public RealFourierTransform(int length)
{
_numberOfData = length;
if (length < 1)
{
throw new ArgumentException("length smaller than 1 is not appropriate here.");
}
else if (length < 3)
{
_method = Method.Trivial;
}
else if (Calc.BinaryMath.IsPowerOfTwo(length))
{
// use Hartley transform
_method = Method.Hartley;
}
else if (Pfa235FFT.CanFactorized(length))
{
// use Pfa235 transform
_method = Method.Pfa235;
_pfa235 = new Pfa235FFT(_numberOfData);
}
else
{
// use chirp transform
_method = Method.Chirp;
}
}
/// <summary>
/// Executes the fourier transformation itself (without data pretreatment).
/// </summary>
/// <exception cref="System.InvalidOperationException">The Fourier transformation was already executed.</exception>
protected virtual void ExecuteFourierTransformation()
{
if (_arraysContainTransformation)
{
throw new InvalidOperationException("The Fourier transformation was already executed.");
}
var numColumns = NumberOfColumns;
var numRows = NumberOfRows;
var rePart = ((IMatrixInArray1DRowMajorRepresentation <double>)_realMatrix).GetArray1DRowMajor();
_imagMatrix = new DoubleMatrixInArray1DRowMajorRepresentation(numRows, numColumns);
var imPart = ((IMatrixInArray1DRowMajorRepresentation <double>)_imagMatrix).GetArray1DRowMajor();
// fourier transform either with Pfa (faster) or with the Chirp-z-transform
if (Pfa235FFT.CanFactorized(numRows) && Pfa235FFT.CanFactorized(numColumns))
{
var fft = new Pfa235FFT(numRows, numColumns);
fft.FFT(rePart, imPart, FourierDirection.Forward);
}
else
{
var matrixRe = new DoubleMatrixInArray1DRowMajorRepresentation(rePart, numRows, numColumns);
ChirpFFT.FourierTransformation2D(matrixRe, _imagMatrix, FourierDirection.Forward);
}
_arraysContainTransformation = true;
}
private static void zzTestImOne_ArbPosBothDim(int u, int v)
{
int upos = rnd.Next(u);
int vpos = rnd.Next(v);
int n = u * v;
double[] re = new double[n];
double[] im = new double[n];
im[upos * v + vpos] = 1;
var fft = new Pfa235FFT(u, v);
fft.FFT(re, im, FourierDirection.Inverse);
for (int i = 0; i < u; i++)
{
for (int j = 0; j < v; j++)
{
Assert.AreEqual(Math.Sin(2 * Math.PI * (((double)i) * upos / u + ((double)j) * vpos / v)), re[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 re[{2},{3}]", u, v, i, j));
Assert.AreEqual(Math.Cos(2 * Math.PI * (((double)i) * upos / u + ((double)j) * vpos / v)), im[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 im[{2},{3}]", u, v, i, j));
}
}
}
private static int GetRandomN(int max)
{
int[] pqr = new int[3];
int n = 0;
do
{
n = rnd.Next(max);
} while (n < 2 || n > max || !Pfa235FFT.Factorize(n, pqr));
return(n);
}
protected static string TwoDimFFT(Altaxo.AltaxoDocument mainDocument, GUI.WorksheetController dg, out double[] rePart, out double[] imPart)
{
int rows = dg.Doc.DataColumns.RowCount;
int cols = dg.Doc.DataColumns.ColumnCount;
// reserve two arrays (one for real part, which is filled with the table contents)
// and the imaginary part - which is left zero here)
rePart = new double[rows * cols];
imPart = new double[rows * cols];
// fill the real part with the table contents
for (int i = 0; i < cols; i++)
{
Altaxo.Data.INumericColumn col = dg.Doc[i] as Altaxo.Data.INumericColumn;
if (null == col)
{
return(string.Format("Can't apply fourier transform, since column number {0}, name:{1} is not numeric", i, dg.Doc[i].FullName));
}
for (int j = 0; j < rows; j++)
{
rePart[i * rows + j] = col[j];
}
}
// test it can be done
if (!Pfa235FFT.CanFactorized(cols))
{
return(string.Format("Can't apply fourier transform, since the number of cols ({0}) are not appropriate for this kind of fourier transform.", cols));
}
if (!Pfa235FFT.CanFactorized(rows))
{
return(string.Format("Can't apply fourier transform, since the number of rows ({0}) are not appropriate for this kind of fourier transform.", rows));
}
// fourier transform
Pfa235FFT fft = new Pfa235FFT(cols, rows);
fft.FFT(rePart, imPart, FourierDirection.Forward);
// replace the real part by the amplitude
for (int i = 0; i < rePart.Length; i++)
{
rePart[i] = Math.Sqrt(rePart[i] * rePart[i] + imPart[i] * imPart[i]);
}
return(null);
}
private void MyRoutine2(double[] real1, FourierDirection dir)
{
int n = real1.Length;
var rnd = new System.Random();
double[] real2 = new double[n];
for (int i = 0; i < n; i++)
{
real2[i] = rnd.NextDouble() / n;
}
var fft = new Pfa235FFT(n);
fft.RealFFT(real2, real1, dir);
}
private static void zzTestZero(int u, int v)
{
int n = u * v;
double[] re = new double[n];
double[] im = new double[n];
var fft = new Pfa235FFT(u, v);
fft.FFT(re, im, FourierDirection.Inverse);
for (int i = 0; i < n; i++)
{
Assert.AreEqual(0, re[i], 0, "FFT of zero should give re=0");
Assert.AreEqual(0, im[i], 0, "FFT of zero should give im=0");
}
}
private static void zzTestReOne_OnePos2ndDim(int u, int v)
{
int n = u * v;
double[] re = new double[n];
double[] im = new double[n];
re[1 * v] = 1;
var fft = new Pfa235FFT(u, v);
fft.FFT(re, im, FourierDirection.Inverse);
for (int i = 0; i < u; i++)
{
for (int j = 0; j < v; j++)
{
Assert.AreEqual(Math.Cos((2 * Math.PI * i) / u), re[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 re[{2},{3}]", u, v, i, j));
Assert.AreEqual(-Math.Sin((2 * Math.PI * i) / u), im[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 im[{2},{3}]", u, v, i, j));
}
}
}
private static void zzTestReOne_OnePosBothDim(int u, int v)
{
Console.WriteLine("TestReOn_OnePosBothDim({0},{1})", u, v);
int n = u * v;
double[] re = new double[n];
double[] im = new double[n];
re[1 * v + 1] = 1;
Pfa235FFT fft = new Pfa235FFT(u, v);
fft.FFT(re, im, FourierDirection.Inverse);
for (int i = 0; i < u; i++)
{
for (int j = 0; j < v; j++)
{
Assert.AreEqual(Math.Cos(2 * Math.PI * (((double)i) / u + ((double)j) / v)), re[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 re[{2},{3}]", u, v, i, j));
Assert.AreEqual(-Math.Sin(2 * Math.PI * (((double)i) / u + ((double)j) / v)), im[i * v + j], n * 1E-15, string.Format("FFT({0},{1}) of re 1 at pos 1 im[{2},{3}]", u, v, i, j));
}
}
}
private void MyFFT(double[] real, double[] imag, FourierDirection direction)
{
var fft = new Pfa235FFT(real.Length);
fft.FFT(real, imag, direction);
}