def get_adc_response(self):
"""Returns sky and ref splines of response"""
import scipy.interpolate.fitpack as fit
sys.modules['__main__'].LFI_response = LFI_response
try:
resp = cPickle.load(open(os.path.join(private.ADC['folder'], "%s_LFI_response.pic" % self.cdstag.lower())))
except exceptions.IOError:
l.warning('NO ADC response for %s' % self.tag)
return fit.splrep(resp.sky_volt_out,resp.sky_volt_in,s=0.0), fit.splrep(resp.load_volt_out,resp.load_volt_in,s=0.0)
def test_cache_argument(self):
x, y = range(5), range(5, 10)
splrep_cache = {
't': array([], float),
'wrk': array([], float),
'iwrk': array([], intc)
}
splrep(x, y, task=0, cache=splrep_cache)
splrep(x, y, task=1, cache=splrep_cache)
def _loss(params, beams, x_nodes):
import time
from scipy.interpolate.fitpack import splev, splrep
import pysynphot as S
### Spline continuum + gaussian line
# l0 = 6563.*(1+params[1])
# if (l0 < 1.12e4) | (l0 > 1.63e4):
# l0 = 1.e4
#
# line = S.GaussianSource(params[2], l0, 10)
tck = splrep(x_nodes, params, k=3, s=0)
xcon = np.arange(0.9e4,1.8e4,0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True)#+line
lnprob = 0
dof = 0
for key in beams.keys():
beam = beams[key]
modelf = beam.compute_model(beam.clip_thumb, xspec=spec.wave, yspec=spec.flux, in_place=False)
lnprob += np.sum(((beam.cutout_scif-modelf)**2/beam.cutout_varf)[beam.cutout_maskf])
dof += beam.cutout_maskf.sum()
print params, lnprob, lnprob/(dof-len(params))
#time.sleep(0.2)
return lnprob
def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1 = a + (b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v,v1 = f(x),f(x1)
put(" u = %s N = %d" % (repr(round(dx,3)),N))
put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep " % (f(0,None)))
for k in range(1,6):
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
tck = splrep(x,v,s=s,per=per,k=k)
uv = splev(dx,tckp)
err1 = abs(uv[1]-f(uv[0]))
err2 = abs(splev(uv[0],tck)-f(uv[0]))
assert_(err1 < 1e-2)
assert_(err2 < 1e-2)
put(" %d : %s %.1e %.1e" %
(k,repr([round(z,3) for z in uv]),
err1,
err2))
put("Derivatives of parametric cubic spline at u (first function):")
k = 3
tckp,u = splprep([x,v],s=s,per=per,k=k,nest=-1)
for d in range(1,k+1):
uv = splev(dx,tckp,d)
put(" %s " % (repr(uv[0])))
def _loss(params, beams, x_nodes):
import time
from scipy.interpolate.fitpack import splev, splrep
import pysynphot as S
### Spline continuum + gaussian line
# l0 = 6563.*(1+params[1])
# if (l0 < 1.12e4) | (l0 > 1.63e4):
# l0 = 1.e4
#
# line = S.GaussianSource(params[2], l0, 10)
tck = splrep(x_nodes, params, k=3, s=0)
xcon = np.arange(0.9e4, 1.8e4, 0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True) #+line
lnprob = 0
dof = 0
for key in beams.keys():
beam = beams[key]
modelf = beam.compute_model(beam.clip_thumb,
xspec=spec.wave,
yspec=spec.flux,
in_place=False)
lnprob += np.sum(((beam.cutout_scif - modelf)**2 /
beam.cutout_varf)[beam.cutout_maskf])
dof += beam.cutout_maskf.sum()
print params, lnprob, lnprob / (dof - len(params))
#time.sleep(0.2)
return lnprob
def check_3(self,
f=f1,
per=0,
s=0,
a=0,
b=2 * pi,
N=20,
xb=None,
xe=None,
ia=0,
ib=2 * pi,
dx=0.2 * pi):
if xb is None: xb = a
if xe is None: xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
nk = []
put(" k : Roots of s(x) approx %s x in [%s,%s]:"%\
(f(None),`round(a,3)`,`round(b,3)`))
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
roots = sproot(tck)
if k == 3:
assert_allclose(roots, pi * array([1, 2, 3, 4]), rtol=1e-3)
put(' %d : %s' % (k, ` roots.tolist() `))
def check_3(self,
f=f1,
per=0,
s=0,
a=0,
b=2 * pi,
N=20,
xb=None,
xe=None,
ia=0,
ib=2 * pi,
dx=0.2 * pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
put(" k : Roots of s(x) approx %s x in [%s,%s]:" %
(f(None), repr(round(a, 3)), repr(round(b, 3))))
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
if k == 3:
roots = sproot(tck)
assert_allclose(splev(roots, tck), 0, atol=1e-10, rtol=1e-10)
assert_allclose(roots, pi * array([1, 2, 3, 4]), rtol=1e-3)
put(' %d : %s' % (k, repr(roots.tolist())))
else:
assert_raises(ValueError, sproot, tck)
def __init__(self, knots_x, knots_y, n_points):
self.knots_x = knots_x
self.knots_y = knots_y
tck = splrep(knots_x, knots_y)
self.spline_x = np.linspace(knots_x[0], knots_x[-1], n_points)
self.spline_y = splev(self.spline_x, tck)
def check_4(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None: xb=a
if xe is None: xe=b
x=a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
x1=a+(b-a)*arange(1,N,dtype=float)/float(N-1) # middle points of the nodes
v,v1=f(x),f(x1)
nk=[]
put(" u = %s N = %d"%(repr(round(dx,3)),N))
put(" k : [x(u), %s(x(u))] Error of splprep Error of splrep "%(f(0,None)))
for k in range(1,6):
tckp,u=splprep([x,v],s=s,per=per,k=k,nest=-1)
tck=splrep(x,v,s=s,per=per,k=k)
uv=splev(dx,tckp)
err1 = abs(uv[1]-f(uv[0]))
err2 = abs(splev(uv[0],tck)-f(uv[0]))
assert_(err1 < 1e-2)
assert_(err2 < 1e-2)
put(" %d : %s %.1e %.1e"%\
(k,repr([round(z,3) for z in uv]),
err1,
err2))
put("Derivatives of parametric cubic spline at u (first function):")
k=3
tckp,u=splprep([x,v],s=s,per=per,k=k,nest=-1)
for d in range(1,k+1):
uv=splev(dx,tckp,d)
put(" %s "%(repr(uv[0])))
def __init__(self, knots_x, knots_y, n_points):
self.knots_x = knots_x
self.knots_y = knots_y
tck = splrep(knots_x, knots_y)
self.spline_x = np.linspace(knots_x[0], knots_x[-1], n_points)
self.spline_y = splev(self.spline_x, tck)
def _obj_beam_fit(params, beams, x_nodes):
"""
params = [2.953e-03, 1.156e+00, 1.297e+01, 9.747e-01 , 9.970e-01 , 8.509e-01, 1.076e+00 , 1.487e+00 , 7.864e-01, 1.072e+00 , 1.015e+00]
"""
import time
from scipy.interpolate.fitpack import splev, splrep
import pysynphot as S
### Spline continuum + gaussian line
l0 = 6563.*(1+params[1])
if (l0 < 1.12e4) | (l0 > 1.63e4):
return -np.inf
line = S.GaussianSource(params[2], l0, 10)
tck = splrep(x_nodes, params[3:], k=3, s=0)
xcon = np.arange(0.9e4,1.8e4,0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True)+line
lnprob = 0
for key in beams.keys():
beam = beams[key]
modelf = beam.compute_model(beam.clip_thumb, xspec=spec.wave, yspec=spec.flux, in_place=False)
lnprob += -0.5*np.sum(((beam.cutout_scif-params[0]-modelf)**2/beam.cutout_varf)[beam.cutout_maskf])
if ~np.isfinite(lnprob):
lnprob = -np.inf
print params, lnprob
#time.sleep(0.2)
return lnprob
def test_1d_shape(self):
x = [1,2,3,4,5]
y = [4,5,6,7,8]
tck = splrep(x, y)
z = splev([1], tck)
assert_equal(z.shape, (1,))
z = splev(1, tck)
assert_equal(z.shape, ())
def __init__(self):
# non-uniform grid, just to make it sure
x = np.linspace(0, 1, 100)**3
y = np.sin(20 * x)
self.spl = splrep(x, y)
# double check that knots are non-uniform
assert_(np.diff(self.spl[0]).ptp() > 0)
def make_diff_func(self) :
''' everytime parameters are changed, the diffusion
function must be REMADE !!
'''
if self.difftype == 'const':
self.diff = lambda y: zeros(len(y), float) + self.param[0]
self.diff_u= lambda y: zeros(len(y), float) + 0.
elif self.difftype == 'power':
self.diff = lambda y: y**self.param[0] \
* (self.param[1]+self.param[2]*y+self.param[3]*y**2)
self.diff_u= lambda y: self.param[0]*y**(self.param[0]-1.) \
* (self.param[1]+self.param[2]*y+self.param[3]*y**2) + \
y**self.param[0] * (self.param[2]+2.*self.param[3]*y)
elif self.difftype == 'bspline':
#create an interp object
from scipy.interpolate.fitpack import splrep,splev
#paramuval should be list of u values
#param should be list of D(u) values
#create the data of the cubic bspline:
# no smoother so s = 0
self.splinedata = splrep(self.paramuval, self.param,
xb = None, xe = None, s=0,
k = 3, full_output = 0, quiet = 1)
self.diff = lambda y: splev(y, self.splinedata, der = 0)
self.diff_u = lambda y: splev(y, self.splinedata, der = 1)
elif self.difftype == 'bspline1storder':
#create an interp object
from scipy.interpolate.fitpack import splrep,splev
#paramuval should be list of u values
#param should be list of D(u) values
#create the data of the linear bspline:
# no smoother so s = 0
self.splinedata = splrep(self.paramuval, self.param,
xb = None, xe = None, s=0,
k = 1, full_output = 0, quiet = 1)
self.diff = lambda y: splev(y, self.splinedata, der = 0)
self.diff_u = lambda y: splev(y, self.splinedata, der = 1)
elif self.difftype == '1D2pint':
#interpolation with 2 points (=piecewise linear)
self.diff = GridUtils.GridFunc1D([self.paramuval],self.param)
self.diff_u = None
else:
print ('Unknown diffusion type given', self.difftype)
sys.exit()
#value of diffusion is again in agreement with par
self.modified = False
def test_1d_shape(self):
x = [1,2,3,4,5]
y = [4,5,6,7,8]
tck = splrep(x, y)
z = splev([1], tck)
assert_equal(z.shape, (1,))
z = splev(1, tck)
assert_equal(z.shape, ())
def __init__(self):
# non-uniform grid, just to make it sure
x = np.linspace(0, 1, 100)**3
y = np.sin(20 * x)
self.spl = splrep(x, y)
# double check that knots are non-uniform
assert_(np.diff(self.spl[0]).ptp() > 0)
def test_2d_shape(self):
x = [1, 2, 3, 4, 5]
y = [4, 5, 6, 7, 8]
tck = splrep(x, y)
t = np.array([[1.0, 1.5, 2.0, 2.5], [3.0, 3.5, 4.0, 4.5]])
z = splev(t, tck)
z0 = splev(t[0], tck)
z1 = splev(t[1], tck)
assert_equal(z, np.row_stack((z0, z1)))
def check_1(self,
f=f1,
per=0,
s=0,
a=0,
b=2 * pi,
N=20,
at=0,
xb=None,
xe=None):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
x1 = a + (b - a) * arange(1, N, dtype=float) / float(
N - 1) # middle points of the nodes
v, v1 = f(x), f(x1)
nk = []
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h**(.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
if at:
t = tck[0][k:-k]
else:
t = x1
nd = []
for d in range(k + 1):
tol = err_est(k, d)
err = norm2(f(t, d) - splev(t, tck, d)) / norm2(f(t, d))
assert_(err < tol, (k, d, err, tol))
nd.append((err, tol))
nk.append(nd)
put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" %
(f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(
a, 3)), repr(round(b, 3))))
if at:
str = "at knots"
else:
str = "at the middle of nodes"
put(" per=%d s=%s Evaluation %s" % (per, repr(s), str))
put(" k : |f-s|^2 |f'-s'| |f''-.. |f'''-. |f''''- |f'''''")
k = 1
for l in nk:
put(' %d : ' % k)
for r in l:
put(' %.1e %.1e' % r)
put('\n')
k = k + 1
def test_2d_shape(self):
x = [1, 2, 3, 4, 5]
y = [4, 5, 6, 7, 8]
tck = splrep(x, y)
t = np.array([[1.0, 1.5, 2.0, 2.5], [3.0, 3.5, 4.0, 4.5]])
z = splev(t, tck)
z0 = splev(t[0], tck)
z1 = splev(t[1], tck)
assert_equal(z, np.row_stack((z0, z1)))
def check_2(self,
f=f1,
per=0,
s=0,
a=0,
b=2 * pi,
N=20,
xb=None,
xe=None,
ia=0,
ib=2 * pi,
dx=0.2 * pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h**(.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
nk = []
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
nk.append([splint(ia, ib, tck), spalde(dx, tck)])
put("\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]" %
(f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(
a, 3)), repr(round(b, 3))))
put(" per=%d s=%s N=%d [a, b] = [%s, %s] dx=%s" %
(per, repr(s), N, repr(round(ia, 3)), repr(round(
ib, 3)), repr(round(dx, 3))))
put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k"
)
k = 1
for r in nk:
if r[0] < 0:
sr = '-'
else:
sr = ' '
put(" %d %s%.8f %.1e " %
(k, sr, abs(r[0]), abs(r[0] - (f(ib, -1) - f(ia, -1)))))
d = 0
for dr in r[1]:
err = abs(1 - dr / f(dx, d))
tol = err_est(k, d)
assert_(err < tol, (k, d))
put(" %.1e %.1e" % (err, tol))
d = d + 1
put("\n")
k = k + 1
def compute_colors(N):
xref = np.linspace(0, 1, CMRref.shape[0])
x = np.linspace(0, 1, N)
cmap = np.zeros((N, 3))
for i in range(3):
tck = splrep(xref, CMRref[:, i], s=0) # cubic spline (default) without smoothing
cmap[:, i] = splev(x, tck)
# Limit to range [0,1]
cmap -= np.min(cmap)
cmap /= np.max(cmap)
return cmap
def test_extrapolation_modes(self):
# test extrapolation modes
# * if ext=0, return the extrapolated value.
# * if ext=1, return 0
# * if ext=2, raise a ValueError
# * if ext=3, return the boundary value.
x = [1, 2, 3]
y = [0, 2, 4]
tck = splrep(x, y, k=1)
rstl = [[-2, 6], [0, 0], None, [0, 4]]
for ext in (0, 1, 3):
assert_array_almost_equal(splev([0, 4], tck, ext=ext), rstl[ext])
assert_raises(ValueError, splev, [0, 4], tck, ext=2)
def compute_colors(N):
xref = np.linspace(0, 1, CMRref.shape[0])
x = np.linspace(0, 1, N)
cmap = np.zeros((N, 3))
for i in range(3):
tck = splrep(xref, CMRref[:, i],
s=0) # cubic spline (default) without smoothing
cmap[:, i] = splev(x, tck)
# Limit to range [0,1]
cmap -= np.min(cmap)
cmap /= np.max(cmap)
return cmap
def test_extrapolation_modes(self):
# test extrapolation modes
# * if ext=0, return the extrapolated value.
# * if ext=1, return 0
# * if ext=2, raise a ValueError
# * if ext=3, return the boundary value.
x = [1,2,3]
y = [0,2,4]
tck = splrep(x, y, k=1)
rstl = [[-2, 6], [0, 0], None, [0, 4]]
for ext in (0, 1, 3):
assert_array_almost_equal(splev([0, 4], tck, ext=ext), rstl[ext])
assert_raises(ValueError, splev, [0, 4], tck, ext=2)
def check_1(self, f=f1, per=0, s=0, a=0, b=2 * pi, N=20, at=0, xb=None, xe=None):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
x1 = a + (b - a) * arange(1, N, dtype=float) / float(N - 1) # middle points of the nodes
v, v1 = f(x), f(x1)
nk = []
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h ** (0.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
if at:
t = tck[0][k:-k]
else:
t = x1
nd = []
for d in range(k + 1):
tol = err_est(k, d)
err = norm2(f(t, d) - splev(t, tck, d)) / norm2(f(t, d))
assert_(err < tol, (k, d, err, tol))
nd.append((err, tol))
nk.append(nd)
put(
"\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]"
% (f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(a, 3)), repr(round(b, 3)))
)
if at:
str = "at knots"
else:
str = "at the middle of nodes"
put(" per=%d s=%s Evaluation %s" % (per, repr(s), str))
put(" k : |f-s|^2 |f'-s'| |f''-.. |f'''-. |f''''- |f'''''")
k = 1
for l in nk:
put(" %d : " % k)
for r in l:
put(" %.1e %.1e" % r)
put("\n")
k = k + 1
def check_3(self,f=f1,per=0,s=0,a=0,b=2*pi,N=20,xb=None,xe=None,
ia=0,ib=2*pi,dx=0.2*pi):
if xb is None: xb=a
if xe is None: xe=b
x=a+(b-a)*arange(N+1,dtype=float)/float(N) # nodes
v=f(x)
nk=[]
put(" k : Roots of s(x) approx %s x in [%s,%s]:"%\
(f(None),repr(round(a,3)),repr(round(b,3))))
for k in range(1,6):
tck=splrep(x,v,s=s,per=per,k=k,xe=xe)
roots = sproot(tck)
if k == 3:
assert_allclose(roots, pi*array([1, 2, 3, 4]),
rtol=1e-3)
put(' %d : %s'%(k,repr(roots.tolist())))
def interp_masked1d(marr, kind='linear'):
"""
Interpolates masked values in an array according to the given method.
Parameters
----------
marr : MaskedArray
Array to fill
kind : {'constant', 'linear', 'cubic', quintic'}, optional
Type of interpolation
"""
if np.ndim(marr) > 1:
raise ValueError("array must be 1 dimensional!")
#
marr = marray(marr, copy=True)
if getmask(marr) is nomask:
return marr
#
unmaskedIndices = (~marr._mask).nonzero()[0]
if unmaskedIndices.size < 2:
return marr
#
kind = kind.lower()
if kind == 'constant':
return forward_fill(marr)
try:
k = {'linear' : 1,
'cubic' : 3,
'quintic' : 5}[kind.lower()]
except KeyError:
raise ValueError("Unsupported interpolation type.")
first_unmasked, last_unmasked = flatnotmasked_edges(marr)
vals = marr.data[unmaskedIndices]
from scipy.interpolate import fitpack
tck = fitpack.splrep(unmaskedIndices, vals, k=k)
maskedIndices = marr._mask.nonzero()[0]
interpIndices = maskedIndices[(maskedIndices > first_unmasked) & \
(maskedIndices < last_unmasked)]
marr[interpIndices] = fitpack.splev(interpIndices, tck).astype(marr.dtype)
return marr
def check_2(self, f=f1, per=0, s=0, a=0, b=2 * pi, N=20, xb=None, xe=None, ia=0, ib=2 * pi, dx=0.2 * pi):
if xb is None:
xb = a
if xe is None:
xe = b
x = a + (b - a) * arange(N + 1, dtype=float) / float(N) # nodes
v = f(x)
def err_est(k, d):
# Assume f has all derivatives < 1
h = 1.0 / float(N)
tol = 5 * h ** (0.75 * (k - d))
if s > 0:
tol += 1e5 * s
return tol
nk = []
for k in range(1, 6):
tck = splrep(x, v, s=s, per=per, k=k, xe=xe)
nk.append([splint(ia, ib, tck), spalde(dx, tck)])
put(
"\nf = %s s=S_k(x;t,c) x in [%s, %s] > [%s, %s]"
% (f(None), repr(round(xb, 3)), repr(round(xe, 3)), repr(round(a, 3)), repr(round(b, 3)))
)
put(
" per=%d s=%s N=%d [a, b] = [%s, %s] dx=%s"
% (per, repr(s), N, repr(round(ia, 3)), repr(round(ib, 3)), repr(round(dx, 3)))
)
put(" k : int(s,[a,b]) Int.Error Rel. error of s^(d)(dx) d = 0, .., k")
k = 1
for r in nk:
if r[0] < 0:
sr = "-"
else:
sr = " "
put(" %d %s%.8f %.1e " % (k, sr, abs(r[0]), abs(r[0] - (f(ib, -1) - f(ia, -1)))))
d = 0
for dr in r[1]:
err = abs(1 - dr / f(dx, d))
tol = err_est(k, d)
assert_(err < tol, (k, d))
put(" %.1e %.1e" % (err, tol))
d = d + 1
put("\n")
k = k + 1
def interp_masked1d(marr, kind='linear'):
"""
Interpolates masked values in an array according to the given method.
Parameters
----------
marr : MaskedArray
Array to fill
kind : {'constant', 'linear', 'cubic', quintic'}, optional
Type of interpolation
"""
if np.ndim(marr) > 1:
raise ValueError("array must be 1 dimensional!")
#
marr = marray(marr, copy=True)
if getmask(marr) is nomask:
return marr
#
unmaskedIndices = (~marr._mask).nonzero()[0]
if unmaskedIndices.size < 2:
return marr
#
kind = kind.lower()
if kind == 'constant':
return forward_fill(marr)
try:
k = {'linear': 1, 'cubic': 3, 'quintic': 5}[kind.lower()]
except KeyError:
raise ValueError("Unsupported interpolation type.")
first_unmasked, last_unmasked = flatnotmasked_edges(marr)
vals = marr.data[unmaskedIndices]
from scipy.interpolate import fitpack
tck = fitpack.splrep(unmaskedIndices, vals, k=k)
maskedIndices = marr._mask.nonzero()[0]
interpIndices = maskedIndices[(maskedIndices > first_unmasked) & \
(maskedIndices < last_unmasked)]
marr[interpIndices] = fitpack.splev(interpIndices, tck).astype(marr.dtype)
return marr
def interp_masked1d(marr, kind='linear'):
"""interp_masked1d(marr, king='linear')
Interpolates masked values in marr according to method kind.
kind must be one of 'constant', 'linear', 'cubic', quintic'
"""
if numeric.ndim(marr) > 1:
raise ValueError("array must be 1 dimensional!")
#
marr = marray(marr, copy=True)
if getmask(marr) is nomask:
return marr
#
unmaskedIndices = (~marr._mask).nonzero()[0]
if unmaskedIndices.size < 2:
return marr
#
kind = kind.lower()
if kind == 'constant':
return forward_fill(marr)
try:
k = {'linear' : 1,
'cubic' : 3,
'quintic' : 5}[kind.lower()]
except KeyError:
raise ValueError("Unsupported interpolation type.")
first_unmasked, last_unmasked = flatnotmasked_edges(marr)
vals = marr.data[unmaskedIndices]
tck = fitpack.splrep(unmaskedIndices, vals, k=k)
maskedIndices = marr._mask.nonzero()[0]
interpIndices = maskedIndices[(maskedIndices > first_unmasked) & \
(maskedIndices < last_unmasked)]
marr[interpIndices] = fitpack.splev(interpIndices, tck).astype(marr.dtype)
return marr
def test_splev_der_k():
# regression test for gh-2188: splev(x, tck, der=k) gives garbage or crashes
# for x outside of knot range
# test case from gh-2188
tck = (np.array([0., 0., 2.5,
2.5]), np.array([-1.56679978, 2.43995873, 0., 0.]), 1)
t, c, k = tck
x = np.array([-3, 0, 2.5, 3])
# an explicit form of the linear spline
assert_allclose(splev(x, tck), c[0] + (c[1] - c[0]) * x / t[2])
assert_allclose(splev(x, tck, 1), (c[1] - c[0]) / t[2])
# now check a random spline vs splder
np.random.seed(1234)
x = np.sort(np.random.random(30))
y = np.random.random(30)
t, c, k = splrep(x, y)
x = [t[0] - 1., t[-1] + 1.]
tck2 = splder((t, c, k), k)
assert_allclose(splev(x, (t, c, k), k), splev(x, tck2))
def _obj_beam_fit(params, beams, x_nodes):
"""
params = [2.953e-03, 1.156e+00, 1.297e+01, 9.747e-01 , 9.970e-01 , 8.509e-01, 1.076e+00 , 1.487e+00 , 7.864e-01, 1.072e+00 , 1.015e+00]
"""
import time
from scipy.interpolate.fitpack import splev, splrep
import pysynphot as S
### Spline continuum + gaussian line
l0 = 6563. * (1 + params[1])
if (l0 < 1.12e4) | (l0 > 1.63e4):
return -np.inf
line = S.GaussianSource(params[2], l0, 10)
tck = splrep(x_nodes, params[3:], k=3, s=0)
xcon = np.arange(0.9e4, 1.8e4, 0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True) + line
lnprob = 0
for key in beams.keys():
beam = beams[key]
modelf = beam.compute_model(beam.clip_thumb,
xspec=spec.wave,
yspec=spec.flux,
in_place=False)
lnprob += -0.5 * np.sum(((beam.cutout_scif - params[0] - modelf)**2 /
beam.cutout_varf)[beam.cutout_maskf])
if ~np.isfinite(lnprob):
lnprob = -np.inf
print params, lnprob
#time.sleep(0.2)
return lnprob
def test_splev_der_k():
# regression test for gh-2188: splev(x, tck, der=k) gives garbage or crashes
# for x outside of knot range
# test case from gh-2188
tck = (np.array([0., 0., 2.5, 2.5]),
np.array([-1.56679978, 2.43995873, 0., 0.]),
1)
t, c, k = tck
x = np.array([-3, 0, 2.5, 3])
# an explicit form of the linear spline
assert_allclose(splev(x, tck), c[0] + (c[1] - c[0]) * x/t[2])
assert_allclose(splev(x, tck, 1), (c[1]-c[0]) / t[2])
# now check a random spline vs splder
np.random.seed(1234)
x = np.sort(np.random.random(30))
y = np.random.random(30)
t, c, k = splrep(x, y)
x = [t[0] - 1., t[-1] + 1.]
tck2 = splder((t, c, k), k)
assert_allclose(splev(x, (t, c, k), k), splev(x, tck2))
def setup_fit():
snlim = 0
snlim = 1./np.sqrt(len(beams))
Rmax = 5
for key in FLT.keys():
beam = beams[key]
beam.cutout_sci = beam.get_cutout(FLT[key].im['SCI'].data)*1
beam.cutout_dq = beam.get_cutout(FLT[key].im['DQ'].data)*1
beam.cutout_err = beam.get_cutout(FLT[key].im['ERR'].data)*1
beam.cutout_mask = (beam.cutout_dq-(beam.cutout_dq & 512) == 0) & (beam.cutout_err > 0) & (beam.cutout_err < 10)
sh = beam.cutout_sci.shape
yp, xp = np.indices(beam.thumb.shape)
r = np.sqrt((xp-sh[0]/2)**2+(yp-sh[0]/2)**2)
beam.norm = beam.thumb[r <= Rmax].sum()/1.e-17
beam.clip_thumb = beam.thumb*(r <= Rmax)
beam.compute_model(beam.clip_thumb)
sn = beam.model/beam.cutout_err
#beam.mask &= (sn > 0.5) & (beam.err > 0)
beam.cutout_mask &= (sn > snlim) & (beam.cutout_err > 0)
beam.cutout_sci[~beam.cutout_mask] = 0
beam.cutout_err[~beam.cutout_mask] = 0
beam.cutout_var = beam.cutout_err**2
beam.cutout_scif = beam.cutout_sci.flatten()
beam.cutout_varf = beam.cutout_var.flatten()
beam.cutout_maskf = beam.cutout_mask.flatten()
ds9.view((beam.cutout_scif-beam.cutout_modelf).reshape(beam.cutout_sci.shape)*beam.cutout_mask)
##
x_nodes = np.arange(1.0e4,1.71e4,0.1e4)
x_nodes = np.arange(1.0e4,1.71e4,0.03e4)
x_nodes = np.arange(1.05e4,1.71e4,0.075e4)
init = np.append([0, 1.148, 500], np.ones(len(x_nodes)))
init = np.append([0, 1.2078, 500], np.ones(len(x_nodes)))
step_sig = np.append([0.01,0.1,50], np.ones(len(x_nodes))*0.1)
init = np.append([0, 1.0, 500], np.ones(len(x_nodes)))
step_sig = np.append([0.0,0.2,150], np.ones(len(x_nodes))*0.1)
### don't fit redshift
#init = np.append([0, 1.0, 0], np.ones(len(x_nodes)))
#step_sig = np.append([0.0,0.,0], np.ones(len(x_nodes))*0.2)
obj_fun = _obj_beam_fit
obj_args = [beams, x_nodes]
ndim, nwalkers = len(init), len(init)*2
p0 = [(init+np.random.normal(size=ndim)*step_sig)
for i in xrange(nwalkers)]
NTHREADS, NSTEP = 2, 5
sampler = emcee.EnsembleSampler(nwalkers, ndim, obj_fun, args = obj_args,
threads=NTHREADS)
#
t0 = time.time()
result = sampler.run_mcmc(p0, NSTEP)
t1 = time.time()
print 'Sampler: %.1f s' %(t1-t0)
param_names = ['bg', 'z', 'Ha']
param_names.extend(['spl%d' %i for i in range(len(init)-3)])
import unicorn.interlace_fit
chain = unicorn.interlace_fit.emceeChain(chain=sampler.chain, param_names=param_names)
#obj_fun(chain.map, beams)
#obj_fun(init, beams, x_nodes)
params = chain.map*1.
#params = init
### Show spectra
from scipy.interpolate.fitpack import splev, splrep
# NDRAW=100
# draw = chain.draw_random(NDRAW)
# for i in range(NDRAW):
# line = S.GaussianSource(draw[i,2], 6563.*(1+draw[i,1]), 10)
# tck = splrep(x_nodes, draw[i,3:], k=3, s=0)
# xcon = np.arange(0.9e4,1.8e4,0.01e4)
# ycon = splev(xcon, tck, der=0, ext=0)
# spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True)+line
# plt.plot(spec.wave, spec.flux, alpha=0.1, color='red')
#
line = S.GaussianSource(params[2], 6563.*(1+params[1]), 10)
tck = splrep(x_nodes, params[3:], k=3, s=0)
xcon = np.arange(0.9e4,1.8e4,0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
pspec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True)+line
for key in beams.keys():
beam = beams[key]
beam.compute_model(beam.clip_thumb, xspec=pspec.wave, yspec=pspec.flux, in_place=True)
xfull, yfull, mfull, cfull = [], [], [], []
for i, key in enumerate(beams.keys()):
beam = beams[key]
#ds9.frame(i+1)
#ds9.view((beam.sci-beam.model)*beam.mask)
ls = 'steps-mid'
marker = 'None'
#ls = '-'
#ls, marker = 'None', '.'
xfull = np.append(xfull, beam.lam)
ybeam = (beam.cutout_sci-params[0]*beam.cutout_mask).sum(axis=0)[sh[0]/2:-sh[0]/2]/beam.ysens/beam.norm
yfull = np.append(yfull, ybeam)
#plt.plot(beam.lam, ybeam, color='black', alpha=0.5, linestyle=ls, marker=marker)
cbeam = ((beam.cutout_m-beam.omodel)*beam.cutout_mask).sum(axis=0)[sh[0]/2:-sh[0]/2]/beam.ysens/beam.norm
cfull = np.append(cfull, cbeam)
mbeam = ((beam.model)*beam.mask).sum(axis=0)[sh[0]/2:-sh[0]/2]/beam.ysens/beam.norm
mfull = np.append(mfull, mbeam)
plt.plot(beam.lam, ybeam-cbeam, color='black', linestyle=ls, alpha=0.5)
plt.plot(beam.lam, mbeam, color='blue', linestyle=ls, alpha=0.5)
#nx = 20
kern = np.ones(nx)/nx
so = np.argsort(xfull)
plt.plot(xfull[so][nx/2::nx], nd.convolve((yfull-cfull)[so], kern)[nx/2::nx], color='orange', linewidth=2, alpha=0.8, linestyle='steps-mid')
plt.plot(xfull[so][nx/2::nx], nd.convolve(mfull[so], kern)[nx/2::nx], color='green', linewidth=2, alpha=0.8, linestyle='steps-mid')
plt.ylim(0,5)
plt.xlim(1.e4,1.78e4)
from scipy.optimize import fmin_bfgs
p0 = fmin_bfgs(_loss, init[3:], args=(beams, x_nodes), gtol=1.e-3, epsilon=1.e-3, maxiter=100)
params = np.array(init)
params[3:] = p0
def setup_fit():
snlim = 0
snlim = 1. / np.sqrt(len(beams))
Rmax = 5
for key in FLT.keys():
beam = beams[key]
beam.cutout_sci = beam.get_cutout(FLT[key].im['SCI'].data) * 1
beam.cutout_dq = beam.get_cutout(FLT[key].im['DQ'].data) * 1
beam.cutout_err = beam.get_cutout(FLT[key].im['ERR'].data) * 1
beam.cutout_mask = (beam.cutout_dq - (beam.cutout_dq & 512) == 0) & (
beam.cutout_err > 0) & (beam.cutout_err < 10)
sh = beam.cutout_sci.shape
yp, xp = np.indices(beam.thumb.shape)
r = np.sqrt((xp - sh[0] / 2)**2 + (yp - sh[0] / 2)**2)
beam.norm = beam.thumb[r <= Rmax].sum() / 1.e-17
beam.clip_thumb = beam.thumb * (r <= Rmax)
beam.compute_model(beam.clip_thumb)
sn = beam.model / beam.cutout_err
#beam.mask &= (sn > 0.5) & (beam.err > 0)
beam.cutout_mask &= (sn > snlim) & (beam.cutout_err > 0)
beam.cutout_sci[~beam.cutout_mask] = 0
beam.cutout_err[~beam.cutout_mask] = 0
beam.cutout_var = beam.cutout_err**2
beam.cutout_scif = beam.cutout_sci.flatten()
beam.cutout_varf = beam.cutout_var.flatten()
beam.cutout_maskf = beam.cutout_mask.flatten()
ds9.view((beam.cutout_scif - beam.cutout_modelf).reshape(
beam.cutout_sci.shape) * beam.cutout_mask)
##
x_nodes = np.arange(1.0e4, 1.71e4, 0.1e4)
x_nodes = np.arange(1.0e4, 1.71e4, 0.03e4)
x_nodes = np.arange(1.05e4, 1.71e4, 0.075e4)
init = np.append([0, 1.148, 500], np.ones(len(x_nodes)))
init = np.append([0, 1.2078, 500], np.ones(len(x_nodes)))
step_sig = np.append([0.01, 0.1, 50], np.ones(len(x_nodes)) * 0.1)
init = np.append([0, 1.0, 500], np.ones(len(x_nodes)))
step_sig = np.append([0.0, 0.2, 150], np.ones(len(x_nodes)) * 0.1)
### don't fit redshift
#init = np.append([0, 1.0, 0], np.ones(len(x_nodes)))
#step_sig = np.append([0.0,0.,0], np.ones(len(x_nodes))*0.2)
obj_fun = _obj_beam_fit
obj_args = [beams, x_nodes]
ndim, nwalkers = len(init), len(init) * 2
p0 = [(init + np.random.normal(size=ndim) * step_sig)
for i in xrange(nwalkers)]
NTHREADS, NSTEP = 2, 5
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
obj_fun,
args=obj_args,
threads=NTHREADS)
#
t0 = time.time()
result = sampler.run_mcmc(p0, NSTEP)
t1 = time.time()
print 'Sampler: %.1f s' % (t1 - t0)
param_names = ['bg', 'z', 'Ha']
param_names.extend(['spl%d' % i for i in range(len(init) - 3)])
import unicorn.interlace_fit
chain = unicorn.interlace_fit.emceeChain(chain=sampler.chain,
param_names=param_names)
#obj_fun(chain.map, beams)
#obj_fun(init, beams, x_nodes)
params = chain.map * 1.
#params = init
### Show spectra
from scipy.interpolate.fitpack import splev, splrep
# NDRAW=100
# draw = chain.draw_random(NDRAW)
# for i in range(NDRAW):
# line = S.GaussianSource(draw[i,2], 6563.*(1+draw[i,1]), 10)
# tck = splrep(x_nodes, draw[i,3:], k=3, s=0)
# xcon = np.arange(0.9e4,1.8e4,0.01e4)
# ycon = splev(xcon, tck, der=0, ext=0)
# spec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True)+line
# plt.plot(spec.wave, spec.flux, alpha=0.1, color='red')
#
line = S.GaussianSource(params[2], 6563. * (1 + params[1]), 10)
tck = splrep(x_nodes, params[3:], k=3, s=0)
xcon = np.arange(0.9e4, 1.8e4, 0.01e4)
ycon = splev(xcon, tck, der=0, ext=0)
pspec = S.ArraySpectrum(xcon, ycon, fluxunits='flam', keepneg=True) + line
for key in beams.keys():
beam = beams[key]
beam.compute_model(beam.clip_thumb,
xspec=pspec.wave,
yspec=pspec.flux,
in_place=True)
xfull, yfull, mfull, cfull = [], [], [], []
for i, key in enumerate(beams.keys()):
beam = beams[key]
#ds9.frame(i+1)
#ds9.view((beam.sci-beam.model)*beam.mask)
ls = 'steps-mid'
marker = 'None'
#ls = '-'
#ls, marker = 'None', '.'
xfull = np.append(xfull, beam.lam)
ybeam = (beam.cutout_sci - params[0] * beam.cutout_mask).sum(
axis=0)[sh[0] / 2:-sh[0] / 2] / beam.ysens / beam.norm
yfull = np.append(yfull, ybeam)
#plt.plot(beam.lam, ybeam, color='black', alpha=0.5, linestyle=ls, marker=marker)
cbeam = ((beam.cutout_m - beam.omodel) * beam.cutout_mask).sum(
axis=0)[sh[0] / 2:-sh[0] / 2] / beam.ysens / beam.norm
cfull = np.append(cfull, cbeam)
mbeam = ((beam.model) * beam.mask).sum(
axis=0)[sh[0] / 2:-sh[0] / 2] / beam.ysens / beam.norm
mfull = np.append(mfull, mbeam)
plt.plot(beam.lam,
ybeam - cbeam,
color='black',
linestyle=ls,
alpha=0.5)
plt.plot(beam.lam, mbeam, color='blue', linestyle=ls, alpha=0.5)
#nx = 20
kern = np.ones(nx) / nx
so = np.argsort(xfull)
plt.plot(xfull[so][nx / 2::nx],
nd.convolve((yfull - cfull)[so], kern)[nx / 2::nx],
color='orange',
linewidth=2,
alpha=0.8,
linestyle='steps-mid')
plt.plot(xfull[so][nx / 2::nx],
nd.convolve(mfull[so], kern)[nx / 2::nx],
color='green',
linewidth=2,
alpha=0.8,
linestyle='steps-mid')
plt.ylim(0, 5)
plt.xlim(1.e4, 1.78e4)
from scipy.optimize import fmin_bfgs
p0 = fmin_bfgs(_loss,
init[3:],
args=(beams, x_nodes),
gtol=1.e-3,
epsilon=1.e-3,
maxiter=100)
params = np.array(init)
params[3:] = p0
diodes=[]
for rad in ['0','1']:
for diode in ['0','1']:
diodes.append(str(horn)+rad+diode)
for diode in diodes:
#first do 91-952, read response file then go thru ODs
fl=glob(adc_dir+'/'+'ADCDX12_%s*_952_*.pic' % diode)
if len(fl)>0:
respfile=fl[0]
if os.path.exists(respfile):
resp = read_LFI_response(respfile)
horn = resp.keys['horn']
rad = resp.keys['radiometer']
det = resp.keys['detector']
sky_spline = fit.splrep(resp.sky_volt_out,resp.sky_volt_in,s=0.0)
ref_spline = fit.splrep(resp.load_volt_out,resp.load_volt_in,s=0.0)
for od in range(91,953):
rawfile=rawdata_dir+'od%s_rca%s.fits' % (od,diode)
corrfile=adc_corr_data_dir+'od%s_rca%s.fits' % (od,diode)
if not(os.path.exists(corrfile)):
if os.path.exists(rawfile):
hdulist = fits.open(rawfile)
data = hdulist[1].data
sky_volt = data.field('SKY')
load_volt = data.field('REF')
sky_cor = fit.splev(sky_volt,sky_spline)
load_cor = fit.splev(load_volt,ref_spline)
data.field('SKY')[:] = sky_cor
data.field('REF')[:] = load_cor
hdulist[1].header.update('hierarch instrument','LFI_ADC_corr')
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate.fitpack import splrep, splev
from util.point import Point
from walking.helpers import bezier_curves
from walking.helpers.bezier_curves import LineSegment
x = (0, 2.0, 6.0, 8.0)
y = (-47.7, -44.7, -44.7, -47.7)
tck = splrep(x, y)
x2 = np.linspace(0, 8)
y2 = splev(x2, tck)
points = [Point((x_, 0, y_)) for (x_, y_) in zip(x, y)]
l1 = LineSegment(points[0], points[1])
l2 = LineSegment(points[1], points[2])
l3 = LineSegment(points[2], points[3])
yy2 = [
bezier_curves.get_interpolated_position(x2_ / 8, l1, l2, l3)[2]
for x2_ in x2
]
plt.plot(x, y, 'o', x, y, '--', x2, y2, x2, yy2)
plt.show()
import numpy as np import matplotlib.pyplot as plt from scipy.interpolate.fitpack import splrep, splev from util.point import Point from walking.helpers import bezier_curves from walking.helpers.bezier_curves import LineSegment x = (0, 2.0, 6.0, 8.0) y = (-47.7, -44.7, -44.7, -47.7) tck = splrep(x, y) x2 = np.linspace(0, 8) y2 = splev(x2, tck) points = [Point((x_, 0, y_)) for (x_, y_) in zip(x, y)] l1 = LineSegment(points[0], points[1]) l2 = LineSegment(points[1], points[2]) l3 = LineSegment(points[2], points[3]) yy2 = [bezier_curves.get_interpolated_position(x2_/8, l1, l2, l3)[2] for x2_ in x2] plt.plot(x, y, 'o', x, y, '--', x2, y2, x2, yy2) plt.show()
def test_task_argument(self):
x, y = range(5), range(5, 10)
splrep(x, y, task=0)
with pytest.raises(ValueError):
splrep(x, y, task=1)
yi = np.zeros(np.shape(xi))
yi_hd = np.zeros(np.shape(xi_hd))
yi[:] = f(xi[:])
yi_hd = f(xi_hd[:])
#xi = np.linspace(-2, 2, 101)
#yi = 10 * xi / (1 + 100 * np.power(xi, 2))
data = np.c_[xi, yi]
p = poly.NewtonPolynomial(points=data)
d4p = deriv.dr_dxr(p, r=4)
norm = norm.Norm(d4p)
T, eps = cut.cutab(norm, xi, eps, r)
tck = fitpack.splrep(xi, yi, t=T[1:-1])
fit = fitpack.splev(xi, tck)
error = np.abs(fit - yi)
print '*' * 10 + " FIRST ERROR RATIO " + '*' * 10 + '\n\n'
print "error / tol = %f" % (error.max() / tol)
while error.max() > tol:
T, eps = cut.cutab(norm, xi, eps, r)
print "\n\nRun %d" % run_count
print "eps = %e in outer loop" % eps
eps = eps / 2
tck = fitpack.splrep(xi, yi, t=T[1:-1])
fit = fitpack.splev(xi, tck)
fit_hd = fitpack.splev(xi_hd, tck)
fT = np.zeros(np.shape(T))
fT[:] = f(T[:])
