# netket.operator.DiscreteOperator#

class netket.operator.DiscreteOperator[source]#

This class is the base class for operators defined on a discrete Hilbert space. Users interested in implementing new quantum Operators for discrete Hilbert spaces should derive their own class from this class

Inheritance
Attributes
H#

Returns the Conjugate-Transposed operator

T#

Returns the transposed operator

dtype#

The dtype of the operatorâ€™s matrix elements âŸ¨Ïƒ|OÌ‚|Ïƒâ€™âŸ©.

hilbert#

The hilbert space associated to this observable.

is_hermitian#

Returns true if this operator is hermitian.

max_conn_size#

The maximum number of non zero âŸ¨x|O|xâ€™âŸ© for every x.

Methods
__call__(v)[source]#

Call self as a function.

Return type:

ndarray

Parameters:

v (ndarray)

apply(v)[source]#
Return type:

ndarray

Parameters:

v (ndarray)

collect()#

Returns a guaranteed concrete instance of an operator.

As some operations on operators return lazy wrappers (such as transpose, hermitian conjugateâ€¦), this is used to obtain a guaranteed non-lazy operator.

Return type:

AbstractOperator

conj(*, concrete=False)#
Return type:

AbstractOperator

conjugate(*, concrete=False)#

Returns the complex-conjugate of this operator.

Parameters:

concrete â€“ if True returns a concrete operator and not a lazy wrapper

Return type:

AbstractOperator

Returns:

if concrete is not True, self or a lazy wrapper; the complex-conjugated operator otherwise

get_conn(x)[source]#

Finds the connected elements of the Operator. Starting from a given quantum number x, it finds all other quantum numbers xâ€™ such that the matrix element $$O(x,x')$$ is different from zero. In general there will be several different connected states xâ€™ satisfying this condition, and they are denoted here $$x'(k)$$, for $$k=0,1...N_{\mathrm{connected}}$$.

Parameters:

x (ndarray) â€“ An array of shape (hilbert.size, ) containing the quantum numbers x.

Returns:

The connected states xâ€™ of shape (N_connected,hilbert.size) array: An array containing the matrix elements $$O(x,x')$$ associated to each xâ€™.

Return type:

matrix

Raises:

ValueError â€“ If the given quantum number is not compatible with the hilbert space.

get_conn_flattened(x, sections)[source]#

Finds the connected elements of the Operator.

Starting from a given quantum number $$x$$, it finds all other quantum numbers $$x'$$ such that the matrix element $$O(x,x')$$ is different from zero. In general there will be several different connected states $$x'$$ satisfying this condition, and they are denoted here $$x'(k)$$, for $$k=0,1...N_{\mathrm{connected}}$$.

This is a batched version, where x is a matrix of shape (batch_size,hilbert.size).

Parameters:
• x (ndarray) â€“ A matrix of shape (batch_size, hilbert.size) containing the batch of quantum numbers x.

• sections (ndarray) â€“ An array of sections for the flattened xâ€™. See numpy.split for the meaning of sections.

Returns:

The connected states xâ€™, flattened together in

a single matrix. An array containing the matrix elements $$O(x,x')$$ associated to each xâ€™.

Return type:

(matrix, array)

Finds the connected elements of the Operator.

Starting from a batch of quantum numbers $$x={x_1, ... x_n}$$ of size $$B \times M$$ where $$B$$ size of the batch and $$M$$ size of the hilbert space, finds all states $$y_i^1, ..., y_i^K$$ connected to every $$x_i$$.

Returns a matrix of size $$B \times K_{max} \times M$$ where $$K_{max}$$ is the maximum number of connections for every $$y_i$$.

Parameters:

x (ndarray) â€“ A N-tensor of shape $$(...,hilbert.size)$$ containing the batch/batches of quantum numbers $$x$$.

Returns:

The connected states xâ€™, in a N+1-tensor and an N-tensor containing the matrix elements $$O(x,x')$$ associated to each xâ€™ for every batch.

Return type:

(x_primes, mels)

n_conn(x, out=None)[source]#

Return the number of states connected to x.

Parameters:
• x (matrix) â€“ A matrix of shape (batch_size,hilbert.size) containing the batch of quantum numbers x.

• out (array) â€“ If None an output array is allocated.

Returns:

The number of connected states xâ€™ for each x[i].

Return type:

array

to_dense()[source]#

Returns the dense matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces or sufficiently sparse operators.

This method requires an indexable Hilbert space.

Return type:

ndarray

Returns:

The dense matrix representation of the operator as a Numpy array.

to_linear_operator()[source]#
to_qobj()[source]#

Convert the operator to a qutipâ€™s Qobj.

Returns:

A qutip.Qobj object.

to_sparse()[source]#

Returns the sparse matrix representation of the operator. Note that, in general, the size of the matrix is exponential in the number of quantum numbers, and this operation should thus only be performed for low-dimensional Hilbert spaces or sufficiently sparse operators.

This method requires an indexable Hilbert space.

Return type:

csr_matrix

Returns:

The sparse matrix representation of the operator.

transpose(*, concrete=False)#

Returns the transpose of this operator.

Parameters:

concrete â€“ if True returns a concrete operator and not a lazy wrapper

Return type:

AbstractOperator

Returns:

if concrete is not True, self or a lazy wrapper; the transposed operator otherwise