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 ...
4
votes
1answer
62 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 ...
5
votes
2answers
202 views
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 ...
6
votes
2answers
137 views
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 ...
2
votes
1answer
98 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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votes
0answers
58 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?
...
3
votes
2answers
88 views
LAPACK - singular matrixes - 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 ...
4
votes
1answer
153 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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vote
1answer
89 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
4
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1answer
153 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 ...
8
votes
2answers
264 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 ...
5
votes
1answer
105 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 ...
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votes
1answer
313 views
BLAS/LAPACK subroutine to add two matrices with different offsets and leading dimensions
I currently searching for a subroutine from BLAS or LAPACK which realizes the following operation
A = alpha*A + beta * B
where A and B have different leading ...
7
votes
1answer
206 views
Does PETSc ever make use of LAPACK libraries for sparse matrix math?
Does compiling PETSc with an external BLAS/LAPACK library significantly affect performance on sparse matrices, or does it only use those libraries for dense matrix math?
4
votes
1answer
62 views
Efficient computation of the extension of a linear basis to completion when the basis is almost complete (ideally using LAPACK routines)
I have a $p \times n$ matrix $B$ (where $n < p$) with orthonormal columns and would like to find a numerically efficient way to extend this matrix to get a complete $p$-dimensional orthonormal ...
6
votes
3answers
1k views
Understanding how Numpy does SVD
I have been using different methods to calculate both the rank of a matrix and the solution of a matrix system of equations. I came across the function linalg.svd. Comparing this to my own effort of ...
6
votes
2answers
571 views
What is the corresponding LAPACK function behind Matlab [Q,R,E]=qr(A)?
I currently trying to cheaply compute a good rank estimate for a matrix $A$. Therefore I compute a columnt pivoting QR decompostion using
[Q,R,E]=qr(A)
in ...
9
votes
3answers
452 views
Why isn't my Matrix-Vector Multiplication Scaling?
Sorry for the long post but I wanted to include everything that I thought was relevant in the first go.
What I want
I am implementing a parallel version of Krylov Subspace Methods for Dense ...
4
votes
2answers
894 views
How do I use ScaLapack/PBLAS for Matrix-Vector Multiplication?
After going to all possible "Introductions" to ScaLapack, I still can't understand how to carry out a simple PDGEMV operation using it.
Here is what I must do :
...
6
votes
1answer
480 views
How does LAPACK solve tridiagonal systems and why
In my project I have to solve a couple of tridiagonal matrices at every time step, so it is crucial to have a good solver for those. I did my own implementation, just the classical way to do it ...
5
votes
4answers
240 views
Easily accessible scientific code that uses LAPACK
I would like to analyze some well-used scientific codes that make heavy use of LAPACK. I.e. I'm looking for codes that both spend a lot of time within LAPACK functions and use LAPACK non-trivially ...
9
votes
3answers
466 views
Matrix exponential of a real asymmetric matrix with Fortran 95 and LAPACK
I recently asked a question along the same lines for skew-Hermitian matrices. Inspired by the success of that question, and after banging my head against a wall for a couple of hours, I'm looking at ...
8
votes
3answers
414 views
Matrix exponential of a skew-Hermitian matrix with fortran 95 and LAPACK
I'm just getting tucked into fortran 95 for some quantum mechanics simulations. Honestly, I've been spoiled by Octave so I've taken matrix exponentiation for granted. Given a (small, $n\leq 36$) ...
