3D interpolation on table with 3 variables on MATLAB

This is my second program on matlab and I'm not sure how to do this as the tutorials online take all the variables seperately. I have a table that looks like below. The first row is an axis and the first column is another axis. For example I would like to get the z value where x = 2900 and y=45, so I would be interpolating between the values

	1300	    2600	    3750	    4500	    5800	    7100	    8400	    9700	    11000	    12300	    13000
25	0.096234615	0.239117308	0.385056	0.487474444	0.675744828	0.874833803	1.082447024	1.296634021	1.516019091	1.739652846	1.861441923
40	1.511103846	1.893471154	2.130796	2.259105556	2.44990431	2.612664789	2.755516071	2.883509278	2.999915455	3.106855691	3.161123462
50	1.522857692	1.911469231	2.153716	2.284784444	2.480200862	2.647233099	2.794057143	2.925745876	3.045581818	3.155847967	3.211885385
65										3.2499565
70	1.536080769	1.932405769	2.180456	2.315132222	2.515931034	2.687854225	2.839305952	2.975464948	3.099495909	3.213846748	3.271903462
75	1.538284615	1.936078846	2.18504	    2.320225556	2.522023276	2.694714085	2.847036905	2.983931959	3.108698636	3.223707317	3.282188077
89	2.761419231	2.986578846	3.182314667	3.308544444	3.524443966	3.736471127	3.944945833	4.149721134	4.350806364		
107	3.320461538	3.590432692	3.826112	3.977681111	4.237236207	4.492266197	4.742825595	4.989038144			
132	4.096215385	4.429363462	4.719992	4.907214444	5.227143103	5.541824648	5.850966667				
158	4.902823077	5.302086538	5.64978	    5.873674444	6.256731897	6.633349296					
172	5.336980769	5.771873077	6.1502	    6.394043333	6.811125862	7.22114507					
194	7.255061538	6.611538462	6.243153333	6.10436	    6.053547414						
232	8.675807692	7.906665385	7.466062667	7.30002	    7.239393966						
250	10.04953846	9.052298077	8.514525333	8.338423333							
275	11.05449231	9.957344231	9.366130667	9.172244444							
310	13.30755769	11.71417692	10.73216267	10.30784556							
348	14.93913846	13.15035	12.04777067								

Answer 1

[amin]

Hi Hugh,

I am not sure about the Z matrix, and I replaced 0 in the empty positions, and of course, you can change it. For instance, at the fourth row of matrix Z, I assumed that all the elements are zero except the fourth one. In the end, I added a part to plot the data and visualise it.

I hope it helps!

x=[25 40 50 65 70 75 89 107 132 158 172 194 232 250 275 310 348];
y=[1300	2600 3750 4500 5800 7100 8400 9700 11000 12300 13000];
Z=[ 0.096234615	0.239117308	0.385056	0.487474444	0.675744828	0.874833803	1.082447024	1.296634021	1.516019091	1.739652846	1.861441923;
	1.511103846	1.893471154	2.130796	2.259105556	2.44990431	2.612664789	2.755516071	2.883509278	2.999915455	3.106855691	3.161123462;
	1.522857692	1.911469231	2.153716	2.284784444	2.480200862	2.647233099	2.794057143	2.925745876	3.045581818	3.155847967	3.211885385;
			0		0			0		3.2499565   0           0           0           0           0           0           0;
	1.536080769	1.932405769	2.180456	2.315132222	2.515931034	2.687854225	2.839305952	2.975464948	3.099495909	3.213846748	3.271903462;
	1.538284615	1.936078846	2.18504	    2.320225556	2.522023276	2.694714085	2.847036905	2.983931959	3.108698636	3.223707317	3.282188077;
	2.761419231	2.986578846	3.182314667	3.308544444	3.524443966	3.736471127	3.944945833	4.149721134	4.350806364 0           0		;
	3.320461538	3.590432692	3.826112	3.977681111	4.237236207	4.492266197	4.742825595	4.989038144	0           0           0		;
	4.096215385	4.429363462	4.719992	4.907214444	5.227143103	5.541824648	5.850966667	0           0           0           0		;	
	4.902823077	5.302086538	5.64978	    5.873674444	6.256731897	6.633349296	0           0           0           0           0		;		
	5.336980769	5.771873077	6.1502	    6.394043333	6.811125862	7.22114507	0           0           0           0           0		;		
	7.255061538	6.611538462	6.243153333	6.10436	    6.053547414	0           0           0           0           0           0		;			
	8.675807692	7.906665385	7.466062667	7.30002	    7.239393966	0           0           0           0           0           0		;			
	10.04953846	9.052298077	8.514525333	8.338423333	0           0           0           0           0           0           0		;				
	11.05449231	9.957344231	9.366130667	9.172244444	0           0           0           0           0           0           0   	;					
	13.30755769	11.71417692	10.73216267	10.30784556	0           0           0           0           0           0           0		;				
	14.93913846	13.15035	12.04777067	0           0           0           0           0           0           0           0          ];
%Interploated value at 45 and 2900:
interp2(y,x,Z,2900,45) 
%Plot the graph:
[X,Y] = meshgrid(x,y);
Zq = interp2(y,x,Z,Y,X);
surf(Y,X,Zq)