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 ...

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Solving linear system $Ax=b$ with Hessenberg matrix using lapack

I need to solve a linear system of the form $$Ax = b$$ where $A$ is upper Hessenberg matrix with the lower bandwidth equal to 1, $b$ is the RHS vector and $x$ is the solution vector. I have a C++ ...
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145 views

Best Open Source BLAS / LAPACK package

I was wondering what is a more optimized open source BLAS/LAPACK package with respect to modern multi-core processors (Haswell and beyond). Is there any distribution that can attain performance close ...
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51 views

Using DSYEV in LAPACK

I am calculating eigenvalues of a symmetric matrix using DSYEV in LAPACK.The concerned matrix is in a lower triangular form in a .dat file. I was searching for a simple explanation of the parameters ...
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63 views

Code to update dense QR and Cholesky factorizations

I am looking for some production-ready code to update dense QR and/or Cholesky factorizations (by adding / removing rows and columns or making small-rank updates -- yes, I need all these cases). I ...
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93 views

Total Flop count for LAPACK DPOSV

I am looking at the LAPACK DPOSV routine that computes the solution to the real system of linear equations A * X = B. The routine description can be found here: http://www.math.utah.edu/software/...
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102 views

Lapack routines for solving A x = 0 [duplicate]

I am looking for a LAPACK routine that allows to find a non-trivial solution to the following equation: A x = 0 provided that A is a n×n square singular non-symmetric band matrix. In reality A ...
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123 views

Optimized parallel routine for $X' W X$ with $W$ diagonal

$X$ is a dense matrix of real doubles, typically of size 20 million rows and 500 columns, and $W$ is a diagonal matrix of real, non-negative doubles stored as a vector. I'm working in C and have ...
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97 views

Kronecker products and basis contractions (ie. B.A.Transpose[B]) in C?

I have implemented a basis transformation in C of the following form kron[A,A]*B*Transpose[kron[A,A]] where A and ...
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181 views

Finite Difference Beam Propagation Method problem

I am trying to implement the finite difference beam propagation method to study the propagation of a TE light signal through a waveguide. However, my solutions are exponentially growing, and display ...
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140 views

What is wrong with this matrix multiplication?

I am attempting to write a matrix multiplication routine because I need to do some analysis in CUDA and I want to validate it with CPU code. I am trying to use <...
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386 views

BLAS, LAPACK or ATLAS for Matrix Multiplication in C

I am trying to find the most optimized way to perform Matrix Multiplication of very large sizes in C language and under Windows 7 or Ubuntu 14.04. And searching led me to BLAS, LAPACK and ATLAS. ...
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116 views

R: system is exactly singular: U[1,1]=0

I like to analyze correlation between 3 matrix data(LAI, prcp, tavg). The dimensions of the matrix are x=751, y=601, z=634. My ...
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61 views

large eigenvalues with LAPACK

I have question about LAPACK. I calculate eigenvalues of a $16\times16$ Hermitian complex matrix with small entries by ZHEEV ...
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77 views

Level 3 BLAS accelerated solver for banded linear systems.

At the moment I consider the following problem. I have a huge dense banded matrix $A$ which I want to factorize and use to solve linear systems $Ax=b$. $b$ has around more than 100 columns. At the ...
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77 views

Computing eigenpairs of singular matrix with ZGEEV?

I've never run into a singular matrix before, so bear with me. I have a complex non-symmetric matrix (about 1000 x 1000) that I know has a couple zero eigenvalues. It isn't guaranteed to be ...
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54 views

LAPACK DGGEVX: BALANC option

I'm using DGGEVX routine from LAPACKE with BALANC option as shown below, but to my surprise changing BALANC option from 'N' to ...
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1k views

Eigenvectors: MATLAB vs LAPACK DGGEV or DGGEVX

If we call LAPACK DGGEV or DGGEVX routines for two badly-conditioned matrices in a C++ code, will we get the same eigen-values &...
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60 views

Matrix size LAPACK can support with level-3 BLAS

I am a newbie in using LAPACK library. I know that LAPACK's internal rountines break the large problem into smaller problems recursively (I am considering level-3 BLAS). If we consider matrix ...
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370 views

Schur(QZ) Decomposition Differences

I am having issues understanding why different languages are producing different answers for the Schur(QZ) decomposition. I am working on writing some old stuff from Matlab into Julia and Python and ...
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138 views

Azimuthal average in Fortran? Find indexes in Fortran?

I am working on an eigenvalue problem in fortran. I have used Lapack to solve the problem and get the eigenvalues and eigenvectors. This is done for $201\times101$ wavenumbers, only half the wavespace ...
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67 views

How much time does DSYEV take to diagonalise a $N \times N $

I have been using a DSYEV, for some time. My instructor told me to calculate how much time does DSYEV take to diagonalise a $N \times N $. I know, in our case matrix M is symmetric. Standard ...
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241 views

BLAS/LAPACK Non absolute sum

I need to know if there is some function in BLAS/LAPACK or some other Scientific Library that returns a non absolute sum of a vector/matrix. I've found the 'asum', but it returns only the absolute ...
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589 views

Impact of frequent row major / column major conversions using LAPACK/BLAS?

If you call a library like LAPACK or BLAS (which are written in FORTRAN and use column major order) from a C-like language that uses row major order, won't you lose performance and use a lot of memory ...
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429 views

How can QR iteration with complex matrices produce complex diagonal entries?

In Lapack (zhseqr) and matlab, the eigenvalues of a complex matrix are computed successfully. I notice that QR iteration or algorithm is involved with that process. QR iteration repeats to call QR ...
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78 views

Threaded QR with column pivoting

My program needs to perform pivoted QR decomposition on tall (e.g. 1e9 by 100) matrices. I run into the bottleneck that the major computational time of my program is spent on doing serial pivoted-QR ...
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523 views

Flop counts for LAPACK symmetric eigenvalue routines DSYEV, DSYEVD, DSYEVX and DSYEVR

LAPACK has following 4 routines for calculating eigenvalues of a real symmetric matrix; namely DSYEV, DSYEVD, DSYEVX and DSYEVR (DSYEVR being the recommended one). If I were to calculate both ...
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Why would this a pair of E5-2670 cpus be faster than 4 E5-2640 cpus for large matrix diagonalisation problems?

Not really much more to say; Of several computers available for use, these are two of the larger ones; one has 2x E5-2670, and the other has 4x E5-4640. The problems we're looking at essentially boil ...
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625 views

Fast vector - “diagonal” matrix multiplication

Let $\mathbf{1}\in\mathbb{R}^d$ be a vector with all elements equal to $1$. Define: $$\mathbf{D} = \mathrm{diag}(\mathbf{1}^\top,\mathbf{1}^\top,\ldots,\mathbf{1}^\top) = \begin{bmatrix} 1 \cdots 1 &...
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117 views

Do vendors release their own LAPACK library?

Every CPU vendor seems to make BLAS libraries that are specialized to run on their hardware. Do they do the same for LAPACK? Or is that a non-issue because LAPACK is written entirely in terms of BLAS ...
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82 views

cgees subroutine

I'm tryng to learn to use a lapack subroutine but I got stuck. I hope this is the right forum... In this fortran program I'd like as a test to find the Shur form of the matrix ((0,1)(1,0)) using cgees,...
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689 views

Solving for null space of a matrix with mkl LAPACK

I want to find a solution for $xA=0$, where $A$ is a square matrix. I know that most of the LAPACK routines solve for $Ax=b$. So I take $A^T$ as a, and set $b=0$. I have an additional restriction of $\...
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326 views

how to use lanczos code from netlib for large sparse symmetric matrix?

I want to use lanczos method to calculate the few lowest eigenvalue and eigen-vector of a large sparse symmetric matrix(~50k x ~50k). In http://www.netlib.org/lanczos/index.html I found the codes ...
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599 views

Eigenvectors: Mathematica vs. LAPACK dgeev

I've been using LAPACK dgeev in FORTRAN in the last months spending hours to diagonalize ~4000*4000 matrices. It takes about 2'75 hours to find eigenvalues and ...
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928 views

what is difference “DSYEV(LAPACK SUBROUTINE)” and “Lanczos”?

I am working on Fermion and Boson Hubbard Models, in which the dimension of Hilbert Spaces are quite large (~50k). Because the Hamiltonian matrix is ~50k X ~50k, to diagonalize these big sparse ...
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92 views

Lapack++ for QR algorithm

I have recently started using Lapack++ which I found convenient for my programming purpose, in general. Now, I need to solve a matrix using QR algorithm. I've searched the user manual and I found a ...
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What is the relationship of BLAS, LAPACK, and other linear algebra libraries?

I have been looking into C++ linear algebra libraries for a project I've been working on. Something that I still don't have any grasp on is the connection of BLAS and LAPACK to other linear algebra ...
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411 views

lapack singular matrix

I'd like to find a condition that allows me to determine if a matrix is invertible or not. naively, I computed the determinant to see if it was zero. but then I realized that even for very small ...
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671 views

lapack dorgqr qr decomposition matrix $m\times n$ with $m<n$

I'd like to do a $A=QR$ decomposition of a matrix $A$, with $m\times n$. I use dgeqrf_ (or dgeqp3_) to proceed to the first part ...
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620 views

Is there any benefit to compiling LAPACK from source versus installing the prebuilt package from Ubuntu?

I know that ATLAS is able to optimize itself for the machine it is compiled on and thus maximum benefits are found by compiling from source. Is there any benefit to compiling LAPACK from source? It ...
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206 views

$\mathbf{UDU}^\top$ decomposition routines in LAPACK/Eigen?

I would like to compute the decomposition of a real symmetric positive definite matrix $\mathbf{A} = \mathbf{UDU}^\top$. LINPACK seems to have it as DSIFA, but I ...
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Solving a sparse and highly ill-conditioned system

I intend to solve Ax = b where A is complex, sparse, unsymmetric and highly ill-conditioned (condition number ~ 1E+20) square or rectangular matrix. I have been able to solve the system with ZGELSS in ...
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solve $xA=b$ for $x$ using LAPACK and BLAS

I am porting an existing code from MATLAB to C++ and have a linear system to solve $xA=b$ (rather than the more typical form $Ax=b$) The matrix $A$ is dense, and of general form, but is no larger ...
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319 views

Singular matrix - but SVD works - what does the eigenvalues mean? Find I the “dependent” lines?

please can I ask a bit stupid question? I have a complex matrix A as a set of equations. I wanted to find the solution of Ax=b where b is vector of right-hand side. So I have called zgetrf on A (does ...
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125 views

FFT - function only in sine series? Can be done with MKL / Lapack?

please can I ask, how one can make from function sine series (Fourier transform) with MKL? I can do "normal" exponential FFT with MKL (Lapack of course), how can I say that I want only sine series? ...
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261 views

LAPACK - singular matrices - what does the positive integer info mean?

please can you help me with my code - I use Lapack to solve complex matrix (quite biq) and do it in two steps: I call zgetrf (LU factorization) and then ...
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2k views

Threaded OpenBlas benchmark slower than system blas?

I'm not sure if I did something wrong or if I just didn't understand the concept of an optimized BLAS. I'm a FEM engineer trying to optimize my setup on a small cluster computer (six nodes). I'm ...
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134 views

Understanding Inner blocking size in lapack/plasma

I could not get accurate description that aids to my understanding of inner blocking size parameter that is used in many LAPACK routines(such as DGEQRT, DLARFB). Thanks
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1k views

Magma vs. Plasma

I'm having a difficult time understanding the difference between the linear algebra packages MAGMA and PLASMA from just a quick glance. It looks like MAGMA is oriented towards GPU's and vector ...
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1k views

What are the fastest available implementations of BLAS/LAPACK or other linear algebra routines on GPU systems?

nVidia, for example, has CUBLAS, which promises 7-14x speedup. Naively, this is nowhere near the theoretical throughput of any of nVidia's GPU cards. What are the challenges in speeding up linear ...
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170 views

Dense generalized hermitian indefinite eigenvalue problem

Lapack contains a driver routine to solve dense generalized Hermitian positive definite eigenvalue problems of the form $Ax=\lambda Bx$, where $A$ and $B$ are both Hermitian, and $B$ is positive ...