Usage from Fortran

We provide Fortran interfaces that are very similar to those in C/C++. We deliberately use “legacy” Fortran style (in the terminology of FFTW), enabling the widest applicability and avoiding the complexity of later Fortran features. Namely, we use f77, with two features from f90: dynamic allocation and derived types. The latter is only needed if options must be changed from default values. We also include, listed at the bottom below, a “modern” f90 demo using a module.

Quick-start example

To perform a double-precision 1D type 1 transform from M nonuniform points xj with strengths cj, to N output modes whose coefficients will be written into the fk array, using 9-digit tolerance, the \(+i\) imaginary sign, and default options, the declarations and call are

     integer ier,iflag
     integer*8 N,M
     real*8, allocatable :: xj(:)
     real*8 tol
     complex*16, allocatable :: cj(:),fk(:)
     integer*8, allocatable :: null

!    (...allocate xj, cj, and fk, and fill xj and cj here...)

     tol = 1.0D-9
     iflag = +1
     call finufft1d1(M,xj,cj,iflag,tol,N,fk,null,ier)

which writes the output to fk, and the status to the integer ier. Since the default is CMCL mode ordering, the output for frequency index k is found in fk(k+N/2+1). ier=0 indicates success, otherwise error codes are as in here. All available OMP threads are used, unless FINUFFT was built single-threaded. (Note that here the unallocated null is simply a way to pass a NULL pointer to our C++ wrapper; another would be %val(0_8).) For a minimally complete test code demonstrating the above see fortran/examples/simple1d1.f.


Higher-dimensional arrays are stored in Fortran ordering with \(x\) (N1) the fastest direction, and, in the vectorized (“many”) calls, the transform number is slowest (transforms are stacked not interleaved). For instance, for the 2D type 1 vectorized transform finufft2d1many(ntrans,M,xj,yj,cj,iflag,tol,N1,N2,fk,opts,ier) with CMCL mode-ordering, the (k1,k2) frequency coefficient from transform number t is to be found at fk(k1+N1/2+1 + (k2+N2/2)*N1 + t*N1*N2).

From the fortran/examples/ directory, to compile (eg using GCC/linux) and link such a program against the FINUFFT static library, one must list dependent libraries by hand:

gfortran -I../../include simple1d1.f -o simple1d1 ../../lib-static/libfinufft.a -lfftw3 -lfftw3_omp -lgomp -lstdc++

Then to execute run ./simple1d1. Alternatively, a smaller executable results by linking against the dynamic (.so) library (which links all dependent libraries):

gfortran -I../../include simple1d1.f -o simple1d1 -L../../lib -Wl,-rpath=$FINUFFT/lib -lfinufft

where $FINUFFT must be replaced by (or be an environment variable set to) the absolute install path for this repository. Note the use of rpath to make an executable that may be run from, or moved to, any directory. Alternatively you may want to compile with g++ and use -lgfortran at the end of the compile statement instead of -lstdc++. In Mac OSX, replace fftw3_omp by fftw3_threads, and if you use clang, -lgomp by -lomp. See makefile and*.


Our simple interface is designed to be a near drop-in replacement for the native f90 CMCL libraries of Greengard-Lee. The differences are: i) we added a penultimate argument in the list which allows options to be changed, and ii) our normalization differs for type 1 transforms (divide FINUFFT output by \(M\) to match CMCL output).

Changing options

To choose non-default options in the above example, create an options derived type, set it to default values, change whichever you wish, and pass it to FINUFFT, for instance

     include 'finufft.fh'
     type(finufft_opts) opts

!    (...declare, allocate, and fill stuff as above...)

     call finufft_default_opts(opts)
     opts%debug = 2
     opts%upsampfac = 1.25d0
     call finufft1d1(M,xj,cj,iflag,tol,N,fk,opts,ier)

See fortran/examples/simple1d1.f for the complete code, and below for the complete list of Fortran subroutines available, and more complicated examples.

See modeord in Options to instead use FFT-style mode ordering, which simply differs by an fftshift (as it is commonly called).

Summary of Fortran interface

The names of routines and the meanings of all arguments is identical to the C/C++ routines. Eg, finufft2d3 means double-precision 2D transform of type 3. finufft2d3many means applying double-precision 2D transforms of type 3 to a stack of many strength vectors (vectorized interface). finufft2d3f means single-precision 2D type 3. The guru interface has very similar arguments to its C/C++ version. Compared to C/C++, all argument lists have ier appended at the end, to which the status is written; this is the same as the return value in the C/C++ interfaces. These routines and arguments are, in double-precision:

     include 'finufft.fh'
!    (or in F90 one may instead "use finufft_mod")

     integer ier,iflag,ntrans,type,dim
     integer*8 M,N1,N2,N3,Nk
     integer*8 plan,n_modes(3)
     real*8, allocatable :: xj(:),yj(:),zj(:), sk(:),tk(:),uk(:)
     real*8 tol
     complex*16, allocatable :: cj(:), fk(:)
     type(finufft_opts) opts

!    simple interface
     call finufft1d1(M,xj,cj,iflag,tol,N1,fk,opts,ier)
     call finufft1d2(M,xj,cj,iflag,tol,N1,fk,opts,ier)
     call finufft1d3(M,xj,cj,iflag,tol,Nk,sk,fk,opts,ier)
     call finufft2d1(M,xj,yj,cj,iflag,tol,N1,N2,fk,opts,ier)
     call finufft2d2(M,xj,yj,cj,iflag,tol,N1,N2,fk,opts,ier)
     call finufft2d3(M,xj,yj,cj,iflag,tol,Nk,sk,tk,fk,opts,ier)
     call finufft3d1(M,xj,yj,zj,cj,iflag,tol,N1,N2,N3,fk,opts,ier)
     call finufft3d2(M,xj,yj,zj,cj,iflag,tol,N1,N2,N3,fk,opts,ier)
     call finufft3d3(M,xj,yj,zj,cj,iflag,tol,Nk,sk,tk,uk,fk,opts,ier)

!    vectorized interface
     call finufft1d1many(ntrans,M,xj,cj,iflag,tol,N1,fk,opts,ier)
     call finufft1d2many(ntrans,M,xj,cj,iflag,tol,N1,fk,opts,ier)
     call finufft1d3many(ntrans,M,xj,cj,iflag,tol,Nk,sk,fk,opts,ier)
     call finufft2d1many(ntrans,M,xj,yj,cj,iflag,tol,N1,N2,fk,opts,ier)
     call finufft2d2many(ntrans,M,xj,yj,cj,iflag,tol,N1,N2,fk,opts,ier)
     call finufft2d3many(ntrans,M,xj,yj,cj,iflag,tol,Nk,sk,tk,fk,opts,ier)
     call finufft3d1many(ntrans,M,xj,yj,zj,cj,iflag,tol,N1,N2,N3,fk,opts,ier)
     call finufft3d2many(ntrans,M,xj,yj,zj,cj,iflag,tol,N1,N2,N3,fk,opts,ier)
     call finufft3d3many(ntrans,M,xj,yj,zj,cj,iflag,tol,Nk,sk,tk,uk,fk,opts,ier)

!    guru interface
     call finufft_makeplan(type,dim,n_modes,iflag,ntrans,tol,plan,opts,ier)
     call finufft_setpts(plan,M,xj,yj,zj,Nk,sk,yk,uk,ier)
     call finufft_execute(plan,cj,fk,ier)
     call finufft_destroy(plan,ier)

The single-precision (ie, real*4 and complex*8) functions are identical except with the replacement of finufft with finufftf in each function name. All are defined (from the C++ side) in fortran/finufftfort.cpp.

Code examples

The fortran/examples directory contains the following demos, mostly in both precisions. Each has a math test to check the correctness of some or all outputs:

simple1d1.f        - 1D type 1, simple interface, default and various opts
guru1d1.f          - 1D type 1, guru interface, default and various opts
nufft1d_demo.f     - 1D types 1,2,3, minimally changed from CMCL demo codes
nufft2d_demo.f     - 2D "
nufft3d_demo.f     - 3D "
nufft2dmany_demo.f - 2D types 1,2,3, vectorized (many strengths) interface
simple1d1.f90      - modern Fortran90 version of simple1d1 using module

These are the double-precision file names; the single precision have a suffix f before the .f (apart from the f90 which has no single-precision version). The last four here are modified from demos in the CMCL NUFFT libraries. The first three of these have been changed only to use FINUFFT. The final tolerance they request is tol=1d-16. For this case FINUFFT will report a warning that it cannot achieve it, and gets merely around \(10^{-14}\). The last four demos require direct summation (slow) reference implementations of the transforms in fortran/directft, modified from their CMCL counterparts only to remove the \(1/M\) prefactor for type 1 transforms.

All demos have self-contained example GCC compilation/linking commands in their comment headers. For dynamic linking so that execution works from any directory, bake in an absolute path via the compile flag -Wl,-rpath,$(FINUFFT)/lib.

For authorship and licensing of the Fortran wrappers, see the README in the fortran directory.