allclose(ctf.dot(a1 + 1j, ctf.astensor(a1)),
numpy.dot(a1 + 1j, a1)))
a2 = ctf.astensor(a1).dot(a1 + 0j)
self.assertTrue(a2.dtype == numpy.complex128)
def test_tree_ctr(self):
X = []
for i in range(10):
X.append(ctf.random.random((8, 8)))
scl = ctf.einsum("ab,ac,ad,ae,af,bg,cg,dg,eg,fg",X[0],X[1],X[2],X[3],X[4],X[5],X[6],X[7],X[8],X[9])
C = ctf.dot(X[0],X[5])
for i in range(1,5):
C = C * ctf.dot(X[i],X[5+i])
scl2 = ctf.vecnorm(C,1)
self.assertTrue(numpy.abs(scl-scl2)<1.e-4)
def test_solve(self):
n = 11
for k in [1, 4, 12, 15, 31]:
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((n, n), dtype=dt)
A = ctf.dot(A.T(), A)
C = ctf.random.random((k, n), dtype=dt)
Y = ctf.solve_spd(A, C)
#print(C,Y)
#print(n,k)
self.assertTrue(allclose(ctf.dot(Y, A), C))
def test_cholesky(self):
n = 4
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((n,n))
A = ctf.astensor(A,dtype=dt)
A = ctf.dot(A.T(), A)
L = ctf.cholesky(A)
D = L.T() * L
D.i("ii") << -1.0*L.i("ii")*L.i("ii")
self.assertTrue(abs(ctf.vecnorm(D))<= 1.e-6)
self.assertTrue(allclose(A, ctf.dot(L,L.T())))
def test_svd(self):
m = 9
n = 5
k = 5
for dt in [numpy.float32, numpy.float64, numpy.complex64, numpy.complex128]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[U,S,VT]=ctf.svd(A,k)
[U1,S1,VT1]=la.svd(ctf.to_nparray(A),full_matrices=False)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U.T(), U)))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT, VT.T())))
def test_batch_svd(self):
m = 9
n = 5
q = 7
k = 5
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((q, m, n))
A = ctf.astensor(A, dtype=dt)
[U, S, VT] = ctf.svd_batch(A, k)
for i in range(q):
self.assertTrue(
allclose(A[i], ctf.dot(U[i],
ctf.dot(ctf.diag(S[i]), VT[i]))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U[i].T(), U[i])))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT[i],
VT[i].T())))
m = 7
n = 8
q = 2
k = 3
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((q, m, n))
A = ctf.astensor(A, dtype=dt)
[U, S, VT] = ctf.svd_batch(A, k)
for i in range(q):
[nU, nS, nVT] = np.linalg.svd(A[i].to_nparray())
self.assertTrue(
allclose(
np.dot(nU[:, :k], np.dot(np.diag(nS[:k]), nVT[:k, :])),
ctf.dot(U[i], ctf.dot(ctf.diag(S[i]), VT[i]))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U[i].T(), U[i])))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT[i],
VT[i].T())))
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_svd_rand(self):
m = 19
n = 15
k = 13
for dt in [numpy.float32, numpy.float64, numpy.complex64, numpy.complex128]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[U,S,VT]=ctf.svd_rand(A,k,5,1)
self.assertTrue(allclose(ctf.eye(k),ctf.dot(U.T(),U)))
self.assertTrue(allclose(ctf.eye(k),ctf.dot(VT,VT.T())))
[U2,S2,VT2]=ctf.svd(A,k)
rs1 = ctf.vecnorm(A - ctf.dot(U*S,VT))
rs2 = ctf.vecnorm(A - ctf.dot(U2*S2,VT2))
rA = ctf.vecnorm(A)
self.assertTrue(rs1 < rA)
self.assertTrue(rs2 < rs1)
self.assertTrue(numpy.abs(rs1 - rs2)<3.e-1)
def test_qr(self):
for (m, n) in [(8, 4), (4, 7), (3, 3)]:
for dt in [np.float32, np.float64, np.complex64, np.complex128]:
A = ctf.random.random((m, n))
A = ctf.astensor(A, dtype=dt)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
else:
self.assertTrue(allclose(ctf.eye(m), ctf.dot(Q, Q.T())))
A = ctf.tensor((m, n), dtype=np.complex64)
rA = ctf.tensor((m, n), dtype=np.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=np.float32)
iA.fill_random()
A.imag(iA)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(
allclose(ctf.eye(n, dtype=np.complex64),
ctf.dot(ctf.conj(Q.T()), Q)))
else:
self.assertTrue(
allclose(ctf.eye(m, dtype=np.complex64),
ctf.dot(Q, ctf.conj(Q.T()))))
A = ctf.tensor((m, n), dtype=np.complex128)
rA = ctf.tensor((m, n), dtype=np.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=np.float64)
iA.fill_random()
A.imag(iA)
[Q, R] = ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q, R)))
if (m >= n):
self.assertTrue(
allclose(ctf.eye(n, dtype=np.complex128),
ctf.dot(ctf.conj(Q.T()), Q)))
else:
self.assertTrue(
allclose(ctf.eye(m, dtype=np.complex128),
ctf.dot(Q, ctf.conj(Q.T()))))
def test_hypersparse_dot(self):
A = ctf.tensor((37, 513), sp=True)
A.fill_sp_random(0., 1., 1. / 2047)
B = ctf.tensor((513, 17))
C = ctf.tensor((37, 17), sp=True)
C.i("ij") << A.i("ik") * B.i("kj")
C2 = ctf.tensor((37, 17))
C2 = ctf.dot(A, B)
self.assertTrue(allclose(C, C2))
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 test_qr(self):
m = 8
n = 4
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex64), ctf.dot(ctf.conj(Q.T()), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex128), ctf.dot(ctf.conj(Q.T()), Q)))
def test_qr(self):
m = 8
n = 4
for dt in [numpy.float32, numpy.float64, numpy.complex64, numpy.complex128]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n), ctf.dot(Q.T(), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex64), ctf.dot(ctf.conj(Q.T()), Q)))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[Q,R]=ctf.qr(A)
self.assertTrue(allclose(A, ctf.dot(Q,R)))
self.assertTrue(allclose(ctf.eye(n,dtype=numpy.complex128), ctf.dot(ctf.conj(Q.T()), Q)))
def test_dot_2d(self):
a1 = numpy.random.random(4)
a2 = numpy.random.random((4,3))
self.assertTrue(ctf.dot(ctf.astensor(a1), ctf.astensor(a2)).shape == (3,))
self.assertTrue(allclose(ctf.dot(a1, ctf.astensor(a2)), numpy.dot(a1, a2)))
self.assertTrue(ctf.dot(ctf.astensor(a2).T(), a1).shape == (3,))
self.assertTrue(allclose(ctf.dot(ctf.astensor(a2).T(), a1), numpy.dot(a2.T, a1)))
with self.assertRaises(ValueError):
ctf.dot(a2, a2)
self.assertTrue(allclose(ctf.dot(ctf.astensor(a2).T(), a2), numpy.dot(a2.T, a2)))
self.assertTrue(allclose(ctf.astensor(a2).dot(a2.T), a2.dot(a2.T)))
def LS_CG(Ax0,b,Z,x0,r,regParam):
rk = b - Ax0
sk = rk
xk = x0
for i in range(sk.shape[0]): # how many iterations?
Ask = ctf.tensor(r)
Ask.i("i") << Z.i("ti") * Z.i("tj") * sk.i("j") # A @ sk
Ask += regParam*sk
rnorm = ctf.dot(rk,rk)
#print("rnorm",rnorm.to_nparray())
if rnorm.to_nparray() < 1.e-16:
break
#print(ctf.dot(sk, Ask))
alpha = rnorm/ctf.dot(sk, Ask)
xk1 = xk + alpha * sk
rk1 = rk - alpha * Ask
beta = ctf.dot(rk1,rk1)/rnorm
sk1 = rk1 + beta*sk
rk = rk1
xk = xk1
sk = sk1
#print("rk",ctf.vecnorm(rk))
return xk
def test_svd(self):
m = 9
n = 5
k = 5
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m,n))
A = ctf.astensor(A,dtype=dt)
[U,S,VT]=ctf.svd(A,k)
[U1,S1,VT1]=la.svd(ctf.to_nparray(A),full_matrices=False)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U.T(), U)))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT, VT.T())))
A = ctf.tensor((m,n),dtype=numpy.complex64)
rA = ctf.tensor((m,n),dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[U,S,VT]=ctf.svd(A,k)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex64), ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex64), ctf.dot(VT, ctf.conj(VT.T()))))
A = ctf.tensor((m,n),dtype=numpy.complex128)
rA = ctf.tensor((m,n),dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m,n),dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[U,S,VT]=ctf.svd(A,k)
self.assertTrue(allclose(A, ctf.dot(U,ctf.dot(ctf.diag(S),VT))))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex128), ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(allclose(ctf.eye(k,dtype=numpy.complex128), ctf.dot(VT, ctf.conj(VT.T()))))
def test_dot_1d(self):
a1 = numpy.ones(4)
self.assertTrue(allclose(ctf.dot(ctf.astensor(a1), a1), numpy.dot(a1, a1)))
self.assertTrue(allclose(ctf.dot(a1+1j, ctf.astensor(a1)), numpy.dot(a1+1j, a1)))
a2 = ctf.astensor(a1).dot(a1+0j)
self.assertTrue(a2.dtype == numpy.complex128)
def davidson(mult_by_A, N, neig, x0=None, Adiag=None, verbose=4):
"""Diagonalize a matrix via non-symmetric Davidson algorithm.
mult_by_A() is a function which takes a vector of length N
and returns a vector of length N.
neig is the number of eigenvalues requested
"""
if rank == 0:
log = lib.logger.Logger(sys.stdout, verbose)
else:
log = lib.logger.Logger(sys.stdout, 0)
cput1 = (time.clock(), time.time())
Mmin = min(neig, N)
Mmax = min(N, 2000)
tol = 1e-6
def mult(arg):
return mult_by_A(arg)
if Adiag is None:
Adiag = np.zeros(N, np.complex)
for i in range(N):
test = np.zeros(N, np.complex)
test[i] = 1.0
Adiag[i] = mult(test)[i]
else:
Adiag = Adiag.to_nparray()
idx = Adiag.argsort()
lamda_k_old = 0
lamda_k = 0
target = 0
conv = False
if x0 is not None:
assert x0.shape == (Mmin, N)
b = x0.copy()
Ab = tuple([mult(b[m, :]) for m in range(Mmin)])
Ab = ctf.vstack(Ab).transpose()
evals = np.zeros(neig, dtype=np.complex)
evecs = []
for istep, M in enumerate(range(Mmin, Mmax + 1)):
if M == Mmin:
b = ctf.zeros((N, M))
if rank == 0:
ind = [i * M + m for m, i in zip(range(M), idx)]
fill = np.ones(len(ind))
b.write(ind, fill)
else:
b.write([], [])
Ab = tuple([mult(b[:, m]) for m in range(M)])
Ab = ctf.vstack(Ab).transpose()
else:
Ab = ctf.hstack((Ab, mult(b[:, M - 1]).reshape(N, -1)))
Atilde = ctf.dot(b.conj().transpose(), Ab)
Atilde = Atilde.to_nparray()
lamda, alpha = diagonalize_asymm(Atilde)
lamda_k_old, lamda_k = lamda_k, lamda[target]
alpha_k = ctf.astensor(alpha[:, target])
if M == Mmax:
break
q = ctf.dot(Ab - lamda_k * b, alpha_k)
qnorm = ctf.norm(q)
log.info(
'davidson istep = %d root = %d E = %.15g dE = %.9g residual = %.6g',
istep, target, lamda_k.real, (lamda_k - lamda_k_old).real, qnorm)
cput1 = log.timer('davidson iter', *cput1)
if ctf.norm(q) < tol:
evecs.append(ctf.dot(b, alpha_k))
evals[target] = lamda_k
if target == neig - 1:
conv = True
break
else:
target += 1
eps = 1e-10
xi = q / (lamda_k - Adiag + eps)
bxi, R = ctf.qr(ctf.hstack((b, xi.reshape(N, -1))))
nlast = bxi.shape[-1] - 1
b = ctf.hstack(
(b, bxi[:, nlast].reshape(N, -1))
) #can not replace nlast with -1, (inconsistent between numpy and ctf)
evecs = ctf.vstack(tuple(evecs))
return conv, evals, evecs
def inv(matrix):
U, s, V = ctf.svd(matrix)
return ctf.dot(ctf.transpose(V),
ctf.dot(ctf.diag(s**-1), ctf.transpose(U)))
def naive_gemm(A, B, n, b):
C = ctf.dot(A, B)
C += C.reshape((n, b, n, b)).transpose([2, 1, 0, 3]).reshape(
(n * b, n * b))
return C
#!/usr/bin/env python
import ctf
from ctf import random
A = ctf.random.random((32,32))
[U,S,VT]=ctf.svd(A)
err = A-ctf.dot(U,ctf.dot(ctf.diag(S),VT))
success=True
err_nrm = err.norm2()
if err_nrm > 1.E-6:
success=False
if ctf.comm().rank() == 0:
if success:
print("success, norm is ", err_nrm)
else:
print("failure, norm is ", err_nrm)
ctf.MPI_Stop()
#!/usr/bin/env python
import ctf
import sys
from ctf import random
A = ctf.random.random((32,32))
[U,S,VT]=ctf.svd(A)
err = A-ctf.dot(U,ctf.dot(ctf.diag(S),VT))
success=True
err_nrm = err.norm2()
if err_nrm > 1.E-6:
success=False
if ctf.comm().rank() == 0:
if success:
print("success, norm is ", err_nrm)
else:
print("failure, norm is ", err_nrm)
ctf.MPI_Stop()
sys.exit(not success)
def dot(A, B):
return ctf.dot(A, B)
def test_svd(self):
m = 9
n = 5
k = 5
for dt in [numpy.float32, numpy.float64]:
A = ctf.random.random((m, n))
A = ctf.astensor(A, dtype=dt)
[U, S, VT] = ctf.svd(A, k)
[U1, S1, VT1] = la.svd(ctf.to_nparray(A), full_matrices=False)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(U.T(), U)))
self.assertTrue(allclose(ctf.eye(k), ctf.dot(VT, VT.T())))
A = ctf.tensor((m, n), dtype=numpy.complex64)
rA = ctf.tensor((m, n), dtype=numpy.float32)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=numpy.float32)
iA.fill_random()
A.imag(iA)
[U, S, VT] = ctf.svd(A, k)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex64),
ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex64),
ctf.dot(VT, ctf.conj(VT.T()))))
A = ctf.tensor((m, n), dtype=numpy.complex128)
rA = ctf.tensor((m, n), dtype=numpy.float64)
rA.fill_random()
A.real(rA)
iA = ctf.tensor((m, n), dtype=numpy.float64)
iA.fill_random()
A.imag(iA)
[U, S, VT] = ctf.svd(A, k)
self.assertTrue(allclose(A, ctf.dot(U, ctf.dot(ctf.diag(S), VT))))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex128),
ctf.dot(ctf.conj(U.T()), U)))
self.assertTrue(
allclose(ctf.eye(k, dtype=numpy.complex128),
ctf.dot(VT, ctf.conj(VT.T()))))
