def coeffmult(fc, gc):
"""Coefficient-Space multiplication of equal-length first-kind
Chebyshev series."""
Fc = np.append(2. * fc[:1], (fc[1:], fc[:0:-1]))
Gc = np.append(2. * gc[:1], (gc[1:], gc[:0:-1]))
ak = ifft(fft(Fc) * fft(Gc))
ak = np.append(ak[:1], ak[1:] + ak[:0:-1]) * .25
ak = ak[:fc.size]
inputcfs = np.append(fc, gc)
out = np.real(ak) if np.isreal(inputcfs).all() else ak
return out
def coeffmult(fc, gc):
"""Coefficient-Space multiplication of equal-length first-kind
Chebyshev series."""
Fc = np.append( 2.*fc[:1], (fc[1:], fc[:0:-1]) )
Gc = np.append( 2.*gc[:1], (gc[1:], gc[:0:-1]) )
ak = ifft( fft(Fc) * fft(Gc) )
ak = np.append( ak[:1], ak[1:] + ak[:0:-1] ) * .25
ak = ak[:fc.size]
inputcfs = np.append(fc, gc)
out = np.real(ak) if np.isreal(inputcfs).all() else ak
return out
def coeffs2vals2(coeffs):
"""Map first-kind Chebyshev polynomial coefficients to
function values at Chebyshev points of 2nd kind"""
n = coeffs.size
if n <= 1:
vals = coeffs
return vals
coeffs = coeffs.copy()
coeffs[1:n - 1] = .5 * coeffs[1:n - 1]
tmp = np.append(coeffs, coeffs[n - 2:0:-1])
if np.isreal(coeffs).all():
vals = fft(tmp)
vals = np.real(vals)
elif np.isreal(1j * coeffs).all():
vals = fft(np.imag(tmp))
vals = 1j * np.real(vals)
else:
vals = fft(tmp)
vals = vals[n - 1::-1]
return vals
def coeffs2vals2(coeffs):
"""Map first-kind Chebyshev polynomial coefficients to
function values at Chebyshev points of 2nd kind"""
n = coeffs.size
if n <= 1:
vals = coeffs
return vals
coeffs = coeffs.copy()
coeffs[1:n-1] = .5 * coeffs[1:n-1]
tmp = np.append( coeffs, coeffs[n-2:0:-1] )
if np.isreal(coeffs).all():
vals = fft(tmp)
vals = np.real(vals)
elif np.isreal(1j*coeffs).all():
vals = fft(np.imag(tmp))
vals = 1j * np.real(vals)
else:
vals = fft(tmp)
vals = vals[n-1::-1]
return vals