def convolve_poly_split(A, B, wf=dft.omega2, error=0):
lenA, lenB = len(A), len(B)
if lenA != lenB:
raise Exception('Coefficient arrays must be of the same length')
## 1. pad A and B with zeros until their lengths are an integral
## power of 2
padded_A = dft.pad_with_zeros(A)
padded_B = dft.pad_with_zeros(B)
## 2. pad A and B more so that their length is 2*n, where n is
## the length of padded_A.
padded_A = pad_with_zeros_until_required_length(padded_A,
2 * len(padded_A))
padded_B = pad_with_zeros_until_required_length(padded_B,
2 * len(padded_A))
## 3. compute dft of padded A and B
fft_A = dft.recursive_fft(padded_A, wf=wf, error=error)
fft_B = dft.recursive_fft(padded_B, wf=wf, error=error)
## 4. compute pointwise multiplication of A and B
C = []
for a, b in zip(fft_A, fft_B):
C.append(a * b)
## 5. compute inverse dft of A*B and split the output into
## real and imaginary numbers.
reals, imags = dft.recursive_inverse_fft_split(C, wf=wf, error=error)
## 6. the degree of A and B is lenA-1. the degree of A*B is
## 2*(lenA-1) = 2*lenA - 2.
return reals[0:2 * lenA - 1], imags[0:2 * lenA - 1]
def convolve_poly_split(A, B, wf=dft.omega2, error=0):
lenA, lenB = len(A), len(B)
if lenA != lenB:
raise Exception('Coefficient arrays must be of the same length')
## 1. pad A and B with zeros until their lengths are an integral
## power of 2
padded_A = dft.pad_with_zeros(A)
padded_B = dft.pad_with_zeros(B)
## 2. pad A and B more so that their length is 2*n, where n is
## the length of padded_A.
padded_A = pad_with_zeros_until_required_length(padded_A, 2*len(padded_A))
padded_B = pad_with_zeros_until_required_length(padded_B, 2*len(padded_A))
## 3. compute dft of padded A and B
fft_A = dft.recursive_fft(padded_A, wf=wf, error=error)
fft_B = dft.recursive_fft(padded_B, wf=wf, error=error)
## 4. compute pointwise multiplication of A and B
C = []
for a, b in zip(fft_A, fft_B):
C.append(a*b)
## 5. compute inverse dft of A*B and split the output into
## real and imaginary numbers.
reals, imags = dft.recursive_inverse_fft_split(C, wf=wf, error=error)
## 6. the degree of A and B is lenA-1. the degree of A*B is
## 2*(lenA-1) = 2*lenA - 2.
return reals[0:2*lenA-1], imags[0:2*lenA-1]
def convolve_poly(A, B, wf=dft.omega2, error=0):
## 1. ensure that coefficient arrays A and B are of the same length
lenA, lenB = len(A), len(B)
if lenA != lenB:
raise Exception('Coefficient arrays must be of the same length')
## 2. pad A and B until their lengths are an integral power of 2
padded_A = dft.pad_with_zeros(A)
padded_B = dft.pad_with_zeros(B)
## 3. pad A and B more so that their lengths are 2n, where n
## is the length of padded A
padded_A = pad_with_zeros_until_required_length(A, 2 * len(padded_A))
padded_B = pad_with_zeros_until_required_length(B, 2 * len(padded_A))
## 4. compute dft of padded A and B
fft_A = dft.recursive_fft(padded_A, wf=wf, error=error)
fft_B = dft.recursive_fft(padded_B, wf=wf, error=error)
## 5. compute pointwise multiplication of A and B
C = []
for a, b in zip(fft_A, fft_B):
C.append(a * b)
## 6. compute inverse dft and return the first 2*lenA-2 elements.
return dft.recursive_inverse_fft(C, wf=wf, error=error)[0:2 * lenA - 1]
def convolve_poly(A, B, wf=dft.omega2, error=0):
## 1. ensure that coefficient arrays A and B are of the same length
lenA, lenB = len(A), len(B)
if lenA != lenB:
raise Exception('Coefficient arrays must be of the same length')
## 2. pad A and B until their lengths are an integral power of 2
padded_A = dft.pad_with_zeros(A)
padded_B = dft.pad_with_zeros(B)
## 3. pad A and B more so that their lengths are 2n, where n
## is the length of padded A
padded_A = pad_with_zeros_until_required_length(A, 2*len(padded_A))
padded_B = pad_with_zeros_until_required_length(B, 2*len(padded_A))
## 4. compute dft of padded A and B
fft_A = dft.recursive_fft(padded_A, wf=wf, error=error)
fft_B = dft.recursive_fft(padded_B, wf=wf, error=error)
## 5. compute pointwise multiplication of A and B
C = []
for a, b in zip(fft_A, fft_B):
C.append(a*b)
## 6. compute inverse dft and return the first 2*lenA-2 elements.
return dft.recursive_inverse_fft(C, wf=wf, error=error)[0:2*lenA-1]
