Singular Value Decomposition (SVD) in C - 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)

Related

How to tell BLAS that output matrix is symmetric?

I have two n x k complex matrices A and B. I need to calculate C = A B^H. C is guaranteed to be real, symmetric and all elements will be non-negative. These matrices will be pretty large so I am going to be using either CBLAS or MKL in C for this purpose. However, I cannot find a way to tell BLAS that C is symmetric, at least based on the quick reference document. This is important as it would halve the computation time. The xHER2K routine will give me a B A^H term which I don't want. Please suggest a way to proceed in this matter.

Singular Value Decomposition of 4x4 matrix in 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.

armadillo sparse lu (or cholesky) decomposition

I need to solve a linear equation (Ax = b), with a large sparse A and with différents b multiple time. Thus, an LU (or Cholesky if A is symmetric), factorisation is highly preferable.
I'm using the armadillo library and I've heard that one can use the function:
spsolve(x, A, b, "superlu");
In order to solve such a system. I'm not very concerned about retrieving the L and U matrices. However, it is of primal importance that both L and U aren't recomputed every time I call spsolve.
Does spsolve(x, A, b, "superlu") store the LU decomposition and if not, is there a way to retrieve said matrices?
The fact is that armadillo is, essentially, a "wrap-up" for software developed by the other teams; this particularly is correct for the superlu sparse solver. The feature that you are asking for (solving a series of systems of equations with one and the same matrix but different right-hand sides) may not exist in armadillo at all. You should probably use a sparse linear solver directly (not necessarily superlu) that has that feature embedded. In case if you system is very large, so a factorisation-based solver cannot cope with that, an iterative solver may do, and there is an option to go in such case: since modern CPUs are multi-core, several independent solution processes can be run in parallel. One such iterative solver is described in the following blog (you may ask questions and/or participate in discussion there): http://comecau.blogspot.com/2018_09_05_archive.html

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.

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?

Resources