def gamma_E_profile(self):
r = self.r_profile
# exclude first and last grid point, since those are potentially artificial
D = diff_matrix(r[1], r[-2], len(r) - 2, order=4)
omega0 = self.omega0_estimate_profile[1:-1]
ddr_omega0 = np.dot(D, omega0)
ddr_omega0 = np.concatenate(
([ddr_omega0[0]], ddr_omega0, [ddr_omega0[-1]]))
return -r * ddr_omega0 / (self.q)
def dpsiNdr(psi, r):
from diff_matrix import diff_matrix
psi_array = numpy.array([psi(ri) for ri in r])
psiN_array = psi_array / psi_array[-1]
rmin = r[0]
rmax = r[-1]
N = len(r)
diff_matrix = diff_matrix(rmin, rmax, N)
dpsiNdr_array = numpy.dot(diff_matrix, psiN_array)
return dpsiNdr_array
y,ddx_y=derivative_bezier_transition(flist,ddx_flist,plist,dlist,x)
fig = plt.figure()
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
plt.plot(x,y(x),'o')
plt.hold(True)
plt.plot(x,flist[0](x))
plt.plot(x,flist[1](x))
plt.plot(x,flist[2](x))
ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
plt.plot(x,ddx_y(x),'o')
plt.hold(True)
D=diff_matrix(x[0],x[-1],len(x))
plt.plot(x, numpy.dot(D,y(x)))
#ax = fig.add_subplot(numRows, numCols, plotNum); plotNum += 1
#t=numpy.linspace(0,1)
#P0=numpy.array([9,0])
#P1=numpy.array([10,-2])
#P2=numpy.array([13,-3])
#y=bezier_func_y(P0,P1,P2)(t)
#x=bezier_func_x(P0,P1,P2)(t)
#plt.plot(x,y)
return (min_val,max_val,psiMin,psiMax)
def generate_sin_profile(xPed,xPedGrad,psiMinPed,psiMaxPed):
(min_val,max_val,psiMin,psiMax) = parameter_wrapper(xPed,xPedGrad,psiMinPed,psiMaxPed)
return (sin_profile(min_val,max_val,psiMin,psiMax),ddx_sin_profile(min_val,max_val,psiMin,psiMax))
if __name__ == "__main__":
xped=1.0
w = 2
dxdr = 0.1
xsol = xped - dxdr*w
psiN0 = 1.0
psiN1 = psiN0 + w*2
psiN=np.linspace(psiN0,psiN1)
D=diff_matrix(psiN[0],psiN[-1],len(psiN))
x=sin_profile(xsol,xped,psiN0,psiN1)
dxdpsiN = ddx_sin_profile(xsol,xped,psiN0,psiN1)
numerical_dxdpsiN = np.dot(D,x(psiN))
plt.subplot(2, 1, 1)
plt.hold(True)
plt.plot(psiN,x(psiN))
plt.subplot(2, 1, 2)
plt.hold(True)
plt.plot(psiN,dxdpsiN(psiN))
plt.plot(psiN,numerical_dxdpsiN)