I need to calculate some points. First I am going to explain the problem. I have a vector of data named X.
X=[20 50 100 150 200 300]
I need to generate some data and I am using this method:
a11=sqrt(1-0/20)-sqrt(1-20/20);
That is the result for 20 or X(1). Then I need to calculate this:
a21=sqrt(1-0/50)-sqrt(1-20/50);
a22=sqrt(1-20/50)-sqrt(1-50/50);
This is the result for 50 or X(2).
For X(3) i need a31,a32,a33, for X(4) i need a41,a42,a43,a44 ... Then I need to put that values in matrix in respect to X.
The matrix should look like:
20 a11
50 a21 a22
100 a31 a32 a33
150 a41 a42 a43 a44
.
.
.
Thank you.
Just to add a loop-free solution:
X = [20 50 100 150 200 300];
X2 = [0 X];
outmat = [X.', tril(-diff(sqrt(1-(1./X).'*X2),1,2))];
The non-trivial part of the output matrix works like this: it first computes the sqrt(1-X(k)/X(l)) kinds of values in a matrix, essentially creating the matrix as a dyadic product of X and X2 (the latter is X extended with a leading 0 element). Then, we compute the diff of this matrix along its second dimension: be careful that the second input parameter of diff gives the order of the numerical derivative. Then we cut out the lower-triangular part with tril.