Instruction:
Explain what the following Python 3 code does
def flatten_hierarchical_dict(original_dict, separator='.', max_recursion_depth=None):
    if max_recursion_depth is not None and max_recursion_depth <= 0:
        # we reached the maximum recursion depth, refuse to go further
        return original_dict
    if max_recursion_depth is None:
        next_recursion_depth = None
    else:
        next_recursion_depth = max_recursion_depth - 1
    dict1 = {}
    for k in original_dict:
        if not isinstance(original_dict[k], dict):
            dict1[k] = original_dict[k]
        else:
            dict_recursed = flatten_hierarchical_dict(
                original_dict[k], separator, next_recursion_depth)
            dict1.update(
                dict([(k + separator + x, dict_recursed[x]) for x in dict_recursed]))
    return dict1

Response: Flatten a dictionary of hierarchical items.


Instruction:
How would you implement a function in Python 3 that
returns a random string of Nchars characters. Characters are sampled from randstrbase.

Response:
def random_str(Nchars=6, randstrbase='0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'):
    """Return a random string of <Nchars> characters. Characters are sampled
    uniformly from <randstrbase>.
    """
    return ''.join([randstrbase[random.randint(0, len(randstrbase) - 1)] for i in range(Nchars)])


Instruction:
Can you generate a brief explanation for the following Python 3 code
def listB1(fsns, xlsname, dirs, whattolist = None, headerformat = 'org_%05d.header'):
    if whattolist is None:
        whattolist = [('FSN', 'FSN'), ('Time', 'MeasTime'), ('Energy', 'Energy'),
                    ('Distance', 'Dist'), ('Position', 'PosSample'),
                    ('Transmission', 'Transm'), ('Temperature', 'Temperature'),
                    ('Title', 'Title'), ('Date', ('Day', 'Month', 'Year', 'Hour', 'Minutes'), '%02d.%02d.%04d %02d:%02d')]
    wb = xlwt.Workbook(encoding = 'utf8')
    ws = wb.add_sheet('Measurements')
    for i in range(len(whattolist)):
        ws.write(0, i, whattolist[i][0])
    i = 1
    for fsn in fsns:
        try:
            hed = readB1header(findfileindirs(headerformat % fsn, dirs))
        except IOError:
            continue
        # for each param structure create a line in the table
        for j in range(len(whattolist)):
            # for each parameter to be listed, create a column
            if np.isscalar(whattolist[j][1]):
                # if the parameter is a scalar, make it a list
                fields = tuple([whattolist[j][1]])
            else:
                fields = whattolist[j][1]
            if len(whattolist[j]) == 2:
                if len(fields) >= 2:
                    strtowrite = ''.join([str(hed[f]) for f in fields])
                else:
                    strtowrite = hed[fields[0]]
            elif len(whattolist[j]) >= 3:
                strtowrite = whattolist[j][2] % tuple([hed[f] for f in fields])
            else:
                assert False
            ws.write(i, j, strtowrite)
        i += 1
    wb.save(xlsname)

Response: This function lists the contents of a single file in a single cell.


Instruction:
Given the following Python 3 function, write the documentation
def fit_shullroess(q, Intensity, Error, R0=None, r=None):
    q = np.array(q)
    Intensity = np.array(Intensity)
    Error = np.array(Error)
    if R0 is None:
        r0s = np.linspace(1, 2 * np.pi / q.min(), 1000)
        def naive_fit_chi2(q, Intensity, r0):
            p = np.polyfit(np.log(q ** 2 + 3 / r0 ** 2), np.log(Intensity), 1)
            return ((np.polyval(p, q) - Intensity) ** 2).sum() / (len(q) - 3)
        chi2 = np.array([naive_fit_chi2(q, Intensity, r0) for r0 in r0s.tolist()])
        R0 = r0s[chi2 == chi2.min()][0]
    def naive_fit(q, Intensity, r0):
        p = np.polyfit(np.log(q ** 2 + 3 / r0 ** 2), np.log(Intensity), 1)
        return np.exp(p[1]), -2 * p[0] - 4
    K, n = naive_fit(q, Intensity, R0)
    def SR_function(q, A, r0, n):
        return A * (q ** 2 + 3 / r0 ** 2) ** (-(n + 4.) * 0.5)
    p, dp, statdict = easylsq.nlsq_fit(q, Intensity, Error, SR_function, (K, R0, n))
    n = ErrorValue(p[2], dp[2])
    r0 = ErrorValue(p[1], dp[1])
    A = ErrorValue(p[0], dp[0])
    if r is None:
        r = np.linspace(np.pi / q.max(), np.pi / q.min(), 1000)
    return A, r0, n, r, maxwellian(r, r0, n), statdict

Response: This function is used to fit a single object in a set of objects.


Instruction:
Here you have a function in Python 3, explain what it does
def maxwellian(r, r0, n):
    r0 = ErrorValue(r0)
    n = ErrorValue(n)

    expterm = np.exp(-r ** 2 / r0.val ** 2)
    dmaxdr0 = -2 * r ** n.val * r0.val ** (-n.val - 4) * ((n.val + 1) * r0.val ** 2 - 2 * r ** 2) * expterm / gamma((n.val + 1) * 0.5)
    dmaxdn = -r ** n.val * r0.val ** (-n.val - 1) * expterm * (2 * np.log(r0.val) - 2 * np.log(r) + psi((n.val + 1) * 0.5)) / gamma((n.val + 1) * 0.5)

    maxwellian = 2 * r ** n.val * r0.val ** (-n.val - 1) * expterm / gamma((n.val + 1) * 0.5)
    dmaxwellian = (dmaxdn ** 2 * n.err ** 2 + dmaxdr0 ** 2 * r0.err ** 2) ** 0.5
    return ErrorValue(maxwellian, dmaxwellian)

Response: Maxwellian - like distribution of spherical particles in a single species.


Instruction:
Make a summary of the following Python 3 code
def findfileindirs(filename, dirs=None, use_pythonpath=True, use_searchpath=True, notfound_is_fatal=True, notfound_val=None):
    if os.path.isabs(filename):
        if os.path.exists(filename):
            return filename
        elif notfound_is_fatal:
            raise IOError('File ' + filename + ' not found.')
        else:
            return notfound_val
    if dirs is None:
        dirs = []
    dirs = normalize_listargument(dirs)
    if not dirs:  # dirs is empty
        dirs = ['.']
    if use_pythonpath:
        dirs.extend(sys.path)
    if use_searchpath:
        dirs.extend(sastool_search_path)
    # expand ~ and ~user constructs
    dirs = [os.path.expanduser(d) for d in dirs]
    logger.debug('Searching for file %s in several folders: %s' % (filename, ', '.join(dirs)))
    for d in dirs:
        if os.path.exists(os.path.join(d, filename)):
            logger.debug('Found file %s in folder %s.' % (filename, d))
            return os.path.join(d, filename)
    logger.debug('Not found file %s in any folders.' % filename)
    if notfound_is_fatal:
        raise IOError('File %s not found in any of the directories.' % filename)
    else:
        return notfound_val

Response: Find file in multiple directories.


Instruction:
How would you implement a function in Python 3 that
calculates the two - theta matrix for a scattering matrix.

Response:
def twotheta(matrix, bcx, bcy, pixsizeperdist):
    """Calculate the two-theta matrix for a scattering matrix

    Inputs:
        matrix: only the shape of it is needed
        bcx, bcy: beam position (counting from 0; x is row, y is column index)
        pixsizeperdist: the pixel size divided by the sample-to-detector
            distance

    Outputs:
        the two theta matrix, same shape as 'matrix'.
    """
    col, row = np.meshgrid(list(range(matrix.shape[1])), list(range(matrix.shape[0])))
    return np.arctan(np.sqrt((row - bcx) ** 2 + (col - bcy) ** 2) * pixsizeperdist)


Instruction:
Make a summary of the following Python 3 code
def angledependentabsorption(twotheta, transmission):
    cor = np.ones(twotheta.shape)
    if transmission == 1:
        return cor
    mud = -np.log(transmission)

    cor[twotheta > 0] = transmission * mud * (1 - 1 / np.cos(twotheta[twotheta > 0])) / (np.exp(-mud / np.cos(twotheta[twotheta > 0])) - np.exp(-mud))
    return cor

Response:
Correction for angle - dependent absorption of the sample
Taxonomy


Instruction:
Can you generate the documentation for the following Python 3 function
def find_file(self, filename: str, strip_path: bool = True, what='exposure') -> str:
        if what == 'exposure':
            path = self._path
        elif what == 'header':
            path = self._headerpath
        elif what == 'mask':
            path = self._maskpath
        else:
            path = self._path
        tried = []
        if strip_path:
            filename = os.path.split(filename)[-1]
        for d in path:
            if os.path.exists(os.path.join(d, filename)):
                tried.append(os.path.join(d, filename))
                return os.path.join(d, filename)
        raise FileNotFoundError('Not found: {}. Tried: {}'.format(filename, ', '.join(tried)))

Response: Find the file in the path


Instruction:
Can you implement a function in Python 3 that
searches a file or directory relative to the base path

Response:
def get_subpath(self, subpath: str):
        """Search a file or directory relative to the base path"""
        for d in self._path:
            if os.path.exists(os.path.join(d, subpath)):
                return os.path.join(d, subpath)
        raise FileNotFoundError


Instruction:
Write a Python 3 script for
loading an exposure from a file.

Response:
def new_from_file(self, filename: str, header_data: Optional[Header] = None,
                      mask_data: Optional[np.ndarray] = None):
        """Load an exposure from a file."""


Instruction:
Write a Python 3 function that can
calculate the sum of pixels not counting the masked ones.

Response:
def sum(self, only_valid=True) -> ErrorValue:
        """Calculate the sum of pixels, not counting the masked ones if only_valid is True."""
        if not only_valid:
            mask = 1
        else:
            mask = self.mask
        return ErrorValue((self.intensity * mask).sum(),
                          ((self.error * mask) ** 2).sum() ** 0.5)


Instruction:
How would you explain what the following Python 3 function does
def mean(self, only_valid=True) -> ErrorValue:
        if not only_valid:
            intensity = self.intensity
            error = self.error
        else:
            intensity = self.intensity[self.mask]
            error = self.error[self.mask]
        return ErrorValue(intensity.mean(),
                          (error ** 2).mean() ** 0.5)

Response: Calculate the mean of the pixels not counting the masked ones.


Instruction:
How would you implement a function in Python 3 that
calculates the two - theta array

Response:
def twotheta(self) -> ErrorValue:
        """Calculate the two-theta array"""
        row, column = np.ogrid[0:self.shape[0], 0:self.shape[1]]
        rho = (((self.header.beamcentery - row) * self.header.pixelsizey) ** 2 +
               ((self.header.beamcenterx - column) * self.header.pixelsizex) ** 2) ** 0.5
        assert isinstance(self.header.pixelsizex, ErrorValue)
        assert isinstance(self.header.pixelsizey, ErrorValue)
        assert isinstance(rho, ErrorValue)
        return (rho / self.header.distance).arctan()


Instruction:
Given the following Python 3 function, write the documentation
def pixel_to_q(self, row: float, column: float):
        qrow = 4 * np.pi * np.sin(
            0.5 * np.arctan(
                (row - float(self.header.beamcentery)) *
                float(self.header.pixelsizey) /
                float(self.header.distance))) / float(self.header.wavelength)
        qcol = 4 * np.pi * np.sin(0.5 * np.arctan(
                (column - float(self.header.beamcenterx)) *
                float(self.header.pixelsizex) /
                float(self.header.distance))) / float(self.header.wavelength)
        return qrow, qcol

Response: Return the q coordinates of a given pixel.


Instruction:
Write a Python 3 script for
plotting the image of the current state of the object.

Response:
def imshow(self, *args, show_crosshair=True, show_mask=True,
               show_qscale=True, axes=None, invalid_color='black',
               mask_opacity=0.8, show_colorbar=True, **kwargs):
        """Plot the matrix (imshow)

        Keyword arguments [and their default values]:

        show_crosshair [True]: if a cross-hair marking the beam position is
            to be plotted.
        show_mask [True]: if the mask is to be plotted.
        show_qscale [True]: if the horizontal and vertical axes are to be
            scaled into q
        axes [None]: the axes into which the image should be plotted. If
            None, defaults to the currently active axes (returned by plt.gca())
        invalid_color ['black']: the color for invalid (NaN or infinite) pixels
        mask_opacity [0.8]: the opacity of the overlaid mask (1 is fully
            opaque, 0 is fully transparent)
        show_colorbar [True]: if a colorbar is to be added. Can be a boolean
            value (True or False) or an instance of matplotlib.axes.Axes, into
            which the color bar should be drawn.

        All other keywords are forwarded to plt.imshow() or
            matplotlib.Axes.imshow()

        Returns: the image instance returned by imshow()
        """
        if 'aspect' not in kwargs:
            kwargs['aspect'] = 'equal'
        if 'interpolation' not in kwargs:
            kwargs['interpolation'] = 'nearest'
        if 'origin' not in kwargs:
            kwargs['origin'] = 'upper'
        if show_qscale:
            ymin, xmin = self.pixel_to_q(0, 0)
            ymax, xmax = self.pixel_to_q(*self.shape)
            if kwargs['origin'].upper() == 'UPPER':
                kwargs['extent'] = [xmin, xmax, -ymax, -ymin]
            else:
                kwargs['extent'] = [xmin, xmax, ymin, ymax]
            bcx = 0
            bcy = 0
        else:
            bcx = self.header.beamcenterx
            bcy = self.header.beamcentery
            xmin = 0
            xmax = self.shape[1]
            ymin = 0
            ymax = self.shape[0]
            if kwargs['origin'].upper() == 'UPPER':
                kwargs['extent'] = [0, self.shape[1], self.shape[0], 0]
            else:
                kwargs['extent'] = [0, self.shape[1], 0, self.shape[0]]
        if axes is None:
            axes = plt.gca()
        ret = axes.imshow(self.intensity, **kwargs)
        if show_mask:
            # workaround: because of the colour-scaling we do here, full one and
            #   full zero masks look the SAME, i.e. all the image is shaded.
            #   Thus if we have a fully unmasked matrix, skip this section.
            #   This also conserves memory.
            if (self.mask == 0).sum():  # there are some masked pixels
                # we construct another representation of the mask, where the masked pixels are 1.0, and the
                # unmasked ones will be np.nan. They will thus be not rendered.
                mf = np.ones(self.mask.shape, np.float)
                mf[self.mask != 0] = np.nan
                kwargs['cmap'] = matplotlib.cm.gray_r
                kwargs['alpha'] = mask_opacity
                kwargs['norm'] = matplotlib.colors.Normalize()
                axes.imshow(mf, **kwargs)
        if show_crosshair:
            ax = axes.axis()  # save zoom state
            axes.plot([xmin, xmax], [bcy] * 2, 'w-')
            axes.plot([bcx] * 2, [ymin, ymax], 'w-')
            axes.axis(ax)  # restore zoom state
        axes.set_facecolor(invalid_color)
        if show_colorbar:
            if isinstance(show_colorbar, matplotlib.axes.Axes):
                axes.figure.colorbar(
                        ret, cax=show_colorbar)
            else:
                # try to find a suitable colorbar axes: check if the plot target axes already
                # contains some images, then check if their colorbars exist as
                # axes.
                cax = [i.colorbar[1]
                       for i in axes.images if i.colorbar is not None]
                cax = [c for c in cax if c in c.figure.axes]
                if cax:
                    cax = cax[0]
                else:
                    cax = None
                axes.figure.colorbar(ret, cax=cax, ax=axes)
        axes.figure.canvas.draw()
        return ret


Instruction:
Make a summary of the following Python 3 code
def radial_average(self, qrange=None, pixel=False, returnmask=False,
                       errorpropagation=3, abscissa_errorpropagation=3,
                       raw_result=False) -> Curve:
        """Do a radial averaging

        Inputs:
            qrange: the q-range. If None, auto-determine. If 'linear', auto-determine
                with linear spacing (same as None). If 'log', auto-determine
                with log10 spacing.
            pixel: do a pixel-integration (instead of q)
            returnmask: if the effective mask matrix is to be returned.
            errorpropagation: the type of error propagation (3: highest of squared or
                std-dev, 2: squared, 1: linear, 0: independent measurements of
                the same quantity)
            abscissa_errorpropagation: the type of the error propagation in the
                abscissa (3: highest of squared or std-dev, 2: squared, 1: linear,
                0: independent measurements of the same quantity)
            raw_result: if True, do not pack the result in a SASCurve, return the
                individual np.ndarrays.

        Outputs:
            the one-dimensional curve as an instance of SASCurve (if pixel is
                False) or SASPixelCurve (if pixel is True), if raw_result was True.
                otherwise the q (or pixel), dq (or dpixel), I, dI, area vectors
            the mask matrix (if returnmask was True)
        """
        retmask = None
        if isinstance(qrange, str):
            if qrange == 'linear':
                qrange = None
                autoqrange_linear = True
            elif qrange == 'log':
                qrange = None
                autoqrange_linear = False
            else:
                raise ValueError(
                        'Value given for qrange (''%s'') not understood.' % qrange)
        else:
            autoqrange_linear = True  # whatever
        if pixel:
            abscissa_kind = 3
        else:
            abscissa_kind = 0
        res = radint_fullq_errorprop(self.intensity, self.error, self.header.wavelength.val,
                                     self.header.wavelength.err, self.header.distance.val,
                                     self.header.distance.err, self.header.pixelsizey.val,
                                     self.header.pixelsizex.val, self.header.beamcentery.val,
                                     self.header.beamcentery.err, self.header.beamcenterx.val,
                                     self.header.beamcenterx.err, (self.mask == 0).astype(np.uint8),
                                     qrange, returnmask=returnmask, errorpropagation=errorpropagation,
                                     autoqrange_linear=autoqrange_linear, abscissa_kind=abscissa_kind,
                                     abscissa_errorpropagation=abscissa_errorpropagation)
        q, dq, I, E, area = res[:5]
        if not raw_result:
            c = Curve(q, I, E, dq)
            if returnmask:
                return c, res[5]
            else:
                return c
        else:
            if returnmask:
                return q, dq, I, E, area, res[5]
            else:
                return q, dq, I, E, area

Response: This function performs a radial averaging of the current state of the object.


Instruction:
How would you explain what the following Python 3 function does
def mask_negative(self):
        self.mask = np.logical_and(self.mask, ~(self.intensity < 0))

Response: Extend the mask with the image elements where the intensity is negative.


Instruction:
How would you implement a function in Python 3 that
extends the mask with the image elements where the intensity is NaN.

Response:
def mask_nan(self):
        """Extend the mask with the image elements where the intensity is NaN."""
        self.mask = np.logical_and(self.mask, ~(np.isnan(self.intensity)))


Instruction:
Write a Python 3 function that can
extend the mask with the image elements where the intensity is NaN.

Response:
def mask_nonfinite(self):
        """Extend the mask with the image elements where the intensity is NaN."""
        self.mask = np.logical_and(self.mask, (np.isfinite(self.intensity)))


Instruction:
Create a Python 3 function to
sample - to - detector distance

Response:
def distance(self) -> ErrorValue:
        """Sample-to-detector distance"""
        if 'DistCalibrated' in self._data:
            dist = self._data['DistCalibrated']
        else:
            dist = self._data["Dist"]
        if 'DistCalibratedError' in self._data:
            disterr = self._data['DistCalibratedError']
        elif 'DistError' in self._data:
            disterr = self._data['DistError']
        else:
            disterr = 0.0
        return ErrorValue(dist, disterr)


Instruction:
Can you implement a function in Python 3 that
dates of the experiment

Response:
def date(self) -> datetime.datetime:
        """Date of the experiment (start of exposure)"""
        return self._data['Date'] - datetime.timedelta(0, float(self.exposuretime), 0)


Instruction:
Create a Python 3 function to
return the flux in photons.

Response:
def flux(self) -> ErrorValue:
        """X-ray flux in photons/sec."""
        try:
            return ErrorValue(self._data['Flux'], self._data.setdefault('FluxError',0.0))
        except KeyError:
            return 1 / self.pixelsizex / self.pixelsizey / ErrorValue(self._data['NormFactor'],
                                                                      self._data.setdefault('NormFactorError',0.0))


Instruction:
Given the following Python 3 function, write the documentation
def nonlinear_leastsquares(x: np.ndarray, y: np.ndarray, dy: np.ndarray, func: Callable, params_init: np.ndarray,
                           verbose: bool = False, **kwargs):
    """Perform a non-linear least squares fit, return the results as
    ErrorValue() instances.

    Inputs:
        x: one-dimensional numpy array of the independent variable
        y: one-dimensional numpy array of the dependent variable
        dy: absolute error (square root of the variance) of the dependent
            variable. Either a one-dimensional numpy array or None. In the array
            case, if any of its elements is NaN, the whole array is treated as
            NaN (= no weighting)
        func: a callable with the signature
            func(x,par1,par2,par3,...)
        params_init: list or tuple of the first estimates of the
            parameters par1, par2, par3 etc. to be fitted
        `verbose`: if various messages useful for debugging should be printed on
            stdout.

        other optional keyword arguments will be passed to leastsq().

    Outputs: par1, par2, par3, ... , statdict
        par1, par2, par3, ...: fitted values of par1, par2, par3 etc
            as instances of ErrorValue.
        statdict: dictionary of various statistical parameters:
            'DoF': Degrees of freedom
            'Chi2': Chi-squared
            'Chi2_reduced': Reduced Chi-squared
            'R2': Coefficient of determination
            'num_func_eval': number of function evaluations during fit.
            'func_value': the function evaluated in the best fitting parameters
            'message': status message from leastsq()
            'error_flag': integer status flag from leastsq() ('ier')
            'Covariance': covariance matrix (variances in the diagonal)
            'Correlation_coeffs': Pearson's correlation coefficients (usually
                denoted by 'r') in a matrix. The diagonal is unity.

    Notes:
        for the actual fitting, nlsq_fit() is used, which in turn delegates the
            job to scipy.optimize.leastsq().
    """
    newfunc, newparinit = hide_fixedparams(func, params_init)
    p, dp, statdict = nlsq_fit(x, y, dy, newfunc, newparinit, verbose, **kwargs)
    p, statdict['Covariance'] = resubstitute_fixedparams(p, params_init, statdict['Covariance'])
    dp, statdict['Correlation_coeffs'] = resubstitute_fixedparams(dp, [type(p_)(0) for p_ in params_init], statdict['Correlation_coeffs'])
    def convert(p_, dp_):
        if isinstance(p_, FixedParameter) or isinstance(dp_, FixedParameter):
            return p_
        else:
            return ErrorValue(p_, dp_)
    return tuple([convert(p_, dp_) for (p_, dp_) in zip(p, dp)] + [statdict])

Response: This function is used to fit a nonlinear least squares problem.


Instruction:
Can you create a Python 3 function that
performs a non - linear orthogonal distance regression on the given set of elements.

Response:
def nonlinear_odr(x, y, dx, dy, func, params_init, **kwargs):
    """Perform a non-linear orthogonal distance regression, return the results as
    ErrorValue() instances.

    Inputs:
        x: one-dimensional numpy array of the independent variable
        y: one-dimensional numpy array of the dependent variable
        dx: absolute error (square root of the variance) of the independent
            variable. Either a one-dimensional numpy array or None. If None,
            weighting is disabled. Non-finite (NaN or inf) elements signify
            that the corresponding element in x is to be treated as fixed by
            ODRPACK.
        dy: absolute error (square root of the variance) of the dependent
            variable. Either a one-dimensional numpy array or None. If None,
            weighting is disabled.
        func: a callable with the signature
            func(x,par1,par2,par3,...)
        params_init: list or tuple of the first estimates of the
            parameters par1, par2, par3 etc. to be fitted

        other optional keyword arguments will be passed to leastsq().

    Outputs: par1, par2, par3, ... , statdict
        par1, par2, par3, ...: fitted values of par1, par2, par3 etc
            as instances of ErrorValue.
        statdict: dictionary of various statistical parameters:
            'DoF': Degrees of freedom
            'Chi2': Chi-squared
            'Chi2_reduced': Reduced Chi-squared
            'num_func_eval': number of function evaluations during fit.
            'func_value': the function evaluated in the best fitting parameters
            'message': status message from leastsq()
            'error_flag': integer status flag from leastsq() ('ier')
            'Covariance': covariance matrix (variances in the diagonal)
            'Correlation_coeffs': Pearson's correlation coefficients (usually
                denoted by 'r') in a matrix. The diagonal is unity.

    Notes:
        for the actual fitting, the module scipy.odr is used.
    """
    odrmodel=odr.Model(lambda pars, x: func(x,*pars))
    if dx is not None:
        # treat non-finite values as fixed
        xfixed=np.isfinite(dx)
    else:
        xfixed=None

    odrdata=odr.RealData(x, y, sx=dx,sy=dy, fix=xfixed)
    odrodr=odr.ODR(odrdata,odrmodel,params_init,ifixb=[not(isinstance(p,FixedParameter)) for p in params_init],
                   **kwargs)
    odroutput=odrodr.run()
    statdict=odroutput.__dict__.copy()
    statdict['Covariance']=odroutput.cov_beta
    statdict['Correlation_coeffs']=odroutput.cov_beta/np.outer(odroutput.sd_beta,odroutput.sd_beta)
    statdict['DoF']=len(x)-len(odroutput.beta)
    statdict['Chi2_reduced']=statdict['res_var']
    statdict['func_value']=statdict['y']
    statdict['Chi2']=statdict['sum_square']
    def convert(p_, dp_, pi):
        if isinstance(pi, FixedParameter):
            return FixedParameter(p_)
        else:
            return ErrorValue(p_, dp_)
    return tuple([convert(p_, dp_, pi) for (p_, dp_, pi) in zip(odroutput.beta, odroutput.sd_beta, params_init)] + [statdict])


Instruction:
Explain what the following Python 3 code does
def simultaneous_nonlinear_leastsquares(xs, ys, dys, func, params_inits, verbose=False, **kwargs):
    p, dp, statdict = simultaneous_nlsq_fit(xs, ys, dys, func, params_inits,
                                            verbose, **kwargs)
    params = [[ErrorValue(p_, dp_) for (p_, dp_) in zip(pcurrent, dpcurrent)]
              for (pcurrent, dpcurrent) in zip(p, dp)]
    return tuple(params + [statdict])

Response: A function that fit a set of parameters and return the fitted parameters as instances of ErrorValue.


Instruction:
Create a Python 3 function to
perform a non - linear least squares fit on the base of the unity tree.

Response:
def nlsq_fit(x, y, dy, func, params_init, verbose=False, **kwargs):
    """Perform a non-linear least squares fit

    Inputs:
        x: one-dimensional numpy array of the independent variable
        y: one-dimensional numpy array of the dependent variable
        dy: absolute error (square root of the variance) of the dependent
            variable. Either a one-dimensional numpy array or None. In the array
            case, if any of its elements is NaN, the whole array is treated as
            NaN (= no weighting)
        func: a callable with the signature
            func(x,par1,par2,par3,...)
        params_init: list or tuple of the first estimates of the
            parameters par1, par2, par3 etc. to be fitted
        `verbose`: if various messages useful for debugging should be printed on
            stdout.

        other optional keyword arguments will be passed to leastsq().

    Outputs: p, dp, statdict where
        p: list of fitted values of par1, par2 etc.
        dp: list of estimated errors
        statdict: dictionary of various statistical parameters:
            'DoF': Degrees of freedom
            'Chi2': Chi-squared
            'Chi2_reduced': Reduced Chi-squared
            'R2': Coefficient of determination
            'num_func_eval': number of function evaluations during fit.
            'func_value': the function evaluated in the best fitting parameters
            'message': status message from leastsq()
            'error_flag': integer status flag from leastsq() ('ier')
            'Covariance': covariance matrix (variances in the diagonal)
            'Correlation_coeffs': Pearson's correlation coefficients (usually
                denoted by 'r') in a matrix. The diagonal is unity.

    Notes:
        for the actual fitting, scipy.optimize.leastsq() is used.
    """
    if verbose:
        t0 = time.monotonic()
        print("nlsq_fit starting.")
    else:
        t0 = 0
    func_orig = func
    params_init_orig = params_init
    func, params_init = hide_fixedparams(func_orig, params_init_orig)
    if (dy is None) or (dy == np.nan).sum() > 0 or (dy <= 0).sum() > 0:
        if verbose:
            print("nlsq_fit: no weighting")
        dy = None

    def objectivefunc(params, x, y, dy):
        """The target function for leastsq()."""
        if dy is None:
            return (func(x, *(params.tolist())) - y)
        else:
            return (func(x, *(params.tolist())) - y) / dy
    # do the fitting
    if verbose:
        print("nlsq_fit: now doing the fitting...")
        t1 = time.monotonic()
    else:
        t1 = 0
    par, cov, infodict, mesg, ier = leastsq(objectivefunc,
                                            np.array(params_init),
                                            (x, y, dy), full_output=True,
                                            **kwargs)
    if verbose:
        print("nlsq_fit: fitting done in %.2f seconds." % (time.monotonic() - t1))
        print("nlsq_fit: status from scipy.optimize.leastsq(): %d (%s)" % (ier, mesg))
        print("nlsq_fit: extracting statistics.")
    # test if the covariance was singular (cov is None)
    if cov is None:
        cov = np.ones((len(par), len(par))) * np.nan  # set it to a NaN matrix
    # calculate the Pearson's R^2 parameter (coefficient of determination)
    if dy is None:
        sserr = np.sum(((func(x, *(par.tolist())) - y)) ** 2)
        sstot = np.sum((y - np.mean(y)) ** 2)
    else:
        sserr = np.sum(((func(x, *(par.tolist())) - y) / dy) ** 2)
        sstot = np.sum((y - np.mean(y)) ** 2 / dy ** 2)
    r2 = 1 - sserr / sstot
    # assemble the statistics dictionary
    statdict = {'DoF' : len(x) - len(par),  # degrees of freedom
                'Chi2' : (infodict['fvec'] ** 2).sum(),
                'R2' : r2,
                'num_func_eval' : infodict['nfev'],
                'func_value' : func(x, *(par.tolist())),
                'message' : mesg,
                'error_flag' : ier,
               }
    statdict['Chi2_reduced'] = statdict['Chi2'] / statdict['DoF']
    statdict['Covariance'] = cov * statdict['Chi2_reduced']
    par, statdict['Covariance'] = resubstitute_fixedparams(par, params_init_orig, statdict['Covariance'])
    # calculate the estimated errors of the fit parameters
    dpar = np.sqrt(statdict['Covariance'].diagonal())
    # Pearson's correlation coefficients (usually 'r') in a matrix.
    statdict['Correlation_coeffs'] = statdict['Covariance'] / np.outer(dpar,
                                                                       dpar)
    if verbose:
        print("nlsq_fit: returning with results.")
        print("nlsq_fit: total time: %.2f sec." % (time.monotonic() - t0))
    return par, dpar, statdict


Instruction:
Create a Python 3 function to
do a simultaneous nonlinear least - squares fit on a single base language tree.

Response:
def simultaneous_nlsq_fit(xs, ys, dys, func, params_inits, verbose=False,
                             **kwargs):
    """Do a simultaneous nonlinear least-squares fit

    Input:
    ------
    `xs`: tuple of abscissa vectors (1d numpy ndarrays)
    `ys`: tuple of ordinate vectors (1d numpy ndarrays)
    `dys`: tuple of the errors of ordinate vectors (1d numpy ndarrays or Nones)
    `func`: fitting function (the same for all the datasets)
    `params_init`: tuples of *lists* or *tuples* (not numpy ndarrays!) of the
        initial values of the parameters to be fitted. The special value `None`
        signifies that the corresponding parameter is the same as in the
        previous dataset. Of course, none of the parameters of the first dataset
        can be None.
    `verbose`: if various messages useful for debugging should be printed on
        stdout.

    additional keyword arguments get forwarded to nlsq_fit()

    Output:
    -------
    `p`: tuple of a list of fitted parameters
    `dp`: tuple of a list of errors of the fitted parameters
    `statdict`: statistics dictionary. This is of the same form as in
        `nlsq_fit` except that func_value is a sequence of one-dimensional
        np.ndarrays containing the best-fitting function values for each curve.
    """
    if not isinstance(xs, collections.Sequence) or \
        not isinstance(ys, collections.Sequence) or \
        not isinstance(dys, collections.Sequence) or \
        not isinstance(params_inits, collections.Sequence):
        raise ValueError('Parameters `xs`, `ys`, `dys` and `params_inits` should be tuples or lists.')
    Ndata = len(xs)
    if len(ys) != Ndata or len(dys) != Ndata or len(params_inits) != Ndata:
        raise ValueError('Parameters `xs`, `ys`, `dys` and `params_inits` should have the same length.')

    if not all([isinstance(x, collections.Sequence) for x in params_inits]):
        raise ValueError('Elements of `params_inits` should be tuples or Python lists.')
    Ns = set([len(x) for x in params_inits])
    if len(Ns) != 1:
        raise ValueError('Elements of `params_inits` should have the same length.')
    Npar = Ns.pop()
    for i in range(Ndata):
        if dys[i] is None:
            dys[i] = np.ones(len(xs[i]), np.double) * np.nan
    # concatenate the x, y and dy vectors
    xcat = np.concatenate(xs)
    ycat = np.concatenate(ys)
    dycat = np.concatenate(dys)
    # find the start and end indices for each dataset in the concatenated datasets.
    lens = [len(x) for x in xs]
    starts = [int(sum(lens[:i])) for i in range(len(lens))]
    ends = [int(sum(lens[:i + 1])) for i in range(len(lens))]

    # flatten the initial parameter list. A single list is needed, where the
    # constrained parameters occur only once. Of course, we have to do some
    # bookkeeping to be able to find the needed parameters for each sub-range
    # later during the fit.
    paramcat = []  # this will be the concatenated list of parameters
    param_indices = []  # this will have the same structure as params_inits (i.e.
        # a tuple of tuples of ints). Each tuple corresponds to a dataset.
        # Each integer number in each tuple holds
        # the index of the corresponding fit parameter in the
        # concatenated parameter list.
    for j in range(Ndata):  # for each dataset
        param_indices.append([])
        jorig = j
        for i in range(Npar):
            j = jorig
            while params_inits[j][i] is None and (j >= 0):
                j = j - 1
            if j < 0:
                raise ValueError('None of the parameters in the very first dataset should be `None`.')
            if jorig == j:  # not constrained parameter
                paramcat.append(params_inits[j][i])
                param_indices[jorig].append(len(paramcat) - 1)
            else:
                param_indices[jorig].append(param_indices[j][i])

    if verbose:
        print("Number of datasets for simultaneous fitting:", Ndata)
        print("Total number of data points:", len(xcat))
        print("Number of parameters in each dataset:", Npar)
        print("Total number of parameters:", Ndata * Npar)
        print("Number of independent parameters:", len(paramcat))
    # the flattened function
    def func_flat(x, *params):
        y = []
        for j in range(Ndata):
            if verbose > 1:
                print("Simultaneous fitting: evaluating function for dataset #", j, "/", Ndata)
            pars = [params[i] for i in param_indices[j]]
            y.append(func(x[starts[j]:ends[j]], *pars))
        return np.concatenate(tuple(y))

    # Now we reduced the problem to a single least-squares fit. Carry it out and
    # interpret the results.
    pflat, dpflat, statdictflat = nlsq_fit(xcat, ycat, dycat, func_flat, paramcat, verbose, **kwargs)
    for n in ['func_value', 'R2', 'Chi2', 'Chi2_reduced', 'DoF', 'Covariance', 'Correlation_coeffs']:
        statdictflat[n + '_global'] = statdictflat[n]
        statdictflat[n] = []
    p = []
    dp = []
    for j in range(Ndata):  # unpack the results
        p.append([pflat[i] for i in param_indices[j]])
        dp.append([dpflat[i] for i in param_indices[j]])
        statdictflat['func_value'].append(statdictflat['func_value_global'][starts[j]:ends[j]])
        if np.isfinite(dys[j]).all():
            statdictflat['Chi2'].append((((statdictflat['func_value'][-1] - ys[j]) / dys[j]) ** 2).sum())
            sstot = np.sum((ys[j] - np.mean(ys[j])) ** 2 / dys[j] ** 2)
        else:
            statdictflat['Chi2'].append(((statdictflat['func_value'][-1] - ys[j]) ** 2).sum())
            sstot = np.sum((ys[j] - np.mean(ys[j])) ** 2)
        sserr = statdictflat['Chi2'][-1]
        statdictflat['R2'].append(1 - sserr / sstot)
        statdictflat['DoF'].append(len(xs[j] - len(p[-1])))
        statdictflat['Covariance'].append(slice_covarmatrix(statdictflat['Covariance_global'], param_indices[j]))
        statdictflat['Correlation_coeffs'].append(slice_covarmatrix(statdictflat['Correlation_coeffs_global'], param_indices[j]))
        statdictflat['Chi2_reduced'].append(statdictflat['Chi2'][-1] / statdictflat['DoF'][-1])
    return p, dp, statdictflat


Instruction:
Given the following Python 3 function, write the documentation
def tostring(self: 'ErrorValue', extra_digits: int = 0, plusminus: str = ' +/- ', fmt: str = None) -> str:
        if isinstance(fmt, str) and fmt.lower().endswith('tex'):
            return re.subn('(\d*)(\.(\d)*)?[eE]([+-]?\d+)',
                           lambda m: (r'$%s%s\cdot 10^{%s}$' % (m.group(1), m.group(2), m.group(4))).replace('None',
                                                                                ''),
                           self.tostring(extra_digits=extra_digits, plusminus=plusminus, fmt=None))[0]
        if isinstance(self.val, numbers.Real):
            try:
                Ndigits = -int(math.floor(math.log10(self.err))) + extra_digits
            except (OverflowError, ValueError):
                return str(self.val) + plusminus + str(self.err)
            else:
                return str(round(self.val, Ndigits)) + plusminus + str(round(self.err, Ndigits))
        return str(self.val) + ' +/- ' + str(self.err)

Response: Convert the ErrorValue object into a string representation.


Instruction:
Can you generate the documentation for the following Python 3 function
def random(self: 'ErrorValue') -> np.ndarray:
        if isinstance(self.val, np.ndarray):
            # IGNORE:E1103
            return np.random.randn(self.val.shape) * self.err + self.val
        else:
            return np.random.randn() * self.err + self.val

Response: Sample a random number of the distribution defined by the error and variance of the object.


Instruction:
Write a Python 3 function that can
evaluate a function with error propagation.

Response:
def evalfunc(cls, func, *args, **kwargs):
        """Evaluate a function with error propagation.

        Inputs:
        -------
            ``func``: callable
                this is the function to be evaluated. Should return either a
                number or a np.ndarray.
            ``*args``: other positional arguments of func. Arguments which are
                not instances of `ErrorValue` are taken as constants.

            keyword arguments supported:
                ``NMC``: number of Monte-Carlo steps. If not defined, defaults
                to 1000
                ``exceptions_to_retry``: list of exception types to ignore:
                    if one of these is raised the given MC step is repeated once
                    again. Notice that this might induce an infinite loop!
                    The exception types in this list should be subclasses of
                    ``Exception``.
                ``exceptions_to_skip``: list of exception types to skip: if
                    one of these is raised the given MC step is skipped, never
                    to be repeated. The exception types in this list should be
                    subclasses of ``Exception``.

        Output:
        -------
            ``result``: an `ErrorValue` with the result. The error is estimated
                via a Monte-Carlo approach to Gaussian error propagation.
        """

        def do_random(x):
            if isinstance(x, cls):
                return x.random()
            else:
                return x

        if 'NMC' not in kwargs:
            kwargs['NMC'] = 1000
        if 'exceptions_to_skip' not in kwargs:
            kwargs['exceptions_to_skip'] = []
        if 'exceptions_to_repeat' not in kwargs:
            kwargs['exceptions_to_repeat'] = []
        meanvalue = func(*args)
        # this way we get either a number or a np.array
        stdcollector = meanvalue * 0
        mciters = 0
        while mciters < kwargs['NMC']:
            try:
                # IGNORE:W0142
                stdcollector += (func(*[do_random(a)
                                        for a in args]) - meanvalue) ** 2
                mciters += 1
            except Exception as e:  # IGNORE:W0703
                if any(isinstance(e, etype) for etype in kwargs['exceptions_to_skip']):
                    kwargs['NMC'] -= 1
                elif any(isinstance(e, etype) for etype in kwargs['exceptions_to_repeat']):
                    pass
                else:
                    raise
        return cls(meanvalue, stdcollector ** 0.5 / (kwargs['NMC'] - 1))


Instruction:
Implement a Python 3 function for
returning the F - factor amplitude of a sphere normalized to F ( q = 0 ) = V

Response:
def Fsphere(q, R):
    """Scattering form-factor amplitude of a sphere normalized to F(q=0)=V

    Inputs:
    -------
        ``q``: independent variable
        ``R``: sphere radius

    Formula:
    --------
        ``4*pi/q^3 * (sin(qR) - qR*cos(qR))``
    """
    return 4 * np.pi / q ** 3 * (np.sin(q * R) - q * R * np.cos(q * R))


Instruction:
Can you create a Python 3 function that
generalizes Guinier scattering of a set of variables.

Response:
def GeneralGuinier(q, G, Rg, s):
    """Generalized Guinier scattering

    Inputs:
    -------
        ``q``: independent variable
        ``G``: factor
        ``Rg``: radius of gyration
        ``s``: dimensionality parameter (can be 1, 2, 3)

    Formula:
    --------
        ``G/q**(3-s)*exp(-(q^2*Rg^2)/s)``
    """
    return G / q ** (3 - s) * np.exp(-(q * Rg) ** 2 / s)


Instruction:
Can you generate a brief explanation for the following Python 3 code
def GuinierPorod(q, G, Rg, alpha):
    return GuinierPorodMulti(q, G, Rg, alpha)

Response: Empirical Guinier - Porod scattering.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def PorodGuinierPorod(q, a, alpha, Rg, beta):
    return PorodGuinierMulti(q, a, alpha, Rg, beta)

Response: Empirical Porod - Guinier - Porod scattering.


Instruction:
Here you have a function in Python 3, explain what it does
def GuinierPorodGuinier(q, G, Rg1, alpha, Rg2):
    return GuinierPorodMulti(q, G, Rg1, alpha, Rg2)

Response: Empirical Guinier - Porod - Guinier scattering.


Instruction:
Write a Python 3 function for
damping power - law of a set of variables.

Response:
def DampedPowerlaw(q, a, alpha, sigma):
    """Damped power-law

    Inputs:
    -------
        ``q``: independent variable
        ``a``: factor
        ``alpha``: exponent
        ``sigma``: hwhm of the damping Gaussian

    Formula:
    --------
        ``a*q^alpha*exp(-q^2/(2*sigma^2))``
    """
    return a * q ** alpha * np.exp(-q ** 2 / (2 * sigma ** 2))


Instruction:
Can you implement a function in Python 3 that
logs Normal Spheres in the hierarchy of non - correlated spheres.

Response:
def LogNormSpheres(q, A, mu, sigma, N=1000):
    """Scattering of a population of non-correlated spheres (radii from a log-normal distribution)

    Inputs:
    -------
        ``q``: independent variable
        ``A``: scaling factor
        ``mu``: expectation of ``ln(R)``
        ``sigma``: hwhm of ``ln(R)``

    Non-fittable inputs:
    --------------------
        ``N``: the (integer) number of spheres

    Formula:
    --------
        The integral of ``F_sphere^2(q,R) * P(R)`` where ``P(R)`` is a
        log-normal distribution of the radii.

    """
    Rmin = 0
    Rmax = np.exp(mu + 3 * sigma)
    R = np.linspace(Rmin, Rmax, N + 1)[1:]
    P = 1 / np.sqrt(2 * np.pi * sigma ** 2 * R ** 2) * np.exp(-(np.log(R) - mu) ** 2 / (2 * sigma ** 2))
    def Fsphere_outer(q, R):
        qR = np.outer(q, R)
        q1 = np.outer(q, np.ones_like(R))
        return 4 * np.pi / q1 ** 3 * (np.sin(qR) - qR * np.cos(qR))
    I = (Fsphere_outer(q, R) ** 2 * np.outer(np.ones_like(q), P))
    return A * I.sum(1) / P.sum()


Instruction:
Can you tell what is the following Python 3 function doing
def GaussSpheres(q, A, R0, sigma, N=1000, weighting='intensity'):
    Rmin = max(0, R0 - 3 * sigma)
    Rmax = R0 + 3 * sigma
    R = np.linspace(Rmin, Rmax, N + 1)[1:]
    P = 1 / np.sqrt(2 * np.pi * sigma ** 2) * np.exp(-(R - R0) ** 2 / (2 * sigma ** 2))
    def Fsphere_outer(q, R):
        qR = np.outer(q, R)
        return 3 / qR ** 3 * (np.sin(qR) - qR * np.cos(qR))
    V=R**3*4*np.pi/3.
    if weighting=='intensity':
        P=P*V*V
    elif weighting=='volume':
        P=P*V
    elif weighting=='number':
        pass
    else:
        raise ValueError('Invalid weighting: '+str(weighting))
    I = (Fsphere_outer(q, R) ** 2 * np.outer(np.ones_like(q), P))
    return A * I.sum(1) / P.sum()

Response: Computes the scattering of non - correlated spheres in a single population of non - correlated spheres.


Instruction:
Can you implement a function in Python 3 that
sums of a Power - law a Guinier - Porod curve and a constant.

Response:
def PowerlawGuinierPorodConst(q, A, alpha, G, Rg, beta, C):
    """Sum of a Power-law, a Guinier-Porod curve and a constant.

    Inputs:
    -------
        ``q``: independent variable (momentum transfer)
        ``A``: scaling factor of the power-law
        ``alpha``: power-law exponent
        ``G``: scaling factor of the Guinier-Porod curve
        ``Rg``: Radius of gyration
        ``beta``: power-law exponent of the Guinier-Porod curve
        ``C``: additive constant

    Formula:
    --------
        ``A*q^alpha + GuinierPorod(q,G,Rg,beta) + C``
    """
    return PowerlawPlusConstant(q, A, alpha, C) + GuinierPorod(q, G, Rg, beta)


Instruction:
Explain what the following Python 3 code does
def GuinierPorodMulti(q, G, *Rgsalphas):
    scalefactor = G
    funcs = [lambda q: Guinier(q, G, Rgsalphas[0])]
    indices = np.ones_like(q, dtype=np.bool)
    constraints = []
    for i in range(1, len(Rgsalphas)):
        if i % 2:
            # Rgsalphas[i] is an exponent, Rgsalphas[i-1] is a radius of gyration
            qsep = _PGgen_qsep(Rgsalphas[i], Rgsalphas[i - 1], 3)
            scalefactor = _PGgen_A(Rgsalphas[i], Rgsalphas[i - 1], 3, scalefactor)
            funcs.append(lambda q, a=scalefactor, alpha=Rgsalphas[i]: Powerlaw(q, a, alpha))
        else:
            # Rgsalphas[i] is a radius of gyration, Rgsalphas[i-1] is a power-law exponent
            qsep = _PGgen_qsep(Rgsalphas[i - 1], Rgsalphas[i], 3)
            scalefactor = _PGgen_G(Rgsalphas[i - 1], Rgsalphas[i], 3, scalefactor)
            funcs.append(lambda q, G=scalefactor, Rg=Rgsalphas[i]: Guinier(q, G, Rg))
        # this belongs to the previous
        constraints.append(indices & (q < qsep))
        indices[q < qsep] = False
    constraints.append(indices)
    return np.piecewise(q, constraints, funcs)

Response: Empirical multi - part Guinier - Porod scattering.


Instruction:
Write a Python 3 function for
generalizing multi - part Guinier - Porod scattering.

Response:
def GeneralGuinierPorod(q, factor, *args, **kwargs):
    """Empirical generalized multi-part Guinier-Porod scattering

    Inputs:
    -------
        ``q``: independent variable
        ``factor``: factor for the first branch
        other arguments (*args): the defining arguments of the consecutive
             parts: radius of gyration (``Rg``) and dimensionality
             parameter (``s``) for Guinier and exponent (``alpha``) for
             power-law parts.
        supported keyword arguments:
            ``startswithguinier``: True if the first segment is a Guinier-type
            scattering (this is the default) or False if it is a power-law

    Formula:
    --------
        The intensity is a piecewise function with continuous first derivatives.
        The separating points in ``q`` between the consecutive parts and the
        intensity factors of them (except the first) are determined from
        conditions of smoothness (continuity of the function and its first
        derivative) at the border points of the intervals. Guinier-type
        (``G*q**(3-s)*exp(-q^2*Rg1^2/s)``) and Power-law type (``A*q^alpha``)
        parts follow each other in alternating sequence. The exact number of
        parts is determined from the number of positional arguments (*args).

    Literature:
    -----------
        B. Hammouda: A new Guinier-Porod model. J. Appl. Crystallogr. (2010) 43,
            716-719.
    """
    if kwargs.get('startswithguinier', True):
        funcs = [lambda q, A = factor:GeneralGuinier(q, A, args[0], args[1])]
        i = 2
        guiniernext = False
    else:
        funcs = [lambda q, A = factor: Powerlaw(q, A, args[0])]
        i = 1
        guiniernext = True
    indices = np.ones_like(q, dtype=np.bool)
    constraints = []
    while i < len(args):
        if guiniernext:
            # args[i] is a radius of gyration, args[i+1] is a dimensionality parameter, args[i-1] is a power-law exponent
            qsep = _PGgen_qsep(args[i - 1], args[i], args[i + 1])
            factor = _PGgen_G(args[i - 1], args[i], args[i + 1], factor)
            funcs.append(lambda q, G=factor, Rg=args[i], s=args[i + 1]: GeneralGuinier(q, G, Rg, s))
            guiniernext = False
            i += 2
        else:
            # args[i] is an exponent, args[i-2] is a radius of gyration, args[i-1] is a dimensionality parameter
            qsep = _PGgen_qsep(args[i], args[i - 2], args[i - 1])
            factor = _PGgen_A(args[i], args[i - 2], args[i - 1], factor)
            funcs.append(lambda q, a=factor, alpha=args[i]: a * q ** alpha)
            guiniernext = True
            i += 1
        # this belongs to the previous
        constraints.append(indices & (q < qsep))
        indices[q < qsep] = False
    constraints.append(indices)
    return np.piecewise(q, constraints, funcs)


Instruction:
How would you explain what the following Python 3 function does
def DebyeChain(q, Rg):
    a = (q * Rg) ** 2
    return 2 * (np.exp(-a) - 1 + a) / a ** 2

Response: Returns the scattering form - factor intensity of a Gaussian chain.


Instruction:
Can you write a function in Python 3 where it
generalizes excluded - volume Gaussian chain.

Response:
def ExcludedVolumeChain(q, Rg, nu):
    """Scattering intensity of a generalized excluded-volume Gaussian chain

    Inputs:
    -------
        ``q``: independent variable
        ``Rg``: radius of gyration
        ``nu``: excluded volume exponent

    Formula:
    --------
        ``(u^(1/nu)*gamma(0.5/nu)*gammainc_lower(0.5/nu,u)-
            gamma(1/nu)*gammainc_lower(1/nu,u)) / (nu*u^(1/nu))``
        where ``u = q^2*Rg^2*(2*nu+1)*(2*nu+2)/6`` is the reduced scattering
        variable, ``gamma(x)`` is the gamma function and ``gammainc_lower(x,t)``
        is the lower incomplete gamma function.

    Literature:
    -----------
        SASFit manual 6. nov. 2010. Equation (3.60b)
    """
    u = (q * Rg) ** 2 * (2 * nu + 1) * (2 * nu + 2) / 6.
    return (u ** (0.5 / nu) * gamma(0.5 / nu) * gammainc(0.5 / nu, u) -
            gamma(1. / nu) * gammainc(1. / nu, u)) / (nu * u ** (1. / nu))


Instruction:
Write a Python 3 script for
sampling a patch from the data object.

Response:
def sample(self, data, interval):
        '''Sample a patch from the data object

        Parameters
        ----------
        data : dict
            A data dict as produced by pumpp.Pump.transform

        interval : slice
            The time interval to sample

        Returns
        -------
        data_slice : dict
            `data` restricted to `interval`.
        '''
        data_slice = dict()

        for key in data:
            if '_valid' in key:
                continue

            index = [slice(None)] * data[key].ndim

            # if we have multiple observations for this key, pick one
            index[0] = self.rng.randint(0, data[key].shape[0])
            index[0] = slice(index[0], index[0] + 1)

            for tdim in self._time[key]:
                index[tdim] = interval

            data_slice[key] = data[key][tuple(index)]

        return data_slice


Instruction:
Create a Python 3 function to
generate a generator of indices for the set of keys in the data dictionary.

Response:
def indices(self, data):
        '''Generate patch indices

        Parameters
        ----------
        data : dict of np.ndarray
            As produced by pumpp.transform

        Yields
        ------
        start : int >= 0
            The start index of a sample patch
        '''
        duration = self.data_duration(data)

        if self.duration > duration:
            raise DataError('Data duration={} is less than '
                            'sample duration={}'.format(duration, self.duration))

        while True:
            # Generate a sampling interval
            yield self.rng.randint(0, duration - self.duration + 1)


Instruction:
Write a Python 3 script for
generating patch start indices for the set of keys in the data dictionary

Response:
def indices(self, data):
        '''Generate patch start indices

        Parameters
        ----------
        data : dict of np.ndarray
            As produced by pumpp.transform

        Yields
        ------
        start : int >= 0
            The start index of a sample patch
        '''
        duration = self.data_duration(data)

        for start in range(0, duration - self.duration, self.stride):
            yield start


Instruction:
Can you generate a brief explanation for the following Python 3 code
def indices(self, data):
        '''Generate patch indices

        Parameters
        ----------
        data : dict of np.ndarray
            As produced by pumpp.transform

        Yields
        ------
        start : int >= 0
            The start index of a sample patch
        '''
        duration = self.data_duration(data)

        while True:
            # Generate a sampling interval
            yield self.rng.randint(0, duration - self.min_duration + 1)

Response: Generate a generator of indices for the set of keys in the data dictionary.


Instruction:
How would you code a function in Python 3 to
apply the name scope to a key.

Response:
def scope(self, key):
        '''Apply the name scope to a key

        Parameters
        ----------
        key : string

        Returns
        -------
        `name/key` if `name` is not `None`;
        otherwise, `key`.
        '''
        if self.name is None:
            return key
        return '{:s}/{:s}'.format(self.name, key)


Instruction:
Write a Python 3 script for
registering a field as a tensor with the given shape and type.

Response:
def register(self, field, shape, dtype):
        '''Register a field as a tensor with specified shape and type.

        A `Tensor` of the given shape and type will be registered in this
        object's `fields` dict.

        Parameters
        ----------
        field : str
            The name of the field

        shape : iterable of `int` or `None`
            The shape of the output variable.
            This does not include a dimension for multiple outputs.

            `None` may be used to indicate variable-length outputs

        dtype : type
            The data type of the field

        Raises
        ------
        ParameterError
            If dtype or shape are improperly specified
        '''
        if not isinstance(dtype, type):
            raise ParameterError('dtype={} must be a type'.format(dtype))

        if not (isinstance(shape, Iterable) and
                all([s is None or isinstance(s, int) for s in shape])):
            raise ParameterError('shape={} must be an iterable of integers'.format(shape))

        self.fields[self.scope(field)] = Tensor(tuple(shape), dtype)


Instruction:
Write a Python 3 script for
merging an array of output dicts into a single dictionary with properly scoped names.

Response:
def merge(self, data):
        '''Merge an array of output dictionaries into a single dictionary
        with properly scoped names.

        Parameters
        ----------
        data : list of dict
            Output dicts as produced by `pumpp.task.BaseTaskTransformer.transform`
            or `pumpp.feature.FeatureExtractor.transform`.

        Returns
        -------
        data_out : dict
            All elements of the input dicts are stacked along the 0 axis,
            and keys are re-mapped by `scope`.
        '''
        data_out = dict()

        # Iterate over all keys in data
        for key in set().union(*data):
            data_out[self.scope(key)] = np.stack([np.asarray(d[key]) for d in data],
                                                 axis=0)
        return data_out


Instruction:
Write a Python 3 function for
adding an operator to the Slicer object

Response:
def add(self, operator):
        '''Add an operator to the Slicer

        Parameters
        ----------
        operator : Scope (TaskTransformer or FeatureExtractor)
            The new operator to add
        '''
        if not isinstance(operator, Scope):
            raise ParameterError('Operator {} must be a TaskTransformer '
                                 'or FeatureExtractor'.format(operator))
        for key in operator.fields:
            self._time[key] = []
            # We add 1 to the dimension here to account for batching
            for tdim, idx in enumerate(operator.fields[key].shape, 1):
                if idx is None:
                    self._time[key].append(tdim)


Instruction:
Write a Python 3 function for
computing the valid data duration of a dict

Response:
def data_duration(self, data):
        '''Compute the valid data duration of a dict

        Parameters
        ----------
        data : dict
            As produced by pumpp.transform

        Returns
        -------
        length : int
            The minimum temporal extent of a dynamic observation in data
        '''
        # Find all the time-like indices of the data
        lengths = []
        for key in self._time:
            for idx in self._time.get(key, []):
                lengths.append(data[key].shape[idx])

        return min(lengths)


Instruction:
Here you have a function in Python 3, explain what it does
def crop(self, data):
        '''Crop a data dictionary down to its common time

        Parameters
        ----------
        data : dict
            As produced by pumpp.transform

        Returns
        -------
        data_cropped : dict
            Like `data` but with all time-like axes truncated to the
            minimum common duration
        '''

        duration = self.data_duration(data)
        data_out = dict()
        for key in data:
            idx = [slice(None)] * data[key].ndim
            for tdim in self._time.get(key, []):
                idx[tdim] = slice(duration)
            data_out[key] = data[key][tuple(idx)]

        return data_out

Response: Crop a data dictionary down to its common time - like axes truncated to the minimum common duration


Instruction:
Create a Python 3 function to
compute the Mel spectrogram of the audio buffer y.

Response:
def transform_audio(self, y):
        '''Compute the Mel spectrogram

        Parameters
        ----------
        y : np.ndarray
            The audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape=(n_frames, n_mels)
                The Mel spectrogram
        '''
        n_frames = self.n_frames(get_duration(y=y, sr=self.sr))

        mel = np.sqrt(melspectrogram(y=y, sr=self.sr,
                                     n_fft=self.n_fft,
                                     hop_length=self.hop_length,
                                     n_mels=self.n_mels,
                                     fmax=self.fmax)).astype(np.float32)

        mel = fix_length(mel, n_frames)

        if self.log:
            mel = amplitude_to_db(mel, ref=np.max)

        return {'mag': mel.T[self.idx]}


Instruction:
Write a Python 3 function for
emptying vector annotations. This returns an empty vector annotation with a single observation vector consisting of all - zeroes.

Response:
def empty(self, duration):
        '''Empty vector annotations.

        This returns an annotation with a single observation
        vector consisting of all-zeroes.

        Parameters
        ----------
        duration : number >0
            Length of the track

        Returns
        -------
        ann : jams.Annotation
            The empty annotation
        '''
        ann = super(VectorTransformer, self).empty(duration)

        ann.append(time=0, duration=duration, confidence=0,
                   value=np.zeros(self.dimension, dtype=np.float32))
        return ann


Instruction:
Write a Python 3 script to
apply the vector transformation.

Response:
def transform_annotation(self, ann, duration):
        '''Apply the vector transformation.

        Parameters
        ----------
        ann : jams.Annotation
            The input annotation

        duration : number > 0
            The duration of the track

        Returns
        -------
        data : dict
            data['vector'] : np.ndarray, shape=(dimension,)

        Raises
        ------
        DataError
            If the input dimension does not match
        '''
        _, values = ann.to_interval_values()
        vector = np.asarray(values[0], dtype=self.dtype)
        if len(vector) != self.dimension:
            raise DataError('vector dimension({:0}) '
                            '!= self.dimension({:1})'
                            .format(len(vector), self.dimension))

        return {'vector': vector}


Instruction:
Create a Python 3 function to
set the transition matrix according to self - loop probabilities.

Response:
def set_transition(self, p_self):
        '''Set the transition matrix according to self-loop probabilities.

        Parameters
        ----------
        p_self : None, float in (0, 1), or np.ndarray [shape=(n_labels,)]
            Optional self-loop probability(ies), used for Viterbi decoding
        '''
        if p_self is None:
            self.transition = None
        else:
            self.transition = np.empty((len(self._classes), 2, 2))
            if np.isscalar(p_self):
                self.transition = transition_loop(2, p_self)
            elif len(p_self) != len(self._classes):
                raise ParameterError('Invalid p_self.shape={} for vocabulary size={}'.format(p_self.shape, len(self._classes)))
            else:
                for i in range(len(self._classes)):
                    self.transition[i] = transition_loop(2, p_self[i])


Instruction:
Write a Python 3 script to
empty label annotations. Empty label annotations.

Response:
def empty(self, duration):
        '''Empty label annotations.

        Constructs a single observation with an empty value (None).

        Parameters
        ----------
        duration : number > 0
            The duration of the annotation
        '''
        ann = super(DynamicLabelTransformer, self).empty(duration)
        ann.append(time=0, duration=duration, value=None)
        return ann


Instruction:
Can you create a Python 3 function that
transforms an annotation to dynamic label encoding.

Response:
def transform_annotation(self, ann, duration):
        '''Transform an annotation to dynamic label encoding.

        Parameters
        ----------
        ann : jams.Annotation
            The annotation to convert

        duration : number > 0
            The duration of the track

        Returns
        -------
        data : dict
            data['tags'] : np.ndarray, shape=(n, n_labels)
                A time-varying binary encoding of the labels
        '''
        intervals, values = ann.to_interval_values()

        # Suppress all intervals not in the encoder
        tags = []
        for v in values:
            if v in self._classes:
                tags.extend(self.encoder.transform([[v]]))
            else:
                tags.extend(self.encoder.transform([[]]))

        tags = np.asarray(tags)
        target = self.encode_intervals(duration, intervals, tags)

        return {'tags': target}


Instruction:
How would you explain what the following Python 3 function does
def inverse(self, encoded, duration=None):
        '''Inverse transformation'''

        ann = jams.Annotation(namespace=self.namespace, duration=duration)
        for start, end, value in self.decode_intervals(encoded,
                                                       duration=duration,
                                                       transition=self.transition,
                                                       p_init=self.p_init,
                                                       p_state=self.p_state):
            # Map start:end to frames
            f_start, f_end = time_to_frames([start, end],
                                            sr=self.sr,
                                            hop_length=self.hop_length)

            confidence = np.mean(encoded[f_start:f_end+1, value])

            value_dec = self.encoder.inverse_transform(np.atleast_2d(value))[0]

            for vd in value_dec:
                ann.append(time=start,
                           duration=end-start,
                           value=vd,
                           confidence=confidence)

        return ann

Response: Inverse transformation of the resource.


Instruction:
Implement a function in Python 3 to
transform an annotation to static label encoding.

Response:
def transform_annotation(self, ann, duration):
        '''Transform an annotation to static label encoding.

        Parameters
        ----------
        ann : jams.Annotation
            The annotation to convert

        duration : number > 0
            The duration of the track

        Returns
        -------
        data : dict
            data['tags'] : np.ndarray, shape=(n_labels,)
                A static binary encoding of the labels
        '''
        intervals = np.asarray([[0, 1]])
        values = list([obs.value for obs in ann])
        intervals = np.tile(intervals, [len(values), 1])

        # Suppress all intervals not in the encoder
        tags = [v for v in values if v in self._classes]
        if len(tags):
            target = self.encoder.transform([tags]).astype(np.bool).max(axis=0)
        else:
            target = np.zeros(len(self._classes), dtype=np.bool)

        return {'tags': target}


Instruction:
Explain what the following Python 3 code does
def inverse(self, encoded, duration=None):
        '''Inverse static tag transformation'''

        ann = jams.Annotation(namespace=self.namespace, duration=duration)

        if np.isrealobj(encoded):
            detected = (encoded >= 0.5)
        else:
            detected = encoded

        for vd in self.encoder.inverse_transform(np.atleast_2d(detected))[0]:
            vid = np.flatnonzero(self.encoder.transform(np.atleast_2d(vd)))
            ann.append(time=0,
                       duration=duration,
                       value=vd,
                       confidence=encoded[vid])
        return ann

Response: Inverse static tag transformation


Instruction:
Explain what the following Python 3 code does
def transform_audio(self, y):
        '''Compute the time position encoding

        Parameters
        ----------
        y : np.ndarray
            Audio buffer

        Returns
        -------
        data : dict
            data['relative'] = np.ndarray, shape=(n_frames, 2)
            data['absolute'] = np.ndarray, shape=(n_frames, 2)

                Relative and absolute time positional encodings.
        '''

        duration = get_duration(y=y, sr=self.sr)
        n_frames = self.n_frames(duration)

        relative = np.zeros((n_frames, 2), dtype=np.float32)
        relative[:, 0] = np.cos(np.pi * np.linspace(0, 1, num=n_frames))
        relative[:, 1] = np.sin(np.pi * np.linspace(0, 1, num=n_frames))

        absolute = relative * np.sqrt(duration)

        return {'relative': relative[self.idx],
                'absolute': absolute[self.idx]}

Response: Compute the time position encoding of the audio buffer y.


Instruction:
Can you implement a function in Python 3 that
adds an operation to this pump.

Response:
def add(self, operator):
        '''Add an operation to this pump.

        Parameters
        ----------
        operator : BaseTaskTransformer, FeatureExtractor
            The operation to add

        Raises
        ------
        ParameterError
            if `op` is not of a correct type
        '''
        if not isinstance(operator, (BaseTaskTransformer, FeatureExtractor)):
            raise ParameterError('operator={} must be one of '
                                 '(BaseTaskTransformer, FeatureExtractor)'
                                 .format(operator))

        if operator.name in self.opmap:
            raise ParameterError('Duplicate operator name detected: '
                                 '{}'.format(operator))

        super(Pump, self).add(operator)
        self.opmap[operator.name] = operator
        self.ops.append(operator)


Instruction:
Make a summary of the following Python 3 code
def transform(self, audio_f=None, jam=None, y=None, sr=None, crop=False):
        '''Apply the transformations to an audio file, and optionally JAMS object.

        Parameters
        ----------
        audio_f : str
            Path to audio file

        jam : optional, `jams.JAMS`, str or file-like
            Optional JAMS object/path to JAMS file/open file descriptor.

            If provided, this will provide data for task transformers.

        y : np.ndarray
        sr : number > 0
            If provided, operate directly on an existing audio buffer `y` at
            sampling rate `sr` rather than load from `audio_f`.

        crop : bool
            If `True`, then data are cropped to a common time index across all
            fields.  Otherwise, data may have different time extents.

        Returns
        -------
        data : dict
            Data dictionary containing the transformed audio (and annotations)

        Raises
        ------
        ParameterError
            At least one of `audio_f` or `(y, sr)` must be provided.

        '''

        if y is None:
            if audio_f is None:
                raise ParameterError('At least one of `y` or `audio_f` '
                                     'must be provided')

            # Load the audio
            y, sr = librosa.load(audio_f, sr=sr, mono=True)

        if sr is None:
            raise ParameterError('If audio is provided as `y`, you must '
                                 'specify the sampling rate as sr=')

        if jam is None:
            jam = jams.JAMS()
            jam.file_metadata.duration = librosa.get_duration(y=y, sr=sr)

        # Load the jams
        if not isinstance(jam, jams.JAMS):
            jam = jams.load(jam)

        data = dict()

        for operator in self.ops:
            if isinstance(operator, BaseTaskTransformer):
                data.update(operator.transform(jam))
            elif isinstance(operator, FeatureExtractor):
                data.update(operator.transform(y, sr))
        if crop:
            data = self.crop(data)
        return data

Response: Apply the transformations to an audio file and optionally JAMS object.


Instruction:
Here you have a function in Python 3, explain what it does
def sampler(self, n_samples, duration, random_state=None):
        '''Construct a sampler object for this pump's operators.

        Parameters
        ----------
        n_samples : None or int > 0
            The number of samples to generate

        duration : int > 0
            The duration (in frames) of each sample patch

        random_state : None, int, or np.random.RandomState
            If int, random_state is the seed used by the random number
            generator;

            If RandomState instance, random_state is the random number
            generator;

            If None, the random number generator is the RandomState instance
            used by np.random.

        Returns
        -------
        sampler : pumpp.Sampler
            The sampler object

        See Also
        --------
        pumpp.sampler.Sampler
        '''

        return Sampler(n_samples, duration,
                       random_state=random_state,
                       *self.ops)

Response: Construct a sampler object for this pump s operators.


Instruction:
Can you tell what is the following Python 3 function doing
def fields(self):
        '''A dictionary of fields constructed by this pump'''
        out = dict()
        for operator in self.ops:
            out.update(**operator.fields)

        return out

Response: A dictionary of fields constructed by this pump


Instruction:
Given the following Python 3 function, write the documentation
def layers(self):
        '''Construct Keras input layers for all feature transformers
        in the pump.

        Returns
        -------
        layers : {field: keras.layers.Input}
            A dictionary of keras input layers, keyed by the corresponding
            fields.
        '''

        layermap = dict()
        for operator in self.ops:
            if hasattr(operator, 'layers'):
                layermap.update(operator.layers())
        return layermap

Response:
Construct Keras input layers for all feature transformers
        in the pump.


Instruction:
Can you write a function in Python 3 where it
sets the beat - tracking transition matrix according to the self - loop probabilities.

Response:
def set_transition_beat(self, p_self):
        '''Set the beat-tracking transition matrix according to
        self-loop probabilities.

        Parameters
        ----------
        p_self : None, float in (0, 1), or np.ndarray [shape=(2,)]
            Optional self-loop probability(ies), used for Viterbi decoding
        '''
        if p_self is None:
            self.beat_transition = None
        else:
            self.beat_transition = transition_loop(2, p_self)


Instruction:
Here you have a function in Python 3, explain what it does
def set_transition_down(self, p_self):
        '''Set the downbeat-tracking transition matrix according to
        self-loop probabilities.

        Parameters
        ----------
        p_self : None, float in (0, 1), or np.ndarray [shape=(2,)]
            Optional self-loop probability(ies), used for Viterbi decoding
        '''
        if p_self is None:
            self.down_transition = None
        else:
            self.down_transition = transition_loop(2, p_self)

Response: Set the downbeat - tracking transition matrix according to the self - loop probabilities.


Instruction:
Can you write a function in Python 3 where it
applies the beat transformer to the specific resource.

Response:
def transform_annotation(self, ann, duration):
        '''Apply the beat transformer

        Parameters
        ----------
        ann : jams.Annotation
            The input annotation

        duration : number > 0
            The duration of the audio

        Returns
        -------
        data : dict
            data['beat'] : np.ndarray, shape=(n, 1)
                Binary indicator of beat/non-beat

            data['downbeat'] : np.ndarray, shape=(n, 1)
                Binary indicator of downbeat/non-downbeat

            mask_downbeat : bool
                True if downbeat annotations are present
        '''

        mask_downbeat = False

        intervals, values = ann.to_interval_values()
        values = np.asarray(values)

        beat_events = intervals[:, 0]
        beat_labels = np.ones((len(beat_events), 1))

        idx = (values == 1)
        if np.any(idx):
            downbeat_events = beat_events[idx]
            downbeat_labels = np.ones((len(downbeat_events), 1))
            mask_downbeat = True
        else:
            downbeat_events = np.zeros(0)
            downbeat_labels = np.zeros((0, 1))

        target_beat = self.encode_events(duration,
                                         beat_events,
                                         beat_labels)

        target_downbeat = self.encode_events(duration,
                                             downbeat_events,
                                             downbeat_labels)

        return {'beat': target_beat,
                'downbeat': target_downbeat,
                'mask_downbeat': mask_downbeat}


Instruction:
Can you tell what is the following Python 3 function doing
def inverse(self, encoded, downbeat=None, duration=None):
        '''Inverse transformation for beats and optional downbeats'''

        ann = jams.Annotation(namespace=self.namespace, duration=duration)

        beat_times = np.asarray([t for t, _ in self.decode_events(encoded,
                                                                  transition=self.beat_transition,
                                                                  p_init=self.beat_p_init,
                                                                  p_state=self.beat_p_state) if _])
        beat_frames = time_to_frames(beat_times,
                                     sr=self.sr,
                                     hop_length=self.hop_length)

        if downbeat is not None:
            downbeat_times = set([t for t, _ in self.decode_events(downbeat,
                                                                   transition=self.down_transition,
                                                                   p_init=self.down_p_init,
                                                                   p_state=self.down_p_state) if _])
            pickup_beats = len([t for t in beat_times
                                if t < min(downbeat_times)])
        else:
            downbeat_times = set()
            pickup_beats = 0

        value = - pickup_beats - 1
        for beat_t, beat_f in zip(beat_times, beat_frames):
            if beat_t in downbeat_times:
                value = 1
            else:
                value += 1
            confidence = encoded[beat_f]
            ann.append(time=beat_t,
                       duration=0,
                       value=value,
                       confidence=confidence)

        return ann

Response: Inverse transformation for beats and optional downbeats


Instruction:
Make a summary of the following Python 3 code
def transform_annotation(self, ann, duration):
        '''Transform an annotation to the beat-position encoding

        Parameters
        ----------
        ann : jams.Annotation
            The annotation to convert

        duration : number > 0
            The duration of the track

        Returns
        -------
        data : dict
            data['position'] : np.ndarray, shape=(n, n_labels) or (n, 1)
                A time-varying label encoding of beat position
        '''

        # 1. get all the events
        # 2. find all the downbeats
        # 3. map each downbeat to a subdivision counter
        #       number of beats until the next downbeat
        # 4. pad out events to intervals
        # 5. encode each beat interval to its position

        boundaries, values = ann.to_interval_values()
        # Convert to intervals and span the duration
        # padding at the end of track does not propagate the right label
        # this is an artifact of inferring end-of-track from boundaries though
        boundaries = list(boundaries[:, 0])
        if boundaries and boundaries[-1] < duration:
            boundaries.append(duration)
        intervals = boundaries_to_intervals(boundaries)
        intervals, values = adjust_intervals(intervals, values,
                                             t_min=0,
                                             t_max=duration,
                                             start_label=0,
                                             end_label=0)

        values = np.asarray(values, dtype=int)
        downbeats = np.flatnonzero(values == 1)

        position = []
        for i, v in enumerate(values):
            # If the value is a 0, mark it as X and move on
            if v == 0:
                position.extend(self.encoder.transform(['X']))
                continue

            # Otherwise, let's try to find the surrounding downbeats
            prev_idx = np.searchsorted(downbeats, i, side='right') - 1
            next_idx = 1 + prev_idx

            if prev_idx >= 0 and next_idx < len(downbeats):
                # In this case, the subdivision is well-defined
                subdivision = downbeats[next_idx] - downbeats[prev_idx]
            elif prev_idx < 0 and next_idx < len(downbeats):
                subdivision = np.max(values[:downbeats[0]+1])
            elif next_idx >= len(downbeats):
                subdivision = len(values) - downbeats[prev_idx]

            if subdivision > self.max_divisions or subdivision < 1:
                position.extend(self.encoder.transform(['X']))
            else:
                position.extend(self.encoder.transform(['{:02d}/{:02d}'.format(subdivision, v)]))

        dtype = self.fields[self.scope('position')].dtype

        position = np.asarray(position)
        if self.sparse:
            position = position[:, np.newaxis]

        target = self.encode_intervals(duration, intervals, position,
                                       multi=False, dtype=dtype)
        return {'position': target}

Response: Transform an annotation to the beat - position encoding


Instruction:
Can you generate a brief explanation for the following Python 3 code
def transform_audio(self, y):
        '''Compute the tempogram

        Parameters
        ----------
        y : np.ndarray
            Audio buffer

        Returns
        -------
        data : dict
            data['tempogram'] : np.ndarray, shape=(n_frames, win_length)
                The tempogram
        '''
        n_frames = self.n_frames(get_duration(y=y, sr=self.sr))

        tgram = tempogram(y=y, sr=self.sr,
                          hop_length=self.hop_length,
                          win_length=self.win_length).astype(np.float32)

        tgram = fix_length(tgram, n_frames)
        return {'tempogram': tgram.T[self.idx]}

Response: Compute the tempogram of the current object.


Instruction:
Make a summary of the following Python 3 code
def transform_audio(self, y):
        '''Apply the scale transform to the tempogram

        Parameters
        ----------
        y : np.ndarray
            The audio buffer

        Returns
        -------
        data : dict
            data['temposcale'] : np.ndarray, shape=(n_frames, n_fmt)
                The scale transform magnitude coefficients
        '''
        data = super(TempoScale, self).transform_audio(y)
        data['temposcale'] = np.abs(fmt(data.pop('tempogram'),
                                        axis=1,
                                        n_fmt=self.n_fmt)).astype(np.float32)[self.idx]
        return data

Response: Apply the scale transform to the tempogram


Instruction:
How would you implement a function in Python 3 that
applies the structure agreement transformation.

Response:
def transform_annotation(self, ann, duration):
        '''Apply the structure agreement transformation.

        Parameters
        ----------
        ann : jams.Annotation
            The segment annotation

        duration : number > 0
            The target duration

        Returns
        -------
        data : dict
            data['agree'] : np.ndarray, shape=(n, n), dtype=bool
        '''

        intervals, values = ann.to_interval_values()

        intervals, values = adjust_intervals(intervals, values,
                                             t_min=0, t_max=duration)
        # Re-index the labels
        ids, _ = index_labels(values)

        rate = float(self.hop_length) / self.sr
        # Sample segment labels on our frame grid
        _, labels = intervals_to_samples(intervals, ids, sample_size=rate)

        # Make the agreement matrix
        return {'agree': np.equal.outer(labels, labels)}


Instruction:
How would you explain what the following Python 3 function does
def transform_audio(self, y):
        '''Compute the STFT magnitude and phase.

        Parameters
        ----------
        y : np.ndarray
            The audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape=(n_frames, 1 + n_fft//2)
                STFT magnitude

            data['phase'] : np.ndarray, shape=(n_frames, 1 + n_fft//2)
                STFT phase
        '''
        n_frames = self.n_frames(get_duration(y=y, sr=self.sr))

        D = stft(y, hop_length=self.hop_length,
                 n_fft=self.n_fft)

        D = fix_length(D, n_frames)

        mag, phase = magphase(D)
        if self.log:
            mag = amplitude_to_db(mag, ref=np.max)

        return {'mag': mag.T[self.idx].astype(np.float32),
                'phase': np.angle(phase.T)[self.idx].astype(np.float32)}

Response: Compute the STFT magnitude and phase of the audio buffer.


Instruction:
Can you generate a brief explanation for the following Python 3 code
def transform_audio(self, y):
        '''Compute the STFT with phase differentials.

        Parameters
        ----------
        y : np.ndarray
            the audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape=(n_frames, 1 + n_fft//2)
                The STFT magnitude

            data['dphase'] : np.ndarray, shape=(n_frames, 1 + n_fft//2)
                The unwrapped phase differential
        '''
        data = super(STFTPhaseDiff, self).transform_audio(y)
        data['dphase'] = self.phase_diff(data.pop('phase'))
        return data

Response: Compute the STFT with phase differentials.


Instruction:
Write a Python 3 script for
computing the STFT data from the audio data.

Response:
def transform_audio(self, y):
        '''Compute the STFT

        Parameters
        ----------
        y : np.ndarray
            The audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape=(n_frames, 1 + n_fft//2)
                The STFT magnitude
        '''
        data = super(STFTMag, self).transform_audio(y)
        data.pop('phase')

        return data


Instruction:
Can you generate the documentation for the following Python 3 function
def _pad_nochord(target, axis=-1):
    '''Pad a chord annotation with no-chord flags.

    Parameters
    ----------
    target : np.ndarray
        the input data

    axis : int
        the axis along which to pad

    Returns
    -------
    target_pad
        `target` expanded by 1 along the specified `axis`.
        The expanded dimension will be 0 when `target` is non-zero
        before padding, and 1 otherwise.
    '''
    ncmask = ~np.max(target, axis=axis, keepdims=True)

    return np.concatenate([target, ncmask], axis=axis)

Response: Pad a chord annotation with no - chord flags.


Instruction:
Here you have a function in Python 3, explain what it does
def empty(self, duration):
        '''Empty chord annotations

        Parameters
        ----------
        duration : number
            The length (in seconds) of the empty annotation

        Returns
        -------
        ann : jams.Annotation
            A chord annotation consisting of a single `no-chord` observation.
        '''
        ann = super(ChordTransformer, self).empty(duration)

        ann.append(time=0,
                   duration=duration,
                   value='N', confidence=0)

        return ann

Response:
Empty chord annotations

        Parameters
        ----------
        duration : number
            The length (in seconds) of the empty annotation

        Returns
        -------
        ann : jams.Annotation
            A chord annotation consisting of a single `no-chord` observation.


Instruction:
How would you implement a function in Python 3 that
applies the chord transformation.

Response:
def transform_annotation(self, ann, duration):
        '''Apply the chord transformation.

        Parameters
        ----------
        ann : jams.Annotation
            The chord annotation

        duration : number > 0
            The target duration

        Returns
        -------
        data : dict
            data['pitch'] : np.ndarray, shape=(n, 12)
            data['root'] : np.ndarray, shape=(n, 13) or (n, 1)
            data['bass'] : np.ndarray, shape=(n, 13) or (n, 1)

            `pitch` is a binary matrix indicating pitch class
            activation at each frame.

            `root` is a one-hot matrix indicating the chord
            root's pitch class at each frame.

            `bass` is a one-hot matrix indicating the chord
            bass (lowest note) pitch class at each frame.

            If sparsely encoded, `root` and `bass` are integers
            in the range [0, 12] where 12 indicates no chord.

            If densely encoded, `root` and `bass` have an extra
            final dimension which is active when there is no chord
            sounding.
        '''
        # Construct a blank annotation with mask = 0
        intervals, chords = ann.to_interval_values()

        # Get the dtype for root/bass
        if self.sparse:
            dtype = np.int
        else:
            dtype = np.bool

        # If we don't have any labeled intervals, fill in a no-chord
        if not chords:
            intervals = np.asarray([[0, duration]])
            chords = ['N']

        # Suppress all intervals not in the encoder
        pitches = []
        roots = []
        basses = []

        # default value when data is missing
        if self.sparse:
            fill = 12
        else:
            fill = False

        for chord in chords:
            # Encode the pitches
            root, semi, bass = mir_eval.chord.encode(chord)
            pitches.append(np.roll(semi, root))

            if self.sparse:
                if root in self._classes:
                    roots.append([root])
                    basses.append([(root + bass) % 12])
                else:
                    roots.append([fill])
                    basses.append([fill])
            else:
                if root in self._classes:
                    roots.extend(self.encoder.transform([[root]]))
                    basses.extend(self.encoder.transform([[(root + bass) % 12]]))
                else:
                    roots.extend(self.encoder.transform([[]]))
                    basses.extend(self.encoder.transform([[]]))

        pitches = np.asarray(pitches, dtype=np.bool)
        roots = np.asarray(roots, dtype=dtype)
        basses = np.asarray(basses, dtype=dtype)

        target_pitch = self.encode_intervals(duration, intervals, pitches)

        target_root = self.encode_intervals(duration, intervals, roots,
                                            multi=False,
                                            dtype=dtype,
                                            fill=fill)
        target_bass = self.encode_intervals(duration, intervals, basses,
                                            multi=False,
                                            dtype=dtype,
                                            fill=fill)

        if not self.sparse:
            target_root = _pad_nochord(target_root)
            target_bass = _pad_nochord(target_bass)

        return {'pitch': target_pitch,
                'root': target_root,
                'bass': target_bass}


Instruction:
Can you generate the documentation for the following Python 3 function
def transform_annotation(self, ann, duration):
        '''Apply the chord transformation.

        Parameters
        ----------
        ann : jams.Annotation
            The chord annotation

        duration : number > 0
            The target duration

        Returns
        -------
        data : dict
            data['pitch'] : np.ndarray, shape=(n, 12)

            `pitch` is a binary matrix indicating pitch class
            activation at each frame.
        '''
        data = super(SimpleChordTransformer,
                     self).transform_annotation(ann, duration)

        data.pop('root', None)
        data.pop('bass', None)
        return data

Response: Apply the chord transformation.


Instruction:
How would you explain what the following Python 3 function does
def set_transition(self, p_self):
        '''Set the transition matrix according to self-loop probabilities.

        Parameters
        ----------
        p_self : None, float in (0, 1), or np.ndarray [shape=(n_labels,)]
            Optional self-loop probability(ies), used for Viterbi decoding
        '''
        if p_self is None:
            self.transition = None
        else:
            self.transition = transition_loop(len(self._classes), p_self)

Response: Set the transition matrix according to self - loop probabilities.


Instruction:
Implement a function in Python 3 to
simplify a chord string down to the vocabulary space

Response:
def simplify(self, chord):
        '''Simplify a chord string down to the vocabulary space'''
        # Drop inversions
        chord = re.sub(r'/.*$', r'', chord)
        # Drop any additional or suppressed tones
        chord = re.sub(r'\(.*?\)', r'', chord)
        # Drop dangling : indicators
        chord = re.sub(r':$', r'', chord)

        # Encode the chord
        root, pitches, _ = mir_eval.chord.encode(chord)

        # Build the query
        # To map the binary vector pitches down to bit masked integer,
        # we just dot against powers of 2
        P = 2**np.arange(12, dtype=int)
        query = self.mask_ & pitches[::-1].dot(P)

        if root < 0 and chord[0].upper() == 'N':
            return 'N'
        if query not in QUALITIES:
            return 'X'

        return '{}:{}'.format(PITCHES[root], QUALITIES[query])


Instruction:
Implement a Python 3 function for
transforming an annotation to chord - tag encoding

Response:
def transform_annotation(self, ann, duration):
        '''Transform an annotation to chord-tag encoding

        Parameters
        ----------
        ann : jams.Annotation
            The annotation to convert

        duration : number > 0
            The duration of the track

        Returns
        -------
        data : dict
            data['chord'] : np.ndarray, shape=(n, n_labels)
                A time-varying binary encoding of the chords
        '''

        intervals, values = ann.to_interval_values()

        chords = []
        for v in values:
            chords.extend(self.encoder.transform([self.simplify(v)]))

        dtype = self.fields[self.scope('chord')].dtype

        chords = np.asarray(chords)

        if self.sparse:
            chords = chords[:, np.newaxis]

        target = self.encode_intervals(duration, intervals, chords,
                                       multi=False, dtype=dtype)

        return {'chord': target}


Instruction:
Can you implement a function in Python 3 that
computes the CQT magnitude and phase of the audio buffer.

Response:
def transform_audio(self, y):
        '''Compute the CQT

        Parameters
        ----------
        y : np.ndarray
            The audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape = (n_frames, n_bins)
                The CQT magnitude

            data['phase']: np.ndarray, shape = mag.shape
                The CQT phase
        '''
        n_frames = self.n_frames(get_duration(y=y, sr=self.sr))

        C = cqt(y=y, sr=self.sr, hop_length=self.hop_length,
                fmin=self.fmin,
                n_bins=(self.n_octaves * self.over_sample * 12),
                bins_per_octave=(self.over_sample * 12))

        C = fix_length(C, n_frames)

        cqtm, phase = magphase(C)
        if self.log:
            cqtm = amplitude_to_db(cqtm, ref=np.max)

        return {'mag': cqtm.T.astype(np.float32)[self.idx],
                'phase': np.angle(phase).T.astype(np.float32)[self.idx]}


Instruction:
Implement a Python 3 function for
computing CQT magnitude. Parameters ---------- y : np.ndarray the audio buffer Returns ------- data : dict data['mag'] : np.ndarray, shape=(n_frames, n_bins) The CQT magnitude

Response:
def transform_audio(self, y):
        '''Compute CQT magnitude.

        Parameters
        ----------
        y : np.ndarray
            the audio buffer

        Returns
        -------
        data : dict
            data['mag'] : np.ndarray, shape=(n_frames, n_bins)
                The CQT magnitude
        '''
        data = super(CQTMag, self).transform_audio(y)
        data.pop('phase')
        return data