How to mirror a function vertically?

I have a function with non equal step size in the x axis. How can I mirror it vertically?

Here is my code:

close all; clear all; clc;

depth=[ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.6 1.8 2 2.2 2.4 2.6 2.7 2.8 2.9 3 3.2 3.3 3.4 3.5 3.6 3.7 3.8 4 4.2 4.4 4.6 4.8 4.9 5 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.2 6.3 6.4 6.5 6.6 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16 16.2 16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8 23 23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.4 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 27.6 27.8 28 28.2 28.4 28.6 28.8 29 29.2 29.4 29.6 29.8 30]; rel_dose=[ 61.8 63.2 66 73.8 81.3 86.4 90.5 93.9 96 97.4 98.6 99.2 99.9 99.8 100.7 100 99.2 98.9 98 97.2 96.3 96.1 95.7 95.2 94.7 94.1 93.8 92.8 92.4 92.2 91.7 91.1 90.2 89.6 88.9 88.1 87.2 87.1 86 85.3 85 84.4 84 83.8 83.4 83 82.5 82.1 81.3 81.1 80.3 80.4 79.7 78.7 78.7 77.9 78 77.3 77.2 76.4 76.3 75.6 75.2 74.8 74.1 73.2 72.4 71.9 71.1 70.4 69.7 68.9 68 67.4 66.6 65.9 65.3 64.6 64 63.1 62.4 61.9 61.3 60.5 59.6 59.2 58.5 58 57.4 56.7 56.1 55.5 54.7 54.1 53.8 53 52.4 51.6 51.2 50.8 50.1 49.5 49 48.3 47.8 47.6 46.8 46.3 45.8 45.5 45.1 44.4 43.8 43.5 42.9 42.5 42 41.4 41 40.4 40.3 39.8 39.3 38.9 38.4 38 37.5 37.1 36.6 36.3 35.9 35.4 35.1 34.9 34.4 34.1 33.8 33.4 33 32.6 32.2 31.9 31.5 31.1 30.8 30.4 30.1 29.7 29.5 29.2 28.8 28.4 28.2 27.9 27.5 27.2 26.9 26.6 26.4 25.9 25.9 25.5 25.3 25.1 24.7 24.5 24.2 23.9 23.7 23.3 23.1 22.9 22.7 22.4 22.2];

Seperatio_pt = find(depth==10); depth=depth(1:Seperatio_pt);

rel_dose_1=rel_dose(1:Seperatio_pt); rel_dose_2=rel_dose_1(length(rel_dose_1):-1:1)

figure; plot(depth,rel_dose_1, 'r', 'linewidth', 3);

xlabel('Depth (cm)'); ylabel('Relative Dose (%)'); title('(Normalized Relative Dose as a Function of Depth for a 6 MV POP; FS=10x10 cm2; separation=10 cm'); hold on

plot(depth,rel_dose_2, 'b', 'linewidth', 3);

[Mohsen]

If you run the code, you will see the 2 curves rel_dose_1 and rel_dose_2. Basically, rel_dose_2 should be an inverted version of rel_dose_1 with respect to the midpoint of rel_dose_1. I used the following code to do this:

rel_dose_2=rel_dose_1(length(rel_dose_1):-1:1);

Then, I plotted both as a function of x (depth). This would have worked very well if the step size in the x-axis was constant. However, since that is not the case, the rel_dose_2 is not a perfect mirrored version of the rel_dose_1. I think I have to create a for loop to do this correctly...

Answer 1

[Mohsen]

close all; clear all; clc;

depth=[ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.6 1.8 2 2.2 2.4 2.6 2.7 2.8 2.9 3 3.2 3.3 3.4 3.5 3.6 3.7 3.8 4 4.2 4.4 4.6 4.8 4.9 5 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.2 6.3 6.4 6.5 6.6 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16 16.2 16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8 23 23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.4 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 27.6 27.8 28 28.2 28.4 28.6 28.8 29 29.2 29.4 29.6 29.8 30]; rel_dose=[ 61.8 63.2 66 73.8 81.3 86.4 90.5 93.9 96 97.4 98.6 99.2 99.9 99.8 100.7 100 99.2 98.9 98 97.2 96.3 96.1 95.7 95.2 94.7 94.1 93.8 92.8 92.4 92.2 91.7 91.1 90.2 89.6 88.9 88.1 87.2 87.1 86 85.3 85 84.4 84 83.8 83.4 83 82.5 82.1 81.3 81.1 80.3 80.4 79.7 78.7 78.7 77.9 78 77.3 77.2 76.4 76.3 75.6 75.2 74.8 74.1 73.2 72.4 71.9 71.1 70.4 69.7 68.9 68 67.4 66.6 65.9 65.3 64.6 64 63.1 62.4 61.9 61.3 60.5 59.6 59.2 58.5 58 57.4 56.7 56.1 55.5 54.7 54.1 53.8 53 52.4 51.6 51.2 50.8 50.1 49.5 49 48.3 47.8 47.6 46.8 46.3 45.8 45.5 45.1 44.4 43.8 43.5 42.9 42.5 42 41.4 41 40.4 40.3 39.8 39.3 38.9 38.4 38 37.5 37.1 36.6 36.3 35.9 35.4 35.1 34.9 34.4 34.1 33.8 33.4 33 32.6 32.2 31.9 31.5 31.1 30.8 30.4 30.1 29.7 29.5 29.2 28.8 28.4 28.2 27.9 27.5 27.2 26.9 26.6 26.4 25.9 25.9 25.5 25.3 25.1 24.7 24.5 24.2 23.9 23.7 23.3 23.1 22.9 22.7 22.4 22.2];

Seperation_pt = find(depth==10); depth_1=depth(1:Seperation_pt); depth_2=zeros(1,length(depth_1)); depth_2(1)=depth_1(length(depth_1));

for i = 2:length(depth_1) increment=depth_1(i)-depth_1(i-1); depth_2(i)=depth_2(i-1)-increment; end

rel_dose_1=rel_dose(1:Seperation_pt);

figure; plot(depth_1,rel_dose_1, 'r', 'linewidth', 3);

xlabel('Depth (cm)'); ylabel('Relative Dose (%)'); title('(Normalized Relative Dose as a Function of Depth for a 6 MV POP; FS=10x10 cm2; separation=10 cm'); hold on

plot(depth_2,rel_dose_1, 'b', 'linewidth', 3);