pencil.math.derivatives

Differential operators in different coordinate systems.

Submodules

Attributes

`xder`
`yder`
`zder`
`xder2`
`yder2`
`zder2`
`xder3`
`yder3`
`zder3`
`xder5`
`yder5`
`zder5`
`xder6`
`yder6`
`zder6`

Functions

`div`(f[, dx, dy, dz, x, y, coordinate_system, grid])	div(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system="cartesian", grid=None)
`curl`(f[, dx, dy, dz, x, y, run2D, coordinate_system, grid])	curl(f, dx=None, dy=None, dz=None, x=None, y=None, run2D=False, coordinate_system="cartesian", grid=None)
`grad`(f[, dx, dy, dz, x, y, coordinate_system, grid])	grad(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system="cartesian", grid=None)
`curl2`(f[, dx, dy, dz, x, y, coordinate_system, grid])	curl2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system="cartesian", grid=None)
`del2`(f[, dx, dy, dz, x, y, coordinate_system, grid])	del2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system="cartesian", grid=None)
`curl3`(f, dx, dy, dz[, x, y, coordinate_system])	curl3(f, dx, dy, dz, x=None, y=None, coordinate_system="cartesian")
`del6`(f[, dx, dy, dz, grid])	del6(f, dx=None, dy=None, dz=None, grid=None)
`gij`(f, dx, dy, dz[, nder])	Calculate del6 (defined here as d^6/dx^6 + d^6/dy^6 + d^6/dz^6, rather
`traceless_strain`(f, dx, dy, dz[, x, y, z, ...])
`simple_centered`(x, y)	Calculate dy by center differencing using array slices

Package Contents

pencil.math.derivatives.xder

pencil.math.derivatives.yder

pencil.math.derivatives.zder

pencil.math.derivatives.xder2

pencil.math.derivatives.yder2

pencil.math.derivatives.zder2

pencil.math.derivatives.xder3

pencil.math.derivatives.yder3

pencil.math.derivatives.zder3

pencil.math.derivatives.xder5

pencil.math.derivatives.yder5

pencil.math.derivatives.zder5

pencil.math.derivatives.xder6

pencil.math.derivatives.yder6

pencil.math.derivatives.zder6

pencil.math.derivatives.div(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system='cartesian', grid=None)

div(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system=”cartesian”, grid=None)

Take divergence of pencil code vector array f in various coordinate systems.

Parameters:

f (ndarray) – Pencil code vector array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’, ‘cylindrical’ and ‘spherical’.
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None

pencil.math.derivatives.curl(f, dx=None, dy=None, dz=None, x=None, y=None, run2D=False, coordinate_system='cartesian', grid=None)

curl(f, dx=None, dy=None, dz=None, x=None, y=None, run2D=False, coordinate_system=”cartesian”, grid=None)

Take the curl of a pencil code vector array f in various coordinate systems.

Parameters:

f (ndarray) – Pencil code scalar array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
run2D (bool) – Deals with pure 2-D snapshots. !Only for Cartesian grids at the moment! Requires grid!=None.
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’, ‘cylindrical’ and ‘spherical’. !Does not work for 2d runs yet!
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None

pencil.math.derivatives.grad(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system='cartesian', grid=None)

grad(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system=”cartesian”, grid=None)

Take the gradient of a pencil code scalar array f in various coordinate systems.

Parameters:

f (ndarray) – Pencil code scalar array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’, ‘cylindrical’ and ‘spherical’.
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None

pencil.math.derivatives.curl2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system='cartesian', grid=None)

curl2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system=”cartesian”, grid=None)

Take the double curl of a pencil code vector array f.

Parameters:

f (ndarray) – Pencil code vector array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’, ‘cylindrical’ and ‘spherical’.
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None

pencil.math.derivatives.del2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system='cartesian', grid=None)

del2(f, dx=None, dy=None, dz=None, x=None, y=None, coordinate_system=”cartesian”, grid=None)

Calculate del2, the Laplacian of a scalar field f.

Parameters:

f (ndarray) – Pencil code vector array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’, ‘cylindrical’ and ‘spherical’.
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays. These will not have any effect if grid!=None

pencil.math.derivatives.curl3(f, dx, dy, dz, x=None, y=None, coordinate_system='cartesian')

curl3(f, dx, dy, dz, x=None, y=None, coordinate_system=”cartesian”)

Take the triple curl of a pencil code vector array f. Supports only equidistant grids.

Parameters:

f (ndarray) – Pencil code vector array f.
dx (floats) – Grid spacing in the three dimensions.
dy (floats) – Grid spacing in the three dimensions.
dz (floats) – Grid spacing in the three dimensions.
x (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays.
y (ndarrays) – Radial (x) and polar (y) coordinates, 1d arrays.
coordinate_system (string) – Coordinate system under which to take the divergence. Takes ‘cartesian’ and ‘cylindrical’.

pencil.math.derivatives.del6(f, dx=None, dy=None, dz=None, grid=None)

del6(f, dx=None, dy=None, dz=None, grid=None)

Calculate del6 (defined here as d^6/dx^6 + d^6/dy^6 + d^6/dz^6, rather than del2^3) of a scalar f for hyperdiffusion.

Parameters:

f (ndarray) – Pencil code scalar array f.
grid (pencil.read.grids.Grid) – Pencil grid object. See pc.read.grid().
compatibility) (Deprecated parameters (only for backwards)
--------------------------------------------------------
dx (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dy (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None
dz (floats) – Grid spacing in the three dimensions. These will not have any effect if grid!=None

pencil.math.derivatives.gij(f, dx, dy, dz, nder=6): Calculate del6 (defined here as d^6/dx^6 + d^6/dy^6 + d^6/dz^6, rather than del2^3) of a scalar f for hyperdiffusion.

pencil.math.derivatives.traceless_strain(f, dx, dy, dz, x=None, y=None, z=None, coordinate_system='cartesian')

pencil.math.derivatives.simple_centered(x, y): Calculate dy by center differencing using array slices