public void multiresolution(double[,] Xin, int N, int K, WaveletTransformType transform,
WaveletBoundaryCondition boundary, out double[,] Xmra)
{
/* Peform a multirsolution analysis using the DWT or MODWT matrix
* obtained from `decompose.' The inverse transform will be applied
* to selected wavelet detail coefficients. The wavelet smooth
* coefficients from the original transform are added to the K+1
* column in order to preserve the additive decomposition.
* Reflection is used as the default boundary condition.
*
* Input:
* Xin = dmatrix from `decompose'
* N = number of rows in Xin
* K = number of details in Xin
* f = wavelet filter structure
* method = character string (either "dwt" or "modwt")
*
* Output:
* Xmra = dmatrix containg K wavelet details and 1 wavelet smooth */
int i, k, t, length;
double[] zero, Xout, Win;
if (boundary == WaveletBoundaryCondition.Reflect)
{
length = 2 * N;
}
else
{
length = N;
}
zero = new double[length];
Xout = new double[length];
Win = new double[length];
Xmra = new double[N, K + 1];
//printf("##### Length = %d #####\n", length);
for (k = 0; k < K; k++)
{
for (t = 0; t < length; t++)
{
Win[t] = Xin[t, k];
zero[t] = 0.0;
}
if (transform == WaveletTransformType.DWT)
{
idwt(Win, zero, (int)(N / Math.Pow(2, k)), out Xout);
}
else if (transform == WaveletTransformType.MODWT)
{
imodwt(Win, zero, length, k, out Xout);
}
for (i = k; i >= 0; i--)
{
for (t = 0; t < length; t++)
{
Win[t] = Xout[t];
}
if (transform == WaveletTransformType.DWT)
{
idwt(zero, Win, (int)(N / Math.Pow(2, i)), out Xout);
}
else
{
imodwt(zero, Win, length, i, out Xout);
}
}
for (t = 0; t < N; t++)
{
Xmra[t, k] = Xout[t];
}
}
/* One more iteration is required on the wavelet smooth coefficients
* to complete the additive decomposition. */
for (t = 0; t < length; t++)
{
Win[t] = Xin[t, K - 1];
zero[t] = 0.0;
}
if (transform == WaveletTransformType.DWT)
{
idwt(zero, Win, (int)(N / Math.Pow(2, K)), out Xout);
}
else
{
imodwt(zero, Win, length, K, out Xout);
}
for (i = K; i >= 0; i--)
{
for (t = 0; t < length; t++)
{
Win[t] = Xout[t];
}
if (transform == WaveletTransformType.DWT)
{
idwt(zero, Win, (int)(N / Math.Pow(2, i)), out Xout);
}
else
{
imodwt(zero, Win, length, i, out Xout);
}
for (t = 0; t < length; t++)
{
Win[t] = Xout[t];
zero[t] = 0.0;
}
}
for (t = 0; t < N; t++)
{
Xmra[t, K] = Xout[t];
}
}
public void decompose(double[] X, int N, int K, WaveletTransformType transform,
WaveletBoundaryCondition boundary, out double[,] Xout)
{
/* Peform the discrete wavelet transform (DWT) or maximal overlap
* discrete wavelet transform (MODWT) to a time-series and obtain a
* specified number (K) of wavelet coefficients and subsequent
* wavelet smooth. Reflection is used as the default boundary
* condition.
*
* Input:
* X = time-series (dvector of data)
* K = number of details desired
* f = wavelet filter structure
* method = character string (either "dwt" or "modwt")
* boundary = boundary condition (either "period" or "reflect")
*
* Output: Xout = dmatrix of wavelet coefficients and smooth
* (length = N for "period" and 2N for "reflect") */
int i, k;
int scale, length;
double[] Wout, Vout, Vin;
/* Dyadic vector length required for DWT */
if (transform == WaveletTransformType.DWT && N % 2 != 0)
{
throw new InvalidDataException("...data must have dyadic length for DWT...");
}
/* The choice of boundary methods affect things... */
if (boundary == WaveletBoundaryCondition.Reflect)
{
length = 2 * N;
scale = length;
Wout = new double[length];
Vout = new double[length];
Vin = new double[length];
Xout = new double[length, K];
reflect_vector(X, N, Vin);
/* printf("Boundary Treatment is REFLECTION...\n"); */
}
else
{
length = N;
scale = N;
Wout = new double[length];
Vout = new double[length];
Vin = new double[length];
Xout = new double[length, K];
for (i = 0; i < length; i++)
{
Vin[i] = X[i];
}
/* printf("Boundary Treatment is PERIODIC...\n"); */
}
/* printf("##### Length = %d #####\n", length); */
for (k = 0; k < K; k++)
{
for (i = 0; i < length; i++)
{
Wout[i] = 0.0;
Vout[i] = 0.0;
}
if (transform == WaveletTransformType.DWT)
{
dwt(Vin, scale, out Wout, out Vout);
}
else if (transform == WaveletTransformType.MODWT)
{
modwt(Vin, length, k, out Wout, out Vout);
}
for (i = 0; i < N; i++)
{
Xout[i, k] = Wout[i];
}
for (i = 0; i < length; i++)
{
Vin[i] = Vout[i];
}
scale -= scale / 2;
}
for (i = 0; i < length; i++)
{
Xout[i, K - 1] = Wout[i]; /* GMA */
}
}
