Data: Interp1 spline and cubic method

Question

jacob Mitch 2019-11-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/488737-data-interp1-spline-and-cubic-method

编辑： Matt J 2019-11-1

Im just trying to figure out how I would use the Interp1 function with the spline method and the Interp1 withe cubic method for approximation. Are the Interp1 function and some call to spline linked in the same code.

For example how would you approximate this data using the Interp1 function and spline method/ whats the difference between the cubic method.

year=[1;2;3;4;5;6;7;8;9;10];
pop=[5;10;15;20;25;30;35;40;50;60];

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Answer 1

Matt J 2019-11-1

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/488737-data-interp1-spline-and-cubic-method#answer_399380

编辑：Matt J 2019-11-1

how would you approximate this data using the Interp1 function and spline method

For example,

year=[1;2;3;4;5;6;7;8;9;10];
pop=[5;10;15;20;25;30;35;40;50;60];
interp1(year,pop, 2.5,'spline')

whats the difference between the cubic method.

It's just a different interpolation kernel. The cubic method will gives an interpolated curve that is only once-differentiable, but it will follow the shape of the data more closely than a spline interpolation. Example:

y=[zeros(1,10) 1 1.15 1.15 1  zeros(1,10)];
x=1:numel(y);
xq=linspace(1,numel(y),1000);
plot(x,y,'o',xq,interp1(y,xq,'spline'), xq, interp1(y,xq,'cubic'))
legend('', 'Spline','Cubic')

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jacob Mitch 2019-11-1

Hi thanks Im trying to graph it as well as you have but mine looks mess, I'm trying but it doesnt look like yours. Thanks again!

year=[1;2;3;4;5;6;7;8;9;10];
pop=[5;nan;15;20;nan;30;nan;40;50;60];
NotMissing=~isnan(pop);
newp=pop(NotMissing,1);
newyear=year(NotMissing,1);
vq1 = interp1(newyear,newp,year,'spline');
plot(newyear,newp,'o',year,interp1(newp,year,'spline'), year, interp1(newp,year,'cubic'))
legend('', 'Spline','Cubic')

Matt J 2019-11-1

编辑：Matt J 2019-11-1

This might be what you want

year=[1;2;3;4;5;6;7;8;9;10];
pop=[5;nan;15;20;nan;30;nan;40;50;60];
newp = fillmissing( pop, 'pchip','SamplePoints',year);
yq=linspace(1,10,100);
plot(year,newp,'o',...
     yq,interp1(newp,yq,'spline'),'x',...
     yq, interp1(newp,yq,'cubic'));
 
legend('Data', 'Spline/Pchip','Cubic/Pchip')