TABLE OF CONTENTS Since the programming is likely to be the main botleneck in the use of an electronic computer we have given a good deal of thought to the preparation of standard routines of considerable generality for the more important processes involved in computation. By this means we hope to reduce the time taken to code up large-scale computing problems, by building them up, as it were, from prefabricated units.
- J. H. WILKINSON, The Automatic Computing Engine at the National Physical Laboratory (1948)
In spite of the self-contained nature of the linear algebra field, experience has shown that even here the preparation of a fully tested set of algorithms is a far greater task than had been anticipated.
- J. H. WILKINSON and C. REINSCH, Handbook for Automatic Computation: Linear Algebra (1971)
In this appendix we briefly describe some of the freely available program libraries that have been mentioned in this book. These packages are all available from netlib (see B.2).
The Basic Linear Algebra Subprograms (BLAS) are sets of Fortran primitives for matrix and vector operations. They cover all the common operations in linear algebra. There are three levels, corresponding to the types of object operated upon. In the examples below, x and y are vectors, A, B, C are rectangular matrices, and T is a square triangular matrix. Names of BLAS routines are given in parentheses. The leading "x" denotes the Fortran data type, whose possible values...
