line source
+ − % DIFF differentiates the data in AO.
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ − %
+ − % DESCRIPTION: DIFF differentiates the data in AO. The result is a data
+ − % series the same length as the input series.
+ − % In case of method 'diff' computes the difference between two samples, in which
+ − % case the resulting time object has the length of the input
+ − % series -1 sample.
+ − % CALL: bs = diff(a1,a2,a3,...,pl)
+ − % bs = diff(as,pl)
+ − % bs = as.diff(pl)
+ − %
+ − % INPUTS: aN - input analysis objects
+ − % as - input analysis objects array
+ − % pl - input parameter list
+ − %
+ − % OUTPUTS: bs - array of analysis objects, one for each input,
+ − % containing the differentiated data
+ − %
+ − % <a href="matlab:utils.helper.displayMethodInfo('ao', 'diff')">Parameters Description</a>
+ − %
+ − % REFERENCES:
+ − % [1] L. Ferraioli, M. Hueller and S. Vitale, Discrete derivative
+ − % estimation in LISA Pathfinder data reduction,
+ − % <a
+ − % href="matlab:web('http://www.iop.org/EJ/abstract/0264-9381/26/9/094013/','-browser')">Class. Quantum Grav. 26 (2009) 094013.</a>
+ − % [2] L. Ferraioli, M. Hueller and S. Vitale, Discrete derivative
+ − % estimation in LISA Pathfinder data reduction
+ − % <a href="matlab:web('http://arxiv.org/abs/0903.0324v1','-browser')">http://arxiv.org/abs/0903.0324v1</a>
+ − %
+ − % VERSION: $Id: diff.m,v 1.36 2011/08/03 19:18:56 adrien Exp $
+ − %
+ − %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+ −
+ − % PARAMETERS: method - the method to use: [default: '3POINT']
+ − % 'diff' - like MATLABs diff
+ − % compute difference between each two samples
+ − % xaxis will be integers from 1 to length
+ − % of resulting object
+ − % '2POINT' - 2 point derivative computed as
+ − % [y(i+1)-y(i)]./[x(i+1)-x(i)].
+ − % '3POINT' - 3 point derivative. Compute derivative
+ − % at i as [y(i+1)-y(i-1)] / [x(i+1)-x(i-1)].
+ − % For i==1, the output is computed as
+ − % [y(2)-y(1)]/[x(2)-x(1)]. The last sample
+ − % is computed as [y(N)-y(N-1)]/[x(N)-x(N-1)].
+ − % '5POINT' - 5 point derivative. Compute derivative dx
+ − % at i as
+ − % [-y(i+2)+8*y(i+1)-8*y(i-1)+y(i-2)] /
+ − % [3*(x(i+2)-x(i-2))].
+ − % For i==1, the output is computed as
+ − % [y(2)-y(1)]/[x(2)-x(1)]. The last sample
+ − % is computed as [y(N)-y(N-1)]/[x(N)-x(N-1)].
+ − % 'ORDER2' - Compute derivative using a 2nd order
+ − % method.
+ − % 'ORDER2SMOOTH' - Compute derivative using a 2nd order
+ − % method with a parabolic fit to 5
+ − % consecutive samples.
+ − % 'filter' - applies an IIR filter built from a
+ − % single pole at the chosen frequency. The
+ − % filter is applied forwards and backwards
+ − % (filtfilt) to achieve the desired f^2
+ − % response. This only works for time-series
+ − % AOs. For this method, you can specify the
+ − % pole frequency with an additional parameter
+ − % 'f0' [default: 1/Nsecs]
+ − % 'FPS' - Calculates five points derivative using
+ − % utils.math.fpsder function. If you call
+ − % with this oprtion you may add also the
+ − % parameters:
+ − % 'ORDER' derivative order, supperted
+ − % values are:
+ − % 'ZERO', 'FIRST', 'SECOND'
+ − % 'COEFF' coefficient used for the
+ − % derivation. Refers to the fpsder help
+ − % for further details.
+ − %
+ − %
+ −
+ − function varargout = diff(varargin)
+ −
+ − % Check if this is a call for parameters
+ − if utils.helper.isinfocall(varargin{:})
+ − varargout{1} = getInfo(varargin{3});
+ − return
+ − end
+ −
+ − import utils.const.*
+ − utils.helper.msg(msg.PROC3, 'running %s/%s', mfilename('class'), mfilename);
+ −
+ − % Collect input variable names
+ − in_names = cell(size(varargin));
+ − for ii = 1:nargin,in_names{ii} = inputname(ii);end
+ −
+ − % Collect all AOs and plists
+ − [as, ao_invars] = utils.helper.collect_objects(varargin(:), 'ao', in_names);
+ − pl = utils.helper.collect_objects(varargin(:), 'plist', in_names);
+ −
+ − % Decide on a deep copy or a modify
+ − bs = copy(as, nargout);
+ −
+ − % combine plists
+ − pl = parse(pl, getDefaultPlist());
+ −
+ − % Extract method
+ − method = find(pl, 'method');
+ −
+ − for jj = 1:numel(bs)
+ −
+ − % Diff can't work for cdata objects since we need x data
+ − if isa(bs(jj).data, 'cdata')
+ − error('### diff doesn''t work with cdata AOs since we need an x-data vector.');
+ − end
+ −
+ − % Compute derivative with selected method
+ − switch lower(method)
+ − case 'diff'
+ − yunit = bs(jj).yunits;
+ − y = bs(jj).y;
+ − x = bs(jj).x;
+ − newX = x(1:end-1); % cut the last sample from the time series to make x and y same length
+ − dy = diff(y);
+ − bs(jj).data.setY(dy);
+ − bs(jj).data.setX(newX);
+ − bs(jj).setYunits(yunit);
+ − case '2point'
+ − x = bs(jj).data.getX;
+ − dx = diff(x);
+ − y = bs(jj).data.getY;
+ − dy = diff(y);
+ − z = dy./dx;
+ − bs(jj).data.setY(z);
+ − bs(jj).data.setX((x(1:end-1)+x(2:end))/2);
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case '3point'
+ − x = bs(jj).data.getX;
+ − dx = diff(x);
+ − y = bs(jj).data.getY;
+ − z = zeros(size(y));
+ − z(2:end-1) = (y(3:end)-y(1:end-2)) ./ (dx(2:end)+dx(1:end-1));
+ − z(1) = (y(2)-y(1)) ./ (dx(1));
+ − z(end) = 2*z(end-1)-z(end-2);
+ − bs(jj).data.setY(z);
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case '5point'
+ − x = bs(jj).data.getX;
+ − dx = diff(x);
+ − y = bs(jj).data.getY;
+ − z = zeros(size(y));
+ − z(1) = (y(2)-y(1)) ./ (dx(1));
+ − z(2) = (y(3)-y(1))./(dx(2)+dx(1));
+ − z(3:end-2) = (-y(5:end) + 8.*y(4:end-1) - 8.*y(2:end-3) + y(1:end-4)) ./ (3.*(x(5:end)-x(1:end-4)));
+ − z(end-1) = 2*z(end-2)-z(end-3);
+ − z(end) = 2*z(end-1)-z(end-2);
+ − bs(jj).data.setY(z);
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case 'order2'
+ − x = bs(jj).data.getX;
+ − dx = diff(x);
+ − y = bs(jj).data.getY;
+ − z = zeros(size(y));
+ − m = length(y);
+ − % y'(x1)
+ − z(1) = (1/dx(1)+1/dx(2))*(y(2)-y(1))+...
+ − dx(1)/(dx(1)*dx(2)+dx(2)^2)*(y(1)-y(3));
+ − % y'(xm)
+ − z(m) = (1/dx(m-2)+1/dx(m-1))*(y(m)-y(m-1))+...
+ − dx(m-1)/(dx(m-1)*dx(m-2)+dx(m-2)^2)*(y(m-2)-y(m));
+ − % y'(xi) (i>1 & i<m)
+ − dx1 = repmat(dx(1:m-2),1,1);
+ − dx2 = repmat(dx(2:m-1),1,1);
+ − y1 = y(1:m-2); y2 = y(2:m-1); y3 = y(3:m);
+ − z(2:m-1) = 1./(dx1.*dx2.*(dx1+dx2)).*...
+ − (-dx2.^2.*y1+(dx2.^2-dx1.^2).*y2+dx1.^2.*y3);
+ − bs(jj).data.setY(z);
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case 'order2smooth'
+ − x = bs(jj).data.getX;
+ − y = bs(jj).data.getY;
+ − dx = diff(x);
+ − m = length(y);
+ − if max(abs(diff(dx)))>sqrt(eps(max(abs(dx))))
+ − error('### The x-step must be constant for method ''ORDER2SMOOTH''')
+ − elseif m<5
+ − error('### Length of y must be at least 5 for method ''ORDER2SMOOTH''.')
+ − end
+ − h = mean(dx);
+ − z = zeros(size(y));
+ − % y'(x1)
+ − z(1) = sum(y(1:5).*[-54; 13; 40; 27; -26])/70/h;
+ − % y'(x2)
+ − z(2) = sum(y(1:5).*[-34; 3; 20; 17; -6])/70/h;
+ − % y'(x{m-1})
+ − z(m-1) = sum(y(end-4:end).*[6; -17; -20; -3; 34])/70/h;
+ − % y'(xm)
+ − z(m) = sum(y(end-4:end).*[26; -27; -40; -13; 54])/70/h;
+ − % y'(xi) (i>2 & i<(N-1))
+ − Dc = [2 1 0 -1 -2];
+ − tmp = convn(Dc,y)/10/h;
+ − z(3:m-2) = tmp(5:m);
+ − bs(jj).data.setY(z);
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case 'filter'
+ − error('### Comming with release 2.5');
+ − case 'fps'
+ − order = find(pl, 'ORDER');
+ − coeff = find(pl, 'COEFF');
+ − x = bs(jj).data.getX;
+ − dx = x(2)-x(1);
+ − fs = 1/dx;
+ − y = bs(jj).data.getY;
+ − params = struct('ORDER', order, 'COEFF', coeff, 'FS', fs);
+ − z = utils.math.fpsder(y, params);
+ − bs(jj).data.setY(z);
+ − % setting units
+ − switch lower(order)
+ − case 'first'
+ − bs(jj).data.setYunits(bs(jj).data.yunits./bs(jj).data.xunits);
+ − case 'second'
+ − bs(jj).data.setYunits(bs(jj).data.yunits.*bs(jj).data.xunits.^(-2));
+ − end
+ − otherwise
+ − error('### Unknown method for computing the derivative.');
+ − end
+ −
+ − % name for this object
+ − bs(jj).name = sprintf('diff(%s)', ao_invars{jj});
+ − % add history
+ − bs(jj).addHistory(getInfo('None'), pl, ao_invars(jj), bs(jj).hist);
+ − end
+ −
+ − % Clear the errors since they don't make sense anymore
+ − clearErrors(bs);
+ −
+ − % Set output
+ − if nargout == numel(bs)
+ − % List of outputs
+ − for ii = 1:numel(bs)
+ − varargout{ii} = bs(ii);
+ − end
+ − else
+ − % Single output
+ − varargout{1} = bs;
+ − end
+ − end
+ −
+ − %--------------------------------------------------------------------------
+ − % Get Info Object
+ − %--------------------------------------------------------------------------
+ − function ii = getInfo(varargin)
+ −
+ − if nargin == 1 && strcmpi(varargin{1}, 'None')
+ − sets = {};
+ − pl = [];
+ − else
+ − sets = {'Default'};
+ − pl = getDefaultPlist;
+ − end
+ − % Build info object
+ − ii = minfo(mfilename, 'ao', 'ltpda', utils.const.categories.sigproc, '$Id: diff.m,v 1.36 2011/08/03 19:18:56 adrien Exp $', sets, pl);
+ − end
+ −
+ − %--------------------------------------------------------------------------
+ − % Get Default Plist
+ − %--------------------------------------------------------------------------
+ −
+ − function plout = getDefaultPlist()
+ − persistent pl;
+ − if exist('pl', 'var')==0 || isempty(pl)
+ − pl = buildplist();
+ − end
+ − plout = pl;
+ − end
+ −
+ − function pl = buildplist()
+ − pl = plist();
+ −
+ − % Method
+ − p = param({'method',['The method to use. Choose between:<ul>', ...
+ − '' ...
+ − '<li>''2POINT'' - 2 point derivative computed as [y(i+1)-y(i)]./[x(i+1)-x(i)]', ...
+ − '</li>' ...
+ − '<li>''3POINT'' - 3 point derivative. Compute derivative dx at i as <br>', ...
+ − '<tt>[y(i+1)-y(i-1)] / [x(i+1)-x(i-1)]</tt><br>', ...
+ − 'For <tt>i==1</tt>, the output is computed as <tt>[y(2)-y(1)]/[x(2)-x(1)]</tt>.<br>', ...
+ − 'The last sample is computed as <tt>[y(N)-y(N-1)]/[x(N)-x(N-1)]</tt>', ...
+ − '</li>' ...
+ − '<li>''5POINT'' - 5 point derivative. Compute derivative dx at i as <br>', ...
+ − '<tt>[-y(i+2)+8*y(i+1)-8*y(i-1)+y(i-2)] / [3*(x(i+2)-x(i-2))]</tt><br>', ...
+ − 'For <tt>i==1</tt>, the output is computed as <tt>[y(2)-y(1)]/[x(2)-x(1)]</tt><br>', ...
+ − 'The last sample is computed as <tt>[y(N)-y(N-1)]/[x(N)-x(N-1)]</tt>', ...
+ − '</li>' ...
+ − '<li>''ORDER2'' - Compute derivative using a 2nd order method', ...
+ − '</li>' ...
+ − '<li>''ORDER2SMOOTH'' - Compute derivative using a 2nd order method<br>', ...
+ − 'with a parabolic fit to 5 consecutive samples', ...
+ − '</li>' ...
+ − '<li>''filter'' - applies an IIR filter built from a single pole at the chosen frequency.<br>', ...
+ − 'The filter is applied forwards and backwards (filtfilt) to achieve the desired f^2<br>', ...
+ − 'response. This only works for time-series AOs.<br>', ...
+ − 'For this method, you can specify the pole frequency with an additional parameter ''F0'' (see below):', ...
+ − '</li>'...
+ − '<li>''FPS'' - Calculates five points derivative using utils.math.fpsder.<br>', ...
+ − 'When calling with this option you may add also the parameters ''ORDER'' (see below)<br>', ...
+ − 'and ''COEFF'' (see below)' ...
+ − '</li>' ...
+ − ]}, {1, {'2POINT', '3POINT', '5POINT', 'ORDER2', 'ORDER2SMOOTH', 'FILTER', 'FPS'}, paramValue.SINGLE});
+ − pl.append(p);
+ −
+ − % F0
+ − p = param({'f0','The pole frequency for the ''filter'' method.'}, {1, {'1/Nsecs'}, paramValue.OPTIONAL});
+ − pl.append(p);
+ −
+ − % Order
+ − p = param({'ORDER','Derivative order'}, {1, {'ZERO', 'FIRST', 'SECOND'}, paramValue.SINGLE});
+ − pl.append(p);
+ −
+ − % Coeff
+ − p = param({'COEFF',['Coefficient used for the derivation. <br>', ...
+ − 'Refer to the <a href="matlab:doc(''utils.math.fpsder'')">fpsder help</a> for further details']}, paramValue.EMPTY_DOUBLE);
+ − pl.append(p);
+ −
+ − end
+ −