I am working on a project involving calculating the work volume for a device.
Given that I have two angles, beta1 and beta2 between let's say 0-10 degrees ([deg] used for simplification here, in reality in [rad]),
I want to calculate the work volume for different combinations of e.g.
beta1 = 1 [deg]
and at the same time
beta2 = 8 [deg]
I can't get my head around how to do it. I tried to cheat by running the FOR loop for 1000 values of beta1 and then a random entry from the beta2 array, but obviously it is not very reliable.
Here is the code: (it is a mess, but it is just trigonometry)
for ii=1:1000
for jj=randi(1000)
T_0{ii} = [0 0 0 (l_joint/beta1(ii))*tan(beta1(ii)/2); 0 1 0 0; 0 0 1 0; 0 0 0 1];
T_1{ii} = [cos(beta1(ii)) -sin(beta1(ii))*cos(alpha1) sin(beta1(ii))*sin(alpha1) ...
((l_joint/beta1(ii))*tan(beta1(ii)/2)+l_disk+(l_joint/beta2(ii))*tan(beta2(jj)/2))*cos(beta1(ii)); ...
sin(beta1(ii)) cos(beta1(ii))*cos(alpha1) -cos(beta1(ii))*sin(alpha1) ...
((l_joint/beta1(ii))*tan(beta1(ii)/2)+l_disk+(l_joint/beta2(jj))*tan(beta2(jj)/2))*sin(beta1(ii)); ...
0 sin(alpha1) cos(alpha1) 0; ...
0 0 0 1];
T_2{ii} = [cos(beta2(jj)) -sin(beta2(jj))*cos(alpha2) sin(beta2(jj))*sin(alpha2) ...
((l_disk+(l_joint/beta2(jj))*tan(beta2(jj)/2)))*cos(beta2(jj)); ...
sin(beta2(jj)) cos(beta2(jj))*cos(alpha2) -cos(beta2(jj))*sin(alpha2) ...
((l_disk+(l_joint/beta2(jj))*tan(beta2(jj)/2)))*sin(beta2(jj)); ...
0 sin(alpha2) cos(alpha2) 0; ...
0 0 0 1];
T_section{ii} = (T_0{ii}*T_1{ii}*T_2{ii})^n;
end end
As far as i can work out, you have a function T_section with 2 parameters beta1 and beta2 and are asking how to calculate the value of the function T_section(beta1, beta2) for all combinations of beta1 and beta2. You can calculate and visualize the results of a 2-D function in MATLAB like this:
beta1 = 0:0.1:10;
beta2 = 0:0.1:10;
[B1, B2] = meshgrid(beta1, beta2);
T_section = sind(10*B2)*cosd(20*B1); % replace with actual function
surf(beta1, beta2, T_section,'EdgeColor','none')
xlabel('\beta_1'); ylabel('\beta_2');
which yields this plot:
No need for loops here, vectorizing your calculations in MATLAB is very likely much faster (see the excellent MATLAB documentation, e.g. http://de.mathworks.com/help/matlab/matlab_prog/vectorization.html). You should probably also read the documentation about meshgrid (doc meshgrid on the console).
Related
I have a big matrix (500212x7) and a column vector like below
matrix F vector P
0001011 4
0001101 3
1101100 6
0000110 1
1110000 7
The vector contains indices considered within the matrix rows. P(1) is meant to point at F(1,4), P(2) at F(2,3) and so on.
I want to negate a bit in each row in F in a column pointed by P element (in the same row).
I thought of things like
F(:,P(1)) = ~F(:,P(1));
F(:,P(:)) = ~F(:,P(:));
but of course these scenarios won't produce the result I expect as the first line won't make P element change and the second one won't even let me start the program because a full vector cannot make an index.
The idea is I need to do this for all F and P rows (changing/incrementing "simultaneously") but take the value of P element.
I know this is easily achieved with for loop but due to large dimensions of the F array such a way to solve the problem is completely unacceptable.
Is there any kind of Matlab wizardry that lets solving such a task with the use of matrix operations?
I know this is easily achieved with for loop but due to large dimensions of the F array such a way to solve the problem is completely unacceptable.
You should never make such an assumption. First implement the loop, then check to see if it really is too slow for you or not, then worry about optimizing.
Here I'm comparing Luis' answer and the trival loop:
N = 500212;
F = rand(N,7) > 0.6;
P = randi(7,N,1);
timeit(#()method1(F,P))
timeit(#()method2(F,P))
function F = method1(F,P)
ind = (1:size(F,1)) + (P(:).'-1)*size(F,1); % create linear index
F(ind) = ~F(ind); % negate those entries
end
function F = method2(F,P)
for ii = 1:numel(P)
F(ii,P(ii)) = ~F(ii,P(ii));
end
end
Timings are 0.0065 s for Luis' answer, and 0.0023 s for the loop (MATLAB Online R2019a).
It is especially true for very large arrays, that loops are faster than vectorized code, if the vectorization requires creating an intermediate array. Memory access is expensive, using more of it makes the code slower.
Lessons: don't dismiss loops, don't prematurely try to optimize, and don't optimize without comparing.
Another solution:
xor( F, 1:7 == P )
Explanation:
1:7 == P generates one-hot arrays.
xor will cause a bit to retain its value against a 0, and flip it against a 1
Not sure if it qualifies as wizardry, but linear indexing does exactly what you want:
F = [0 0 0 1 0 1 1; 0 0 0 1 1 0 1; 1 1 0 1 1 0 0; 0 0 0 0 1 1 0; 1 1 1 0 0 0 0];
P = [4; 3; 6; 1; 7];
ind = (1:size(F,1)) + (P(:).'-1)*size(F,1); % create linear index
F(ind) = ~F(ind); % negate those entries
I'm trying to generate coordinates in a mulidimensional array.
the range for each digit in the coords is -1 to 1. <=> seems like the way to go comparing two random numbers. I'm having trouble because randomizing it takes forever, coords duplicate and sometimes don't fill all the way through. I've tried uniq! which only causes the initialization to run forever while it tries to come up with the different iterations.
the coords look something like this. (-1, 0, 1, 0, 0)
5 digits give position. I could write them out but I'd like to generate the coords each time the program is initiated. The coords would then be assigned to a hash tied to a key. 1 - 242.
I could really use some advice.
edited to add code. It does start to iterate but it doesn't fill out properly. Short of just writing out an array with all possible combos and randomizing before merging it with the key. I can't figure out how.
room_range = (1..241)
room_num = [*room_range]
p room_num
$rand_loc_cords = []
def Randy(x)
srand(x)
y = (rand(100) + 1) * 1500
z = (rand(200) + 1) * 1000
return z <=> y
end
def rand_loc
until $rand_loc_cords.length == 243 do
x = Time.new.to_i
$rand_loc_cords.push([Randy(x), Randy(x), Randy(x), Randy(x), Randy(x)])
$rand_loc_cords.uniq!
p $rand_loc_cords
end
#p $rand_loc_cords
end
rand_loc
You are trying to get all possible permutations of -1, 0 and 1 with a length of 5 by sheer luck, which can take forever. There are 243 of them (3**5) indeed:
coords = [-1,0,1].repeated_permutation(5).to_a
Shuffle the array if the order should be randomized.
I have the 137x19 cell array Location(1,4).loc and I want to find the number of times that horizontal consecutive values are present in Location(1,4).loc. I have used this code:
x=Location(1,4).loc;
y={x(:,1),x(:,2)};
for ii=1:137
cnt(ii,1)=sum(strcmp(x(:,1),y{1,1}{ii,1})&strcmp(x(:,2),y{1,2}{ii,1}));
end
y={x(:,1),x(:,2),x(:,3)};
for ii=1:137
cnt(ii,2)=sum(strcmp(x(:,1),y{1,1}{ii,1})&strcmp(x(:,2),y{1,2}{ii,1})&strcmp(x(:,3),y{1,3}{ii,1}));
end
y={x(:,1),x(:,2),x(:,3),x(:,4)};
for ii=1:137
cnt(ii,3)=sum(strcmp(x(:,1),y{1,1}{ii,1})&strcmp(x(:,2),y{1,2}{ii,1})&strcmp(x(:,3),y{1,3}{ii,1})&strcmp(x(:,4),y{1,4}{ii,1}));
end
y={x(:,1),x(:,2),x(:,3),x(:,4),x(:,5)};
for ii=1:137
cnt(ii,4)=sum(strcmp(x(:,1),y{1,1}{ii,1})&strcmp(x(:,2),y{1,2}{ii,1})&strcmp(x(:,3),y{1,3}{ii,1})&strcmp(x(:,4),y{1,4}{ii,1})&strcmp(x(:,5),y{1,5}{ii,1}));
end
... continue for all the columns. This code run and gives me the correct result but it's not automated and it's slow. Can you give me ideas to automate and speed up the code?
I think I will write an answer to this since I've not done so for a while.
First convert your cell Array to a matrix,this will ease the following steps by a lot. Then diff is the way to go
A = randi(5,[137,19]);
DiffA = diff(A')'; %// Diff creates a matrix that is 136 by 19, where each consecutive value is subtracted by its previous value.
So a 0 in DiffA would represent 2 consecutive numbers in A are equal, 2 consecutive 0s would mean 3 consecutive numbers in A are equal.
idx = DiffA==0;
cnt(:,1) = sum(idx,2);
To do 3 consecutive number counts, you could do something like:
idx2 = abs(DiffA(:,1:end-1))+abs(DiffA(:,2:end)) == 0;
cnt(:,2) = sum(idx2,2);
Or use another Diff, the abs is used to avoid negative number + positive number that also happens to give 0; otherwise only 0 + 0 will give you a 0; you can now continue this pattern by doing:
idx3 = abs(DiffA(:,1:end-2))+abs(DiffA(:,2:end-1))+abs(DiffA(:,3:end)) == 0
cnt(:,3) = sum(idx3,2);
In loop format:
absDiffA = abs(DiffA)
for ii = 1:W
absDiffA = abs(absDiffA(:,1:end-1) + absDiffA(:,1+1:end));
idx = (absDiffA == 0);
cnt(:,ii) = sum(idx,2);
end
NOTE: this method counts [0,0,0] twice when evaluating 2 consecutives, and once when evaluating 3 consecutives.
Suppose we have an array
A = zeros([1,10]);
We have several indexes with possible duplicate say:
indSeq = [1,1,2,3,4,4,4];
How can we increase A(i) by the number of i in the index sequence i.e. A(1) = 2, A(2) = 1, A(3) = 1, A(4) = 3?
The code A(indSeq) = A(indSeq)+1 does not work.
I know that I can use the following for loop to achieve the goal, but I wonder if there is anyway that we can avoid for-loop? We can assume that the indSeq is sorted.
A for-loop solution:
for i=1:length(indSeq)
A(indSeq(i)) = A(indSeq(i))+1;
end;
You can use accumarray for such a label based counting job, like so -
accumarray(indSeq(:),1)
Benchmarking
As suggested in the other answer, you can also use hist/histc. Let's benchmark these two for a large datasize. The benchmarking code I used had -
%// Create huge random array filled with ints that are duplicated & sorted
maxn = 100000;
N = 10000000;
indSeq = sort(randi(maxn,1,N));
disp('--------------------- With HISTC')
tic,histc(indSeq,unique(indSeq));toc
disp('--------------------- With ACCUMARRAY')
tic,accumarray(indSeq(:),1);toc
Runtime output -
--------------------- With HISTC
Elapsed time is 1.028165 seconds.
--------------------- With ACCUMARRAY
Elapsed time is 0.220202 seconds.
This is run-length encoding, and the following code should do the trick for you.
A=zeros(1,10);
indSeq = [1,1,2,3,4,4,4,7,1];
indSeq=sort(indSeq); %// if your input is always sorted, you don't need to do this
pos = [1; find(diff(indSeq(:)))+1; numel(indSeq)+1];
A(indSeq(pos(1:end-1)))=diff(pos)
which returns
A =
3 1 1 3 0 0 1 0 0 0
This algorithm was written by Luis Mendo for MATL.
I think what you are looking for is the number of occurences of unique values of the array. This can be accomplished with:
[num, val] = hist(indSeq,unique(indSeq));
the output of your example is:
num = 2 1 1 3
val = 1 2 3 4
so num is the number of times val occurs. i.e. the number 1 occurs 2 times in your example
Take this simple example:
a = [1 2i];
x = zeros(1,length(a));
for n=1:length(a)
x(n) = isreal(a(n));
end
In an attempt to vectorize the code, I tried:
y = arrayfun(#isreal,a);
But the results are not the same:
x =
1 0
y =
0 0
What am I doing wrong?
This certainly appears to be a bug, but here's a workaround:
>> y = arrayfun(#(x) isreal(x(1)),a)
ans =
1 0
Why does this work? I'm not totally sure, but it appears that when you perform an indexing operation on the variable before calling ISREAL it removes the "complex" attribute from the array element if the imaginary component is zero. Try this in the Command Window:
>> a = [1 2i]; %# A complex array
>> b = a(1); %# Indexing element 1 removes the complex attribute...
>> c = complex(a(1)); %# ...but we can put that attribute back
>> whos
Name Size Bytes Class Attributes
a 1x2 32 double complex
b 1x1 8 double %# Not complex
c 1x1 16 double complex %# Still complex
Apparently, ARRAYFUN must internally maintain the "complex" attribute of the array elements it passes to ISREAL, thus treating them all as being complex numbers even if the imaginary component is zero.
It might help to know that MATLAB stores the real/complex parts of a matrix separately. Try the following:
>> format debug
>> a = [1 2i];
>> disp(a)
Structure address = 17bbc5b0
m = 1
n = 2
pr = 1c6f18a0
pi = 1c6f0420
1.0000 0 + 2.0000i
where pr is a pointer to the memory block containing the real part of all values, and pi pointer to the complex part of all values in the matrix. Since all elements are stored together, then in this case they all have a complex part.
Now compare these two approaches:
>> arrayfun(#(x)disp(x),a)
Structure address = 17bbcff8
m = 1
n = 1
pr = 1bb8a8d0
pi = 1bb874d0
1
Structure address = 17c19aa8
m = 1
n = 1
pr = 1c17b5d0
pi = 1c176470
0 + 2.0000i
versus
>> for n=1:2, disp(a(n)), end
Structure address = 17bbc930
m = 1
n = 1
pr = 1bb874d0
pi = 0
1
Structure address = 17bbd180
m = 1
n = 1
pr = 1bb874d0
pi = 1bb88310
0 + 2.0000i
So it seems that when you access a(1) in the for loop, the value returned (in the ans variable) has a zero complex-part (null pi), thus is considered real.
One the other hand, ARRAYFUN seems to be directly accessing the values of the matrix (without returning them in ANS variable), thus it has access to both pr and pi pointers which are not null, thus are all elements are considered non-real.
Please keep in mind this just my interpretation, and I could be mistaken...
Answering really late on this one... The MATLAB function ISREAL operates in a really rather counter-intuitive way for many purposes. It tells you if a given array taken as a whole has no complex part at all - it tells you about the storage, it doesn't really tell you anything about the values in the array. It's a bit like the ISSPARSE function in that regard. So, for example
isreal(complex(1)) % returns FALSE
What you'll find in MATLAB is that certain operations automatically trim any all-zero imaginary parts. So, for example
x = complex(1);
isreal(x); % FALSE, we just forced there to be an imaginary part
isreal(x(1)); % TRUE - indexing realised it could drop the zero imaginary part
isreal(x(:)); % FALSE - "(:)" indexing is just a reshape, not real indexing
In short, MATLAB really needs a function which answers the question "does this value have zero imaginary part", in an elementwise way on an array.