John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. Flame: Formal linear algebra methods environment. Transactions on Mathematical Software, 27(4):422--455, December 2001.  Home/Search   Document Not in Database   Summary   Related Articles   Check

No context found.

J. A. Gunnels, F. G. Gustavson, G. M. Henry, and R. A. van de Geijn. Flame: Formal linear algebra methods environment. ACM Trans. Math. Soft., 27(4):422--455, December 2001.

....often encountered and con dence in code is diminished. Thus a carefully designed API should avoid explicit indexing whenever possible. We have illustrated to the high performance linear algebra library community the bene ts of the formal derivation of algorithms in a series of previous papers [8, 12, 4]. While there we alluded at an API that allows code to re ect algorithms that have been derived to be correct, in this paper we explicitly give this API for the MATLAB [11] M script programming language. Notice that in [14] we present a similar API for the C programming language. Our FLAME lab ....

....For performance reasons, it is often necessary to formulate the algorithm as a blocked algorithm as illustrated in Fig. 2. The performance bene t comes from the fact that the algorithm is rich in matrix multiplication which allows processors with multi level memories to achieve high performance [7, 2, 8, 5]. Note 7 The algorithm in Fig. 2 is implemented by the more traditional MATLAB code given in Fig. 3. We claim that the introduction of indices to explicitly indicate the regions involved in the update complicates readability and reduces con dence in the correctness of the MATLAB implementation. ....

J. A. Gunnels, F. G. Gustavson, G. M. Henry, and R. A. van de Geijn. FLAME: Formal linear algebra methods environment. ACM Trans. Math. Soft., 27(4):422-455, December 2001.

....on the subject still appear with great regularity. Matrix multiplication continues to be of importance because a broad range of high performance packages that support directly or indirectly scienti c computation depend, to a large degree, on the performance of the matrix multiplication kernel [3, 13, 28, 5]. New contributions continue to be made because the gap between the performance of the CPU and the bandwidth to the memory continues to widen and new architectural features are introduced into computers, which require new techniques or re nements of old techniques, for matrix multiplication. Two ....

....becoming increasingly complex the task of providing a complete set of (especially level 3) BLAS was becoming a substantial burden on the vendors. Fortunately, it was shown that high performance level 3 BLAS could be coded to be portable by casting these operations in terms of matrix multiplication [23, 16, 24, 13]. This reduced the cost of implementing the level 3 BLAS to the cost of implementing matrix multiplication. Next, it was recognized that by combining a blocking strategy with a carefully crafted inner kernel, which performs matrix multiplication with blocks that are roughly of a size so that they ....

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. Flame: Formal linear algebra methods environment. ACM Trans. Math. Soft., 27(4):422-455, December 2001. 17

....how similar interfaces can be de ned for other languages, including Fortran, C , and MATLAB M script. 1 Introduction This paper is the fourth in a series that illustrate to the high performance linear algebra library community the bene ts of the formal derivation of algorithms. The rst paper [12] gave a broad outline of the approach, introducing the concept of formal derivation and its application to dense linear algebra algorithms. In that paper we also showed that by introducing an Application Programming Interface (API) for coding the provably correct algorithms, claims about the ....

....2g. For performance reasons it is often necessary to formulate the algorithm as a blocked algorithm as illustrated in Fig. 2. The performance bene t comes from the fact that the algorithm is rich in matrix multiplication which allows processors with multi level memories to achieve high performance [10, 3, 12, 8]. Note 7 The algorithm in Fig. 2 is implemented by the Matlab code given in Fig. 3. We would like to claim that the introduction of indices to explicitly indicate the regions involved in the update complicates readability and reduces con dence in the correctness of the Matlab implementation. ....

[Article contains additional citation context not shown here]

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. Flame: Formal linear algebra methods environment. ACM Trans. Math. Soft., 27(4):422-455, December 2001.

....we apply this methodology to the derivation of algorithms for dense linear algebra operations. This paper is the third in what we hope will be a series that illustrate to the high performance linear algebra library community the bene ts of the formal derivation of algorithms. The rst paper [11] gave a broad outline of the approach, introducing the concept of formal derivation and its application to dense linear algebra algorithms. In that paper we also showed that by introducing an Application Programming Interface (API) for coding the provably correct algorithms, claims about the ....

....time, we do not have a clean characterization of the operations that fall into this category. Over the last few years, we have shown that it includes all Basic Linear Algebra Subprograms (BLAS) levels 1, 2, and 3) 1, 2, 17, 6, 5, 13] all major factorization algorithms (LU, Cholesky, and QR) [11], matrix inversion (of general, symmetric, and triangular matrices) 18] and a large number of operations that arise in control theory [19] A subset of these operations is given in Fig. 1. The format of the paper is that of a tutorial and includes exercises for the reader. We assume only that ....

[Article contains additional citation context not shown here]

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. Flame: Formal linear algebra methods environment. ACM Trans. Math. Soft., 27(4):422-455, December 2001.

....be expected to yield high performance. Finally, we report performance on the Intel (R) Pentium III processor that is superior to that reported previously in the literature for this operation. 1 Introduction In a recent paper the Formal Linear Algebra Methods Environment (FLAME) was introduced [10]. FLAME is both a systematic approach for deriving (dense) linear algebra algorithms and a library for the implementation of the resulting algorithms. The rationale is that by formally deriving algorithms, correctness can be asserted. Moreover, by providing a framework for coding that mirrors the ....

J. Gunnels, G. Henry, and R.A. van de Geijn. FLAME: Formal linear algebra methods environment. ACM Trans. on Math. Software, 2001. To appear.

No context found.

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. Flame: Formal linear algebra methods environment. Transactions on Mathematical Software, 27(4):422--455, December 2001.

No context found.

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. FLAME: Formal Linear Algebra Methods Environment. ACM Transactions on Mathematical Software, 27(4), December 2001.

No context found.

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. FLAME: Formal Linear Algebra Methods Environment. ACM Transactions on Mathematical Software, 27(4), December 2001.

No context found.

John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. FLAME: Formal Linear Algebra Methods Environment. ACM Transactions on Mathematical Software, 27(4), December 2001.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC