def yder_6th(f,dy,x=[],y=[],z=[],param=[],dim=[]):
if (f.ndim != 3 and f.ndim != 4):
print("%s dimension arrays not handled." % (str(f.ndim)))
raise ValueError
if not param:
param=read_param(quiet=True)
if not dim:
dim=read_dim()
if len(y) < 1:
gd = read_grid(quiet=True)
y = gd.y
dy=N.gradient(y)
if (dim.ny!=1):
dy2 = 1./(60.*dy)
dfdy = N.zeros_like(f)
m1 = 3
m2 = f.shape[-2]-3
if (m2 > m1 and dim.ny != 1):
for m in range(m1,m2):
dfdy[...,m,:] = dy2[m]*( +45.*(f[...,m+1,:]-f[...,m-1,:])
-9.*(f[...,m+2,:]-f[...,m-2,:])
+ (f[...,m+3,:]-f[...,m-3,:]) )
else:
dfdy = 0.
if param.coord_system == ('cylindric' or 'spherical'):
if len(x) < 1:
gd=read_grid(quiet=True)
x=gd.x
dfdy /= x
return dfdy
def zder_6th(f,dz,x=[],y=[],z=[],run2D=False,param=[],dim=[]):
if (f.ndim != 3 and f.ndim != 4):
print("%s dimension arrays not handled." % (str(f.ndim)))
raise ValueError
if not param:
param=read_param(quiet=True)
if not dim:
dim=read_dim()
if len(z) < 1:
gd = read_grid(quiet=True)
z = gd.z
dz=N.gradient(z)
if (dim.nz!=1):
dz2 = 1./(60.*dz)
dfdz = N.zeros_like(f)
n1 = 3
if run2D:
n2 = f.shape[1]-3
else:
n2 = f.shape[-3]-3
if (n2 > n1 and dim.nz!=1):
if (run2D):
# f[...,z,x] or f[...,z,y]
for n in range(n1,n2):
dfdz[...,n,:] = dz2[n]*(+45.*(f[...,n+1,:]-f[...,n-1,:])
-9.*(f[...,n+2,:]-f[...,n-2,:])
+(f[...,n+3,:]-f[...,n-3,:]) )
else:
# f[...,z,y,x]
for n in range(n1,n2):
dfdz[...,n,:,:] = dz2[n]*(+45.*(f[...,n+1,:,:]-f[...,n-1,:,:])
-9.*(f[...,n+2,:,:]-f[...,n-2,:,:])
+(f[...,n+3,:,:]-f[...,n-3,:,:]) )
else:
dfdz=0
if param.coord_system == 'spherical':
if (len(x) or len(y)) < 1:
gd=read_grid(quiet=True)
x=gd.x; y=gd.y
sin_y = N.sin(y)
siny1 = 1./sin_y
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
siny1[i_sin] = 0.
x_1, sin1th = N.meshgrid(1./x, siny1)
dfdz *= x_1*sin1th
return dfdz
def laplacian(f, dx, dy, dz, x=[], y=[], z=[], param=[], dim=[]):
"""
take the laplacian of a pencil code scalar array
"""
if not param:
param = read_param(quiet=True)
if not dim:
dim = read_dim()
if len(x) < 1:
gd = read_grid(quiet=True)
x = gd.x
y = gd.y
z = gd.z
laplacian = N.empty(f.shape)
laplacian = xder2(f,dx,x=x,y=y,z=z,param=param,dim=dim) +\
yder2(f,dy,x=x,y=y,z=z,param=param,dim=dim) +\
zder2(f,dz,x=x,y=y,z=z,param=param,dim=dim)
if param.coord_system == 'cylindric':
laplacian += xder(f, dx, x=x, y=y, z=z, param=param, dim=dim) / x
if param.coord_system == 'spherical':
sin_y = N.sin(y)
cos_y = N.cos(y)
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
cos_y[i_sin] = 0.
sin_y[i_sin] = 1
x_2, cotth = N.meshgrid(1. / x**2, cos_y / sin_y)
laplacian += 2*xder(f,dx,x=x,y=y,z=z,param=param,dim=dim)/x +\
yder(f,dy,x=x,y=y,z=z,param=param,dim=dim)*x_2*cotth
return laplacian
def div(f, dx, dy, dz, x=[], y=[], z=[], param=[], dim=[]):
"""
take divergence of pencil code vector array
"""
if (f.ndim != 4):
print(
"div: must have vector 4-D array f[mvar,mz,my,mx] for divergence")
raise ValueError
if not param:
param = read_param(quiet=True)
if not dim:
dim = read_dim()
gd = read_grid(quiet=True, param=param)
if len(x) < 1:
x = gd.x
y = gd.y
z = gd.z
div = xder(f[0,...],dx,x=x,y=y,z=z,param=param,dim=dim) +\
yder(f[1,...],dy,x=x,y=y,z=z,param=param,dim=dim) +\
zder(f[2,...],dz,x=x,y=y,z=z,param=param,dim=dim)
if param.coord_system == 'cylindric':
div += f[0, ...] / x
if param.coord_system == 'spherical':
sin_y = N.sin(y)
cos_y = N.cos(y)
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
cos_y[i_sin] = 0.
sin_y[i_sin] = 1
x_1, cotth = N.meshgrid(1. / gd.x, cos_y / sin_y)
div += 2 * f[0, ...] * x_1 + f[1, ...] * x_1 * cotth
return div
def del2(f, dx, dy, dz, x=[], y=[], z=[]):
"""taken from pencil code's sub.f90
! calculate del6 (defined here as d^6/dx^6 + d^6/dy^6 + d^6/dz^6, rather
! than del2^3) of a scalar for hyperdiffusion
Duplcation of laplacian why? Fred - added curvelinear
"""
param = read_param(quiet=True)
gd = read_grid(quiet=True)
if len(x) < 1:
x = gd.x
if len(y) < 1:
y = gd.y
if len(z) < 1:
z = gd.z
del2 = xder2(f, dx, x=x, y=y, z=z)
del2 = del2 + yder2(f, dy, x=x, y=y, z=z)
del2 = del2 + zder2(f, dz, x=x, y=y, z=z)
if param.coord_system == 'cylindric':
del2 += xder(f, dx, x=x, y=y, z=z) / x
if param.coord_system == 'spherical':
sin_y = N.sin(y)
cos_y = N.cos(y)
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
cos_y[i_sin] = 0.
sin_y[i_sin] = 1
x_2, cotth = N.meshgrid(1. / x**2, cos_y / sin_y)
del2 += 2*xder(f,dx,x=x,y=y,z=z)/x +\
yder(f,dy,x=x,y=y,z=z)*x_2*cotth
return del2
def curl(f, dx, dy, dz, x=[], y=[], z=[], run2D=False, param=[], dim=[]):
"""
take the curl of a pencil code vector array.
23-fev-2009/dintrans+morin: introduced the run2D parameter to deal
with pure 2-D snapshots (solved the (x,z)-plane pb)
"""
if (f.shape[0] != 3):
print("curl: must have vector 4-D array f[3,mz,my,mx] for curl")
raise ValueError
if not param:
param = read_param(quiet=True)
if not dim:
dim = read_dim()
if len(x) < 1:
gd = read_grid(quiet=True, param=param)
x = gd.x
y = gd.y
z = gd.z
curl = N.empty_like(f)
if (not (run2D)):
# 3-D case
curl[0,...] = yder(f[2,...],dy,x=x,y=y,z=z,param=param,dim=dim) -\
zder(f[1,...],dz,x=x,y=y,z=z,param=param,dim=dim)
curl[1,...] = zder(f[0,...],dz,x=x,y=y,z=z,param=param,dim=dim) -\
xder(f[2,...],dx,x=x,y=y,z=z,param=param,dim=dim)
curl[2,...] = xder(f[1,...],dx,x=x,y=y,z=z,param=param,dim=dim) -\
yder(f[0,...],dy,x=x,y=y,z=z,param=param,dim=dim)
elif (dim.ny == 1):
# 2-D case in the (x,z)-plane
# f[...,nz,1,nx] if run2D=False or f[...,nz,nx] if run2D=True
curl[0,...] = zder(f,dz,x=x,y=y,z=z,run2D=run2D,param=param, \
dim=dim)[0,...] - xder(f,dx,x=x,y=y,z=z,param=param,dim=dim)[2,...]
elif (dim.nz == 1):
# 2-D case in the (x,y)-plane
# f[...,1,ny,nx] if run2D=False or f[...,ny,nx] if run2D=True
curl[0,...] = xder(f,dx,x=x,y=y,z=z,param=param,dim=dim)[1,...] -\
yder(f,dy,x=x,y=y,z=z,param=param,dim=dim)[0,...]
if param.coord_system == 'cylindric':
# 2-D case in the (r,theta)-plane
if run2D:
curl[0, ...] += f[1, ...] / x
else:
# 3-D case
curl[2, ...] += f[1, ...] / x
if param.coord_system == 'spherical':
sin_y = N.sin(y)
cos_y = N.cos(y)
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
cos_y[i_sin] = 0.
sin_y[i_sin] = 1
x_1, cotth = N.meshgrid(1. / x, cos_y / sin_y)
curl[0, ...] += f[2, ...] * x_1 * cotth
curl[1, ...] -= f[2, ...] / x
curl[2, ...] += f[1, ...] / x
return curl
def xder_6th(f,dx,x=[],y=[],z=[],param=[],dim=[]):
if (f.ndim != 3 and f.ndim != 4):
print("%s dimension arrays not handled." % (str(f.ndim)))
raise ValueError
if not param:
param=read_param(quiet=True)
if not dim:
dim=read_dim()
if len(x) < 1:
gd = read_grid(quiet=True)
x = gd.x
dx=N.gradient(x)
if (dim.nx!=1):
dx2 = 1./(60.*dx)
dfdx = N.zeros_like(f)
l1 = 3
l2 = f.shape[-1]-3
if (l2 > l1 and dim.nx!=1):
for l in range(l1,l2):
dfdx[...,l] = dx2[l]*( +45.*(f[...,l+1]-f[...,l-1])
-9.*(f[...,l+2]-f[...,l-2])
+ (f[...,l+3]-f[...,l-3]) )
else:
dfdx = 0.
return dfdx
def curl2(f, dx, dy, dz, x=[], y=[], z=[]):
"""
take the double curl of a pencil code vector array.
"""
if (f.ndim != 4 or f.shape[0] != 3):
print("curl2: must have vector 4-D array f[3,mz,my,mx] for curl2")
raise ValueError
param = read_param(quiet=True)
gd = read_grid(quiet=True)
if len(x) < 1:
x = gd.x
if len(y) < 1:
y = gd.y
if len(z) < 1:
z = gd.z
curl2 = N.empty(f.shape)
curl2[0,...] = xder(yder(f[1,...],dy,x=x,y=y,z=z) +
zder(f[2,...],dz,x=x,y=y,z=z),dx,x=x,y=y,z=z) -\
yder2(f[0,...],dy,x=x,y=y,z=z) -\
zder2(f[0,...],dz,x=x,y=y,z=z)
curl2[1,...] = yder(xder(f[0,...],dx,x=x,y=y,z=z) +
zder(f[2,...],dz,x=x,y=y,z=z),dy,x=x,y=y,z=z) -\
xder2(f[1,...],dx,x=x,y=y,z=z) -\
zder2(f[1,...],dz,x=x,y=y,z=z)
curl2[2,...] = zder(xder(f[0,...],dx,x=x,y=y,z=z) +
yder(f[1,...],dy,x=x,y=y,z=z),dz,x=x,y=y,z=z) -\
xder2(f[2,...],dx,x=x,y=y,z=z) -\
yder2(f[2,...],dy,x=x,y=y,z=z)
if param.coord_system == 'cylindric':
curl2[0, ...] += yder(f[1, ...], dy, x=x, y=y, z=z) / x**2
curl2[1, ...] += f[1, ...] / gd.x**2 - xder(
f[1, ...], dx, x=x, y=y, z=z) / x
curl2[2, ...] += (zder(f[0, ...], dz, x=x, y=y, z=z) -
xder(f[2, ...], dx, x=x, y=y, z=z)) / x
if param.coord_system == 'spherical':
sin_y = N.sin(y)
cos_y = N.cos(y)
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
cos_y[i_sin] = 0.
sin_y[i_sin] = 1
x_1, cotth = N.meshgrid(1. / x, cos_y / sin_y)
sin2th, x_2 = N.meshgrid(1. / x**2, 1 / sin_y**2)
curl2[0,...] += (yder(f[1,...],dy,x=x,y=y,z=z) +
zder(f[2,...],dz,x=x,y=y,z=z))/x +\
x_1*cotth*(xder(f[1,...],dx,x=x,y=y,z=z) -
yder(f[0,...],dy,x=x,y=y,z=z) + f[1,...]/x )
curl2[1,...] += zder(f[2,...],dz,x=x,y=y,z=z)*x_1*cotth -\
2*xder(f[1,...],dx,x=x,y=y,z=z)/x
curl2[2,...] += x_2*sin2th*f[2,...] - \
2*xder(f[2,...],dx,x=x,y=y,z=z)/x - (
yder(f[2,...],dy,x=x,y=y,z=z) +
zder(f[1,...],dz,x=x,y=y,z=z))*x_1*cotth
return curl2
def zder2_6th(f,dz,x=[],y=[],z=[],param=[],dim=[]):
if (f.ndim != 3 and f.ndim != 4):
print("%s dimension arrays not handled." % (str(f.ndim)))
raise ValueError
if (len(z) < 1):
gd=read_grid(quiet=True)
z=gd.z
if not param:
param=read_param(quiet=True)
if not dim:
dim=read_dim()
dz = N.gradient(z)
if (dim.nz!=1):
dz2 = 1./(180.*dz**2.)
dfdz = N.zeros_like(f)
n1 = 3
n2 = f.shape[-3]-3
if (n2 > n1 and dim.nz!=1):
for n in range(n1,n2):
dfdz[...,n,:,:] = dz2[n]*(-490.* f[...,n,:,:]
+270.*(f[...,n-1,:,:]+f[...,n+1,:,:])
- 27.*(f[...,n-2,:,:]+f[...,n+2,:,:])
+ 2.*(f[...,n-3,:,:]+f[...,n+3,:,:]) )
else:
dfdz = 0.
if param.coord_system == 'spherical':
if (len(x) or len(y)) < 1:
gd=read_grid(quiet=True)
x=gd.x; y=gd.y
sin_y = N.sin(y)
siny1 = 1./sin_y
i_sin = N.where(N.abs(sin_y) < 1e-5)[0]
if i_sin.size > 0:
siny1[i_sin] = 0.
x_2, sin2th = N.meshgrid(1./x**2, siny1**2)
dfdz *= x_2*sin2th
return dfdz
def del6(f, dx, dy, dz, x=[], y=[], z=[]):
"""taken from pencil code's sub.f90
! calculate del6 (defined here as d^6/dx^6 + d^6/dy^6 + d^6/dz^6, rather
! than del2^3) of a scalar for hyperdiffusion
"""
gd = read_grid(quiet=True)
if len(x) < 1:
x = gd.x
if len(y) < 1:
y = gd.y
if len(z) < 1:
z = gd.z
del6 = xder6(f, dx, x=x, y=y, z=z)
del6 = del6 + yder6(f, dy, x=x, y=y, z=z)
del6 = del6 + zder6(f, dz, x=x, y=y, z=z)
return del6
def grad(f, dx, dy, dz, x=[], y=[], z=[], param=[], dim=[]):
"""
take the gradient of a pencil code scalar array.
"""
if (f.ndim != 3):
print("grad: must have scalar 3-D array f[mz,my,mx] for gradient")
raise ValueError
if not param:
param = read_param(quiet=True)
if not dim:
dim = read_dim()
if len(x) < 1:
gd = read_grid(quiet=True)
x = gd.x
y = gd.y
z = gd.z
grad = N.empty((3, ) + f.shape)
grad[0, ...] = xder(f, dx, x=x, y=y, z=z, param=param, dim=dim)
grad[1, ...] = yder(f, dy, x=x, y=y, z=z, param=param, dim=dim)
grad[2, ...] = zder(f, dz, x=x, y=y, z=z, param=param, dim=dim)
return grad