pencil.math.derivatives.der_nonequi

Functions

der_6th(f, dx_1, axis)	der_6th(f, dx_1, axis)
der2_6th(f, dx_1, dx_tilde, axis)	der2_6th(f, dx_1, dx_tilde, axis)
der6_2nd(f, dx_1, axis)	der6_2nd(f, dx_1, axis)
xder_6th(f[, dx, dx_1])	xder_6th(f, dx=None, dx_1=None)
yder_6th(f[, dy, dy_1])	Same as xder_6th, but for y axis
zder_6th(f[, dz, dz_1])	Same as xder_6th, but for z axis
xder2_6th(f[, dx, dx_1, dx_tilde])	xder2_6th(f, dx=None, dx_1=None)
yder2_6th(f[, dy, dy_1, dy_tilde])	Same as xder2_6th, but for y axis
zder2_6th(f[, dz, dz_1, dz_tilde])	Same as xder2_6th, but for z axis
xder6_2nd(f[, dx, dx_1])	xder6_2nd(f, dx=None, dx_1=None)
yder6_2nd(f[, dy, dy_1])	Same as xder6_2nd, but for y axis
zder6_2nd(f[, dz, dz_1])	Same as xder6_2nd, but for z axis

Module Contents

pencil.math.derivatives.der_nonequi.der_6th(f, dx_1, axis)

der_6th(f, dx_1, axis)

Compute the 1st order derivative, 6th order accurate in x. Adapted from der2_main in deriv.f90. This supports nonequidistant grids.

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx_1 (1D array) – grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.

• axis (int) – Axis of f along which the derivative should be taken.

pencil.math.derivatives.der_nonequi.der2_6th(f, dx_1, dx_tilde, axis)

der2_6th(f, dx_1, dx_tilde, axis)

Compute the 2nd order derivative, 6th order accurate in x. Adapted from der2_main in deriv.f90. This supports nonequidistant grids.

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx_1 (1D array) – grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.

• dx_tilde (1D array) – grid.dx_tilde (or dy_tilde or dz_tilde). Is just zero for equidistant grids.

• axis (int) – Axis of f along which the derivative should be taken.

pencil.math.derivatives.der_nonequi.der6_2nd(f, dx_1, axis)

der6_2nd(f, dx_1, axis)

Compute the 6th order derivative, with 2nd order error in x. Adapted from der6_main in deriv.f90. This supports nonequidistant grids.

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx_1 (1D array) – grid.dx_1 (or dy_1 or dz_1), where grid is a Pencil grid object, and the array passed should correspond to the variable that is differentiated. In the case of equidistant grids, all elements are just 1/grid_spacing.

• axis (int) – Axis of f along which the derivative should be taken.

pencil.math.derivatives.der_nonequi.xder_6th(f, dx=None, dx_1=None)

xder_6th(f, dx=None, dx_1=None)

Compute the 1st order derivative, 6th order accurate in x.

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx (float) – Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 argument is ignored.

• dx_1 (ndarray) – Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant

pencil.math.derivatives.der_nonequi.yder_6th(f, dy=None, dy_1=None)

Same as xder_6th, but for y axis

pencil.math.derivatives.der_nonequi.zder_6th(f, dz=None, dz_1=None)

Same as xder_6th, but for z axis

pencil.math.derivatives.der_nonequi.xder2_6th(f, dx=None, dx_1=None, dx_tilde=None)

xder2_6th(f, dx=None, dx_1=None)

Compute the 2nd order derivative, 6th order accurate in x.

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx (float) – Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 and dx_tilde arguments are ignored.

• dx_1 (ndarray) – Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant

• dx_tilde (1D array) – grid.dx_tilde (or dy_tilde or dz_tilde). Is just zero for equidistant grids.

pencil.math.derivatives.der_nonequi.yder2_6th(f, dy=None, dy_1=None, dy_tilde=None)

Same as xder2_6th, but for y axis

pencil.math.derivatives.der_nonequi.zder2_6th(f, dz=None, dz_1=None, dz_tilde=None)

Same as xder2_6th, but for z axis

pencil.math.derivatives.der_nonequi.xder6_2nd(f, dx=None, dx_1=None)

xder6_2nd(f, dx=None, dx_1=None)

Compute the 6th order derivative, with 2nd order error in x

Parameters:

• f (ndarray) – Array for which to compute the derivative.

• dx (float) – Grid-spacing in x. For nonequidistant grids, leave this as None and specify dx_1 (=grid.dx_1) instead. If this is specified, the dx_1 argument is ignored.

• dx_1 (ndarray) – Inverse grid spacing. Specify this and leave dx=None if your grid is nonequidistant

pencil.math.derivatives.der_nonequi.yder6_2nd(f, dy=None, dy_1=None)

Same as xder6_2nd, but for y axis

pencil.math.derivatives.der_nonequi.zder6_2nd(f, dz=None, dz_1=None)

Same as xder6_2nd, but for z axis