## Numerical Recipes in Fortran 90: Volume 2, Volume 2 of Fortran Numerical Recipes: The Art of Parallel Scientific ComputingThe Fortran 90 computer language is not just the long-awaited updating of Fortran to modern computing practices. It is also at the cutting edge of a much wider revolution in computing, that of multiprocessor computers and widespread parallel programming, a revolution rapidly moving to the desktop. Numerical Recipes in Fortran 90, as Volume 2 of the Fortran Numerical Recipes series, takes up where Volume I (now available as Numerical Recipes in Fortran 77) leaves off. Volume 2 (this volume) begins with three completely new chapters that provide a detailed introduction to the Fortran 90 language and then present the basic concepts of parallel programming, all with the same clarity and good cheer for which Numerical Recipes is famous. The authors explain why Fortran 90, and the general approach of "thinking parallel" that they advocate, is of immediate benefit to all scientific programmers, even on today's single-processor PCs and workstations, and even before multiprocessor machines arrive on the desktop. Routines coded with parallel language features are usually shorter, clearer, and closer to the underlying scientific ideas than their traditionally coded, do-loop laden counter-parts. All 350 plus routines from the second edition of Numerical Recipes are in this volume, almost all of them completely reworked algorithmically so as to be "parallel-ready" and to utilize Fortran 90's advanced language features. The introductory discussions and mathematical derivations of Volume I are not repeated in this volume (it is assumed that the reader will use this volume in conjunction with Volume l), so the text discussion that accompanies the individual routines focuses instead on Fortran 90 language tips, and on conceptual "parallel hints." Numerous such discussions are sprinkled throughout this volume. Also included is a foreword by Michael Metcalf, one of Fortran 90's original designers. |

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### Contents

Preface to Volume | 922 |

Numerical Recipes in Fortran 77 | 923 |

License Information xvii | 931 |

Introduction to Parallel Programming | 962 |

Numerical Recipes Utility Functions for Fortran 90 | 987 |

Code Chapters | 1009 |

B3 Interpolation and Extrapolation | 1043 |

B4 Integration of Functions | 1052 |

B12 Fast Fourier Transform | 1235 |

B13 Fourier and Spectral Applications | 1253 |

B14 Statistical Description of Data | 1269 |

B15 Modeling of Data | 1285 |

B16 Integration of Ordinary Differential Equations | 1297 |

B17 Two Point Boundary Value Problems | 1314 |

B18 Integral Equations and Inverse Theory | 1325 |

B19 Partial Differential Equations | 1332 |

B5 Evaluation of Functions | 1070 |

B6 Special Functions | 1083 |

B7 Random Numbers | 1141 |

B8 Sorting | 1167 |

B9 Root Finding and Nonlinear Sets of Equations | 1182 |

B10 Minimization or Maximization of Functions | 1201 |

B11 Eigensystems | 1225 |

B20 LessNumerical Algorithms | 1343 |

References | 1359 |

C2 Alphabetical Listing of Explicit Interfaces | 1384 |

C3 Index of Programs and Dependencies | 1434 |

1447 | |

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### Common terms and phrases

a,b REAL SP algorithm ALLOCATABLE allocate argument arth call assert call nrerror call swap CHARACTER(1 coefficients COMPLEX SPC Compute convergence data1 data2 deallocate diagonal DIMENSION size DIMENSION size(x discrete Fourier transform do-loop double precision dydz elements end do END END FUNCTION func end if end END INTERFACE INTERFACE END SUBROUTINE equation evaluated exit end fºo Fortran 77 Fortran 90 func END FUNCTION func END INTERFACE FUNCTION func END IMPLICIT NONE INTEGER(I4B IMPLICIT NONE REAL indz initial input integer INTENT INOUT INTENT(OUT INTERFACE FUNCTION func INTERFACE INTERFACE SUBROUTINE intrinsic ishft isign iterations LOGICAL LGT loop machines mask matrix MAXIT MODULE n=size nran nrtype IMPLICIT nrtype INTEGER(I4B nrtype REAL SP nrutil Numerical Recipes output overloaded parallel PARAMETER POINTER polynomial prob recursive recursive doubling routine returns scalar ſº stepsize SUBROUTINE derivs transform Types and ranks variables vector wksp x REAL SP zero