# pyerrors.mpm

View Source

    import numpy as np
    import scipy.linalg
    from .obs import Obs
    from .linalg import svd, eig

    def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
        """Matrix pencil method to extract k energy levels from data

        Implementation of the matrix pencil method based on
        eq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

        Parameters
        ----------
        data : list
            can be a list of Obs for the analysis of a single correlator, or a list of lists
            of Obs if several correlators are to analyzed at once.
        k : int
            Number of states to extract (default 1).
        p : int
            matrix pencil parameter which filters noise. The optimal value is expected between
            len(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is
            to len(data)/2 but could possibly suppress more noise (default len(data)//2).
        """
        if isinstance(corrs[0], Obs):
            data = [corrs]
        else:
            data = corrs

        lengths = [len(d) for d in data]
        if lengths.count(lengths[0]) != len(lengths):
            raise Exception('All datasets have to have the same length.')

        data_sets = len(data)
        n_data = len(data[0])

        if p is None:
            p = max(n_data // 2, k)
        if n_data <= p:
            raise Exception('The pencil p has to be smaller than the number of data samples.')
        if p < k or n_data - p < k:
            raise Exception('Cannot extract', k, 'energy levels with p=', p, 'and N-p=', n_data - p)

        # Construct the hankel matrices
        matrix = []
        for n in range(data_sets):
            matrix.append(scipy.linalg.hankel(data[n][:n_data - p], data[n][n_data - p - 1:]))
        matrix = np.array(matrix)
        # Construct y1 and y2
        y1 = np.concatenate(matrix[:, :, :p])
        y2 = np.concatenate(matrix[:, :, 1:])
        # Apply SVD to y2
        u, s, vh = svd(y2, **kwargs)
        # Construct z from y1 and SVD of y2, setting all singular values beyond the kth to zero
        z = np.diag(1. / s[:k]) @ u[:, :k].T @ y1 @ vh.T[:, :k]
        # Return the sorted logarithms of the real eigenvalues as Obs
        energy_levels = np.log(np.abs(eig(z, **kwargs)))
        return sorted(energy_levels, key=lambda x: abs(x.value))

def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
View Source

    def matrix_pencil_method(corrs, k=1, p=None, **kwargs):
        """Matrix pencil method to extract k energy levels from data

        Implementation of the matrix pencil method based on
        eq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

        Parameters
        ----------
        data : list
            can be a list of Obs for the analysis of a single correlator, or a list of lists
            of Obs if several correlators are to analyzed at once.
        k : int
            Number of states to extract (default 1).
        p : int
            matrix pencil parameter which filters noise. The optimal value is expected between
            len(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is
            to len(data)/2 but could possibly suppress more noise (default len(data)//2).
        """
        if isinstance(corrs[0], Obs):
            data = [corrs]
        else:
            data = corrs

        lengths = [len(d) for d in data]
        if lengths.count(lengths[0]) != len(lengths):
            raise Exception('All datasets have to have the same length.')

        data_sets = len(data)
        n_data = len(data[0])

        if p is None:
            p = max(n_data // 2, k)
        if n_data <= p:
            raise Exception('The pencil p has to be smaller than the number of data samples.')
        if p < k or n_data - p < k:
            raise Exception('Cannot extract', k, 'energy levels with p=', p, 'and N-p=', n_data - p)

        # Construct the hankel matrices
        matrix = []
        for n in range(data_sets):
            matrix.append(scipy.linalg.hankel(data[n][:n_data - p], data[n][n_data - p - 1:]))
        matrix = np.array(matrix)
        # Construct y1 and y2
        y1 = np.concatenate(matrix[:, :, :p])
        y2 = np.concatenate(matrix[:, :, 1:])
        # Apply SVD to y2
        u, s, vh = svd(y2, **kwargs)
        # Construct z from y1 and SVD of y2, setting all singular values beyond the kth to zero
        z = np.diag(1. / s[:k]) @ u[:, :k].T @ y1 @ vh.T[:, :k]
        # Return the sorted logarithms of the real eigenvalues as Obs
        energy_levels = np.log(np.abs(eig(z, **kwargs)))
        return sorted(energy_levels, key=lambda x: abs(x.value))

Matrix pencil method to extract k energy levels from data

Implementation of the matrix pencil method based on eq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

###### Parameters

- data (list): can be a list of Obs for the analysis of a single correlator, or a list of lists of Obs if several correlators are to analyzed at once.
- k (int): Number of states to extract (default 1).
- p (int): matrix pencil parameter which filters noise. The optimal value is expected between len(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is to len(data)/2 but could possibly suppress more noise (default len(data)//2).