def r_mat_corr(yerroblist,
ytimestep,
y_strlst,
r_diag,
corr=0.3,
tau=1.,
cut_off=4.):
""" Creates a correlated R matrix.
"""
r_corr = np.eye(len(ytimestep)) #MAKE SURE ALL VALUES ARE FLOATS FIRST!!!!
for i in xrange(len(ytimestep)):
if y_strlst[i] == 'nee_day' or y_strlst[i] == 'nee_night':
for j in xrange(len(ytimestep)):
if y_strlst[j] == 'nee_day' or y_strlst[j] == 'nee_night':
if abs(ytimestep[i] - ytimestep[j]) < cut_off:
r_corr[i, j] = corr*np.exp(-(abs(float(ytimestep[i])-float(ytimestep[j]))**2)/float(tau)**2) \
+ (1-corr)*smp.KroneckerDelta(ytimestep[i], ytimestep[j])
if y_strlst[j] == 'nee_day' and y_strlst[i] == 'nee_night':
r_corr[i, j] = corr * np.exp(
-(abs(float(ytimestep[i]) - float(ytimestep[j]))**
2) / float(tau)**2)
elif y_strlst[i] == 'nee_day' and y_strlst[
j] == 'nee_night':
r_corr[i, j] = corr * np.exp(
-(abs(float(ytimestep[i]) - float(ytimestep[j]))**
2) / float(tau)**2)
if y_strlst[i] == 'nee':
for j in xrange(len(ytimestep)):
if y_strlst[j] == 'nee':
if abs(ytimestep[i] - ytimestep[j]) < cut_off:
r_corr[i, j] = corr*np.exp(-(abs(float(ytimestep[i])-float(ytimestep[j]))**2)/float(tau)**2) \
+ (1-corr)*smp.KroneckerDelta(ytimestep[i], ytimestep[j])
r = np.dot(np.dot((np.sqrt(r_diag)), r_corr), np.sqrt(r_diag))
return r_corr, r
def _set_legcoefficients(self):
"""
set Legrende coefficients
needs to be a function that can be later evaluated by subsituting 'n'
"""
# only 3 coefficients are needed to correctly represent
# the Rayleigh scattering function
self.ncoefs = 3
n = sp.Symbol('n')
self.legcoefs = ((3. / (16. * sp.pi)) * ((4. / 3.) *
sp.KroneckerDelta(0, n) +
(2. / 3.) *
sp.KroneckerDelta(2, n))
).expand()
def test_kronecker_delta():
x = Symbol("x")
y = Symbol("y")
e1 = sympy.KroneckerDelta(sympy.Symbol("x"), sympy.Symbol("y"))
e2 = KroneckerDelta(x, y)
assert sympify(e1) == e2
assert e2._sympy_() == e1
def KroneckerDelta(i, j, simplify=True):
"""Kronecker delta symbol.
Return :class:`One` (`i` equals `j`)), :class:`Zero` (`i` and `j` are
non-symbolic an unequal), or a :class:`ScalarValue` wrapping SymPy's
:class:`~sympy.functions.special.tensor_functions.KroneckerDelta`.
>>> i, j = IdxSym('i'), IdxSym('j')
>>> KroneckerDelta(i, i)
One
>>> KroneckerDelta(1, 2)
Zero
>>> KroneckerDelta(i, j)
KroneckerDelta(i, j)
By default, the Kronecker delta is returned in a simplified form, e.g::
>>> KroneckerDelta((i+1)/2, (j+1)/2)
KroneckerDelta(i, j)
This may be suppressed by setting `simplify` to False::
>>> KroneckerDelta((i+1)/2, (j+1)/2, simplify=False)
KroneckerDelta(i/2 + 1/2, j/2 + 1/2)
Raises:
TypeError: if `i` or `j` is not an integer or sympy expression. There
is no automatic sympification of `i` and `j`.
"""
from qalgebra.core.scalar_algebra import One, ScalarValue
if not isinstance(i, (int, sympy.Basic)):
raise TypeError(
"i is not an integer or sympy expression: %s" % type(i)
)
if not isinstance(j, (int, sympy.Basic)):
raise TypeError(
"j is not an integer or sympy expression: %s" % type(j)
)
if i == j:
return One
else:
delta = sympy.KroneckerDelta(i, j)
if simplify:
delta = _simplify_delta(delta)
return ScalarValue.create(delta)
def _set_legcoefficients(self):
self.ncoefs = 1
n = sp.Symbol('n')
self.legcoefs = (1. / sp.pi) * sp.KroneckerDelta(0, n)
import galgebra.ga, sympy, operator, numpy
base = galgebra.ga.Ga('\u0411', coords=sympy.symbols('x:z', real=True))
assert base.mvr() == tuple(
operator.matmul(*(numpy.array(_) for _ in (
base.mv(), base.g_inv)))) # base.g_inv is the inverse matrix of base.g
for down in range(base.n):
for up in range(base.n):
assert (base.mv()[down]
| base.mvr()[up]).simplify() == sympy.KroneckerDelta(down, up)
sc.plot_log2D((kmesh[0][:, :, 10], kmesh[1][:, :, 10]),
phi11[:, :, 10],
label_S="$\log_{10}{S}$",
C=10**-2,
fig_num='a',
nl=30,
minS=-1.5)
# In[R-K in multidimensions]
# Functions
dZsy = sympy.Matrix(3, 1, lambda i, j: sympy.var('dZ%d' % (i + 1)))
Msy = sympy.Matrix(
3, 1, lambda i, j: (-sympy.KroneckerDelta(i, 0) + 2 * ksy[0] * ksy[i] /
(ksy.dot(ksy))) * dZsy[2])
x = sympy.symbols("x")
y = sympy.Function("y")
f = y(x)**2 + x
f_np = sympy.lambdify((y(x), x), f)
y0 = 0
xp = np.linspace(0, 1.9, 100)
yp = sp.integrate.odeint(f_np, y0, xp)
xm = np.linspace(0, -5, 100)
ym = sp.integrate.odeint(f_np, y0, xm)
fig, ax = plt.subplots(1, 1, figsize=(4, 4))
plot_direction_field(x, y(x), f, ax=ax)
ax.plot(xm, ym, 'b', lw=2)
ax.plot(xp, yp, 'r', lw=2)