module NumRu::GPhys::Derivative in derivative.rb

Index

• module NumRu::GPhys::Derivative
  • threepoint_O2nd_deriv
    • First derivative (2nd Order difference use three point.)
  • cderiv
    • First derivative (using center difference method)
  • deriv2d
    • 2nd derivative

module NumRu::GPhys::Derivative

Module functions of Derivative Operater for GPhys.

threepoint_O2nd_deriv(gp, dim_or_dimname, bc=LINEAR_EXT))

Derivate z respect to dim th dimension with 2nd Order difference. return an NArray which result of the difference z divided difference x (in other wards,

(s**2*z_{i+1} + (t**2 - s**2)*f_{i} - t**2*f_{i-1}) / (s*t*(s + t)):
now s represents (x_{i} - x_{i-1}) ,t represents (x_{i+1} - x_{i})
and _{i} represents the suffix of {i} th element in the ((<dim>)) th 
dimension of array. ).

ARGUMENTS

• z (NArray): a NArray which you want to derivative.
• x (NArray): a NArray represents the dimension which derivative respect to. z.rank must be 1.
• dim (Numeric): a Numeric represents the dimention which derivative respect to. you can give number count backward (dim<0), but z.rank ¡Üdim must be > 0.
• bc (Numeric) : a Numeric which represent boundary condition. Supported conditions are:
  • LINEAR_EXT(=1) : default value
  • CYCLIC_EXT(=2)

RETURN VALUE

• O2nd_deriv_data (NArray): (s**2*z_{i+1} + (t**2 - s**2)*f_{i} - t**2*f_{i-1}) / (s*t*(s + t))

cderiv(gp, dim_or_dimname, bc=LINEAR_EXT, altcoord=nil)

Derivate gp respect to dim th or dimname dimension with center difference. return a GPhys which result of the difference gp divided difference axis. ( in other wards, (z_{i+1} - z_{i-1}) / (x_{i+1} - x_{i-1}): now x is axis array which you wants to respects to, _{i} represents the suffix of {i} th element in the dim th dimension of array. ).

ARGUMENTS

• gp (GPhys): a GPhys which you want to derivative.
• dim_or_dimname (Numeric or String): a Numeric or String represents the dimension which derivate respect to. you can give number count backward (dim<0), but z.rank ¡Üdim must be > 0.
• bc (Numeric) : a Numeric which represent boundary condition. Supported conditions are:
  • LINEAR_EXT(=1) : default value
  • CYCLIC_EXT(=2)
• altcoord (nil or 1D VArray): if a VArray, it is used as the coordiante variable with which differentiation is made. -- conveneient to make deribative in a different cooridate scaling. (e.g., differenciate in radian, while the coordinate is in degrees)

RETURN VALUE

• a GPhys

deriv2nd(gp, dim_or_dimname, bc=LINEAR_EXT, altcoord=nil)

2nd Derivate gp respect to dim th or dimname dimension covering non-uniform grids. Based on:

( (z_{i+1}-z_{i})/(x_{i+1}-x_{i}) - (z_{i}-z_{i-1})/(x_{i}-x_{i-1}) )
/ ((x_{i+1}-x_{i-1})/2)

See cderiv for usage.