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Numerical recipes example book
Bulkin Pergmn
of Mathnnnticol Biology Journals
Ltd. Printed
Society for Mathematical
Vol. 49. No. 6, pp. 761-776.
1987
in Great Britain.
Biology
BOOK
REVIEWS
Numerical Recipes:
The Art of Scientijc Computing, William H. Press, Brian P. Flannery, Saul A. Tenkolsky and William T. Vetterling. Cambridge University Press, Cambridge, 1986. U.SS39.50, 818 pp. Numerical Recipes Example Book (FORTRAN or Pascal), U.S.$18.95 each (paperback), 179 pp. Numerical Recipes FORTRAN Diskette, U.S.S.19.95: Numerical Recipes Pascal Diskette, U.S.$19.95: Numerical Recipes Example Diskette (FORTRAN or Pascal), U.SJi19.95 each.
The two major scientific subroutine libraries used on mainframe computers are IMSL (International Mathematical and Statistical Libraries) (IMSL, Inc., 2500 ParkWest Tower One, 2500 CityWest Blvd., Houston, TX 77042-3020) and NAG (Numerical Algorithm Group, Inc., 1131 Warren Ave., Downers Grove, IL 60515). IMSL is more widely used in the U.S.A. and NAG is more widely used in Europe. The main difference between these two libraries is that IMSL has more statistical functions than NAG. IMSL is also available for MS-DOS microcomputers at a rather steep price; however, large institutions can buy a site license at a much cheaper cost per user. I do not know if NAG is available for microcomputers. However, with publication of Numerical Recipes for a minimum cost of $60 one can have a very complete set of mathematical utilities for either FORTRAN or Pascal. For $20 less one could get by with just the book. For $40 more one can get an example book and disk. The programs are in source code only on the disk, so the user must compile them and perhaps build libraries of them. They can be used either on mainframes or microcomputers. There are an amazing number of excellent numerical algorithms in this book. The authors claim to include everything standard up to partial differential equations, but then they attach a 53 page last chapter on partial differential equations. The table of contents is a good indication of the scope of the book: Preliminaries (18 pp.) Solution of Linear Algebraic Equations (58 pp.) Interpolation and Extrapolation (25 pp.) Integration of Functions (29 pp.) Evaluation of Functions (24 pp.) Special Functions (36 pp. j 761
762
BOOK REVIEWS
Random Numbers (35 pp.) Sorting (14 pp.) Root Finding and Nonlinear Sets of Equations (34 pp.) Minimization and Maximization of Functions (61 pp.) Eigensystems (46 pp.) Fourier Transform Spectral Methods (73 pp.) Statistical Description of Data (44 pp.) Modeling of Data (49 pp.) Integration of Ordinary Differential Equations (31 pp.) Two Point Boundary Value Problems (37 pp.) Partial Differential Equations (53 pp.) The main body of the book contains listings of the FORTRAN programs and Pascal versions of the programs are included at the rear of the book. Separate diskettes are available at $20 each for these two versions of the programs. The FORTRAN programs are written in structured style using FORTRAN-77. Since C is rapidly becoming a preferred programming language, it would be icing on the cake if a C diskette could be made available in the future. Then the three diskettes could be used as excellent examples of programming in the three languages for students learning how to program. I have used this book as supplementary material for a computational physics course based on Koonin’s text (Computational Physics, S. E. Koonin, Benjamin-Cummings Publishing, Menlo Park, CA, 1986) and will do so again in the future. The algorithms will not always do exactly what one wants, so one may occasionally have to alter the source codeu. For example, I wanted to calculate a series of spherical Bessel functions. The Bessel function routines in the book are only for calculating a single cylindrical Bessel function. I had to rewrite the code considerably to efficiently calculate the series I wanted. The index is very complete. The comments in the program listings in the book are not included in the programs on the diskette to save space. This book is one of the most significant books ever published-for scientists and engineers who do computing. Every desk should have a copy and its accompanying disk(s). L. DAVID ROPER Departinent of Physics Virginia Polytechnic Institute and State University Blacksburg, VA 24061, U.S.A.
of Mathnnnticol Biology Journals
Ltd. Printed
Society for Mathematical
Vol. 49. No. 6, pp. 761-776.
1987
in Great Britain.
Biology
BOOK
REVIEWS
Numerical Recipes:
The Art of Scientijc Computing, William H. Press, Brian P. Flannery, Saul A. Tenkolsky and William T. Vetterling. Cambridge University Press, Cambridge, 1986. U.SS39.50, 818 pp. Numerical Recipes Example Book (FORTRAN or Pascal), U.S.$18.95 each (paperback), 179 pp. Numerical Recipes FORTRAN Diskette, U.S.S.19.95: Numerical Recipes Pascal Diskette, U.S.$19.95: Numerical Recipes Example Diskette (FORTRAN or Pascal), U.SJi19.95 each.
The two major scientific subroutine libraries used on mainframe computers are IMSL (International Mathematical and Statistical Libraries) (IMSL, Inc., 2500 ParkWest Tower One, 2500 CityWest Blvd., Houston, TX 77042-3020) and NAG (Numerical Algorithm Group, Inc., 1131 Warren Ave., Downers Grove, IL 60515). IMSL is more widely used in the U.S.A. and NAG is more widely used in Europe. The main difference between these two libraries is that IMSL has more statistical functions than NAG. IMSL is also available for MS-DOS microcomputers at a rather steep price; however, large institutions can buy a site license at a much cheaper cost per user. I do not know if NAG is available for microcomputers. However, with publication of Numerical Recipes for a minimum cost of $60 one can have a very complete set of mathematical utilities for either FORTRAN or Pascal. For $20 less one could get by with just the book. For $40 more one can get an example book and disk. The programs are in source code only on the disk, so the user must compile them and perhaps build libraries of them. They can be used either on mainframes or microcomputers. There are an amazing number of excellent numerical algorithms in this book. The authors claim to include everything standard up to partial differential equations, but then they attach a 53 page last chapter on partial differential equations. The table of contents is a good indication of the scope of the book: Preliminaries (18 pp.) Solution of Linear Algebraic Equations (58 pp.) Interpolation and Extrapolation (25 pp.) Integration of Functions (29 pp.) Evaluation of Functions (24 pp.) Special Functions (36 pp. j 761
762
BOOK REVIEWS
Random Numbers (35 pp.) Sorting (14 pp.) Root Finding and Nonlinear Sets of Equations (34 pp.) Minimization and Maximization of Functions (61 pp.) Eigensystems (46 pp.) Fourier Transform Spectral Methods (73 pp.) Statistical Description of Data (44 pp.) Modeling of Data (49 pp.) Integration of Ordinary Differential Equations (31 pp.) Two Point Boundary Value Problems (37 pp.) Partial Differential Equations (53 pp.) The main body of the book contains listings of the FORTRAN programs and Pascal versions of the programs are included at the rear of the book. Separate diskettes are available at $20 each for these two versions of the programs. The FORTRAN programs are written in structured style using FORTRAN-77. Since C is rapidly becoming a preferred programming language, it would be icing on the cake if a C diskette could be made available in the future. Then the three diskettes could be used as excellent examples of programming in the three languages for students learning how to program. I have used this book as supplementary material for a computational physics course based on Koonin’s text (Computational Physics, S. E. Koonin, Benjamin-Cummings Publishing, Menlo Park, CA, 1986) and will do so again in the future. The algorithms will not always do exactly what one wants, so one may occasionally have to alter the source codeu. For example, I wanted to calculate a series of spherical Bessel functions. The Bessel function routines in the book are only for calculating a single cylindrical Bessel function. I had to rewrite the code considerably to efficiently calculate the series I wanted. The index is very complete. The comments in the program listings in the book are not included in the programs on the diskette to save space. This book is one of the most significant books ever published-for scientists and engineers who do computing. Every desk should have a copy and its accompanying disk(s). L. DAVID ROPER Departinent of Physics Virginia Polytechnic Institute and State University Blacksburg, VA 24061, U.S.A.