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_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 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_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 eaccsd_diag(eom, imds=None):
if imds is None: imds = eom.make_imds()
t1, t2 = imds.t1, imds.t2
nocc, nvir = t1.shape
foo = imds.eris.foo
fvv = imds.eris.fvv
Hr1 = imds.Lvv.diagonal()
Hr1 = tensor(Hr1)
if eom.partition == 'mp':
jab = fvv.diagonal()[None, :, None]
jab = jab + fvv.diagonal()[None, None, :]
jab = jab - foo.diagonal()[:, None, None]
Hr2 = tensor(jab)
else:
jab = imds.Lvv.diagonal().reshape(1, nvir, 1)
jab = jab + imds.Lvv.diagonal().reshape(1, 1, nvir)
jab = jab - imds.Loo.diagonal().reshape(nocc, 1, 1)
wab = ctf.einsum("abab->ab", imds.Wvvvv.array)
wjb = ctf.einsum('jbjb->jb', imds.Wovov.array)
wjb2 = ctf.einsum('jbbj->jb', imds.Wovvo.array)
wja = ctf.einsum('jaja->ja', imds.Wovov.array)
jab = jab + wab.reshape(1, nvir, nvir)
jab = jab - wjb.reshape(nocc, 1, nvir)
jab = jab + 2 * wjb2.reshape(nocc, 1, nvir)
jab -= ctf.einsum('jb,ab->jab', wjb2, ctf.eye(nvir))
jab = jab - wja.reshape(nocc, nvir, 1)
Hr2 = tensor(jab)
Hr2 -= 2 * lib.einsum('ijab,ijab->jab', t2, imds.Woovv)
Hr2 += lib.einsum('ijab,ijba->jab', t2, imds.Woovv)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
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 ipccsd_diag(eom, imds=None):
if imds is None: imds = eom.make_imds()
t1, t2 = imds.t1, imds.t2
nocc, nvir = t1.shape
foo = imds.eris.foo
fvv = imds.eris.fvv
Hr1 = -imds.Loo.diagonal()
Hr1 = tensor(Hr1)
if eom.partition == 'mp':
ijb = -foo.diagonal().reshape(nocc, 1, 1)
ijb = ijb - foo.diagonal().reshape(1, nocc, 1)
ijb = ijb + fvv.diagonal().reshape(1, 1, nvir)
Hr2 = tensor(ijb)
else:
wij = ctf.einsum('ijij->ij', imds.Woooo.array)
wjb = ctf.einsum('jbjb->jb', imds.Wovov.array)
wjb2 = ctf.einsum('jbbj->jb', imds.Wovvo.array)
wib = ctf.einsum('ibib->ib', imds.Wovov.array)
ijb = imds.Lvv.diagonal().reshape(1, 1, nvir)
ijb = ijb - imds.Loo.diagonal().reshape(nocc, 1, 1)
ijb = ijb - imds.Loo.diagonal().reshape(1, nocc, 1)
#print(ijb.shape, wjb.shape)
ijb = ijb + wij.reshape(nocc, nocc, 1)
ijb = ijb - wjb.reshape(1, nocc, nvir)
ijb = ijb + 2 * wjb2.reshape(1, nocc, nvir)
ijb = ijb - ctf.einsum('ij,jb->ijb', ctf.eye(nocc), wjb2)
ijb = ijb - wib.reshape(nocc, 1, nvir)
Hr2 = tensor(ijb)
Hr2 -= 2. * lib.einsum('ijcb,jibc->ijb', t2, imds.Woovv)
Hr2 += lib.einsum('ijcb,ijbc->ijb', t2, imds.Woovv)
vector = eom.amplitudes_to_vector(Hr1, Hr2)
return vector
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_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 updateH(A, W, regParam, omega, m, n, k):
'''Gets the new H matrix by using the formula, subbing H for W'''
H = ctf.zeros((n, k))
identity = ctf.eye(k)
for i in range(n):
newW = getNewWCTF(omega[:, i], W, m, n, k)
newMat = ctf.zeros((k, k))
newMat.i("xy") << newW.i("bx") * newW.i("by")
newMat.i("xy") << regParam * identity.i("xy")
inverseFirstPart = CTFinverse(newMat)
temp = ctf.zeros((k))
temp.i("j") << inverseFirstPart.i("ja") * W.i("ba") * A[:, i].i("b")
H[i] = temp
return H
def updateW(A, H, regParam, omega, m, n, k):
'''Gets the new W matrix by using the formula'''
Wctf = ctf.zeros((m, k))
identity = ctf.eye(k)
for i in range(m):
newH = getNewHCTF(omega[i], H, m, n, k)
newMat = ctf.zeros((k, k))
newMat.i(
"xy") << newH.i("bx") * newH.i("by") + regParam * identity.i("xy")
inverseFirstPart = CTFinverse(newMat)
temp = ctf.zeros((k))
temp.i("j") << inverseFirstPart.i("ja") * H.i("ba") * A[i].i("b")
Wctf[i] = temp
return Wctf
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_solve_tri(self):
n = 4
m = 7
for dt in [np.float32, np.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)) + ctf.eye(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)) + np.eye(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_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_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_eye(self):
a0 = ctf.identity(4)
a1 = ctf.eye(4)
self.assertTrue(ctf.all(a0 == a1))
a1 = ctf.eye(4, dtype=numpy.complex128)
self.assertTrue(a1.dtype == numpy.complex128)
def test_eye(self):
a0 = ctf.identity(4)
a1 = ctf.eye(4)
self.assertTrue(ctf.all(a0==a1))
a1 = ctf.eye(4, dtype=numpy.complex128)
self.assertTrue(a1.dtype == numpy.complex128)
def eye(*args):
return ctf.eye(*args)
def test_tsvd(self):
lens = [4,5,6,3]
for dt in [numpy.float32, numpy.float64, numpy.complex64, numpy.complex128]:
A = ctf.tensor(lens,dtype=dt)
A.fill_random()
[U,S,VT]=A.i("ijkl").svd("ija","akl")
A.i("ijkl") << -1.0*U.i("ija")*S.i("a")*VT.i("akl")
self.assertTrue(ctf.vecnorm(A)/A.tot_size()<1.e-6)
A = ctf.tensor(lens,dtype=dt)
A.fill_random()
[U,S,VT]=A.i("ijkl").svd("ika","ajl")
A.i("ijkl") << -1.0*U.i("ika")*S.i("a")*VT.i("ajl")
self.assertTrue(ctf.vecnorm(A)/A.tot_size()<1.e-6)
A = ctf.tensor(lens,dtype=dt)
A.fill_random()
[U,S,VT]=A.i("ijkl").svd("ika","ajl")
[U,S1,VT]=A.i("ijkl").svd("ika","ajl",4)
[U,S2,VT]=A.i("ijkl").svd("ika","ajl",4,numpy.abs(S[3])*(1.-1.e-5))
self.assertTrue(allclose(S1,S2))
[U,S2,VT]=A.i("ijkl").svd("ika","ajl",4,numpy.abs(S[2]))
self.assertTrue(not allclose(S1.shape,S2.shape))
[U,S2,VT]=A.i("ijkl").svd("ika","ajl",4,numpy.abs(S[5]))
self.assertTrue(allclose(S1,S2))
[U,S,VT]=A.i("ijkl").svd("iakj","la")
A.i("ijkl") << -1.0*U.i("iakj")*S.i("a")*VT.i("la")
self.assertTrue(ctf.vecnorm(A)/A.tot_size()<1.e-6)
A.fill_random()
[U,S,VT]=A.i("ijkl").svd("alk","jai")
A.i("ijkl") << -1.0*U.i("alk")*S.i("a")*VT.i("jai")
self.assertTrue(ctf.vecnorm(A)/A.tot_size()<1.e-6)
K = ctf.tensor((U.shape[0],U.shape[0]),dtype=dt)
K.i("ab") << U.i("alk") * U.i("blk")
self.assertTrue(allclose(K,ctf.eye(U.shape[0])))
0.*K.i("ab") << VT.i("jai") * VT.i("jbi")
self.assertTrue(allclose(K,ctf.eye(U.shape[0])))
A.fill_random()
[U,S,VT]=A.i("ijkl").svd("alk","jai",4,0,True)
nrm1 = ctf.vecnorm(A)
A.i("ijkl") << -1.0*U.i("alk")*S.i("a")*VT.i("jai")
self.assertTrue(ctf.vecnorm(A)<nrm1)
K = ctf.tensor((U.shape[0],U.shape[0]),dtype=dt)
K.i("ab") << U.i("alk") * U.i("blk")
self.assertTrue(allclose(K,ctf.eye(U.shape[0])))
0.*K.i("ab") << VT.i("jai") * VT.i("jbi")
self.assertTrue(allclose(K,ctf.eye(U.shape[0])))
T = ctf.tensor((4,3,6,5,1,7),dtype=dt)
[U,S,VT] = T.i("abcdef").svd("crd","aerfb")
T.i("abcdef") << -1.0*U.i("crd")*S.i("r")*VT.i("aerfb")
self.assertTrue(ctf.vecnorm(T)/T.tot_size()<1.e-6)
K = ctf.tensor((S.shape[0],S.shape[0]),dtype=dt)
K.i("rs") << U.i("crd")*U.i("csd")
self.assertTrue(allclose(K,ctf.eye(S.shape[0])))
K = ctf.tensor((S.shape[0],S.shape[0]),dtype=dt)
K.i("rs") << VT.i("aerfb")*VT.i("aesfb")
self.assertTrue(allclose(K,ctf.eye(S.shape[0])))
