qsymm.model module

class qsymm.model.BlochCoeff(hop, coeff)

Bases: tuple

copy()

tosympy(momenta, nsimplify=False)

class qsymm.model.BlochModel(hamiltonian=None, locals=None, momenta=('k_x', 'k_y', 'k_z'), keep=None, shape=None, format=None)

Bases: Model

conj()

Complex conjugation.

rotate_momenta(R)

Rotate momenta with rotation matrix R.

subs(*args, **kwargs)

Substitute symbolic expressions. See Model.subs.

tomodel(nsimplify=False)

Convert to Model.

tosympy(nsimplify=False)

Return sympy representation of the Model. If nsimplify=True, attempt to rewrite numerical coefficients as exact formulas.

transform_symbolic(func)

Transform keys by applying func to all of them. Useful for symbolic substitutions, differentiation, etc.

class qsymm.model.Model(hamiltonian=None, locals=None, momenta=('k_x', 'k_y', 'k_z'), keep=None, symbol_normalizer=None, normalize=False, shape=None, format=None)

Bases: UserDict

T()

Transpose

allclose(other, rtol=1e-05, atol=1e-08, equal_nan=False)

Test whether two Models are approximately equal

around(decimals=3)

Return Model with matrices rounded to given number of decimals.

conj()

Complex conjugation

copy()

Return a copy.

eliminate_zeros(rtol=1e-05, atol=1e-08)

Return a model with small terms removed. Tolerances are in Frobenius matrix norm, relative tolerance compares to the value with largest norm.

evalf(subs=None)

Evaluate using parameter values in subs.

lambdify(nsimplify=False, *, onsite=False, hopping=False)

Return a callable object for the model, with sympy symbols as parameters.

Parameters:

• nsimplify (bool, default False) – Whether or not to attempt to rewrite numerical coefficients as exact symbols in sympification.

• onsite (bool, default False) – If True, adds ‘site’ as the first argument to the callable object. Helpful for passing Model objects to kwant Builder objects as onsite functions.

• hopping (bool, default False) – If True, adds ‘site1’ and ‘site2’ as the first two arguments to the callable object. Helpful for passing Model objects to kwant Builder objects as hopping functions.

• Notes –

• True (onsite and hopping are mutually exclusive. If both are set to) –

:param : :param an error is thrown.:

reshape(*args, **kwargs)

Reshape, see numpy.reshape.

rotate_momenta(R)

Rotate momenta with rotation matrix R.

subs(*args, **kwargs)

Substitute symbolic expressions. See documentation of sympy.Expr.subs() for details.

Allows for the replacement of momenta in the Model object. Replacing a momentum k with a sympy.Symbol object p replaces the momentum k with p in the Model. Replacing a momentum k with a number removes the momentum k from the Model momenta. Replacing a momentum k with a sympy expression that does not contain any of the Model.momenta also removes the momentum k from the momenta.

toarray()

Convert to dense numpy ndarray format.

tocsr()

Convert to sparse csr format.

tosympy(nsimplify=False)

Return sympy representation of the Model. If nsimplify=True, attempt to rewrite numerical coefficients as exact formulas.

trace()

Take trace of the matrix and return a scalar valued Model.

transform_symbolic(func)

Transform keys by applying func to all of them. Useful for symbolic substitutions, differentiation, etc.

value_list(key_list)

Return a list of the matrix coefficients corresponding to the keys in key_list.

zeros_like()

Return an empty model object that inherits the other properties

qsymm.model.substitute_exponents(expr)

Substitute trignometric functions with exp.

sin(X) -> (e^(I * X) - e^(-I * X)) / (2 * I) cos(X) -> (e^(I * X) + e^(-I * X)) / 2 exp(X) -> e^X