RuntimeWarning: divide by zero encountered in det about thewalrus HOT 9 CLOSED

import thewalrus as tw
tw.about()

Python version:            3.9.0
The Walrus version:        0.20.0
Numpy version:             1.23.5
Scipy version:             1.10.1
SymPy version:             1.12
Numba version:             0.57.0

import multiprocessing
from multiprocessing import Pool

import numpy as np
from scipy.special import factorial as fac

from thewalrus._hafnian import hafnian, reduction
from thewalrus._torontonian import tor
from thewalrus.quantum import (
    Amat,
    Covmat,
    Qmat,
    Xmat,
    gen_Qmat_from_graph,
    is_classical_cov,
    reduced_gaussian,
    density_matrix_element,
)

# ===============================================================================================
# Hafnian sampling
# ===============================================================================================

# pylint: disable=too-many-branches
def generate_hafnian_sample(
    cov, mean, hbar=2, cutoff=6, max_photons=30, approx=False, approx_samples=1e5
):  # pylint: disable=too-many-branches
    r"""Returns a single sample from the Hafnian of a Gaussian state.

    Args:
        cov (array): a :math:`2N\times 2N` ``np.float64`` covariance matrix
            representing an :math:`N` mode quantum state. This can be obtained
            via the ``scovmavxp`` method of the Gaussian backend of Strawberry Fields.
        mean (array): a :math:`2N`` ``np.float64`` vector of means representing the Gaussian
            state.
        hbar (float): (default 2) the value of :math:`\hbar` in the commutation
            relation :math:`[\x,\p]=i\hbar`.
        cutoff (int): the Fock basis truncation.
        max_photons (int): specifies the maximum number of photons that can be counted.
        approx (bool): if ``True``, the approximate hafnian algorithm is used.
            Note that this can only be used for real, non-negative matrices.
        approx_samples: the number of samples used to approximate the hafnian if ``approx=True``.

    Returns:
        np.array[int]: a photon number sample from the Gaussian states.
    """
    N = len(cov) // 2
    result = []
    prev_prob = 1.0
    nmodes = N
    if mean is None:
        local_mu = np.zeros(2 * N)
    else:
        local_mu = mean
    A = Amat(Qmat(cov), hbar=hbar)

    for k in range(nmodes):
        probs1 = np.zeros([cutoff + 1], dtype=np.float64)
        kk = np.arange(k + 1)
        mu_red, V_red = reduced_gaussian(local_mu, cov, kk)

        if approx:
            Q = Qmat(V_red, hbar=hbar)
            A = Amat(Q, hbar=hbar, cov_is_qmat=True)

        for i in range(cutoff):
            indices = result + [i]
            ind2 = indices + indices
            if approx:
                factpref = np.prod(fac(indices))
                mat = reduction(A, ind2)
                probs1[i] = (
                    hafnian(np.abs(mat.real), approx=True, num_samples=approx_samples) / factpref
                )
            else:
                probs1[i] = density_matrix_element(
                    mu_red, V_red, indices, indices, include_prefactor=True, hbar=hbar
                ).real

        if approx:
            probs1 = probs1 / np.sqrt(np.linalg.det(Q).real)

        probs2 = probs1 / prev_prob
        probs3 = np.maximum(
            probs2, np.zeros_like(probs2)
        )  # pylint: disable=assignment-from-no-return
        ssum = np.sum(probs3)
        if ssum < 1.0:
            probs3[-1] = 1.0 - ssum

        # The following normalization of probabilities is needed when approx=True
        if approx:
            if ssum > 1.0:
                probs3 = probs3 / ssum

        result.append(np.random.choice(a=range(len(probs3)), p=probs3))
        if result[-1] == cutoff:
            return -1
        if sum(result) > max_photons:
            return -1
        prev_prob = probs1[result[-1]]

    return result


def _hafnian_sample(args):
    r"""Returns samples from the Hafnian of a Gaussian state.

    Note: this is a wrapper function, instead of using this function
    directly, please use either :func:`torontonian_sample_state` or
    :func:`torontonian_sample_graph`.

    Args:
        args (list): a list containing the following parameters:

            cov (array)
                a :math:`2N\times 2N` ``np.float64`` covariance matrix
                representing an :math:`N` mode quantum state. This can be obtained
                via the ``scovmavxp`` method of the Gaussian backend of Strawberry Fields.

            samples (int)
                the number of samples to return.

            mean (array): a :math:`2N`` ``np.float64`` vector of means representing the Gaussian
                state.

            hbar (float)
                the value of :math:`\hbar` in the commutation relation :math:`[\x,\p]=i\hbar`.

            cutoff (int)
                the Fock basis truncation.

            max_photons (int)
                specifies the maximum number of photons that can be counted.

            approx (bool)
                if ``True``, the approximate hafnian algorithm is used.
                Note that this can only be used for real, non-negative matrices.

            approx_samples (int)
                the number of samples used to approximate the hafnian if ``approx=True``.

    Returns:
        np.array[int]: photon number samples from the Gaussian state
    """
    cov, samples, mean, hbar, cutoff, max_photons, approx, approx_samples = args

    if not isinstance(cov, np.ndarray):
        raise TypeError("Covariance matrix must be a NumPy array.")

    matshape = cov.shape

    if matshape[0] != matshape[1]:
        raise ValueError("Covariance matrix must be square.")

    if np.isnan(cov).any():
        raise ValueError("Covariance matrix must not contain NaNs.")

    samples_array = []
    j = 0

    while j < samples:
        result = generate_hafnian_sample(
            cov,
            mean=mean,
            hbar=hbar,
            cutoff=cutoff,
            max_photons=max_photons,
            approx=approx,
            approx_samples=approx_samples,
        )

        if result != -1:
            # if result == -1, then you never get anything beyond cutoff
            samples_array.append(result)
            j = j + 1

    return np.vstack(samples_array)


def hafnian_sample_state(
    cov,
    samples,
    mean=None,
    hbar=2,
    cutoff=5,
    max_photons=30,
    approx=False,
    approx_samples=1e5,
    pool=False,
):
    r"""Returns samples from the Hafnian of a Gaussian state.

    Args:
        cov (array): a :math:`2N\times 2N` ``np.float64`` covariance matrix
            representing an :math:`N` mode quantum state. This can be obtained
            via the ``scovmavxp`` method of the Gaussian backend of Strawberry Fields.
        samples (int): the number of samples to return.
        mean (array): a :math:`2N`` ``np.float64`` vector of means representing the Gaussian
                state.
        hbar (float): (default 2) the value of :math:`\hbar` in the commutation
            relation :math:`[\x,\p]=i\hbar`.
        cutoff (int): the Fock basis truncation.
        max_photons (int): specifies the maximum number of photons that can be counted.
        approx (bool): if ``True``, the :func:`~.hafnian_approx` function is used
            to approximate the hafnian. Note that this can only be used for
            real, non-negative matrices.
        approx_samples: the number of samples used to approximate the hafnian if ``approx=True``.
        pool (bool): if ``True``, uses ``multiprocessor.Pool`` for parallelization of samples

    Returns:
        np.array[int]: photon number samples from the Gaussian state
    """
    if not pool:
        params = [cov, samples, mean, hbar, cutoff, max_photons, approx, approx_samples]
        return _hafnian_sample(params)

    pool = Pool()
    nprocs = multiprocessing.cpu_count()
    localsamps = samples // nprocs

    params = [[cov, localsamps, mean, hbar, cutoff, max_photons, approx, approx_samples]] * (nprocs - 1)
    params.append(
        [
            cov,
            samples - localsamps * (nprocs - 1),
            mean,
            hbar,
            cutoff,
            max_photons,
            approx,
            approx_samples,
        ]
    )

    result = np.vstack(pool.map(_hafnian_sample, params))
    pool.close()  # no more tasks
    pool.join()  # wrap up current tasks

    return result


def hafnian_sample_graph(
    A, n_mean, samples=10, cutoff=5, max_photons=30, approx=False, approx_samples=1e5, pool=False
):
    r"""Returns samples from the Gaussian state specified by the adjacency matrix :math:`A`
    and with total mean photon number :math:`n_{mean}`

    Args:
        A (array): a :math:`N\times N` ``np.float64`` (symmetric) adjacency matrix matrix
        n_mean (float): mean photon number of the Gaussian state
        samples (int): the number of samples to return.
        cutoff (int): the Fock basis truncation.
        max_photons (int): specifies the maximum number of photons that can be counted.
        approx (bool): if ``True``, the approximate hafnian algorithm is used.
            Note that this can only be used for real, non-negative matrices.
        approx_samples: the number of samples used to approximate the hafnian if ``approx=True``.
        pool (bool): if ``True``, uses ``multiprocessor.Pool`` for parallelization of samples

    Returns:
        np.array[int]: photon number samples from the Gaussian state
    """
    Q = gen_Qmat_from_graph(A, n_mean)
    cov = Covmat(Q)
    return hafnian_sample_state(
        cov,
        samples,
        mean=None,
        hbar=2,
        cutoff=cutoff,
        max_photons=max_photons,
        approx=approx,
        approx_samples=approx_samples,
        pool=pool,
    )


def seed(seed_val=None):
    r""" Seeds the random number generator used in the sampling algorithms.

    This function is a wrapper around ``numpy.random.seed()``. By setting the seed
    to a specific integer, the sampling algorithms will exhibit deterministic behaviour.

    Args:
        seed_val (int): Seed for RandomState. Must be convertible to 32 bit unsigned integers.
    """
    np.random.seed(seed_val)

/Users/ryuminseok/anaconda3/lib/python3.10/site-packages/numpy/linalg/linalg.py:2154: RuntimeWarning: divide by zero encountered in det
  r = _umath_linalg.det(a, signature=signature)
/Users/ryuminseok/anaconda3/lib/python3.10/site-packages/numpy/linalg/linalg.py:2154: RuntimeWarning: invalid value encountered in det
  r = _umath_linalg.det(a, signature=signature)
OMP: Info #276: omp_set_nested routine deprecated, please use omp_set_max_active_levels instead.
/Users/ryuminseok/anaconda3/lib/python3.10/site-packages/numpy/linalg/linalg.py:2154: RuntimeWarning: divide by zero encountered in det
  r = _umath_linalg.det(a, signature=signature)
/Users/ryuminseok/anaconda3/lib/python3.10/site-packages/numpy/linalg/linalg.py:2154: RuntimeWarning: invalid value encountered in det
  r = _umath_linalg.det(a, signature=signature)

import numpy as np
from thewalrus.samples import hafnian_sample_graph

matrix = np.array(
    [
        [1, 1, 1, 1, 1, 1, 0, 0, 0, 0],
        [1, 1, 1, 1, 1, 1, 0, 0, 0, 0],
        [1, 1, 1, 1, 1, 1, 0, 0, 0, 0],
        [1, 1, 1, 1, 1, 1, 0, 0, 1, 0],
        [1, 1, 1, 1, 1, 1, 0, 1, 0, 0],
        [1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
        [0, 0, 0, 0, 0, 1, 1, 0, 0, 0],
        [0, 0, 0, 0, 1, 0, 0, 1, 0, 0],
        [0, 0, 0, 1, 0, 0, 0, 0, 1, 1],
        [0, 0, 0, 0, 0, 0, 0, 0, 1, 1],
    ]
) - np.eye(10)

s = hafnian_sample_graph(matrix, 6, samples=10)
print(s)