Questions tagged [blas]
Basic Linear Algebra Subprograms - A standard API library with vector-vector, matrix-vector, and matrix-matrix operations.
71
questions
4
votes
2answers
223 views
Getting to know about various BLAS implementations
I keep coming across phrases like "highly optimized BLAS kernels" with "architecture-specific optimizations", but have never been able to find what exactly these optimizations are, ...
1
vote
2answers
409 views
How to set up the differential equation system to speed up computation?
I've set up a system of differential equations, obtained after discretizing pde, in the following way
...
2
votes
1answer
97 views
Efficient change of basis real positive definite symmetric matrix
I need to optimize a code where the most performance critical part is doing a 'change of basis', in other words it is an unitary similarity transformation on a big real positive definite symmetric ...
2
votes
1answer
85 views
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 ...
1
vote
0answers
332 views
What algorithm do BLAS and ATLAS use for matrix multiplication?
I have searched and what I understood was that they use the naive one with several memory and cache optimizations.
However, I wanted to know whether they are using the Strassen or the Coppersmith-...
1
vote
1answer
109 views
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, ...
5
votes
0answers
329 views
Is there any catch on using `zgemm3m` vs regular `zgemm`?
I've just (to my embarrassment) encountered a BLAS-like extension of a matrix-matrix product subroutine gemm in Intel MKL: gemm3m...
2
votes
0answers
42 views
Best way of porting code from the GPU to MPI-nodes
I have a program, structured in two parts, $A$ and $B$. Both parts are capable of running as standalone units, and written in C++. $A$ is written for cluster systems, running entirely on CPU-nodes, ...
2
votes
1answer
119 views
BLAS operation question
I want to perform the following operation:
$$
A = A + U B^T
$$
where $A$ is $m \times n$ dense, $U$ is $m \times m$ upper triangular, and $B$ is $n \times m$ dense. The BLAS function ...
2
votes
3answers
240 views
C standard for computational science
Which C standard should be used for computational science code ?
Should we keep compatibility with C89/90/ANSI or jump to C99 or C11 ?
Context:
Code will use third-party : BLAS, LAPACK, MKL, ...
4
votes
0answers
86 views
Block matrix and DSYRK
I want to compute the matrix
$$
A = \sum_{i=1}^N v_i v_i^T
$$
where each $v_i$ is a given vector of length $2500$, so that $A$ is $2500 \times 2500$, and my $N$ is about 2 million. Rather than call ...
3
votes
2answers
147 views
Parallel assembly of matrix
I have a matrix which I want to assembly quickly, which is in block form:
$$
A = \pmatrix{ A_{11} & A_{12} & A_{13} \\ A_{21} & A_{22} & A_{23} \\ A_{31} & A_{32} & A_{33}}
$$
...
4
votes
1answer
246 views
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 ...
1
vote
0answers
78 views
Fast calculation of $A^T B$
I need to compute a matrix-matrix product, $A^T B$, where $A$ is $n \times r$ sparse, and $B$ is $n \times q$ dense. The number of rows $n$ is far larger than both $r$ and $q$. In fact $n$ is so large ...
1
vote
1answer
204 views
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 ...
1
vote
0answers
124 views
$ A * B $ computation when B is a symmetric matrix in armadillo [closed]
Is there any way to multiply a symmetric matrix by a dense one in armadillo(and use the fact that we have a symmetric matrix)? I know about DSYMM Routine in BLAS,...
1
vote
0answers
154 views
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.
1
vote
0answers
96 views
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 ...
1
vote
1answer
749 views
The difference between mkl_intel_lp64 vs mkl_gf_lp64 in a numerical reproducibility issue with Intel MKL
It has been discussed that Intel MKL can exhibit irreproducible behavior under certain conditions. In fact, this is a known thing and described by Intel as Conditional Numerical Reproducibility.
A ...
1
vote
1answer
180 views
GPU libraries for integer matmul | overflow tolerated
Are there any high performance integer BLAS libraries that implement matrix multiplication i.e. i32gemm and i64gemm ? I need to use them for a cryptographic application and can tolerate overflows, i.e....
2
votes
0answers
135 views
What matrix criteria is "large enough" for Eigen to use a BLAS backend?
Eigen's documentation says that any BLAS back-end can be used (e.g. MKL) to perform the actual matrix calculations.
It is, however, very vague when discussing the criteria as to which the ...
2
votes
1answer
589 views
Distributed (MPI) matrix matrix multiplication
I perform matrix matrix multiplications (between rank-3 and rank-2 arrays) in fortran using following subroutine,
...
17
votes
3answers
2k views
Are BLAS implementations guaranteed to give the exact same result?
Given two different BLAS implementations, can we expect that they make the exact same floating point computations and return the same results? Or can it happen, for instance, that one computes a ...
3
votes
2answers
5k views
BLAS libraries for Octave or Matlab, preferrably with GPU support?
I just searched around a bit for BLAS implementations and was amazed by the sheer amount of libraries around. Does someone know of a benchmark or otherwise rating of the various libraries?
How easy ...
1
vote
1answer
104 views
Set strictly upper triangular part of a matrix to alpha using BLAS or LAPACK
Is there routine in standard BLAS or LAPACK to set strictly-upper triangular part (the part above the diagonal) of a matrix to alpha?
I do not want to change diagonal elements so ...
5
votes
4answers
6k views
Beating typical BLAS libraries matrix multiplication performance
A dull matrix multiplication algorithm where we use the formula
$$C_{ij}=\sum_{k}A_{ik}B_{kj}$$
By literally following this in 3 loops we'll get a very slow program, because we don't utilize ...
5
votes
2answers
1k views
Smart way to multiply 3 matrices
I have a quantum mechanics simulation where I need to multiply three matrices that look like this:
$$\rho(t_1)=U^\dagger \rho(t_0) \, U$$
where $U^\dagger$ is the hermitian conjugate of $U$. This ...
2
votes
2answers
3k views
Fastest way to perform element-wise multiplication on a sparse matrix
I have two large-ish matrices (~100K cols x ~100K rows).
They are sparse and symmetrical (about 0.1% of them values are non-zero).
I want to do element-wise multiplication between them.
Also, I ...
5
votes
0answers
732 views
Sparse matrix format and sparse-matrix sparse-matrix multiplication
I'm having some performance problems with my code dealing with the multiplication of big sparse matrices (stiffness and aerodynamic influence coefficient matrices).
Mainly I have to multiply such ...
1
vote
1answer
382 views
Efficiently rotate vector in 2D (and 3D)
I need to efficiently rotate a 2D (and 3D) vector in a CUDA kernel. I was thinking about generating random unitary rotation matrices. I don't need to know the angle, it just has to be randomly ...
12
votes
0answers
3k views
Optimized 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 ...
3
votes
2answers
322 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 ...
3
votes
2answers
92 views
Do BLAS routines compute their respective operations with minimum error?
Do all BLAS routines compute the respective operation with minimum error ?
i.e. Is the reduction in sdot computed with least error ?
I need to call these ...
1
vote
1answer
362 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 ...
2
votes
0answers
315 views
Sparse Linear Algebra vs Dense Linear Algebra
I am interested in a reference in the literature that discusses the performance of Dense Linear Algebra (blas routines) and dense linear algebra (sparse blas routines).
I am interested in knowing for ...
3
votes
2answers
4k 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. ...
1
vote
1answer
118 views
How to make this matrix efficiently?
Originally posted on stats.stackexchange, I'll pair the post down to something a bit more general.
Suppose I have vectors $\{\mathbf{\delta}, \mathbf{x}_1, \ldots, \mathbf{x}_J\}$, where $\delta \in \...
4
votes
1answer
199 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 ...
11
votes
2answers
596 views
Danger of complex arithmetics in scientific computing
The complex inner product $\langle u,v\rangle$ has two different definitions decided by conventions: $\bar{u}^Tv$ or $u^T\bar{v}$. In BLAS, I found the routines cdotu, zdotu, and cdotc, zdotc. The ...
2
votes
1answer
1k 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 ...
3
votes
2answers
2k 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 ...
3
votes
1answer
252 views
How does matrix-matrix product scale with multiple CPUs?
These days, one can have 64 cores in a single node. I wonder how well the dense matrix-matrix product (SGEMM and DGEMM) scales ...
3
votes
3answers
3k views
Fast vector - "diagonal" matrix multiplication
Let $\mathbf{1}\in\mathbb{R}^d$ be a vector with all elements equal to $1$. Define:
$$\mathbf{D} = \mathrm{diag}(\mathbf{1}^\top,\mathbf{1}^\top,\ldots,\mathbf{1}^\top) =
\begin{bmatrix}
1 \cdots 1 &...
1
vote
2answers
167 views
Do vendors release their own LAPACK library?
Every CPU vendor seems to make BLAS libraries that are specialized to run on their hardware. Do they do the same for LAPACK? Or is that a non-issue because LAPACK is written entirely in terms of BLAS ...
7
votes
1answer
3k views
What is the best way to multiply a diagonal matrix (in fortran)
What is the best way to compute:
$$ Y = D X $$
where $D \in \mathbb{R}^{m\times m}$ is diagonal and $X \in \mathbb{C}^{m \times n}$ is general. I am mostly interested in these two cases:
$m >> ...
4
votes
2answers
323 views
How gracefully does scalapack/pblas revert to lapack/blas in serial
If I use scalapack and pblas, and the code is run in serial (1x1 blacs process grid), how well does scalapack and pblas revert to the performance of lapack/blas?
I am particularly interested in the ...
3
votes
2answers
2k views
How Do I solve large systems given UMFPACK memory limitations?
I am trying to solve a system of equations (A x = b) for 3D heat diffusion (i.e. each equation has at most 7 terms not including the constant "b" term) using UMFPACK with boost numeric bindings to C++....
11
votes
6answers
2k views
Is there a reference-level implementation of BLAS in C/C++?
The netlib BLAS implementation is an excellent reference, being mostly un-optimized and well documented (e.g. zgemm). However, it is in Fortran 77, making it somewhat inaccessible to those with a ...
3
votes
4answers
5k views
How to tell which (sequential or parallel) version of Intel MKL is linked?
Recently I am using Umfpack with Intel MKL BLAS. To link the library to a program one has to link mkl_rt.lib / mkl_rt.so. However there is no word which version: sequential or parallel of library is ...
31
votes
3answers
4k views
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 ...