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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PLASMA usage (Linear algebra routines that supports multithreading)

I have been looking for linear algebra libraries that support multithreading. I have found PLASMA which looks promising. It is from the same group that developed LAPACK. http://icl.cs.utk.edu/...
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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 ...
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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 ...
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2 votes
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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 ...
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Factorization of cubic spline interpolation matrix

In cubic spline interpolation, we use the set of knots and function values $(x_i,y_i),i=1,...,n$ to construct a (tridiagonal) system of equations for the unknowns $\sigma_i$: $$ h_{i-1}\sigma_{i-1} + ...
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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 ...
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Efficient computation of marginalized multivariate normal likelihood

In general,if we know that the marginal Gaussian distribution for some variable $\textbf{x}$ and a conditional Gaussian distribution for some $\textbf{y}|\textbf{x}$ of the forms: $$p(\textbf{x}) = \...
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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. ...
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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 ...
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8 votes
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A misunderstanding or a bug in LAPACK's solver for generalized eigenvalue problems?

In my application, I have two general real matrices $A$,$B$ defined as follows, $$ A=\begin{bmatrix} -s I_3 & A_0 & 0 & 0 \\ A_0^T & -s I_3 & 0 & 0 \\ 0 &...
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Python scipy eigh(Arpack) giving wrong eigenvalues for generalized eigenvalue problem

I am trying to solve a generalized eigenvalue problem using Arpack, right now the code is using LAPACK but that's too slow, we only need a few eigenvalues and the matrices are sparse so using Arpack ...
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Numerical calculation of the Berry connection

I'm doing some numerical calculations involving Hermitian matrices, and derivatives of the eigenvectors. Essentially, I have an n x n, Hermitian matrix H(x), which is dependent on some continuous ...
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Why is LAPACK (seemingly) suboptimal for packed and banded eigenvalue problems?

Based on this LAPACK routines list, it looks like there is no relatively robust representation (RRR) driver routine for either packed or banded symmetric eigenvalue problems. According to the relevant ...
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Is LAPACK behind the cutting edge of dense linear algebra?

I have been digging into some numerical linear algebra lately, and reading in particular about how LAPACK solves symmetric eigenvalue problems. I noticed that the ...
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Functions from Scipy, Blas, or Lapack that compute only upper triangular matrix

My goal is to transform a matrix into upper triangular form in Python. I know the function scipy.linalg.lu will do LU decomposition and get both upper and lower ...
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Library to solve dense linear system with GMRES

I have a fortran 90 code and I want to solve a dense linear system with GMRES. I would prefer the restarted GMRES with preconditioning. Is there some library that you know of that I could use? Now I ...
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How to know which LAPACK's function is used by Scipy's eig function?

As far as I understood, scipy.linalg.eig use wrappers from scipy.lapack to compute the eigenvalues and eigenvectors of a matrix. ...
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Do most statistical packages and libraries in high-level programming languages rely on LAPACK for their matrix inversion operations?

Possible an open-ended question, but I am wondering if most statistical packages and libraries, for instance, Stata, R, Python's NumPy and MATLAB rely on LAPACK algorithms to perform matrix operations,...
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Lapack symmetric update $B^{-1}AB^{-T}$

Does Lapack have a routine that, given symmetric $A=A^T$ and $B$, computes the symmetric matrix $B^{-1}AB^{-T}$ (while preserving symmetry exactly)? It would be enough to have this routine for ...
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Using LAPACK to compute $B^{-1}AB^{-T}$ for thin $B$

How can I use BLAS/LAPACK to compute $$ B^{-1}AB^{-T} $$ where $A\in\mathbb{R}^{n,n}$, $B\in\mathbb{R}^{m,n}$ is full rank matrix with $m>n$, and $B^{-1}y:=\arg \min_{x} \|Bx-y\|_{2}$. In theory, ...
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Inverting a matrix from LU decomposition

The LAPACK routines xGETRI compute the inverse of a matrix $A = PLU$ in its LU decomposed form by first computing $U^{-1}$, and then solving the system: $$ (A^{-1} P) L = U^{-1} $$ My question is: ...
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How to use LAPACK function (DGELSY) in Fortran

I am trying to use Least Squares Minimization to solve a the matrix problem: b = A*x for x. The system is overdetermined, and A is a dense matrix. In the LAPACK library, I believe the routine DGELSY ...
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Stability of SVD, Eigendecompositions, and pseudoinverse procedures in modern LAPACK routines

I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways. One of these claims is that my proposed solution requires no explicit SVD and ...
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LAPACK equivalent on c++ , which is the best one? [duplicate]

I am following a course of computational material physics. The professor uses fortran to code and uses lapack to solve eigenvalue problems. So far I just know c++. There is an equivalent library that ...
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What is the reason that LAPACK uses $\tau$ in QR decomposition (instead of normalizing the reflection vector)?

LAPACK's QR routine stores Q as Householder reflectors. It scales the reflection vector $v$ with $1/v_1$, so the first element of the result becomes $1$, so it doesn't have to be stored. And it stores ...
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Fast matrix multiplication with matrix elements computed on-the-fly (without forming the matrix)

Is there any library or routine for high-performance matrix-matrix product, where the matrix elements are computed on-the-fly using a given function of $i$ and $j$? More specifically, in the problem ...
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Wrong result of 'ddot' from BLAS

I am having trouble with a C/C++ program that uses the BLAS routine ddot. I am running Linux and so far LAPACK routines worked without any problems. I get a wrong ...
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2 votes
1 answer
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Inverting small matrices: canned factorization versus explicit formula

I am interested in solving a large number of small linear systems of equations, $Ax=b$, with $A$ either $2\times2$ or $3\times3$. Assuming none of these systems are actually singular, is there ...
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1 answer
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How many operations are needed for LAPACK's zgesv to solve a linear system?

I have a linear system of complex numbers. I am using LAPACK' zgesv (actually I am using intel MKL LAPACKE, but I am assuming the algorithm is the same). No assumption can be made about the system. I ...
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11 votes
2 answers
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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 ...
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4 votes
1 answer
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Compute bilinear form with LAPACK

I need to compute a bilinear form for a set of left and right vectors $$ w_k = \sum_{i,j} V_{ik}^*A_{ij}U_{jk},$$ where $A_{ij}\in\mathbb{R}$ and $U_{jk}, V_{ik} \in \mathbb{C}$ (Assume that all the ...
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3 votes
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Diagonalizing a block tridiagonal Toepliz Hermitean matrix

I have to diagonalize, within a Fortran-written code, a block tridiagonal Toeplitz Hermitian matrix, e.g. $$ \left[ \begin{array}{ccccc} \ddots & \hat{A} & & & \\ \hat{A}^\dagger &...
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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 ...
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2 answers
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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 ...
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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 ...
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1 vote
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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.
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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 ...
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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: ...
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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 ...
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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: ...
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0 votes
1 answer
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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 ...
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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?
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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_{...
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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 ...
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Matlab, Mathematica & LAPACK returning 3 different eigenvectors

(I'm not sure which of math.se / stackoverflow / scicomp.se is the right place to ask this question) I have a C++ code which generates a complex matrix and then calculates its eigenvalues and ...
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13 votes
5 answers
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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, ...
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1 vote
1 answer
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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 ...
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3 votes
5 answers
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Fast c++ library to solve very big sparse systems

I am working on a project with electrical circuits, where I am trying to compute the voltages at all the nodes of an electrical circuit. I know that the electrical circuit is a perfect grid, so each ...
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1 vote
1 answer
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Efficient computation of $BX=A$ when LU factorization of $A$ is given

First, $AX=B$ is solved, so I have the LU factorization of $A$ computed already. Now I need to solve $BX=A$. Is there any way to reuse this information (LAPACK ...
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2 votes
2 answers
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Efficient computation of AX=B where B has special structure (block-diagonal)

In case B(size ~ 2k, complex double) is block-diagonal, where block size is small(e.g. 2), is there any more efficient way to compute this other than Lapack gesv?
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