MatrixValue fft(MatrixValue x)
{
var length = x.Length;
if (length == 1)
{
return(x.Clone());
}
// Cooley-Tukey FFT
if (length % 2 != 0)
{
throw new YAMPDifferentLengthsException(length, "2^n");
}
// even fft
var even = new MatrixValue(length / 2, 1);
for (var k = 1; k <= even.Length; k++)
{
even[k] = x[2 * k];
}
var q = fft(even);
// odd fft;
var odd = even;
for (var k = 1; k <= odd.Length; k++)
{
odd[k] = x[2 * k - 1];
}
var r = fft(odd);
// combine
var y = new MatrixValue(length, 1);
for (var k = 1; k <= odd.Length; k++)
{
var value = -2 * (k - 1) * Math.PI / length;
var wk = new ScalarValue(Math.Cos(value), Math.Sin(value));
y[k] = q[k] + (wk * r[k]);
y[k + odd.Length] = q[k] - (wk * r[k]);
}
return(y);
}
MatrixValue fft(MatrixValue x)
{
var length = x.Length;
if (length == 1)
{
return x.Clone();
}
// Cooley-Tukey FFT
if (length % 2 != 0)
throw new YAMPDifferentLengthsException(length, "2^n");
// even fft
var even = new MatrixValue(length / 2, 1);
for (var k = 1; k <= even.Length; k++)
{
even[k] = x[2 * k];
}
var q = fft(even);
// odd fft;
var odd = even;
for (var k = 1; k <= odd.Length; k++)
{
odd[k] = x[2 * k - 1];
}
var r = fft(odd);
// combine
var y = new MatrixValue(length, 1);
for (var k = 1; k <= odd.Length; k++)
{
var value = -2 * (k - 1) * Math.PI / length;
var wk = new ScalarValue(Math.Cos(value), Math.Sin(value));
y[k] = q[k] + (wk * r[k]);
y[k + odd.Length] = q[k] - (wk * r[k]);
}
return y;
}
MatrixValue ifft2d(MatrixValue input)
{
var output = input.Clone();
// Rows first:
var x = new MatrixValue(output.DimensionY, 1);
for (var h = 1; h <= output.DimensionX; h++)
{
for (var i = 1; i <= output.DimensionY; i++)
{
x[i] = output[i, h];
}
x = ifft(x);
for (int i = 1; i <= output.DimensionY; i++)
{
output[i, h] = x[i];
}
}
//Columns last
var y = new MatrixValue(output.DimensionX, 1);
for (int h = 1; h <= output.DimensionY; h++)
{
for (int i = 1; i <= output.DimensionX; i++)
{
y[i] = output[h, i];
}
y = ifft(y);
for (int i = 1; i <= output.DimensionX; i++)
{
output[h, i] = y[i];
}
}
return(output);
}
/// <summary>
/// Creates a new Givens decomposition.
/// </summary>
/// <param name="A">The matrix to decompose.</param>
public GivensDecomposition(MatrixValue A)
: base(A)
{
var Q = MatrixValue.One(m);
var R = A.Clone();
// Main loop.
for (int j = 1; j < n; j++)
{
for (int i = m; i > j; i--)
{
var a = R[i - 1, j];
var b = R[i, j];
var G = MatrixValue.One(m);
var beta = (a * a + b * b).Sqrt();
var s = -b / beta;
var c = a / beta;
G[i - 1, i - 1] = c.Conjugate();
G[i - 1, i] = -s.Conjugate();
G[i, i - 1] = s;
G[i, i] = c;
R = G * R;
Q = Q * G.Adjungate();
}
}
for (int j = 0; j < n; j++)
{
if (R[j + 1, j + 1] == ScalarValue.Zero)
{
FullRank = false;
}
}
r = R;
q = Q;
}
/// <summary>
/// Creates a new Givens decomposition.
/// </summary>
/// <param name="A">The matrix to decompose.</param>
public GivensDecomposition(MatrixValue A)
: base(A)
{
var Q = MatrixValue.One(m);
var R = A.Clone();
// Main loop.
for (int j = 1; j < n; j++)
{
for (int i = m; i > j; i--)
{
var a = R[i - 1, j];
var b = R[i, j];
var G = MatrixValue.One(m);
var beta = (a * a + b * b).Sqrt();
var s = -b / beta;
var c = a / beta;
G[i - 1, i - 1] = c.Conjugate();
G[i - 1, i] = -s.Conjugate();
G[i, i - 1] = s;
G[i, i] = c;
R = G * R;
Q = Q * G.Adjungate();
}
}
for (int j = 0; j < n; j++)
{
if (R[j + 1, j + 1] == ScalarValue.Zero)
FullRank = false;
}
r = R;
q = Q;
}
MatrixValue fft2d(MatrixValue input)
{
var output = input.Clone();
// Rows first:
var x = new MatrixValue(output.DimensionY, 1);
for (var h = 1; h <= output.DimensionX; h++)
{
for (var i = 1; i <= output.DimensionY; i++)
{
x[i] = output[i, h];
}
x = fft(x);
for (var i = 1; i <= output.DimensionY; i++)
{
output[i, h] = x[i];
}
}
//Columns last
var y = new MatrixValue(output.DimensionX, 1);
for (var h = 0; h < output.DimensionY; h++)
{
for (var i = 1; i <= output.DimensionX; i++)
{
y[i] = output[h, i];
}
y = fft(y);
for (var i = 1; i <= output.DimensionX; i++)
{
output[h, i] = y[i];
}
}
return output;
}