# Estimate SVD magnitude
# svLiEstNom_mag = FreqTrans.Sigma(I2 + LoEstNom)
svLoEstNom_mag = 1 / FreqTrans.Sigma(SoEstNom) # sigma(I + Lo) = 1 / sigma(So)
svLoEstNomMin_mag = np.min(svLoEstNom_mag, axis=0)
svLoEstUnc_mag = FreqTrans.Sigma(LoEstUnc) # Uncertain SVD magnitude
svLoEstUncMax_mag = np.max(svLoEstUnc_mag, axis=0) # Overly Conservative
cohLoEst_mag = LoEstCoh
cohLoEstMin = np.min(cohLoEst_mag, axis = (0, 1)) # Estimation Coherence
if True:
fig = 1
fig = FreqTrans.PlotSigma(freqLin_hz, svLoLinNomMin_mag, np.ones_like(freqLin_hz), svLoLinUncMax_mag, fig = fig, color = 'k', label = 'Linear')
fig = FreqTrans.PlotSigma(freq_hz[0], svLoEstNomMin_mag, cohLoEstMin, svLoEstUncMax_mag, marker='.', color = 'b', fig = fig, label = 'Estimate (MIMO)')
fig = FreqTrans.PlotSigma(freqLin_hz, (0.4) * np.ones_like(freqLin_hz), linestyle = '--', color = 'r', fig = fig, label = 'Critical Limit')
ax = fig.get_axes()
handles, labels = ax[0].get_legend_handles_labels()
handles = [handles[0], handles[3], handles[1], handles[4], handles[2]]
labels = [labels[0], labels[3], labels[1], labels[4], labels[2]]
ax[0].legend(handles, labels)
fig.suptitle('$L_o$ : ' + '$r_{Exc}$' + ' to ' + '$z$')
#%% Vector Margin Plots - Output Stability
vmLoLinNom_mag, vmLoLinUnc_mag, vmLoLinMin_mag = FreqTrans.VectorMargin(LoLinNom, LoLinUnc, typeUnc = 'circle')
vmLoEstNom_mag, vmLoEstUnc_mag, vmLoEstMin_mag = FreqTrans.VectorMargin(LoEstNom, LoEstUnc, typeUnc = 'circle')
svLaEstNom_mag = 1 / FreqTrans.Sigma(SaEstNom) # sv(I + La) = 1 / sv(Sa)
svLaEstNomMin_mag = np.min(svLaEstNom_mag, axis=0)
svLaEstUnc_mag = FreqTrans.Sigma(LaEstUnc)
svLaEstUncMax_mag = np.max(svLaEstUnc_mag, axis=0)
svLaEstLower_mag = svLaEstNomMin_mag - svLaEstUncMax_mag
LaEstCohMin = np.min(np.min(SaEstCoh, axis=0), axis=0)
if False:
fig = 20
# fig = FreqTrans.PlotSigma(freqLin_hz, svLaLinNom_mag, coher_nd = np.ones_like(freqLin_hz), fig = fig, color = 'k', label = 'Linear')
# fig = FreqTrans.PlotSigma(freqLin_hz, svLaLinNomMin_mag, svUnc_mag = svLaEstUncMax_mag, coher_nd = np.ones_like(freqLin_hz), fig = fig, color = 'k', label = 'Linear')
fig = FreqTrans.PlotSigma(freqLin_hz,
svLaLinNomMin_mag,
coher_nd=np.ones_like(freqLin_hz),
fig=fig,
color='k',
label='Linear')
# fig = FreqTrans.PlotSigma(freq_hz, svLaEstNom_mag, coher_nd = LaEstCohMin, color = 'b', fig = fig, label = 'Estimation (MIMO)')
fig = FreqTrans.PlotSigma(freq_hz[0],
svLaEstNomMin_mag,
svUnc_mag=svLaEstLower_mag,
coher_nd=LaEstCohMin,
color='b',
fig=fig,
label='Estimation with Uncertainty')
# fig = FreqTrans.PlotSigma(freqLin_hz, 0.4 * np.ones_like(freqLin_hz), color = 'r', linestyle = '--', fig = fig, label = 'Critical Limit')
ax = fig.get_axes()
ax[0].set_xlim(0, 10)
# ax[0].set_yscale('log')
ax[0].set_ylim(0, 2)
svTEstUncMax_mag = np.max(svTEstUnc_mag, axis=0) # Overly Conservative
cohTEst_mag = TEstCoh # Estimation Coherence
cohTEstMin = np.min(cohTEst_mag, axis = (0, 1))
# Sampled Systems
svTEstSamp_mag = np.zeros((numOut, nFreq, nSamp), dtype='float')
for iSamp in range(nSamp):
svTEstSamp_mag[..., iSamp] = FreqTrans.Sigma(TEstSamp[..., iSamp])
svTEstSampMin_mag = np.min(svTEstSamp_mag, axis = 0)
if True:
fig = 10
fig = FreqTrans.PlotSigma(freqLin_hz, svTLinNomMin_mag, svUnc_mag = svTLinUncMax_mag, coher_nd = cohTLinMin, fig = fig, color = 'k', label = 'Linear')
fig = FreqTrans.PlotSigma(freq_hz[0], svTEstNomMin_mag, svUnc_mag = svTEstUncMax_mag, coher_nd = cohTEstMin, marker='.', color = 'r', fig = fig, label = 'Estimate (MIMO)')
for iSamp in range(nSamp):
fig = FreqTrans.PlotSigma(freq_hz[0], svTEstSampMin_mag[..., iSamp], svUnc_mag = None, coher_nd = None, marker='.', color = 'gray', linestyle='None', fig = fig, label = 'Sampled (MIMO)')
ax = fig.get_axes()
handles, labels = ax[0].get_legend_handles_labels()
handles = [handles[0], handles[2], handles[1], handles[3]]
labels = [labels[0], labels[2], labels[1], labels[3]]
ax[0].legend(handles, labels)
#%% Vector Margin Plots
vmTLinNom_mag, vmTLinUnc_mag, vmTLinMin_mag = FreqTrans.VectorMargin(TLinNom, TLinUnc, typeUnc = 'circle')
vmTEstNom_mag, vmTEstUnc_mag, vmTEstMin_mag = FreqTrans.VectorMargin(TEstNom, TEstUnc, typeUnc = 'circle')
20 * np.log10(P_N_mag))
fig.suptitle(oDataSegs[iSeg]['Desc'] + ': Spectrogram Null - ' +
sigFbList[iSgnlOut])
#%% Sigma Plot
fig = None
for iSeg in range(0, len(oDataSegs)):
Cmin = np.min(np.min(C[iSeg], axis=0), axis=0)
sNomMin = np.min(sNom[iSeg], axis=0)
sCritMin = np.min(sUnc[iSeg], axis=0)
sNomMinErr = sNomMin - sCritMin
fig = FreqTrans.PlotSigma(freq_hz[0],
sNomMin,
err=sNomMinErr,
coher_nd=Cmin,
fig=fig,
fmt=rtsmSegList[iSeg]['fmt'] + '*-',
label=oDataSegs[iSeg]['Desc'])
fig = FreqTrans.PlotSigma(freq_hz[0],
0.4 * np.ones_like(freq_hz[0]),
fmt='--r',
fig=fig)
ax = fig.get_axes()
ax[0].set_xlim(0, 10)
ax[0].set_ylim(0, 1)
#%% Disk Margin Plots
inPlot = sigExcList # Elements of sigExcList
gain_mag, phase_deg = FreqTrans.GainPhase(T,
magUnit='mag',
phaseUnit='deg',
unwrap=True)
rCritNom_mag, _, _ = FreqTrans.DistCrit(T, typeUnc='ellipse')
#rCritNom_mag, rCritUnc_mag, rCrit_mag = FreqTrans.DistCrit(T, TUnc, typeUnc = 'ellipse')
#rCritNom_mag, rCritUnc_mag, rCrit_mag, pCont_mag = FreqTrans.DistCritEllipse(T, TUnc) # Returns closest approach points
#%% Sigma Plot
Cmin = np.min(np.min(C, axis=0), axis=0)
sigmaNom_magMin = np.min(sigmaNom_mag, axis=0)
fig = 20
fig = FreqTrans.PlotSigma(freqLin_hz,
sigmaLin_mag,
coher_nd=np.ones_like(freqLin_hz),
fig=fig,
fmt='k',
label='Linear')
fig = FreqTrans.PlotSigma(freq_hz,
sigmaNom_mag,
coher_nd=Cmin,
fmt='bo',
fig=fig,
label='Excitation Nominal')
fig = FreqTrans.PlotSigma(freq_hz[0],
0.4 * np.ones_like(freq_hz[0]),
fmt='--r',
fig=fig,
label='Critical Limit')
ax = fig.get_axes()
ax[0].set_xlim(0, 10)
cohLaEst = LaEstCohList[iSeg]
# cohLaEstMin = np.min(cohLaEst, axis = (0,1))
cohLaEstMin = np.mean(cohLaEst, axis=(0, 1))
svNom = svLaEstNomList[iSeg]
svNomMin = np.min(svNom, axis=0)
svUnc = svLaEstUncList[iSeg]
svUncMax = np.max(svUnc, axis=0)
svUncLower = svNomMin - svUncMax
svUncLower[svUncLower < 0] = svNomMin[svUncLower < 0]
fig = FreqTrans.PlotSigma(freq_hz[0],
svNomMin,
svUnc_mag=svUncLower,
coher_nd=cohLaEstMin,
fig=fig,
color=rtsmSegList[iSeg]['color'],
linestyle='-',
label=oDataSegs[iSeg]['Desc'])
fig = FreqTrans.PlotSigma(freq_hz[0],
0.4 * np.ones_like(freq_hz[0]),
color='r',
linestyle='--',
fig=fig)
ax = fig.get_axes()
ax[0].set_xlim(0, 10)
ax[0].set_ylim(0, 1)
#%% Vector Margin Plots
# rCritLiEstNom_mag, _, _ = FreqTrans.DistCrit(LiEstNomList[iSeg], typeUnc = 'ellipse')
rCritLiEstNom_mag, _, _ = FreqTrans.DistCritCirc(LiEstNomList[iSeg])
rCritLiEstNomList_mag.append(rCritLiEstNom_mag)
#%% Sigma Plot
fig = None
for iSeg in range(0, len(oDataSegs)):
Cmin = np.min(np.min(LiEstCohList[iSeg], axis=0), axis=0)
sNomMin = np.min(svLiEstNomList[iSeg], axis=0)
fig = FreqTrans.PlotSigma(freq_hz[0],
svLiEstNomList[iSeg],
coher_nd=Cmin,
fig=fig,
color=rtsmSegList[iSeg]['color'],
linestyle='-',
label=oDataSegs[iSeg]['Desc'])
fig = FreqTrans.PlotSigma(freq_hz[0],
0.4 * np.ones_like(freq_hz[0]),
color='r',
linestyle='--',
fig=fig)
ax = fig.get_axes()
ax[0].set_xlim(0, 10)
# ax[0].set_ylim(0, 1)
#%% Disk Margin Plots
