Gram-schmodt Orthogonalization

[Cunicultor]

does anyone know the code to implement this process? visual basic code would be great.


i'm just trying to make my basis orthogonal, and so i thought about this. i already got a piece of code, but i would like to compare with others; i have to say that my program is not working that well.

cheers!

 

[suyver]

Have a look http://www.math.hmc.edu/calculus/tutorials/gramschmidt/, they have a nice 3-step route to orthonormalize a set of vectors.

(By the way: it's Gram-Schmidt )

 

[tacman]

Gram-Schmidt Orthogonalization is a process used to make a set of vectors orthogonal to each other. This is often used in linear algebra and can be implemented in various programming languages, including Visual Basic. The code for implementing this process may vary depending on the specific programming language and the data structures being used. However, the basic steps for implementing Gram-Schmidt Orthogonalization are as follows:

1. Define the set of vectors that you want to make orthogonal. Let's call this set V and assume it contains n vectors.

2. Create a new set of vectors, let's call it U, with the same number of elements as V.

3. Set the first vector in U to be the same as the first vector in V.

4. For each subsequent vector in V (starting with the second vector), perform the following steps:

a. Calculate the projection of the current vector in V onto all the previous vectors in U. This can be done using the dot product and vector multiplication.

b. Subtract the projection from the current vector in V to get a new vector.

c. Set the corresponding vector in U to be this new vector.

5. Once you have gone through all the vectors in V, the set U will contain a set of orthogonal vectors.

You can then use this code to check if your program is working correctly and compare it with other implementations. I hope this helps!