def oversamplingFilter(n, M, p = 2):
'''
Produce the nxn oversampling filter that is needed to exactly filter dyadic DRT etc.
This version returns values as multiplicative inverses (mod M) for use with the NTT
'''
gcd_table = np.zeros(n)
gcdInv_table = np.zeros(n)
gcd_table[0] = n + int(n)/p
gcdInv_table[0] = nt.minverse(gcd_table[0], M)
gcd_table[1] = 1
gcdInv_table[1] = nt.minverse(gcd_table[1], M)
for j in range(2,n):
u, v, gcd_table[j] = nt.extended_gcd( int(j), int(n) )
gcdInv_table[j] = nt.minverse(gcd_table[j], M)
filter = nt.zeros((n,n))
for j in range(0,n):
for k in range(0,n):
if gcd_table[j] < gcd_table[k]:
filter[j,k] = nt.integer(gcdInv_table[j])
else:
filter[j,k] = nt.integer(gcdInv_table[k])
return filter
def oversampling_1D(n, p = 2, norm = False):
'''
The 1D oversampling. All values are GCDs.
Use the filter versions to remove the oversampling.
'''
gcd_table = np.zeros(n)
gcd_table[0] = n + int(n)/p
gcd_table[1] = 1
for j in range(2,n):
u, v, gcd_table[j] = nt.extended_gcd( int(j), int(n) )
return gcd_table
def oversampling_1D_filter_Integer(n, M, p = 2, norm = False):
'''
The 1D filter for removing oversampling. All values are multiplicative inverses.
To apply this filter multiply with 1D NTT slice
'''
gcd_table = np.zeros(n)
gcdInv_table = nt.zeros(n)
inv = nt.integer(1)
if norm:
inv = nt.integer(nt.minverse(int(n), M))
gcd_table[0] = n + int(n)/p
gcdInv_table[0] = nt.integer(nt.minverse(gcd_table[0], M))
gcd_table[1] = 1
gcdInv_table[1] = nt.integer(nt.minverse(gcd_table[1], M))
for j in range(2,n):
u, v, gcd_table[j] = nt.extended_gcd( int(j), int(n) )
gcdInv_table[j] = (nt.integer(nt.minverse(gcd_table[j], M))*inv)%M
return gcdInv_table
def oversampling(n, p = 2):
'''
Produce the nxn oversampling filter that is needed to exactly filter dyadic DRT etc.
'''
gcd_table = np.zeros(n)
gcd_table[0] = n + n/p
gcd_table[1] = 1
for j in range(2,n):
u, v, gcd_table[j] = nt.extended_gcd( int(j), int(n) )
filter = np.zeros((n,n))
for j in range(0,n):
for k in range(0,n):
if gcd_table[j] < gcd_table[k]:
filter[j,k] = gcd_table[j]
else:
filter[j,k] = gcd_table[k]
return filter
def oversampling_1D_filter(n, p = 2, norm = False):
'''
The 1D filter for removing oversampling. All values are multiplicative inverses.
To apply this filter multiply with 1D FFT slice
'''
normValue = 1
if norm:
normValue = n
gcd_table = np.zeros(n)
gcdInv_table = np.zeros(n)
gcd_table[0] = n + int(n)/p
gcdInv_table[0] = 1.0/gcd_table[0]
gcd_table[1] = 1
gcdInv_table[1] = 1.0/gcd_table[1]
for j in range(2,n):
u, v, gcd_table[j] = nt.extended_gcd( int(j), int(n) )
gcdInv_table[j] = 1.0/(gcd_table[j]*normValue)
return gcdInv_table
