def _reset(self): self._p0 = sstruct([(k,v) for k,v in self._allitems() if k in self._free]) flat_p0_free = flatten(self._p0, include=self._free) self._np = flat_p0_free.size self._f0 = self.eval() self._scalar = not hasattr(self._f0, '__len__') flat_f0_free = flatten(self._f0) self._nf = flat_f0_free.size try: self.deriv(); raise Exception() except NoSubclassMethod: self._deriv = None except: self._deriv = sstruct() for k,v in self._allitems(): if k in self._free: self._deriv._setfield(k, v * 0.0) try: self.dderiv(); raise Exception() except NoSubclassMethod: self._dderiv = None except: self._dderiv = sstruct() for k,v in self._allitems(): if k in self._free: self._dderiv._setfield(k, v * 0.0) try: self.hessian(); raise Exception() except NoSubclassMethod: self._hessian = None except: siz = [self._np, self._np] self._hessian = numpy.matrix(siz, dtype=numpy.float64) # TODO(HHH): use of Hessians currently assumes scalar zero-order function output self.reset() # call developer's subclass method return flat_p0_free
def _reset(self):
self._p0 = sstruct([(k, v) for k, v in self._allitems()
if k in self._free])
flat_p0_free = flatten(self._p0, include=self._free)
self._np = flat_p0_free.size
self._f0 = self.eval()
self._scalar = not hasattr(self._f0, '__len__')
flat_f0_free = flatten(self._f0)
self._nf = flat_f0_free.size
try:
self.deriv()
raise Exception()
except NoSubclassMethod:
self._deriv = None
except:
self._deriv = sstruct()
for k, v in self._allitems():
if k in self._free: self._deriv._setfield(k, v * 0.0)
try:
self.dderiv()
raise Exception()
except NoSubclassMethod:
self._dderiv = None
except:
self._dderiv = sstruct()
for k, v in self._allitems():
if k in self._free: self._dderiv._setfield(k, v * 0.0)
try:
self.hessian()
raise Exception()
except NoSubclassMethod:
self._hessian = None
except:
siz = [self._np, self._np]
self._hessian = numpy.matrix(
siz, dtype=numpy.float64
) # TODO(HHH): use of Hessians currently assumes scalar zero-order function output
self.reset() # call developer's subclass method
return flat_p0_free
def chgrad(self, plot=False, **kwargs):
for k,v in kwargs.items():
self._setfield(k,v)
pflat = self._reset()
out = sstruct()
out.params = self._p0.copy()
out._setfield('f.exact', self._f(pflat, force1D=True))
out._setfield('df.exact', self._df(pflat, force2D=True))
out._setfield('df.approx', out.df.exact * numpy.nan)
try: out._setfield('ddf.exact', self._ddf(pflat, force2D=True))
except NoSubclassMethod: do_ddf = False
else: do_ddf = True; out._setfield('ddf.approx', out.ddf.exact * numpy.nan)
try: out._setfield('H.exact', self._H(pflat))
except NoSubclassMethod: do_hessian = False
else: do_hessian = True; out._setfield('H.approx', out.H.exact * numpy.nan)
fdelta = 1e-4
e = fdelta * abs(pflat)
e = numpy.fmax(1e-12, e)
keepgoing = (e > 0) # all True to start
rpt = 0
while keepgoing.any():
rpt += 1
for iparam in range(self._np):
mask = pflat * 0.0
mask.flat[iparam] = 0.5
p_below = pflat - e * mask
p_above = pflat + e * mask
f_below = self._f(p_below)
f_above = self._f(p_above)
adfj = (f_above - f_below) / e[iparam]
out.df.approx[:, iparam] = adfj # TODO(III): store data from multiple rpts?
if do_hessian or do_ddf:
df_below = self._df(p_below)
df_above = self._df(p_above)
addfj = (df_above - df_below) / e[iparam]
if do_ddf:
out.ddf.approx[:, iparam] = addfj[:, iparam] # TODO(III): store data from multiple rpts?
if do_hessian:
out.H.approx[:, iparam].flat = addfj.flat # TODO(III): store data from multiple rpts?
converged = True # TODO(III): could check for convergence here. currently, only one iteration is performed
if converged: keepgoing[iparam] = False
e[keepgoing] /= 2
unflatten(self, pflat, include=self._free)
self._reset()
out.plabels = ['p'+x for x in flatten(self, include=self._free, labels=True)]
out.flabels = ['f'+x for x in flatten(self.eval(), include=self._free, labels=True)]
fields = ['df', 'ddf', 'H']
for k in fields:
v = out._getfield(k, None)
if v == None: continue
v.abserr = abs(v.exact-v.approx)
v.maxabserr = v.abserr.max()
v.propabserr = v.abserr / numpy.fmax(abs(v.approx), 1e-13)
v.maxpropabserr = v.propabserr.max()
if plot:
import Plotting
pylab = Plotting.load_pylab()
fields = ['df', 'ddf', 'H']
labels = {'df':(out.flabels,out.plabels, 'd%s / d%s'),
'ddf':(out.flabels,out.plabels, 'd^2%s / d%s^2'),
'H':(out.plabels,out.plabels, 'df/(d%s)(d%s)'),
}
got = dict([(k,k in out._fields) for k in fields])
nplots = sum(got.values())
for i,k in enumerate(fields):
v = out._getfield(k, None)
if v == None: continue
if nplots > 1: pylab.subplot(1, nplots, i+1)
x = abs(v.approx.flatten())
y = v.abserr.flatten()
both0 = numpy.logical_and(x==0.0, y==0.0)
x[both0] = numpy.nan
y[both0] = numpy.nan
x[x==0.0] = 1e-13
y[y==0.0] = 1e-13
x = numpy.log10(x)
y = numpy.log10(y)
pylab.cla()
ax = pylab.gca()
ax.indicator, = pylab.plot([numpy.nan,numpy.nan],[numpy.nan,numpy.nan], color=(1,0,1), linewidth=2)
v.handles = pylab.plot(numpy.expand_dims(x,0), numpy.expand_dims(y,0), linestyle='None', marker='o', markersize=10, picker=5)
lab = labels[k]
for j,h in enumerate(v.handles):
subs = numpy.unravel_index(j, v.approx.shape)
h.txt = (lab[2]+'\nprop. abs. err. = %g') % (lab[0][subs[0]], lab[1][subs[1]], v.propabserr.flat[j])
ax.set_xlabel('log10 of abs approx value')
ax.set_ylabel('log10 of abs error')
ax.grid(True)
def onpick(evt):
h = evt.artist
x,y = h.get_xdata(), h.get_ydata()
ax = h.axes
ax.set_title(h.txt)
ind = ax.indicator
xl,yl = numpy.asarray(ax.get_xlim()),numpy.asarray(ax.get_ylim())
ind.set_xdata([x.mean(), xl.mean()])
ind.set_ydata([y.mean(), yl.max() + numpy.diff(yl) * 0.01])
ind.set_clip_on(False)
ind.set_color(h.get_color())
pylab.draw()
pylab.gcf().canvas.mpl_connect('pick_event', onpick)
pylab.draw()
return out
def chgrad(self, plot=False, **kwargs):
for k, v in kwargs.items():
self._setfield(k, v)
pflat = self._reset()
out = sstruct()
out.params = self._p0.copy()
out._setfield('f.exact', self._f(pflat, force1D=True))
out._setfield('df.exact', self._df(pflat, force2D=True))
out._setfield('df.approx', out.df.exact * numpy.nan)
try:
out._setfield('ddf.exact', self._ddf(pflat, force2D=True))
except NoSubclassMethod:
do_ddf = False
else:
do_ddf = True
out._setfield('ddf.approx', out.ddf.exact * numpy.nan)
try:
out._setfield('H.exact', self._H(pflat))
except NoSubclassMethod:
do_hessian = False
else:
do_hessian = True
out._setfield('H.approx', out.H.exact * numpy.nan)
fdelta = 1e-4
e = fdelta * abs(pflat)
e = numpy.fmax(1e-12, e)
keepgoing = (e > 0) # all True to start
rpt = 0
while keepgoing.any():
rpt += 1
for iparam in range(self._np):
mask = pflat * 0.0
mask.flat[iparam] = 0.5
p_below = pflat - e * mask
p_above = pflat + e * mask
f_below = self._f(p_below)
f_above = self._f(p_above)
adfj = (f_above - f_below) / e[iparam]
out.df.approx[:,
iparam] = adfj # TODO(III): store data from multiple rpts?
if do_hessian or do_ddf:
df_below = self._df(p_below)
df_above = self._df(p_above)
addfj = (df_above - df_below) / e[iparam]
if do_ddf:
out.ddf.approx[:,
iparam] = addfj[:,
iparam] # TODO(III): store data from multiple rpts?
if do_hessian:
out.H.approx[:,
iparam].flat = addfj.flat # TODO(III): store data from multiple rpts?
converged = True # TODO(III): could check for convergence here. currently, only one iteration is performed
if converged: keepgoing[iparam] = False
e[keepgoing] /= 2
unflatten(self, pflat, include=self._free)
self._reset()
out.plabels = [
'p' + x for x in flatten(self, include=self._free, labels=True)
]
out.flabels = [
'f' + x
for x in flatten(self.eval(), include=self._free, labels=True)
]
fields = ['df', 'ddf', 'H']
for k in fields:
v = out._getfield(k, None)
if v == None: continue
v.abserr = abs(v.exact - v.approx)
v.maxabserr = v.abserr.max()
v.propabserr = v.abserr / numpy.fmax(abs(v.approx), 1e-13)
v.maxpropabserr = v.propabserr.max()
if plot:
import Plotting
pylab = Plotting.load_pylab()
fields = ['df', 'ddf', 'H']
labels = {
'df': (out.flabels, out.plabels, 'd%s / d%s'),
'ddf': (out.flabels, out.plabels, 'd^2%s / d%s^2'),
'H': (out.plabels, out.plabels, 'df/(d%s)(d%s)'),
}
got = dict([(k, k in out._fields) for k in fields])
nplots = sum(got.values())
for i, k in enumerate(fields):
v = out._getfield(k, None)
if v == None: continue
if nplots > 1: pylab.subplot(1, nplots, i + 1)
x = abs(v.approx.flatten())
y = v.abserr.flatten()
both0 = numpy.logical_and(x == 0.0, y == 0.0)
x[both0] = numpy.nan
y[both0] = numpy.nan
x[x == 0.0] = 1e-13
y[y == 0.0] = 1e-13
x = numpy.log10(x)
y = numpy.log10(y)
pylab.cla()
ax = pylab.gca()
ax.indicator, = pylab.plot([numpy.nan, numpy.nan],
[numpy.nan, numpy.nan],
color=(1, 0, 1),
linewidth=2)
v.handles = pylab.plot(numpy.expand_dims(x, 0),
numpy.expand_dims(y, 0),
linestyle='None',
marker='o',
markersize=10,
picker=5)
lab = labels[k]
for j, h in enumerate(v.handles):
subs = numpy.unravel_index(j, v.approx.shape)
h.txt = (lab[2] + '\nprop. abs. err. = %g') % (
lab[0][subs[0]], lab[1][subs[1]], v.propabserr.flat[j])
ax.set_xlabel('log10 of abs approx value')
ax.set_ylabel('log10 of abs error')
ax.grid(True)
def onpick(evt):
h = evt.artist
x, y = h.get_xdata(), h.get_ydata()
ax = h.axes
ax.set_title(h.txt)
ind = ax.indicator
xl, yl = numpy.asarray(ax.get_xlim()), numpy.asarray(
ax.get_ylim())
ind.set_xdata([x.mean(), xl.mean()])
ind.set_ydata([y.mean(), yl.max() + numpy.diff(yl) * 0.01])
ind.set_clip_on(False)
ind.set_color(h.get_color())
pylab.draw()
pylab.gcf().canvas.mpl_connect('pick_event', onpick)
pylab.draw()
return out