README
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Gosl. fun/fftw. Wrapper to FFTW3
More information is available in the documentation of this package.
This package wraps the Fast Fourier Transform library (FFTW)
Documentation
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Overview ¶
Package fftw wraps the FFTW library to perform Fourier Transforms using the "fast" method by Cooley and Tukey
Index ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
This section is empty.
Types ¶
type Plan1d ¶
type Plan1d struct {
// contains filtered or unexported fields
}
Plan1d implements the FFTW3 plan structure; i.e. a "plan" to compute direct or inverse 1D FTs
Computes:
N-1 -i 2 π j k / N __
forward: X[k] = Σ x[j] ⋅ e with i = √-1
j=0
N-1 +i 2 π j k / N
inverse: Y[k] = Σ y[j] ⋅ e thus x[k] = Y[k] / N
j=0
NOTE: FFTW says "so you should initialize your input data after creating the plan."
Therefore, the plan can be created and reused several times.
[http://www.fftw.org/fftw3_doc/Planner-Flags.html]
Also: "The plan can be reused as many times as needed. In typical high-performance
applications, many transforms of the same size are computed"
[http://www.fftw.org/fftw3_doc/Introduction.html]
Create a new Plan1d with NewPlan1d(...) AND deallocate memory with Free()
func NewPlan1d ¶
func NewPlan1d(data []complex128, inverse, measure bool) (o *Plan1d)
NewPlan1d allocates a new "plan" to compute 1D Fourier Transforms
data -- [modified] data is a complex array of length N.
inverse -- will perform inverse transform; otherwise will perform direct
Note: both transforms are non-normalised;
i.e. the user will have to multiply by (1/n) if computing inverse transforms
measure -- use the FFTW_MEASURE flag for better optimisation analysis (slower initialisation times)
Note: using this flag with given "data" as input will cause the allocation
of a temporary array and the execution of two copy commands with size len(data)
NOTE: (1) the user must remember to call Free to deallocate FFTW data
(2) data will be overwritten
type Plan2d ¶
type Plan2d struct {
// contains filtered or unexported fields
}
Plan2d implements the FFTW3 plan structure; i.e. a "plan" to compute direct or inverse 2D FTs
Computes:
N1-1 N0-1 -i 2 π k1 l1 / N1 -i 2 π k0 l0 / N0
X[l0,l1] = Σ Σ x[k0,k1] ⋅ e ⋅ e
k1=0 k0=0
func NewPlan2d ¶
func NewPlan2d(N0, N1 int, data []complex128, inverse, measure bool) (o *Plan2d)
NewPlan2d allocates a new "plan" to compute 2D Fourier Transforms
N0, N1 -- dimensions
data -- [modified] data is a complex array of length N0*N1 (row-major matrix)
inverse -- will perform inverse transform; otherwise will perform direct
Note: both transforms are non-normalised;
i.e. the user will have to multiply by (1/n) if computing inverse transforms
measure -- use the FFTW_MEASURE flag for better optimisation analysis (slower initialisation times)
Note: using this flag with given "data" as input will cause the allocation
of a temporary array and the execution of two copy commands with size len(data)
NOTE: (1) the user must remember to call Free to deallocate FFTW data
(2) data will be overwritten
A = data is a ROW-MAJOR matrix
_ _
A = | A00→a0 A01→a1 A02→a2 | ⇒ A[i][j]
|_ A10→a3 A11→a4 A12→a5 _|
(n0,n1)=(2,3)
l = 0 1 2 3 4 5
a = [ A00 A01 A02 A10 A11 A12 ] ⇒ a[l]
3⋅0+0 3⋅0+1 3⋅0+2 3⋅1+0 3⋅1+1 3⋅1+2
l = n1⋅i + j i = l // n1 j = l % n1
func (*Plan2d) Get ¶
func (o *Plan2d) Get(i, j int) (v complex128)
Get gets data value located at "i,j". NOTE: this method does not check for out-of-range indices
func (*Plan2d) GetSlice ¶
func (o *Plan2d) GetSlice() (out [][]complex128)
GetSlice gets the output array as a nested slice
func (*Plan2d) Set ¶
func (o *Plan2d) Set(i, j int, v complex128)
Set sets data value located at "i,j". NOTE: this method does not check for out-of-range indices
Source Files