BLACS Overview

Introduction to BLACS Fortran Framework

The Basic Linear Algebra Communication Subprograms (BLACS) is a high-performance Fortran framework that provides a standard interface for communication and basic linear algebra operations in distributed-memory parallel computing. BLACS is widely used in scientific and engineering applications to efficiently solve large-scale computational problems.

History of BLACS

BLACS was initially developed in the 1990s as part of the Scalable Linear Algebra PACKage (ScaLAPACK) project, which aimed to provide a portable and scalable library for solving dense linear algebra problems on distributed-memory parallel computers. The BLACS library was designed to abstract the communication layer between parallel processes and provide a unified interface for distributed matrix operations.

Features of BLACS

1. Process Grid Creation: BLACS allows users to create a logical grid of processes, which can be used to distribute data across a parallel computing system. The grid can be of any size and shape, enabling flexible process layout.

   CALL BLACS_GRIDINIT( ICTXT, ORDER, NP_ROW, NP_COL )

2. Data Distribution: BLACS provides functions to distribute data across the process grid. Users can partition matrices or vectors into blocks and distribute them across the processes in a row-major or column-major order.

   CALL BLACS_DESCINIT( DESC, M, N, MB, NB, IRSRC, ICSRC, CONTEXT, LLD )

3. Block-cyclic Data Redistribution: BLACS supports block-cyclic data redistribution, allowing efficient data movement between different process grids. This feature is particularly useful when performing computations involving distributed matrices with different process layouts.

   CALL BLACS_PBCOFA( CONTXT, MATDESCA, A, LDA, IPIV, INFO )

4. Collective Communication: BLACS provides collective communication operations, such as broadcast, reduction, and scatter-gather, which enable efficient exchange of data among processes in the process grid.

   CALL BLACS_BROADCAST( CONTXT, SCOPE, M, N, A, LDA, ROOT )

5. Process Topology Information: BLACS provides functions to retrieve information about the process grid, such as the total number of processes, the number of rows and columns in the grid, and the rank of the current process.

   CALL BLACS_GRIDINFO( ICTXT, NP_ROW, NP_COL, MY_ROW, MY_COL )

Examples of BLACS Usage

1. Matrix Multiplication: The following example demonstrates how to perform matrix multiplication using BLACS. It assumes that the matrices are already distributed across the process grid.

   CALL BLACS_PDGEMM( 'N', 'N', M, N, K, ALPHA, A, IA, JA, DESCA, B, IB, JB, DESCB, BETA, C, IC, JC, DESCC )

   In this example, M, N, and K denote the dimensions of the matrices A, B, and C, respectively. ALPHA and BETA are scaling factors, and IA, JA, IB, JB, IC, and JC represent the starting indices of the local portions of the matrices. DESCA, DESCB, and DESCC are descriptor arrays that describe the distribution of the matrices.

2. Matrix Transposition: The following example illustrates how to transpose a distributed matrix using BLACS.

   CALL BLACS_PTRAN( 'A', N, A, IA, JA, DESCA, B, IB, JB, DESCB )

   In this example, N represents the dimension of the matrix A, and IA, JA, IB, and JB denote the starting indices of the local portions of the matrices. DESCA and DESCB are descriptor arrays that describe the distribution of the matrices.

Conclusion

BLACS is a powerful Fortran framework that provides a standardized interface for communication and basic linear algebra operations in distributed-memory parallel computing. Its features, such as process grid creation, data distribution, collective communication, and process topology information, enable efficient implementation of parallel algorithms for solving large-scale scientific and engineering problems.

For more information about BLACS, you can visit the official website: BLACS Official Website

Note: The code snippets provided in this tutorial are simplified examples and may require additional setup and initialization steps not shown here.