Why am I getting a matrix of zeros and infs when dividing matrices of the same dimension by element? - matlab

I'm trying to get two matrices to divide, properly, element by element.
Essentially, firstd is a 6x499 and secd is 6x498. I first eliminate firstd's extra elements by doing firstd(:,499)=[]; making it 6x498. Now the next step is to transform firstd into the nominator, nom=((firstd.^2)+1).^1.5; My denominator is just denom=secd;
Both nom and denom have come out as 6x498 matrices with real, non-zero data for each element. However, when doing Rlayer=nom./denom, Rlayer comes out as this ludicrous 6x498 zero-ridden matrix.
I also trimmed out the elements in denom that were =0 by changing them to 0.0001.
Segment of result for Rlayer (Columns 493 through 498)
-0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000
-0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000
-0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000
-0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000
Below are two segments of denom (Columns 487 through 492)
0.0250 0.0281 -0.0281 0.0125 -0.0500 0.0969
-0.0125 0.0750 -0.1219 0.1094 -0.0938 0.0937
0.0344 0.0406 -0.1094 0.1187 -0.1344 0.1531
0.0001 0.0250 0.0001 -0.0437 0.0500 0.0062
0.0781 -0.0219 0.0094 -0.0125 -0.0188 0.1062
0.0250 0.0438 -0.0812 0.0937 -0.1063 0.1562
(Columns 493 through 498)
-0.1187 0.1156 -0.0844 0.0688 -0.0406 0.0125
-0.0969 0.1094 -0.0906 0.0469 0.0062 -0.0156
-0.1375 0.1719 -0.1656 0.0781 0.0187 -0.0531
-0.0562 0.1188 -0.1500 0.1438 -0.1187 0.1187
-0.1781 0.2281 -0.2156 0.1750 -0.1250 0.0812
-0.1750 0.1938 -0.1469 0.0563 0.0031 -0.0156
and this is a segment of nom (Columns 493 through 498)
1.0904 1.0235 1.0881 1.0368 1.0769 1.0514
1.0685 1.0201 1.0769 1.0272 1.0497 1.0532
1.0928 1.0180 1.1210 1.0201 1.0568 1.0685
1.0568 1.0285 1.1001 1.0170 1.0952 1.0260
1.0952 1.0078 1.1380 1.0107 1.1026 1.0272
1.0928 1.0078 1.1077 1.0212 1.0463 1.0480
Why is this division leading to this result? I've tried dividing with rdivide, in a double for loop, and row by row in a for loop. All number types are double.

Related

Augmented matrix rounding issue [duplicate]

This question already has an answer here:
How to round double to something that a 'normal' human can read. (MATLAB)
(1 answer)
Closed 6 years ago.
I am trying to create an augmented matrix to solve a problem, but I can't get to not round the values. The matrix d is trying to be augmented to the matrix Diff. I want the decimal values in Diff to remain decimals and the larger values in d to remain larger values, yet whenever I try to add it, MATLAB automatically reduces all of the values. Why is it doing this and how to fix it?
d = [74000;56000;10500;25000;17500;196000;5000]
d =
74000
56000
10500
25000
17500
196000
5000
Diff = I - A
Diff =
0.8412 -0.0064 -0.0025 -0.3404 -0.0014 -0.0083 -0.1594
-0.0057 0.7355 -0.0436 -0.0099 -0.0083 -0.0201 -0.3413
-0.0264 -0.1506 0.6443 -0.0139 -0.0142 -0.0070 -0.0236
-0.3299 -0.0565 -0.0495 0.6364 -0.0204 -0.0483 -0.0649
-0.0089 -0.0081 -0.0333 -0.0295 0.6588 -0.0237 -0.0020
-0.1190 -0.0901 -0.0996 -0.1260 -0.1722 0.7632 -0.3369
-0.0063 -0.0126 -0.0196 -0.0098 -0.0064 -0.0132 0.9988
Aug = [Diff,d]
Aug =
1.0e+05 *
0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.7400
-0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.5600
-0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.1050
-0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.2500
-0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.1750
-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 1.9600
-0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0500

MATLAB is not rounding any values. If you look at the top left corner when you display Aug, you will see (1.0e+05) which means that all values being displayed are the actual values divided by 1e5 (fixed-decimal floating-point notation). Since you are concatenating very large values (A) with relatively small values (Diff), the significant digits of the small values don't appear because you are not displaying enough decimal points. As a result, they look like 0. This is an artifact of the way that your command window is displaying numbers.
You can change the display format to something else such as "shortg" which is typically used for large data ranges (the default is "short") and you will see that your data is not rounded.
format shortg
[Diff, d]
0.8412 -0.0064 -0.0025 -0.3404 -0.0014 -0.0083 -0.1594 74000
-0.0057 0.7355 -0.0436 -0.0099 -0.0083 -0.0201 -0.3413 56000
-0.0264 -0.1506 0.6443 -0.0139 -0.0142 -0.007 -0.0236 10500
-0.3299 -0.0565 -0.0495 0.6364 -0.0204 -0.0483 -0.0649 25000
-0.0089 -0.0081 -0.0333 -0.0295 0.6588 -0.0237 -0.002 17500
-0.119 -0.0901 -0.0996 -0.126 -0.1722 0.7632 -0.3369 1.96e+05
-0.0063 -0.0126 -0.0196 -0.0098 -0.0064 -0.0132 0.9988 5000
In general, you should rarely rely on the MATLAB command window output for much. If you think your data is being rounded, then you would actually want to test this explicitly.
data = [Diff, d];
isequal(Diff, data(:,1:end-1))
1

How to vectorize this code involving matrix pages in MATLAB?

Is it possible to vectorize, and possibly run on a GPU, the following code
x = linspace(0,100,1000);
h = zeros(size(x));
for i = 1 : length(x)
exprho = expm(-x(i)*rho);
h(i) = trace(drho*exprho*drho*exprho);
end
out = 2 * trapz(x,h);
where rho and drho are two complex Hermitian square matrices of the same size. rho is in fact a quantum density matrix and drho is its derivative with respect to a parameter.
The size can range from 10 x 10 to 300 x 300 approximately but I would also like to reach bigger sizes.
Here are two sample matrices:
rho =
0.4046 0.3849 0.2589 0.1422 0.0676 0.0288 0.0112 0.0040 0.0014 0.0004 0.0001
0.3849 0.3661 0.2462 0.1352 0.0643 0.0274 0.0106 0.0038 0.0013 0.0004 0.0001
0.2589 0.2462 0.1656 0.0910 0.0433 0.0184 0.0071 0.0026 0.0009 0.0003 0.0001
0.1422 0.1352 0.0910 0.0500 0.0238 0.0101 0.0039 0.0014 0.0005 0.0002 0.0000
0.0676 0.0643 0.0433 0.0238 0.0113 0.0048 0.0019 0.0007 0.0002 0.0001 0.0000
0.0288 0.0274 0.0184 0.0101 0.0048 0.0020 0.0008 0.0003 0.0001 0.0000 0.0000
0.0112 0.0106 0.0071 0.0039 0.0019 0.0008 0.0003 0.0001 0.0000 0.0000 0.0000
0.0040 0.0038 0.0026 0.0014 0.0007 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000
0.0014 0.0013 0.0009 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
0.0004 0.0004 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
drho =
0.0366 0.0156 -0.0025 -0.0085 -0.0074 -0.0046 -0.0023 -0.0010 -0.0004 -0.0002 -0.0001
0.0156 -0.0035 -0.0147 -0.0148 -0.0103 -0.0057 -0.0028 -0.0012 -0.0005 -0.0002 -0.0001
-0.0025 -0.0147 -0.0181 -0.0145 -0.0091 -0.0048 -0.0022 -0.0009 -0.0004 -0.0001 -0.0000
-0.0085 -0.0148 -0.0145 -0.0105 -0.0062 -0.0031 -0.0014 -0.0006 -0.0002 -0.0001 -0.0000
-0.0074 -0.0103 -0.0091 -0.0062 -0.0035 -0.0017 -0.0008 -0.0003 -0.0001 -0.0000 -0.0000
-0.0046 -0.0057 -0.0048 -0.0031 -0.0017 -0.0008 -0.0004 -0.0001 -0.0001 -0.0000 -0.0000
-0.0023 -0.0028 -0.0022 -0.0014 -0.0008 -0.0004 -0.0002 -0.0001 -0.0000 -0.0000 -0.0000
-0.0010 -0.0012 -0.0009 -0.0006 -0.0003 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000
-0.0004 -0.0005 -0.0004 -0.0002 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000
-0.0002 -0.0002 -0.0001 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000
-0.0001 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000

Adding a point in 3D graph

I have data as shown below and have no idea why the point (25,25,0) does not plotted into the graph.
X = [0,71,142,213,284,355,426;0,71,142,213,284,355,426;0,71,142,213,284,355,426;0,71,142,213,284,355,426;0,71,142,213,284,355,426;0,71,142,213,284,355,426];
Y = [0,0,0,0,0,0,0;71,71,71,71,71,71,71;142,142,142,142,142,142,142;213,213,213,213,213,213,213;284,284,284,284,284,284,284;355,355,355,355,355,355,355];
IntensityError =
1.0e-04 *
0.4609 0.0000 0.0000 0.0000 0.0000 0.0000 0.4609
0.9217 0.0000 0.0000 0.0000 0.0000 0.0000 0.9217
0 0.0000 0.0000 0.0000 0.0000 0.0000 0
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
mesh(X,Y,Error)
hold on plot3(25,25,0,'*')
When you run the above code, you will see that the point (25,25,0) is not plotted.
I have tried to solve this problem for many days. Please help me.

Not sure what you mean, but the point shows on the figure in my quick test:
X = [0,71,142,213,284,355,426;
0,71,142,213,284,355,426;
0,71,142,213,284,355,426;
0,71,142,213,284,355,426;
0,71,142,213,284,355,426;
0,71,142,213,284,355,426];
Y = [0,0,0,0,0,0,0;
71,71,71,71,71,71,71;
142,142,142,142,142,142,142;
213,213,213,213,213,213,213;
284,284,284,284,284,284,284;
355,355,355,355,355,355,355];
IntensityError = 1.0e-04 *[
0.4609 0.0000 0.0000 0.0000 0.0000 0.0000 0.4609;
0.9217 0.0000 0.0000 0.0000 0.0000 0.0000 0.9217;
0 0.0000 0.0000 0.0000 0.0000 0.0000 0;
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000;
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000;
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];
figure;
mesh(X,Y,IntensityError), hold on;
plot3(25,25,0,'*');

Powers Table MATLAB

For this question, I'm supposed to create a NxN powers table in matlab using arrays.
The code I have so far is as follows:
C = [];
D = [];
N = input('Enter the value you would like to use for your NxN Powers Table: ');
for i = 1:N
for j = 1:N
C = [C;i^j];
end
C = transpose(C);
D = [D;C];
C = [];
end
D
This code works perfectly fine for any numbers from 1-9, as soon as I enter anything greater than that, it prints out weird values.
Here is the output I have using 5 as an input, and the second one is using 10 as an input.
Enter the value you would like to use for your NxN Powers Table: 5
D =
1 1 1 1 1
2 4 8 16 32
3 9 27 81 243
4 16 64 256 1024
5 25 125 625 3125
Enter the value you would like to use for your NxN Powers Table: 10
D =
1.0e+010 *
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0010 0.0060
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0040 0.0282
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0017 0.0134 0.1074
0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0043 0.0387 0.3487
0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0010 0.0100 0.1000 1.0000
Any ideas what could be wrong with my code? Seems like a simple fix, I just can't figure out whats wrong with it. Any help is greatly appreciated. Thanks

Notice the 1.0e+010 *. It means that the numbers should be multiplied by 10000000000. Five digits are not enough to print it. Insert format long or format short g to see the whole numbers.

I think your code works fine. Note that 10^10 = 1e10; the very last element in your output D is indeed 1e10. Check individual elements D(i,j) to verify that those are correct. MATLAB can't display all the elements because some elements are so much larger than other ones; 1e10 has 10 digits in it, for instance, while 1^1 = 1 has 1 digit. So spacing would get screwed up if this behavior didn't happen.

Matrix creation MATLAB

I am building a nxn matrix in matlab with the following code:
x = linspace(a,b,n);
for i=1:n
for j=1:n
A(i,j) = x(j)^(i-1);
end
A
i
b(i) = (1/i)*x(n)^i - (1/i)*x(1)^i;
end
I am testing it with a=1 b=10 and n=10. I get the expected results up to i=8
i =
8
A =
Columns 1 through 7
1 1 1 1 1 1 1
1 2 3 4 5 6 7
1 4 9 16 25 36 49
1 8 27 64 125 216 343
1 16 81 256 625 1296 2401
1 32 243 1024 3125 7776 16807
1 64 729 4096 15625 46656 117649
1 128 2187 16384 78125 279936 823543
1 256 6561 65536 390625 1679616 5764801
Columns 8 through 10
1 1 1
8 9 10
64 81 100
512 729 1000
4096 6561 10000
32768 59049 100000
262144 531441 1000000
2097152 4782969 10000000
16777216 43046721 100000000
however from i=9 on it becomes this:
i =
9
A =
1.0e+09 *
Columns 1 through 9
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0005
0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0008 0.0021 0.0048
0.0000 0.0000 0.0000 0.0001 0.0004 0.0017 0.0058 0.0168 0.0430
0.0000 0.0000 0.0000 0.0003 0.0020 0.0101 0.0404 0.1342 0.3874
Column 10
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0010
0.0100
0.1000
1.0000
Can someone please tell me what is happening? I am not very experienced in matlab (I mostly use c++ or python) and so far can't seem to figure it out myself.

It's just a formatting issue for larger numbers. Try
sprintf('%20.0f', A(end,end))
and you will see that the number is correct. At least up to some point, where you will run into double representation problems...

Because a common scaling is applied to your data display. See in your output:
A =
1.0e+09 *
A common factor of 10^9 was factored out of every entry in your matrix.
You may want to adjust your output display using:
format short g