def NumbaConv(h, M, xdtype):
L = len(h)
outlen = M + L - 1
xdtype = np.dtype(xdtype)
htype = numba.__getattribute__(str(h.dtype))
xtype = numba.__getattribute__(str(xdtype))
outdtype = np.result_type(h.dtype, xdtype)
outtype = numba.__getattribute__(str(outdtype))
#@jit(restype=outtype[::1], argtypes=[htype[::1], xtype[::1]])
@jit
def conv(h, x):
out = np.zeros(outlen, outdtype)
for m in range(M):
for l in range(L):
out[m + l] += h[l]*x[m]
return out
@filter_dec(h, M)
def numba_conv(x):
out = conv(h, x)
return out
return numba_conv
def NumbaFFTW(h, M, xdtype=np.complex_, powerof2=True):
L = len(h)
outlen = M + L - 1
nfft = outlen
if powerof2:
nfft = pow2(nfft)
outdtype = np.result_type(h.dtype, xdtype)
fftdtype = np.result_type(outdtype, np.complex64) # output is always complex, promote using smallest
# speed not critical here, just use numpy fft
# cast to outdtype so we use same type of fft as when transforming x
hpad = zero_pad(h, nfft).astype(outdtype)
if np.iscomplexobj(hpad):
H = np.fft.fft(hpad)
else:
H = np.fft.rfft(hpad)
H = (H / nfft).astype(fftdtype) # divide by nfft b/c FFTW's ifft does not do this
xpad = pyfftw.n_byte_align(np.zeros(nfft, outdtype), 16) # outdtype so same type fft as h->H
X = pyfftw.n_byte_align(np.zeros(len(H), fftdtype), 16) # len(H) b/c rfft may be used
xfft = pyfftw.FFTW(xpad, X, threads=_THREADS)
y = pyfftw.n_byte_align_empty(nfft, 16, outdtype)
ifft = pyfftw.FFTW(X, y, direction='FFTW_BACKWARD', threads=_THREADS)
xtype = numba.__getattribute__(str(np.dtype(xdtype)))
outtype = numba.__getattribute__(str(outdtype))
ffttype = numba.__getattribute__(str(fftdtype))
#@jit(restype=outtype[::1],
#argtypes=[outtype[::1], ffttype[::1], ffttype[::1], outtype[::1], xtype[::1]])
#def filt(xpad, X, H, y, x):
#xpad[:M] = x
#xfft.execute() # input in xpad, result in X
#X[:] = H*X
#ifft.execute() # input in X, result in y
#yc = y[:outlen].copy()
#return yc
#@filter_dec(h, M, nfft=nfft, H=H)
#def numba_fftw(x):
#return filt(xpad, X, H, y, x)
#@jit(argtypes=[xtype[::1]])
@jit
def numba_fftw(x):
xpad[:M] = x
xfft.execute() # input in xpad, result in X
X[:] = H*X # want expression that is optimized by numba but writes into X
ifft.execute() # input in X, result in y
yc = y[:outlen].copy()
return yc
numba_fftw = filter_dec(h, M, nfft=nfft, H=H)(numba_fftw)
return numba_fftw
def ShiftConvNumbaFFT(h, N, M, xdtype=np.complex_, powerof2=True):
# implements Doppler filter:
# y[n, p] = SUM_k (exp(2*pi*j*n*(k - (L-1))/N) * h[k]) * x[p - k]
# = SUM_k (exp(-2*pi*j*n*k/N) * s*[k]) * x[p - (L-1) + k]
L = len(h)
outlen = M + L - 1
nfft = outlen
if powerof2:
nfft = pow2(nfft)
dopplermat = np.exp(2*np.pi*1j*np.arange(N)[:, np.newaxis]*(np.arange(L) - (L - 1))/N)
dopplermat.astype(np.result_type(h.dtype, np.complex64)) # cast to complex type with precision of h
hbank = h*dopplermat
# speed not critical here, just use numpy fft
hbankpad = zero_pad(hbank, nfft)
H = np.fft.fft(hbankpad) / nfft # divide by nfft b/c FFTW's ifft does not do this
xcdtype = np.result_type(xdtype, np.complex64) # cast to complex type with precision of x
xpad = pyfftw.n_byte_align(np.zeros(nfft, xcdtype), 16)
X = pyfftw.n_byte_align(np.zeros(nfft, xcdtype), 16)
xfft = pyfftw.FFTW(xpad, X, threads=_THREADS)
ydtype = np.result_type(H.dtype, xcdtype)
Y = pyfftw.n_byte_align_empty(H.shape, 16, ydtype)
y = pyfftw.n_byte_align_empty(H.shape, 16, ydtype)
ifft = pyfftw.FFTW(Y, y, direction='FFTW_BACKWARD', threads=_THREADS)
xtype = numba.__getattribute__(str(np.dtype(xdtype)))
#htype = numba.__getattribute__(str(H.dtype))
#xctype = numba.__getattribute__(str(X.dtype))
#ytype = numba.__getattribute__(str(Y.dtype))
#@jit(argtypes=[htype[:, ::1], xctype[::1], ytype[:, ::1], xtype[::1]])
#def fun(H, X, Y, x):
#xpad[:M] = x
#xfft.execute() # input is xpad, output is X
#Y[:, :] = H*X # need expression optimized by numba but that writes into Y
#ifft.execute() # input is Y, output is y
#yc = np.array(y)[:, :outlen] # need a copy, which np.array provides
#return yc
#@dopplerbank_dec(h, N, M, nfft=nfft, H=H)
#def shiftconv_numba_fft(x):
#return fun(H, X, Y, x)
#@jit(argtypes=[xtype[::1]])
@jit
def shiftconv_numba_fft(x):
xpad[:M] = x
xfft.execute() # input is xpad, output is X
Y[:, :] = X*H # need expression optimized by numba but that writes into Y
ifft.execute() # input is Y, output is y
yc = np.array(y[:, :outlen]) # need a copy, which np.array provides
return yc
shiftconv_numba_fft = dopplerbank_dec(h, N, M, nfft=nfft, H=H)(shiftconv_numba_fft)
return shiftconv_numba_fft
def SweepSpectraNumba(h, N, M, xdtype=np.complex_):
# implements Doppler filter:
# y[n, p] = SUM_k exp(2*pi*j*n*(k - (L-1))/N) * (h[k] * x[p - k])
# = SUM_k exp(-2*pi*j*n*k/N) * (s*[k] * x[p - (L-1) + k])
L = len(h)
outlen = M + L - 1
# when N < L, still need to take FFT with nfft >= L so we don't lose data
# then subsample to get our N points that we desire
step = L // N + 1
nfft = N*step
hrev = h[::-1]
xpad = np.zeros(M + 2*(L - 1), xdtype) # x[0] at xpad[L - 1]
demodpad = np.zeros((outlen, nfft), np.result_type(xdtype, h.dtype, np.complex64))
demodpad = pyfftw.n_byte_align(demodpad, 16)
y = pyfftw.n_byte_align(np.zeros_like(demodpad), 16)
fft = pyfftw.FFTW(demodpad, y, threads=_THREADS)
xtype = numba.__getattribute__(str(np.dtype(xdtype)))
#@jit(argtypes=[xtype[::1]])
@jit
def sweepspectra_numba(x):
xpad[(L - 1):outlen] = x
for p in range(outlen):
demodpad[p, :L] = hrev*xpad[p:(p + L)]
fft.execute() # input is demodpad, output is y
yc = np.array(y[:, ::step].T) # we need a copy, which np.array provides
return yc
sweepspectra_numba = dopplerbank_dec(h, N, M)(sweepspectra_numba)
return sweepspectra_numba
def _make_numba_cubic_solver(dtype):
eps = slippy.CUBIC_EPS
s_dtype = str(dtype)
if not s_dtype.startswith("float"):
raise ValueError("can only make cubic solver for single and double floats")
def solve_cubic_numba_base(b, c, d, r1, r2, r3):
for i in range(len(b)):
if np.abs(d[i]) < eps:
# cancel and find remaining roots by quadratic formula
r1[i] = 0
diff = np.sqrt(b[i] * b[i] - 4 * c[i]) / 2
r2[i] = (-b[i]) / 2 + diff
r3[i] = (-b[i]) / 2 - diff
else:
# convert to depressed cubic
p = c[i] - b[i] ** 2 / 3
q = 2 * b[i] ** 3 / 27 - b[i] * c[i] / 3 + d[i]
if np.abs(p) < eps:
r1[i] = np.sign(-q) * np.abs(q) ** (1 / 3) - b[i] / 3
r2[i] = r1[i]
r3[i] = r1[i]
elif np.abs(q) < eps:
r3[i] = - b[i] / 3
if p < 0:
diff = np.sqrt(-p)
r2[i] = diff - b[i] / 3
r1[i] = - diff - b[i] / 3
else:
r1[i] = r3[i]
r2[i] = r3[i]
else:
e = q * q / 4 + p * p * p / 27
if np.abs(e) < eps:
r2[i] = -1.5 * q / p - b[i] / 3
r3[i] = 3 * q / p - b[i] / 3
f_prime2 = 3 * r2[i] ** 2 + 2 * b[i] * r2[i] + c[i]
f_prime3 = 3 * r3[i] ** 2 + 2 * b[i] * r3[i] + c[i]
if np.abs(f_prime2) < np.abs(f_prime3):
r1[i] = r2[i]
else:
r1[i] = r3[i]
elif e > 0:
u = -q / 2 - np.sqrt(e)
u = np.sign(u) * np.abs(u) ** (1 / 3)
r1[i] = u - p / (3 * u) - b[i] / 3
r2[i] = r1[i]
r3[i] = r1[i]
else:
u = 2 * np.sqrt(-p / 3)
t = np.arccos(3 * q / p / u) / 3
k = 2 * np.pi / 3
r1[i] = u * np.cos(t) - b[i] / 3
r2[i] = u * np.cos(t - k) - b[i] / 3
r3[i] = u * np.cos(t - 2 * k) - b[i] / 3
# sort the array
r1[i], r2[i], r3[i] = np.sort(np.array([r1[i], r2[i], r3[i]]))
numba_type = numba.__getattribute__(s_dtype)
raw_func = numba.guvectorize([(numba_type[:], numba_type[:], numba_type[:],
numba_type[:], numba_type[:], numba_type[:])],
"(n),(n),(n)->(n),(n),(n)",
nopython=True)(solve_cubic_numba_base)
def full_func(b, c, d):
r1 = np.zeros_like(b)
r2 = np.zeros_like(b)
r3 = np.zeros_like(b)
raw_func(b, c, d, r1, r2, r3)
return r1, r2, r3
return full_func