# Source code for deltasigma._bquantize

# -*- coding: utf-8 -*-
# _bquantize.py
# Bipolar quantization module
# This file is part of python-deltasigma.
#
# python-deltasigma is a 1:1 Python replacement of Richard Schreier's
# MATLAB delta sigma toolbox (aka "delsigma"), upon which it is heavily based.
# The delta sigma toolbox is (c) 2009, Richard Schreier.
#
# python-deltasigma is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# LICENSE file for the licensing terms.

"""This module provides the bquantize() function, used to bidirectionally
quantize a vector to signed digits.
"""

from __future__ import division, print_function

import numpy as np

from ._constants import eps
from ._utils import empty, mfloor

[docs]def bquantize(x, nsd=3, abstol=eps, reltol=10 * eps): """Bidirectionally quantize a 1D vector x to nsd signed digits. This method will terminate early if the error is less than the specified tolerances. The quantizer details are repeated here for the user's convenience: The quantizer is ideal, producing integer outputs centered about zero. Quantizers with an even number of levels are of the mid-rise type and produce outputs which are odd integers. Quantizers with an odd number of levels are of the mid-tread type and produce outputs which are even integers. .. image:: ../doc/_static/quantizer_model.png :align: center :alt: Quantizer model **Parameters:** x : array_like or sequence the data to be quantized. nsd : int, optional The number of signed digits. abstol and reltol : floats, optional If not supplied, the absolute tolerance and the relative tolerance default to eps and 10*eps, resp. **Returns:** y : list List of objects described below. y is a list of instances with the same length as x and the following attributes: * y[i].val is the quantized value in floating-point form, * y[i].csd is a 2-by-nsd (or less) matrix containing the powers of two (first row) and their signs (second row). .. seealso:: :func:bunquantize, :func:ds_quantize """ n = x.shape[0] if isinstance(x, np.ndarray) else len(x) #q = np.zeros((2*n, nsd)) in the original source #rep? y = [empty() for i in range(n)] offset = -np.log2(0.75) for i in range(n): xp = x[i] y[i].val = 0. y[i].csd = np.zeros((2, 0), dtype='int16') for _ in range(nsd): error = np.abs(y[i].val - x[i]) if error <= abstol and error <= np.abs(x[i]) * reltol: # rep? in the orig: or break p = mfloor(np.log2(np.abs(xp)) + offset) p2 = 2 ** p sx = np.sign(xp) xp = xp - sx * p2 y[i].val = y[i].val + sx * p2 addme = np.array((p, sx)).reshape((2, 1)) y[i].csd = np.concatenate((y[i].csd, addme), axis=1) return y