Singular Value Decomposition of 4x4 matrix in C - c

I am ultimately trying to create a pseudoinverse function using svd methodology. I want to first create a SVD function that will give me the U, E and V matrices that I will later use in the formula below to get the pseudoinverse:
I am not sure how to code these matrices. I understand how to do this by hand through eigen values and vectors but not sure how to translate that to c code.
I have already created functions for Transpose and matrix multiplication. Now its a matter of finding these 3 matrices.

You can see a similar asked question with a link to a source file.
They recommend to use openCV built-in function - you can find it here - the purpose is to use a ready function from the openCV library.

Related

Function for language C that replicates the results of eig in MATLAB

I want to find the function of calculating eigenvalue and eigenvectors in language C which has same results as MATLAB's eig function.
I'm currently using GNU Scientific Library eigenvalue solver. However, it can't get same eigenvectors as the results of MATLAB eig function when the eigenvalues are overlapped.
How can I replicate MATLAB's results in C?
Matlab uses either the Cholesky decomposition algorithm or the generalized Schur decomposition algorithm: you'll have to implement one of those in order to try and get close to what's done in Matlab.
An example of how the first method could be implemented in C can be found here.

What code is responsible for adding two matrices in Numpy?

I'm writing a program in C that adds two matrices (I'm also using BLAS). I want to see how this is done in numpy, to make sure I do matrix addition efficiently:
https://github.com/numpy/numpy
Can anyone help me find the C source code in numpy Github repository that does matrix addition?

Implementing Matlab mrdivide using QR Decomposition and Solving in C

I've used x=B/A (mrdivide) in Matlab to find x in equation xA=B. I am trying to achieve this without Matlab environment using a C based fixed point library for microcontrollers called libfixmatrix.
How would I proceed with using QR Decomposition and Solve function's of libfixmatrix to solve xA=B?
QR Decomposition and Solving is equivalent to solving for Ax=B. But I have a scenario where x is in equation xA=B
It was mentioned in the readme of the repository that :
Libfixmatrix is suited well for tasks involving small matrices (often
less than 10x10)
Is it efficient to use libfixmatrix for say 80*80 ?
just a silly suggestion:
x.A = B
x.A.inverse(A) = B.inverse(A)
x = B.inverse(A)
So you just need to compute Inverse matrix and matrix multiplication which are basic operations. Use Sub-determinant approach. Also if A,B are not square matrices resize them so they are.

Singular Value Decomposition (SVD) in C

I am doing the five point essential matrix estimation in C where I need to implement SVD. I found an opensource implementation in c http://www.public.iastate.edu/~dicook/JSS/paper/code/svd.c that works on mxn matrices where m>n. The problem is that the matrix that I want to decompose is a (5x9) matrix and therefore n>m. I need the right orthogonal transformation matrix v where svd(A)=udv'
To ensure (m>n) I tried to do svd(transpose(A))=u2*d2*v2
I found that u=v2, but v is different from u2 and I need v.
How to implement SVD in C successfully for an 5x9 matrix?
Late to the party, but for future reference one can obtain a SVD implementation in C from the book "Numerical Recipes in C by William H. Press et al", in Chapter 2.6, Page 67, SVD Algorithm. To quote the book
Here is the algorithm for constructing the singular value decomposition of any
matrix.
So I'm assuming the matrix to be decomposed can be square, m < n or n < m
Warning: When googling SVD implementations in C check what assumptions are made w.r.t the input matrix. Some assume the matrix is square, some do not, etc...
Alternatively, you can use the SVD in LAPACK. Stephen Canon provided a code example on another SO question on how to use dgesdd to perform SVD. (link here)

Eigenvector (Spectral) Decomposition

I am trying to find a program in C code that will allow me to compute a eigenvalue (spectral) decomposition for a square matrix. I am specifically trying to find code where the highest eigenvalue (and therefore its associated eigenvalue) are located int the first column.
The reason I need the output to be in this order is because I am trying to compute eigenvector centrality and therefore I only really need to calculate the eigenvector associated with the highest eigenvalue. Thanks in advance!
In any case I would recommend to use a dedicated linear algebra package like Lapack (Fortran but can be called from C) or CLapack. Both are free and offer routines for almost any eigenvalue problem. If the matrix is large it might be preferable to exploit its sparseness e.g. by using Arpack. All of these libraries tend to sort the eigenvectors according to the eigenvalues if they can (real or purely imaginary eigenvalues).
See the book "Numerical recipes in C"
And the #1 google hit (search: eigenvalue decomposition code C#)
http://crsouza.blogspot.com/2010/06/generalized-eigenvalue-decomposition-in.html
does not help?

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