def cdf_inv(z, r, rho):
"""
Calculates the inverse CDF as a function of r over the whole disk
Parameters
----------
z : SimArray or array
2D z-positions that rho is calculated at. z[i,j] is the ith z bin
at r[j]
r : SimArray or array
Radial bins (1D array) the z and rho are calculated at
rho : SimArray or array
2D array of density values. rho[i,j] is rho at z[i,j], r[j]
Returns
-------
f : function
Inverse CDF. f(m, r) = z returns the z value for radius and 0<m<1.
r and m are 1-D arrays of the same length, or numbers.
"""
nz, nr = z.shape
f = np.zeros(z.shape)
zout = 0.*z
for i in range(nr):
f[:,i], zout[:,i] = cdf_inv_z(z[:,i], rho[:,i])
cdf_inv_spl = meshinterp(r, f.T, zout.T)
def fspl(m, R):
"""
Normalized inverse CDF at R. Calcuates z as a function of m
Parameters
----------
m : 1D array or float
Number(s) between 0 and 1
R : 1D SimArray, array, or float
Radius at which to calculate the CDF inverse along rho
Returns
-------
z : SimArray
z positions
"""
return cdf_inv_spl(R, m)
return fspl
def cdf_inv(z, r, rho):
"""
Calculates the inverse CDF as a function of r over the whole disk
Parameters
----------
z : SimArray or array
2D z-positions that rho is calculated at. z[i,j] is the ith z bin
at r[j]
r : SimArray or array
Radial bins (1D array) the z and rho are calculated at
rho : SimArray or array
2D array of density values. rho[i,j] is rho at z[i,j], r[j]
Returns
-------
f : function
Inverse CDF. f(m, r) = z returns the z value for radius and 0<m<1.
r and m are 1-D arrays of the same length, or numbers.
"""
nz, nr = z.shape
f = np.zeros(z.shape)
zout = 0. * z
for i in range(nr):
f[:, i], zout[:, i] = cdf_inv_z(z[:, i], rho[:, i])
cdf_inv_spl = meshinterp(r, f.T, zout.T)
def fspl(m, R):
"""
Normalized inverse CDF at R. Calcuates z as a function of m
Parameters
----------
m : 1D array or float
Number(s) between 0 and 1
R : 1D SimArray, array, or float
Radius at which to calculate the CDF inverse along rho
Returns
-------
z : SimArray
z positions
"""
return cdf_inv_spl(R, m)
return fspl
def rhointerp(z, r, rho):
"""
Generates a callable interpolation of rho on the z, r points
Parameters
----------
z : 2D SimArray or array
z[i,j] is the ith z value at r[j]
r : 1D SimArray or array
Radial positions
rho : SimArray
density at points z[i,j], r[j]
Returns
-------
rhospline : function
An interpolation function for estimating rho as a function of z, r
"""
f = meshinterp(r, z.T, rho.T)
def rhospline(Z, R):
"""
Returns rho evaluated at Z, R. Z and R must be 1D and the same length
Parameters
----------
Z, R : SimArray, array, or float
Z, R positions to estimate the density at. Must be same length
Returns
-------
rho : SimArray
Density evaluated at the Z,R positions
"""
return f(R, Z)
return rhospline
def rhointerp(z, r, rho):
"""
Generates a callable interpolation of rho on the z, r points
Parameters
----------
z : 2D SimArray or array
z[i,j] is the ith z value at r[j]
r : 1D SimArray or array
Radial positions
rho : SimArray
density at points z[i,j], r[j]
Returns
-------
rhospline : function
An interpolation function for estimating rho as a function of z, r
"""
f = meshinterp(r, z.T, rho.T)
def rhospline(Z, R):
"""
Returns rho evaluated at Z, R. Z and R must be 1D and the same length
Parameters
----------
Z, R : SimArray, array, or float
Z, R positions to estimate the density at. Must be same length
Returns
-------
rho : SimArray
Density evaluated at the Z,R positions
"""
return f(R, Z)
return rhospline