Left to Right and vice versa: Applying Fractal Symbolic Analysis to Restructuring Linear Algebra Codes
نویسندگان
چکیده
We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we show how fractal symbolic analysis can be used to convert between left-looking and right-looking versions of three kernels of central importance in computational science: Cholesky factorization, LU factorization with pivoting, and triangular solve.
منابع مشابه
Left-Looking to Right-Looking and Vice Versa: An Application of Fractal Symbolic Analysis to Linear Algebra Code Restructuring
We have recently developed a new program analysis strat egy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis In this paper we show how fractal symbolic analysis can be used to convert between left looking and right looking versions of three kernels of central importance in compu tational science Cholesky factorization LU factorization...
متن کاملFractal Symbolic Analysis for Program Transformations
Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A well-known limitation of dependence analysis is that it examines only the memory locations read and written by a statement, and does not assume any particular interpretation for the operations in that statement. Exploiting the semantics of these operations enables a wider...
متن کاملFrequency Response Analysis of a Capacitive Micro-beam Resonator Considering Residual and Axial Stresses and Temperature Changes Effects
This paper presents a study on the frequency response of a capacitive micro-beam resonator under various applied stresses. The governing equation whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear electrostatic equation. Due to the nonlinearity and complexity of the derived equation analytical solution are not generally available; therefore, the ...
متن کاملMax-Plus algebra on tensors and its properties
In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.
متن کاملExpansionary-contradictory Policies in Stock Companies Using Left and Right Returns to Scales in Data Envelopment Analysis Models
The purpose of this paper is to evaluate the returns to scale of the Tehran Stock Exchange based on new models in data envelopment analysis. Using this assessment, it is possible to judge the application of contradictory or expansion policies in stock companies. To this end, there is a need for models in the data envelopment analysis that can assess the left and right returns to scales of the d...
متن کامل