CULA was developed to be a GPU-accelerated linear algebra library that utilizes the NVIDIA CUDA parallel computing architecture to dramatically improve the computation speed of sophisticated mathematics.
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It has the ability to perform general matrix and vector operations including: matrix and vector addition, subtraction, multiplication, inner products, eigenvalues, normalization, determinant, inverse, QR decomposition, LU decomposition, LU factorization, QR factorization, Cholesky factorization, inversion, spectral decomposition, conjugate gradients, conjugate transpose, singular value decomposition, and Cauchy principal value.
Its key features include: Support for scientific data types including complex and integer types, Support for automatic overflow detection and handling, Support for N-dimensional arrays, Support for multiple multi-threading models including shared memory, Support for arbitrary array dimensionality including odd dimension, Support for arbitrary GPU execution model including both single- and multi-GPUs, Support for various range of GPU (e.g. different manufacturer, model, memory capacity, speed, etc.), Support for various openCL kernels, Support for GPU accelerated FFT.
It provides a set of packages that are well-suited for linear algebra applications, including: Basic linear algebra package – an integrated, high-performance linear algebra library, Basic linear algebra package – a linear algebra package that provides a complete set of linear algebra routines and tools (including preconditioners, iterative solvers, eigenvalue computations), Basic linear algebra package – a linear algebra package that provides a set of routines to solve various linear algebra problems (e.g. the LU decomposition, QR decomposition, Cholesky factorization), Basic linear algebra package – a linear algebra package that provides a set of routines to compute various linear algebra quantities (e.g. determinant, singular values, etc.), Basic linear algebra package – a linear algebra package that provides a set of functions to compute eigenvalues and eigenvectors.
It also has a set of packages that are well-suited for numerical analysis including: Basic numerical analysis package – an integrated, high-performance numerical analysis library (including finite differences, finite volumes, initial value/boundary value, and differential equation solvers), Basic numerical analysis package – a numerical analysis package that provides an integrated set of numerical analysis functions (including finite differences, finite volumes, initial value/boundary value, and differential equation solvers), Basic numerical analysis package – a numerical analysis
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DESCRIPTION is derived from the National Sciences Foundation (NSF) Data Encryption Standard (DES) specification and has been rigorously tested against the specification. DES is a variant of DES/ECB (or ECB-DES). DES can operate in either electronic or optical mode. Electronic mode consists of a stream of data bits fed into a DES encryption circuit and a DES decryption circuit that outputs encrypted data. In optical mode, data is entered into the DES encryption circuit via a non-linear optical device and the encrypted output of the DES encryption circuit is the data. DES can be operated in both electronic and optical modes, either simultaneously or separately. In some cases, the operational mode is affected by the input or output data.
DESCRIPTION provides a user-friendly interface to DES. The C code implements the high-speed mode (16-bit key size and variable data bit size) of the data encryption standard (DES). The C code also implements the high-speed mode of DES, as specified in the
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CULA is a set of high-level computational kernels (CUDA functions) to access and manipulate arrays of data of any dimension. CULA provides common algebra, linear algebra and matrix operations, with a focus on linear algebra. It consists of two separate parts, a set of CUDA functions and a library that provides an abstraction of the CULA functions.
CUDA Toolkit is a collection of tools that support CUDA development. It includes the CUDA developer environment and supports parallel computing via CUDA, C++ compiler, etc.
CUDA Runtime is a kernel-to-kernel communication mechanism between the GPU and CPU to implement device-to-device (D2D) communication via shared memory. It allows GPU kernel launch from a CPU thread, a mechanism for CPU-to-GPU communication, and an I/O mechanism that provides direct communication between host and GPU.
CUDA Samples and Examples
CUDA Samples and Examples is a set of samples, examples, and tools for the CUDA platform. It covers a variety of topics, such as basic computer graphics, parallel computing, CUDA programming, CUDA programming languages, CUDA hardware details, and CUDA compatibility with non-NVIDIA hardware. The set of samples and tools is based on the CUDA C SDK.
CUDA Tools is a set of utilities for the CUDA platform. It includes the CDPP and RTA tools. The CDPP tool uses the CUDA Driver API to access CUDA and CUDA GPU capabilities, the CDPP-IR tool performs CUDA-to-CDPP IR transformation of CUDA kernels and the RTA tool provides an easy-to-use, easy-to-use interface for creating a device heap.
CUDA SDK is the complete CUDA C API, C++ API, and sample application suite. It contains the CUDA C API, CUDA C++ API, CUDA Runtime API, CUDA Samples and Examples, CUDA Toolkit, CUDA Toolkit Runtime, and CUDA compiler as a set of CUDA libraries and tools.
CUDA Fundamentals is a user’s guide to the CUDA programming language and framework.
What’s New In?
CULA was designed to implement common linear algebra algorithms as a toolkit. It provides a set of API functions for manipulating matrices and vectors. At the core of the API are two kinds of functions:
Functions that operate on vectors (e.g. vecAdd, vecScale)
Functions that operate on matrices (e.g. matMul, matDot)
The API provides convenient vector operations like addition and scaling with the well-known matrix multiplication operation. The API is targeted towards linear algebra experts, who are familiar with linear algebra operations and want to use them in CUDA.
CULA includes a complete set of matrix operations, which includes matrix inversion, LU decomposition, LU factorization, eigenvalue decomposition, singular value decomposition, QR decomposition, etc.
The basic linear algebra operations in CULA are implemented as the CUDA kernels. The CUDA kernels can be either called from C/C++ or via the API function. CULA supports CUDA programming in the development of linear algebra algorithms.
CULA supports both CPU- and GPU-based implementations. For each of the matrix operations, the CPU version is simple but slow. The GPU version is much more efficient and has much higher performance. For the basic operations, the GPU version is always faster than the CPU version. For the more sophisticated operations, there are situations that can lead to a GPU-parallelized version being slower than the CPU version. However, these situations are rare, so users of CULA are recommended to always use the GPU version.
CULA is freely available under the Apache 2.0 open-source license. CULA supports both academic and non-academic use.
CULA GitHub Repository:
CULA is open-source. You can download the latest CULA version from GitHub:
CULA GitHub Project Repository:
All the source code files in CULA GitHub repository are under the Apache 2.0 open-source license.
New CULA Version (CULA Version 1.0.0):
We plan to upgrade CULA to version 1.0.0 soon. In CULA Version 1.0.0, we remove all support for CUDA programming from CULA. CULA will support CUDA programming from C++ and user-defined kernels from now on. If you are using CULA 1.0.0, please use the API function for matrix operations.
There is a CULA developer’s kit that can be downloaded from the CULA GitHub repository:
Processor: Intel Core 2 Duo
RAM: 4 GB
OS: Windows 7/8/10
Video: NVIDIA Geforce GTX 550 TI 512 MB or greater. AMD Radeon HD 6670 1 GB or greater.
Operating System: Windows 7, 8, or 10.
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