def test_derivatives():
x, y, vary = test_dat(multichannel=True)
# ======================= #
# xd = _np.linspace(0, 15, 100)
# _plt.plot(x, y, "o")
# p , e = curve_fit(_ms.piecewise_2line, x, y)
# _plt.plot(xd, _ms.piecewise_2line(xd, *p))
# from model_spec import model_chieff as fmodel
#
# mn = 1 # model_number
# np = 4 # npoly
# yd, gd, info = fmodel(af=None, XX=xd, model_number=mn, npoly=np)
# p0 = info.af
#
# p, e = fit_leastsq(p0, x, y, fmodel, (mn, np, 1) )
# _plt.plot(xd, fmodel(*p, XX=xd, model_number=mn, npoly=np, nargout=1) )
# yxp, yxvp, dydxp, vardydxp = spline_bs(x, y, vary, x, nmonti=30000, func="pchip")
# yxp, yxvp, dydxp, vardydxp = spline_bs(x, y, vary, x, nmonti=30000, func="pchip")
# yxp, yxvp, dydxp, vardydxp = spline_bs(x, y, vary, x, nmonti=300, func="spline")
dydx, vardydx = deriv_bsgaussian(x, y, vary, axis=0, nmonti=300,
sigma=0.8, mode='nearest')
yxp, yxvp = deriv_bsgaussian(x, y, vary, axis=0, nmonti=300,
sigma=0.8, mode='nearest', derivorder=0)
_, _, yx, yxv = _ut.trapz_var(x, dydx, None, vardydx)
yx += (y[0] - _ut.interp(x, yx, ei=None, xo=x[0]))
# ==== #
_plt.figure()
ax1 = _plt.subplot(2,1,1)
ax1.plot(x, y, "ko")
# Integrals
ax1.plot(x, yx, 'k-',
x, yx+_np.sqrt(yxv), 'k--',
x, yx-_np.sqrt(yxv), 'k--')
ax1.plot(x, yxp, 'g-',
x, yxp+_np.sqrt(yxvp), 'g--',
x, yxp-_np.sqrt(yxvp), 'g--')
# Derivatives
ax2 = _plt.subplot(2,1,2, sharex=ax1)
ax2.plot(x, dydx, 'k-',
x, dydx+_np.sqrt(vardydx), 'k--',
x, dydx-_np.sqrt(vardydx), 'k--')
def upsample(u_t, Fs, Fs_new, plotit=False):
# Upsample a signal to a higher sampling rate
# Use cubic interpolation to increase the sampling rate
nt = len(u_t)
tt = _np.arange(0, nt, 1) / Fs
ti = _np.arange(tt[0], tt[-1], 1 / Fs_new)
# _ut.interp(xi,yi,ei,xo)
u_n = _ut.interp(tt, u_t, ei=None,
xo=ti) # TODO!: Add quadratic interpolation
# uinterp = interp1d(tt, u_t, kind='cubic', axis=0)
# u_n = uinterp(ti)
return u_n
def downsample(u_t, Fs, Fs_new, plotit=False):
"""
The proper way to downsample a signal.
First low-pass filter the signal
Interpolate / Decimate the signal down to the new sampling frequency
"""
tau = 2 / Fs_new
nt = len(u_t)
tt = _np.arange(0, nt, 1) / Fs
# tt = tt.reshape(nt, 1)
# tt = (_np.arange(0, 1/Fs, nt)).reshape(nt, 1)
try:
nch = _np.size(u_t, axis=1)
except:
nch = 1
u_t = u_t.reshape(nt, nch)
# end try
# ----------- #
#2nd order LPF gets converted to a 4th order LPF by filtfilt
lowpass_n, lowpass_d = _dsp.butter(2, 2.0 / (Fs * tau), btype='low')
if plotit:
# ------- #
#Calculate the frequency response of the lowpass filter,
w, h = _dsp.freqz(lowpass_n, lowpass_d, worN=12000) #
#Convert to frequency vector from rad/sample
w = (Fs / (2.0 * _np.pi)) * w
# ------- #
_plt.figure(num=3951)
# _fig.clf()
_ax1 = _plt.subplot(3, 1, 1)
_ax1.plot(tt, u_t, 'k')
_ax1.set_ylabel('Signal', color='k')
_ax1.set_xlabel('t [s]')
_ax2 = _plt.subplot(3, 1, 2)
_ax2.plot(w, 20 * _np.log10(abs(h)), 'b')
_ax2.plot(1.0 / tau, 0.5 * _np.sqrt(2), 'ko')
_ax2.set_ylabel('|LPF| [dB]', color='b')
_ax2.set_xlabel('Frequency [Hz]')
_ax2.set_title('Digital LPF frequency response (Stage 1)')
_plt.xscale('log')
_plt.grid(which='both', axis='both')
_plt.axvline(1.0 / tau, color='k')
_plt.grid()
_plt.axis('tight')
# endif plotit
# nskip = int(_np.round(Fs/Fs_new))
# ti = tt[0:nt:nskip]
ti = _np.arange(0, nt / Fs, 1 / Fs_new)
u_n = _np.zeros((len(ti), nch), dtype=_np.float64)
for ii in range(nch):
# (Non-Causal) LPF
u_t[:, ii] = _dsp.filtfilt(lowpass_n, lowpass_d, u_t[:, ii])
# _ut.interp(xi,yi,ei,xo)
u_n[:, ii] = _ut.interp(tt, u_t[:, ii], ei=None, xo=ti)
# uinterp = interp1d(tt, u_t[:, ii], kind='cubic', axis=0)
# u_n[:, ii] = uinterp(ti)
#endif
if plotit:
_ax1.plot(ti, u_n, 'b-')
_ax3 = _plt.subplot(3, 1, 3, sharex=_ax1)
_ax3.plot(tt, u_t, 'k')
_ax3.set_ylabel('Filt. Signal', color='k')
_ax3.set_xlabel('t [s]')
# _plt.show(hfig, block=False)
_plt.draw()
# _plt.show()
# endif plotit
return u_n
def test_derivatives():
x, y, vary = test_dat(multichannel=True)
# ======================= #
dydx0, vardydx0 = findiff1d(x, y, vary, order=1)
dydx2, vardydx2 = findiff1d(x, y, vary, order=2)
dydx4, vardydx4 = findiff1d(x, y, vary, order=4)
#
ndydx0, nvardydx0 = findiffnp(x, y, vary, order=1)
ndydx2, nvardydx2 = findiffnp(x, y, vary, order=2)
dydx5, vardydx5 = findiff1dr(x, y, vary)
# integrate derivative and compare to source
_, _, yx0, yxv0 = _ut.trapz_var(x, dydx0, None, vardydx0)
yx0 += (y[0] - _ut.interp(x, yx0, ei=None, xo=x[0]))
_, _, nyx0, nyxv0 = _ut.trapz_var(x, ndydx0, None, nvardydx0)
nyx0 += (y[0] - _ut.interp(x, nyx0, ei=None, xo=x[0]))
# 2nd order
_, _, yx2, yxv2 = _ut.trapz_var(x, dydx2, None, vardydx2)
# _, _, yx2, yxv2 = _ut.trapz_var(x, yx2, None, yxv2)
yx2 += (y[0] - _ut.interp(x, yx2, ei=None, xo=x[0]))
_, _, nyx2, nyxv2 = _ut.trapz_var(x, ndydx2, None, nvardydx2)
# _, _, nyx2, nyxv2 = _ut.trapz_var(x, nyx2, None, nyxv2)
nyx2 += (y[0] - _ut.interp(x, nyx2, ei=None, xo=x[0]))
# 4th order
_, _, yx4, yxv4 = _ut.trapz_var(x, dydx4, None, vardydx4)
yx4 += (y[0] - _ut.interp(x, yx4, ei=None, xo=x[0]))
# Cylinrdical
_, _, yx5, yxv5 = _ut.trapz_var(x, dydx5, None, vardydx5)
yx5 += (y[0] - _ut.interp(x, yx5, ei=None, xo=x[0]))
# ==== #
_plt.figure()
ax1 = _plt.subplot(2, 1, 1)
ax1.plot(x, y, "ko")
# Integrals
ax1.plot(x, yx0, 'r-', x, yx0 + _np.sqrt(yxv0), 'r--', x,
yx0 - _np.sqrt(yxv0), 'r--')
ax1.plot(x, nyx0, 'b-', x, nyx0 + _np.sqrt(nyxv0), 'b--', x,
nyx0 - _np.sqrt(nyxv0), 'b--')
ax1.plot(x, yx2, 'g-', x, yx2 + _np.sqrt(yxv2), 'g--', x,
yx2 - _np.sqrt(yxv2), 'g--')
ax1.plot(x, nyx2, 'm-', x, nyx2 + _np.sqrt(nyxv2), 'm--', x,
nyx2 - _np.sqrt(nyxv2), 'm--')
ax1.plot(x, yx4, 'y-', x, yx4 + _np.sqrt(yxv4), 'y--', x,
yx4 - _np.sqrt(yxv4), 'y--')
ax1.plot(x, yx5, 'g.-', x, yx5 + _np.sqrt(yxv5), 'g.-', x,
yx5 - _np.sqrt(yxv5), 'g.-')
# Derivatives
ax2 = _plt.subplot(2, 1, 2)
ax2.plot(x, dydx0, 'r-', x, dydx0 + _np.sqrt(vardydx0), 'r--', x,
dydx0 - _np.sqrt(vardydx0), 'r--')
ax2.plot(x, ndydx0, 'b-', x, ndydx0 + _np.sqrt(nvardydx0), 'b--', x,
ndydx0 - _np.sqrt(nvardydx0), 'b--')
ax2.plot(x, dydx2, 'g-', x, dydx2 + _np.sqrt(vardydx2), 'g--', x,
dydx2 - _np.sqrt(vardydx2), 'g--')
ax2.plot(x, ndydx2, 'm-', x, ndydx2 + _np.sqrt(nvardydx2), 'm--', x,
ndydx2 - _np.sqrt(nvardydx2), 'm--')
ax2.plot(x, dydx4, 'y-', x, dydx4 + _np.sqrt(vardydx4), 'y--', x,
dydx4 - _np.sqrt(vardydx4), 'y--')
ax2.plot(x, dydx5, 'g.-', x, dydx5 + _np.sqrt(vardydx5), 'g.-', x,
dydx5 - _np.sqrt(vardydx5), 'g.-')
def fit_profile(roa, ne, varne, rvec, loggradient=True, derivfunc=None):
if derivfunc is None: derivfunc = findiffnp # endif
# ================= #
# Preconditioning #
# ================= #
xfit = _ut.cylsym_odd(roa)
if loggradient:
yfit = _ut.cylsym_even(_np.log(ne))
vfit = _ut.cylsym_even(varne / (ne**2.0))
else:
yfit = _ut.cylsym_even(ne)
vfit = _ut.cylsym_even(varne)
# endif
ne = _np.atleast_2d(ne)
roa = _np.atleast_2d(roa)
rvec = _np.atleast_2d(rvec)
xfit = _np.atleast_2d(xfit)
yfit = _np.atleast_2d(yfit)
vfit = _np.atleast_2d(vfit)
if _np.size(ne, axis=0) == 1: ne = ne.T # endif
if _np.size(roa, axis=0) == 1: roa = roa.T # endif
if _np.size(rvec, axis=0) == 1: rvec = rvec.T # endif
if _np.size(xfit, axis=0) == 1: xfit = xfit.T # endif
if _np.size(yfit, axis=0) == 1: yfit = yfit.T # endif
if _np.size(vfit, axis=0) == 1: vfit = vfit.T # endif
ysh = _np.shape(yfit)
if _np.shape(yfit) != _np.shape(xfit):
xfit = _np.tile(xfit, ysh[1])
if _np.size(rvec, axis=1) != _np.size(yfit, axis=1):
rvec = _np.tile(rvec, ysh[1])
if _np.size(roa, axis=1) != _np.size(ne, axis=1):
roa = _np.tile(roa, ysh[1])
# endif
# =============== #
dyfdr = _np.zeros((len(rvec), ysh[1]), dtype=_np.float64)
vardyfdr = _np.zeros_like(dyfdr)
yf = _np.zeros_like(dyfdr)
varyf = _np.zeros_like(vardyfdr)
for ii in range(_np.size(dyfdr, axis=1)):
# if ii == 1:
# print('what')
# # endif
dydr, vardydr = derivfunc(xfit[:, ii], yfit[:, ii], vfit[:, ii])
# dydr, vardydr = deriv_bsgaussian(xfit[:,ii], yfit[:,ii], vfit[:,ii])
dyfdr[:, ii], vardyfdr[:, ii] = _ut.interp(xfit[:, ii], dydr,
_np.sqrt(vardydr), rvec[:,
ii])
_, _, yf[:, ii], varyf[:, ii] = _ut.trapz_var(rvec[:, ii],
dyfdr[:, ii],
None,
vardyfdr[:, ii],
dim=0)
yf[:, ii] += (ne[0, ii] -
_ut.interp(rvec[:, ii], yf[:, ii], None, roa[0, ii]))
# endfor
if _np.size(yf, axis=1) == 1:
yf = yf.reshape(len(rvec), )
dyfdr = dyfdr.reshape(len(rvec), )
varyf = varyf.reshape(len(rvec), )
vardyfdr = vardyfdr.reshape(len(rvec), )
# end if
return yf, dyfdr, varyf, vardyfdr
def interp_profile(roa, ne, varne, rvec, loggradient=True, **kwargs):
# ================= #
# Preconditioning #
# ================= #
roa = roa.copy()
ne = ne.copy()
varne = varne.copy()
rvec = rvec.copy()
if roa[0] == 0.0:
xfit = _np.concatenate((-_np.flipud(roa), roa[1:]))
yfit = _np.concatenate((_np.flipud(ne), ne[1:]))
vfit = _np.concatenate((_np.flipud(varne), varne[1:]))
else:
xfit = _ut.cylsym_odd(roa)
yfit = _ut.cylsym_even(ne)
vfit = _ut.cylsym_even(varne)
# end if
if loggradient:
yfit = _np.log(ne)
vfit = varne / (ne**2.0)
# endif
ne = _np.atleast_2d(ne)
roa = _np.atleast_2d(roa)
rvec = _np.atleast_2d(rvec)
xfit = _np.atleast_2d(xfit)
yfit = _np.atleast_2d(yfit)
vfit = _np.atleast_2d(vfit)
if _np.size(ne, axis=0) == 1: ne = ne.T # endif
if _np.size(roa, axis=0) == 1: roa = roa.T # endif
if _np.size(rvec, axis=0) == 1: rvec = rvec.T # endif
if _np.size(xfit, axis=0) == 1: xfit = xfit.T # endif
if _np.size(yfit, axis=0) == 1: yfit = yfit.T # endif
if _np.size(vfit, axis=0) == 1: vfit = vfit.T # endif
ysh = _np.shape(yfit)
if _np.shape(yfit) != _np.shape(xfit):
xfit = _np.tile(xfit, ysh[1])
if _np.size(rvec, axis=1) != _np.size(yfit, axis=1):
rvec = _np.tile(rvec, ysh[1])
if _np.size(roa, axis=1) != _np.size(ne, axis=1):
roa = _np.tile(roa, ysh[1])
# endif
# =============== #
dyfdr = _np.zeros((len(rvec), ysh[1]), dtype=_np.float64)
vardyfdr = _np.zeros_like(dyfdr)
yf = _np.zeros_like(dyfdr)
varyf = _np.zeros_like(vardyfdr)
for ii in range(_np.size(dyfdr, axis=1)):
y, vy = deriv_bsgaussian(xfit[:, ii],
yfit[:, ii],
vfit[:, ii],
derivorder=0,
**kwargs)
dydr, vardydr = deriv_bsgaussian(xfit[:, ii],
yfit[:, ii],
vfit[:, ii],
derivorder=1,
**kwargs)
yf[:, ii], varyf[:, ii] = _ut.interp(xfit[:, ii], y, _np.sqrt(vy),
rvec[:, ii])
dyfdr[:, ii], vardyfdr[:, ii] = _ut.interp(xfit[:, ii], dydr,
_np.sqrt(vardydr), rvec[:,
ii])
# _, _, yf[:,ii], varyf[:,ii] = _ut.trapz_var1d(rvec[:,ii], dyfdr[:,ii], None, vardyfdr[:,ii])
## _, _, yf[:,ii], varyf[:,ii] = _ut.trapz_var(rvec[:,ii], dyfdr[:,ii], None, vardyfdr[:,ii], dim=0)
#
# yf[:,ii] += (ne[0,ii]-_ut.interp(rvec[:,ii], yf[:,ii], None, roa[0,ii]))
# endfor
if _np.size(yf, axis=1) == 1:
yf = yf.reshape(len(rvec), )
dyfdr = dyfdr.reshape(len(rvec), )
varyf = varyf.reshape(len(rvec), )
vardyfdr = vardyfdr.reshape(len(rvec), )
# end if
return yf, dyfdr, varyf, vardyfdr