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>
/// Copy-Constructor
/// </summary>
/// <remarks>
/// Setup fast Fourier transform / back-transform for one, two or three
/// dimensions. The dimensions n1,n2,and n3 must be of the form
/// n = (2**p) * (3**q) * (5**r)
/// otherwise an error will be generated and the error handler function
/// Matpack.Error() is called. On instantiation some trigonometric tables
/// will be allocated and calculated. This approach avoids multiple
/// twiddle factor recalculations if several FFTs are calculated for data
/// with the same dimensions. Sometimes it is convenient to define an
/// "empty" setup (first constructor) and assign a setup later (see
/// copying and assignment). As default the multi-dimensional data
/// are expected in row order (C convention). If you want to transform
/// data stored in column order (Fortran convention) use the member
/// function SetOrder() to change the order - see below. For optimizations
/// on vector machines with separate memory banks an extra leading dimension
/// can be defined to avoid bank conflicts - also see SetOrder().
/// </remarks>
public Pfa235FFT(Pfa235FFT fft)
{
// copy all elements
id = fft.id;
ndim = fft.ndim;
trisize = fft.trisize;
row_order = fft.row_order;
for (int i = 0; i < 3; i++)
{
dim[i] = fft.dim[i];
trindex[i] = fft.trindex[i];
}
// allocate and copy trigs
trigs = new double[trisize];
Array.Copy(fft.trigs, 0, this.trigs, 0, fft.trigs.Length);
}
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;
}
/// <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))
{
Pfa235FFT 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 void MyFFT(double[] real, double[] imag, FourierDirection direction)
{
Pfa235FFT fft = new Pfa235FFT(real.Length);
fft.FFT(real, imag, direction);
}
private void MyRoutine2(double[] real1, FourierDirection dir)
{
int n = real1.Length;
System.Random rnd = new System.Random();
double[] real2 = new double[n];
for (int i = 0; i < n; i++)
real2[i] = rnd.NextDouble() / n;
Pfa235FFT fft = new Pfa235FFT(n);
fft.RealFFT(real2, real1, dir);
}
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;
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.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 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;
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 * 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 zzTestZero(int u, int v)
{
int n = u * v;
double[] re = new double[n];
double[] im = new double[n];
Pfa235FFT 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");
}
}