plotting 3 independent data and 1 response (output)

Hello

I have data of 3 independent variables and one output. you can think of it as 3 columns of data and one response variable. I wonder if I can plot a surface that shows the variation in the respons or output variable as the other 3 data variables change.

Thank you

Aziz

Answer 1

[William Rose]

@Abdulaziz Abutunis,

What you are requesting would require a 4 dimensional plot. Let's call the output variable P and the inputs x,y,z. Several options exist:

1. Make surface plots of P on the vertical axis versus pairs of input variables, while holding the third variable constant: P vs x,y at fixed z; P vs y,z at fixed x; P vs z,x at fixedy.

2. Calculate a surface of constant P and make a 3D plot of that surface in x,y,z space. This sounds hard but Matlab has a great funciton, isosurface(), to make this easy.

The plots below illustrate option 1 (left) and option 2 (right), for the function

p(x,y,z)=(1-abs(x))*cos(y*pi/2)*cos(z*pi*3);

Code to make the figures is attached. The same color scale is used in both sets of plots. The left hand plots have p() on the vertical axis; the right hand plots show surface of constant p, in x,y,z space. For the plots on the right, I rotated each plot by hand to a perspective that I liked more than the default perspective, before doing the screen shot. When you hover the cursor over the plot area for a few seconds, some icons appear at the top right of the plot area. One icon is a little cube with a circular arrow around it. Click it. Then you can click and driag in the plot area to rotate it in 3D.

[Abdulaziz Abutunis]

Hi William, Thank you for the good explanation. I have a question, can this code be applied to 3D plot experimental data where there is no function that describes the relationship between the x,y,z, and the output "P"

Thanks

Aziz

[William Rose]

@Abdulaziz Abutunis

Aziz, You could do this with experimental data. To use these plotting routines, your data needs to be sampled on a regular grid that has constant spacing along each axis. The spacing can be different on different axes. If your experimental samples are not all regularly spaced, or if you have a grid with some missing data, you would need to interpolate your data to estimate the values on a regular 3D grid. For visually pleasing results in 3D, you need a reasonablty dense grid, such as a minimm of 10 points along each dimension, in my opinion. In the example I posted, there were 21 points in each dimension, i.e. points - a lot of points!

Once you figure out how to do 3D interpolation, it is easy to generate a lot of points by interpolation. You will have to use your good judgeent to decide if you believe in those estimated values. It is good to be cautious if the interpolated data set is several times larger than the experimental data set.

To do 3D interpolation, use F=scatteredInterpolant(). The Matlab Help for scatteredInterpolant() has some good examples. An important difference between the examples in the Help and your situation is that you will need to read the experimental data from a file, before you call scatteredInterpolant().

Bill

[Abdulaziz Abutunis]

Thank you.. I will work on that

Regards

Aziz

Answer 2

[William Rose]

@Abdulaziz Abutunis

This version of the code reads 4D experimental data (x,y,z,p) from a file and plots it in multiple ways, like script I posted previously. Experimental data may not be exactly on a grid, or may have missing data points. Therefore the experimental data is interpolated and evaluated at all points on a 3D grid before plotting.

The output from the program is two figures with three plots each. Figure 1 (left) shows interpolated p versus x,y at a fixed level of z, and p vs. y,z at fixed x, and p versus x,z at fixed y. Figure 2 shows three iso-p-surfaces in x,y,z space, i.e. three surfaces, each of which has a constant value of p. These figures use datat file 3 described beow.

Attached files: the script to read, interpolate, and plot the data; four text files of simulated data to use as inputs to the program. Each text file has four columns: x,y,z,p. Simulated data files:

1. fourDdataGridN00.txt: 11x11x11 values of p on a regular x,y,z grid, with no measurement noise.

2. fourDdataRandN00.txt: 512 values of p at randomly chosen points in the sample volume, with no measurement noise.

3. fourDdataRandN02.txt: 512 values of p at randomly chosen points in the sample volume, with measurement amplitude=0.02.

4. fourDdataRandN04.txt: 512 values of p at randomly chosen points in the sample volume, with measurement amplitude=0.04.

[Abdulaziz Abutunis]

Wow that is so kind of you William, your codes are really helpful. I appreciate your help.

Best regards

Aziz

[William Rose]

You are welcome, Prof.@Abdulaziz Abutunis.