Scalable Linear Algebra on a Relational Database System

DISTAL: The Distributed Tensor Algebra Compiler

“…Related work in the database community has taken steps to extend relational database engines to support distributed linear algebra [28] and distributed tensor computations [19].…”

“…Figure 2 shows DISTAL's three input sub-languages: a computation language that describes the desired kernel (lines [18][19], a scheduling language that describes how to optimize the computation (lines [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], and a format language that describes how the tensors are stored (lines [4][5][6][7][8][9][10][11][12][13][14][15]. In this section, we give background on each of these three components.…”

Declarative Data Analytics: A Survey

“…In-database Linear Algebra. Following the same direction of modelling machine learning algorithms inside the database, a very recent approach [36] demonstrates the support for linear algebra inside relational databases by extending the relational model with three data types, matrix, vector and labelled scalar, as well as a set of operations over the aforementioned types. These types can be used for attributes when creating a table, i.e.…”

“…Apart from altering the order of matrix multiplication chains, most of the rewritings at the logical level are based on simple mathematical properties. When linear algebra operators are integrated to a relational database as suggested in [36], reorderings between relational and linear algebra operators can also be applied based on the dimensions of the matrices. For example, in a SQL query that involves both joining tables and multiplying matrices, the order of joins can play an important role on the size of the result of matrix multiplication.…”

“…cpmm LOP in line 5, which is a cross product based algorithm for distributed matrix multiplication. Finally, in the context of work for in-database linear algebra [36] described in section 4.5.3, preliminary ideas on executing plans which involve both relational and linear algebra operators more efficiently are explored. For example, when combining matrix multiplication with join operators, an optimizer aware of the dimensions of the involved matrices can choose a better plan.…”