This question already has answers here:
Subscript indices must either be real positive integers or logicals, generic solution
(3 answers)
Closed 6 years ago.
Not sure if I should have posted this here or on the Maths stackexchange, so sorry if it's the wrong place. I'm very new to MATLAB and programming in general, and am having some troubles trying to solve an ODE problem using finite difference methods for an assignment.
My finite difference equation is:
z(t+dt) = (dt^2*(γ^2*h*sin(γ*t)-β*z(t)) - z(t-dt)*(1-dt*α)+2*z(t))/(1 + dt*α)
Where t is a 51x1 array for the time increments. Basically I want to calculate z(t) for t values from 0 to 1 in increments of 0.02. I have the initial conditions z(0) = 0 and z(Δt) = 0.
My current code (not everything, but the bit that's giving me trouble:
dt = 0.02
t = [0:dt:T]';
z(0) = 0
z(dt)= 0
for i = t
z(i+dt) = (dt^2*(gamma^2.*h.*sin(gamma*t)-beta*z(i)) - z(i-dt)*(1-dt*alpha)+2*z(i))/(1 + dt*alpha)
end
Alpha, beta and gamma are all constants in this case, they're defined earlier in the code.
I keep getting the error "Subscript indices must either be real positive integers or logicals." I understand that MATLAB arrays begin with element 1 and not 0, so trying to access element 0 will give an error.
I'm not sure if the error is with how I've entered my finite difference function, or the initial conditions. By setting i = t, am I running the for loop for those values of t, or for those elements in the matrix? E.g. when i = 0, is it trying to access the 0 element of the matrix, or is it setting the i variable in the equation to 0 like I want it to?
Any help would be greatly appreciated.
Thankyou!
problem is with dt and I think dt is not integer value and cannot be used for indexing array. index of arrays are always integer values in Matlab. Please try below code and check if solves the problem
t = [0:dt:T]';
z(1) = 0
z(2)= 0
for i = 2 : length(t)
z(i) = (dt^2*(gamma^2.*h.*sin(gamma*t(i))-beta*z(i)) - z(i-1)*(1-dt*alpha)+2*z(i))/(1 + dt*alpha)
end
Related
This is probably a trivial question, but I want to select a portion of a complex array in order to plot it in Matlab. My MWE is
n = 100;
t = linspace(-1,1,n);
x = rand(n,1)+1j*rand(n,1);
plot(t(45):t(55),real(x(45):x(55)),'.--')
plot(t(45):t(55),imag(x(45):x(55)),'.--')
I get an error
Error using plot
Vectors must be the same length.
because the real(x(45):x(55)) bit returns an empty matrix: Empty matrix: 1-by-0. What is the easiest way to fix this problem without creating new vectors for the real and imaginary x?
It was just a simple mistake. You were doing t(45):t(55), but t is generated by rand, so t(45) would be, say, 0.1, and t(55), 0.2, so 0.1:0.2 is only 0.1. See the problem?
Then when you did it for x, the range was different and thus the error.
What you want is t(45:55), to specify the vector positions from 45 to 55.
This is what you want:
n = 100;
t = linspace(-1,1,n);
x = rand(n,1)+1j*rand(n,1);
plot(t(45:55),real(x(45:55)),'.--')
plot(t(45:55),imag(x(45:55)),'.--')
I would like to compute the product of the next n adjacent elements of a matrix. The number n of elements to be multiplied should be given in function's input.
For example for this input I should compute the product of every 3 consecutive elements, starting from the first.
[p, ind] = max_product([1 2 2 1 3 1],3);
This gives [1*2*2, 2*2*1, 2*1*3, 1*3*1] = [4,4,6,3].
Is there any practical way to do it? Now I do this using:
for ii = 1:(length(v)-2)
p = prod(v(ii:ii+n-1));
end
where v is the input vector and n is the number of elements to be multiplied.
in this example n=3 but can take any positive integer value.
Depending whether n is odd or even or length(v) is odd or even, I get sometimes right answers but sometimes an error.
For example for arguments:
v = [1.35912281237829 -0.958120385352704 -0.553335935098461 1.44601450110386 1.43760259196739 0.0266423803393867 0.417039432979809 1.14033971399183 -0.418125096873537 -1.99362640306847 -0.589833539347417 -0.218969651537063 1.49863539349242 0.338844452879616 1.34169199365703 0.181185490389383 0.102817336496793 0.104835620599133 -2.70026800170358 1.46129128974515 0.64413523430416 0.921962619821458 0.568712984110933]
n = 7
I get the error:
Index exceeds matrix dimensions.
Error in max_product (line 6)
p = prod(v(ii:ii+n-1));
Is there any correct general way to do it?
Based on the solution in Fast numpy rolling_product, I'd like to suggest a MATLAB version of it, which leverages the movsum function introduced in R2016a.
The mathematical reasoning is that a product of numbers is equal to the exponent of the sum of their logarithms:
A possible MATLAB implementation of the above may look like this:
function P = movprod(vec,window_sz)
P = exp(movsum(log(vec),[0 window_sz-1],'Endpoints','discard'));
if isreal(vec) % Ensures correct outputs when the input contains negative and/or
P = real(P); % complex entries.
end
end
Several notes:
I haven't benchmarked this solution, and do not know how it compares in terms of performance to the other suggestions.
It should work correctly with vectors containing zero and/or negative and/or complex elements.
It can be easily expanded to accept a dimension to operate along (for array inputs), and any other customization afforded by movsum.
The 1st input is assumed to be either a double or a complex double row vector.
Outputs may require rounding.
Update
Inspired by the nicely thought answer of Dev-iL comes this handy solution, which does not require Matlab R2016a or above:
out = real( exp(conv(log(a),ones(1,n),'valid')) )
The basic idea is to transform the multiplication to a sum and a moving average can be used, which in turn can be realised by convolution.
Old answers
This is one way using gallery to get a circulant matrix and indexing the relevant part of the resulting matrix before multiplying the elements:
a = [1 2 2 1 3 1]
n = 3
%// circulant matrix
tmp = gallery('circul', a(:))
%// product of relevant parts of matrix
out = prod(tmp(end-n+1:-1:1, end-n+1:end), 2)
out =
4
4
6
3
More memory efficient alternative in case there are no zeros in the input:
a = [10 9 8 7 6 5 4 3 2 1]
n = 2
%// cumulative product
x = [1 cumprod(a)]
%// shifted by n and divided by itself
y = circshift( x,[0 -n] )./x
%// remove last elements
out = y(1:end-n)
out =
90 72 56 42 30 20 12 6 2
Your approach is correct. You should just change the for loop to for ii = 1:(length(v)-n+1) and then it will work fine.
If you are not going to deal with large inputs, another approach is using gallery as explained in #thewaywewalk's answer.
I think the problem may be based on your indexing. The line that states for ii = 1:(length(v)-2) does not provide the correct range of ii.
Try this:
function out = max_product(in,size)
size = size-1; % this is because we add size to i later
out = zeros(length(in),1) % assuming that this is a column vector
for i = 1:length(in)-size
out(i) = prod(in(i:i+size));
end
Your code works when restated like so:
for ii = 1:(length(v)-(n-1))
p = prod(v(ii:ii+(n-1)));
end
That should take care of the indexing problem.
using bsxfun you create a matrix each row of it contains consecutive 3 elements then take prod of 2nd dimension of the matrix. I think this is most efficient way:
max_product = #(v, n) prod(v(bsxfun(#plus, (1 : n), (0 : numel(v)-n)')), 2);
p = max_product([1 2 2 1 3 1],3)
Update:
some other solutions updated, and some such as #Dev-iL 's answer outperform others, I can suggest fftconv that in Octave outperforms conv
If you can upgrade to R2017a, you can use the new movprod function to compute a windowed product.
This question already has answers here:
Broadcast array multiplication in Fortran 90/95
(3 answers)
Closed 6 years ago.
Suppose I have a matrix A in fortran which is (n,m), and a vector B which is (1,m). I want to subtract the vector B from all rows of A without using a loop.
As of now I have only been able to do it with a loop:
PROGRAM Subtract
IMPLICIT NONE
REAL, DIMENSION(250,5) :: A
INTEGER, DIMENSION(1,5) :: B
INTEGER :: i
B(1,1) = 1
B(1,2) = 2
B(1,3) = 3
B(1,4) = 4
B(1,5) = 5
CALL RANDOM_NUMBER(A)
do i=1,250
A(i,:) = A(i,:) - B(1,:)
end do
end program
But this is very inefficient. E.g. in matlab one can do it in one line using the function reptmat.
Any suggestion on better way to do this?
You can use spread for this:
A = A - spread( B(1,:), 1, 250 )
Please note that Fortran is column-major, so B(1,:) is in general not contiguous in memory, and a temporary array is created.
[ It is in your case since you have only one column - but still worth mentioning. ]
In the same way, looping over the first index of A is inefficient.
It would probably speed things up a lot if you transposed your matrices.
Then, a loop solution might even be faster than the one using spread. (But this depends on the compiler. )
This question already has answers here:
How to generate the first twenty powers of x?
(4 answers)
Closed 7 years ago.
I have 1000 matrices with dimensions 2x2.
What I now need to do is to get 30 consecutive powers of those matrices (A^2, A^3... ...A^30) and store them all.
I found a topic that suggested using bsxfun:
Vectorizing the creation of a matrix of successive powers
However, bsxfun does not work with cell arrays ("Error using bsxfun
Operands must be numeric arrays").
What can I do?
PS. A secondary question: once I have them, I want to plot 4 graphs (each corresponding to 1 of the elements of the 2x2 matrices) with 30 positions (x-axis) which will show confidence bands (16th and 84th percentile).
EDIT: Someone linked to a question that was similar to the one that I linked. From what I can understand, the question there is about a vector, not array of matrices.
Assuming your array A is 2-by-2-by-1000, here are two loops to make things work:
A = rand(2,2,1000);
K = 30;
%%
N = size(A,3);
APower = zeros(2,2,N,K);
APower(:,:,:,1) = A;
for i = 1:N
for k = 2:K
APower(:,:,i,k) = A(:,:,i)*APower(:,:,i,k-1);
%// Alternatively you could use:
%APower(:,:,i,k) = A(:,:,i)^k;
end
end
You need to replicate the matrix 30 times to do this using cellfun. For example,
a = repmat(A{1},1,30);% Select one of your A matrices
b = num2cell(1:30);
x = cellfun(#(a,b) a^b,a,b,'UniformOutput',false)
Since you need to run cellfun for each element of A another way is to use arrayfun as below.
a = A{1};
b = 1:30;
x = arrayfun(#(b) a^b,b,'UniformOutput',false)
Can anyone tell me if there is a way (in MATLAB) to check whether a certain value is equal to any of the values stored within another array?
The way I intend to use it is to check whether an element index in one matrix is equal to the values stored in another array (where the stored values are the indices of the elements which meet a certain criteria).
So, if the indices of the elements which meet the criteria are stored in the matrix below:
criteriacheck = [3 5 6 8 20];
Going through the main array (called array) and checking if the index matches:
for i = 1:numel(array)
if i == 'Any value stored in criteriacheck'
%# "Do this"
end
end
Does anyone have an idea of how I might go about this?
The excellent answer previously given by #woodchips applies here as well:
Many ways to do this. ismember is the first that comes to mind, since it is a set membership action you wish to take. Thus
X = primes(20);
ismember([15 17],X)
ans =
0 1
Since 15 is not prime, but 17 is, ismember has done its job well here.
Of course, find (or any) will also work. But these are not vectorized in the sense that ismember was. We can test to see if 15 is in the set represented by X, but to test both of those numbers will take a loop, or successive tests.
~isempty(find(X == 15))
~isempty(find(X == 17))
or,
any(X == 15)
any(X == 17)
Finally, I would point out that tests for exact values are dangerous if the numbers may be true floats. Tests against integer values as I have shown are easy. But tests against floating point numbers should usually employ a tolerance.
tol = 10*eps;
any(abs(X - 3.1415926535897932384) <= tol)
you could use the find command
if (~isempty(find(criteriacheck == i)))
% do something
end
Note: Although this answer doesn't address the question in the title, it does address a more fundamental issue with how you are designing your for loop (the solution of which negates having to do what you are asking in the title). ;)
Based on the for loop you've written, your array criteriacheck appears to be a set of indices into array, and for each of these indexed elements you want to do some computation. If this is so, here's an alternative way for you to design your for loop:
for i = criteriacheck
%# Do something with array(i)
end
This will loop over all the values in criteriacheck, setting i to each subsequent value (i.e. 3, 5, 6, 8, and 20 in your example). This is more compact and efficient than looping over each element of array and checking if the index is in criteriacheck.
NOTE: As Jonas points out, you want to make sure criteriacheck is a row vector for the for loop to function properly. You can form any matrix into a row vector by following it with the (:)' syntax, which reshapes it into a column vector and then transposes it into a row vector:
for i = criteriacheck(:)'
...
The original question "Can anyone tell me if there is a way (in MATLAB) to check whether a certain value is equal to any of the values stored within another array?" can be solved without any loop.
Just use the setdiff function.
I think the INTERSECT function is what you are looking for.
C = intersect(A,B) returns the values common to both A and B. The
values of C are in sorted order.
http://www.mathworks.de/de/help/matlab/ref/intersect.html
The question if i == 'Any value stored in criteriacheck can also be answered this way if you consider i a trivial matrix. However, you are proably better off with any(i==criteriacheck)