Four vector-matrix primitives

1989 ◽  
Author(s):  
A. Agrawal ◽  
G. E. Blelloch ◽  
R. L. Krawitz ◽  
C. A. Phillips
Keyword(s):  
Vector Matrix

Four Vector-Matrix Primitives

1989 ◽  
Author(s):  
Ajit Agrawal ◽  
Guy E. Blelloch ◽  
Robert L. Krawitz ◽  
Cynthia A. Phillips
Keyword(s):  
Vector Matrix

scholarly journals Tetrahedra of varying density and their applications

2021 ◽  
Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch
Keyword(s):  
Tetrahedral Mesh ◽  
Rotational Inertia ◽  
Exact Mass ◽  
Accurate Analysis ◽  
Exact Integration ◽  
Voronoi Cells ◽  
Current State ◽  
Chebyshev Norm ◽  
Exact Calculations ◽  
Vector Matrix

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract

SYSTEMC IMPLEMENTATION AND PERFORMANCE EVALUATION OF A DECOUPLED GENERAL-PURPOSE MATRIX PROCESSOR

2010 ◽  
Vol 20 (02) ◽  
pp. 103-121 ◽  
Author(s):  
MOSTAFA I. SOLIMAN ◽  
ABDULMAJID F. Al-JUNAID
Keyword(s):  
Performance Evaluation ◽  
Matrix Multiplication ◽  
General Purpose ◽  
System Level ◽  
Memory Latency ◽  
Single Chip ◽  
Wide Range ◽  
Matrix Unit ◽  
And Performance ◽  
Vector Matrix

Technological advances in IC manufacturing provide us with the capability to integrate more and more functionality into a single chip. Today's modern processors have nearly one billion transistors on a single chip. With the increasing complexity of today's system, the designs have to be modeled at a high-level of abstraction before partitioning into hardware and software components for final implementation. This paper explains in detail the implementation and performance evaluation of a matrix processor called Mat-Core with SystemC (system level modeling language). Mat-Core is a research processor aiming at exploiting the increasingly number of transistors per IC to improve the performance of a wide range of applications. It extends a general-purpose scalar processor with a matrix unit. To hide memory latency, the extended matrix unit is decoupled into two components: address generation and data computation, which communicate through data queues. Like vector architectures, the data computation unit is organized in parallel lanes. However, on parallel lanes, Mat-Core can execute matrix-scalar, matrix-vector, and matrix-matrix instructions in addition to vector-scalar and vector-vector instructions. For controlling the execution of vector/matrix instructions on the matrix core, this paper extends the well known scoreboard technique. Furthermore, the performance of Mat-Core is evaluated on vector and matrix kernels. Our results show that the performance of four lanes Mat-Core with matrix registers of size 4 × 4 or 16 elements each, queues size of 10, start up time of 6 clock cycles, and memory latency of 10 clock cycles is about 0.94, 1.3, 2.3, 1.6, 2.3, and 5.5 FLOPs per clock cycle; achieved on scalar-vector multiplication, SAXPY, Givens, rank-1 update, vector-matrix multiplication, and matrix-matrix multiplication, respectively.

Three-Dimensional nand Flash for Vector–Matrix Multiplication

2019 ◽  
Vol 27 (4) ◽  
pp. 988-991 ◽  
Author(s):  
Panni Wang ◽  
Feng Xu ◽  
Bo Wang ◽  
Bin Gao ◽  
Huaqiang Wu ◽  
...  
Keyword(s):  
Matrix Multiplication ◽  
Three Dimensional ◽  
Nand Flash ◽  
Vector Matrix

scholarly journals Thermal Disturbances in Twinned Orthotropic Thermoelastic Material

2018 ◽  
Vol 23 (4) ◽  
pp. 897-910 ◽  
Author(s):  
L. Rani ◽  
V. Singh
Keyword(s):  
Fourier Transforms ◽  
Crystallographic Axis ◽  
Physical Domain ◽  
Matrix Differential Equation ◽  
Special Cases ◽  
Eigen Value ◽  
Basic Equations ◽  
Matrix Differential ◽  
Thermally Conducting ◽  
Vector Matrix

Abstract This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

scholarly journals Image segmentation through the scale-space random walker

2021 ◽  
Author(s):  
Richard Rzeszutek
Keyword(s):  
Random Walks ◽  
Graphics Processing Unit ◽  
Scale Space ◽  
Gaussian Kernel ◽  
Processing Unit ◽  
Random Walker ◽  
User Input ◽  
Segmentation Boundary ◽  
Vector Matrix ◽  
Graphics Processing

This thesis proposes an extension to the Random Walks assisted segmentation algorithm that allows it to operate on a scale-space. Scale-space is a multi-resolution signal analysis method that retains all of the structures in an image through progressive blurring with a Gaussian kernel. The input of the algorithm is setup so that Random Walks will operate on the scale-space, rather than the image itself. The result is that the finer scales retain the detail in the image and the coarser scales filter out the noise. This augmented algorithm is referred to as "Scale-Space Random Walks" (SSRW) and it is shown in both artifical and natural images to be superior to Random Walks when an image has been corrupted by noise. It is also shown that SSRW can impove the segmentation when texture, such as the artifical edges created by JPEG compression, has made the segmentation boundary less accurate. This thesis also presents a practical application of the SSRW in an assisted rotoscoping tool. The tool is implemented as a plugin for a popular commerical compositing application that leverages the power of a Graphics Processing Unit (GPU) to improve the algorithm's performance so that it is near-realtime. Issues such as memory handling, user input and performing vector-matrix algebra are addressed.

scholarly journals From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations

2020 ◽  
Vol 53 (4) ◽  
pp. 1101-1107
Author(s):  
Leslie Glasser
Keyword(s):  
Euclidean Space ◽  
Matrix Functions ◽  
Practical Application ◽  
Torsion Angles ◽  
Molecular Systems ◽  
The Matrix ◽  
Molecular Bond ◽  
Crystal Space ◽  
Vector Matrix ◽  
Computational Form

Values of molecular bond lengths, bond angles and (less frequently) bond torsion angles are readily available from databases, from crystallographic software, and/or from interactive molecular and crystal visualization programs such as Jmol. However, the methods used to calculate these values are less well known. In this paper, the computational methods are described in detail, and live Excel implementations, which permit readers to readily perform the calculations for their own molecular systems, are provided. The methods described apply to both fractional coordinates in crystal space and Cartesian coordinates in Euclidean space (space in which the geometric postulates of Euclid are valid) and are vector/matrix based. In their simplest computational form, they are applied as algebraic expansions which are summed. They are also available in matrix formulations, which are readily manipulated and calculated using the matrix functions of Excel. In particular, their general formulation as metric matrices is introduced. The methods in use are illustrated by a detailed example of the calculations. This contribution provides a significant practical application which can also act as motivation for the study of matrix mathematics with respect to its many uses in chemistry.

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