How to determine index for gradient?

Hello,

I'm trying to determine the index for a change in gradient along the radial direction from x=0 to x=1, which is expected to be negative. My code which runs but doesn't give correct result. Kindly have a look at the same and suggest me the possible correction(s) please.

data.variable.gradpressure = 10000 x 100 matrix

data.variable.x = 1 x 100 vector

Moreover the matchflag is also false when I try to match the columns which are both equal.

The code is as below:

% Determine the index for negative gradient from x=0 to x=1 
clear grad_width;
global grad_width;
global data;

match_flags = false(size(data.variable.gradpressure,1),1);  % Logical vector for matching rows

% Check if any row of pressure equals x
for i = 1:size(data.variable.x, 1)
    if isequal(data.variable.gradpressure(:,i)', data.variable.x(:,i))
        match_flags(i) = true;
    end
end
%disp(match_flags)

threshold_fraction = 0.1;

% Preallocate result arrays
nTimes = length(data.variable.t);
grad_foot_idx = zeros(nTimes,1);
grad_head_idx = zeros(nTimes,1);
grad_width = zeros(nTimes,1);

for i = 1:nTimes
    gradp = data.variable.gradpressure(i,:);  % 1D vector at time i

    % Avoid division by zero
    valid = gradp(1:end-1) ~= 0;

    % Compute gradient change (like second derivative)
    change_gp = zeros(1, length(gradp)-1);
    change_gp(valid) = diff(gradp)./gradp(1:end-1);  % Central diff approx

    % Find steepest drop (most negative change)
    [max_grad1, max_grad1_idx] = min(abs(change_gp));  % Min of |second derivative|
    grad_threshold = threshold_fraction * abs(max_grad1);

    % Search left (foot)
    left_idx = max_grad1_idx;
    while left_idx > 1 && abs(change_gp(left_idx)) > grad_threshold
        left_idx = left_idx - 1;
    end

    % Search right (head)
    right_idx = max_grad1_idx;
    while right_idx < length(change_gp) && abs(change_gp(right_idx)) > grad_threshold
        right_idx = right_idx + 1;
    end

    % Store
    grad_foot_idx(i) = left_idx;
    grad_head_idx(i) = right_idx;
    grad_width(i) = data.variable.x(right_idx) - data.variable.x(left_idx);
end

% Display last result (or modify to plot or analyze all)
disp(grad_width(end));

Answer 1

[Alan Stevens]

"Moreover the matchflag is also false when I try to match the columns which are both equal."

This suggests you are comparing floating point numbers which, though superficially look the same, are not actually identical because of the limited precision of stored floating point numbers. Rather than testing for exact equality, it's better to test for a small difference. For example, if x and y are floating point numbers then use something like:

matchflag = abs(x-y)<1e-15

[Steven Lord]

If the poster was using release R2024b or later they could use the isapprox function.

x = 0:0.1:1;
0.3 == x % all false

ans = 1×11 logical array
   0   0   0   0   0   0   0   0   0   0   0

ind = isapprox(0.3, x) % one true

ind = 1×11 logical array
   0   0   0   1   0   0   0   0   0   0   0

y = x(ind) % "close enough" to 0.3

y = 0.3000