def vals2coeffs2(vals):
"""Map function values at Chebyshev points of 2nd kind to
first-kind Chebyshev polynomial coefficients"""
n = vals.size
if n <= 1:
coeffs = vals
return coeffs
tmp = np.append(vals[::-1], vals[1:-1])
if np.isreal(vals).all():
coeffs = ifft(tmp)
coeffs = np.real(coeffs)
elif np.isreal(1j * vals).all():
coeffs = ifft(np.imag(tmp))
coeffs = 1j * np.real(coeffs)
else:
coeffs = ifft(tmp)
coeffs = coeffs[:n]
coeffs[1:n - 1] = 2 * coeffs[1:n - 1]
return coeffs
def vals2coeffs2(vals):
"""Map function values at Chebyshev points of 2nd kind to
first-kind Chebyshev polynomial coefficients"""
n = vals.size
if n <= 1:
coeffs = vals
return coeffs
tmp = np.append( vals[::-1], vals[1:-1] )
if np.isreal(vals).all():
coeffs = ifft(tmp)
coeffs = np.real(coeffs)
elif np.isreal( 1j*vals ).all():
coeffs = ifft(np.imag(tmp))
coeffs = 1j * np.real(coeffs)
else:
coeffs = ifft(tmp)
coeffs = coeffs[:n]
coeffs[1:n-1] = 2*coeffs[1:n-1]
return coeffs
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