# Questions tagged [lapack]

LAPACK (Linear Algebra PACKage) is a commonly used library of subroutines for numerical linear algebra tasks, including solutions of linear sets of equations, linear least squares, eigenvalue problems, and singular value decomposition. LAPACK routines may be used with fortran, C and relatives and a variety of other languages.

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### Benchmark problems for eigenvalue reordering algorithms sought

Every real matrix $A$ can be reduce to real Schur form $T = U^T A U$ using an orthogonal similiary transform $U$. Here the matrix $T$ is quasi-triangular form with 1 by 1 or 2 by 2 blocks on the main ...
2answers
136 views

### Is there a simple way to add a sparse matrix to an LU decomposition of a dense matrix?

I am solving a parabolic equation in the form: $$\left( {M \over\tau_j} + A \right) u^{j+1} = M f^j + {u^j \over \tau_j},$$ where $A$ and $f$ are a dense stiffness matrix and the right hand side of ...
1answer
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### Efficiently compute a projection matrix from Householders reflectors

Let $A \in \mathbb{R}^{m \times n}$ where $m \geq n$. Let $B$ and $\tau$ be the result of applying LAPACK's dgeqrfp method (R on the upper right triangle, and the ...
3answers
19k views

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

I'm new to computational science and I already have learned basic methods for integration, interpolation, methods like RK4, Numerov etc on c++ but recently my professor asked me to learn how to use ...
1answer
93 views

### Faster eigenvector routine for non-symmetric matrices with real eigensystem?

I have non-symmetric real-valued matrices with real-valued eigensystems. How to compute eigenvectors efficiently? Using scipy.linalg.eig (which calls ...
1answer
87 views

### Trace of inverse from LU decomposition

Given an LU decomposition of $A\in \mathbb{R}^{n\times n}$, is there a way to compute $\operatorname{trace}(A^{-1})$ with lower complexity than that of the inversion ($O(n^3)$ in practice)? This ...
1answer
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2answers
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### Does LAPACK offer routines for Krylov sub-space based solvers and nonlinear solvers?

I have skimmed through the LAPACK user guide, but I could not find if LAPACK offers routines for Krylov Subspace based methods (such as CG or BiCGSTAB etc) and Newton method based nonlinear solvers. ...
1answer
124 views

### Diagonalization of Hermitian matrices vs Unitary matrices

What are the general algorithms used for diagonalization of large Hermitian matrices and Unitary matrices? ($>5000 \times 5000$) LAPACK seems to diagonalize Hermitian matrices almost 20 times as ...
2answers
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2answers
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### Does armadillo library slow down the execution of matrix operations?

I've converted a MATLAB code to C++ to speed it up, using the Armadillo library to handle matrix operations in C++, but surprisingly it is 10 times slower than the MATLAB code! So I test the ...
1answer
110 views

### Problem with 'dsysv' from LAPACK

I am having trouble with a C program that uses the function dsysv from LAPACK. Everything compiles and works without any errors, my only problem is, that the ...
4answers
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### Rapidly determining whether or not a dense matrix is of low rank

In a software project that I'm working on, certain computations are vastly easier for dense low-rank matrices. Some problem instances involve dense low-rank matrices, but they're given to me in full, ...
1answer
299 views

### C++: Efficient library for dense linear algebra operations (determinant & principal minors)

I usually work with Python, but my basic knowledge of c++ allows me to switch when I need to increase the speed of my code. Currently, I have a python script that (among other things) computes the ...
1answer
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### LAPACK: ZGETRF with INFO greater than zero but ZGETRI does not fail.

I am computing the inverse of a complex matrix. I execute ZGETRF but U(2,2) = 0. When I compute ZGETRI, the inverse is determined. Can I trust this inverse?
0answers
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### Kronecker product of matrices

I have to use Kronecker product of a matrix with a unit matrix is there any routine in ScaLapack or Lapack which can do so efficiently.
1answer
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### LAPACK zlapmt_ freezes code [closed]

I'm using LAPACK's zggev_ routine to solve some generalized eigenvalue problem. While it produces the correct results, I want the eigenvalues and according eigenvectors sorted by absolute value. For ...
1answer
281 views

### How to do a Generalized Complex Schur (or QZ) Decomposition with Eigen C++? [closed]

I would like to do a Generalized Schur (or QZ) decomposition for a pair of complex matrices $A$ and $B$. I found the following class: ...
0answers
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### Eigenvalue problem (LAPACK)

I am working on a project in numerical analysis which I have to program in C (using Lapack and Blas). Matrix is given which is tridiagonal and "almost" symmetric (one element is to be changed to make ...
1answer
93 views

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

I've encountered an odd issue with solving for the eigenvalues of the following matrix, in Matlab format: ...
1answer
148 views

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

I have a matrix of the form And I would like to invert it. Currently I am using the lapack routines zgetrf and zgetri. I.e. I am performing LU factorisation. My question: Are there any packaged ...
1answer
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### What is the difference in the pivoting strategies between LAPACK's dpstrf and dpst2 and why?

dpstf and dpstrf sometimes give different pivot results. Of course I can read the source code, but I don't get the idea from it. Since pivoting is for stability of the Cholesky decomposition, one of ...
0answers
225 views

### How to make LAPACK eigenvectors orthogonal like Matlab?

I'm using LAPACK zgeev to calculate eigenvectors of a symmetric complex matrix of high dimensions ($n \approx 2000$). I need these eigenvectors to satisfy \sum_{...
1answer
547 views

### LAPACK sorting eigenvalues differently each time

I'm using LAPACK zgeev routine to get eigenvalues and eigenvectors of a symmetric matrix in C++. Problem is zgeev is being called in a loop but it sorts eigenvalues (and eigenvectors) differently ...