FFT Code Examples

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 11/07/2023

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FFT Code Examples

This section presents examples of using the FFT interface functions described in "Fourier Transform Functions".

Here are the examples of two one-dimensional computations. These examples use the default settings for all of the configuration parameters, which are specified in "Configuration Settings".

In the Fortran examples, the use mkl_dfti statement assumes that:

The mkl_dfti.f90 module definition file is already compiled.
The mkl_dfti.mod module file is available.

One-dimensional In-place FFT

! Fortran example.
! 1D complex to complex, and real to conjugate-even
Use MKL_DFTI
Complex :: X(32)
Real :: Y(34)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc1_Handle, My_Desc2_Handle
Integer :: Status
!...put input data into X(1),...,X(32); Y(1),...,Y(32)
 
! Perform a complex to complex transform
Status = DftiCreateDescriptor( My_Desc1_Handle, DFTI_SINGLE,&
   DFTI_COMPLEX, 1, 32 )
Status = DftiCommitDescriptor( My_Desc1_Handle )
Status = DftiComputeForward( My_Desc1_Handle, X )
Status = DftiFreeDescriptor(My_Desc1_Handle)
! result is given by {X(1),X(2),...,X(32)}
 
! Perform a real to complex conjugate-even transform
Status = DftiCreateDescriptor(My_Desc2_Handle, DFTI_SINGLE,&
   DFTI_REAL, 1, 32)
Status = DftiCommitDescriptor(My_Desc2_Handle)
Status = DftiComputeForward(My_Desc2_Handle, Y)
Status = DftiFreeDescriptor(My_Desc2_Handle)
! result is given in CCS format.

One-dimensional Out-of-place FFT

! Fortran example.
! 1D complex to complex, and real to conjugate-even
Use MKL_DFTI
Complex :: X_in(32)
Complex :: X_out(32)
Real :: Y_in(32)
Real :: Y_out(34)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc1_Handle, My_Desc2_Handle
Integer :: Status
...put input data into X_in(1),...,X_in(32); Y_in(1),...,Y_in(32)
! Perform a complex to complex transform
Status = DftiCreateDescriptor( My_Desc1_Handle, DFTI_SINGLE,
DFTI_COMPLEX, 1, 32 )
Status = DftiSetValue( My_Desc1_Handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE)
Status = DftiCommitDescriptor( My_Desc1_Handle )
Status = DftiComputeForward( My_Desc1_Handle, X_in, X_out )
Status = DftiFreeDescriptor(My_Desc1_Handle)
! result is given by {X_out(1),X_out(2),...,X_out(32)}
! Perform a real to complex conjugate-even transform
Status = DftiCreateDescriptor(My_Desc2_Handle, DFTI_SINGLE,
DFTI_REAL, 1, 32)
Status = DftiSetValue( My_Desc2_Handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE)
Status = DftiCommitDescriptor(My_Desc2_Handle)
Status = DftiComputeForward(My_Desc2_Handle, Y_in, Y_out)
Status = DftiFreeDescriptor(My_Desc2_Handle)
! result is given by Y_out in CCS format.

Two-dimensional FFT

The following is an example of two simple two-dimensional transforms. Notice that the data and result parameters in computation functions are all declared as assumed-size rank-1 array DIMENSION(0:*). Therefore two-dimensional array must be transformed to one-dimensional array by EQUIVALENCE statement or other facilities of Fortran.

! Fortran example.
! 2D complex to complex, and real to conjugate-even
Use MKL_DFTI
Complex ::  X_2D(32,100)
Real :: Y_2D(34, 102)
Complex ::  X(3200)
Real :: Y(3468)
Equivalence (X_2D, X)
Equivalence (Y_2D, Y)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc1_Handle, My_Desc2_Handle
Integer :: Status, L(2)
!...put input data into X_2D(j,k), Y_2D(j,k), 1<=j=32,1<=k<=100
!...set L(1) = 32, L(2) = 100
!...the transform is a 32-by-100
 
! Perform a complex to complex transform
Status = DftiCreateDescriptor( My_Desc1_Handle, DFTI_SINGLE,&
          DFTI_COMPLEX, 2, L)
Status = DftiCommitDescriptor( My_Desc1_Handle)
Status = DftiComputeForward( My_Desc1_Handle, X)
Status = DftiFreeDescriptor(My_Desc1_Handle)
! result is given by X_2D(j,k), 1<=j<=32, 1<=k<=100
 
! Perform a real to complex conjugate-even transform
Status = DftiCreateDescriptor( My_Desc2_Handle, DFTI_SINGLE,&
          DFTI_REAL, 2, L)
Status = DftiCommitDescriptor( My_Desc2_Handle)
Status = DftiComputeForward( My_Desc2_Handle, Y)
Status = DftiFreeDescriptor(My_Desc2_Handle)
! result is given by the complex value z(j,k) 1<=j<=32; 1<=k<=100
! and is stored in CCS format

The following example demonstrates how you can change the default configuration settings by using the DftiSetValue function.

For instance, to preserve the input data after the FFT computation, the configuration of DFTI_PLACEMENT should be changed to "not in place" from the default choice of "in place."

The code below illustrates how this can be done:

Changing Default Settings

! Fortran example
! 1D complex to complex, not in place
Use MKL_DFTI
Complex :: X_in(32), X_out(32)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc_Handle
Integer :: Status
!...put input data into X_in(j), 1<=j<=32
Status = DftiCreateDescriptor( My_Desc_Handle,& DFTI_SINGLE, DFTI_COMPLEX, 1, 32)
Status = DftiSetValue( My_Desc_Handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE)
Status = DftiCommitDescriptor( My_Desc_Handle)
Status = DftiComputeForward( My_Desc_Handle, X_in, X_out)
Status = DftiFreeDescriptor (My_Desc_Handle)
! result is X_out(1),X_out(2),...,X_out(32)

Using Status Checking Functions

This example illustrates the use of status checking functions described in "Fourier Transform Functions".

! Fortran
type(DFTI_DESCRIPTOR), POINTER :: desc
integer status
! ...descriptor creation and other code
status =  DftiCommitDescriptor(desc)
if (status .ne. 0) then
  if (.not. DftiErrorClass(status,DFTI_NO_ERROR) then
     print *, 'Error: ', DftiErrorMessage(status)
  endif
endif

Computing 2D FFT by One-Dimensional Transforms

Below is an example where a 20-by-40 two-dimensional FFT is computed explicitly using one-dimensional transforms. Notice that the data and result parameters in computation functions are all declared as assumed-size rank-1 array DIMENSION(0:*). Therefore two-dimensional array must be transformed to one-dimensional array by EQUIVALENCE statement or other facilities of Fortran.

! Fortran
use mkl_dfti
Complex ::  X_2D(20,40)
Complex ::  X(800)
Equivalence (X_2D, X)
INTEGER :: STRIDE(2)
type(DFTI_DESCRIPTOR), POINTER :: Desc_Handle_Dim1
type(DFTI_DESCRIPTOR), POINTER :: Desc_Handle_Dim2
! ...
Status = DftiCreateDescriptor(Desc_Handle_Dim1, DFTI_SINGLE,&
                                 DFTI_COMPLEX, 1, 20 )
Status = DftiCreateDescriptor(Desc_Handle_Dim2, DFTI_SINGLE,&
                                 DFTI_COMPLEX, 1, 40 )
! perform 40 one-dimensional transforms along 1st dimension
Status = DftiSetValue( Desc_Handle_Dim1, DFTI_NUMBER_OF_TRANSFORMS, 40 )
Status = DftiSetValue( Desc_Handle_Dim1, DFTI_INPUT_DISTANCE, 20 )
Status = DftiSetValue( Desc_Handle_Dim1, DFTI_OUTPUT_DISTANCE, 20 )
Status = DftiCommitDescriptor( Desc_Handle_Dim1 )
Status = DftiComputeForward( Desc_Handle_Dim1, X )
! perform 20 one-dimensional transforms along 2nd dimension
Stride(1) = 0; Stride(2) = 20
Status = DftiSetValue( Desc_Handle_Dim2, DFTI_NUMBER_OF_TRANSFORMS, 20 )
Status = DftiSetValue( Desc_Handle_Dim2, DFTI_INPUT_DISTANCE, 1 )
Status = DftiSetValue( Desc_Handle_Dim2, DFTI_OUTPUT_DISTANCE, 1 )
Status = DftiSetValue( Desc_Handle_Dim2, DFTI_INPUT_STRIDES, Stride )
Status = DftiSetValue( Desc_Handle_Dim2, DFTI_OUTPUT_STRIDES, Stride )
Status = DftiCommitDescriptor( Desc_Handle_Dim2 )
Status = DftiComputeForward( Desc_Handle_Dim2, X )
Status = DftiFreeDescriptor( Desc_Handle_Dim1 )
Status = DftiFreeDescriptor( Desc_Handle_Dim2 )

The following code illustrates real multi-dimensional transforms with CCE format storage of conjugate-even complex matrix. Example "Two-Dimensional REAL In-place FFT (Fortran Interface)" is two-dimensional in-place transform and Example "Two-Dimensional REAL Out-of-place FFT (Fortran Interface)" is two-dimensional out-of-place transform in Fortran interface. Note that the data and result parameters in computation functions are all declared as assumed-size rank-1 array DIMENSION(0:*). Therefore two-dimensional array must be transformed to one-dimensional array by EQUIVALENCE statement or other facilities of Fortran.

Two-Dimensional REAL In-place FFT

! Fortran example.
! 2D and real to conjugate-even
Use MKL_DFTI
Real :: X_2D(34,100) ! 34  = (32/2 + 1)*2
Real :: X(3400)
Equivalence (X_2D, X)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc_Handle
Integer :: Status, L(2)
Integer :: strides_in(3)
Integer :: strides_out(3)
! ...put input data into X_2D(j,k), 1<=j=32,1<=k<=100
! ...set L(1) = 32, L(2) = 100
! ...set strides_in(1) = 0, strides_in(2) = 1, strides_in(3) = 34
! ...set strides_out(1) = 0, strides_out(2) = 1, strides_out(3) = 17
! ...the transform is a 32-by-100
! Perform a real to complex conjugate-even transform
Status = DftiCreateDescriptor( My_Desc_Handle, DFTI_SINGLE,&
DFTI_REAL, 2, L )
Status = DftiSetValue(My_Desc_Handle, DFTI_CONJUGATE_EVEN_STORAGE,&
DFTI_COMPLEX_COMPLEX)
Status = DftiSetValue(My_Desc_Handle, DFTI_INPUT_STRIDES, strides_in)
Status = DftiSetValue(My_Desc_Handle, DFTI_OUTPUT_STRIDES, strides_out)
Status = DftiCommitDescriptor( My_Desc_Handle)
Status = DftiComputeForward( My_Desc_Handle, X )
Status = DftiFreeDescriptor(My_Desc_Handle)
! result is given by the complex value z(j,k) 1<=j<=17; 1<=k<=100 and
! is stored in real matrix X_2D in CCE format.

Two-Dimensional REAL Out-of-place FFT

! Fortran example.
! 2D and real to conjugate-even
Use MKL_DFTI
Real :: X_2D(32,100)
Complex :: Y_2D(17, 100) ! 17 = 32/2 + 1
Real :: X(3200)
Complex :: Y(1700)
Equivalence (X_2D, X)
Equivalence (Y_2D, Y)
type(DFTI_DESCRIPTOR), POINTER :: My_Desc_Handle
Integer :: Status, L(2)
Integer :: strides_out(3)
 
! ...put input data into X_2D(j,k), 1<=j=32,1<=k<=100
! ...set L(1) = 32, L(2) = 100
! ...set strides_out(1) = 0, strides_out(2) = 1, strides_out(3) = 17
 
! ...the transform is a 32-by-100
! Perform a real to complex conjugate-even transform
Status = DftiCreateDescriptor( My_Desc_Handle, DFTI_SINGLE,&
DFTI_REAL, 2, L )
Status = DftiSetValue(My_Desc_Handle,&
DFTI_CONJUGATE_EVEN_STORAGE, DFTI_COMPLEX_COMPLEX)
Status = DftiSetValue( My_Desc_Handle, DFTI_PLACEMENT, DFTI_NOT_INPLACE )
Status = DftiSetValue(My_Desc_Handle,&
DFTI_OUTPUT_STRIDES, strides_out)
 
Status = DftiCommitDescriptor(My_Desc_Handle)
Status = DftiComputeForward(My_Desc_Handle, X, Y)
Status = DftiFreeDescriptor(My_Desc_Handle)
! result is given by the complex value z(j,k) 1<=j<=17; 1<=k<=100 and
! is stored in complex matrix Y_2D in CCE format.

Parent topic: Fourier Transform Functions Code Examples

Examples of Using OpenMP* Threading for FFT Computation

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

FFT Code Examples

One-dimensional In-place FFT

One-dimensional Out-of-place FFT

Two-dimensional FFT

Changing Default Settings

Using Status Checking Functions

Computing 2D FFT by One-Dimensional Transforms

Two-Dimensional REAL In-place FFT

Two-Dimensional REAL Out-of-place FFT