Python numpy 模块，vdot() 实例源码
我们从Python开源项目中，提取了以下50个代码示例，用于说明如何使用numpy.vdot()。
def vdot(a, b):
"""Returns the dot product of two vectors.
The input arrays are flattened into 1-D vectors and then it performs inner
product of these vectors.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: Zero-dimensional array of the dot product result.
.. seealso:: :func:`numpy.vdot`
"""
if a.size != b.size:
raise ValueError('Axis dimension mismatch')
if a.dtype.kind == 'c':
a = a.conj()
return core.tensordot_core(a, b, None, 1, 1, a.size, ())
def test_sandwich(nr_sites, local_dim, rank, rgen, dtype):
mps = factory.random_mpa(nr_sites, local_dim, rank,
randstate=rgen, dtype=dtype, normalized=True)
mps2 = factory.random_mpa(nr_sites, local_dim, rank,
randstate=rgen, dtype=dtype, normalized=True)
mpo = factory.random_mpa(nr_sites, [local_dim] * 2, rank,
randstate=rgen, dtype=dtype)
mpo.canonicalize()
mpo /= mp.trace(mpo)
vec = mps.to_array().ravel()
op = mpo.to_array_global().reshape([local_dim**nr_sites] * 2)
res_arr = np.vdot(vec, np.dot(op, vec))
res_mpo = mp.inner(mps, mp.dot(mpo, mps))
res_sandwich = mp.sandwich(mpo, mps)
assert_almost_equal(res_mpo, res_arr)
assert_almost_equal(res_sandwich, res_arr)
vec2 = mps2.to_array().ravel()
res_arr = np.vdot(vec2, np.dot(op, vec))
res_mpo = mp.inner(mps2, mp.dot(mpo, mps))
res_sandwich = mp.sandwich(mpo, mps, mps2)
assert_almost_equal(res_mpo, res_arr)
assert_almost_equal(res_sandwich, res_arr)
def test_adjoint(dtype, shearletSystem):
"""Validate the adjoint."""
shape = tuple(shearletSystem['size'])
# load data
X = np.random.randn(*shape).astype(dtype)
# decomposition
coeffs = pyshearlab.SLsheardec2D(X, shearletSystem)
# adjoint
Xadj = pyshearlab.SLshearadjoint2D(coeffs, shearletSystem)
assert Xadj.dtype == X.dtype
assert Xadj.shape == X.shape
# <Ax, Ax> should equal <x, AtAx>
assert (pytest.approx(np.vdot(coeffs, coeffs), rel=1e-3, abs=0) ==
np.vdot(X, Xadj))
def test_adjoint_of_inverse(dtype, shearletSystem):
"""Validate the adjoint of the inverse."""
X = np.random.randn(*shearletSystem['size']).astype(dtype)
# decomposition
coeffs = pyshearlab.SLsheardec2D(X, shearletSystem)
# reconstruction
Xrec = pyshearlab.SLshearrec2D(coeffs, shearletSystem)
Xrecadj = pyshearlab.SLshearrecadjoint2D(Xrec, shearletSystem)
assert Xrecadj.dtype == X.dtype
assert Xrecadj.shape == coeffs.shape
# <A^-1x, A^-1x> = <A^-* A^-1 x, x>.
assert (pytest.approx(np.vdot(Xrec, Xrec), rel=1e-3, abs=0) ==
np.vdot(Xrecadj, coeffs))
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def vdot(a, b):
"""Returns the dot product of two vectors.
The input arrays are flattened into 1-D vectors and then it performs inner
product of these vectors.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: Zero-dimensional array of the dot product result.
.. seealso:: :func:`numpy.vdot`
"""
if a.size != b.size:
raise ValueError('Axis dimension mismatch')
return core.tensordot_core(a, b, None, 1, 1, a.size, ())
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def rotation_matrix(a, b):
"""
Create rotation matrix to rotate vector a into b.
After http://math.stackexchange.com/a/476311
Parameters
----------
a,b
xyz-vectors
"""
v = np.cross(a, b)
sin = np.linalg.norm(v)
if sin == 0:
return np.identity(3)
cos = np.vdot(a, b)
vx = np.mat([[0, -v[2], v[1]], [v[2], 0., -v[0]], [-v[1], v[0], 0.]])
R = np.identity(3) + vx + vx * vx * (1 - cos) / (sin ** 2)
return R
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def get_expectation_value(self, terms_dict, ids):
"""
Return the expectation value of a qubit operator w.r.t. qubit ids.
Args:
terms_dict (dict): Operator dictionary (see QubitOperator.terms)
ids (list[int]): List of qubit ids upon which the operator acts.
Returns:
Expectation value
"""
expectation = 0.
current_state = _np.copy(self._state)
for (term, coefficient) in terms_dict:
self._apply_term(term, ids)
delta = coefficient * _np.vdot(current_state, self._state).real
expectation += delta
self._state = _np.copy(current_state)
return expectation
def berry_curvature(H,kx,ky,mu,d=10**-6):
'''
Calculate the Berry curvature of the occupied bands for a Hamiltonian with the given chemical potential using the Kubo formula.
Parameters
----------
H : callable
Input function which returns the Hamiltonian as a 2D array.
kx,ky : float
The two parameters which specify the 2D point at which the Berry curvature is to be calculated.
They are also the input parameters to be conveyed to the function H.
mu : float
The chemical potential.
d : float, optional
The spacing to be used to calculate the derivatives.
Returns
-------
float
The calculated Berry curvature for function H at point kx,ky with chemical potential mu.
'''
result=0
Vx=(H(kx+d,ky)-H(kx-d,ky))/(2*d)
Vy=(H(kx,ky+d)-H(kx,ky-d))/(2*d)
Es,Evs=eigh(H(kx,ky))
for n in xrange(Es.shape[0]):
for m in xrange(Es.shape[0]):
if Es[n]<=mu and Es[m]>mu:
result-=2*(np.vdot(np.dot(Vx,Evs[:,n]),Evs[:,m])*np.vdot(Evs[:,m],np.dot(Vy,Evs[:,n]))/(Es[n]-Es[m])**2).imag
return result
def FBFMPOS(engine,app):
'''
This method calculates the profiles of spin-1-excitation states.
'''
result=[]
table=engine.config.table(mask=['spin','nambu'])
U1,U2,vs=engine.basis.U1,engine.basis.U2,sl.eigh(engine.matrix(k=app.k),eigvals_only=False)[1]
for i,index in enumerate(sorted(table,key=table.get)):
result.append([i])
gs=np.vdot(U2[table[index],:,:].reshape(-1),U2[table[index],:,:].reshape(-1))*(1 if engine.basis.polarization=='up' else -1)
dw=optrep(HP.FQuadratic(1.0,(index.replace(spin=0,nambu=HP.CREATION),index.replace(spin=0,nambu=HP.ANNIHILATION)),seqs=(table[index],table[index])),app.k,engine.basis)
up=optrep(HP.FQuadratic(1.0,(index.replace(spin=1,nambu=HP.CREATION),index.replace(spin=1,nambu=HP.ANNIHILATION)),seqs=(table[index],table[index])),app.k,engine.basis)
for pos in app.ns or (0,):
result[-1].append((np.vdot(vs[:,pos],up.dot(vs[:,pos]))-np.vdot(vs[:,pos],dw.dot(vs[:,pos]))-gs)*(-1 if engine.basis.polarization=='up' else 1))
result=np.asarray(result)
assert nl.norm(np.asarray(result).imag)<HP.RZERO
result=result.real
name='%s_%s'%(engine,app.name)
if app.savedata: np.savetxt('%s/%s.dat'%(engine.dout,name),result)
if app.plot: app.figure('L',result,'%s/%s'%(engine.dout,name),legend=['Level %s'%n for n in app.ns or (0,)])
if app.returndata: return result
def overlap(*args):
'''
Calculate the overlap between two vectors or among a matrix and two vectors.
Usage:
* ``overlap(vector1,vector2)``, with
vector1,vector2: 1d ndarray
The vectors between which the overlap is to calculate.
* ``overlap(vector1,matrix,vector2)``, with
vector1,vector2: 1d ndarray
The ket and bra in the overlap.
matrix: 2d ndarray-like
The matrix between the two vectors.
'''
assert len(args) in (2,3)
if len(args)==2:
return np.vdot(args[0],args[1])
else:
return np.vdot(args[0],args[1].dot(args[2]))
def test_basic(self):
dt_numeric = np.typecodes['AllFloat'] + np.typecodes['AllInteger']
dt_complex = np.typecodes['Complex']
# test real
a = np.eye(3)
for dt in dt_numeric + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test complex
a = np.eye(3) * 1j
for dt in dt_complex + 'O':
b = a.astype(dt)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), 3)
# test boolean
b = np.eye(3, dtype=np.bool)
res = np.vdot(b, b)
assert_(np.isscalar(res))
assert_equal(np.vdot(b, b), True)
def test_vdot_uncontiguous(self):
for size in [2, 1000]:
# Different sizes match different branches in vdot.
a = np.zeros((size, 2, 2))
b = np.zeros((size, 2, 2))
a[:, 0, 0] = np.arange(size)
b[:, 0, 0] = np.arange(size) + 1
# Make a and b uncontiguous:
a = a[..., 0]
b = b[..., 0]
assert_equal(np.vdot(a, b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy()),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy(), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a.copy('F'), b),
np.vdot(a.flatten(), b.flatten()))
assert_equal(np.vdot(a, b.copy('F')),
np.vdot(a.flatten(), b.flatten()))
def test_inner_vec(nr_sites, local_dim, rank, rgen, dtype):
mp_psi1 = factory.random_mpa(nr_sites, local_dim, rank, randstate=rgen,
dtype=dtype)
psi1 = mp_psi1.to_array().ravel()
mp_psi2 = factory.random_mpa(nr_sites, local_dim, rank, randstate=rgen,
dtype=dtype)
psi2 = mp_psi2.to_array().ravel()
inner_np = np.vdot(psi1, psi2)
inner_mp = mp.inner(mp_psi1, mp_psi2)
assert_almost_equal(inner_mp, inner_np)
assert inner_mp.dtype == dtype
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def get_shortest_bases_from_extented_bases(extended_bases, tolerance):
def mycmp(x, y):
return cmp(np.vdot(x,x), np.vdot(y,y))
basis = np.zeros((7,3), dtype=float)
basis[:4] = extended_bases
basis[4] = extended_bases[0] + extended_bases[1]
basis[5] = extended_bases[1] + extended_bases[2]
basis[6] = extended_bases[2] + extended_bases[0]
# Sort bases by the lengthes (shorter is earlier)
basis = sorted(basis, cmp=mycmp)
# Choose shortest and linearly independent three bases
# This algorithm may not be perfect.
for i in range(7):
for j in range(i+1, 7):
for k in range(j+1, 7):
if abs(np.linalg.det([basis[i],basis[j],basis[k]])) > tolerance:
return np.array([basis[i],basis[j],basis[k]])
print ("Delaunary reduction is failed.")
return basis[:3]
#
# Other tiny tools
#
def get_angles( lattice ):
"""
Get alpha, beta and gamma angles from lattice vectors.
>>> get_angles( np.diag([1,2,3]) )
(90.0, 90.0, 90.0)
"""
a, b, c = get_cell_parameters( lattice )
alpha = np.arccos(np.vdot(lattice[1], lattice[2]) / b / c ) / np.pi * 180
beta = np.arccos(np.vdot(lattice[2], lattice[0]) / c / a ) / np.pi * 180
gamma = np.arccos(np.vdot(lattice[0], lattice[1]) / a / b ) / np.pi * 180
return alpha, beta, gamma
def check_duality_gap(a, b, M, G, u, v, cost):
cost_dual = np.vdot(a, u) + np.vdot(b, v)
# Check that dual and primal cost are equal
np.testing.assert_almost_equal(cost_dual, cost)
[ind1, ind2] = np.nonzero(G)
# Check that reduced cost is zero on transport arcs
np.testing.assert_array_almost_equal((M - u.reshape(-1, 1) - v.reshape(1, -1))[ind1, ind2],
np.zeros(ind1.size))
def vectorize_and_dot_dataset(dataset):
dots = numpy.zeros(len(dataset))
labels = numpy.zeros(len(dataset))
i = 0
for row in dataset:
#Get the vectors for each word in the body and headline
split_headline = hf.split_words(row['headline'])
split_body = hf.split_words_special(row['body'], split_code)
headline_vectors = vectorize_wordlist(split_headline)
body_vectors = vectorize_wordlist(split_body)
#Sum the words in the body, sum the words in the headline
summed_headline_vector = numpy.sum(headline_vectors, axis=0)
summed_body_vector = numpy.sum(body_vectors, axis=0)
#Normalize
normalized_headline_vector = normalize(summed_headline_vector.reshape(1,-1))
normalized_body_vector = normalize(summed_body_vector.reshape(1,-1))
#Save the row vector
row['row_vector'] = numpy.concatenate( (normalized_headline_vector[0], normalized_body_vector[0]), axis=0)
row['isRelated'] = 0 if row['stance'] == 'unrelated' else 1
# Data relating to the relationship between the headline/body can be appended to row['row_vector']
if True:
extra_nodes = []
#Save the dot product
dot = numpy.vdot(normalized_headline_vector, normalized_body_vector)
extra_nodes.append(dot)
#Jaccard distance
jaccard = jaccard_distance(set(split_headline), set(split_body))
extra_nodes.append(jaccard)
#Sentiment analysis
extra_nodes.append( sentiment_analyzer.polarity_scores(row['headline'])['compound'] )
extra_nodes.append( sentiment_analyzer.polarity_scores(" ".join(split_body))['compound'] )
row['row_vector'] = numpy.append(row['row_vector'], extra_nodes)
# return dots, labels
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def _calculate(self):
min_, max_ = self._bounds
n = np.prod(self.reference.shape)
f = n * (max_ - min_)**2
diff = self.other - self.reference
value = np.vdot(diff, diff) / f
# calculate the gradient only when needed
self._g_diff = diff
self._g_f = f
gradient = None
return value, gradient
def calc_cost(self):
cost = sum(self.E[key] * self.E[key] for key in self.E)
cost += self.l*(np.vdot(self.B, self.B) + np.vdot(self.C, self.C))
return cost
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def test_blas_dot(backend, n):
b = backend()
x = (np.random.rand(n) + 1j * np.random.rand(n))
y = (np.random.rand(n) + 1j * np.random.rand(n))
x = np.require(x, dtype=np.dtype('complex64'), requirements='F')
y = np.require(y, dtype=np.dtype('complex64'), requirements='F')
x_d = b.copy_array(x)
y_d = b.copy_array(y)
y_exp = np.vdot(x, y).real
y_act = b.dot(x_d, y_d)
np.testing.assert_allclose(y_exp, y_act, atol=1e-5)
def dot(self, x, y):
""" returns x^T * y """
assert isinstance(x, self.dndarray)
assert isinstance(y, self.dndarray)
return np.vdot( x._arr, y._arr ).real
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def test_refcount_vdot(self, level=rlevel):
# Changeset #3443
_assert_valid_refcount(np.vdot)
def test_vdot_array_order(self):
a = np.array([[1, 2], [3, 4]], order='C')
b = np.array([[1, 2], [3, 4]], order='F')
res = np.vdot(a, a)
# integer arrays are exact
assert_equal(np.vdot(a, b), res)
assert_equal(np.vdot(b, a), res)
assert_equal(np.vdot(b, b), res)
def Tdot(self, fn, dtype):
from pyculib.blas.binding import cuBlas
x = np.random.random(10).astype(dtype)
y = np.random.random(10).astype(dtype)
d_x = cuda.to_device(x)
d_y = cuda.to_device(y)
blas = cuBlas()
got = getattr(blas, fn)(x.size, d_x, 1, d_y, 1)
if fn.endswith('c'):
exp = np.vdot(x, y)
else:
exp = np.dot(x, y)
self.assertTrue(np.allclose(got, exp))
def Tdotc(self, fn, dtype):
x = np.random.random(10).astype(dtype)
y = np.random.random(10).astype(dtype)
got = self.blas.dotc(x, y)
exp = np.vdot(x, y)
self.assertTrue(np.allclose(got, exp))
def compute_correlation(matrix_a, matrix_b):
correlation = numpy.vdot(matrix_a, matrix_b)
correlation /= numpy.linalg.norm(matrix_a)*numpy.linalg.norm(matrix_b)
correlation = (correlation + 1)/2
return correlation
def berry_phase(H,path,ns):
'''
Calculate the Berry phase of some bands of a Hamiltonian along a certain path.
Parameters
----------
H : callable
Input function which returns the Hamiltonian as a 2D array.
path : iterable
The path along which to calculate the Berry phase.
ns : iterable of int
The sequences of bands whose Berry phases are wanted.
Returns
-------
1d ndarray
The wanted Berry phase of the selected bands.
'''
ns=np.array(ns)
for i,parameters in enumerate(path):
new=eigh(H(**parameters))[1][:,ns]
if i==0:
result=np.ones(len(ns),new.dtype)
evs=new
else:
for j in xrange(len(ns)):
result[j]*=np.vdot(old[:,j],new[:,j])
old=new
else:
for j in xrange(len(ns)):
result[j]*=np.vdot(old[:,j],evs[:,j])
return np.angle(result)/np.pi
def iter(self):
'''
The Lanczos iteration.
'''
while len(self.candidates)>0:
v=self.candidates.pop(0)
norm=nl.norm(v)
if norm>self.dtol:
break
elif self.niter>=self.nc:
self.deflations.append(self.niter-self.nc)
else:
self.stop=True
if not self.stop:
self.vectors[self.niter]=v/norm
if self.niter-self.nc-1>=0:
self._T_[self.niter,self.niter-self.nc-1]=norm
else:
self.P[self.niter,self.niter-self.nc-1+self.nv0]=norm
for k,vc in enumerate(self.candidates):
overlap=np.vdot(self.vectors[self.niter],vc)
if k+self.niter>=self.nc:
self._T_[self.niter,k+self.niter-self.nc]=overlap
else:
self.P[self.niter,self.niter-self.nc+k+self.nv0]=overlap
vc-=overlap*self.vectors[self.niter]
v=self.matrix.dot(self.vectors[self.niter])
for k in xrange(max(self.niter-self.nc-1,0),self.niter):
self._T_[k,self.niter]=np.conjugate(self._T_[self.niter,k])
v-=self._T_[k,self.niter]*self.vectors[k]
for k in it.chain(self.deflations,[self.niter]):
overlap=np.vdot(self.vectors[k],v)
if k in set(self.deflations)|{self.niter}:
self._T_[k,self.niter]=overlap
self._T_[self.niter,k]=np.conjugate(overlap)
v-=overlap*self.vectors[k]
self.candidates.append(v)
if not self.keepstate and self.niter>=self.nc and self.niter-self.nc not in self.deflations: self.vectors[self.niter-self.nc]=None
self.niter+=1