I'm using vDSP from Accelerate framework to perform a fft2d operation in a 2d array that comes from a mesh grid.
The problem is that I get an array of 0 in the imaginary part that don't match with the same operation in python using pylab.fft2.
If I increment the array size, the results don't be zero but don't match anyway so, I'm doing something bad.
Can someone let me a hand? This is my first stack overflow question but I'm stuck for two weeks now.
This is the mesh grid (4x8 for this example)
[
[1.80485138784544e-35, 2.61027906966774e-23, 1.26641655490943e-14, 2.06115362243857e-09, 1.1253517471926e-07, 2.06115362243857e-09, 1.26641655490943e-14, 2.61027906966774e-23],
[2.93748211171084e-30, 4.24835425529162e-18, 2.06115362243857e-09, 0.000335462627902512, 0.0183156388887342, 0.000335462627902512, 2.06115362243857e-09, 4.24835425529162e-18],
[1.60381089054866e-28, 2.31952283024359e-16, 1.1253517471926e-07, 0.0183156388887342, 1.0, 0.0183156388887342, 1.1253517471926e-07, 2.31952283024359e-16],
[2.93748211171084e-30, 4.24835425529162e-18, 2.06115362243857e-09, 0.000335462627902512, 0.0183156388887342, 0.000335462627902512, 2.06115362243857e-09, 4.24835425529162e-18]
]
Here is the fft2 function:
func fft2(arr: [[Complex<Double>]]) -> [[Complex<Double>]] {
let nRows = arr.count
let nCols = arr[0].count
let N = nRows * nCols
let radix = FFTRadix(FFT_RADIX2)
let pass = vDSP_Length(Int(log2(Double(N))))
// Create FFTSetup
let setup = vDSP_create_fftsetupD(pass, radix)
// Direction
let dir = FFTDirection(FFT_FORWARD)
// Get real and imag doubles from the [Complex]
// (all imag parts are 0.0 on this example)
let (real, imag) = complex2DArrayToDouble(arr)
// Pack 2d arrays as 1d (function bellow)
var realArray = pack2dArray(real, rows: nRows, cols: nCols)
var imagArray = pack2dArray(imag, rows: nRows, cols: nCols)
// Create the split complex with the packed arrays
var splitComplex = DSPDoubleSplitComplex(
realp: &realArray,
imagp: &imagArray)
let log2n0c = vDSP_Length(Int(log2(Double(nCols))))
let log2n1r = vDSP_Length(Int(log2(Double(nRows))))
let rowStride = vDSP_Stride(nRows)
let colStride = vDSP_Stride(1) // Use all cols
// Perform the fft2d
vDSP_fft2d_zipD(setup, &splitComplex, rowStride, colStride, log2n0c, log2n1r, dir)
// Destroy setup
vDSP_destroy_fftsetupD(setup)
// Pack the 1d arrays on 2d arrays again
let resultReal = unpack2dArray(realArray, rows: nRows, cols: nCols)
let resultImag = unpack2dArray(imagArray, rows: nRows, cols: nCols)
// Ignore this...
return complexFrom2DArray([[Double]](), imag: [[Double]]())
}
And finally here are the functions that I use for pack and unpack the arrays from/to 2d to 1d
func pack2dArray(arr: [[Double]], rows: Int, cols: Int) -> [Double] {
var resultArray = zeros(rows * cols)
for Iy in 0...cols-1 {
for Ix in 0...rows-1 {
let index = Iy * rows + Ix
resultArray[index] = arr[Ix][Iy]
}
}
return resultArray
}
func unpack2dArray(arr: [Double], rows: Int, cols: Int) -> [[Double]] {
var resultArray = [[Double]](count: rows, repeatedValue: zeros(cols))
for Iy in 0...cols-1 {
for Ix in 0...rows-1 {
let index = Iy * rows + Ix
resultArray[Ix][Iy] = arr[index]
}
}
return resultArray
}
I will appreciate any info about this and I can change this to C or Objective-C if is easiest to make it works like in python.
Swift results:
[
[(1.07460475603902+0.0.i), (-1.06348244974363+0.0.i), (1.03663115699765+0.0.i), (-1.00978033088166+0.0.i), (0.998658491216246+0.0.i), (-1.00978033088166+0.0.i), (1.03663115699765+0.0.i), (-1.06348244974363+0.0.i)],
[(-1.03663138619031+0.0.i), (1.02590210946989+0.0.i), (-0.999999662394501+0.0.i), (0.974097665459761+0.0.i), (-0.963368838879988+0.0.i), (0.974097665459761+0.0.i), (-0.999999662394501+0.0.i), (1.02590210946989+0.0.i)],
[(0.998658482971633+0.0.i), (-0.988322230996495+0.0.i), (0.963368617931946+0.0.i), (-0.938415438518917+0.0.i), (0.928079620195301+0.0.i), (-0.938415438518917+0.0.i), (0.963368617931946+0.0.i), (-0.988322230996495+0.0.i)],
[(-1.03663138619031+0.0.i), (1.02590210946989+0.0.i), (-0.999999662394501+0.0.i), (0.974097665459761+0.0.i), (-0.963368838879988+0.0.i), (0.974097665459761+0.0.i), (-0.999999662394501+0.0.i), (1.02590210946989+0.0.i)]
]
Python results:
[
[ 1.07460476 +0.00000000e+00j, -1.06348245 +1.98409020e-17j, 1.03663116 +0.00000000e+00j -1.00978033 -1.97866921e-17j, 0.99865849 +0.00000000e+00j -1.00978033 -1.98409020e-17j, 1.03663116 +0.00000000e+00j -1.06348245 +1.97866921e-17j]
[-1.03663139 +0.00000000e+00j, 1.02590211 -1.90819560e-17j, -0.99999966 +0.00000000e+00j, 0.97409767 +1.90819558e-17j, -0.96336884 +0.00000000e+00j, 0.97409767 +1.90819560e-17j, -0.99999966 +0.00000000e+00j, 1.02590211 -1.90819558e-17j]
[ 0.99865848 +0.00000000e+00j, 0.98832223 +1.83230190e-17j, 0.96336862 +0.00000000e+00j, 0.93841544 -1.83772293e-17j, 0.92807962 +0.00000000e+00j, 0.93841544 -1.83230190e-17j, 0.96336862 +0.00000000e+00j, 0.98832223 +1.83772293e-17j]
[-1.03663139 +0.00000000e+00j, 1.02590211 -1.90819560e-17j, -0.99999966 +0.00000000e+00j, 0.97409767 +1.90819558e-17j, -0.96336884 +0.00000000e+00j, 0.97409767 +1.90819560e-17j, -0.99999966 +0.00000000e+00j, 1.02590211 -1.90819558e-17j]
]
Regards and thanks so much in advance!!
Edit 1
Here is a version on C of the same code: http://pastebin.com/C9RPgu68
And here is the python code: http://pastebin.com/rr4e6rku
The different output such as
Swift: (-1.06348244974363+0.0.i)
Python: -1.06348245 +1.98409020e-17j
does not indicate a wrong result. First, the Swift code apparently
uses a fixed-point representation, so that 1.98409020 ⋅ 10-17 is rounded to 0.0. Second, even if you expect the
result to be exactly zero, a small non-zero value is to be expected due to the limited precision
of binary floating point numbers (about 16 decimal digits for a 64-bit Double).