I want to create the surface plot by surface command for my sets of data.

In my data there is temperature in one column,speed in one column and modulus of elasticity in one column.I would like to take temperature as X and Speed as Y and Modulus of elasticity as Z.I am trying to use the surface command but it is showing error such as 'Data dimension must agree',I am attaching the script please find the attachment.

[Walter Roberson]

Note: the file you attached under the name youngsmodulus.xls is not a .xls file: it is a .xlsx file. It may be necessary to rename it to .xlsx extension in order to use it.

[Prateek Srivastava]

yes actually we cannot attach xlsx when we are asking the question in matlab so that is the reason I have attached the xls file.

[Walter Roberson]

You can zip any kind of file and attach the .zip

Answer 1

[Walter Roberson]

You have scattered data; it is not possible to surface() it.

N = 20;
mins = min(A); maxs = max(A);
[Temperature, Speed] = ndgrid(linspace(mins(1),maxs(1),N), linspace(mins(2),maxs(2),N));
F = scatteredInterpolant(A(:,1),A(:,2),A(:,3));
vq = F(Temperature,Speed);
surf(Temperature, Speed, vq);

[Prateek Srivastava]

it worked thanks a lot but can you explain what is the use of creating N ,mins, maxs, and than what is the point of using ngrid .Also you use scatteredInterpolant and letter 'F' .Could you please explain what do you mean by scattered data.I am new to Matlab. Thanks a Lot.

[Walter Roberson]

You have 7 points at various locations on a 2D grid, and you have the resulting value for each of those 7 locations. You cannot create a surface directly from points that are scattered. (You could triangulate to create flat faces, but the resulting graph would not be smooth at all.)

So instead what you do is create a regular grid of points and ask MATLAB to interpolate what the likely value would be at each of the points based upon the known values. There are different models that you can use about how much each of the surrounding points influence any given point; the default method for scatteredInterpolant is bilinear.

The next question becomes which points you should sample at to get a representative smooth graph. Typically you would choose points equally spaced between the minimum and maximum data value for the given axes. But how many equally spaced points? That is an arbitrary choice: the more you use the smoother the plot will be but the more computation it will take. I made it easy to change the number of points in each direction by putting it into the variable N. N is the total number of points to use in each direction, including the two endpoints. (For example, if N were 3, then the three points would be the minimum, the maximum, and half way between.) Once you know the points you want to select in each direction, ndgrid() is used to create full 2D grids of coordinates.

scatteredInterpolant is the newest of the several routines that can accept a list of arbitrary X, Y, and Z points and allow interpolation based upon those points. scatteredInterpolant returns an Object (in the "object-oriented sense). When you invoke the object with function-like syntax, inputing arrays of coordinates, then MATLAB uses the data stored in the object to predict (interpolate) the value at each of the locations that were passed in. The vq variable in the code is the returned values, the modulus predicted for each of the grid points specified by the Temperature, Speed 2D grids.

[Prateek Srivastava]

Very nicely Explained ,thanks a lot for your help.If i have any other doubts regarding Matlab can I ask you or email you the questions,or do I need to ask in the community only.Anyway thanks for the help once again very nicely and clearly explained.

[Walter Roberson]

I prefer if you ask in the community.

[Prateek Srivastava]

ok i will do it.

[Prateek Srivastava]

Could you also explain how could I find the function F in the script because I have to describe the function and its formulation to find the optimal temperature and speed for the process. Basically I need to find the function like x2 − 4x + 7.

[Walter Roberson]

The function generated is piecewise in 2d. It is a bunch of "if x is in this range and y is in this range then the formula is such and such. The function is not a smooth function, with discontinuous derivatives at every boundary between cells.

[Prateek Srivastava]

but could I get some kind of equation from these results so that I could put some kind of constant value and optimize the process for further use,some kind of formulation for this kind of function.

[Walter Roberson]

No, scatteredInterpolant cannot return equations.

You could in theory replicate the functionality by using a Delaunay triangulation to divide the surface up into triangles according to which points are closest. That done, you could go through and construct a table of linear constraints that define the boundaries of each of the triangles, along with the triangular interpolation coefficients that are relevant to the interior of that triangle. That done, if you have the Symbolic Toolbox, you could construct a big piecewise() -- if the x, y have this relationship then this calculation, if the x, y have this other relationship then this other calculation, and so on.

You will likely find that in practice, optimization over such a piecewise equation does not work very well.

But I suspect that what you are really looking for is a single non-piecewise surface equation generated out of the known points. If so, then the answer is that given any finite number of points specified to finite precision, and corresponding result values, that there are an infinite number of surface equations that fit the points exactly (to within round-off).

This is the infinity of continuous numbers, the uncountable infinity, not the mere countable infinity, so it turns out that allowing for the possibility that the measurements might not be exact (noise in the system or imprecision in the readings) does not increase the number of potential solutions, since as far as we can tell there is no "larger" infinity except as pure abstractions.

When there are an infinite number of possible functions that all fit the known data exactly (to round-off) then the probability that any given function is the "real" function for the system is precisely zero.

The situation is extremely different if you know the form of the function and are just missing the values of the coefficients. You do not have enough data to fit anything more complicated than a cubic in one of your variables with a quadratic in the other (total power 6), and it should be obvious from the surface plot that a surface that simple is not an adequate explanation for the surface you are getting. But it is possible, you can fit up to 6 degrees of freedom with 7 data points, if you know the form of the equation.