We consider a vacuum vessel embodied as a toroidal volume defined by a 2D arbitrary polygon representing in cross-section in (R,Z) coordinates. We want to efficiently mesh both the volume and the 3D surface of the vessel.
As input, we provide the cross-section polygon and a list dV defining the three resolutions dV = [dR,dZ,dRphi], where each resolution is a distance in meters in the corresponding direction (note the use of dRphi instead of dphi for that purpose). Indeed, we do not want a simple cylindrical mesh, as we want to capture details in the toroidal (Rphi) direction with a similar accuracy for every value of R.
In most uses, we will only need a fraction of the total mesh. Hence, the routine should not compute the total mesh but only the fraction we need. For a given resolution dV (i.e. a given tuple of dR,dZ,dRphi), there should be only one possible mesh. This way, the fraction of interest can be defined either by its physical limits (DR,DZ,DPhi) or by the indices of the mesh elements which are required.
Hence, we need a methods to
Not returning the whole mesh makes sense since it may well be a huge array (memory-expensive). The computation should be as fast as possible.
For a given input cross-section polygon VPoly, provided with the required resolutions dR, dZ and dRphi, the total mesh is a torus of rectangular cross-section (R goes from a minimum to a maximum, as Z, and phi goes from -pi to pi). This simplifies the computation of the indices without making the result heavier since only the relevant mesh elements are returned. The limits of the desired submesh can be provided as DR, DZ and DPhi (note that the toroidal limit is angular as opposed to the toroidal resolution).
The minimum and maximim boundaries of R and Z are also provided. They could be deduced from VPOly but they are explicitly provided for two reasons:
The indices are return in numeric form (not boolean), and computed as follows:
Hence, we first describe the innermost column (starting from the lowest horizontal ring), and we gradually moved towards the outermost column.
This is necessary since due the desired quasi-constant toroidal accuracy, the number of mesh elements in the toroidal direction is a function of R.
The strategy for meshing the surface is similar, expect that here there are only two resolutions, dL and dRPhi, where dL is the resolution in the poloidal direction along the segments of VPoly.
In [4]:
A = np.random.random((100,))
%timeit len(A)
%timeit A.size
The slowest run took 44.64 times longer than the fastest. This could mean that an intermediate result is being cached.
10000000 loops, best of 3: 90.8 ns per loop
The slowest run took 36.53 times longer than the fastest. This could mean that an intermediate result is being cached.
10000000 loops, best of 3: 111 ns per loop
In [55]:
10%2
Out[55]:
0
In [14]:
import numpy as np
# Preliminary function to get optimal resolution from input resolution
def _Ves_mesh_dlfromL_numpy(LMinMax, dL, DL=None, margin=1.e-9):
""" Get the actual reolution from the desired resolution and MinMax and limits """
# Get the number of mesh elements in LMinMax
N = np.ceil(np.diff(LMinMax)/dL)[0]
# Derive the real (effective) resolution
dLr = (np.diff(LMinMax)/N)[0]
# Get desired limits if any
DL = LMinMax if DL is None else DL
# Get the extreme indices of the mesh elements that really need to be created within those limits
abs0 = np.abs(DL[0]-LMinMax[0])
if abs0-dLr*np.floor(abs0/dLr)<margin*dLr:
nL0 = np.round((DL[0]-LMinMax[0])/dLr)
else:
nL0 = np.floor((DL[0]-LMinMax[0])/dLr)
abs1 = np.abs(DL[1]-LMinMax[0])
if abs1-dLr*np.floor(abs1/dLr)<margin*dLr:
nL1 = np.round((DL[1]-LMinMax[0])/dLr)-1
else:
nL1 = np.floor((DL[1]-LMinMax[0])/dLr)
# Get the corresponding indices
indL = np.arange(nL0,nL1+1,1).astype(int)
# Get the centers of the mesh elements
L = LMinMax[0] + (0.5 + indL)*dLr
return L, dLr, indL, N
def _Ves_Vmesh_Phi_numpy(DPhi, dPhir, NRPhi, margin=1.e-9):
""" Get the min and max indices of the relevant Phi for each R (to be finished) """
nPhi0 = np.nan*np.ones((dPhir.size,))
nPhi1 = np.nan*np.ones((dPhir.size,))
abs0 = np.abs(DPhi[0]+np.pi)
ind0 = abs0-dPhir*np.floor(abs0/dPhir)<margin*dPhir
nPhi0[ind0] = np.round((DPhi[0]+np.pi)/dPhir[ind0])
nPhi0[~ind0] = np.floor((DPhi[0]+np.pi)/dPhir[~ind0])
abs1 = np.abs(DPhi[1]+np.pi)
ind1 = abs1-dPhir*np.floor(abs1/dPhir)<margin*dPhir
nPhi1[ind1] = np.round((DPhi[1]+np.pi)/dPhir[ind1])-1
nPhi1[~ind1] = np.floor((DPhi[1]+np.pi)/dPhir[~ind1])
assert np.all(nPhi0>=0) and np.all(nPhi0<=NRPhi)
assert np.all(nPhi1>=0) and np.all(nPhi1<=NRPhi)
return nPhi0, nPhi1
def _Ves_Vmesh_Tor_SubFromD_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, DR=None, DZ=None, DPhi=None, VPoly=None, Out='(X,Y,Z)', margin=1.e-9):
""" Return the desired submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) """
# Get the actual R and Z resolutions and mesh elements
R0, dRr0, indR0, NR0 = _Ves_mesh_dlfromL_numpy(RMinMax, dR, None, margin=margin)
R, dRr, indR, NR = _Ves_mesh_dlfromL_numpy(RMinMax, dR, DR, margin=margin)
Z, dZr, indZ, NZ = _Ves_mesh_dlfromL_numpy(ZMinMax, dZ, DZ, margin=margin)
Rn, Zn = len(R), len(Z)
# Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
NRPhi0 = np.ceil(2.*np.pi*R0/dRPhi)
NRPhi = np.ceil(2.*np.pi*R/dRPhi)
dPhir = 2.*np.pi/NRPhi
# Get the limits if any (and make sure to replace them in the proper quadrants)
DPhi = [-np.pi,np.pi] if DPhi is None else np.arctan2(np.sin(DPhi),np.cos(DPhi))
# Later we'll have to remember that the lower limit may be greater than the upper limit due to 2pi modulo
# Get the two extreme indices of the Phi elements inside the limits for each R
nPhi0, nPhi1 = _Ves_Vmesh_Phi_numpy(DPhi, dPhir, NRPhi, margin=margin)
# Compute the centers and indices, using a for loop (no choice) on R
NRZPhi_cum0 = np.concatenate(([0],NZ*np.cumsum(NRPhi0[:-1])))
PtsRZP, dV, ind = [], [], []
for ii in range(0,Rn):
# Get the phi values
if DPhi[0]<DPhi[1]:
indPhi = np.arange(nPhi0[ii],nPhi1[ii]+1)
else:
indPhi = np.concatenate((np.arange(nPhi0[ii],NRPhi[ii]),np.arange(0,nPhi1[ii]+1)))
Phin = len(indPhi)
phi = -np.pi + (0.5 + indPhi)*dPhir[ii]
# Get the (R,Z,phi) points
PtsRZP.append( np.array([R[ii]*np.ones((Phin*Zn,)), np.repeat(Z,Phin), np.tile(phi,Zn)]) )
# Get the volume
dV.append( dRr*dZr*dPhir[ii]*R[ii]*np.ones((Phin*Zn,)) )
# Get the indices
indii = R0==R[ii]
ind.append( NRZPhi_cum0[indii] + (indZ[:,np.newaxis]*NRPhi[ii] + indPhi[np.newaxis,:]).flatten() )
PtsRZP = np.concatenate(tuple(PtsRZP),axis=1)
dV = np.concatenate(tuple(dV))
ind = np.concatenate(tuple(ind))
# To be commented out once debugged
assert ind.size==PtsRZP.shape[1]
assert ind.size==dV.size
assert np.unique(ind).size==ind.size
dRPhir = (dPhir*R)
"""
if not VPoly is None:
indin = _Ves_isInside(VPoly, 'Tor', None, PtsRZP[:-1,:], In='(R,Z)')
PtsRZP, dV, ind = PtsRZP[:,indin], dV[indin], ind[indin]
Ru = np.unique(PtsRZP[0,:])
if not Ru==R:
indii = np.array([R[ii] in Ru for ii in range(0,len(R))], dtype=bool)
dRPhir = dRPhir[indii]
"""
if Out.lower()=='(x,y,z)':
Pts = np.array([PtsRZP[0,:]*np.cos(PtsRZP[2,:]), PtsRZP[0,:]*np.sin(PtsRZP[2,:]), PtsRZP[1,:]])
else:
Pts = PtsRZP
return Pts, dV, ind, dRr, dZr, dRPhir
def _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, ind, Out='(X,Y,Z)', margin=1.e-9):
""" Return the desired submesh indicated by the (numerical) indices, for the desired resolution (dR,dZ,dRphi) """
# Get the actual R and Z resolutions and mesh elements
R, dRr, indR, NR = _Ves_mesh_dlfromL_numpy(RMinMax, dR, None, margin=margin)
Z, dZr, indZ, NZ = _Ves_mesh_dlfromL_numpy(ZMinMax, dZ, None, margin=margin)
Rn, Zn = len(R), len(Z)
# Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
NRPhi = np.ceil(2.*np.pi*R/dRPhi)
dPhir = 2.*np.pi/NRPhi
NRZPhi_cum = np.concatenate(([0],NZ*np.cumsum(NRPhi[:-1])))
# Get R, Z, and Phi indices
Nind = ind.size
indR = ind[:,np.newaxis]-NRZPhi_cum[np.newaxis,:]<0
indRtemp = np.tile(np.arange(0,NR),(Nind,1))
indRtemp[indR] = np.nan
indR = np.nanmax(indRtemp, axis=1).astype(int)
indZ = ((ind - NRZPhi_cum[indR]) // NRPhi[indR]).astype(int)
indPhi = ind - NRZPhi_cum[indR] - indZ*NRPhi[indR]
# Derive R, Z and phi values
PtsRZP = np.array([R[indR], Z[indZ], np.nan*np.ones((Nind,))])
dV = np.nan*np.ones((Nind,))
Ru = np.unique(PtsRZP[0,:])
dRPhir = np.nan*np.ones((len(Ru),))
for ii in range(0,len(Ru)):
indRii = (R==Ru[ii]).nonzero()[0]
indRu = (PtsRZP[0,:]==Ru[ii]).nonzero()[0]
PtsRZP[2,indRu] = -np.pi + (0.5+indPhi[indRu])*dPhir[indRii]
dRPhir[ii] = dPhir[indRii]*Ru[ii]
dV[indRu] = dRr*dZr*dRPhir[ii]
if Out.lower()=='(x,y,z)':
Pts = np.array([PtsRZP[0,:]*np.cos(PtsRZP[2,:]), PtsRZP[0,:]*np.sin(PtsRZP[2,:]), PtsRZP[1,:]])
else:
Pts = PtsRZP
return Pts, dV, dRr, dZr, dRPhir
In [2]:
# Check and debug
[dR, dZ, dRPhi], RMinMax, ZMinMax = [0.03]*3, [2.,3.], [-1.,1.]
DR, DZ, DPhi = [2.15,2.6], [-0.21,0.51], [7.*np.pi/4.,5.*np.pi/4.]
Pts0, dV0, ind0, dRr0, dZr0, dRPhir0 = _Ves_Vmesh_Tor_SubFromD_numpy(dR,dZ,dRPhi, RMinMax,ZMinMax, Out='(X,Y,Z)')
PtsRZP0 = np.array([np.hypot(Pts0[0,:],Pts0[1,:]), Pts0[2,:],np.arctan2(Pts0[1,:],Pts0[0,:])])
Pts0b, dV0b, dRr0b, dZr0b, dRPhir0b = _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, ind0, Out='(X,Y,Z)')
print "Check 0", [np.allclose(Pts0,Pts0b,atol=1.e-14,rtol=0.,equal_nan=True) for (A,B) in [(Pts0,Pts0b),(dV0,dV0b),(dRr0,dRr0b),(dZr0,dZr0b),(dRPhir0,dRPhir0b)]]
Pts, dV, ind, dRr, dZr, dRPhir = _Ves_Vmesh_Tor_SubFromD_numpy(dR,dZ,dRPhi, RMinMax,ZMinMax, DR=DR,DZ=DZ,DPhi=DPhi, Out='(X,Y,Z)')
PtsRZP = np.array([np.hypot(Pts[0,:],Pts[1,:]), Pts[2,:],np.arctan2(Pts[1,:],Pts[0,:])])
Ptsb, dVb, dRrb, dZrb, dRPhirb = _Ves_Vmesh_Tor_SubFromInd_numpy(dR,dZ,dRPhi, RMinMax,ZMinMax, ind, Out='(X,Y,Z)')
print "Check 1", [np.allclose(A,B,atol=1.e-14,rtol=0.,equal_nan=True) for (A,B) in [(Pts,Ptsb),(dV,dVb),(dRr,dRrb),(dZr,dZrb),(dRPhir,dRPhirb)]]
Check 0 [True, True, True, True, True]
Check 1 [True, True, True, True, True]
In [3]:
# Plot for check and debug
import matplotlib.pyplot as plt
plt.figure(figsize=(16,10))
plt.subplot(1,2,1, aspect="equal", adjustable="datalim")
plt.plot(PtsRZP0[0,:],PtsRZP0[1,:],'.b', PtsRZP[0,:],PtsRZP[1,:],'.r', markersize=2)
plt.plot([DR[0],DR[1],DR[1],DR[0],DR[0]], [DZ[0],DZ[0],DZ[1],DZ[1],DZ[0]],'--k')
plt.subplot(1,2,2, aspect="equal", adjustable="datalim")
plt.plot(Pts0[0,:],Pts0[1,:],'.b', Pts[0,:],Pts[1,:],'.r', markersize=2)
thet = np.linspace(DPhi[0],DPhi[1],100) if DPhi[0]<DPhi[1] else np.linspace(DPhi[0],DPhi[1]+2.*np.pi,100)
X = np.concatenate((DR[0]*np.cos(thet),DR[1]*np.cos(thet[::-1]),[DR[0]*np.cos(thet[0])]))
Y = np.concatenate((DR[0]*np.sin(thet),DR[1]*np.sin(thet[::-1]),[DR[0]*np.sin(thet[0])]))
plt.plot(X,Y,'--k')
plt.show()
In [6]:
# Check and debug
[dR, dZ, dRPhi], RMinMax, ZMinMax = [0.02]*3, [2.,3.], [-1.,1.]
DR, DZ, DPhi = [2.15,2.6], [-0.21,0.51], [7.*np.pi/4.,5.*np.pi/4.]
Pts0, dV0, ind0, dRr0, dZr0, dRPhir0 = _Ves_Vmesh_Tor_SubFromD_numpy(dR,dZ,dRPhi, RMinMax,ZMinMax, Out='(X,Y,Z)')
%timeit out = _Ves_Vmesh_Tor_SubFromD_numpy(dR,dZ,dRPhi, RMinMax,ZMinMax, Out='(X,Y,Z)')
%timeit out = _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, ind0, Out='(X,Y,Z)')
1 loop, best of 3: 773 ms per loop
1 loop, best of 3: 6.31 s per loop
In [1]:
%load_ext cython
In [52]:
%%cython -a
cimport cython
import numpy as np
cimport numpy as cnp
from cpython cimport bool
from libc.math cimport ceil as Cceil, abs as Cabs, floor as Cfloor, round as Cround
from libc.math cimport cos as Ccos, sin as Csin, atan2 as Catan2, pi as Cpi
from matplotlib.path import Path
import datetime as dtm
# Preliminary function to get optimal resolution from input resolution
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_mesh_dlfromL_cython(double[::1] LMinMax, double dL, DL=None, double margin=1.e-9):
""" Get the actual reolution from the desired resolution and MinMax and limits """
# Get the number of mesh elements in LMinMax
cdef double N = Cceil((LMinMax[1]-LMinMax[0])/dL)
# Derive the real (effective) resolution
cdef double dLr = (LMinMax[1]-LMinMax[0])/N
# Get desired limits if any
cdef double[::1] DLc, L
cdef long [::1] indL
#cdef cnp.ndarray[double,ndim=1] indL, L
cdef double abs0, abs1, A
cdef int nL0, nL1, Nind, ii, jj
if DL is None:
DLc = LMinMax
else:
if DL[0] is None:
DL[0] = LMinMax[0]
if DL[1] is None:
DL[1] = LMinMax[1]
DLc = np.array(DL)
# Get the extreme indices of the mesh elements that really need to be created within those limits
abs0 = Cabs(DLc[0]-LMinMax[0])
if abs0-dLr*Cfloor(abs0/dLr)<margin*dLr:
nL0 = int(Cround((DLc[0]-LMinMax[0])/dLr))
else:
nL0 = int(Cfloor((DLc[0]-LMinMax[0])/dLr))
abs1 = Cabs(DLc[1]-LMinMax[0])
if abs1-dLr*Cfloor(abs1/dLr)<margin*dLr:
nL1 = int(Cround((DLc[1]-LMinMax[0])/dLr)-1)
else:
nL1 = int(Cfloor((DLc[1]-LMinMax[0])/dLr))
# Get the corresponding indices
Nind = nL1+1-nL0
indL = np.empty((Nind,),dtype=int)#np.linspace(nL0,nL1,Nind,endpoint=True)
L = np.empty((Nind,))
for ii in range(0,Nind):
jj = nL0+ii
indL[ii] = jj
L[ii] = LMinMax[0] + (0.5 + (<double>jj))*dLr
return np.asarray(L), dLr, np.asarray(indL), N
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Vmesh_Tor_SubFromD_cython(double dR, double dZ, double dRPhi,
double[::1] RMinMax, double[::1] ZMinMax,
DR=None, DZ=None, DPhi=None, VPoly=None,
str Out='(X,Y,Z)', double margin=1.e-9):
" Return the desired submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
cdef double[::1] R0, R, Z, dRPhir, dPhir, NRPhi#, dPhi, NRZPhi_cum0, indPhi, phi
cdef double dRr0, dRr, dZr, DPhi0, DPhi1
cdef double abs0, abs1, phi, indiijj
cdef long[::1] indR0, indR, indZ, Phin, NRPhi0
cdef int NR0, NR, NZ, Rn, Zn, nRPhi0, indR0ii, ii, jj, nPhi0, nPhi1, zz, NP, NRPhi_int, Rratio
cdef cnp.ndarray[double,ndim=2] Pts, indI
cdef cnp.ndarray[double,ndim=1] dV, ind
# Get the actual R and Z resolutions and mesh elements
R0, dRr0, indR0, NR0 = _Ves_mesh_dlfromL_cython(RMinMax, dR, None, margin=margin)
R, dRr, indR, NR = _Ves_mesh_dlfromL_cython(RMinMax, dR, DR, margin=margin)
Z, dZr, indZ, NZ = _Ves_mesh_dlfromL_cython(ZMinMax, dZ, DZ, margin=margin)
Rn = len(R)
Zn = len(Z)
# Get the limits if any (and make sure to replace them in the proper quadrants)
if DPhi is None:
DPhi0, DPhi1 = -Cpi, Cpi
else:
DPhi0, DPhi1 = Catan2(Csin(DPhi[0]),Ccos(DPhi[0])), Catan2(Csin(DPhi[1]),Ccos(DPhi[1]))
dRPhir, dPhir = np.empty((Rn,)), np.empty((Rn,))
Phin = np.empty((Rn,),dtype=int)
NRPhi = np.empty((Rn,))
NRPhi0 = np.zeros((Rn,),dtype=int)
nRPhi0, indR0ii = 0, 0
NP, NPhimax = 0, 0
Rratio = int(Cceil(R[Rn-1]/R[0]))
for ii in range(0,Rn):
# Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
NRPhi[ii] = Cceil(2.*Cpi*R[ii]/dRPhi)
NRPhi_int = int(NRPhi[ii])
dPhir[ii] = 2.*Cpi/NRPhi[ii]
dRPhir[ii] = dPhir[ii]*R[ii]
# Get index and cumulated indices from background
for jj in range(indR0ii,NR0):
if R0[jj]==R[ii]:
indR0ii = jj
break
else:
nRPhi0 += <long>Cceil(2.*Cpi*R0[jj]/dRPhi)
NRPhi0[ii] = nRPhi0*NZ
# Get indices of phi
# Get the extreme indices of the mesh elements that really need to be created within those limits
abs0 = Cabs(DPhi0+Cpi)
if abs0-dPhir[ii]*Cfloor(abs0/dPhir[ii])<margin*dPhir[ii]:
nPhi0 = int(Cround((DPhi0+Cpi)/dPhir[ii]))
else:
nPhi0 = int(Cfloor((DPhi0+Cpi)/dPhir[ii]))
abs1 = Cabs(DPhi1+Cpi)
if abs1-dPhir[ii]*Cfloor(abs1/dPhir[ii])<margin*dPhir[ii]:
nPhi1 = int(Cround((DPhi1+Cpi)/dPhir[ii])-1)
else:
nPhi1 = int(Cfloor((DPhi1+Cpi)/dPhir[ii]))
if DPhi0<DPhi1:
#indI.append(list(range(nPhi0,nPhi1+1)))
Phin[ii] = nPhi1+1-nPhi0
if ii==0:
indI = np.ones((Rn,Phin[ii]*Rratio+1))
for jj in range(0,Phin[ii]):
indI[ii,jj] = <double>( nPhi0+jj )
else:
#indI.append(list(range(nPhi0,NRPhi_int)+list(range(0,nPhi1+1))))
Phin[ii] = nPhi1+1+NRPhi_int-nPhi0
if ii==0:
indI = np.ones((Rn,Phin[ii]*Rratio+1))
for jj in range(0,NRPhi_int-nPhi0):
indI[ii,jj] = <double>( nPhi0+jj )
for jj in range(NRPhi_int-nPhi0,Phin[ii]):
indI[ii,jj] = <double>( jj- (NRPhi_int-nPhi0) )
NP += Zn*Phin[ii]
Pts = np.empty((3,NP))
ind = np.empty((NP,))
dV = np.empty((NP,))
# Compute Pts, dV and ind
# This triple loop is the longest part, it takes ~90% of the CPU time
NP = 0
if Out.lower()=='(x,y,z)':
for ii in range(0,Rn):
for zz in range(0,Zn):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
phi = -Cpi + (0.5+indiijj)*dPhir[ii]
Pts[0,NP] = R[ii]*Ccos(phi)
Pts[1,NP] = R[ii]*Csin(phi)
Pts[2,NP] = Z[zz]
ind[NP] = NRPhi0[ii] + indZ[zz]*NRPhi[ii] + indiijj
dV[NP] = dRr*dZr*dRPhir[ii]
NP += 1
else:
for ii in range(0,Rn):
for zz in range(0,Zn):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
Pts[0,NP] = R[ii]
Pts[1,NP] = Z[zz]
Pts[2,NP] = -Cpi + (0.5+indiijj)*dPhir[ii]
ind[NP] = NRPhi0[ii] + indZ[zz]*NRPhi[ii] + indiijj
dV[NP] = dRr*dZr*dRPhir[ii]
NP += 1
if not VPoly is None:
indin = Path(VPoly.T).contains_points(PtsRZP[:-1,:].T, transform=None, radius=0.0)
PtsRZP, dV, ind = PtsRZP[:,indin], dV[indin], ind[indin]
Ru = np.unique(PtsRZP[0,:])
if not Ru==R:
indii = np.array([R[ii] in Ru for ii in range(0,len(R))], dtype=bool)
dRPhir = dRPhir[indii]
return Pts, dV, ind.astype(int), dRr, dZr, np.asarray(dRPhir)
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Vmesh_Tor_SubFromInd_cython(double dR, double dZ, double dRPhi,
double[::1] RMinMax, double[::1] ZMinMax, long[::1] ind,
str Out='(X,Y,Z)', double margin=1.e-9):
""" Return the desired submesh indicated by the (numerical) indices, for the desired resolution (dR,dZ,dRphi) """
cdef double[::1] R, Z, dRPhirRef, dPhir, Ru, dRPhir
cdef double dRr, dZr, phi
cdef long[::1] indR, indZ, NRPhi0, NRPhi
cdef long NR, NZ, Rn, Zn, NP=len(ind), Rratio
cdef int ii, jj, iiR, iiZ, iiphi
cdef double[:,::1] Phi
cdef cnp.ndarray[double,ndim=2] Pts=np.empty((3,NP))
cdef cnp.ndarray[double,ndim=1] dV=np.empty((NP,))
# Get the actual R and Z resolutions and mesh elements
R, dRr, indR, NR = _Ves_mesh_dlfromL_cython(RMinMax, dR, None, margin=margin)
Z, dZr, indZ, NZ = _Ves_mesh_dlfromL_cython(ZMinMax, dZ, None, margin=margin)
Rn, Zn = len(R), len(Z)
# Number of Phi per R
dRPhirRef, dPhir = np.empty((NR,)), np.empty((NR,))
Ru, dRPhir = np.zeros((NR,)), np.nan*np.ones((NR,))
NRPhi, NRPhi0 = np.empty((NR,),dtype=int), np.empty((NR+1,),dtype=int)
Rratio = int(Cceil(R[NR-1]/R[0]))
for ii in range(0,NR):
NRPhi[ii] = <long>(Cceil(2.*Cpi*R[ii]/dRPhi))
dRPhirRef[ii] = 2.*Cpi*R[ii]/<double>(NRPhi[ii])
dPhir[ii] = 2.*Cpi/<double>(NRPhi[ii])
if ii==0:
NRPhi0[ii] = 0
Phi = np.empty((NR,NRPhi[ii]*Rratio+1))
else:
NRPhi0[ii] = NRPhi0[ii-1] + NRPhi[ii-1]*NZ
for jj in range(0,NRPhi[ii]):
Phi[ii,jj] = -Cpi + (0.5+<double>jj)*dPhir[ii]
if Out.lower()=='(x,y,z)':
for ii in range(0,NP):
for jj in range(0,NR+1):
if ind[ii]-NRPhi0[jj]<0.:
break
iiR = jj-1
iiZ = (ind[ii] - NRPhi0[iiR])//NRPhi[iiR]
iiphi = ind[ii] - NRPhi0[iiR] - iiZ*NRPhi[iiR]
phi = Phi[iiR,iiphi]
Pts[0,ii] = R[iiR]*Ccos(phi)
Pts[1,ii] = R[iiR]*Csin(phi)
Pts[2,ii] = Z[iiZ]
dV[ii] = dRr*dZr*dRPhirRef[iiR]
if Ru[iiR]==0.:
dRPhir[iiR] = dRPhirRef[iiR]
Ru[iiR] = 1.
else:
for ii in range(0,NP):
for jj in range(0,NR+1):
if ind[ii]-NRPhi0[jj]<0.:
break
iiR = jj-1
iiZ = (ind[ii] - NRPhi0[iiR])//NRPhi[iiR]
iiphi = ind[ii] - NRPhi0[iiR] - iiZ*NRPhi[iiR]
Pts[0,ii] = R[iiR]
Pts[1,ii] = Z[iiZ]
Pts[2,ii] = Phi[iiR,iiphi]
dV[ii] = dRr*dZr*dRPhirRef[iiR]
if Ru[iiR]==0.:
dRPhir[iiR] = dRPhirRef[iiR]
Ru[iiR] = 1.
return Pts, dV, dRr, dZr, np.asarray(dRPhir)[~np.isnan(dRPhir)]
def _Ves_Vmesh_Lin_SubFromD_cython(double dX, double dY, double dZ,
double[::1] XMinMax, double[::1] YMinMax, double[::1] ZMinMax,
DX=None, DY=None, DZ=None, VPoly=None,
double margin=1.e-9):
" Return the desired submesh indicated by the limits (DX,DY,DZ), for the desired resolution (dX,dY,dZ) "
cdef double[::1] X, Y, Z
cdef double dXr, dYr, dZr, dV
cdef cnp.ndarray[long,ndim=1] indX, indY, indZ
cdef int NX, NY, NZ, Xn, Yn, Zn
cdef cnp.ndarray[double,ndim=2] Pts
cdef cnp.ndarray[long,ndim=1] ind
# Get the actual X, Y and Z resolutions and mesh elements
X, dXr, indX, NX = _Ves_mesh_dlfromL_cython(XMinMax, dX, DX, margin=margin)
Y, dYr, indY, NY = _Ves_mesh_dlfromL_cython(YMinMax, dY, DY, margin=margin)
Z, dZr, indZ, NZ = _Ves_mesh_dlfromL_cython(ZMinMax, dZ, DZ, margin=margin)
Xn, Yn, Zn = len(X), len(Y), len(Z)
Pts = np.array([np.tile(X,(Yn*Zn,1)).flatten(), np.tile(np.repeat(Y,Xn),(Zn,1)).flatten(), np.repeat(Z,Xn*Yn)])
ind = np.repeat(NX*NY*indZ,Xn*Yn) + np.tile(np.repeat(NX*indY,Xn),(Zn,1)).flatten() + np.tile(indX,(Yn*Zn,1)).flatten()
dV = dXr*dYr*dZr
#if VPoly is not None:
# indin = _Ves_isInside(Pts[:-1,:], VPoly=VPoly, VType='Lin', In='(X,Y)')
# Pts, dV, ind = Pts[:,indin], dV[indin], ind[indin]
return Pts, dV, ind.astype(int), dXr, dYr, dZr
def _Ves_Vmesh_Lin_SubFromInd_cython(double dX, double dY, double dZ,
double[::1] XMinMax, double[::1] YMinMax, double[::1] ZMinMax,
cnp.ndarray[long,ndim=1] ind, double margin=1.e-9):
" Return the desired submesh indicated by the limits (DX,DY,DZ), for the desired resolution (dX,dY,dZ) "
cdef cnp.ndarray[double,ndim=1] X, Y, Z
cdef double dXr, dYr, dZr, dV
cdef long[::1] bla
cdef cnp.ndarray[long,ndim=1] indX, indY, indZ
cdef int NX, NY, NZ, Xn, Yn, Zn
cdef cnp.ndarray[double,ndim=2] Pts
# Get the actual X, Y and Z resolutions and mesh elements
X, dXr, bla, NX = _Ves_mesh_dlfromL_cython(XMinMax, dX, None, margin=margin)
Y, dYr, bla, NY = _Ves_mesh_dlfromL_cython(YMinMax, dY, None, margin=margin)
Z, dZr, bla, NZ = _Ves_mesh_dlfromL_cython(ZMinMax, dZ, None, margin=margin)
#print NX, NY, NZ
indZ = ind // (NX*NY)
indY = (ind - NX*NY*indZ) // NX
indX = ind - NX*NY*indZ - NX*indY
#print ind
#print indZ
#print indY
#print indX
Pts = np.array([X[indX.astype(int)], Y[indY.astype(int)], Z[indZ.astype(int)]])
dV = dXr*dYr*dZr
return Pts, dV, dXr, dYr, dZr
Out[52]:
Cython: _cython_magic_ffb7650808bb7830760fff8d6d047f13.pyx
Generated by Cython 0.25.2
Yellow lines hint at Python interaction.
Click on a line that starts with a "+" to see the C code that Cython generated for it.
+001: cimport cython
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003: cimport numpy as cnp
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006: from libc.math cimport cos as Ccos, sin as Csin, atan2 as Catan2, pi as Cpi
007:
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011: @cython.cdivision(True)
012: @cython.wraparound(False)
013: @cython.boundscheck(False)
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015: """ Get the actual reolution from the desired resolution and MinMax and limits """
016: # Get the number of mesh elements in LMinMax
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024: cdef double abs0, abs1, A
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062: str Out='(X,Y,Z)', double margin=1.e-9):
063: " Return the desired submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
064:
065: cdef double[::1] R0, R, Z, dRPhir, dPhir, NRPhi#, dPhi, NRZPhi_cum0, indPhi, phi
066: cdef double dRr0, dRr, dZr, DPhi0, DPhi1
067: cdef double abs0, abs1, phi, indiijj
068: cdef long[::1] indR0, indR, indZ, Phin, NRPhi0
069: cdef int NR0, NR, NZ, Rn, Zn, nRPhi0, indR0ii, ii, jj, nPhi0, nPhi1, zz, NP, NRPhi_int, Rratio
070: cdef cnp.ndarray[double,ndim=2] Pts, indI
071: cdef cnp.ndarray[double,ndim=1] dV, ind
072:
073: # Get the actual R and Z resolutions and mesh elements
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+090: nRPhi0, indR0ii = 0, 0
__pyx_t_11 = 0;
__pyx_t_19 = 0;
__pyx_v_nRPhi0 = __pyx_t_11;
__pyx_v_indR0ii = __pyx_t_19;
+091: NP, NPhimax = 0, 0
__pyx_t_19 = 0;
__pyx_t_20 = 0;
__pyx_v_NP = __pyx_t_19;
__pyx_v_NPhimax = __pyx_t_20;
+092: Rratio = int(Cceil(R[Rn-1]/R[0]))
__pyx_t_21 = (__pyx_v_Rn - 1);
__pyx_t_22 = 0;
__pyx_v_Rratio = ((int)ceil(((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_21)) ))) / (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_22)) ))))));
+093: for ii in range(0,Rn):
__pyx_t_19 = __pyx_v_Rn;
for (__pyx_t_11 = 0; __pyx_t_11 < __pyx_t_19; __pyx_t_11+=1) {
__pyx_v_ii = __pyx_t_11;
094: # Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
+095: NRPhi[ii] = Cceil(2.*Cpi*R[ii]/dRPhi)
__pyx_t_23 = __pyx_v_ii;
__pyx_t_24 = __pyx_v_ii;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_NRPhi.data) + __pyx_t_24)) )) = ceil((((2. * M_PI) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_23)) )))) / __pyx_v_dRPhi));
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__pyx_t_25 = __pyx_v_ii;
__pyx_v_NRPhi_int = ((int)(*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_NRPhi.data) + __pyx_t_25)) ))));
+097: dPhir[ii] = 2.*Cpi/NRPhi[ii]
__pyx_t_26 = __pyx_v_ii;
__pyx_t_27 = __pyx_v_ii;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_27)) )) = ((2. * M_PI) / (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_NRPhi.data) + __pyx_t_26)) ))));
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__pyx_t_28 = __pyx_v_ii;
__pyx_t_29 = __pyx_v_ii;
__pyx_t_30 = __pyx_v_ii;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhir.data) + __pyx_t_30)) )) = ((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_28)) ))) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_29)) ))));
099: # Get index and cumulated indices from background
+100: for jj in range(indR0ii,NR0):
__pyx_t_31 = __pyx_v_NR0;
for (__pyx_t_32 = __pyx_v_indR0ii; __pyx_t_32 < __pyx_t_31; __pyx_t_32+=1) {
__pyx_v_jj = __pyx_t_32;
+101: if R0[jj]==R[ii]:
__pyx_t_33 = __pyx_v_jj;
__pyx_t_34 = __pyx_v_ii;
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if (__pyx_t_14) {
/* … */
}
+102: indR0ii = jj
__pyx_v_indR0ii = __pyx_v_jj;
+103: break
goto __pyx_L13_break;
104: else:
+105: nRPhi0 += <long>Cceil(2.*Cpi*R0[jj]/dRPhi)
/*else*/ {
__pyx_t_35 = __pyx_v_jj;
__pyx_v_nRPhi0 = (__pyx_v_nRPhi0 + ((long)ceil((((2. * M_PI) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R0.data) + __pyx_t_35)) )))) / __pyx_v_dRPhi))));
+106: NRPhi0[ii] = nRPhi0*NZ
__pyx_t_36 = __pyx_v_ii;
*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_36)) )) = (__pyx_v_nRPhi0 * __pyx_v_NZ);
}
}
__pyx_L13_break:;
107: # Get indices of phi
108: # Get the extreme indices of the mesh elements that really need to be created within those limits
+109: abs0 = Cabs(DPhi0+Cpi)
__pyx_v_abs0 = fabs((__pyx_v_DPhi0 + M_PI));
+110: if abs0-dPhir[ii]*Cfloor(abs0/dPhir[ii])<margin*dPhir[ii]:
__pyx_t_37 = __pyx_v_ii;
__pyx_t_38 = __pyx_v_ii;
__pyx_t_39 = __pyx_v_ii;
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if (__pyx_t_14) {
/* … */
goto __pyx_L15;
}
+111: nPhi0 = int(Cround((DPhi0+Cpi)/dPhir[ii]))
__pyx_t_40 = __pyx_v_ii;
__pyx_v_nPhi0 = ((int)round(((__pyx_v_DPhi0 + M_PI) / (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_40)) ))))));
112: else:
+113: nPhi0 = int(Cfloor((DPhi0+Cpi)/dPhir[ii]))
/*else*/ {
__pyx_t_41 = __pyx_v_ii;
__pyx_v_nPhi0 = ((int)floor(((__pyx_v_DPhi0 + M_PI) / (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_41)) ))))));
}
__pyx_L15:;
+114: abs1 = Cabs(DPhi1+Cpi)
__pyx_v_abs1 = fabs((__pyx_v_DPhi1 + M_PI));
+115: if abs1-dPhir[ii]*Cfloor(abs1/dPhir[ii])<margin*dPhir[ii]:
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__pyx_t_43 = __pyx_v_ii;
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if (__pyx_t_14) {
/* … */
goto __pyx_L16;
}
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__pyx_v_nPhi1 = ((int)(round(((__pyx_v_DPhi1 + M_PI) / (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_45)) ))))) - 1.0));
117: else:
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}
__pyx_L16:;
119:
+120: if DPhi0<DPhi1:
__pyx_t_14 = ((__pyx_v_DPhi0 < __pyx_v_DPhi1) != 0);
if (__pyx_t_14) {
/* … */
goto __pyx_L17;
}
121: #indI.append(list(range(nPhi0,nPhi1+1)))
+122: Phin[ii] = nPhi1+1-nPhi0
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*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_Phin.data) + __pyx_t_47)) )) = ((__pyx_v_nPhi1 + 1) - __pyx_v_nPhi0);
+123: if ii==0:
__pyx_t_14 = ((__pyx_v_ii == 0) != 0);
if (__pyx_t_14) {
/* … */
}
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127: else:
128: #indI.append(list(range(nPhi0,NRPhi_int)+list(range(0,nPhi1+1))))
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167:
168: """
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170: # indin = _Ves_isInside(VPoly, 'Tor', None, PtsRZP[:-1,:], In='(R,Z)')
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179:
180: @cython.cdivision(True)
181: @cython.wraparound(False)
182: @cython.boundscheck(False)
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__pyx_t_14 = __pyx_v_NR;
for (__pyx_t_20 = 0; __pyx_t_20 < __pyx_t_14; __pyx_t_20+=1) {
__pyx_v_ii = __pyx_t_20;
+207: NRPhi[ii] = <long>(Cceil(2.*Cpi*R[ii]/dRPhi))
__pyx_t_21 = __pyx_v_ii;
__pyx_t_22 = __pyx_v_ii;
*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_22)) )) = ((long)ceil((((2. * M_PI) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_21)) )))) / __pyx_v_dRPhi)));
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__pyx_t_23 = __pyx_v_ii;
__pyx_t_24 = __pyx_v_ii;
__pyx_t_25 = __pyx_v_ii;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhirRef.data) + __pyx_t_25)) )) = (((2. * M_PI) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_23)) )))) / ((double)(*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_24)) )))));
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__pyx_t_27 = __pyx_v_ii;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_27)) )) = ((2. * M_PI) / ((double)(*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_26)) )))));
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__pyx_t_28 = ((__pyx_v_ii == 0) != 0);
if (__pyx_t_28) {
/* … */
goto __pyx_L9;
}
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*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_29)) )) = 0;
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__PYX_XDEC_MEMVIEW(&__pyx_v_Phi, 1);
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__pyx_t_31.data = NULL;
213: else:
+214: NRPhi0[ii] = NRPhi0[ii-1] + NRPhi[ii-1]*NZ
/*else*/ {
__pyx_t_32 = (__pyx_v_ii - 1);
__pyx_t_33 = (__pyx_v_ii - 1);
__pyx_t_34 = __pyx_v_ii;
*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_34)) )) = ((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_32)) ))) + ((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_33)) ))) * __pyx_v_NZ));
}
__pyx_L9:;
+215: for jj in range(0,NRPhi[ii]):
__pyx_t_35 = __pyx_v_ii;
__pyx_t_36 = (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_35)) )));
for (__pyx_t_37 = 0; __pyx_t_37 < __pyx_t_36; __pyx_t_37+=1) {
__pyx_v_jj = __pyx_t_37;
+216: Phi[ii,jj] = -Cpi + (0.5+<double>jj)*dPhir[ii]
__pyx_t_38 = __pyx_v_ii;
if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 216, __pyx_L1_error) }
__pyx_t_39 = __pyx_v_ii;
__pyx_t_40 = __pyx_v_jj;
*((double *) ( /* dim=1 */ ((char *) (((double *) ( /* dim=0 */ (__pyx_v_Phi.data + __pyx_t_39 * __pyx_v_Phi.strides[0]) )) + __pyx_t_40)) )) = ((-M_PI) + ((0.5 + ((double)__pyx_v_jj)) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dPhir.data) + __pyx_t_38)) )))));
}
}
217:
+218: if Out.lower()=='(x,y,z)':
__pyx_t_9 = __Pyx_PyObject_GetAttrStr(__pyx_v_Out, __pyx_n_s_lower); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 218, __pyx_L1_error)
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if (__pyx_t_28) {
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goto __pyx_L12;
}
+219: for ii in range(0,NP):
__pyx_t_14 = __pyx_v_NP;
for (__pyx_t_20 = 0; __pyx_t_20 < __pyx_t_14; __pyx_t_20+=1) {
__pyx_v_ii = __pyx_t_20;
+220: for jj in range(0,NR+1):
__pyx_t_36 = (__pyx_v_NR + 1);
for (__pyx_t_37 = 0; __pyx_t_37 < __pyx_t_36; __pyx_t_37+=1) {
__pyx_v_jj = __pyx_t_37;
+221: if ind[ii]-NRPhi0[jj]<0.:
__pyx_t_41 = __pyx_v_ii;
__pyx_t_42 = __pyx_v_jj;
__pyx_t_28 = ((((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_41)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_42)) )))) < 0.) != 0);
if (__pyx_t_28) {
/* … */
}
}
__pyx_L16_break:;
+222: break
goto __pyx_L16_break;
+223: iiR = jj-1
__pyx_v_iiR = (__pyx_v_jj - 1);
+224: iiZ = (ind[ii] - NRPhi0[iiR])//NRPhi[iiR]
__pyx_t_43 = __pyx_v_ii;
__pyx_t_44 = __pyx_v_iiR;
__pyx_t_45 = __pyx_v_iiR;
__pyx_v_iiZ = (((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_43)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_44)) )))) / (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_45)) ))));
+225: iiphi = ind[ii] - NRPhi0[iiR] - iiZ*NRPhi[iiR]
__pyx_t_46 = __pyx_v_ii;
__pyx_t_47 = __pyx_v_iiR;
__pyx_t_48 = __pyx_v_iiR;
__pyx_v_iiphi = (((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_46)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_47)) )))) - (__pyx_v_iiZ * (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_48)) )))));
+226: phi = Phi[iiR,iiphi]
if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 226, __pyx_L1_error) }
__pyx_t_49 = __pyx_v_iiR;
__pyx_t_50 = __pyx_v_iiphi;
__pyx_v_phi = (*((double *) ( /* dim=1 */ ((char *) (((double *) ( /* dim=0 */ (__pyx_v_Phi.data + __pyx_t_49 * __pyx_v_Phi.strides[0]) )) + __pyx_t_50)) )));
+227: Pts[0,ii] = R[iiR]*Ccos(phi)
__pyx_t_51 = __pyx_v_iiR;
__pyx_t_52 = 0;
__pyx_t_53 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_52, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_53, __pyx_pybuffernd_Pts.diminfo[1].strides) = ((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_51)) ))) * cos(__pyx_v_phi));
+228: Pts[1,ii] = R[iiR]*Csin(phi)
__pyx_t_54 = __pyx_v_iiR;
__pyx_t_55 = 1;
__pyx_t_56 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_55, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_56, __pyx_pybuffernd_Pts.diminfo[1].strides) = ((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_54)) ))) * sin(__pyx_v_phi));
+229: Pts[2,ii] = Z[iiZ]
__pyx_t_57 = __pyx_v_iiZ;
__pyx_t_58 = 2;
__pyx_t_59 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_58, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_59, __pyx_pybuffernd_Pts.diminfo[1].strides) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_Z.data) + __pyx_t_57)) )));
+230: dV[ii] = dRr*dZr*dRPhirRef[iiR]
__pyx_t_60 = __pyx_v_iiR;
__pyx_t_61 = __pyx_v_ii;
*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_dV.rcbuffer->pybuffer.buf, __pyx_t_61, __pyx_pybuffernd_dV.diminfo[0].strides) = ((__pyx_v_dRr * __pyx_v_dZr) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhirRef.data) + __pyx_t_60)) ))));
+231: if Ru[iiR]==0.:
__pyx_t_62 = __pyx_v_iiR;
__pyx_t_28 = (((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_Ru.data) + __pyx_t_62)) ))) == 0.) != 0);
if (__pyx_t_28) {
/* … */
}
}
+232: dRPhir[iiR] = dRPhirRef[iiR]
__pyx_t_63 = __pyx_v_iiR;
__pyx_t_64 = __pyx_v_iiR;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhir.data) + __pyx_t_64)) )) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhirRef.data) + __pyx_t_63)) )));
+233: Ru[iiR] = 1.
__pyx_t_65 = __pyx_v_iiR;
*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_Ru.data) + __pyx_t_65)) )) = 1.;
234: else:
+235: for ii in range(0,NP):
/*else*/ {
__pyx_t_14 = __pyx_v_NP;
for (__pyx_t_20 = 0; __pyx_t_20 < __pyx_t_14; __pyx_t_20+=1) {
__pyx_v_ii = __pyx_t_20;
+236: for jj in range(0,NR+1):
__pyx_t_36 = (__pyx_v_NR + 1);
for (__pyx_t_37 = 0; __pyx_t_37 < __pyx_t_36; __pyx_t_37+=1) {
__pyx_v_jj = __pyx_t_37;
+237: if ind[ii]-NRPhi0[jj]<0.:
__pyx_t_66 = __pyx_v_ii;
__pyx_t_67 = __pyx_v_jj;
__pyx_t_28 = ((((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_66)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_67)) )))) < 0.) != 0);
if (__pyx_t_28) {
/* … */
}
}
__pyx_L22_break:;
+238: break
goto __pyx_L22_break;
+239: iiR = jj-1
__pyx_v_iiR = (__pyx_v_jj - 1);
+240: iiZ = (ind[ii] - NRPhi0[iiR])//NRPhi[iiR]
__pyx_t_68 = __pyx_v_ii;
__pyx_t_69 = __pyx_v_iiR;
__pyx_t_70 = __pyx_v_iiR;
__pyx_v_iiZ = (((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_68)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_69)) )))) / (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_70)) ))));
+241: iiphi = ind[ii] - NRPhi0[iiR] - iiZ*NRPhi[iiR]
__pyx_t_71 = __pyx_v_ii;
__pyx_t_72 = __pyx_v_iiR;
__pyx_t_73 = __pyx_v_iiR;
__pyx_v_iiphi = (((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_71)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_72)) )))) - (__pyx_v_iiZ * (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi.data) + __pyx_t_73)) )))));
+242: Pts[0,ii] = R[iiR]
__pyx_t_74 = __pyx_v_iiR;
__pyx_t_75 = 0;
__pyx_t_76 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_75, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_76, __pyx_pybuffernd_Pts.diminfo[1].strides) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_R.data) + __pyx_t_74)) )));
+243: Pts[1,ii] = Z[iiZ]
__pyx_t_77 = __pyx_v_iiZ;
__pyx_t_78 = 1;
__pyx_t_79 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_78, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_79, __pyx_pybuffernd_Pts.diminfo[1].strides) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_Z.data) + __pyx_t_77)) )));
+244: Pts[2,ii] = Phi[iiR,iiphi]
if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 244, __pyx_L1_error) }
__pyx_t_80 = __pyx_v_iiR;
__pyx_t_81 = __pyx_v_iiphi;
__pyx_t_82 = 2;
__pyx_t_83 = __pyx_v_ii;
*__Pyx_BufPtrStrided2d(double *, __pyx_pybuffernd_Pts.rcbuffer->pybuffer.buf, __pyx_t_82, __pyx_pybuffernd_Pts.diminfo[0].strides, __pyx_t_83, __pyx_pybuffernd_Pts.diminfo[1].strides) = (*((double *) ( /* dim=1 */ ((char *) (((double *) ( /* dim=0 */ (__pyx_v_Phi.data + __pyx_t_80 * __pyx_v_Phi.strides[0]) )) + __pyx_t_81)) )));
+245: dV[ii] = dRr*dZr*dRPhirRef[iiR]
__pyx_t_84 = __pyx_v_iiR;
__pyx_t_85 = __pyx_v_ii;
*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_dV.rcbuffer->pybuffer.buf, __pyx_t_85, __pyx_pybuffernd_dV.diminfo[0].strides) = ((__pyx_v_dRr * __pyx_v_dZr) * (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhirRef.data) + __pyx_t_84)) ))));
+246: if Ru[iiR]==0.:
__pyx_t_86 = __pyx_v_iiR;
__pyx_t_28 = (((*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_Ru.data) + __pyx_t_86)) ))) == 0.) != 0);
if (__pyx_t_28) {
/* … */
}
}
}
__pyx_L12:;
+247: dRPhir[iiR] = dRPhirRef[iiR]
__pyx_t_87 = __pyx_v_iiR;
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286: double[::1] XMinMax, double[::1] YMinMax, double[::1] ZMinMax,
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+311: dV = dXr*dYr*dZr
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312:
+313: return Pts, dV, dXr, dYr, dZr
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314:
315:
316:
In [17]:
[dR, dZ, dRPhi], RMinMax, ZMinMax = np.asarray([0.01]*3), np.array([2.,3.]), np.array([-1.,1.])
DR, DZ, DPhi = [2.15,2.6], [-0.21,0.51], [7.*np.pi/4.,5.*np.pi/4.]
Ptsc, dVc, indc, dRrc, dZrc, dRPhirc = _Ves_Vmesh_Tor_SubFromD_cython(dR, dZ, dRPhi, RMinMax, ZMinMax,
DR=DR, DZ=DZ, DPhi=DPhi, VPoly=None,
Out='(R,Z,phi)', margin=1.e-9)
PtsnI, dVnI, dRrnI, dZrnI, dRPhirnI = _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax,
ind=indc, Out='(R,Z,Phi)', margin=1.e-9)
PtscI, dVcI, dRrcI, dZrcI, dRPhircI = _Ves_Vmesh_Tor_SubFromInd_cython(dR, dZ, dRPhi, RMinMax, ZMinMax,
ind=indc, Out='(R,Z,phi)', margin=1.e-9)
print dRPhirc.shape, dRPhirnI.shape, dRPhircI.shape
print dRPhirnI
print dRPhircI
(46,) (46,) (46,)
[ 0.0099981 0.00999282 0.00999493 0.00999702 0.0099991 0.00999391
0.00999598 0.00999803 0.00999291 0.00999496 0.00999699 0.009999
0.00999397 0.00999598 0.00999797 0.00999994 0.00999499 0.00999696
0.00999891 0.00999403 0.00999598 0.00999791 0.00999982 0.00999502
0.00999693 0.00999882 0.00999409 0.00999598 0.00999785 0.00999971
0.00999505 0.0099969 0.00999874 0.00999414 0.00999598 0.0099978
0.00999961 0.00999507 0.00999688 0.00999867 0.00999419 0.00999598
0.00999775 0.00999951 0.0099951 0.00999685]
[ 0.0099981 0.00999282 0.00999493 0.00999702 0.0099991 0.00999391
0.00999598 0.00999803 0.00999291 0.00999496 0.00999699 0.009999
0.00999397 0.00999598 0.00999797 0.00999994 0.00999499 0.00999696
0.00999891 0.00999403 0.00999598 0.00999791 0.00999982 0.00999502
0.00999693 0.00999882 0.00999409 0.00999598 0.00999785 0.00999971
0.00999505 0.0099969 0.00999874 0.00999414 0.00999598 0.0099978
0.00999961 0.00999507 0.00999688 0.00999867 0.00999419 0.00999598
0.00999775 0.00999951 0.0099951 0.00999685]
In [34]:
LMinMax, dL, DL, margin = np.array([0.,10.]), 0.0001, [1.,9.], 1.e-9
Ln, dLrn, indLn, NLn = _Ves_mesh_dlfromL_numpy(LMinMax, dL, DL=DL, margin=margin)
Lc, dLrc, indLc, NLc = _Ves_mesh_dlfromL_cython(LMinMax, dL, DL=DL, margin=margin)
# Check and debug Tor
[dR, dZ, dRPhi], RMinMax, ZMinMax = np.asarray([0.02]*3), np.array([4.,8.]), np.array([-4.,4.])
DR, DZ, DPhi = np.array([5.,6.5]), np.array([-1.5,2.]), np.array([-np.pi/4.,np.pi/4.])
Ptsn, dVn, indn, dRrn, dZrn, dRPhirn = _Ves_Vmesh_Tor_SubFromD_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax,
DR=DR, DZ=DZ, DPhi=DPhi, VPoly=None,
Out='(R,Z,Phi)', margin=1.e-9)
Ptsc, dVc, indc, dRrc, dZrc, dRPhirc = _Ves_Vmesh_Tor_SubFromD_cython(dR, dZ, dRPhi, RMinMax, ZMinMax,
DR=DR, DZ=DZ, DPhi=DPhi, VPoly=None,
Out='(R,Z,phi)', margin=1.e-9)
PtsnI, dVnI, dRrnI, dZrnI, dRPhirnI = _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax,
ind=indn, Out='(R,Z,Phi)', margin=1.e-9)
PtscI, dVcI, dRrcI, dZrcI, dRPhircI = _Ves_Vmesh_Tor_SubFromInd_cython(dR, dZ, dRPhi, RMinMax, ZMinMax,
ind=indc, Out='(R,Z,Phi)', margin=1.e-9)
print Ptsn.shape[1], 'points'
%timeit Ln, dLrn, indLn, NLn = _Ves_mesh_dlfromL_numpy(LMinMax, dL, DL=DL, margin=margin)
%timeit Lc, dLrc, indLc, NLc = _Ves_mesh_dlfromL_cython(LMinMax, dL, DL=DL, margin=margin)
print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Ln,Lc),(dLrn,dLrc),(indLn,indLc),(NLn,NLc)]]
%timeit out = _Ves_Vmesh_Tor_SubFromD_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, DR=DR, DZ=DZ, DPhi=DPhi, VPoly=None)
%timeit out = _Ves_Vmesh_Tor_SubFromD_cython(dR, dZ, dRPhi, RMinMax, ZMinMax, DR=DR, DZ=DZ, DPhi=DPhi, VPoly=None, Out='(X,Y,Z)')
print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Ptsn,Ptsc),(dVn,dVc),(indn,indc),(dRPhirn,dRPhirc)]]
%timeit out = _Ves_Vmesh_Tor_SubFromInd_numpy(dR, dZ, dRPhi, RMinMax, ZMinMax, ind=indn, Out='(R,Z,Phi)', margin=1.e-9)
%timeit out = _Ves_Vmesh_Tor_SubFromInd_cython(dR, dZ, dRPhi, RMinMax, ZMinMax, ind=indc, Out='(R,Z,Phi)', margin=1.e-9)
print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(PtsnI,PtscI),(dVnI,dVcI),(dRPhirnI,dRPhircI)]]
print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Ptsc,PtscI),(dVc,dVcI),(dRPhirc,dRPhircI)]]
5940900 points
1000 loops, best of 3: 909 µs per loop
1000 loops, best of 3: 550 µs per loop
[True, True, True, True]
1 loop, best of 3: 1.01 s per loop
1 loop, best of 3: 541 ms per loop
[True, True, True, True]
1 loop, best of 3: 25.2 s per loop
1 loop, best of 3: 1.31 s per loop
[True, True, True]
[True, True, True]
In [18]:
# Check and debug Lin
[dX, dY, dZ], XMinMax, YMinMax, ZMinMax = np.asarray([0.01]*3), np.array([-1,1.]), np.array([-1.,1]), np.array([0.,4.])
DX, DY, DZ = [-0.5,0.5], [-0.5,0.5], [1.,3.]
Ptsn, dVn, indn, dXrn, dYrn, dZrn = _Ves_Vmesh_Lin_SubFromD_cython(dX, dY, dZ, XMinMax, YMinMax, ZMinMax,
DX=DX, DY=DY, DZ=DZ, VPoly=None, margin=1.e-9)
Ptsc, dVc, dXrc, dYrc, dZrc = _Ves_Vmesh_Lin_SubFromInd_cython(dX, dY, dZ, XMinMax, YMinMax, ZMinMax,
indn, margin=1.e-9)
print Ptsn.shape[1], 'points'
%timeit out = _Ves_Vmesh_Lin_SubFromD_cython(dX, dY, dZ, XMinMax, YMinMax, ZMinMax, DX=DX, DY=DY, DZ=DZ, VPoly=None, margin=1.e-9)
%timeit out = _Ves_Vmesh_Lin_SubFromInd_cython(dX, dY, dZ, XMinMax, YMinMax, ZMinMax, indn, margin=1.e-9)
print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Ptsn,Ptsc),(dVn,dVc)]]
2000000 points
10 loops, best of 3: 86.7 ms per loop
10 loops, best of 3: 235 ms per loop
[True, True]
In [1]:
%load_ext cython
In [9]:
%%cython -a
cimport cython
cimport numpy as cnp
from cpython cimport bool
from libc.math cimport sqrt as Csqrt, ceil as Cceil, round as Cround, floor as Cfloor, abs as Cabs
from libc.math cimport cos as Ccos, sin as Csin, atan2 as Catan2, pi as Cpi
from matplotlib.path import Path
import numpy as np
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_mesh_dlfromL_cython(double[::1] LMinMax, double dL, DL=None, double margin=1.e-9):
""" Get the actual reolution from the desired resolution and MinMax and limits """
# Get the number of mesh elements in LMinMax
cdef double N = Cceil((LMinMax[1]-LMinMax[0])/dL)
# Derive the real (effective) resolution
cdef double dLr = (LMinMax[1]-LMinMax[0])/N
# Get desired limits if any
cdef double[::1] DLc, L
cdef long [::1] indL
#cdef cnp.ndarray[double,ndim=1] indL, L
cdef double abs0, abs1, A
cdef int nL0, nL1, Nind, ii, jj
cdef list dl
if DL is None:
DLc = LMinMax
else:
dl = list(DL)
if dl[0] is None:
dl[0] = LMinMax[0]
if dl[1] is None:
dl[1] = LMinMax[1]
DLc = np.array(dl)
# Get the extreme indices of the mesh elements that really need to be created within those limits
abs0 = Cabs(DLc[0]-LMinMax[0])
if abs0-dLr*Cfloor(abs0/dLr)<margin*dLr:
nL0 = int(Cround((DLc[0]-LMinMax[0])/dLr))
else:
nL0 = int(Cfloor((DLc[0]-LMinMax[0])/dLr))
abs1 = Cabs(DLc[1]-LMinMax[0])
if abs1-dLr*Cfloor(abs1/dLr)<margin*dLr:
nL1 = int(Cround((DLc[1]-LMinMax[0])/dLr)-1)
else:
nL1 = int(Cfloor((DLc[1]-LMinMax[0])/dLr))
# Get the corresponding indices
Nind = nL1+1-nL0
indL = np.empty((Nind,),dtype=int)#np.linspace(nL0,nL1,Nind,endpoint=True)
L = np.empty((Nind,))
for ii in range(0,Nind):
jj = nL0+ii
indL[ii] = jj
L[ii] = LMinMax[0] + (0.5 + (<double>jj))*dLr
return np.asarray(L), dLr, np.asarray(indL), N
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_mesh_CrossPoly(double[:,::1] VPoly, double dL, D1=None, D2=None, double margin=1.e-9, double DIn=0., VIn=None):
cdef int ii, jj, nn=0, NP=VPoly.shape[1]
cdef double[::1] LMinMax, L
cdef double v0, v1, dlr
cdef long[::1] indL
cdef cnp.ndarray[long,ndim=1] N, ind
cdef cnp.ndarray[double,ndim=1] dLr, Rref
cdef cnp.ndarray[double,ndim=2] PtsCross
cdef list LPtsCross=[], LdLr=[], Lind=[], LRref=[], VPolybis=[]
LMinMax = np.array([0.,1.],dtype=float)
N = np.empty((NP-1,),dtype=int)
if DIn==0.:
for ii in range(0,NP-1):
v0, v1 = VPoly[0,ii+1]-VPoly[0,ii], VPoly[1,ii+1]-VPoly[1,ii]
LMinMax[1] = Csqrt(v0**2 + v1**2)
L, dlr, indL, N[ii] = _Ves_mesh_dlfromL_cython(LMinMax, dL, DL=None, margin=margin)
VPolybis.append((VPoly[0,ii],VPoly[1,ii]))
v0, v1 = v0/LMinMax[1], v1/LMinMax[1]
for jj in range(0,N[ii]):
LdLr.append(dlr)
LRref.append(VPoly[0,ii] + L[jj]*v0)
LPtsCross.append((VPoly[0,ii] + L[jj]*v0, VPoly[1,ii] + L[jj]*v1))
Lind.append(nn)
nn += 1
VPolybis.append((VPoly[0,ii] + jj*dlr*v0, VPoly[1,ii] + jj*dlr*v1))
VPolybis.append((VPoly[0,0],VPoly[1,0]))
else:
for ii in range(0,NP-1):
v0, v1 = VPoly[0,ii+1]-VPoly[0,ii], VPoly[1,ii+1]-VPoly[1,ii]
LMinMax[1] = Csqrt(v0**2 + v1**2)
L, dlr, indL, N[ii] = _Ves_mesh_dlfromL_cython(LMinMax, dL, DL=None, margin=margin)
VPolybis.append((VPoly[0,ii],VPoly[1,ii]))
v0, v1 = v0/LMinMax[1], v1/LMinMax[1]
for jj in range(0,N[ii]):
LdLr.append(dlr)
LRref.append(VPoly[0,ii] + L[jj]*v0)
LPtsCross.append((VPoly[0,ii] + L[jj]*v0 + DIn*VIn[0,ii], VPoly[1,ii] + L[jj]*v1 + DIn*VIn[1,ii]))
Lind.append(nn)
nn += 1
VPolybis.append((VPoly[0,ii] + jj*dlr*v0, VPoly[1,ii] + jj*dlr*v1))
VPolybis.append((VPoly[0,0],VPoly[1,0]))
PtsCross, dLr, ind, Rref = np.array(LPtsCross).T, np.array(LdLr), np.array(Lind,dtype=int), np.array(LRref)
if D1 is not None:
indin = (PtsCross[0,:]>=D1[0]) & (PtsCross[0,:]<=D1[1])
PtsCross = PtsCross[:,indin]
dLr, ind = dLr[indin], ind[indin]
if D2 is not None:
indin = (PtsCross[1,:]>=D2[0]) & (PtsCross[1,:]<=D2[1])
PtsCross = PtsCross[:,indin]
dLr, ind = dLr[indin], ind[indin]
return PtsCross, dLr, ind, N, Rref, np.array(VPolybis).T
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_Tor_SubFromD_cython(double dL, double dRPhi,
double[:,::1] VPoly,
DR=None, DZ=None, DPhi=None,
double DIn=0., VIn=None, PhiMinMax=None,
str Out='(X,Y,Z)', double margin=1.e-9):
" Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
cdef double[::1] R, Z, dPhir, NRPhi#, dPhi, NRZPhi_cum0, indPhi, phi
cdef double dRr0, dRr, dZr, DPhi0, DPhi1, DPhiMinMax
cdef double abs0, abs1, phi, indiijj
cdef long[::1] indR0, indR, indZ, Phin, NRPhi0, Indin
cdef int NR0, NR, NZ, Rn, Zn, nRPhi0, indR0ii, ii, jj0, jj, nPhi0, nPhi1, zz, NP, NRPhi_int, Rratio, Ln
cdef cnp.ndarray[double,ndim=2] Pts, indI, PtsCross, VPbis
cdef cnp.ndarray[double,ndim=1] R0, dS, ind, dLr, Rref, dRPhir
cdef cnp.ndarray[long,ndim=1] indL, NL
# Pre-format input
if PhiMinMax is None:
PhiMinMax = [-Cpi,Cpi]
DPhiMinMax = 2.*Cpi
else:
PhiMinMax = [Catan2(Csin(PhiMinMax[0]),Ccos(PhiMinMax[0])), Catan2(Csin(PhiMinMax[1]),Ccos(PhiMinMax[1]))]
if PhiMinMax[1]>=PhiMinMax[0]:
DPhiMinMax = PhiMinMax[1]-PhiMinMax[0]
else:
DPhiMinMax = 2.*Cpi + PhiMinMax[1] - PhiMinMax[0]
# Get the actual R and Z resolutions and mesh elements
PtsCross, dLr, indL, NL, Rref, VPbis = _Ves_mesh_CrossPoly(VPoly, dL, D1=None, D2=None, margin=margin, DIn=DIn, VIn=VIn)
R0 = np.copy(Rref)
NR0 = R0.size
indin = np.ones((PtsCross.shape[1],),dtype=bool)
if DR is not None:
indin = indin & (R0>=DR[0]) & (R0<=DR[1])
if DZ is not None:
indin = indin & (PtsCross[1,:]>=DZ[0]) & (PtsCross[1,:]<=DZ[1])
PtsCross, dLr, indL, Rref = PtsCross[:,indin], dLr[indin], indL[indin], Rref[indin]
Ln = indin.sum()
Indin = indin.nonzero()[0]
# Get the limits if any (and make sure to replace them in the proper quadrants)
if DPhi is None:
DPhi0, DPhi1 = PhiMinMax[0], PhiMinMax[1]
else:
DPhi0 = PhiMinMax[0] if DPhi[0] is None else Catan2(Csin(DPhi[0]),Ccos(DPhi[0]))
DPhi1 = PhiMinMax[1] if DPhi[1] is None else Catan2(Csin(DPhi[1]),Ccos(DPhi[1]))
dRPhir, dPhir = np.empty((Ln,)), np.empty((Ln,))
Phin = np.empty((Ln,),dtype=int)
NRPhi = np.empty((Ln,))
NRPhi0 = np.zeros((Ln,),dtype=int)
nRPhi0, indR0ii = 0, 0
NP, NPhimax = 0, 0
Rratio = int(Cceil(np.max(Rref)/np.min(Rref)))
for ii in range(0,Ln):
# Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
NRPhi[ii] = Cceil(DPhiMinMax*Rref[ii]/dRPhi)
NRPhi_int = int(NRPhi[ii])
dPhir[ii] = DPhiMinMax/NRPhi[ii]
dRPhir[ii] = dPhir[ii]*Rref[ii]
# Get index and cumulated indices from background
for jj0 in range(indR0ii,NR0):
if jj0==Indin[ii]:
indR0ii = jj0
break
else:
nRPhi0 += <long>Cceil(DPhiMinMax*R0[jj0]/dRPhi)
NRPhi0[ii] = nRPhi0
# Get indices of phi
# Get the extreme indices of the mesh elements that really need to be created within those limits
abs0 = Cabs(DPhi0-PhiMinMax[0])
if abs0-dPhir[ii]*Cfloor(abs0/dPhir[ii])<margin*dPhir[ii]:
nPhi0 = int(Cround((DPhi0-PhiMinMax[0])/dPhir[ii]))
else:
nPhi0 = int(Cfloor((DPhi0-PhiMinMax[0])/dPhir[ii]))
abs1 = Cabs(DPhi1-PhiMinMax[0])
if abs1-dPhir[ii]*Cfloor(abs1/dPhir[ii])<margin*dPhir[ii]:
nPhi1 = int(Cround((DPhi1-PhiMinMax[0])/dPhir[ii])-1)
else:
nPhi1 = int(Cfloor((DPhi1-PhiMinMax[0])/dPhir[ii]))
if DPhi0<DPhi1:
Phin[ii] = nPhi1+1-nPhi0
if ii==0:
indI = np.ones((Ln,Phin[ii]*Rratio+1))
for jj in range(0,Phin[ii]):
indI[ii,jj] = <double>( nPhi0+jj )
else:
Phin[ii] = nPhi1+1+NRPhi_int-nPhi0
if ii==0:
indI = np.ones((Ln,Phin[ii]*Rratio+1))
for jj in range(0,NRPhi_int-nPhi0):
indI[ii,jj] = <double>( nPhi0+jj )
for jj in range(NRPhi_int-nPhi0,Phin[ii]):
indI[ii,jj] = <double>( jj- (NRPhi_int-nPhi0) )
NP += Phin[ii]
# Finish counting to get total number of points
if jj0<=NR0-1:
for jj0 in range(indR0ii,NR0):
nRPhi0 += <long>Cceil(DPhiMinMax*R0[jj0]/dRPhi)
# Compute Pts, dV and ind
Pts = np.empty((3,NP))
ind = np.empty((NP,))
dS = np.empty((NP,))
# This triple loop is the longest part, it takes ~90% of the CPU time
NP = 0
if Out.lower()=='(x,y,z)':
for ii in range(0,Ln):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
phi = PhiMinMax[0] + (0.5+indiijj)*dPhir[ii]
Pts[0,NP] = PtsCross[0,ii]*Ccos(phi)
Pts[1,NP] = PtsCross[0,ii]*Csin(phi)
Pts[2,NP] = PtsCross[1,ii]
ind[NP] = NRPhi0[ii] + indiijj
dS[NP] = dLr[ii]*dRPhir[ii]
NP += 1
else:
for ii in range(0,Ln):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
Pts[0,NP] = PtsCross[0,ii]
Pts[1,NP] = PtsCross[1,ii]
Pts[2,NP] = PhiMinMax[0] + (0.5+indiijj)*dPhir[ii]
ind[NP] = NRPhi0[ii] + indiijj
dS[NP] = dLr[ii]*dRPhir[ii]
NP += 1
return Pts, dS, ind.astype(int), NL, dLr, Rref, dRPhir, nRPhi0, VPbis
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_Tor_SubFromInd_cython(double dL, double dRPhi,
double[:,::1] VPoly, long[::1] ind,
double DIn=0., VIn=None, PhiMinMax=None,
str Out='(X,Y,Z)', double margin=1.e-9):
""" Return the desired submesh indicated by the (numerical) indices, for the desired resolution (dR,dZ,dRphi) """
cdef double[::1] dRPhirRef, dPhir
cdef long[::1] indL, NRPhi0, NRPhi
cdef long NR, NZ, Rn, Zn, NP=len(ind), Rratio
cdef int ii, jj0, jj, iiL, iiphi, Ln, nn=0, kk=0, nRPhi0
cdef double[:,::1] Phi
cdef cnp.ndarray[double,ndim=2] Pts=np.empty((3,NP)), indI, PtsCross, VPbis
cdef cnp.ndarray[double,ndim=1] R0, dS=np.empty((NP,)), dLr, dRPhir, Rref
cdef cnp.ndarray[long,ndim=1] NL
# Pre-format input
if PhiMinMax is None:
PhiMinMax = [-Cpi,Cpi]
DPhiMinMax = 2.*Cpi
else:
PhiMinMax = [Catan2(Csin(PhiMinMax[0]),Ccos(PhiMinMax[0])), Catan2(Csin(PhiMinMax[1]),Ccos(PhiMinMax[1]))]
if PhiMinMax[1]>=PhiMinMax[0]:
DPhiMinMax = PhiMinMax[1]-PhiMinMax[0]
else:
DPhiMinMax = 2.*Cpi + PhiMinMax[1] - PhiMinMax[0]
# Get the actual R and Z resolutions and mesh elements
PtsCross, dLr, indL, NL, Rref, VPbis = _Ves_mesh_CrossPoly(VPoly, dL, D1=None, D2=None, margin=margin, DIn=DIn, VIn=VIn)
Ln = dLr.size
# Number of Phi per R
dRPhirRef, dPhir, dRPhir = np.empty((Ln,)), np.empty((Ln,)), -np.ones((Ln,))
NRPhi, NRPhi0 = np.empty((Ln,),dtype=int), np.empty((Ln,),dtype=int)
Rratio = int(Cceil(np.max(Rref)/np.min(Rref)))
for ii in range(0,Ln):
NRPhi[ii] = <long>(Cceil(DPhiMinMax*Rref[ii]/dRPhi))
dRPhirRef[ii] = DPhiMinMax*Rref[ii]/<double>(NRPhi[ii])
dPhir[ii] = DPhiMinMax/<double>(NRPhi[ii])
if ii==0:
NRPhi0[ii] = 0
Phi = np.empty((Ln,NRPhi[ii]*Rratio+1))
else:
NRPhi0[ii] = NRPhi0[ii-1] + NRPhi[ii-1]
for jj in range(0,NRPhi[ii]):
Phi[ii,jj] = PhiMinMax[0] + (0.5+<double>jj)*dPhir[ii]
nRPhi0 = NRPhi0[Ln-1]+NRPhi[Ln-1]
if Out.lower()=='(x,y,z)':
for ii in range(0,NP):
for jj in range(0,Ln+1):
if ind[ii]-NRPhi0[jj]<0.:
break
iiL = jj-1
iiphi = ind[ii] - NRPhi0[iiL]
Pts[0,ii] = PtsCross[0,iiL]*Ccos(Phi[iiL,iiphi])
Pts[1,ii] = PtsCross[0,iiL]*Csin(Phi[iiL,iiphi])
Pts[2,ii] = PtsCross[1,iiL]
dS[ii] = dLr[iiL]*dRPhirRef[iiL]
if dRPhir[iiL]==-1.:
dRPhir[iiL] = dRPhirRef[iiL]
else:
for ii in range(0,NP):
for jj in range(0,Ln+1):
if ind[ii]-NRPhi0[jj]<0.:
break
iiL = jj-1
iiphi = ind[ii] - NRPhi0[iiL]
Pts[0,ii] = PtsCross[0,iiL]
Pts[1,ii] = PtsCross[1,iiL]
Pts[2,ii] = Phi[iiL,iiphi]
dS[ii] = dLr[iiL]*dRPhirRef[iiL]
if dRPhir[iiL]==-1.:
dRPhir[iiL] = dRPhirRef[iiL]
return Pts, dS, NL, dLr, Rref, dRPhir[dRPhir>-1.], <long>nRPhi0, VPbis
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_TorStruct_SubFromD_cython(double[::1] PhiMinMax, double dL, double dRPhi,
double[:,::1] VPoly,
DR=None, DZ=None, DPhi=None,
double DIn=0., VIn=None,
str Out='(X,Y,Z)', double margin=1.e-9):
" Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
cdef double Dphi, dR0r, dZ0r
cdef int NR0, NZ0, R0n, Z0n, NRPhi0
cdef cnp.ndarray[double, ndim=1] R0, Z0, dsF, dSM, dLr, Rref, dRPhir, dS
cdef cnp.ndarray[long,ndim=1] indR0, indZ0, iind, iindF, indM, NL, ind
cdef cnp.ndarray[double,ndim=2] ptsrz, pts, PtsM, VPbis, Pts
cdef list LPts=[], LdS=[], Lind=[]
# Pre-format input
if DPhi is not None:
if DPhi[0]<=PhiMinMax[0]:
DPhi[0] = None
if DPhi[1]>=PhiMinMax[1]:
DPhi[1] = None
Dphi = DIn/np.max(VPoly[0,:]) if DIn!=0. else 0. # Required distance effective at max R
# Get the mesh for the faces
Faces = False
if DPhi is None or DPhi[0] is None or DPhi[1] is None:
R0, dR0r, indR0, NR0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[0,:]),np.max(VPoly[0,:])]), dL, DL=DR, margin=margin)
Z0, dZ0r, indZ0, NZ0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[1,:]),np.max(VPoly[1,:])]), dL, DL=DZ, margin=margin)
R0n, Z0n = len(R0), len(Z0)
ptsrz = np.array([np.tile(R0,Z0n),np.repeat(Z0,R0n)])
iind = NR0*np.repeat(indZ0,R0n) + np.tile(indR0,Z0n)
indin = Path(VPoly.T).contains_points(ptsrz.T, transform=None, radius=0.0)
if np.any(indin):
ptsrz = ptsrz[:,indin] if indin.sum()>1 else ptsrz[:,indin].reshape((2,1))
iindF = iind[indin]
dsF = dR0r*dZ0r*np.ones((indin.sum(),))
Faces = True
# First face
if (DPhi is None or DPhi[0] is None) and Faces:
if Out.lower()=='(x,y,z)':
pts = np.array([ptsrz[0,:]*Ccos(PhiMinMax[0]+Dphi), ptsrz[0,:]*Csin(PhiMinMax[0]+Dphi), ptsrz[1,:]])
else:
pts = np.array([ptsrz[0,:],ptsrz[1,:],(PhiMinMax[0]+Dphi)*np.ones((indin.sum(),))])
LPts.append( pts )
Lind.append( iindF )
LdS.append( dsF )
# Main body
PtsM, dSM, indM, NL, dLr, Rref, dRPhir, nRPhi0, VPbis = _Ves_Smesh_Tor_SubFromD_cython(dL, dRPhi, VPoly,
DR=DR, DZ=DZ, DPhi=DPhi,
DIn=DIn, VIn=VIn, PhiMinMax=PhiMinMax,
Out=Out, margin=margin)
if PtsM.shape[1]>=1:
if PtsM.shape[1]==1:
LPts.append(PtsM.reshape((3,1)))
else:
LPts.append(PtsM)
Lind.append( indM + NR0*NZ0 )
LdS.append( dSM )
# Second face
if (DPhi is None or DPhi[1] is None) and Faces:
if Out.lower()=='(x,y,z)':
pts = np.array([ptsrz[0,:]*Ccos(PhiMinMax[1]-Dphi), ptsrz[0,:]*Csin(PhiMinMax[1]-Dphi), ptsrz[1,:]])
else:
pts = np.array([ptsrz[0,:],ptsrz[1,:],(PhiMinMax[1]-Dphi)*np.ones((indin.sum(),))])
LPts.append( pts )
Lind.append( iindF + NR0*NZ0 + nRPhi0 )
LdS.append( dsF )
# Aggregate
if len(LPts)==1:
Pts = LPts[0]
ind = Lind[0]
dS = LdS[0]
else:
Pts = np.concatenate(tuple(LPts),axis=1)
ind = np.concatenate(tuple(Lind)).astype(int)
dS = np.concatenate(tuple(LdS))
return Pts, dS, ind, NL, dLr, Rref, dR0r, dZ0r, dRPhir, VPbis
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_TorStruct_SubFromInd_cython(double[::1] PhiMinMax, double dL, double dRPhi,
double[:,::1] VPoly, cnp.ndarray[long,ndim=1] ind,
double DIn=0., VIn=None,
str Out='(X,Y,Z)', double margin=1.e-9):
" Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
cdef double Dphi, dR0r, dZ0r
cdef int NR0, NZ0, R0n, Z0n, NRPhi0
cdef cnp.ndarray[double, ndim=1] R0, Z0, dsF, dSM, dLr, Rref, dRPhir, dS
cdef cnp.ndarray[long,ndim=1] bla, indR0, indZ0, iind, iindF, indM, NL
cdef cnp.ndarray[double,ndim=2] ptsrz, pts, PtsM, VPbis, Pts
cdef list LPts=[], LdS=[], Lind=[]
# Pre-format input
Dphi = DIn/np.max(VPoly[0,:]) if DIn!=0. else 0. # Required distance effective at max R
# Get the basic meshes for the faces
R0, dR0r, bla, NR0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[0,:]),np.max(VPoly[0,:])]), dL, DL=None, margin=margin)
Z0, dZ0r, bla, NZ0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[1,:]),np.max(VPoly[1,:])]), dL, DL=None, margin=margin)
PtsM, dSM, indM, NL, dLr, Rref, dRPhir, nRPhi0, VPbis = _Ves_Smesh_Tor_SubFromD_cython(dL, dRPhi, VPoly,
DR=None, DZ=None, DPhi=None,
DIn=DIn, VIn=VIn, PhiMinMax=PhiMinMax,
Out=Out, margin=margin)
# First face
ii = (ind<NR0*NZ0).nonzero()[0]
nii = len(ii)
if nii>0:
indZ0 = ind[ii] // NR0
indR0 = (ind[ii]-indZ0*NR0)
if Out.lower()=='(x,y,z)':
pts = np.array([R0[indR0]*Ccos(PhiMinMax[0]+Dphi), R0[indR0]*Csin(PhiMinMax[0]+Dphi), Z0[indZ0]])
else:
pts = np.array([R0[indR0], Z0[indZ0], (PhiMinMax[0]+Dphi)*np.ones((nii,))])
pts = pts if nii>1 else pts.reshape((3,1))
LPts.append( pts )
LdS.append( dR0r*dZ0r*np.ones((nii,)) )
# Main body
ii = (ind>=NR0*NZ0) & (ind<NR0*NZ0+PtsM.shape[1])
nii = len(ii)
if nii>0:
pts = PtsM[:,ind[ii]-NR0*NZ0] if nii>1 else PtsM[:,ind[ii]-NR0*NZ0].reshape((3,1))
LPts.append( PtsM[:,ind[ii]-NR0*NZ0] )
LdS.append( dSM[ind[ii]-NR0*NZ0] )
# Second face
ii = (ind >= NR0*NZ0+PtsM.shape[1] ).nonzero()[0]
nii = len(ii)
if nii>0:
indZ0 = (ind[ii]-(NR0*NZ0+PtsM.shape[1])) // NR0
indR0 = ind[ii]-(NR0*NZ0+PtsM.shape[1]) - indZ0*NR0
if Out.lower()=='(x,y,z)':
pts = np.array([R0[indR0]*Ccos(PhiMinMax[1]-Dphi), R0[indR0]*Csin(PhiMinMax[1]-Dphi), Z0[indZ0]])
else:
pts = np.array([R0[indR0], Z0[indZ0], (PhiMinMax[1]-Dphi)*np.ones((nii,))])
pts = pts if nii>1 else pts.reshape((3,1))
LPts.append( pts )
LdS.append( dR0r*dZ0r*np.ones((nii,)) )
# Aggregate
if len(LPts)==1:
Pts = LPts[0]
dS = LdS[0]
elif len(LPts)>1:
Pts = np.concatenate(tuple(LPts),axis=1)
dS = np.concatenate(tuple(LdS))
return Pts, dS, NL, dLr, Rref, dR0r, dZ0r, dRPhir, VPbis
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_Lin_SubFromD_cython(double[::1] XMinMax, double dL, double dX,
double[:,::1] VPoly,
DX=None, DY=None, DZ=None,
double DIn=0., VIn=None, double margin=1.e-9):
" Return the desired surfacic submesh indicated by the limits (DX,DY,DZ), for the desired resolution (dX,dL) "
cdef cnp.ndarray[double,ndim=1] X, Y0, Z0
cdef double dXr, dY0r, dZ0r
cdef int NY0, NZ0, Y0n, Z0n, NX, Xn, Ln, NR0
cdef cnp.ndarray[double,ndim=2] Pts, PtsCross, VPbis
cdef cnp.ndarray[double,ndim=1] dS, dLr, Rref
cdef cnp.ndarray[long,ndim=1] indX, indY0, indZ0, indL, NL, ind
# Preformat
if DX is not None:
if DX[0]<=XMinMax[0]:
DX[0] = None
if DX[1]>=XMinMax[1]:
DX[1] = None
if DY is not None:
if DY[0]<=np.min(VPoly[0,:]):
DY[0] = None
if DY[1]>=np.max(VPoly[0,:]):
DY[1] = None
if DZ is not None:
if DZ[0]<=np.min(VPoly[1,:]):
DZ[0] = None
if DZ[1]>=np.max(VPoly[1,:]):
DZ[1] = None
# Get the mesh for the faces
Y0, dY0r, indY0, NY0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[0,:]),np.max(VPoly[0,:])]), dL, DL=DY, margin=margin)
Z0, dZ0r, indZ0, NZ0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[1,:]),np.max(VPoly[1,:])]), dL, DL=DZ, margin=margin)
Y0n, Z0n = len(Y0), len(Z0)
# Get the actual R and Z resolutions and mesh elements
X, dXr, indX, NX = _Ves_mesh_dlfromL_cython(XMinMax, dX, DL=DX, margin=margin)
Xn = len(X)
PtsCross, dLr, indL, NL, Rref, VPbis = _Ves_mesh_CrossPoly(VPoly, dL, D1=None, D2=None, margin=margin, DIn=DIn, VIn=VIn)
NR0 = Rref.size
indin = np.ones((PtsCross.shape[1],),dtype=bool)
if DY is not None:
if DY[0] is not None:
indin = indin & (PtsCross[0,:]>=DY[0])
if DY[1] is not None:
indin = indin & (PtsCross[0,:]<=DY[1])
if DZ is not None:
if DZ[0] is not None:
indin = indin & (PtsCross[1,:]>=DZ[0])
if DZ[1] is not None:
indin = indin & (PtsCross[1,:]<=DZ[1])
PtsCross, dLr, indL, Rref = PtsCross[:,indin], dLr[indin], indL[indin], Rref[indin]
Ln = indin.sum()
# Agregating
Pts = np.array([np.repeat(X,Ln), np.tile(PtsCross[0,:],Xn), np.tile(PtsCross[1,:],Xn)])
ind = NY0*NZ0 + np.repeat(indX*NR0,Ln) + np.tile(indL,Xn)
dS = np.tile(dLr*dXr,Xn)
if DX is None or DX[0] is None:
pts = np.array([(XMinMax[0]+DIn)*np.ones((Y0n*Z0n,)), np.tile(Y0,Z0n), np.repeat(Z0,Y0n)])
iind = NY0*np.repeat(indZ0,Y0n) + np.tile(indY0,Z0n)
indin = Path(VPoly.T).contains_points(pts[1:,:].T, transform=None, radius=0.0)
if np.any(indin):
pts = pts[:,indin].reshape((3,1)) if indin.sum()==1 else pts[:,indin]
Pts = np.concatenate((pts,Pts),axis=1)
ind = np.concatenate((iind[indin], ind))
dS = np.concatenate((dY0r*dZ0r*np.ones((indin.sum(),)),dS))
if DX is None or DX[1] is None:
pts = np.array([(XMinMax[1]-DIn)*np.ones((Y0n*Z0n,)), np.tile(Y0,Z0n), np.repeat(Z0,Y0n)])
iind = NY0*NZ0 + NX*NR0 + NY0*np.repeat(indZ0,Y0n) + np.tile(indY0,Z0n)
indin = Path(VPoly.T).contains_points(pts[1:,:].T, transform=None, radius=0.0)
if np.any(indin):
pts = pts[:,indin].reshape((3,1)) if indin.sum()==1 else pts[:,indin]
Pts = np.concatenate((Pts,pts),axis=1)
ind = np.concatenate((ind,iind[indin]))
dS = np.concatenate((dS,dY0r*dZ0r*np.ones((indin.sum(),))))
return Pts, dS, ind, NL, dLr, Rref, dXr, dY0r, dZ0r, VPbis
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_Lin_SubFromInd_cython(double[::1] XMinMax, double dL, double dX,
double[:,::1] VPoly, cnp.ndarray[long,ndim=1] ind,
double DIn=0., VIn=None, double margin=1.e-9):
" Return the desired surfacic submesh indicated by ind, for the desired resolution (dX,dL) "
cdef double dXr, dY0r, dZ0r
cdef int NX, NY0, NZ0, Ln, NR0, nii
cdef list LPts, LdS
cdef cnp.ndarray[double,ndim=2] Pts, PtsCross, VPbis
cdef cnp.ndarray[double,ndim=1] X, Y0, Z0, dS, dLr, Rref
cdef cnp.ndarray[long,ndim=1] indX, indY0, indZ0, indL, NL, ii
# Get the mesh for the faces
Y0, dY0r, bla, NY0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[0,:]),np.max(VPoly[0,:])]), dL, DL=None, margin=margin)
Z0, dZ0r, bla, NZ0 = _Ves_mesh_dlfromL_cython(np.array([np.min(VPoly[1,:]),np.max(VPoly[1,:])]), dL, DL=None, margin=margin)
# Get the actual R and Z resolutions and mesh elements
X, dXr, bla, NX = _Ves_mesh_dlfromL_cython(XMinMax, dX, DL=None, margin=margin)
PtsCross, dLr, bla, NL, Rref, VPbis = _Ves_mesh_CrossPoly(VPoly, dL, D1=None, D2=None, margin=margin, DIn=DIn, VIn=VIn)
Ln = PtsCross.shape[1]
LPts, LdS = [], []
# First face
ii = (ind<NY0*NZ0).nonzero()[0]
nii = len(ii)
if nii>0:
indZ0 = ind[ii] // NY0
indY0 = (ind[ii]-indZ0*NY0)
if nii==1:
LPts.append( np.array([[XMinMax[0]+DIn], [Y0[indY0]], [Z0[indZ0]]]) )
else:
LPts.append( np.array([(XMinMax[0]+DIn)*np.ones((nii,)), Y0[indY0], Z0[indZ0]]) )
LdS.append( dY0r*dZ0r*np.ones((nii,)) )
# Cylinder
ii = ((ind>=NY0*NZ0) & (ind<NY0*NZ0+NX*Ln)).nonzero()[0]
nii = len(ii)
if nii>0:
indX = (ind[ii]-NY0*NZ0) // Ln
indL = (ind[ii]-NY0*NZ0 - Ln*indX)
if nii==1:
LPts.append( np.array([[X[indX]], [PtsCross[0,indL]], [PtsCross[1,indL]]]) )
LdS.append( np.array([dXr*dLr[indL]]) )
else:
LPts.append( np.array([X[indX], PtsCross[0,indL], PtsCross[1,indL]]) )
LdS.append( dXr*dLr[indL] )
# End face
ii = (ind >= NY0*NZ0+NX*Ln).nonzero()[0]
nii = len(ii)
if nii>0:
indZ0 = (ind[ii]-NY0*NZ0-NX*Ln) // NY0
indY0 = ind[ii]-NY0*NZ0-NX*Ln - NY0*indZ0
if nii==1:
LPts.append( np.array([[XMinMax[1]-DIn], [Y0[indY0]], [Z0[indZ0]]]) )
else:
LPts.append( np.array([(XMinMax[1]-DIn)*np.ones((nii,)), Y0[indY0], Z0[indZ0]]) )
LdS.append( dY0r*dZ0r*np.ones((nii,)) )
# Format output
if len(LPts)==1:
Pts, dS = LPts[0], LdS[0]
else:
Pts = np.concatenate(tuple(LPts),axis=1)
dS = np.concatenate(tuple(LdS))
return Pts, dS, NL, dLr, Rref, dXr, dY0r, dZ0r, VPbis
##################### New version
def _getBoundsInter2AngSeg(bool Full, double Phi0, double Phi1, double DPhi0, double DPhi1):
""" Return Inter=True if an intersection exist (all angles in radians in [-pi;pi])
If Inter, return Bounds, a list of tuples indicating the segments defining the intersection, with
The intervals are ordered from lowest index to highst index (with respect to [Phi0,Phi1])
"""
if Full:
Bounds = [[DPhi0,DPhi1]] if DPhi0<=DPhi1 else [[-Cpi,DPhi1],[DPhi0,Cpi]]
Inter = True
else:
Inter, Bounds = False, None
if Phi0<=Phi1:
if DPhi0<=DPhi1:
if DPhi0<=Phi1 and DPhi1>=Phi0:
Inter = True
Bounds = [[None,None]]
Bounds[0][0] = Phi0 if DPhi0<=Phi0 else DPhi0
Bounds[0][1] = Phi1 if DPhi1>=Phi1 else DPhi1
else:
if DPhi0<=Phi1 or DPhi1>=Phi0:
Inter = True
if DPhi0<=Phi1 and DPhi1>=Phi0:
Bounds = [[Phi0,DPhi1],[DPhi0,Phi1]]
else:
Bounds = [[None,None]]
if DPhi0<=Phi1:
Bounds[0][0] = Phi0 if DPhi0<=Phi0 else DPhi0
Bounds[0][1] = Phi1
else:
Bounds[0][0] = Phi0
Bounds[0][1] = Phi1 if DPhi1>=Phi1 else DPhi1
else:
if DPhi0<=DPhi1:
if DPhi0<=Phi1 or DPhi1>=Phi0:
Inter = True
if DPhi0<=Phi1 and DPhi1>=Phi0:
Bounds = [[Phi0,DPhi1],[DPhi0,Phi1]]
else:
Bounds = [[None,None]]
if DPhi0<=Phi1:
Bounds[0][0] = DPhi0
Bounds[0][1] = Phi1 if DPhi1>=Phi1 else DPhi1
else:
Bounds[0][0] = Phi0 if DPhi0<=Phi0 else DPhi0
Bounds[0][1] = DPhi1
else:
Inter = True
if DPhi0>=Phi0 and DPhi1>=Phi0:
Bounds = [[Phi0,DPhi1],[DPhi0,Cpi],[-Cpi,Phi1]]
elif DPhi0<=Phi1 and DPhi1<=Phi1:
Bounds = [[Phi0,Cpi],[-Cpi,DPhi1],[DPhi0,Phi1]]
else:
Bounds = [[None,Cpi],[-Cpi,None]]
Bounds[0][0] = Phi0 if DPhi0<=Phi0 else DPhi0
Bounds[1][1] = Phi1 if DPhi1>=Phi1 else DPhi1
return Inter, Bounds
@cython.cdivision(True)
@cython.wraparound(False)
@cython.boundscheck(False)
def _Ves_Smesh_Tor_SubFromD_bis(double dL, double dRPhi,
double[:,::1] VPoly,
DR=None, DZ=None, DPhi=None,
double DIn=0., VIn=None, PhiMinMax=None,
str Out='(X,Y,Z)', double margin=1.e-9):
" Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
cdef double[::1] R, Z, dPhir, NRPhi#, dPhi, NRZPhi_cum0, indPhi, phi
cdef double dRr0, dRr, dZr, DPhi0, DPhi1, DDPhi, DPhiMinMax
cdef double abs0, abs1, phi, indiijj
cdef long[::1] indR0, indR, indZ, Phin, NRPhi0, Indin
cdef int NR0, NR, NZ, Rn, Zn, nRPhi0, indR0ii, ii, jj0=0, jj, nPhi0, nPhi1, zz, NP, NRPhi_int, Rratio, Ln
cdef cnp.ndarray[double,ndim=2] Pts, indI, PtsCross, VPbis
cdef cnp.ndarray[double,ndim=1] R0, dS, ind, dLr, Rref, dRPhir
cdef cnp.ndarray[long,ndim=1] indL, NL
# Pre-format input
if PhiMinMax is None:
PhiMinMax = [-Cpi,Cpi]
DPhiMinMax = 2.*Cpi
Full = True
else:
PhiMinMax = [Catan2(Csin(PhiMinMax[0]),Ccos(PhiMinMax[0])), Catan2(Csin(PhiMinMax[1]),Ccos(PhiMinMax[1]))]
DPhiMinMax = PhiMinMax[1]-PhiMinMax[0] if PhiMinMax[1]>=PhiMinMax[0] else 2.*Cpi + PhiMinMax[1] - PhiMinMax[0]
Full = False
# Get the limits if any (and make sure to replace them in the proper quadrants)
if DPhi is None:
DPhi0, DPhi1 = PhiMinMax[0], PhiMinMax[1]
else:
DPhi0 = PhiMinMax[0] if DPhi[0] is None else Catan2(Csin(DPhi[0]),Ccos(DPhi[0]))
DPhi1 = PhiMinMax[1] if DPhi[1] is None else Catan2(Csin(DPhi[1]),Ccos(DPhi[1]))
DDPhi = DPhi1-DPhi0 if DPhi1>DPhi0 else 2.*Cpi+DPhi1-DPhi0
Inter, Bounds = _getBoundsInter2AngSeg(Full, PhiMinMax[0], PhiMinMax[1], DPhi0, DPhi1)
BC = list(Bounds)
nBounds = len(Bounds)
for ii in range(0,nBounds):
if BC[ii][0]<PhiMinMax[0]:
BC[ii][0] += 2.*Cpi
if BC[ii][1]<=PhiMinMax[0]:
BC[ii][1] += 2.*Cpi
if Inter:
# Get the actual R and Z resolutions and mesh elements
PtsCross, dLr, indL, NL, Rref, VPbis = _Ves_mesh_CrossPoly(VPoly, dL, D1=None, D2=None, margin=margin, DIn=DIn, VIn=VIn)
R0 = np.copy(Rref)
NR0 = R0.size
indin = np.ones((PtsCross.shape[1],),dtype=bool)
if DR is not None:
indin = indin & (R0>=DR[0]) & (R0<=DR[1])
if DZ is not None:
indin = indin & (PtsCross[1,:]>=DZ[0]) & (PtsCross[1,:]<=DZ[1])
PtsCross, dLr, indL, Rref = PtsCross[:,indin], dLr[indin], indL[indin], Rref[indin]
Ln = indin.sum()
Indin = indin.nonzero()[0]
dRPhir, dPhir = np.empty((Ln,)), np.empty((Ln,))
Phin = np.zeros((Ln,),dtype=int)
NRPhi = np.empty((Ln,))
NRPhi0 = np.zeros((Ln,),dtype=int)
nRPhi0, indR0ii = 0, 0
NP, NPhimax = 0, 0
Rratio = int(Cceil(np.max(Rref)/np.min(Rref)))
indBounds = np.empty((2,nBounds),dtype=int)
for ii in range(0,Ln):
# Get the actual RPhi resolution and Phi mesh elements (! depends on R !)
NRPhi[ii] = Cceil(DPhiMinMax*Rref[ii]/dRPhi)
NRPhi_int = int(NRPhi[ii])
dPhir[ii] = DPhiMinMax/NRPhi[ii]
dRPhir[ii] = dPhir[ii]*Rref[ii]
# Get index and cumulated indices from background
for jj0 in range(indR0ii,NR0):
if jj0==Indin[ii]:
indR0ii = jj0
break
else:
nRPhi0 += <long>Cceil(DPhiMinMax*R0[jj0]/dRPhi)
NRPhi0[ii] = nRPhi0
# Get indices of phi
# Get the extreme indices of the mesh elements that really need to be created within those limits
for kk in range(0,nBounds):
abs0 = Cabs(BC[kk][0]-PhiMinMax[0])
if abs0-dPhir[ii]*Cfloor(abs0/dPhir[ii])<margin*dPhir[ii]:
nPhi0 = int(Cround(abs0/dPhir[ii]))
else:
nPhi0 = int(Cfloor(abs0/dPhir[ii]))
abs1 = Cabs(BC[kk][1]-PhiMinMax[0])
if abs1-dPhir[ii]*Cfloor(abs1/dPhir[ii])<margin*dPhir[ii]:
nPhi1 = int(Cround(abs1/dPhir[ii]))
else:
nPhi1 = int(Cfloor(abs1/dPhir[ii]))
indBounds[0,kk] = nPhi0
indBounds[1,kk] = nPhi1
Phin[ii] += nPhi1+1-nPhi0
if ii==0:
indI = np.ones((Ln,Phin[ii]*Rratio+1))
jj = 0
for kk in range(0,nBounds):
for kkb in range(indBounds[0,kk],indBounds[1,kk]+1):
indI[ii,jj] = <double>( kkb )
jj += 1
NP += Phin[ii]
# Finish counting to get total number of points
if jj0<=NR0-1:
for jj0 in range(indR0ii,NR0):
nRPhi0 += <long>Cceil(DPhiMinMax*R0[jj0]/dRPhi)
# Compute Pts, dV and ind
Pts = np.empty((3,NP))
ind = np.empty((NP,))
dS = np.empty((NP,))
# This triple loop is the longest part, it takes ~90% of the CPU time
NP = 0
if Out.lower()=='(x,y,z)':
for ii in range(0,Ln):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
phi = PhiMinMax[0] + (0.5+indiijj)*dPhir[ii]
Pts[0,NP] = PtsCross[0,ii]*Ccos(phi)
Pts[1,NP] = PtsCross[0,ii]*Csin(phi)
Pts[2,NP] = PtsCross[1,ii]
ind[NP] = NRPhi0[ii] + indiijj
dS[NP] = dLr[ii]*dRPhir[ii]
NP += 1
else:
for ii in range(0,Ln):
for jj in range(0,Phin[ii]):
indiijj = indI[ii,jj]
Pts[0,NP] = PtsCross[0,ii]
Pts[1,NP] = PtsCross[1,ii]
Pts[2,NP] = PhiMinMax[0] + (0.5+indiijj)*dPhir[ii]
ind[NP] = NRPhi0[ii] + indiijj
dS[NP] = dLr[ii]*dRPhir[ii]
NP += 1
else:
Pts, dS, ind, NL, dRPhir, nRPhi0 = None, None, None, None, None, None
return Pts, dS, ind.astype(int), NL, dLr, Rref, dRPhir, nRPhi0, VPbis
Out[9]:
Cython: _cython_magic_8152fc40fb05daa7217c00b66474f995.pyx
Generated by Cython 0.25.2
Yellow lines hint at Python interaction.
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001:
+002: cimport cython
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015: """ Get the actual reolution from the desired resolution and MinMax and limits """
016: # Get the number of mesh elements in LMinMax
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018: # Derive the real (effective) resolution
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020: # Get desired limits if any
021: cdef double[::1] DLc, L
022: cdef long [::1] indL
023: #cdef cnp.ndarray[double,ndim=1] indL, L
024: cdef double abs0, abs1, A
025: cdef int nL0, nL1, Nind, ii, jj
026: cdef list dl
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/* … */
goto __pyx_L3;
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029: else:
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036: # Get the extreme indices of the mesh elements that really need to be created within those limits
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/* … */
goto __pyx_L6;
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040: else:
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goto __pyx_L7;
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045: else:
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125: str Out='(X,Y,Z)', double margin=1.e-9):
126: " Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
127: cdef double[::1] R, Z, dPhir, NRPhi#, dPhi, NRZPhi_cum0, indPhi, phi
128: cdef double dRr0, dRr, dZr, DPhi0, DPhi1, DPhiMinMax
129: cdef double abs0, abs1, phi, indiijj
130: cdef long[::1] indR0, indR, indZ, Phin, NRPhi0, Indin
131: cdef int NR0, NR, NZ, Rn, Zn, nRPhi0, indR0ii, ii, jj0, jj, nPhi0, nPhi1, zz, NP, NRPhi_int, Rratio, Ln
132: cdef cnp.ndarray[double,ndim=2] Pts, indI, PtsCross, VPbis
133: cdef cnp.ndarray[double,ndim=1] R0, dS, ind, dLr, Rref, dRPhir
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135:
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249:
250:
251:
252:
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296: else:
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for (__pyx_t_42 = 0; __pyx_t_42 < __pyx_t_41; __pyx_t_42+=1) {
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301:
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for (__pyx_t_18 = 0; __pyx_t_18 < __pyx_t_41; __pyx_t_18+=1) {
__pyx_v_ii = __pyx_t_18;
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for (__pyx_t_26 = 0; __pyx_t_26 < __pyx_t_48; __pyx_t_26+=1) {
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if (__pyx_t_10) {
/* … */
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goto __pyx_L16_break;
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if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 309, __pyx_L1_error) }
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__pyx_t_59 = 0;
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if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 310, __pyx_L1_error) }
__pyx_t_61 = __pyx_v_iiL;
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__pyx_t_65 = 1;
__pyx_t_66 = __pyx_v_iiL;
__pyx_t_67 = 2;
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+312: dS[ii] = dLr[iiL]*dRPhirRef[iiL]
__pyx_t_69 = __pyx_v_iiL;
__pyx_t_70 = __pyx_v_iiL;
__pyx_t_71 = __pyx_v_ii;
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__pyx_t_72 = __pyx_v_iiL;
__pyx_t_10 = (((*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_dRPhir.rcbuffer->pybuffer.buf, __pyx_t_72, __pyx_pybuffernd_dRPhir.diminfo[0].strides)) == -1.) != 0);
if (__pyx_t_10) {
/* … */
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}
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__pyx_t_73 = __pyx_v_iiL;
__pyx_t_74 = __pyx_v_iiL;
*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_dRPhir.rcbuffer->pybuffer.buf, __pyx_t_74, __pyx_pybuffernd_dRPhir.diminfo[0].strides) = (*((double *) ( /* dim=0 */ ((char *) (((double *) __pyx_v_dRPhirRef.data) + __pyx_t_73)) )));
315:
316: else:
+317: for ii in range(0,NP):
/*else*/ {
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for (__pyx_t_18 = 0; __pyx_t_18 < __pyx_t_41; __pyx_t_18+=1) {
__pyx_v_ii = __pyx_t_18;
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__pyx_t_48 = (__pyx_v_Ln + 1);
for (__pyx_t_26 = 0; __pyx_t_26 < __pyx_t_48; __pyx_t_26+=1) {
__pyx_v_jj = __pyx_t_26;
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__pyx_t_75 = __pyx_v_ii;
__pyx_t_76 = __pyx_v_jj;
__pyx_t_10 = ((((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_75)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_76)) )))) < 0.) != 0);
if (__pyx_t_10) {
/* … */
}
}
__pyx_L22_break:;
+320: break
goto __pyx_L22_break;
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__pyx_v_iiL = (__pyx_v_jj - 1);
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__pyx_t_77 = __pyx_v_ii;
__pyx_t_78 = __pyx_v_iiL;
__pyx_v_iiphi = ((*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_ind.data) + __pyx_t_77)) ))) - (*((long *) ( /* dim=0 */ ((char *) (((long *) __pyx_v_NRPhi0.data) + __pyx_t_78)) ))));
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__pyx_t_79 = 0;
__pyx_t_80 = __pyx_v_iiL;
__pyx_t_81 = 0;
__pyx_t_82 = __pyx_v_ii;
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if (unlikely(!__pyx_v_Phi.memview)) { __Pyx_RaiseUnboundLocalError("Phi"); __PYX_ERR(0, 325, __pyx_L1_error) }
__pyx_t_87 = __pyx_v_iiL;
__pyx_t_88 = __pyx_v_iiphi;
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__pyx_t_94 = __pyx_v_iiL;
__pyx_t_10 = (((*__Pyx_BufPtrStrided1d(double *, __pyx_pybuffernd_dRPhir.rcbuffer->pybuffer.buf, __pyx_t_94, __pyx_pybuffernd_dRPhir.diminfo[0].strides)) == -1.) != 0);
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/* … */
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__pyx_L12:;
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__Pyx_INCREF(((PyObject *)__pyx_v_Pts));
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PyTuple_SET_ITEM(__pyx_t_6, 0, ((PyObject *)__pyx_v_Pts));
__Pyx_INCREF(((PyObject *)__pyx_v_dS));
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PyTuple_SET_ITEM(__pyx_t_6, 1, ((PyObject *)__pyx_v_dS));
__Pyx_INCREF(((PyObject *)__pyx_v_NL));
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PyTuple_SET_ITEM(__pyx_t_6, 2, ((PyObject *)__pyx_v_NL));
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PyTuple_SET_ITEM(__pyx_t_6, 3, ((PyObject *)__pyx_v_dLr));
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PyTuple_SET_ITEM(__pyx_t_6, 4, ((PyObject *)__pyx_v_Rref));
__Pyx_GIVEREF(__pyx_t_14);
PyTuple_SET_ITEM(__pyx_t_6, 5, __pyx_t_14);
__Pyx_GIVEREF(__pyx_t_4);
PyTuple_SET_ITEM(__pyx_t_6, 6, __pyx_t_4);
__Pyx_INCREF(((PyObject *)__pyx_v_VPbis));
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PyTuple_SET_ITEM(__pyx_t_6, 7, ((PyObject *)__pyx_v_VPbis));
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__pyx_t_6 = 0;
goto __pyx_L0;
330:
331:
332: @cython.cdivision(True)
333: @cython.wraparound(False)
334: @cython.boundscheck(False)
+335: def _Ves_Smesh_TorStruct_SubFromD_cython(double[::1] PhiMinMax, double dL, double dRPhi,
/* Python wrapper */
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339: str Out='(X,Y,Z)', double margin=1.e-9):
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654: """ Return Inter=True if an intersection exist (all angles in radians in [-pi;pi])
655:
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722: str Out='(X,Y,Z)', double margin=1.e-9):
723: " Return the desired surfacic submesh indicated by the limits (DR,DZ,DPhi), for the desired resolution (dR,dZ,dRphi) "
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859:
860:
861:
In [10]:
VPoly = np.ascontiguousarray([[1,10.,20,20,10,1,1],[0,-10.,0,10,20,10,0.]])
VIn = VPoly[:,1:]-VPoly[:,:-1]
VIn = np.array([-VIn[1,:],VIn[0,:]])
VIn = VIn/np.sqrt(np.sum(VIn**2,axis=0))[np.newaxis,:]
DIn = -0.1
Ptsm, dLm, indm, Nm, Rrefm, VPbism = _Ves_mesh_CrossPoly(VPoly, 1., D1=[0,25], D2=[-25,25], DIn=DIn, VIn=VIn)
#%timeit out = _Ves_mesh_CrossPoly(VPoly, 0.1)
#print np.all(indm==np.unique(indm))
Pts, dS, ind, NL, dLr, Rref, dRPhir, nRPhi0, VPbis = _Ves_Smesh_Tor_SubFromD_cython(0.5, 0.5, VPoly, DR=[0,25], DZ=[-25,25], DPhi=[0,np.pi/2.], Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
Ptsi, dSi, NLi, dLri, Rrefi, dRPhiri, nRPhi0i, VPbisi = _Ves_Smesh_Tor_SubFromInd_cython(0.5, 0.5, VPoly, ind, Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_Tor_SubFromD_cython(0.1, 0.1, VPoly, DR=None, DZ=None, DPhi=None, Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_Tor_SubFromInd_cython(0.5, 0.5, VPoly, ind, Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
print([np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Pts,Ptsi),(dS,dSi),(NL,NLi),(dLr,dLri),(Rref,Rrefi),(dRPhir,dRPhiri),(nRPhi0,nRPhi0i),(VPbis,VPbisi)]])
Ptsb, dSb, indb, NLb, dLrb, Rrefb, dRPhirb, nRPhi0b, VPbisb = _Ves_Smesh_Tor_SubFromD_bis(0.5, 0.5, VPoly, DR=[0,25], DZ=[-25,25], DPhi=[0,np.pi/2.], Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
print([np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(Pts,Ptsb),(dS,dSb),(ind,indb),(NL,NLb),(dLr,dLrb),(Rref,Rrefb),(dRPhir,dRPhirb),(nRPhi0,nRPhi0b),(VPbis,VPbisb)]])
PhiMinMax = np.array([-np.pi/2.,0.])
#Ptsb, dSb, indb, NLb, dLrb, Rrefb, dRPhirb, nRPhi0b, VPbisb = _Ves_Smesh_Tor_SubFromD_bis(0.5, 0.5, VPoly, PhiMinMax=PhiMinMax, DR=[0,25], DZ=[-25,25], DPhi=[0,np.pi/2.], Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
#PhiMinMax = np.array([-np.pi/2.,0.])
#PtsS, dSS, indS, NL, dLr, Rref, dR0r, dZ0r, dRPhir, VPbis = _Ves_Smesh_TorStruct_SubFromD_cython(PhiMinMax, 0.5, 0.5, VPoly, DR=[0.,25.], DZ=[-25.,25.], DPhi=[-np.pi/8.,0.], Out='(x,y,z)', DIn=DIn, VIn=VIn)
#PtsSi, dSSi, NLi, dLri, Rrefi, dR0ri, dZ0ri, dRPhiri, VPbisi = _Ves_Smesh_TorStruct_SubFromInd_cython(PhiMinMax, 0.5, 0.5, VPoly, indS, Out='(x,y,z)', DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_TorStruct_SubFromD_cython(PhiMinMax, 0.1, 0.1, VPoly, DR=None, DZ=None, DPhi=None, Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_TorStruct_SubFromInd_cython(PhiMinMax, 0.5, 0.5, VPoly, indS, Out='(X,Y,Z)', DIn=DIn, VIn=VIn)
#print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(PtsS,PtsSi),(dSS,dSSi),(NL,NLi),(dLr,dLri),(Rref,Rrefi),(dR0r,dR0ri),(dZ0r,dZ0ri),(dRPhir,dRPhiri),(nRPhi0,nRPhi0i),(VPbis,VPbisi)]]
#PtsL, dS, ind, NL, dLr, Rref, dXr, dY0r, dZ0r, VPbis = _Ves_Smesh_Lin_SubFromD_cython(np.array([0.,10.]), 0.5, 0.01, VPoly, DY=[0.,25.], DZ=[-25.,25.], DX=None, DIn=DIn, VIn=VIn)
#Ptsi, dSi, NLi, dLri, Rrefi, dXri, dY0ri, dZ0ri, VPbisi = _Ves_Smesh_Lin_SubFromInd_cython(np.array([0.,10.]), 0.5, 0.01, VPoly, ind, DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_Lin_SubFromD_cython(np.array([0.,10.]), 0.5, 0.01, VPoly, DX=None, DY=None, DZ=None, DIn=DIn, VIn=VIn)
#%timeit out = _Ves_Smesh_Lin_SubFromInd_cython(np.array([0.,10.]), 0.5, 0.01, VPoly, ind, DIn=DIn, VIn=VIn)
#print [np.allclose(A,B,atol=1.e-9,rtol=0.,equal_nan=True) for (A,B) in [(PtsL,Ptsi),(dS,dSi),(NL,NLi),(dLr,dLri),(Rref,Rrefi)]]
[True, True, True, True, True, True, True, True]
In [11]:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
"""
f = plt.figure(figsize=(14,10))
ax = f.add_axes([0.1,0.1,0.8,0.8])
ax.plot(VPoly[0,:],VPoly[1,:],'-k')
ax.plot(Ptsm[0,:],Ptsm[1,:], 'xb')
ax.plot(VPbism[0,:], VPbism[1,:],'sr')
"""
f = plt.figure(figsize=(14,10))
ax = f.add_axes([0.1,0.1,0.8,0.8],projection='3d')
ax.plot(Pts[0,:],Pts[1,:], Pts[2,:],'.b')
f = plt.figure(figsize=(14,10))
ax = f.add_axes([0.1,0.1,0.8,0.8],projection='3d')
ax.plot(Ptsb[0,:],Ptsb[1,:], Ptsb[2,:],'.b')
"""
f = plt.figure(figsize=(14,10))
ax = f.add_axes([0.1,0.1,0.8,0.8],projection='3d')
ax.plot(PtsS[0,:],PtsS[1,:], PtsS[2,:],'.b')
f = plt.figure(figsize=(14,10))
ax = f.add_axes([0.1,0.1,0.8,0.8],projection='3d')
ax.plot(PtsL[0,:],PtsL[1,:], PtsL[2,:],'.b')
"""
plt.show()
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Content source: Didou09/tofu
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