Source code for botmpy.common.matrix_ops

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# Copyright (c) 2012-2013, Berlin Institute of Technology
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# Developed by:	Philipp Meier <pmeier82@gmail.com>
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#               Neural Information Processing Group (NI)
#               School for Electrical Engineering and Computer Science
#               Berlin Institute of Technology
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#   Philipp Meier <pmeier82@gmail.com>
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# Changelog:
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"""matrix operations"""
__docformat__ = 'restructuredtext'
__all__ = ['matrix_cond', 'diagonal_loading', 'coloured_loading',
           'matrix_argmax', 'matrix_argmin']

# TODO: should we enforce square matrices for all ops?

## IMPORTS

import scipy as sp
from scipy import linalg as sp_la

## CONSTANTS

SUFFICIENT_CONDITION = 50

## FUNCTIONS

def matrix_pos_def(mat):
    """checks if the matrix is positive definite

    :type mat: ndarray
    :param mat: input matrix
    :returns: True if p.d., False else
    """

    mat = sp.atleast_2d(mat)
    if mat.ndim != 2:
        raise ValueError('expected matrix')
    if mat.size == 0:
        raise ValueError('undefined for empty matrix')
    try:
        sv = sp_la.svd(mat, compute_uv=False)
        return sp.all(sv > 0.0)
    except:
        return False


[docs]def matrix_cond(mat): """yield the matrix condition number w.r.t. l2-norm (using svd) :type mat: ndarray :param mat: input matrix :returns: float - condition number of :mat: or :inf: on error """ mat = sp.atleast_2d(mat) if mat.ndim != 2: raise ValueError('expected matrix') if mat.size == 0: raise ValueError('undefined for empty matrix') try: sv = sp_la.svd(mat, compute_uv=False) return compute_matrix_cond(sv) except: return sp.inf
def compute_matrix_cond(sv): """yield matrix condition number w.r.t. l2-norm given singular values :type sv: ndarray :param sv: vector of singular values sorted s.t. :sv[i]: >= :sv[i+1]: :returns: float - condition number of :mat: or :inf: on error """ sv = sp.atleast_1d(sv) if sv.size == 0: raise ValueError('undefined for empty list') try: return sp.absolute(sv[0] / sv[-1]) except: return sp.inf
[docs]def diagonal_loading(mat, target_cond=SUFFICIENT_CONDITION, overwrite_mat=False): """tries to condition the :mat: by imposing a spherical constraint on the covariance ellipsoid (adding alpha*eye) solves: cond(mat + alpha*I) = target_cond for alpha Note: this is a noop if the condition is already >= target_cond! :type mat: ndarray :param mat: input matrix :type target_cond: float :param target_cond: condition number to archive after loading :type overwrite_mat: bool :param overwrite_mat: if True, operate inplace and overwrite :mat: :returns: ndarray - matrix like :mat: conditioned s.t. cond = target_cond """ mat = sp.atleast_2d(mat) if mat.size == 0: raise ValueError('undefined for empty matrix') svd = sp_la.svd(mat) return compute_diagonal_loading(mat, svd, target_cond, overwrite_mat)
def compute_diagonal_loading(mat, svd, target_cond=SUFFICIENT_CONDITION, overwrite_mat=False): """tries to condition :mat: by imposing a spherical constraint on the covariance ellipsoid (adding alpha*eye) solves: cond(mat + alpha*I) = target_cond for alpha Note: this is a noop if the condition is already >= target_cond! :type mat: ndarray :param mat: input matrix :type svd: tuple :param svd: return tuple of svd(:mat:) - consistency will not be checked! :type target_cond: float :param target_cond: condition number to archive after loading :type overwrite_mat: bool :param overwrite_mat: if True, operate inplace and overwrite :mat: :returns: ndarray - matrix like :mat: conditioned s.t. cond = target_cond """ sv = svd[1] if target_cond == 1.0: return sp.eye(mat.shape[0], mat.shape[1]) if target_cond > compute_matrix_cond(sv): return mat if overwrite_mat is True: rval = mat else: rval = mat.copy() alpha = (sv[0] - target_cond * sv[-1]) / (target_cond - 1) return rval + alpha * sp.eye(rval.shape[0], rval.shape[1])
[docs]def coloured_loading(mat, target_cond=SUFFICIENT_CONDITION, overwrite_mat=False): """tries to condition :mat: by inflating the badly conditioned subspace of :mat: using a spherical constraint. :type mat: ndarray :param mat: input matrix :type target_cond: float :param target_cond: condition number to archive after loading :type overwrite_mat: bool :param overwrite_mat: if True, operate inplace and overwrite :mat: :returns: ndarray - matrix like :mat: conditioned s.t. cond = target_cond """ mat = sp.atleast_2d(mat) if mat.size == 0: raise ValueError('undefined for empty matrix') svd = sp_la.svd(mat) return compute_coloured_loading(mat, svd, target_cond, overwrite_mat)
def compute_coloured_loading(mat, svd, target_cond=SUFFICIENT_CONDITION, overwrite_mat=False): """tries to condition :mat: by inflating the badly conditioned subspace of :mat: using a spherical constraint. :type mat: ndarray :param mat: input matrix :type svd: tuple :param svd: return tuple of svd(:mat:) - consistency will not be checked! :type target_cond: float :param target_cond: condition number to archive after loading :type overwrite_mat: bool :param overwrite_mat: if True, operate inplace and overwrite :mat: :returns: ndarray - matrix like :mat: conditioned s.t. cond = target_cond """ U, sv = svd[0], svd[1] if target_cond == 1.0: return sp.eye(mat.shape[0]) if target_cond > compute_matrix_cond(sv): return mat if overwrite_mat is True: rval = mat else: rval = mat.copy() min_s = sv[0] / target_cond for i in xrange(sv.size): col_idx = -1 - i if sv[col_idx] < min_s: alpha = min_s - sv[col_idx] rval += alpha * sp.outer(U[:, col_idx], U[:, col_idx]) return rval
[docs]def matrix_argmax(mat): """returns the indices (row,col) of the maximum value in :mat: :type mat: ndarray :param mat: input matrix :returns: tuple - (row,col) of the maximum value in :mat: """ idx = sp.nanargmax(mat) j = int(idx % mat.shape[1]) i = int(sp.floor(idx / mat.shape[1])) return i, j # XXX # DO NOT USE THIS VERSION; SINCE IT DOES NOT WORK IF THE EXTREMUM IS NOT # UNIQUE! # fout = [] # for i in reversed(xrange(mat.ndim)): # fout.append(mat.max(axis=i).argmax()) # return tuple(fout)
[docs]def matrix_argmin(mat): """returns the indices (row,col) of the minimum value in :mat: :type mat: ndarray :param mat: input matrix :returns: tuple - (row,col) of the minimum value in :mat: """ idx = sp.nanargmin(mat) j = int(idx % mat.shape[1]) i = int(sp.floor(idx / mat.shape[1])) return i, j # XXX # DO NOT USE THIS VERSION; SINCE IT DOES NOT WORK IF THE EXTREMUM IS NOT # UNIQUE! # fout = [] # for i in reversed(xrange(mat.ndim)): # fout.append(mat.min(axis=i).argmin()) # return tuple(fout) ## MAIN
if __name__ == '__main__': pass

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