FFTW 3.3.10

Table of Contents

• 1 Introduction

• 2 Tutorial

  • 2.1 Complex One-Dimensional DFTs
  • 2.2 Complex Multi-Dimensional DFTs
  • 2.3 One-Dimensional DFTs of Real Data
  • 2.4 Multi-Dimensional DFTs of Real Data
  • 2.5 More DFTs of Real Data
    • 2.5.1 The Halfcomplex-format DFT
    • 2.5.2 Real even/odd DFTs (cosine/sine transforms)
    • 2.5.3 The Discrete Hartley Transform

• 3 Other Important Topics

  • 3.1 SIMD alignment and fftw_malloc

  • 3.2 Multi-dimensional Array Format

    • 3.2.1 Row-major Format
    • 3.2.2 Column-major Format
    • 3.2.3 Fixed-size Arrays in C
    • 3.2.4 Dynamic Arrays in C
    • 3.2.5 Dynamic Arrays in C—The Wrong Way

  • 3.3 Words of Wisdom—Saving Plans

  • 3.4 Caveats in Using Wisdom

• 4 FFTW Reference

  • 4.1 Data Types and Files

    • 4.1.1 Complex numbers
    • 4.1.2 Precision
    • 4.1.3 Memory Allocation

  • 4.2 Using Plans

  • 4.3 Basic Interface

    • 4.3.1 Complex DFTs
    • 4.3.2 Planner Flags
    • 4.3.3 Real-data DFTs
    • 4.3.4 Real-data DFT Array Format
    • 4.3.5 Real-to-Real Transforms
    • 4.3.6 Real-to-Real Transform Kinds

  • 4.4 Advanced Interface

    • 4.4.1 Advanced Complex DFTs
    • 4.4.2 Advanced Real-data DFTs
    • 4.4.3 Advanced Real-to-real Transforms

  • 4.5 Guru Interface

    • 4.5.1 Interleaved and split arrays
    • 4.5.2 Guru vector and transform sizes
    • 4.5.3 Guru Complex DFTs
    • 4.5.4 Guru Real-data DFTs
    • 4.5.5 Guru Real-to-real Transforms
    • 4.5.6 64-bit Guru Interface

  • 4.6 New-array Execute Functions

  • 4.7 Wisdom

    • 4.7.1 Wisdom Export
    • 4.7.2 Wisdom Import
    • 4.7.3 Forgetting Wisdom
    • 4.7.4 Wisdom Utilities

  • 4.8 What FFTW Really Computes

    • 4.8.1 The 1d Discrete Fourier Transform (DFT)
    • 4.8.2 The 1d Real-data DFT
    • 4.8.3 1d Real-even DFTs (DCTs)
    • 4.8.4 1d Real-odd DFTs (DSTs)
    • 4.8.5 1d Discrete Hartley Transforms (DHTs)
    • 4.8.6 Multi-dimensional Transforms

• 5 Multi-threaded FFTW

  • 5.1 Installation and Supported Hardware/Software
  • 5.2 Usage of Multi-threaded FFTW
  • 5.3 How Many Threads to Use?
  • 5.4 Thread safety

• 6 Distributed-memory FFTW with MPI

  • 6.1 FFTW MPI Installation

  • 6.2 Linking and Initializing MPI FFTW

  • 6.3 2d MPI example

  • 6.4 MPI Data Distribution

    • 6.4.1 Basic and advanced distribution interfaces
    • 6.4.2 Load balancing
    • 6.4.3 Transposed distributions
    • 6.4.4 One-dimensional distributions

  • 6.5 Multi-dimensional MPI DFTs of Real Data

  • 6.6 Other multi-dimensional Real-Data MPI Transforms

  • 6.7 FFTW MPI Transposes

    • 6.7.1 Basic distributed-transpose interface
    • 6.7.2 Advanced distributed-transpose interface
    • 6.7.3 An improved replacement for MPI_Alltoall

  • 6.8 FFTW MPI Wisdom

  • 6.9 Avoiding MPI Deadlocks

  • 6.10 FFTW MPI Performance Tips

  • 6.11 Combining MPI and Threads

  • 6.12 FFTW MPI Reference

    • 6.12.1 MPI Files and Data Types
    • 6.12.2 MPI Initialization
    • 6.12.3 Using MPI Plans
    • 6.12.4 MPI Data Distribution Functions
    • 6.12.5 MPI Plan Creation
    • 6.12.6 MPI Wisdom Communication

  • 6.13 FFTW MPI Fortran Interface

• 7 Calling FFTW from Modern Fortran

  • 7.1 Overview of Fortran interface

    • 7.1.1 Extended and quadruple precision in Fortran

  • 7.2 Reversing array dimensions

  • 7.3 FFTW Fortran type reference

  • 7.4 Plan execution in Fortran

  • 7.5 Allocating aligned memory in Fortran

  • 7.6 Accessing the wisdom API from Fortran

    • 7.6.1 Wisdom File Export/Import from Fortran
    • 7.6.2 Wisdom String Export/Import from Fortran
    • 7.6.3 Wisdom Generic Export/Import from Fortran

  • 7.7 Defining an FFTW module

• 8 Calling FFTW from Legacy Fortran

  • 8.1 Fortran-interface routines
  • 8.2 FFTW Constants in Fortran
  • 8.3 FFTW Execution in Fortran
  • 8.4 Fortran Examples
  • 8.5 Wisdom of Fortran?

• 9 Upgrading from FFTW version 2

• 10 Installation and Customization

  • 10.1 Installation on Unix
  • 10.2 Installation on non-Unix systems
  • 10.3 Cycle Counters
  • 10.4 Generating your own code

• 11 Acknowledgments

• 12 License and Copyright

• 13 Concept Index

• 14 Library Index

Next: Introduction, Previous: (dir), Up: (dir) [Contents][Index]

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FFTW User Manual

Welcome to FFTW, the Fastest Fourier Transform in the West. FFTW is a collection of fast C routines to compute the discrete Fourier transform. This manual documents FFTW version 3.3.10.

| • Introduction | | | | • Tutorial | | | | • Other Important Topics | | | | • FFTW Reference | | | | • Multi-threaded FFTW | | | | • Distributed-memory FFTW with MPI | | | | • Calling FFTW from Modern Fortran | | | | • Calling FFTW from Legacy Fortran | | | | • Upgrading from FFTW version 2 | | | | • Installation and Customization | | | | • Acknowledgments | | | | • License and Copyright | | | | • Concept Index | | | | • Library Index | | |

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Next: Introduction, Previous: (dir), Up: (dir) [Contents][Index]