def fct(vector):
n = len(vector)
# auxiliary array
aux = np.zeros(n);
for i in range(0, n):
aux[i] = np.sin(np.pi*(i+0.5)/n)*(vector[i] - vector[n-i-1]) + 0.5*(vector[i] + vector[n-i-1])
vCompl = myfft.realfft(aux)
# rearrange to give cosine transform
for i in range(0, n/2):
vector[2*i] = np.cos(np.pi*i/n)*vCompl[i].real + np.sin(np.pi*i/n)*vCompl[i].imag
vector[n-1] = -0.5*vCompl[n/2].real
i = n/2-1;
while i > 0:
vector[2*i-1] = vector[2*i+1] - np.sin(np.pi*i/n)*vCompl[i].real + np.cos(np.pi*i/n)*vCompl[i].imag
vector[2*i+1] *= -1
i -= 1
vector[1] *= -1
return vector
def fst(vector): # fast sine transform
n = len(vector)
# auxiliary array
aux = np.zeros(n)
for i in range(1, n):
aux[i] = np.sin(i * np.pi / n) * (vector[i] + vector[n - i]) + 0.5 * (vector[i] - vector[n - i])
vCompl = myfft.realfft(aux)
# rearrange to give sine transform
vector[0] = -vCompl[0].imag
vector[1] = 0.5 * vCompl[0].real
for i in range(1, n / 2):
vector[2 * i] = -vCompl[i].imag
vector[2 * i + 1] = vector[2 * i - 1] + vCompl[i].real
return vector
def fst(vector): # fast sine transform
n = len(vector)
# auxiliary array
aux = np.zeros(n)
for i in range(1, n):
aux[i] = np.sin(i * np.pi / n) * (vector[i] + vector[n - i]) + 0.5 * (
vector[i] - vector[n - i])
vCompl = myfft.realfft(aux)
# rearrange to give sine transform
vector[0] = -vCompl[0].imag
vector[1] = 0.5 * vCompl[0].real
for i in range(1, n / 2):
vector[2 * i] = -vCompl[i].imag
vector[2 * i + 1] = vector[2 * i - 1] + vCompl[i].real
return vector
