# Tag Info

Accepted

### How to start using LAPACK in c++?

I'm going to disagree with some of the other answers and say that I believe that figuring out how to use LAPACK is important in the field of scientific computing. However, there is a large learning ...
Accepted

### Why is it that SVD routines on nearly square matrices run significantly faster than if the matrix was highly non square?

You are asking for a full (dense) SVD, which also needs to generate the unitary components of $U$ and $V$ which correspond with the null space of your input. for the $1000 \times 800$ case, your input ...

### How to start using LAPACK in c++?

I usually resist telling people what I think they should do rather than answering their question but in this case I'm going to make an exception. Lapack is written in FORTRAN and the API is very ...

### How to start using LAPACK in c++?

Here's another answer in the same vein as the above. You should look into the Armadillo C++ linear algebra library. Pros: The function syntax is high-level (similar to that of MATLAB). So no <...

### Is LAPACK behind the cutting edge of dense linear algebra?

When one says an algorithm is of order $O(n)$, that may mean that the complexity is given by: $c + b*n$. With every new element you add you increase in runtime (effectively). What mathematically ...

### Rapidly determining whether or not a dense matrix is of low rank

The problem, of course, is that computing the true rank (e.g., via a QR decomposition) is not really any cheaper than computing a low-rank representation of the matrix. The best you can probably do ...

### Is LAPACK behind the cutting edge of dense linear algebra?

LAPACK has been on the cutting edge for just about three decades, and probably still is for its niche. However, given given recent developments in libraries for the simpler BLAS-type matrix operations ...
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### Python scipy eigh(Arpack) giving wrong eigenvalues for generalized eigenvalue problem

The matrix B (M in the documentation) needs to positive definite according to the documentation: "If sigma is None, M is positive definite", this is in addition to the first requirement &...
Accepted

### Matrix Balancing Algorithm

Took me quite a while to figure this out and as usual it becomes obvious after you find the culprit. After checking the problematic cases reported in David S. Watkins. A case where balancing is ...

### What's the fastest implementation of elementwise vector multiplication in Fortran?

The cost of the multiplication is almost insignificant compared to the cost of loading the data from memory (and writing it back). If you're worried about performance, you should be thinking about ...

### Rapidly determining whether or not a dense matrix is of low rank

Another approach worth trying is to use Adaptive Cross Approximation (ACA). It is a pretty popular algorithm that has many implementations available online. For the reference, you can see the original ...
Accepted

### LAPACK sorting eigenvalues differently each time

You write, that you are computing the eigenvalues of a symmetric matrix. Does the matrix have real entries? In this case all eigenvalues are real, and you can use a symmetric eigenvalue solver, which ...

### Are there any packaged routines (in lapack or elsewhere) for inverting a banded matrix?

Well, other than the usual "don't invert your matrices unless you need the inverse itself" you can still use the banded routines ?gbtrf and then use ...

### LAPACK non-convergent eigenvalue algorithm for complex but not double matrix

Your matrix is not diagonalizable, in the Jordan decomposition of it there is a block for the eigenvalue $0$ of the form $$\begin{pmatrix}0&0&0\\0&0&1\\0&0&0\end{pmatrix},$$ ...