def getthetaterms(self, dp1, dp1dot):
r"""Return array of integrated values for specified theta function and dphi function.
Parameters
----------
dp1 : array_like
Array of values for dphi1
dp1dot : array_like
Array of values for dphi1dot
Returns
-------
theta_terms : tuple
Tuple of len(k)xlen(q) shaped arrays of integration results in form
Notes
-----
The returned expression is of the form
.. math::
\bigg(\int(\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta)\bigg)
"""
sinth = np.sin(self.theta)
cossinth = np.cos(self.theta) * np.sin(self.theta)
theta_terms = np.empty([4, self.k.shape[0], self.k.shape[0]],
dtype=dp1.dtype)
lenq = len(self.k)
for n in np.atleast_1d(self.kix_wanted):
#Calculate interpolated values of dphi and dphidot
dphi_res = srccython.interpdps(dp1, dp1dot, self.kmin, self.deltak,
n, self.theta, lenq)
#Integrate theta dependence of interpolated values
# dphi terms
theta_terms[0, n] = romb(sinth * dphi_res[0], dx=self.dtheta)
theta_terms[1, n] = romb(cossinth * dphi_res[0], dx=self.dtheta)
# dphidot terms
theta_terms[2, n] = romb(sinth * dphi_res[1], dx=self.dtheta)
theta_terms[3, n] = romb(cossinth * dphi_res[1], dx=self.dtheta)
return theta_terms
def getthetaterms(self, dp1, dp1dot):
r"""Return array of integrated values for specified theta function and dphi function.
Parameters
----------
dp1 : array_like
Array of values for dphi1
dp1dot : array_like
Array of values for dphi1dot
Returns
-------
theta_terms : tuple
Tuple of len(k)xlen(q) shaped arrays of integration results in form
Notes
-----
The returned expression is of the form
.. math::
\bigg(\int(\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta)\bigg)
"""
sinth = np.sin(self.theta)
cossinth = np.cos(self.theta)*np.sin(self.theta)
theta_terms = np.empty([4, self.k.shape[0], self.k.shape[0]], dtype=dp1.dtype)
lenq = len(self.k)
for n in np.atleast_1d(self.kix_wanted):
#Calculate interpolated values of dphi and dphidot
dphi_res = srccython.interpdps(dp1, dp1dot, self.kmin, self.deltak, n, self.theta, lenq)
#Integrate theta dependence of interpolated values
# dphi terms
theta_terms[0,n] = romb(sinth*dphi_res[0], dx=self.dtheta)
theta_terms[1,n] = romb(cossinth*dphi_res[0], dx=self.dtheta)
# dphidot terms
theta_terms[2,n] = romb(sinth*dphi_res[1], dx=self.dtheta)
theta_terms[3,n] = romb(cossinth*dphi_res[1], dx=self.dtheta)
return theta_terms
def J_C(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_C which is the integral for C in terms of constants C5."""
q = self.k
C5k = Cterms[4][..., np.newaxis]
cterm = (C5k*q**2) * dp1dot * preterms[2]
J_C = romb(cterm, self.deltak)
return J_C
def J_C(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_C which is the integral for C in terms of constants C5."""
q = self.k
C5k = Cterms[4][..., np.newaxis]
cterm = (C5k * q**2) * dp1dot * preterms[2]
J_C = romb(cterm, self.deltak)
return J_C
def J_D(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_D which is the integral for D in terms of constants C6 and C7."""
q = self.k
C6k = Cterms[5][..., np.newaxis]
C7k = Cterms[6][..., np.newaxis]
dterm = (C6k*q + C7k*q**3) * dp1dot * preterms[3]
J_D = romb(dterm, self.deltak)
return J_D
def J_B(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_B which is the integral for B in terms of constants C3 and C4."""
q = self.k
C3k = Cterms[2][..., np.newaxis]
C4k = Cterms[3][..., np.newaxis]
bterm = (C3k*q**3 + C4k*q**5) * dp1 * preterms[1]
J_B = romb(bterm, self.deltak)
return J_B
def J_A(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_A which is the integral for A in terms of constants C1 and C2."""
q = self.k
C1k = Cterms[0][..., np.newaxis]
C2k = Cterms[1][..., np.newaxis]
aterm = (C1k*q**2 + C2k*q**4) * dp1 * preterms[0]
J_A = romb(aterm, self.deltak)
return J_A
def J_D(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_D which is the integral for D in terms of constants C6 and C7."""
q = self.k
C6k = Cterms[5][..., np.newaxis]
C7k = Cterms[6][..., np.newaxis]
dterm = (C6k * q + C7k * q**3) * dp1dot * preterms[3]
J_D = romb(dterm, self.deltak)
return J_D
def J_B(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_B which is the integral for B in terms of constants C3 and C4."""
q = self.k
C3k = Cterms[2][..., np.newaxis]
C4k = Cterms[3][..., np.newaxis]
bterm = (C3k * q**3 + C4k * q**5) * dp1 * preterms[1]
J_B = romb(bterm, self.deltak)
return J_B
def J_A(self, preterms, dp1, dp1dot, Cterms):
"""Solution for J_A which is the integral for A in terms of constants C1 and C2."""
q = self.k
C1k = Cterms[0][..., np.newaxis]
C2k = Cterms[1][..., np.newaxis]
aterm = (C1k * q**2 + C2k * q**4) * dp1 * preterms[0]
J_A = romb(aterm, self.deltak)
return J_A
def J_func(self, preterms, dp1, dp1dot, Cterms, Jkey):
"""Generic solution for J_func integral."""
q = self.k
#Set up variables from list of Jterms and constants
#Constant term
Cterm = Cterms[Jkey][..., np.newaxis]
#Index of q
n = self.J_params[Jkey]["n"]
#Get text of dphiterm and set variable
dphitermtext = self.J_params[Jkey]["dphiterm"]
if dphitermtext == "dp1":
dphiterm = dp1
elif dphitermtext == "dp1dot":
dphiterm = dp1dot
#Get preterm index
pretermix = self.J_params[Jkey]["pretermix"]
preterm = preterms[pretermix]
integrand = (Cterm*q**n) * dphiterm * preterm
J_integral = romb(integrand, self.deltak)
return J_integral
def J_func(self, preterms, dp1, dp1dot, Cterms, Jkey):
"""Generic solution for J_func integral."""
q = self.k
#Set up variables from list of Jterms and constants
#Constant term
Cterm = Cterms[Jkey][..., np.newaxis]
#Index of q
n = self.J_params[Jkey]["n"]
#Get text of dphiterm and set variable
dphitermtext = self.J_params[Jkey]["dphiterm"]
if dphitermtext == "dp1":
dphiterm = dp1
elif dphitermtext == "dp1dot":
dphiterm = dp1dot
#Get preterm index
pretermix = self.J_params[Jkey]["pretermix"]
preterm = preterms[pretermix]
integrand = (Cterm * q**n) * dphiterm * preterm
J_integral = romb(integrand, self.deltak)
return J_integral
def getthetaterms(self, dp1, dp1dot):
r"""Return array of integrated values for specified theta function and dphi function.
This modified version only returns the result for one k value.
Parameters
----------
dp1 : array_like
Array of values for dphi1
dp1dot : array_like
Array of values for dphi1dot
Returns
-------
theta_terms : tuple
Tuple of len(k)xlen(q) shaped arrays of integration results in form
Notes
-----
The returned expression is of the form
.. math::
\bigg(\int(\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta)\bigg)
"""
# Sinusoidal theta terms
sinth = np.sin(self.theta)
cossinth = np.cos(self.theta)*sinth
cos2sinth = np.cos(self.theta)*cossinth
sin3th = sinth*sinth*sinth
theta_terms = np.empty([7, self.k.shape[0], self.k.shape[0]], dtype=dp1.dtype)
lenq = len(self.k)
for n in np.atleast_1d(self.kix_wanted):
#klq = klessq(onek, q, theta)
dphi_res = srccython.interpdps(dp1, dp1dot, self.kmin, self.deltak, n, self.theta, lenq)
theta_terms[0,n] = romb(sinth*dphi_res[0], dx=self.dtheta)
theta_terms[1,n] = romb(cossinth*dphi_res[0], dx=self.dtheta)
theta_terms[2,n] = romb(sinth*dphi_res[1], dx=self.dtheta)
theta_terms[3,n] = romb(cossinth*dphi_res[1], dx=self.dtheta)
#New terms for full solution
# E term integration
theta_terms[4,n] = romb(cos2sinth*dphi_res[0], dx=self.dtheta)
#Get klessq for F and G terms
klq2 = klessqksq(self.k[n], self.k, self.theta)
sinklq = sin3th/klq2
#Get rid of NaNs in places where dphi_res=0 or equivalently klq2<self.kmin**2
sinklq[klq2<self.kmin**2] = 0
# F term integration
theta_terms[5,n] = romb(sinklq *dphi_res[0], dx=self.dtheta)
# G term integration
theta_terms[6,n] = romb(sinklq *dphi_res[1], dx=self.dtheta)
return theta_terms
def getthetaterms(self, dp1, dp1dot):
r"""Return array of integrated values for specified theta function and dphi function.
This modified version only returns the result for one k value.
Parameters
----------
dp1 : array_like
Array of values for dphi1
dp1dot : array_like
Array of values for dphi1dot
Returns
-------
theta_terms : tuple
Tuple of len(k)xlen(q) shaped arrays of integration results in form
Notes
-----
The returned expression is of the form
.. math::
\bigg(\int(\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi_1(k-q) d\theta,
\int(\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta,
\int(\cos(\theta)\sin(\theta) \delta\varphi^\dagger_1(k-q) d\theta)\bigg)
"""
# Sinusoidal theta terms
sinth = np.sin(self.theta)
cossinth = np.cos(self.theta) * sinth
cos2sinth = np.cos(self.theta) * cossinth
sin3th = sinth * sinth * sinth
theta_terms = np.empty([7, self.k.shape[0], self.k.shape[0]],
dtype=dp1.dtype)
lenq = len(self.k)
for n in np.atleast_1d(self.kix_wanted):
#klq = klessq(onek, q, theta)
dphi_res = srccython.interpdps(dp1, dp1dot, self.kmin, self.deltak,
n, self.theta, lenq)
theta_terms[0, n] = romb(sinth * dphi_res[0], dx=self.dtheta)
theta_terms[1, n] = romb(cossinth * dphi_res[0], dx=self.dtheta)
theta_terms[2, n] = romb(sinth * dphi_res[1], dx=self.dtheta)
theta_terms[3, n] = romb(cossinth * dphi_res[1], dx=self.dtheta)
#New terms for full solution
# E term integration
theta_terms[4, n] = romb(cos2sinth * dphi_res[0], dx=self.dtheta)
#Get klessq for F and G terms
klq2 = klessqksq(self.k[n], self.k, self.theta)
sinklq = sin3th / klq2
#Get rid of NaNs in places where dphi_res=0 or equivalently klq2<self.kmin**2
sinklq[klq2 < self.kmin**2] = 0
# F term integration
theta_terms[5, n] = romb(sinklq * dphi_res[0], dx=self.dtheta)
# G term integration
theta_terms[6, n] = romb(sinklq * dphi_res[1], dx=self.dtheta)
return theta_terms