Module functions of Derivative Operater for NArray.
threepoint_O2nd_deriv(z, x, dim, 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.
now only LINEAR_EXT(=1) supported. LINEAR_EXT load b_expand_linear_ext which
extend boundary with lenear value.
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(z, x, dim, bc=LINEAR_EXT)
-
Derivate z
respect to dim
th dimension with center difference.
return an NArray which result of the difference z divided difference
x
( in other wards, (z_{i+1} - z_{i-1}) / (x_{i+1} - x_{i-1}):
now _{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.
now only LINEAR_EXT(=1) supported. LINEAR_EXT load
b_expand_linear_ext which extend boundary with lenear value.
RETURN VALUE
- cderiv_data (NArray): (z_{i+1} - z_{i-1}) / (x_{i+1} - x_{i-1})
b_expand_linear_ext(z, dim)
-
expand boundary with linear value. extend array with 1 grid at each
boundary with dim th dimension, and assign th value which diffrential
value between a grid short of boundary and boundary grid in original array.
(on other wards, 2*z_{0}-z_{1} or 2*z_{n-1}-z_{n-2}: now _{i} represents the
suffix of {i} th element in the ((<dim>)) th dimension of array. ).
ARGUMENTS
- z (NArray): a NArray which you want to expand boundary.
- 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.
RETURN VALUE
cdiff(x, dim)
-
Diffrence operater. return an NArray which a difference x
( in other wards, (x_{i+1} - x_{i-1}): now _{i} represents the suffix of
{i} th element in the dim th dimension of array. ).
ARGUMENTS
- x (NArray): a NArray which you want to get difference.
- dim (Numeric): a Numeric representing the dimention which derivative
respect to. you can give number count backward (dim<0), but
z.rank ¡Üdim must be > 0.
RETURN VALUE
- cdiff_data (NArray): (x_{i+1} - x_{i-1})