# csdms-contrib/slepian_alpha

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 function [newval,req,dispos,avma]=discinter(pos,val,req) % [newval,req,dispos,avma]=DISCINTER(pos,val,req) % % For non-monotonous vectors (such as with discontinuities, specified % by two or three times the same value), interpolates, i.e. finds the % interpolated value of input values. % Returns different values than requested! % % Returns NaN outside the range, as in regular interpolation. % Also for regular interpolation, i.e. without discontinuities. % 'pos' must not start with a discontinuity % % The 'newval' belong to an upgoing sorted 'req', possibly with % fewer entries than the input 'req', if the latter was discontinuous % either as 2p or 3p. % % Discontinuities at zero are treated as normal ones, so they might % end up having negative values. So when doing inner products % and stuff, make sure to specify values a little bit out of the range. % % Everything discontinuity related will get differences (intervals) % of 0.5 and 1.5 times smint10, all the rest are real intervals. % Changed smint/10 to smallest of 1 m or smint/10. % % Also returns the vector 'dispos' from DISCIDENT(POS) % Also returns the averaging matrix 'avma' from DISCIDENT(POS) % % See DISCINTEREX, and NODINTER % % For example, an request vector [15 30 80 140 200 300 400 400] has % a discontinuity at 400. But the position/value pair has discons at % 15 80 and 400, specified as a repeated value (2p). % The one at 400 is common, but 15 and 80 aren't % The result is: you get values at % [14 14.5 16 30 79 80.5 81 140 200 300 399 401] % If you ask what the value at 15 is, you can't get a straight answer, but % get three values instead. % If you ask what the value is at 400 and 400, you get the values at 399 and 401 % % Last updated by fjsimons-at-alum.mit.edu, October 18th, 2002 [pos,val,req]=deal(pos(:),val(:),req(:)); if pos(1)>pos(end) pos=flipud(pos); val=flipud(val); fli=1; else fli=0; end % If requested values are 2p-3p-discontinuities in the request array, then % destroy, not even leaving the middle value intact for 3p. difreq=diff(req); smint=min(difreq(~~difreq)); smint10=min(1,smint/10); if sum(~difreq) [a,b]=discident(req); % Leave quasi-3p for quadrature; work with NaN's % Smallest interval of req req(~isnan(a))=req(~isnan(a))-(smint10)*a(~isnan(a)); % For 3p, adjust the middle value, for 2p, leave intact req(~b)=req(~b)-(smint10)/2; end % This makes [400 400] into [399 401] req=sort(req); outsid=reqmax(pos); reqout=req(outsid); req=req(~outsid); outvol=repmat(NaN,sum(outsid),1); % What are the discontinuities of 'pos'? [c,d,posdisc,avma]=discident(pos); dispos=c; % If it was flipped, unflip for output if fli==1 dispos=flipud(dispos); avma=flipud(avma); end % So now the requested vector 'req' is free of discontinuities. % Now need to make sure that the values of 'req' % that would be equal to an element of 'pos' are treated % properly. But 'req' can still have values equal to a discontinuity in pos % this was the original point of this program. flag1=0; if ~isempty(intersect(pos,req)) [pdi,inp,inr]=intersect(posdisc,req); if ~isempty(pdi) % Remediate in the request vector, make it want a "3p-discontinuity" % 3p for integration purposes req(inr)=pdi(:)-repmat(smint10,length(pdi),1); req=[req ; pdi(:)+repmat(smint10,length(pdi),1)]; req=[req ; pdi(:)+repmat(smint10/2,length(pdi),1)]; req=sort(req); end flag1=1; % Else you treat those values % I can take them out, knowing they are not discs in either % vector, lookup their unambiguous value and put them in at % the end, knowing the output was sorted anyway. [reqvol,posinpos,posinreq]=intersect(pos,req); newvol=val(posinpos); req=req(~ismember(1:length(req),posinreq)); end % If there are 2p or 3p discontinuities in the positions if sum(~diff(pos)) posorg=pos; % This removes the discontinuities from 'pos'; % it is assumed that 'pos' and 'req' have no common members. % This is where 'req' gets sorted! pos=unique([pos ; req]); ins=[1:length(pos)]'; % reqpos is the index of req in [pos-disc+req] reqpos=ins(ismember(pos,req)); % reqpos is index of one above req in [pos-disc] reqpos=reqpos-[0:length(reqpos)-1]'; % This need to be the position shift needed to translate % the original pos index into pos-disc [a,ind,c]=degamini(posorg); ind=cumsum([0 ind-1]); ind=ind(:); % What is the index, in the original value matrix, of the % parameter just down the one we are requesting? % And then ups-1 is the one right below ups=reqpos+ind(reqpos); newval=val(ups-1)+(req-posorg(ups-1))./... (posorg(ups)-posorg(ups-1)).*(val(ups)-val(ups-1)); else newval=interp1(pos,val,req,'linear'); end if flag1==1 outrows=sortrows([req newval ; reqvol newvol ; reqout outvol]); else outrows=sortrows([req newval ; reqout outvol]); end [req,newval]=deal(outrows(:,1),outrows(:,2));