diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange/2d.log')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange/2d.log | 4195 |
1 files changed, 2222 insertions, 1973 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log index 4fa17e7..f356a52 100644 --- a/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log +++ b/src/GeneralizedPolynomial-Uniform/Lagrange/2d.log @@ -444,12 +444,13 @@ ftruncate := proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc -# interpolate.maple -- compute generalized interpolation formulas/coefficients -# $Id: interpolate.maple,v 1.4 2002/05/14 15:52:50 jthorn Exp $ +# interpolate.maple -- compute interpolation formulas/coefficients +# $Id: interpolate.maple,v 1.7 2002/08/19 14:30:43 jthorn Exp $ > # # <<<representation of numbers, data values, etc>>> -# Lagrange polynomial_interpolant - compute Lagrange polynomial interpolant +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant # coeff_as_lc_of_data - coefficients of ... (linear combination of data) # # print_coeff__lc_of_data - print C code to compute coefficients @@ -540,6 +541,171 @@ end proc ################################################################################ > # +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# [ +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# ] +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_coord_list = A list of lists of coordinates specifying which +# derivatives are computed by the deriv_proc_list[] +# procedures, for example +# [[x], [y], [x,y]] +# deriv_proc_list = A list of procedures for computing finite-difference +# derivatives. Each procedure should take N_dims integer +# arguments specifying an evaluation point, and return +# a suitable linear combination of the DATA() for the +# derivative at that point. For example +# example, +# [ +# proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# ] +# fn_posn_list = A list of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# [[0,0], [0,1], [1,0], [1,1]] +# deriv_posn_list = A list of positions (each a list of numeric values) +# where the interpolant is to match each possible product +# of 1st derivatives"1st" +# derivatives (actually all derivatives the given data DATA(), +# for example +# [[0,0], [0,1], [1,0], [1,1]] +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), coord_list::list(name), +> deriv_coord_list::list(list(name)), fd_deriv_proc_list::list(procedure), +> fn_posn_list::list(list(numeric)), deriv_posn_list::list(list(numeric)) +> ) +> local fn_eset, +> fn_expr, deriv_eset; +> +# set of equations {fn(posn) = DATA(posn)} +> fn_eset := map( +> # return equation that fn(this point) = DATA(this point) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> {op(fn_posn_list)} +> ); +> +# set of sets of equations +# { +# { deriv1(posn1) = fd_deriv1(posn1), +# deriv2(posn1) = fd_deriv2(posn1), +# ... }, +# { deriv1(posn2) = fd_deriv1(posn2), +# deriv2(posn2) = fd_deriv2(posn2), +# ... }, +# ... +# } +> fn_expr := fn(op(coord_list)); +> map( +> # return set of equations +> # {deriv(posn) = fd_deriv(posn)} +> # for this point +> proc(posn::list(integer)) +> { +> op( +> zip( +> # return equation that +> # deriv(posn) = fd_deriv(posn) +> # for this deriv and this point +> proc(deriv_coords::list(name), fd_deriv_proc::procedure) +> local fn_deriv_proc; +> fn_deriv_proc := unapply( diff(fn_expr,deriv_coords), +> op(coord_list) ); +> fn_deriv_proc(op(posn)) = fd_deriv_proc(op(posn)); +> end proc +> , +> [op(deriv_coord_list)] +> , +> [op(fd_deriv_proc_list)] +> ) +> ) +> } +> end proc +> , +> {op(deriv_posn_list)} +> ); +> +# set of equations {deriv-i(posn-j) = fd_deriv-i(posn-j)} +> deriv_eset := `union`(op(%)); +> +# solve equations for coeffs +> solve(fn_eset union deriv_eset, {op(coeff_list)}); +> +# interpolant as a polynomial in the coordinates +> return subs(%, eval(fn))(op(coord_list)); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), deriv_coord_list::list(list(name)), +fd_deriv_proc_list::list(procedure), fn_posn_list::list(list(numeric)), +deriv_posn_list::list(list(numeric))) +local fn_eset, fn_expr, deriv_eset; + fn_eset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + {op(fn_posn_list)}); + fn_expr := fn(op(coord_list)); + map(proc(posn::list(integer)) + {op(zip(proc(deriv_coords::list(name), fd_deriv_proc::procedure + ) + local fn_deriv_proc; + fn_deriv_proc := + unapply(diff(fn_expr, deriv_coords), op(coord_list)); + fn_deriv_proc(op(posn)) = fd_deriv_proc(op(posn)) + end proc, [op(deriv_coord_list)], [op(fd_deriv_proc_list)]))} + end proc, {op(deriv_posn_list)}); + deriv_eset := `union`(op(%)); + solve(fn_eset union deriv_eset, {op(coeff_list)}); + return subs(%, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# # This function takes as input an interpolating polynomial, expresses # it as a linear combination of the data values, and returns the coefficeints # of that form. @@ -547,8 +713,7 @@ end proc # Arguments: # interpolant = The interpolating polynomial (an algebraic expression # in the coordinates and the data values). -# posn_list = The same list of positions as was used to compute the -# interpolating polynomial. +# posn_list = The same list of data positions used in the interpolant. # # Results: # This function returns the coefficients, as a list of equations of the @@ -916,7 +1081,7 @@ data_var_name := proc(posn::list(numeric), name_prefix::string) end proc # Maple code to compute lists of point positions in hypercube-shaped molecules -# $Id: $ +# $Id: cube_posns.maple,v 1.1.1.1 2002/08/18 15:05:38 jthorn Exp $ > ################################################################################ > @@ -975,6 +1140,18 @@ posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], [1, 2], [2, 2]] +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + > ################################################################################ > @@ -1069,8 +1246,84 @@ posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + # Maple code to define Lagrange interpolating functions/coords/coeffs -# $Id: 1d.maple,v 1.4 2002/05/14 15:54:01 jthorn Exp $ +# $Id: fns.maple,v 1.1 2002/08/18 15:12:13 jthorn Exp $ > ################################################################################ > @@ -1338,12 +1591,12 @@ end proc > end; fn_3d_order4 := proc(x, y, z) c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z - + c112*x*y*z^2 + c010*y + c000 + c100*x + c001*z + c020*y^2 + c110*x*y - + c011*y*z + c101*x*z + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 - + c003*z^3 + c040*y^4 + c400*x^4 + c004*z^4 + c120*x*y^2 + c210*x^2*y - + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 + c310*x^3*y - + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 + c013*y*z^3 - + c103*x*z^3 + + c112*x*y*z^2 + c010*y + c000 + c100*x + c001*z + c110*x*y + c011*y*z + + c101*x*z + c120*x*y^2 + c210*x^2*y + c021*y^2*z + c201*x^2*z + + c130*x*y^3 + c220*x^2*y^2 + c310*x^3*y + c031*y^3*z + c301*x^3*z + + c022*y^2*z^2 + c202*x^2*z^2 + c013*y*z^3 + c103*x*z^3 + c020*y^2 + + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 + + c400*x^4 + c004*z^4 end proc > @@ -1437,7 +1690,7 @@ coeff_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, > ################################################################################ # 2d.maple -- compute Lagrange interpolation coefficients in 2-D -# $Id: $ +# $Id: 2d.maple,v 1.1 2002/08/18 15:12:03 jthorn Exp $ > ################################################################################ > @@ -1466,7 +1719,7 @@ interp_2d_cube_order1_smooth0 := > print_coeff__lc_of_data(%, "coeff_I_", "fp", > "2d.coeffs/2d.cube.order1.smooth0/coeff-I.compute.c"); -bytes used=1000160, alloc=917336, time=0.07 +bytes used=1002060, alloc=917336, time=0.10 > # d/dx > simplify( diff(interp_2d_cube_order1_smooth0,x) ); @@ -1483,11 +1736,11 @@ bytes used=1000160, alloc=917336, time=0.07 1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1) > coeff_as_lc_of_data(%, posn_list_2d_size2); +bytes used=2002752, alloc=1376004, time=0.18 [COEFF(0, 0) = -1/2, COEFF(1, 0) = -1/2, COEFF(0, 1) = 1/2, COEFF(1, 1) = 1/2] > print_coeff__lc_of_data(%, "coeff_dy_", "fp", > "2d.coeffs/2d.cube.order1.smooth0/coeff-dy.compute.c"); -bytes used=2000328, alloc=1376004, time=0.15 > ################################################################################ > @@ -1499,136 +1752,134 @@ bytes used=2000328, alloc=1376004, time=0.15 > interp_2d_cube_order2_smooth0 > := Lagrange_polynomial_interpolant(fn_2d_order2, coeff_list_2d_order2, > coord_list_2d, posn_list_2d_size3); -interp_2d_cube_order2_smooth0 := (1/6 DATA(0, -1) + 1/6 DATA(-1, -1) +interp_2d_cube_order2_smooth0 := (- 1/3 DATA(1, 0) + 1/6 DATA(-1, 1) - - 1/3 DATA(-1, 0) - 1/3 DATA(1, 0) + 1/6 DATA(1, -1) + 1/6 DATA(-1, 1) + + 1/6 DATA(0, 1) + 1/6 DATA(0, -1) - 1/3 DATA(-1, 0) - 1/3 DATA(0, 0) - 2 - + 1/6 DATA(1, 1) - 1/3 DATA(0, 0) + 1/6 DATA(0, 1)) y + (1/6 DATA(-1, 1) - - - 1/6 DATA(1, -1) - 1/6 DATA(0, -1) - 1/6 DATA(-1, -1) + 1/6 DATA(0, 1) + 2 + + 1/6 DATA(1, 1) + 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) y + ( - + 1/6 DATA(1, 1)) y + + - 1/6 DATA(-1, -1) + 1/6 DATA(-1, 1) + 1/6 DATA(0, 1) + 1/6 DATA(1, 1) - (1/4 DATA(1, 1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, -1) - 1/4 DATA(-1, 1)) x y + - 1/6 DATA(0, -1) - 1/6 DATA(1, -1)) y + - + 2/9 DATA(0, -1) - 1/9 DATA(-1, -1) + 2/9 DATA(-1, 0) + 2/9 DATA(1, 0) + (- 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/4 DATA(1, 1) + 1/4 DATA(-1, -1)) x - - 1/9 DATA(1, -1) - 1/9 DATA(-1, 1) - 1/9 DATA(1, 1) + 5/9 DATA(0, 0) + y + 2/9 DATA(1, 0) - 1/9 DATA(-1, 1) + 2/9 DATA(0, 1) + 2/9 DATA(0, -1) - + 2/9 DATA(0, 1) + (- 1/6 DATA(-1, -1) - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + + 2/9 DATA(-1, 0) + 5/9 DATA(0, 0) - 1/9 DATA(1, 1) - 1/9 DATA(-1, -1) - + 1/6 DATA(1, -1) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1)) x + ( + - 1/9 DATA(1, -1) + (- 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) - 1/6 DATA(-1, 1) - 1/6 DATA(-1, -1) + 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + 1/6 DATA(1, -1) + + 1/6 DATA(1, 1) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) x + (1/6 DATA(1, 0) - - 1/3 DATA(0, -1) + 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) - 1/3 DATA(0, 0) + + 1/6 DATA(-1, 1) - 1/3 DATA(0, 1) - 1/3 DATA(0, -1) + 1/6 DATA(-1, 0) - 2 - - 1/3 DATA(0, 1)) x + 2 + - 1/3 DATA(0, 0) + 1/6 DATA(1, 1) + 1/6 DATA(-1, -1) + 1/6 DATA(1, -1)) x > # I > coeff_as_lc_of_data(%, posn_list_2d_size3); - 2 2 -[COEFF(-1, -1) = - 1/6 y + 1/6 y - 1/9 - 1/6 x + 1/4 x y + 1/6 x , + 2 2 +[COEFF(-1, -1) = 1/4 x y + 1/6 y - 1/6 y - 1/6 x - 1/9 + 1/6 x , - 2 2 - COEFF(0, -1) = - 1/6 y + 2/9 + 1/6 y - 1/3 x , + 2 2 + COEFF(0, -1) = - 1/6 y - 1/3 x + 1/6 y + 2/9, - 2 2 - COEFF(1, -1) = - 1/6 y - 1/4 x y + 1/6 x + 1/6 y - 1/9 + 1/6 x , + 2 2 + COEFF(1, -1) = - 1/6 y - 1/9 - 1/4 x y + 1/6 x + 1/6 y + 1/6 x, - 2 2 - COEFF(-1, 0) = - 1/3 y + 2/9 + 1/6 x - 1/6 x, + 2 2 + COEFF(-1, 0) = - 1/3 y + 1/6 x - 1/6 x + 2/9, - 2 2 - COEFF(0, 0) = - 1/3 y - 1/3 x + 5/9, + 2 2 + COEFF(0, 0) = - 1/3 y + 5/9 - 1/3 x , - 2 2 - COEFF(1, 0) = 2/9 - 1/3 y + 1/6 x + 1/6 x, + 2 2 + COEFF(1, 0) = 2/9 - 1/3 y + 1/6 x + 1/6 x , 2 2 - COEFF(-1, 1) = 1/6 y + 1/6 y + 1/6 x - 1/4 x y - 1/6 x - 1/9, + COEFF(-1, 1) = 1/6 y - 1/6 x + 1/6 x + 1/6 y - 1/4 x y - 1/9, - 2 2 - COEFF(0, 1) = 1/6 y - 1/3 x + 2/9 + 1/6 y , + 2 2 + COEFF(0, 1) = 1/6 y + 1/6 y - 1/3 x + 2/9, - 2 2 - COEFF(1, 1) = 1/6 y + 1/6 y + 1/6 x - 1/9 + 1/4 x y + 1/6 x] + 2 2 + COEFF(1, 1) = 1/6 y - 1/9 + 1/6 y + 1/6 x + 1/6 x + 1/4 x y] > print_coeff__lc_of_data(%, "coeff_I_", "fp", > "2d.coeffs/2d.cube.order2.smooth0/coeff-I.compute.c"); -bytes used=3000520, alloc=1769148, time=0.22 -bytes used=4002236, alloc=1834672, time=0.30 +bytes used=3002924, alloc=1769148, time=0.25 +bytes used=4003132, alloc=1834672, time=0.32 > # d/dx > simplify( diff(interp_2d_cube_order2_smooth0,x) ); -1/4 y DATA(1, 1) - 1/4 y DATA(1, -1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(-1, 1) +- 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + 1/4 y DATA(1, 1) + 1/4 y DATA(-1, -1) - - 1/6 DATA(-1, -1) - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) + 1/6 DATA(1, -1) + - 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) - - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) + 1/3 x DATA(-1, -1) + - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) + 1/3 x DATA(1, 0) - + 1/3 x DATA(-1, 0) + 1/3 x DATA(1, 0) + 1/3 x DATA(1, -1) + + 1/3 x DATA(-1, 1) - 2/3 x DATA(0, 1) - 2/3 x DATA(0, -1) - - 2/3 x DATA(0, -1) + 1/3 x DATA(-1, 1) + 1/3 x DATA(1, 1) + + 1/3 x DATA(-1, 0) - 2/3 x DATA(0, 0) + 1/3 x DATA(1, 1) - - 2/3 x DATA(0, 0) - 2/3 x DATA(0, 1) + + 1/3 x DATA(-1, -1) + 1/3 x DATA(1, -1) > coeff_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/4 y - 1/6 + 1/3 x, COEFF(0, -1) = - 2/3 x, +[COEFF(-1, -1) = - 1/6 + 1/4 y + 1/3 x, COEFF(0, -1) = - 2/3 x, - COEFF(1, -1) = 1/6 + 1/3 x - 1/4 y, COEFF(-1, 0) = - 1/6 + 1/3 x, + COEFF(1, -1) = 1/6 - 1/4 y + 1/3 x, COEFF(-1, 0) = - 1/6 + 1/3 x, COEFF(0, 0) = - 2/3 x, COEFF(1, 0) = 1/6 + 1/3 x, - COEFF(-1, 1) = - 1/4 y - 1/6 + 1/3 x, COEFF(0, 1) = - 2/3 x, + COEFF(-1, 1) = - 1/4 y + 1/3 x - 1/6, COEFF(0, 1) = - 2/3 x, COEFF(1, 1) = 1/4 y + 1/3 x + 1/6] > print_coeff__lc_of_data(%, "coeff_dx_", "fp", > "2d.coeffs/2d.cube.order2.smooth0/coeff-dx.compute.c"); -bytes used=5002436, alloc=1834672, time=0.38 +bytes used=5003368, alloc=1834672, time=0.41 > # d/dy > simplify( diff(interp_2d_cube_order2_smooth0,y) ); -1/3 y DATA(0, -1) + 1/3 y DATA(-1, -1) - 2/3 y DATA(-1, 0) - 2/3 y DATA(1, 0) +- 2/3 y DATA(1, 0) + 1/3 y DATA(-1, 1) + 1/3 y DATA(0, 1) + 1/3 y DATA(0, -1) - + 1/3 y DATA(1, -1) + 1/3 y DATA(-1, 1) + 1/3 y DATA(1, 1) + - 2/3 y DATA(-1, 0) - 2/3 y DATA(0, 0) + 1/3 y DATA(1, 1) - - 2/3 y DATA(0, 0) + 1/3 y DATA(0, 1) + 1/6 DATA(-1, 1) - 1/6 DATA(1, -1) + + 1/3 y DATA(-1, -1) + 1/3 y DATA(1, -1) - 1/6 DATA(-1, -1) - - 1/6 DATA(0, -1) - 1/6 DATA(-1, -1) + 1/6 DATA(0, 1) + 1/6 DATA(1, 1) + + 1/6 DATA(-1, 1) + 1/6 DATA(0, 1) + 1/6 DATA(1, 1) - 1/6 DATA(0, -1) - + 1/4 x DATA(1, 1) - 1/4 x DATA(1, -1) + 1/4 x DATA(-1, -1) + - 1/6 DATA(1, -1) - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) - - 1/4 x DATA(-1, 1) + + 1/4 x DATA(1, 1) + 1/4 x DATA(-1, -1) > coeff_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = - 1/6 + 1/4 x + 1/3 y, COEFF(0, -1) = 1/3 y - 1/6, +[COEFF(-1, -1) = 1/3 y - 1/6 + 1/4 x, COEFF(0, -1) = - 1/6 + 1/3 y, - COEFF(1, -1) = 1/3 y - 1/6 - 1/4 x, COEFF(-1, 0) = - 2/3 y, + COEFF(1, -1) = - 1/4 x + 1/3 y - 1/6, COEFF(-1, 0) = - 2/3 y, COEFF(0, 0) = - 2/3 y, COEFF(1, 0) = - 2/3 y, - COEFF(-1, 1) = 1/3 y - 1/4 x + 1/6, COEFF(0, 1) = 1/6 + 1/3 y, + COEFF(-1, 1) = 1/3 y + 1/6 - 1/4 x, COEFF(0, 1) = 1/3 y + 1/6, - COEFF(1, 1) = 1/6 + 1/3 y + 1/4 x] + COEFF(1, 1) = 1/6 + 1/4 x + 1/3 y] > print_coeff__lc_of_data(%, "coeff_dy_", "fp", > "2d.coeffs/2d.cube.order2.smooth0/coeff-dy.compute.c"); > # d^2/dx^2 > simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); -1/3 DATA(-1, -1) + 1/3 DATA(-1, 0) + 1/3 DATA(1, 0) + 1/3 DATA(1, -1) +bytes used=6003876, alloc=1834672, time=0.51 +1/3 DATA(1, 0) + 1/3 DATA(-1, 1) - 2/3 DATA(0, 1) - 2/3 DATA(0, -1) - - 2/3 DATA(0, -1) + 1/3 DATA(-1, 1) + 1/3 DATA(1, 1) - 2/3 DATA(0, 0) + + 1/3 DATA(-1, 0) - 2/3 DATA(0, 0) + 1/3 DATA(1, 1) + 1/3 DATA(-1, -1) - - 2/3 DATA(0, 1) + + 1/3 DATA(1, -1) > coeff_as_lc_of_data(%, posn_list_2d_size3); -bytes used=6002660, alloc=1834672, time=0.47 [COEFF(-1, -1) = 1/3, COEFF(0, -1) = -2/3, COEFF(1, -1) = 1/3, COEFF(-1, 0) = 1/3, COEFF(0, 0) = -2/3, COEFF(1, 0) = 1/3, @@ -1640,7 +1891,7 @@ bytes used=6002660, alloc=1834672, time=0.47 > # d^2/dxdy > simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); - 1/4 DATA(1, 1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, -1) - 1/4 DATA(-1, 1) + - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/4 DATA(1, 1) + 1/4 DATA(-1, -1) > coeff_as_lc_of_data(%, posn_list_2d_size3); [COEFF(-1, -1) = 1/4, COEFF(0, -1) = 0, COEFF(1, -1) = -1/4, COEFF(-1, 0) = 0, @@ -1654,11 +1905,11 @@ bytes used=6002660, alloc=1834672, time=0.47 > # d^2/dy^2 > simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); -1/3 DATA(0, -1) + 1/3 DATA(-1, -1) - 2/3 DATA(-1, 0) - 2/3 DATA(1, 0) +- 2/3 DATA(1, 0) + 1/3 DATA(-1, 1) + 1/3 DATA(0, 1) + 1/3 DATA(0, -1) - + 1/3 DATA(1, -1) + 1/3 DATA(-1, 1) + 1/3 DATA(1, 1) - 2/3 DATA(0, 0) + - 2/3 DATA(-1, 0) - 2/3 DATA(0, 0) + 1/3 DATA(1, 1) + 1/3 DATA(-1, -1) - + 1/3 DATA(0, 1) + + 1/3 DATA(1, -1) > coeff_as_lc_of_data(%, posn_list_2d_size3); [COEFF(-1, -1) = 1/3, COEFF(0, -1) = 1/3, COEFF(1, -1) = 1/3, @@ -1669,6 +1920,7 @@ bytes used=6002660, alloc=1834672, time=0.47 > print_coeff__lc_of_data(%, "coeff_dyy_", "fp", > "2d.coeffs/2d.cube.order2.smooth0/coeff-dyy.compute.c"); +bytes used=7005040, alloc=1834672, time=0.58 > ################################################################################ > @@ -1680,828 +1932,832 @@ bytes used=6002660, alloc=1834672, time=0.47 > interp_2d_cube_order3_smooth0 > := Lagrange_polynomial_interpolant(fn_2d_order3, coeff_list_2d_order3, > coord_list_2d, posn_list_2d_size4); -bytes used=7003016, alloc=1834672, time=0.54 -bytes used=8003280, alloc=1900196, time=0.60 -bytes used=9003556, alloc=1965720, time=0.67 -bytes used=10003800, alloc=1965720, time=0.74 -bytes used=11003984, alloc=1965720, time=0.80 -interp_2d_cube_order3_smooth0 := (1/40 DATA(0, 0) - 1/40 DATA(1, 0) +bytes used=8005308, alloc=1900196, time=0.64 +bytes used=9005464, alloc=1900196, time=0.71 +bytes used=10006780, alloc=1965720, time=0.77 +bytes used=11007312, alloc=1965720, time=0.84 + / +interp_2d_cube_order3_smooth0 := |- 1/25 DATA(0, 0) - 1/100 DATA(1, 0) + \ + + - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) + 2/25 DATA(2, 1) + 7/100 DATA(2, 0) - + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) + 3/40 DATA(-1, 0) + 1/40 DATA(1, -1) + - 9/100 DATA(2, -1) - 3/50 DATA(2, 2) + 2/25 DATA(1, 2) + 7/100 DATA(0, 2) - - 1/40 DATA(0, -1) - 3/40 DATA(-1, -1) + 3/40 DATA(-1, 1) + 13 + - 9/100 DATA(-1, 2) - 1/50 DATA(-1, 0) - --- DATA(-1, 1) + 100 + + 13 \ + + 6/25 DATA(-1, -1) - 1/50 DATA(0, -1) - --- DATA(1, -1)| x y + ( + 100 / - + 1/40 DATA(1, 2) + 3/40 DATA(2, 2) - 3/40 DATA(2, 0) - 3/40 DATA(2, 1) + 1/40 DATA(0, 0) + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 2 / - - 3/40 DATA(-1, 2) - 1/40 DATA(0, 2) + 3/40 DATA(2, -1)) x y + | - \ + + 1/40 DATA(2, 1) - 1/40 DATA(2, 0) - 3/40 DATA(2, -1) + 3/40 DATA(2, 2) - - 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) + - 3/40 DATA(1, 2) - 3/40 DATA(0, 2) + 3/40 DATA(-1, 2) - 1/40 DATA(-1, 0) - 13 - - 1/50 DATA(-1, 0) - --- DATA(1, -1) - 1/50 DATA(0, -1) - 100 + + 1/40 DATA(-1, 1) - 3/40 DATA(-1, -1) + 3/40 DATA(0, -1) - 13 - + 6/25 DATA(-1, -1) - --- DATA(-1, 1) + 2/25 DATA(1, 2) - 3/50 DATA(2, 2) - 100 + 2 + + 3/40 DATA(1, -1)) x y + (1/40 DATA(0, 0) - 1/40 DATA(1, 0) - + 7/100 DATA(2, 0) + 2/25 DATA(2, 1) - 9/100 DATA(-1, 2) + + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 3/40 DATA(2, 1) - 3/40 DATA(2, 0) - \ - + 7/100 DATA(0, 2) - 9/100 DATA(2, -1)| x y + (1/40 DATA(0, 0) - / + + 3/40 DATA(2, -1) + 3/40 DATA(2, 2) + 1/40 DATA(1, 2) - 1/40 DATA(0, 2) - + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 1/40 DATA(-1, 0) + - 3/40 DATA(-1, 2) + 3/40 DATA(-1, 0) + 3/40 DATA(-1, 1) - + 3/40 DATA(1, -1) + 3/40 DATA(0, -1) - 3/40 DATA(-1, -1) + 2 + - 3/40 DATA(-1, -1) - 1/40 DATA(0, -1) + 1/40 DATA(1, -1)) x y - + 1/40 DATA(-1, 1) - 3/40 DATA(1, 2) + 3/40 DATA(2, 2) - 1/40 DATA(2, 0) + 93 37 37 17 + + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) - --- DATA(1, 1) + 200 200 200 200 - + 1/40 DATA(2, 1) + 3/40 DATA(-1, 2) - 3/40 DATA(0, 2) - 3/40 DATA(2, -1)) + 13 17 + - 2/25 DATA(2, 1) + --- DATA(2, 0) - --- DATA(2, -1) + 7/200 DATA(2, 2) + 100 200 - 2 93 37 37 17 - x y + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) - --- DATA(1, 1) - 200 200 200 200 + 13 17 11 + - 2/25 DATA(1, 2) + --- DATA(0, 2) - --- DATA(-1, 2) + -- DATA(-1, 0) + 100 200 50 - 11 11 23 - + -- DATA(-1, 0) - 1/50 DATA(1, -1) + -- DATA(0, -1) - --- DATA(-1, -1) - 50 50 200 + 23 11 + - 1/50 DATA(-1, 1) - --- DATA(-1, -1) + -- DATA(0, -1) - 1/50 DATA(1, -1) + 200 50 - - 1/50 DATA(-1, 1) + (1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1) + + (1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1) - 1/8 DATA(1, 1) - - 1/8 DATA(1, 1) + 1/8 DATA(-1, 0) - 1/24 DATA(1, -1) - 1/24 DATA(0, -1) + - 1/8 DATA(2, 1) + 1/8 DATA(2, 0) - 1/24 DATA(2, -1) + 1/24 DATA(2, 2) - - 1/24 DATA(-1, -1) - 1/8 DATA(-1, 1) + 1/24 DATA(1, 2) + 1/24 DATA(2, 2) + + 1/24 DATA(1, 2) + 1/24 DATA(0, 2) + 1/24 DATA(-1, 2) + 1/8 DATA(-1, 0) - + 1/8 DATA(2, 0) - 1/8 DATA(2, 1) + 1/24 DATA(-1, 2) + 1/24 DATA(0, 2) + - 1/8 DATA(-1, 1) - 1/24 DATA(-1, -1) - 1/24 DATA(0, -1) 3 / 21 19 - - 1/24 DATA(2, -1)) y + |- -- DATA(0, 0) - -- DATA(1, 0) + - 1/24 DATA(1, -1)) y + |- -- DATA(0, 0) - -- DATA(1, 0) \ 80 80 - 11 23 - + 9/80 DATA(0, 1) + -- DATA(1, 1) - -- DATA(-1, 0) + 9/80 DATA(1, -1) - 80 80 + 11 13 17 + + 9/80 DATA(0, 1) + -- DATA(1, 1) + -- DATA(2, 1) - -- DATA(2, 0) + 80 80 80 - 11 13 - + -- DATA(0, -1) + -- DATA(-1, -1) + 7/80 DATA(-1, 1) - 1/80 DATA(1, 2) - 80 80 + + 7/80 DATA(2, -1) - 3/80 DATA(2, 2) - 1/80 DATA(1, 2) + 1/80 DATA(0, 2) - 17 13 - - 3/80 DATA(2, 2) - -- DATA(2, 0) + -- DATA(2, 1) + 3/80 DATA(-1, 2) - 80 80 + 23 13 + + 3/80 DATA(-1, 2) - -- DATA(-1, 0) + 7/80 DATA(-1, 1) + -- DATA(-1, -1) + 80 80 - \ 2 / 57 - + 1/80 DATA(0, 2) + 7/80 DATA(2, -1)| y + |- --- DATA(0, 0) - / \ 400 + 11 \ 2 / 57 + + -- DATA(0, -1) + 9/80 DATA(1, -1)| y + |- --- DATA(0, 0) + 80 / \ 400 - 63 117 103 31 - - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - --- DATA(-1, 0) + 63 117 103 69 + - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(2, 1) 400 400 400 400 - 157 223 109 - - ---- DATA(1, -1) - ---- DATA(0, -1) - ---- DATA(-1, -1) - 1200 1200 1200 + 49 89 149 37 + - --- DATA(2, 0) + ---- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2) + 400 1200 1200 1200 - 111 37 149 49 - + --- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - --- DATA(2, 0) - 400 1200 1200 400 + 43 131 31 111 + + ---- DATA(0, 2) - ---- DATA(-1, 2) - --- DATA(-1, 0) + --- DATA(-1, 1) + 1200 1200 400 400 - 69 131 43 89 \ - + --- DATA(2, 1) - ---- DATA(-1, 2) + ---- DATA(0, 2) + ---- DATA(2, -1)| - 400 1200 1200 1200 / + 109 223 157 \ / + - ---- DATA(-1, -1) - ---- DATA(0, -1) - ---- DATA(1, -1)| y + | + 1200 1200 1200 / \ - / 57 117 63 103 - y + |- --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) - \ 400 400 400 400 + 57 117 63 103 + - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 400 400 400 400 - 223 111 31 109 - - ---- DATA(-1, 0) + --- DATA(1, -1) - --- DATA(0, -1) - ---- DATA(-1, -1) - 1200 400 400 1200 + 37 43 131 149 + + ---- DATA(2, 1) + ---- DATA(2, 0) - ---- DATA(2, -1) - ---- DATA(2, 2) + 1200 1200 1200 1200 - 157 69 149 43 - - ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2) + ---- DATA(2, 0) - 1200 400 1200 1200 + 69 49 89 223 + + --- DATA(1, 2) - --- DATA(0, 2) + ---- DATA(-1, 2) - ---- DATA(-1, 0) + 400 400 1200 1200 - 37 89 49 131 \ - + ---- DATA(2, 1) + ---- DATA(-1, 2) - --- DATA(0, 2) - ---- DATA(2, -1)| - 1200 1200 400 1200 / + 157 109 31 111 + - ---- DATA(-1, 1) - ---- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1) + 1200 1200 400 400 - / 21 19 11 - x + |- -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1) - \ 80 80 80 + \ / 21 19 11 + | x + |- -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1) + / \ 80 80 80 - 11 23 13 - + -- DATA(-1, 0) + 7/80 DATA(1, -1) - -- DATA(0, -1) + -- DATA(-1, -1) - 80 80 80 + - 1/80 DATA(2, 1) + 1/80 DATA(2, 0) + 3/80 DATA(2, -1) - 3/80 DATA(2, 2) - 13 - + 9/80 DATA(-1, 1) + -- DATA(1, 2) - 3/80 DATA(2, 2) + 1/80 DATA(2, 0) - 80 + 13 17 11 + + -- DATA(1, 2) - -- DATA(0, 2) + 7/80 DATA(-1, 2) + -- DATA(-1, 0) + 80 80 80 - 17 \ - - 1/80 DATA(2, 1) + 7/80 DATA(-1, 2) - -- DATA(0, 2) + 3/80 DATA(2, -1)| - 80 / + 13 23 \ + + 9/80 DATA(-1, 1) + -- DATA(-1, -1) - -- DATA(0, -1) + 7/80 DATA(1, -1)| + 80 80 / 2 x + (1/8 DATA(0, 0) - 1/8 DATA(1, 0) + 1/8 DATA(0, 1) - 1/8 DATA(1, 1) - - 1/24 DATA(-1, 0) - 1/8 DATA(1, -1) + 1/8 DATA(0, -1) - 1/24 DATA(-1, -1) + + 1/24 DATA(2, 1) + 1/24 DATA(2, 0) + 1/24 DATA(2, -1) + 1/24 DATA(2, 2) - - 1/24 DATA(-1, 1) + 1/24 DATA(2, 1) - 1/8 DATA(1, 2) + 1/24 DATA(2, 2) + - 1/8 DATA(1, 2) + 1/8 DATA(0, 2) - 1/24 DATA(-1, 2) - 1/24 DATA(-1, 0) - + 1/24 DATA(2, 0) - 1/24 DATA(-1, 2) + 1/8 DATA(0, 2) + 1/24 DATA(2, -1)) + - 1/24 DATA(-1, 1) - 1/24 DATA(-1, -1) + 1/8 DATA(0, -1) - 1/8 DATA(1, -1) - 3 13 - x - 2/25 DATA(1, 2) + 7/200 DATA(2, 2) + --- DATA(2, 0) - 2/25 DATA(2, 1) - 100 - - 17 13 17 - - --- DATA(-1, 2) + --- DATA(0, 2) - --- DATA(2, -1) - 200 100 200 + 3 + ) x > # I > coeff_as_lc_of_data(%, posn_list_2d_size4); -bytes used=12006624, alloc=1965720, time=0.86 - 13 2 3 2 3 13 2 -[COEFF(-1, -1) = -- y - 1/24 y - 3/40 x y - 1/24 x + 6/25 x y + -- x - 80 80 +bytes used=12010552, alloc=1965720, time=0.91 + 2 13 2 3 109 3 23 13 2 +[COEFF(-1, -1) = - 3/40 x y + -- x - 1/24 x - ---- x - 1/24 y - --- + -- y + 80 1200 200 80 - 2 109 23 109 2 3 - - 3/40 x y - ---- x - --- - ---- y, COEFF(0, -1) = - 1/40 x y + 1/8 x - 1200 200 1200 + 2 109 2 + - 3/40 x y - ---- y + 6/25 x y, COEFF(0, -1) = - 1/50 x y + 3/40 x y + 1200 - 2 23 2 11 3 31 11 2 223 - - 1/50 x y + 3/40 x y - -- x + -- - 1/24 y - --- x + -- y - ---- y, - 80 50 400 80 1200 + 11 23 2 223 3 2 31 11 2 3 + + -- - -- x - ---- y + 1/8 x - 1/40 x y - --- x + -- y - 1/24 y , + 50 80 1200 400 80 - 2 2 2 3 111 - COEFF(1, -1) = 9/80 y + 3/40 x y + 1/40 x y - 1/24 y - 1/50 + --- x - 400 + 2 2 111 157 13 3 + COEFF(1, -1) = 9/80 y + 3/40 x y + --- x - ---- y - --- x y - 1/24 y + 400 1200 100 - 157 2 13 3 - - ---- y + 7/80 x - --- x y - 1/8 x , COEFF(2, -1) = - 9/100 x y - 1200 100 + 2 2 3 2 2 + + 1/40 x y + 7/80 x - 1/50 - 1/8 x , COEFF(2, -1) = 7/80 y + 3/40 x y - 2 2 3 89 17 2 3 - + 3/40 x y + 7/80 y - 1/24 y + ---- y - --- - 3/40 x y + 1/24 x - 1200 200 + 2 3 17 3 89 131 + - 3/40 x y - 1/24 y - --- + 1/24 x + ---- y - ---- x - 9/100 x y + 200 1200 1200 - 131 2 11 31 2 - - ---- x + 3/80 x , COEFF(-1, 0) = -- - 1/50 x y - --- y + 3/40 x y - 1200 50 400 + 2 2 11 2 23 2 223 2 + + 3/80 x , COEFF(-1, 0) = 3/40 x y + -- x - -- y - ---- x - 1/40 x y + 80 80 1200 - 223 3 23 2 2 11 2 3 - - ---- x - 1/24 x - -- y - 1/40 x y + -- x + 1/8 y , COEFF(0, 0) = - 1200 80 80 + 3 11 3 31 2 + - 1/50 x y + 1/8 y + -- - 1/24 x - --- y, COEFF(0, 0) = 1/40 x y + 50 400 - 21 2 21 2 3 3 57 57 2 - - 1/25 x y - -- y - -- x + 1/8 x + 1/8 y - --- x - --- y + 1/40 x y - 80 80 400 400 + 2 21 2 3 21 2 3 57 93 + + 1/40 x y - -- y + 1/8 x - -- x + 1/8 y - 1/25 x y - --- x + --- + 80 80 400 200 - 2 93 19 2 63 2 - + 1/40 x y + ---, COEFF(1, 0) = - -- y - --- y - 1/40 x y - 1/100 x y - 200 80 400 + 57 2 37 2 117 + - --- y, COEFF(1, 0) = - 1/40 x y + --- - 1/100 x y + 9/80 x + --- x + 400 200 400 - 3 2 117 37 3 2 - + 1/8 y + 9/80 x + --- x + --- - 1/8 x + 1/40 x y, COEFF(2, 0) = - 400 200 + 3 3 19 2 2 63 + + 1/8 y - 1/8 x - -- y + 1/40 x y - --- y, COEFF(2, 0) = 7/100 x y + 80 400 - 17 2 2 49 3 2 3 2 - - -- y + 1/80 x - --- y + 1/8 y - 1/40 x y + 1/24 x - 3/40 x y - 80 400 + 2 3 43 2 2 3 13 + - 3/40 x y + 1/24 x + ---- x - 1/40 x y + 1/80 x + 1/8 y + --- + 1200 100 - 13 43 2 157 - + 7/100 x y + --- + ---- x, COEFF(-1, 1) = 1/40 x y - 1/50 - ---- x - 100 1200 1200 + 49 17 2 2 13 2 + - --- y - -- y , COEFF(-1, 1) = 9/80 x - --- x y - 1/50 + 3/40 x y + 400 80 100 - 111 3 3 2 13 2 2 - + --- y - 1/24 x - 1/8 y + 3/40 x y - --- x y + 7/80 y + 9/80 x , - 400 100 + 3 157 3 2 111 2 + - 1/8 y - ---- x - 1/24 x + 7/80 y + --- y + 1/40 x y, COEFF(0, 1) = + 1200 400 - 2 37 3 63 19 2 3 - COEFF(0, 1) = - 1/40 x y + --- + 1/8 x - --- x - -- x - 1/8 y - 200 400 80 + 19 2 3 3 2 63 2 + - 1/100 x y - -- x - 1/8 y + 1/8 x + 9/80 y - --- x - 1/40 x y + 80 400 - 2 117 2 103 2 - + 1/40 x y + --- y + 9/80 y - 1/100 x y, COEFF(1, 1) = --- y - 1/40 x y - 400 400 + 2 117 37 2 + + 1/40 x y + --- y + ---, COEFF(1, 1) = - 1/40 x y + 3/50 x y + 400 200 - 11 2 11 2 103 3 2 17 3 - + -- x + -- y + 3/50 x y + --- x - 1/8 x - 1/40 x y - --- - 1/8 y , - 80 80 400 200 + 2 17 103 11 2 3 11 2 103 3 + - 1/40 x y - --- + --- x + -- x - 1/8 y + -- y + --- y - 1/8 x , + 200 400 80 80 400 - 3 2 2 37 3 2 - COEFF(2, 1) = - 1/8 y + 1/40 x y - 3/40 x y + ---- x + 1/24 x - 1/80 x - 1200 + 2 69 13 2 3 3 2 + COEFF(2, 1) = 1/40 x y + --- y + -- y + 1/24 x - 1/8 y - 1/80 x + 400 80 - 13 2 69 2 89 - - 2/25 + -- y + --- y + 2/25 x y, COEFF(-1, 2) = 3/80 y + ---- x - 80 400 1200 + 2 37 2 2 + + 2/25 x y - 3/40 x y + ---- x - 2/25, COEFF(-1, 2) = 7/80 x + 3/40 x y + 1200 - 2 131 2 2 3 3 - + 3/40 x y - ---- y - 3/40 x y + 7/80 x + 1/24 y - 9/100 x y - 1/24 x - 1200 + 131 89 3 17 3 2 + - ---- y + ---- x + 1/24 y - --- - 9/100 x y - 1/24 x + 3/80 y + 1200 1200 200 - 17 49 3 43 2 2 - - ---, COEFF(0, 2) = - --- x + 1/24 y + ---- y - 3/40 x y + 1/80 y - 200 400 1200 + 2 2 3 3 43 + - 3/40 x y , COEFF(0, 2) = 1/80 y + 1/8 x + 7/100 x y + 1/24 y + ---- y + 1200 - 17 2 2 13 3 69 - - -- x - 1/40 x y + --- + 7/100 x y + 1/8 x , COEFF(1, 2) = --- x - 80 100 400 + 49 17 2 13 2 2 2 + - --- x - -- x + --- - 3/40 x y - 1/40 x y , COEFF(1, 2) = - 3/40 x y + 400 80 100 - 2 2 2 37 3 13 2 - - 3/40 x y - 1/80 y + 1/40 x y + ---- y - 2/25 + 1/24 y + -- x - 1200 80 + 37 13 2 2 3 3 69 + + ---- y + -- x - 1/80 y + 2/25 x y - 1/8 x + 1/24 y - 2/25 + --- x + 1200 80 400 - 3 2 3 3 2 - + 2/25 x y - 1/8 x , COEFF(2, 2) = 3/40 x y + 1/24 x + 1/24 y - 3/80 x + 2 149 2 2 3 + + 1/40 x y , COEFF(2, 2) = - ---- y + 3/40 x y + 3/40 x y + 1/24 y + 1200 - 149 149 2 2 - - 3/50 x y - ---- y - ---- x + 3/40 x y - 3/80 y + 7/200] - 1200 1200 + 149 2 2 3 + - ---- x - 3/50 x y - 3/80 x - 3/80 y + 1/24 x + 7/200] + 1200 > print_coeff__lc_of_data(%, "coeff_I_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-I.compute.c"); -bytes used=13006948, alloc=2031244, time=0.93 -bytes used=14011252, alloc=2031244, time=1.01 -bytes used=15011472, alloc=2031244, time=1.11 -bytes used=16011652, alloc=2031244, time=1.19 -bytes used=17011812, alloc=2031244, time=1.29 -bytes used=18012000, alloc=2031244, time=1.39 -bytes used=19012216, alloc=2031244, time=1.50 -bytes used=20012436, alloc=2031244, time=1.62 +bytes used=13010732, alloc=2031244, time=0.98 +bytes used=14014148, alloc=2031244, time=1.07 +bytes used=15014304, alloc=2031244, time=1.17 +bytes used=16014668, alloc=2031244, time=1.25 +bytes used=17019400, alloc=2031244, time=1.35 +bytes used=18019708, alloc=2031244, time=1.44 +bytes used=19019860, alloc=2031244, time=1.54 +bytes used=20020128, alloc=2031244, time=1.65 > # d/dx > simplify( diff(interp_2d_cube_order3_smooth0,x) ); -bytes used=21013024, alloc=2031244, time=1.73 -3/20 x y DATA(-1, 2) + 1/20 x y DATA(0, 0) + 1/20 x y DATA(1, 0) +bytes used=21023596, alloc=2031244, time=1.74 + 23 +- -- x DATA(0, -1) + 7/40 x DATA(1, -1) + 9/40 x DATA(-1, 1) + 40 - - 1/20 x y DATA(0, 1) - 1/20 x y DATA(1, 1) - 1/20 x y DATA(-1, 0) + 57 + + 3/20 x y DATA(1, -1) - 1/20 x y DATA(0, 1) - --- DATA(0, 0) + 400 - + 3/20 x y DATA(1, -1) + 3/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) + 117 63 103 + + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 1/20 x y DATA(2, 1) + 400 400 400 - 57 117 63 103 - - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) - 400 400 400 400 + - 1/20 x y DATA(2, 0) - 3/20 x y DATA(2, -1) + 3/20 x y DATA(2, 2) - 2 - + 1/20 x y DATA(-1, 1) - 3/20 x y DATA(1, 2) - 1/8 x DATA(-1, 2) + - 3/20 x y DATA(1, 2) - 3/20 x y DATA(0, 2) + 3/20 x y DATA(-1, 2) - 2 2 2 - + 3/8 x DATA(0, 2) + 1/8 x DATA(2, -1) + 1/8 x DATA(2, 1) + - 1/20 x y DATA(-1, 0) + 1/20 x y DATA(-1, 1) - 3/20 x y DATA(-1, -1) - 2 - + 1/8 x DATA(2, 0) - 3/20 x y DATA(2, -1) - 3/20 x y DATA(0, 2) + 37 43 + + 3/20 x y DATA(0, -1) + ---- DATA(2, 1) + ---- DATA(2, 0) + 1200 1200 - + 1/20 x y DATA(2, 1) - 1/20 x y DATA(2, 0) + 3/20 x y DATA(2, 2) + 131 149 69 49 + - ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2) - --- DATA(0, 2) + 1200 1200 400 400 - + 2/25 y DATA(2, 1) + 7/100 y DATA(2, 0) + 2/25 y DATA(1, 2) + 89 223 157 + + ---- DATA(-1, 2) - ---- DATA(-1, 0) - ---- DATA(-1, 1) + 1200 1200 1200 - - 9/100 y DATA(2, -1) + 7/100 y DATA(0, 2) - 9/100 y DATA(-1, 2) + 109 31 111 + - ---- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1) + 1200 400 400 - 13 - - 1/50 y DATA(0, -1) - --- y DATA(1, -1) - 1/50 y DATA(-1, 0) - 100 + - 1/20 x y DATA(1, 1) - 1/100 y DATA(0, 1) + 3/50 y DATA(1, 1) - 2 13 - - 3/50 y DATA(2, 2) + 3/40 y DATA(2, -1) - --- y DATA(-1, 1) - 100 + 13 + + -- x DATA(-1, -1) + 1/20 x y DATA(1, 0) + 2/25 y DATA(1, 2) + 40 - 2 - + 6/25 y DATA(-1, -1) + 1/40 y DATA(1, 2) - 1/100 y DATA(0, 1) + 2 2 + + 7/100 y DATA(0, 2) + 1/40 y DATA(0, 1) + 1/40 y DATA(0, 0) - - 1/100 y DATA(1, 0) - 1/25 y DATA(0, 0) + 3/50 y DATA(1, 1) + + 6/25 y DATA(-1, -1) - 1/50 y DATA(0, -1) + 1/20 x y DATA(0, 0) 2 2 2 - - 1/40 y DATA(0, 2) - 3/40 y DATA(2, 1) - 3/40 y DATA(2, 0) + - 1/40 y DATA(1, 0) - 1/40 y DATA(1, 1) - 3/40 y DATA(2, 1) - 2 2 2 - + 3/40 y DATA(2, 2) - 3/40 y DATA(-1, 2) + 3/40 y DATA(-1, 1) - - 2 2 2 - - 1/40 y DATA(0, -1) + 1/40 y DATA(1, -1) + 3/40 y DATA(-1, 0) + 2 2 2 + + 1/40 y DATA(1, 2) - 3/40 y DATA(2, 0) + 3/40 y DATA(2, -1) - 2 2 2 - - 3/40 y DATA(-1, -1) + 1/40 y DATA(0, 1) - 1/40 y DATA(1, 0) + 2 2 2 + + 3/40 y DATA(-1, 1) + 3/40 y DATA(2, 2) - 1/40 y DATA(0, 2) - 2 11 - + 1/40 y DATA(0, 0) + -- x DATA(-1, 0) + 9/40 x DATA(1, 0) - 40 + 2 2 19 + - 3/40 y DATA(-1, 2) - 3/40 y DATA(-1, -1) - -- x DATA(0, 1) + 40 - 19 2 21 13 - - -- x DATA(0, 1) - 1/40 y DATA(1, 1) - -- x DATA(0, 0) + -- x DATA(1, 2) - 40 40 40 + 2 2 2 + + 1/40 y DATA(1, -1) + 3/40 y DATA(-1, 0) - 1/40 y DATA(0, -1) - 23 13 11 - - -- x DATA(0, -1) + -- x DATA(-1, -1) + -- x DATA(1, 1) - 40 40 40 + 21 + - 1/40 x DATA(2, 1) - -- x DATA(0, 0) + 9/40 x DATA(1, 0) + 40 - + 7/40 x DATA(1, -1) + 9/40 x DATA(-1, 1) - 3/40 x DATA(2, 2) + + 1/40 x DATA(2, 0) + 3/40 x DATA(2, -1) - 3/40 x DATA(2, 2) - + 1/40 x DATA(2, 0) - 1/40 x DATA(2, 1) + 7/40 x DATA(-1, 2) + 11 13 17 + + -- x DATA(1, 1) + -- x DATA(1, 2) - -- x DATA(0, 2) + 7/40 x DATA(-1, 2) + 40 40 40 - 2 2 17 - - 3/8 x DATA(1, 0) + 3/8 x DATA(0, 1) - -- x DATA(0, 2) - 40 + 11 + + -- x DATA(-1, 0) - 1/25 y DATA(0, 0) - 1/100 y DATA(1, 0) + 40 - 2 2 - + 3/40 x DATA(2, -1) - 3/8 x DATA(1, -1) + 3/8 x DATA(0, -1) + 13 2 2 + - --- y DATA(1, -1) - 3/8 x DATA(1, 0) + 3/8 x DATA(0, 0) + 100 2 2 2 - + 3/8 x DATA(0, 0) - 3/8 x DATA(1, 1) - 1/8 x DATA(-1, 0) + + 1/8 x DATA(2, 1) + 1/8 x DATA(2, 0) + 1/8 x DATA(2, -1) - 2 2 2 - - 3/8 x DATA(1, 2) - 1/8 x DATA(-1, -1) - 1/8 x DATA(-1, 1) + 2 2 2 + + 1/8 x DATA(2, 2) - 1/8 x DATA(-1, 1) + 3/8 x DATA(0, 2) - 2 223 111 31 - + 1/8 x DATA(2, 2) - ---- DATA(-1, 0) + --- DATA(1, -1) - --- DATA(0, -1) - 1200 400 400 + 2 2 2 + + 3/8 x DATA(0, -1) - 1/8 x DATA(-1, 2) - 1/8 x DATA(-1, 0) - 109 157 69 149 - - ---- DATA(-1, -1) - ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2) - 1200 1200 400 1200 + 2 2 2 + - 3/8 x DATA(1, 2) + 3/8 x DATA(0, 1) - 3/8 x DATA(1, 1) - 43 37 89 49 - + ---- DATA(2, 0) + ---- DATA(2, 1) + ---- DATA(-1, 2) - --- DATA(0, 2) - 1200 1200 1200 400 + 2 2 + - 3/8 x DATA(1, -1) - 1/8 x DATA(-1, -1) + 7/100 y DATA(2, 0) - 131 - - ---- DATA(2, -1) - 1200 + - 9/100 y DATA(2, -1) - 3/50 y DATA(2, 2) - 9/100 y DATA(-1, 2) + + 13 + - 1/50 y DATA(-1, 0) - --- y DATA(-1, 1) + 2/25 y DATA(2, 1) + 100 > coeff_as_lc_of_data(%, posn_list_2d_size4); -bytes used=22015264, alloc=2031244, time=1.80 +bytes used=22023792, alloc=2031244, time=1.80 13 2 109 2 [COEFF(-1, -1) = -- x - 1/8 x - ---- + 6/25 y - 3/20 x y - 3/40 y , 40 1200 - 31 2 2 23 - COEFF(0, -1) = - --- + 3/8 x - 1/40 y - -- x - 1/50 y + 3/20 x y, - 400 40 + 31 23 2 2 + COEFF(0, -1) = - --- - 1/50 y - -- x - 1/40 y + 3/20 x y + 3/8 x , + 400 40 - 2 111 2 13 - COEFF(1, -1) = 3/20 x y + 1/40 y + 7/40 x + --- - 3/8 x - --- y, - 400 100 + 111 2 13 2 + COEFF(1, -1) = --- + 1/40 y - --- y + 7/40 x - 3/8 x + 3/20 x y, + 400 100 - 2 131 2 - COEFF(2, -1) = 1/8 x - 9/100 y - 3/20 x y - ---- + 3/40 y + 3/40 x, - 1200 + 2 131 2 + COEFF(2, -1) = - 9/100 y + 3/40 y - ---- - 3/20 x y + 3/40 x + 1/8 x , + 1200 - 223 2 11 2 - COEFF(-1, 0) = - ---- + 3/40 y - 1/20 x y - 1/50 y + -- x - 1/8 x , - 1200 40 + 2 2 11 223 + COEFF(-1, 0) = - 1/8 x + 3/40 y + -- x - 1/20 x y - ---- - 1/50 y, + 40 1200 - 57 21 2 2 - COEFF(0, 0) = - --- - -- x + 3/8 x - 1/25 y + 1/40 y + 1/20 x y, - 400 40 + 2 2 21 57 + COEFF(0, 0) = - 1/25 y + 1/20 x y + 1/40 y + 3/8 x - -- x - ---, + 40 400 - 117 2 2 - COEFF(1, 0) = 9/40 x + --- - 1/40 y - 1/100 y - 3/8 x + 1/20 x y, - 400 + 117 2 2 + COEFF(1, 0) = - 1/100 y + --- + 1/20 x y + 9/40 x - 1/40 y - 3/8 x , + 400 - 2 43 2 - COEFF(2, 0) = 1/8 x + ---- - 3/40 y + 1/40 x - 1/20 x y + 7/100 y, - 1200 + 2 43 2 + COEFF(2, 0) = 1/40 x - 1/20 x y - 3/40 y + ---- + 7/100 y + 1/8 x , + 1200 - 2 157 13 2 - COEFF(-1, 1) = 1/20 x y - 1/8 x + 9/40 x - ---- - --- y + 3/40 y , - 1200 100 + 157 2 2 13 + COEFF(-1, 1) = - ---- + 1/20 x y - 1/8 x + 3/40 y + 9/40 x - --- y, + 1200 100 - 63 2 19 2 - COEFF(0, 1) = - --- - 1/100 y + 3/8 x - 1/20 x y - -- x + 1/40 y , - 400 40 + 19 2 63 2 + COEFF(0, 1) = - -- x + 1/40 y - --- + 3/8 x - 1/20 x y - 1/100 y, + 40 400 - 11 2 2 103 - COEFF(1, 1) = - 1/20 x y + -- x - 1/40 y - 3/8 x + 3/50 y + ---, - 40 400 + 2 2 11 103 + COEFF(1, 1) = 3/50 y - 1/20 x y - 1/40 y - 3/8 x + -- x + ---, + 40 400 - 2 2 37 - COEFF(2, 1) = - 1/40 x + 1/20 x y + 1/8 x - 3/40 y + ---- + 2/25 y, + 2 2 37 + COEFF(2, 1) = - 3/40 y + 1/20 x y - 1/40 x + 1/8 x + ---- + 2/25 y, 1200 - 89 2 2 - COEFF(-1, 2) = - 9/100 y + 3/20 x y + ---- - 3/40 y + 7/40 x - 1/8 x , - 1200 + 89 2 2 + COEFF(-1, 2) = ---- + 7/40 x - 1/8 x - 9/100 y + 3/20 x y - 3/40 y , + 1200 - 2 2 17 49 - COEFF(0, 2) = - 1/40 y - 3/20 x y + 7/100 y + 3/8 x - -- x - ---, - 40 400 + 17 2 49 2 + COEFF(0, 2) = - -- x - 1/40 y + 7/100 y - --- - 3/20 x y + 3/8 x , + 40 400 - 2 13 69 2 - COEFF(1, 2) = - 3/8 x + -- x + --- - 3/20 x y + 2/25 y + 1/40 y , - 40 400 + 2 69 2 13 + COEFF(1, 2) = 2/25 y - 3/20 x y + 1/40 y + --- - 3/8 x + -- x, + 400 40 - 149 2 2 - COEFF(2, 2) = 3/20 x y - ---- + 1/8 x - 3/40 x + 3/40 y - 3/50 y] - 1200 + 2 2 149 + COEFF(2, 2) = 3/20 x y + 3/40 y + 1/8 x - ---- - 3/40 x - 3/50 y] + 1200 > print_coeff__lc_of_data(%, "coeff_dx_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-dx.compute.c"); -bytes used=23015460, alloc=2031244, time=1.87 -bytes used=24015620, alloc=2031244, time=1.96 -bytes used=25016144, alloc=2096768, time=2.07 -bytes used=26016296, alloc=2096768, time=2.18 +bytes used=23023968, alloc=2031244, time=1.87 +bytes used=24024120, alloc=2031244, time=1.95 +bytes used=25024508, alloc=2031244, time=2.05 +bytes used=26024664, alloc=2031244, time=2.20 > # d/dy > simplify( diff(interp_2d_cube_order3_smooth0,y) ); -bytes used=27016596, alloc=2096768, time=2.28 -- 3/20 x y DATA(-1, 2) + 1/20 x y DATA(0, 0) - 1/20 x y DATA(1, 0) +bytes used=27025556, alloc=2031244, time=2.28 + 13 13 +- 1/50 x DATA(0, -1) - --- x DATA(1, -1) - --- x DATA(-1, 1) + 100 100 - + 1/20 x y DATA(0, 1) - 1/20 x y DATA(1, 1) + 3/20 x y DATA(-1, 0) + 57 + + 1/20 x y DATA(1, -1) + 1/20 x y DATA(0, 1) - --- DATA(0, 0) + 400 - + 1/20 x y DATA(1, -1) - 1/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) + 63 117 103 + - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - 3/20 x y DATA(2, 1) + 400 400 400 - 57 63 117 103 - - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - 400 400 400 400 + - 3/20 x y DATA(2, 0) + 3/20 x y DATA(2, -1) + 3/20 x y DATA(2, 2) - 2 - + 3/20 x y DATA(-1, 1) + 1/20 x y DATA(1, 2) + 3/40 x DATA(-1, 2) + + 1/20 x y DATA(1, 2) - 1/20 x y DATA(0, 2) - 3/20 x y DATA(-1, 2) - 2 2 2 - - 3/40 x DATA(0, 2) - 3/40 x DATA(2, -1) + 1/40 x DATA(2, 1) + + 3/20 x y DATA(-1, 0) + 3/20 x y DATA(-1, 1) - 3/20 x y DATA(-1, -1) - 2 - - 1/40 x DATA(2, 0) + 3/20 x y DATA(2, -1) - 1/20 x y DATA(0, 2) + 69 49 + - 1/20 x y DATA(0, -1) + --- DATA(2, 1) - --- DATA(2, 0) + 400 400 - - 3/20 x y DATA(2, 1) - 3/20 x y DATA(2, 0) + 3/20 x y DATA(2, 2) + 89 149 37 43 + + ---- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(0, 2) + 1200 1200 1200 1200 - 13 17 - + -- y DATA(2, 1) - -- y DATA(2, 0) - 1/40 y DATA(1, 2) - 40 40 + 131 31 111 109 + - ---- DATA(-1, 2) - --- DATA(-1, 0) + --- DATA(-1, 1) - ---- DATA(-1, -1) + 1200 400 400 1200 - + 7/40 y DATA(2, -1) + 1/40 y DATA(0, 2) + 3/40 y DATA(-1, 2) + 223 157 + - ---- DATA(0, -1) - ---- DATA(1, -1) - 1/20 x y DATA(1, 1) + 1200 1200 - 11 23 - + -- y DATA(0, -1) + 9/40 y DATA(1, -1) - -- y DATA(-1, 0) - 40 40 + 11 + + 9/40 y DATA(0, 1) + -- y DATA(1, 1) + 6/25 x DATA(-1, -1) + 40 - 2 - - 3/40 y DATA(2, 2) - 1/8 y DATA(2, -1) + 7/40 y DATA(-1, 1) + - 1/20 x y DATA(1, 0) - 1/40 y DATA(1, 2) + 1/40 y DATA(0, 2) - 13 2 - + -- y DATA(-1, -1) + 1/8 y DATA(1, 2) + 9/40 y DATA(0, 1) - 40 + 2 2 13 + - 3/8 y DATA(0, 1) + 3/8 y DATA(0, 0) + -- y DATA(-1, -1) + 40 - 19 21 11 2 - - -- y DATA(1, 0) - -- y DATA(0, 0) + -- y DATA(1, 1) + 1/8 y DATA(0, 2) - 40 40 40 + 11 2 + + -- y DATA(0, -1) + 1/20 x y DATA(0, 0) + 3/8 y DATA(1, 0) + 40 2 2 2 - - 3/8 y DATA(2, 1) + 3/8 y DATA(2, 0) + 1/8 y DATA(2, 2) + - 3/8 y DATA(1, 1) - 3/8 y DATA(2, 1) + 1/8 y DATA(1, 2) - 2 2 2 - + 1/8 y DATA(-1, 2) - 3/8 y DATA(-1, 1) - 1/8 y DATA(0, -1) - - 2 2 2 - - 1/8 y DATA(1, -1) + 3/8 y DATA(-1, 0) - 1/8 y DATA(-1, -1) + 2 2 2 + + 3/8 y DATA(2, 0) - 1/8 y DATA(2, -1) - 3/8 y DATA(-1, 1) 2 2 2 - - 3/8 y DATA(0, 1) + 3/8 y DATA(1, 0) + 3/8 y DATA(0, 0) + + 1/8 y DATA(2, 2) + 1/8 y DATA(0, 2) + 1/8 y DATA(-1, 2) - - 1/50 x DATA(-1, 0) - 1/100 x DATA(1, 0) - 1/100 x DATA(0, 1) + 2 2 + - 1/8 y DATA(-1, -1) - 1/100 x DATA(0, 1) - 1/8 y DATA(1, -1) - 2 - - 3/8 y DATA(1, 1) - 1/25 x DATA(0, 0) + 2/25 x DATA(1, 2) + 2 2 + + 3/8 y DATA(-1, 0) - 1/8 y DATA(0, -1) + 2/25 x DATA(2, 1) - - 1/50 x DATA(0, -1) + 6/25 x DATA(-1, -1) + 3/50 x DATA(1, 1) + - 1/25 x DATA(0, 0) - 1/100 x DATA(1, 0) + 7/100 x DATA(2, 0) - 13 13 - - --- x DATA(1, -1) - --- x DATA(-1, 1) - 3/50 x DATA(2, 2) - 100 100 + - 9/100 x DATA(2, -1) - 3/50 x DATA(2, 2) + 3/50 x DATA(1, 1) - + 7/100 x DATA(2, 0) + 2/25 x DATA(2, 1) - 9/100 x DATA(-1, 2) + + 2/25 x DATA(1, 2) + 7/100 x DATA(0, 2) - 9/100 x DATA(-1, 2) - 2 2 - + 1/40 x DATA(1, 0) - 1/40 x DATA(0, 1) + 7/100 x DATA(0, 2) + 21 19 + - 1/50 x DATA(-1, 0) - -- y DATA(0, 0) - -- y DATA(1, 0) + 40 40 - 2 2 - - 9/100 x DATA(2, -1) + 3/40 x DATA(1, -1) + 3/40 x DATA(0, -1) + 2 2 + + 9/40 y DATA(1, -1) + 1/40 x DATA(1, 0) + 1/40 x DATA(0, 0) 2 2 2 - + 1/40 x DATA(0, 0) - 1/40 x DATA(1, 1) - 1/40 x DATA(-1, 0) + + 1/40 x DATA(2, 1) - 1/40 x DATA(2, 0) - 3/40 x DATA(2, -1) - 2 2 2 - - 3/40 x DATA(1, 2) - 3/40 x DATA(-1, -1) + 1/40 x DATA(-1, 1) + 2 2 2 + + 3/40 x DATA(2, 2) + 1/40 x DATA(-1, 1) - 3/40 x DATA(0, 2) - 2 31 157 - + 3/40 x DATA(2, 2) - --- DATA(-1, 0) - ---- DATA(1, -1) - 400 1200 + 2 2 2 + + 3/40 x DATA(0, -1) + 3/40 x DATA(-1, 2) - 1/40 x DATA(-1, 0) - 223 109 111 37 - - ---- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(-1, 1) + ---- DATA(1, 2) - 1200 1200 400 1200 + 2 2 2 + - 3/40 x DATA(1, 2) - 1/40 x DATA(0, 1) - 1/40 x DATA(1, 1) - 149 49 69 131 - - ---- DATA(2, 2) - --- DATA(2, 0) + --- DATA(2, 1) - ---- DATA(-1, 2) - 1200 400 400 1200 + 2 2 17 + + 3/40 x DATA(1, -1) - 3/40 x DATA(-1, -1) - -- y DATA(2, 0) + 40 - 43 89 - + ---- DATA(0, 2) + ---- DATA(2, -1) - 1200 1200 + + 7/40 y DATA(2, -1) - 3/40 y DATA(2, 2) + 3/40 y DATA(-1, 2) + + 23 13 + - -- y DATA(-1, 0) + 7/40 y DATA(-1, 1) + -- y DATA(2, 1) + 40 40 > coeff_as_lc_of_data(%, posn_list_2d_size4); - 2 109 2 13 -[COEFF(-1, -1) = - 1/8 y - ---- - 3/40 x + -- y + 6/25 x - 3/20 x y, - 1200 40 + 2 13 109 2 +[COEFF(-1, -1) = - 3/40 x + -- y + 6/25 x - 3/20 x y - ---- - 1/8 y , + 40 1200 - 2 2 223 11 - COEFF(0, -1) = - 1/8 y + 3/40 x - 1/50 x - ---- - 1/20 x y + -- y, - 1200 40 + 2 223 2 11 + COEFF(0, -1) = 3/40 x - ---- - 1/50 x - 1/20 x y - 1/8 y + -- y, + 1200 40 - 13 2 2 157 - COEFF(1, -1) = - --- x - 1/8 y + 9/40 y + 3/40 x - ---- + 1/20 x y, - 100 1200 + 13 157 2 2 + COEFF(1, -1) = 9/40 y - --- x - ---- + 3/40 x + 1/20 x y - 1/8 y , + 100 1200 - 2 2 89 - COEFF(2, -1) = - 1/8 y + 3/20 x y + 7/40 y - 3/40 x - 9/100 x + ----, - 1200 + 2 89 2 + COEFF(2, -1) = - 9/100 x - 1/8 y + 3/20 x y + ---- + 7/40 y - 3/40 x , + 1200 - 23 2 31 2 - COEFF(-1, 0) = - -- y - 1/50 x + 3/8 y - --- - 1/40 x + 3/20 x y, - 40 400 + 23 2 2 31 + COEFF(-1, 0) = - -- y - 1/40 x + 3/8 y + 3/20 x y - --- - 1/50 x, + 40 400 - 21 57 2 2 - COEFF(0, 0) = - -- y - --- + 1/20 x y - 1/25 x + 3/8 y + 1/40 x , - 40 400 + 2 2 57 21 + COEFF(0, 0) = 3/8 y - 1/25 x + 1/40 x - --- + 1/20 x y - -- y, + 400 40 - 2 63 2 19 - COEFF(1, 0) = - 1/100 x + 3/8 y - --- - 1/20 x y + 1/40 x - -- y, - 400 40 + 2 2 63 19 + COEFF(1, 0) = 3/8 y + 1/40 x - --- - 1/100 x - 1/20 x y - -- y, + 400 40 - 2 49 17 2 - COEFF(2, 0) = 3/8 y + 7/100 x - --- - -- y - 1/40 x - 3/20 x y, - 400 40 + 2 17 2 49 + COEFF(2, 0) = - 3/20 x y + 3/8 y - -- y - 1/40 x - --- + 7/100 x, + 40 400 - 2 2 111 13 - COEFF(-1, 1) = - 3/8 y + 1/40 x + 3/20 x y + --- + 7/40 y - --- x, - 400 100 + 111 13 2 2 + COEFF(-1, 1) = --- + 3/20 x y - --- x + 7/40 y - 3/8 y + 1/40 x , + 400 100 - 117 2 2 - COEFF(0, 1) = --- - 1/100 x - 1/40 x + 9/40 y + 1/20 x y - 3/8 y , + 117 2 2 + COEFF(0, 1) = --- - 1/40 x + 1/20 x y - 3/8 y + 9/40 y - 1/100 x, 400 - 11 103 2 2 - COEFF(1, 1) = -- y + --- - 3/8 y + 3/50 x - 1/40 x - 1/20 x y, - 40 400 + 11 2 2 103 + COEFF(1, 1) = -- y - 3/8 y - 1/40 x - 1/20 x y + 3/50 x + ---, + 40 400 - 2 2 69 13 - COEFF(2, 1) = - 3/8 y + 1/40 x + 2/25 x - 3/20 x y + --- + -- y, - 400 40 + 2 69 13 2 + COEFF(2, 1) = 1/40 x + 2/25 x + --- + -- y - 3/20 x y - 3/8 y , + 400 40 - 2 2 131 - COEFF(-1, 2) = 1/8 y + 3/40 x + 3/40 y - 9/100 x - ---- - 3/20 x y, - 1200 + 131 2 2 + COEFF(-1, 2) = - 9/100 x - ---- + 1/8 y - 3/20 x y + 3/40 x + 3/40 y, + 1200 - 2 43 2 - COEFF(0, 2) = 7/100 x - 1/20 x y - 3/40 x + 1/40 y + ---- + 1/8 y , - 1200 + 2 43 2 + COEFF(0, 2) = - 1/20 x y + 7/100 x - 3/40 x + 1/40 y + ---- + 1/8 y , + 1200 - 2 2 37 - COEFF(1, 2) = 1/8 y + 2/25 x - 3/40 x - 1/40 y + ---- + 1/20 x y, - 1200 + 2 2 37 + COEFF(1, 2) = - 3/40 x - 1/40 y + 2/25 x + 1/20 x y + 1/8 y + ----, + 1200 - 2 2 149 - COEFF(2, 2) = 1/8 y + 3/20 x y - 3/50 x + 3/40 x - ---- - 3/40 y] - 1200 + 2 149 2 + COEFF(2, 2) = 1/8 y - ---- + 3/20 x y - 3/50 x - 3/40 y + 3/40 x ] + 1200 > print_coeff__lc_of_data(%, "coeff_dy_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-dy.compute.c"); -bytes used=28017044, alloc=2096768, time=2.36 -bytes used=29017220, alloc=2096768, time=2.45 -bytes used=30017984, alloc=2096768, time=2.55 -bytes used=31018144, alloc=2096768, time=2.67 +bytes used=28025712, alloc=2096768, time=2.36 +bytes used=29025924, alloc=2096768, time=2.45 +bytes used=30026084, alloc=2096768, time=2.55 +bytes used=31026248, alloc=2096768, time=2.66 > # d^2/dx^2 > simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); - 21 19 11 -- -- DATA(0, 0) + 9/40 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1) - 40 40 40 + 21 +3/4 x DATA(0, -1) - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) - -- DATA(0, 0) + 40 - + 1/20 y DATA(2, 1) - 1/20 y DATA(2, 0) - 3/20 y DATA(1, 2) + 19 11 + + 9/40 DATA(1, 0) - -- DATA(0, 1) + -- DATA(1, 1) - 1/40 DATA(2, 1) + 40 40 - - 3/20 y DATA(2, -1) - 3/20 y DATA(0, 2) + 3/20 y DATA(-1, 2) + 13 + + 1/40 DATA(2, 0) + 3/40 DATA(2, -1) - 3/40 DATA(2, 2) + -- DATA(1, 2) + 40 - + 3/20 y DATA(0, -1) + 3/20 y DATA(1, -1) - 1/20 y DATA(-1, 0) + 17 11 + - -- DATA(0, 2) + 7/40 DATA(-1, 2) + -- DATA(-1, 0) + 9/40 DATA(-1, 1) + 40 40 - + 3/20 y DATA(2, 2) + 1/20 y DATA(-1, 1) - 3/20 y DATA(-1, -1) + 13 23 + + -- DATA(-1, -1) - -- DATA(0, -1) + 7/40 DATA(1, -1) - 1/20 y DATA(0, 1) + 40 40 - - 1/20 y DATA(0, 1) + 1/20 y DATA(1, 0) + 1/20 y DATA(0, 0) + - 1/20 y DATA(1, 1) - 1/4 x DATA(-1, -1) - 3/20 y DATA(1, 2) - - 1/20 y DATA(1, 1) - 1/4 x DATA(-1, 0) - 3/4 x DATA(1, 0) + - 3/20 y DATA(0, 2) - 3/20 y DATA(-1, -1) + 3/20 y DATA(0, -1) - + 3/4 x DATA(0, 1) + 3/4 x DATA(0, 0) - 3/4 x DATA(1, 2) + + 3/4 x DATA(0, 1) + 1/4 x DATA(2, 1) + 3/4 x DATA(0, 0) - + 3/4 x DATA(0, -1) - 1/4 x DATA(-1, -1) - 3/4 x DATA(1, 1) + - 3/4 x DATA(1, 0) + 1/4 x DATA(2, 0) + 1/4 x DATA(2, -1) - - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) + 1/4 x DATA(2, 2) + + 1/4 x DATA(2, 2) - 3/4 x DATA(1, 1) - 3/4 x DATA(1, 2) - + 1/4 x DATA(2, 0) + 1/4 x DATA(2, 1) - 1/4 x DATA(-1, 2) + + 3/4 x DATA(0, 2) - 1/4 x DATA(-1, 2) - 1/4 x DATA(-1, 0) - 11 - + 3/4 x DATA(0, 2) + 1/4 x DATA(2, -1) + -- DATA(-1, 0) + 7/40 DATA(1, -1) - 40 + + 1/20 y DATA(0, 0) + 1/20 y DATA(1, 0) + 3/20 y DATA(1, -1) - 23 13 13 - - -- DATA(0, -1) + -- DATA(-1, -1) + 9/40 DATA(-1, 1) + -- DATA(1, 2) - 40 40 40 + - 1/20 y DATA(2, 0) - 3/20 y DATA(2, -1) + 3/20 y DATA(2, 2) - - 3/40 DATA(2, 2) + 1/40 DATA(2, 0) - 1/40 DATA(2, 1) + 7/40 DATA(-1, 2) + + 3/20 y DATA(-1, 2) - 1/20 y DATA(-1, 0) + 1/20 y DATA(-1, 1) - 17 - - -- DATA(0, 2) + 3/40 DATA(2, -1) - 40 + + 1/20 y DATA(2, 1) > coeff_as_lc_of_data(%, posn_list_2d_size4); -bytes used=32018340, alloc=2096768, time=2.81 - 13 23 -[COEFF(-1, -1) = - 3/20 y - 1/4 x + --, COEFF(0, -1) = - -- + 3/20 y + 3/4 x, - 40 40 +bytes used=32026448, alloc=2096768, time=2.74 + 13 23 +[COEFF(-1, -1) = - 1/4 x - 3/20 y + --, COEFF(0, -1) = 3/4 x - -- + 3/20 y, + 40 40 - COEFF(1, -1) = 7/40 + 3/20 y - 3/4 x, + COEFF(1, -1) = - 3/4 x + 3/20 y + 7/40, - COEFF(2, -1) = - 3/20 y + 1/4 x + 3/40, + 11 + COEFF(2, -1) = 3/40 + 1/4 x - 3/20 y, COEFF(-1, 0) = - 1/4 x - 1/20 y + --, + 40 - 11 21 - COEFF(-1, 0) = - 1/4 x + -- - 1/20 y, COEFF(0, 0) = 1/20 y - -- + 3/4 x, - 40 40 + 21 + COEFF(0, 0) = - -- + 1/20 y + 3/4 x, COEFF(1, 0) = 9/40 + 1/20 y - 3/4 x, + 40 - COEFF(1, 0) = 9/40 + 1/20 y - 3/4 x, COEFF(2, 0) = 1/40 - 1/20 y + 1/4 x, + COEFF(2, 0) = 1/40 - 1/20 y + 1/4 x, COEFF(-1, 1) = - 1/4 x + 9/40 + 1/20 y, - 19 - COEFF(-1, 1) = - 1/4 x + 1/20 y + 9/40, COEFF(0, 1) = - 1/20 y - -- + 3/4 x, - 40 + 19 11 + COEFF(0, 1) = 3/4 x - -- - 1/20 y, COEFF(1, 1) = - 3/4 x + -- - 1/20 y, + 40 40 - 11 - COEFF(1, 1) = - 1/20 y + -- - 3/4 x, COEFF(2, 1) = 1/20 y + 1/4 x - 1/40, - 40 + COEFF(2, 1) = - 1/40 + 1/4 x + 1/20 y, COEFF(-1, 2) = 3/20 y - 1/4 x + 7/40, - 17 - COEFF(-1, 2) = 3/20 y - 1/4 x + 7/40, COEFF(0, 2) = - -- - 3/20 y + 3/4 x, - 40 + 17 13 + COEFF(0, 2) = - 3/20 y - -- + 3/4 x, COEFF(1, 2) = - 3/4 x - 3/20 y + --, + 40 40 - 13 - COEFF(1, 2) = -- - 3/20 y - 3/4 x, COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y] - 40 + COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y] > print_coeff__lc_of_data(%, "coeff_dxx_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-dxx.compute.c"); -bytes used=33018592, alloc=2096768, time=2.91 +bytes used=33026764, alloc=2096768, time=2.83 > # d^2/dxdy > simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); -bytes used=34018772, alloc=2096768, time=3.02 -- 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) +3/20 x DATA(0, -1) + 3/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) - 1/25 DATA(0, 0) - - 3/20 y DATA(2, 1) - 3/20 y DATA(2, 0) + 1/20 y DATA(1, 2) + - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) + 2/25 DATA(2, 1) - + 3/20 y DATA(2, -1) - 1/20 y DATA(0, 2) - 3/20 y DATA(-1, 2) + + 7/100 DATA(2, 0) - 9/100 DATA(2, -1) - 3/50 DATA(2, 2) + 2/25 DATA(1, 2) - - 1/20 y DATA(0, -1) + 1/20 y DATA(1, -1) + 3/20 y DATA(-1, 0) + + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) - 1/50 DATA(-1, 0) - + 3/20 y DATA(2, 2) + 3/20 y DATA(-1, 1) - 3/20 y DATA(-1, -1) + 13 13 + - --- DATA(-1, 1) + 6/25 DATA(-1, -1) - 1/50 DATA(0, -1) - --- DATA(1, -1) + 100 100 - + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 0) + 1/20 y DATA(0, 0) + + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 1) - 3/20 x DATA(-1, -1) - - 1/20 y DATA(1, 1) - 1/20 x DATA(-1, 0) + 1/20 x DATA(1, 0) + + 1/20 y DATA(1, 2) - 1/20 y DATA(0, 2) - 3/20 y DATA(-1, -1) - - 1/20 x DATA(0, 1) + 1/20 x DATA(0, 0) - 3/20 x DATA(1, 2) + - 1/20 y DATA(0, -1) - 1/20 x DATA(0, 1) + 1/20 x DATA(2, 1) - + 3/20 x DATA(0, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(1, 1) + + 1/20 x DATA(0, 0) + 1/20 x DATA(1, 0) - 1/20 x DATA(2, 0) - + 3/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) + 3/20 x DATA(2, 2) + - 3/20 x DATA(2, -1) + 3/20 x DATA(2, 2) - 1/20 x DATA(1, 1) - - 1/20 x DATA(2, 0) + 1/20 x DATA(2, 1) + 3/20 x DATA(-1, 2) + - 3/20 x DATA(1, 2) - 3/20 x DATA(0, 2) + 3/20 x DATA(-1, 2) - - 3/20 x DATA(0, 2) - 3/20 x DATA(2, -1) - 1/50 DATA(-1, 0) + - 1/20 x DATA(-1, 0) + 1/20 y DATA(0, 0) - 1/20 y DATA(1, 0) - 13 13 - - --- DATA(1, -1) - 1/50 DATA(0, -1) + 6/25 DATA(-1, -1) - --- DATA(-1, 1) - 100 100 + + 1/20 y DATA(1, -1) - 3/20 y DATA(2, 0) + 3/20 y DATA(2, -1) - + 2/25 DATA(1, 2) - 3/50 DATA(2, 2) + 7/100 DATA(2, 0) + 2/25 DATA(2, 1) + + 3/20 y DATA(2, 2) - 3/20 y DATA(-1, 2) + 3/20 y DATA(-1, 0) - - 9/100 DATA(-1, 2) + 7/100 DATA(0, 2) - 9/100 DATA(2, -1) + + 3/20 y DATA(-1, 1) - 3/20 y DATA(2, 1) > coeff_as_lc_of_data(%, posn_list_2d_size4); -[COEFF(-1, -1) = - 3/20 y - 3/20 x + 6/25, +bytes used=34027108, alloc=2096768, time=2.96 +[COEFF(-1, -1) = - 3/20 y + 6/25 - 3/20 x, - 13 - COEFF(0, -1) = 3/20 x - 1/20 y - 1/50, COEFF(1, -1) = 3/20 x + 1/20 y - ---, - 100 + COEFF(0, -1) = - 1/50 + 3/20 x - 1/20 y, - COEFF(2, -1) = - 9/100 - 3/20 x + 3/20 y, + 13 + COEFF(1, -1) = 3/20 x - --- + 1/20 y, + 100 - COEFF(-1, 0) = - 1/50 - 1/20 x + 3/20 y, + COEFF(2, -1) = - 3/20 x - 9/100 + 3/20 y, - COEFF(0, 0) = - 1/25 + 1/20 y + 1/20 x, + COEFF(-1, 0) = - 1/50 + 3/20 y - 1/20 x, + + COEFF(0, 0) = 1/20 x - 1/25 + 1/20 y, COEFF(1, 0) = - 1/100 + 1/20 x - 1/20 y, - COEFF(2, 0) = - 1/20 x + 7/100 - 3/20 y, + COEFF(2, 0) = - 3/20 y + 7/100 - 1/20 x, - 13 - COEFF(-1, 1) = - --- + 1/20 x + 3/20 y, - 100 + 13 + COEFF(-1, 1) = 1/20 x - --- + 3/20 y, + 100 - COEFF(0, 1) = - 1/20 x - 1/100 + 1/20 y, + COEFF(0, 1) = - 1/100 + 1/20 y - 1/20 x, - COEFF(1, 1) = 3/50 - 1/20 x - 1/20 y, + COEFF(1, 1) = 3/50 - 1/20 y - 1/20 x, - COEFF(2, 1) = - 3/20 y + 1/20 x + 2/25, + COEFF(2, 1) = - 3/20 y + 2/25 + 1/20 x, - COEFF(-1, 2) = - 3/20 y + 3/20 x - 9/100, + COEFF(-1, 2) = 3/20 x - 3/20 y - 9/100, COEFF(0, 2) = 7/100 - 3/20 x - 1/20 y, - COEFF(1, 2) = - 3/20 x + 1/20 y + 2/25, + COEFF(1, 2) = - 3/20 x + 2/25 + 1/20 y, - COEFF(2, 2) = 3/20 x + 3/20 y - 3/50] + COEFF(2, 2) = 3/20 y - 3/50 + 3/20 x] > print_coeff__lc_of_data(%, "coeff_dxy_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-dxy.compute.c"); -bytes used=35018968, alloc=2096768, time=3.11 +bytes used=35027272, alloc=2096768, time=3.05 > # d^2/dy^2 > simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); - 21 19 11 -- -- DATA(0, 0) - -- DATA(1, 0) + 9/40 DATA(0, 1) + -- DATA(1, 1) - 40 40 40 + 21 +- 1/20 x DATA(0, -1) + 1/20 x DATA(1, -1) + 3/20 x DATA(-1, 1) - -- DATA(0, 0) + 40 - - 3/4 y DATA(2, 1) + 3/4 y DATA(2, 0) + 1/4 y DATA(1, 2) + 19 11 13 + - -- DATA(1, 0) + 9/40 DATA(0, 1) + -- DATA(1, 1) + -- DATA(2, 1) + 40 40 40 - - 1/4 y DATA(2, -1) + 1/4 y DATA(0, 2) + 1/4 y DATA(-1, 2) + 17 + - -- DATA(2, 0) + 7/40 DATA(2, -1) - 3/40 DATA(2, 2) - 1/40 DATA(1, 2) + 40 - - 1/4 y DATA(0, -1) - 1/4 y DATA(1, -1) + 3/4 y DATA(-1, 0) + 23 + + 1/40 DATA(0, 2) + 3/40 DATA(-1, 2) - -- DATA(-1, 0) + 7/40 DATA(-1, 1) + 40 - + 1/4 y DATA(2, 2) - 3/4 y DATA(-1, 1) - 1/4 y DATA(-1, -1) + 13 11 + + -- DATA(-1, -1) + -- DATA(0, -1) + 9/40 DATA(1, -1) - 3/4 y DATA(0, 1) + 40 40 - - 3/4 y DATA(0, 1) + 3/4 y DATA(1, 0) + 3/4 y DATA(0, 0) + - 3/4 y DATA(1, 1) - 3/20 x DATA(-1, -1) + 1/4 y DATA(1, 2) - - 3/4 y DATA(1, 1) + 3/20 x DATA(-1, 0) - 1/20 x DATA(1, 0) + + 1/4 y DATA(0, 2) - 1/4 y DATA(-1, -1) - 1/4 y DATA(0, -1) - + 1/20 x DATA(0, 1) + 1/20 x DATA(0, 0) + 1/20 x DATA(1, 2) + + 1/20 x DATA(0, 1) - 3/20 x DATA(2, 1) + 1/20 x DATA(0, 0) - - 1/20 x DATA(0, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(1, 1) + - 1/20 x DATA(1, 0) - 3/20 x DATA(2, 0) + 3/20 x DATA(2, -1) - + 1/20 x DATA(1, -1) + 3/20 x DATA(-1, 1) + 3/20 x DATA(2, 2) + + 3/20 x DATA(2, 2) - 1/20 x DATA(1, 1) + 1/20 x DATA(1, 2) - - 3/20 x DATA(2, 0) - 3/20 x DATA(2, 1) - 3/20 x DATA(-1, 2) + - 1/20 x DATA(0, 2) - 3/20 x DATA(-1, 2) + 3/20 x DATA(-1, 0) - 23 - - 1/20 x DATA(0, 2) + 3/20 x DATA(2, -1) - -- DATA(-1, 0) - 40 + + 3/4 y DATA(0, 0) + 3/4 y DATA(1, 0) - 1/4 y DATA(1, -1) - 11 13 - + 9/40 DATA(1, -1) + -- DATA(0, -1) + -- DATA(-1, -1) + 7/40 DATA(-1, 1) - 40 40 + + 3/4 y DATA(2, 0) - 1/4 y DATA(2, -1) + 1/4 y DATA(2, 2) - 17 13 - - 1/40 DATA(1, 2) - 3/40 DATA(2, 2) - -- DATA(2, 0) + -- DATA(2, 1) - 40 40 + + 1/4 y DATA(-1, 2) + 3/4 y DATA(-1, 0) - 3/4 y DATA(-1, 1) - + 3/40 DATA(-1, 2) + 1/40 DATA(0, 2) + 7/40 DATA(2, -1) + - 3/4 y DATA(2, 1) > coeff_as_lc_of_data(%, posn_list_2d_size4); -bytes used=36019260, alloc=2096768, time=3.25 - 13 11 -[COEFF(-1, -1) = - 1/4 y + -- - 3/20 x, COEFF(0, -1) = - 1/20 x - 1/4 y + --, - 40 40 +bytes used=36028028, alloc=2096768, time=3.15 + 13 11 +[COEFF(-1, -1) = - 1/4 y - 3/20 x + --, COEFF(0, -1) = -- - 1/20 x - 1/4 y, + 40 40 - COEFF(1, -1) = - 1/4 y + 1/20 x + 9/40, + COEFF(1, -1) = 9/40 + 1/20 x - 1/4 y, COEFF(2, -1) = 3/20 x - 1/4 y + 7/40, - 23 - COEFF(2, -1) = 3/20 x - 1/4 y + 7/40, COEFF(-1, 0) = 3/4 y - -- + 3/20 x, - 40 - - 21 19 - COEFF(0, 0) = - -- + 1/20 x + 3/4 y, COEFF(1, 0) = - -- + 3/4 y - 1/20 x, - 40 40 + 23 21 + COEFF(-1, 0) = - -- + 3/4 y + 3/20 x, COEFF(0, 0) = 3/4 y - -- + 1/20 x, + 40 40 - 17 - COEFF(2, 0) = - 3/20 x + 3/4 y - --, COEFF(-1, 1) = 3/20 x - 3/4 y + 7/40, - 40 + 19 17 + COEFF(1, 0) = - -- - 1/20 x + 3/4 y, COEFF(2, 0) = 3/4 y - -- - 3/20 x, + 40 40 - 11 - COEFF(0, 1) = 1/20 x + 9/40 - 3/4 y, COEFF(1, 1) = - 1/20 x + -- - 3/4 y, - 40 + COEFF(-1, 1) = 3/20 x + 7/40 - 3/4 y, COEFF(0, 1) = 1/20 x + 9/40 - 3/4 y, - 13 - COEFF(2, 1) = - 3/20 x + -- - 3/4 y, COEFF(-1, 2) = - 3/20 x + 1/4 y + 3/40, - 40 + 11 13 + COEFF(1, 1) = -- - 3/4 y - 1/20 x, COEFF(2, 1) = -- - 3/20 x - 3/4 y, + 40 40 - COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x, COEFF(1, 2) = 1/20 x - 1/40 + 1/4 y, + COEFF(-1, 2) = 1/4 y + 3/40 - 3/20 x, COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x, - COEFF(2, 2) = 3/20 x + 1/4 y - 3/40] + COEFF(1, 2) = - 1/40 + 1/20 x + 1/4 y, COEFF(2, 2) = 3/20 x + 1/4 y - 3/40] > print_coeff__lc_of_data(%, "coeff_dyy_", "fp", > "2d.coeffs/2d.cube.order3.smooth0/coeff-dyy.compute.c"); -bytes used=37019440, alloc=2096768, time=3.33 +bytes used=37028452, alloc=2096768, time=3.27 > ################################################################################ > @@ -2513,1970 +2769,1963 @@ bytes used=37019440, alloc=2096768, time=3.33 > interp_2d_cube_order4_smooth0 > := Lagrange_polynomial_interpolant(fn_2d_order4, coeff_list_2d_order4, > coord_list_2d, posn_list_2d_size5); -bytes used=38019764, alloc=2096768, time=3.45 -bytes used=39020548, alloc=2096768, time=3.52 -bytes used=40020708, alloc=2162292, time=3.58 -bytes used=41022132, alloc=2162292, time=3.65 -bytes used=42022568, alloc=2162292, time=3.72 -bytes used=43024680, alloc=2162292, time=3.78 - 541 246 -interp_2d_cube_order4_smooth0 := ---- DATA(0, 0) + ---- DATA(1, 0) - 1225 1225 +bytes used=38028660, alloc=2096768, time=3.39 +bytes used=39028828, alloc=2096768, time=3.46 +bytes used=40029048, alloc=2096768, time=3.52 +bytes used=41029524, alloc=2096768, time=3.59 +bytes used=42032252, alloc=2096768, time=3.64 +bytes used=43032424, alloc=2096768, time=3.70 +interp_2d_cube_order4_smooth0 := (- 1/60 DATA(1, 1) - 1/30 DATA(2, 1) + + + 1/30 DATA(2, -1) + 1/60 DATA(2, 2) + 1/120 DATA(1, 2) - 246 24 246 24 - + ---- DATA(0, 1) - ---- DATA(1, 1) + ---- DATA(-1, 0) - ---- DATA(1, -1) - 1225 1225 1225 1225 + - 1/120 DATA(-1, 2) + 1/60 DATA(-1, 1) - 1/60 DATA(-1, -1) - 246 24 24 - + ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(-1, 1) + ( - 1225 1225 1225 + + 1/60 DATA(1, -1) - 1/30 DATA(-2, -1) - 1/60 DATA(2, -2) - - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) + 1/30 DATA(-1, 0) - 1/30 DATA(1, -1) + + 1/60 DATA(-2, -2) + 1/120 DATA(-1, -2) - 1/120 DATA(1, -2) - + 1/30 DATA(-1, -1) + 1/30 DATA(-1, 1) - 1/30 DATA(1, 2) + 1/60 DATA(2, 2) + 3 + - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1)) x y + (- 1/70 DATA(1, 0) - + 1/60 DATA(2, 0) + 1/60 DATA(2, 1) + 1/30 DATA(-1, 2) + 1/60 DATA(2, -1) + - 1/140 DATA(1, 1) - 1/70 DATA(2, 1) - 1/35 DATA(2, 0) - 1/70 DATA(2, -1) - - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1) - 1/60 DATA(-2, -1) + + 1/35 DATA(2, 2) + 1/70 DATA(1, 2) - 1/70 DATA(-1, 2) + 1/70 DATA(-1, 0) - - 1/60 DATA(-2, 0) + 1/60 DATA(2, -2) + 1/30 DATA(-1, -2) + + 1/140 DATA(-1, 1) + 1/140 DATA(-1, -1) - 1/140 DATA(1, -1) - 3 - - 1/30 DATA(1, -2) - 1/60 DATA(-2, -2)) x + (1/20 DATA(0, 0) + + 1/70 DATA(-2, -1) + 1/35 DATA(2, -2) - 1/35 DATA(-2, -2) - - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(-1, 0) + - 1/70 DATA(-1, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, 2) - - 1/30 DATA(1, -1) + 1/20 DATA(0, -1) - 1/30 DATA(-1, -1) + 2 + + 1/35 DATA(-2, 0) + 1/70 DATA(-2, 1)) x y + (1/49 DATA(0, 0) - - 1/30 DATA(-1, 1) - 1/30 DATA(1, 2) + 1/120 DATA(2, 2) + 1/120 DATA(2, 0) + + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) + 1/196 DATA(1, 1) - 1/98 DATA(2, 1) - + 1/120 DATA(2, 1) - 1/30 DATA(-1, 2) + 1/20 DATA(0, 2) + - 1/49 DATA(2, 0) - 1/98 DATA(2, -1) + 1/49 DATA(2, 2) - 1/98 DATA(1, 2) - + 1/120 DATA(2, -1) + 1/120 DATA(-2, 2) + 1/120 DATA(-2, 1) + - 1/49 DATA(0, 2) - 1/98 DATA(-1, 2) + 1/98 DATA(-1, 0) - + 1/120 DATA(-2, -1) + 1/120 DATA(-2, 0) + 1/120 DATA(2, -2) + + 1/196 DATA(-1, 1) + 1/196 DATA(-1, -1) + 1/98 DATA(0, -1) - - 1/30 DATA(-1, -2) + 1/20 DATA(0, -2) - 1/30 DATA(1, -2) + + 1/196 DATA(1, -1) - 1/98 DATA(-2, -1) + 1/49 DATA(2, -2) - 4 - + 1/120 DATA(-2, -2)) x + (1/20 DATA(0, 0) + 1/20 DATA(1, 0) + + 1/49 DATA(-2, -2) - 1/98 DATA(-1, -2) - 1/49 DATA(0, -2) - - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) + 1/20 DATA(-1, 0) - 1/30 DATA(1, -1) + - 1/98 DATA(1, -2) + 1/49 DATA(-2, 2) - 1/49 DATA(-2, 0) - - 1/30 DATA(0, -1) - 1/30 DATA(-1, -1) - 1/30 DATA(-1, 1) + 2 2 /37 21 + - 1/98 DATA(-2, 1)) x y + |--- DATA(1, 1) + --- DATA(2, 1) + \300 200 - + 1/120 DATA(1, 2) + 1/120 DATA(2, 2) + 1/20 DATA(2, 0) - 1/30 DATA(2, 1) + 21 11 21 21 + - --- DATA(2, -1) - --- DATA(2, 2) + --- DATA(1, 2) - --- DATA(-1, 2) + 200 150 200 200 - + 1/120 DATA(-1, 2) + 1/120 DATA(0, 2) - 1/30 DATA(2, -1) + 37 37 37 21 + - --- DATA(-1, 1) + --- DATA(-1, -1) - --- DATA(1, -1) + --- DATA(-2, -1) + 300 300 300 200 - + 1/120 DATA(-2, 2) - 1/30 DATA(-2, 1) - 1/30 DATA(-2, -1) + 11 11 21 21 + + --- DATA(2, -2) - --- DATA(-2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) + 150 150 200 200 - + 1/20 DATA(-2, 0) + 1/120 DATA(2, -2) + 1/120 DATA(-1, -2) + 11 21 \ + + --- DATA(-2, 2) - --- DATA(-2, 1)| x y + (- 1/70 DATA(0, 1) + 150 200 / - 4 / - + 1/120 DATA(0, -2) + 1/120 DATA(1, -2) + 1/120 DATA(-2, -2)) y + | - \ + - 1/140 DATA(1, 1) + 1/70 DATA(2, 1) - 1/70 DATA(2, -1) + 1/35 DATA(2, 2) - 17 31 31 17 - --- DATA(0, 1) + --- DATA(1, 1) - --- DATA(1, -1) - --- DATA(0, -1) - 105 210 210 105 + - 1/70 DATA(1, 2) - 1/35 DATA(0, 2) - 1/70 DATA(-1, 2) - 1/140 DATA(-1, 1) - 31 31 31 - - --- DATA(-1, -1) + --- DATA(-1, 1) + 1/84 DATA(1, 2) - --- DATA(2, 2) - 210 210 420 + + 1/140 DATA(-1, -1) + 1/70 DATA(0, -1) + 1/140 DATA(1, -1) - 11 17 11 - + --- DATA(2, 1) + 1/84 DATA(-1, 2) + --- DATA(0, 2) - --- DATA(2, -1) - 105 420 105 + - 1/70 DATA(-2, -1) - 1/35 DATA(2, -2) - 1/35 DATA(-2, -2) - 31 11 11 31 - - --- DATA(-2, 2) + --- DATA(-2, 1) - --- DATA(-2, -1) + --- DATA(2, -2) - 420 105 105 420 + + 1/70 DATA(-1, -2) + 1/35 DATA(0, -2) + 1/70 DATA(1, -2) - 17 - - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2) - 420 + 2 + + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1)) x y + (- 1/60 DATA(1, 1) - 31 \ /17 31 17 - + --- DATA(-2, -2)| y + |--- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, 0) - 420 / \105 210 105 + + 1/120 DATA(2, 1) - 1/120 DATA(2, -1) + 1/60 DATA(2, 2) - 1/30 DATA(1, 2) - 31 31 31 11 - + --- DATA(1, -1) - --- DATA(-1, -1) - --- DATA(-1, 1) + --- DATA(1, 2) - 210 210 210 105 + + 1/30 DATA(-1, 2) + 1/60 DATA(-1, 1) - 1/60 DATA(-1, -1) - 31 17 11 - - --- DATA(2, 2) + --- DATA(2, 0) + 1/84 DATA(2, 1) - --- DATA(-1, 2) - 420 420 105 + + 1/60 DATA(1, -1) + 1/120 DATA(-2, -1) - 1/60 DATA(2, -2) - 31 - + 1/84 DATA(2, -1) + --- DATA(-2, 2) - 1/84 DATA(-2, 1) - 420 + + 1/60 DATA(-2, -2) - 1/30 DATA(-1, -2) + 1/30 DATA(1, -2) - 17 31 11 - - 1/84 DATA(-2, -1) - --- DATA(-2, 0) - --- DATA(2, -2) - --- DATA(-1, -2) - 420 420 105 + 3 / 57 + - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1)) x y + |- --- DATA(0, 0) + \ 196 - 11 31 \ / 57 - + --- DATA(1, -2) + --- DATA(-2, -2)| x + |- --- DATA(0, 0) - 105 420 / \ 196 + 83 53 181 71 + + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) + ---- DATA(2, 1) + 735 196 1470 5880 - 83 53 181 83 - + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) + --- DATA(-1, 0) - 735 196 1470 735 + 191 71 289 113 + + ---- DATA(2, 0) + ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2) + 5880 5880 5880 735 - 181 53 181 - + ---- DATA(1, -1) - --- DATA(0, -1) + ---- DATA(-1, -1) - 1470 196 1470 + 41 113 83 181 + - --- DATA(0, 2) + --- DATA(-1, 2) + --- DATA(-1, 0) + ---- DATA(-1, 1) + 196 735 735 1470 - 181 113 289 191 - + ---- DATA(-1, 1) + --- DATA(1, 2) - ---- DATA(2, 2) + ---- DATA(2, 0) - 1470 735 5880 5880 + 181 53 181 + + ---- DATA(-1, -1) - --- DATA(0, -1) + ---- DATA(1, -1) + 1470 196 1470 - 71 113 41 71 - + ---- DATA(2, 1) + --- DATA(-1, 2) - --- DATA(0, 2) + ---- DATA(2, -1) - 5880 735 196 5880 + 71 289 289 + + ---- DATA(-2, -1) - ---- DATA(2, -2) - ---- DATA(-2, -2) + 5880 5880 5880 - 289 71 71 - - ---- DATA(-2, 2) + ---- DATA(-2, 1) + ---- DATA(-2, -1) - 5880 5880 5880 + 113 41 113 289 + + --- DATA(-1, -2) - --- DATA(0, -2) + --- DATA(1, -2) - ---- DATA(-2, 2) + 735 196 735 5880 - 191 289 113 41 - + ---- DATA(-2, 0) - ---- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(0, -2) - 5880 5880 735 196 + 191 71 \ 2 + + ---- DATA(-2, 0) + ---- DATA(-2, 1)| x + (1/20 DATA(0, 0) + 5880 5880 / - 113 289 \ 2 - + --- DATA(1, -2) - ---- DATA(-2, -2)| x + (- 1/70 DATA(1, 0) - 735 5880 / + + 1/20 DATA(1, 0) - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(2, 1) - - 1/140 DATA(1, 1) + 1/70 DATA(-1, 0) - 1/140 DATA(1, -1) + + 1/20 DATA(2, 0) - 1/30 DATA(2, -1) + 1/120 DATA(2, 2) + 1/120 DATA(1, 2) - + 1/140 DATA(-1, -1) + 1/140 DATA(-1, 1) + 1/70 DATA(1, 2) + + 1/120 DATA(0, 2) + 1/120 DATA(-1, 2) + 1/20 DATA(-1, 0) - + 1/35 DATA(2, 2) - 1/35 DATA(2, 0) - 1/70 DATA(2, 1) - 1/70 DATA(-1, 2) + - 1/30 DATA(-1, 1) - 1/30 DATA(-1, -1) - 1/30 DATA(0, -1) - - 1/70 DATA(2, -1) - 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + - 1/30 DATA(1, -1) - 1/30 DATA(-2, -1) + 1/120 DATA(2, -2) - + 1/70 DATA(-2, -1) + 1/35 DATA(-2, 0) + 1/35 DATA(2, -2) + + 1/120 DATA(-2, -2) + 1/120 DATA(-1, -2) + 1/120 DATA(0, -2) - 2 - - 1/70 DATA(-1, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, -2)) x y + ( + + 1/120 DATA(1, -2) + 1/120 DATA(-2, 2) + 1/20 DATA(-2, 0) - - 1/60 DATA(1, 1) + 1/60 DATA(1, -1) - 1/60 DATA(-1, -1) + 1/60 DATA(-1, 1) + 4 541 246 + - 1/30 DATA(-2, 1)) y + ---- DATA(0, 0) + ---- DATA(1, 0) + 1225 1225 - + 1/120 DATA(1, 2) + 1/60 DATA(2, 2) - 1/30 DATA(2, 1) - 1/120 DATA(-1, 2) + 246 24 99 96 + + ---- DATA(0, 1) - ---- DATA(1, 1) - ---- DATA(2, 1) + ---- DATA(2, 0) + 1225 1225 1225 1225 - + 1/30 DATA(2, -1) - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1) + 99 51 99 96 + - ---- DATA(2, -1) + ---- DATA(2, 2) - ---- DATA(1, 2) + ---- DATA(0, 2) + 1225 1225 1225 1225 - - 1/30 DATA(-2, -1) - 1/60 DATA(2, -2) + 1/120 DATA(-1, -2) + 99 246 24 + - ---- DATA(-1, 2) + ---- DATA(-1, 0) - ---- DATA(-1, 1) + 1225 1225 1225 - 3 / 57 - - 1/120 DATA(1, -2) + 1/60 DATA(-2, -2)) x y + |- --- DATA(0, 0) - \ 196 + 24 246 24 + - ---- DATA(-1, -1) + ---- DATA(0, -1) - ---- DATA(1, -1) + ( + 1225 1225 1225 - 53 83 181 53 - - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) - --- DATA(-1, 0) - 196 735 1470 196 + - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) - 1/60 DATA(-2, -2) + 1/60 DATA(2, 1) - 181 83 181 - + ---- DATA(1, -1) + --- DATA(0, -1) + ---- DATA(-1, -1) - 1470 735 1470 + + 1/60 DATA(2, 0) + 1/60 DATA(2, -1) + 1/60 DATA(2, 2) - 1/30 DATA(1, 2) - 181 71 289 41 - + ---- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - --- DATA(2, 0) - 1470 5880 5880 196 + + 1/30 DATA(-1, 2) + 1/30 DATA(-1, 0) + 1/30 DATA(-1, 1) - 113 71 191 113 - + --- DATA(2, 1) + ---- DATA(-1, 2) + ---- DATA(0, 2) + --- DATA(2, -1) - 735 5880 5880 735 + + 1/30 DATA(-1, -1) - 1/30 DATA(1, -1) - 1/60 DATA(-2, -1) - 289 113 113 41 - - ---- DATA(-2, 2) + --- DATA(-2, 1) + --- DATA(-2, -1) - --- DATA(-2, 0) - 5880 735 735 196 + + 1/60 DATA(2, -2) - 1/60 DATA(-2, 0) + 1/30 DATA(-1, -2) - 289 71 191 - - ---- DATA(2, -2) + ---- DATA(-1, -2) + ---- DATA(0, -2) - 5880 5880 5880 + 3 + - 1/30 DATA(1, -2) - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1)) x + ( - 71 289 \ 2 - + ---- DATA(1, -2) - ---- DATA(-2, -2)| y + (- 1/30 DATA(0, 1) - 5880 5880 / + 1/20 DATA(0, 0) - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) - 1/30 DATA(1, 1) - - 1/30 DATA(1, 1) + 1/30 DATA(1, -1) + 1/30 DATA(0, -1) + + 1/120 DATA(2, 1) + 1/120 DATA(2, 0) + 1/120 DATA(2, -1) - + 1/30 DATA(-1, -1) - 1/30 DATA(-1, 1) + 1/60 DATA(1, 2) + 1/60 DATA(2, 2) + + 1/120 DATA(2, 2) - 1/30 DATA(1, 2) + 1/20 DATA(0, 2) - 1/30 DATA(-1, 2) - - 1/30 DATA(2, 1) + 1/60 DATA(-1, 2) + 1/60 DATA(0, 2) + 1/30 DATA(2, -1) + - 1/30 DATA(-1, 0) - 1/30 DATA(-1, 1) - 1/30 DATA(-1, -1) - + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1) + 1/30 DATA(-2, -1) + + 1/20 DATA(0, -1) - 1/30 DATA(1, -1) + 1/120 DATA(-2, -1) - - 1/60 DATA(2, -2) - 1/60 DATA(-1, -2) - 1/60 DATA(0, -2) + + 1/120 DATA(2, -2) + 1/120 DATA(-2, -2) - 1/30 DATA(-1, -2) - 3 - - 1/60 DATA(1, -2) - 1/60 DATA(-2, -2)) y + (1/49 DATA(0, 0) + + 1/20 DATA(0, -2) - 1/30 DATA(1, -2) + 1/120 DATA(-2, 2) - + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) + 1/196 DATA(1, 1) + 1/98 DATA(-1, 0) + 4 + + 1/120 DATA(-2, 0) + 1/120 DATA(-2, 1)) x + (1/30 DATA(-2, -1) - + 1/196 DATA(1, -1) + 1/98 DATA(0, -1) + 1/196 DATA(-1, -1) + - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) - 1/30 DATA(2, 1) + 1/30 DATA(2, -1) - + 1/196 DATA(-1, 1) - 1/98 DATA(1, 2) + 1/49 DATA(2, 2) - 1/49 DATA(2, 0) + + 1/60 DATA(2, 2) + 1/60 DATA(1, 2) + 1/60 DATA(0, 2) + 1/60 DATA(-1, 2) - - 1/98 DATA(2, 1) - 1/98 DATA(-1, 2) - 1/49 DATA(0, 2) - 1/98 DATA(2, -1) + - 1/30 DATA(-1, 1) + 1/30 DATA(-1, -1) + 1/30 DATA(0, -1) - + 1/49 DATA(-2, 2) - 1/98 DATA(-2, 1) - 1/98 DATA(-2, -1) + + 1/30 DATA(1, -1) - 1/60 DATA(0, -2) - 1/60 DATA(2, -2) - - 1/49 DATA(-2, 0) + 1/49 DATA(2, -2) - 1/98 DATA(-1, -2) + - 1/60 DATA(-2, -2) - 1/60 DATA(-1, -2) - 1/60 DATA(1, -2) - 2 2 / - - 1/49 DATA(0, -2) - 1/98 DATA(1, -2) + 1/49 DATA(-2, -2)) x y + | - \ + 3 / 57 + + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1)) y + |- --- DATA(0, 0) + \ 196 - 37 37 37 37 - --- DATA(1, 1) - --- DATA(1, -1) + --- DATA(-1, -1) - --- DATA(-1, 1) - 300 300 300 300 + 53 83 181 113 + - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) + --- DATA(2, 1) + 196 735 1470 735 - 21 11 21 21 - + --- DATA(1, 2) - --- DATA(2, 2) + --- DATA(2, 1) - --- DATA(-1, 2) - 200 150 200 200 + 41 113 289 71 + - --- DATA(2, 0) + --- DATA(2, -1) - ---- DATA(2, 2) + ---- DATA(1, 2) + 196 735 5880 5880 - 21 11 21 21 - - --- DATA(2, -1) + --- DATA(-2, 2) - --- DATA(-2, 1) + --- DATA(-2, -1) - 200 150 200 200 + 191 71 53 181 + + ---- DATA(0, 2) + ---- DATA(-1, 2) - --- DATA(-1, 0) + ---- DATA(-1, 1) + 5880 5880 196 1470 - 11 21 21 11 \ - + --- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) - --- DATA(-2, -2)| - 150 200 200 150 / + 181 83 181 + + ---- DATA(-1, -1) + --- DATA(0, -1) + ---- DATA(1, -1) + 1470 735 1470 - x y + (- 1/70 DATA(0, 1) - 1/140 DATA(1, 1) + 1/140 DATA(1, -1) + 113 289 289 + + --- DATA(-2, -1) - ---- DATA(2, -2) - ---- DATA(-2, -2) + 735 5880 5880 - + 1/70 DATA(0, -1) + 1/140 DATA(-1, -1) - 1/140 DATA(-1, 1) + 71 191 71 + + ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(1, -2) + 5880 5880 5880 - - 1/70 DATA(1, 2) + 1/35 DATA(2, 2) + 1/70 DATA(2, 1) - 1/70 DATA(-1, 2) + 289 41 113 \ 2 / + - ---- DATA(-2, 2) - --- DATA(-2, 0) + --- DATA(-2, 1)| y + | + 5880 196 735 / \ - - 1/35 DATA(0, 2) - 1/70 DATA(2, -1) + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + 17 31 11 11 + --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(2, 1) - --- DATA(2, -1) + 105 210 105 105 - - 1/70 DATA(-2, -1) - 1/35 DATA(2, -2) + 1/70 DATA(-1, -2) + 31 17 + - --- DATA(2, 2) + 1/84 DATA(1, 2) + --- DATA(0, 2) + 1/84 DATA(-1, 2) + 420 420 - 2 - + 1/35 DATA(0, -2) + 1/70 DATA(1, -2) - 1/35 DATA(-2, -2)) x y + ( + 31 31 17 31 + + --- DATA(-1, 1) - --- DATA(-1, -1) - --- DATA(0, -1) - --- DATA(1, -1) + 210 210 105 210 - - 1/60 DATA(1, 1) + 1/60 DATA(1, -1) - 1/60 DATA(-1, -1) + 1/60 DATA(-1, 1) + 11 31 31 + - --- DATA(-2, -1) + --- DATA(2, -2) + --- DATA(-2, -2) + 105 420 420 - - 1/30 DATA(1, 2) + 1/60 DATA(2, 2) + 1/120 DATA(2, 1) + 1/30 DATA(-1, 2) + 17 31 + - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2) - --- DATA(-2, 2) + 420 420 - - 1/120 DATA(2, -1) - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1) + 11 \ /17 31 + + --- DATA(-2, 1)| y + |--- DATA(1, 0) + --- DATA(1, 1) + 1/84 DATA(2, 1) + 105 / \105 210 - + 1/120 DATA(-2, -1) - 1/60 DATA(2, -2) - 1/30 DATA(-1, -2) + 17 31 11 + + --- DATA(2, 0) + 1/84 DATA(2, -1) - --- DATA(2, 2) + --- DATA(1, 2) + 420 420 105 - 3 99 - + 1/30 DATA(1, -2) + 1/60 DATA(-2, -2)) x y - ---- DATA(1, 2) - 1225 + 11 17 31 31 + - --- DATA(-1, 2) - --- DATA(-1, 0) - --- DATA(-1, 1) - --- DATA(-1, -1) + 105 105 210 210 - 51 96 99 99 - + ---- DATA(2, 2) + ---- DATA(2, 0) - ---- DATA(2, 1) - ---- DATA(-1, 2) - 1225 1225 1225 1225 + 31 31 31 + + --- DATA(1, -1) - 1/84 DATA(-2, -1) - --- DATA(2, -2) + --- DATA(-2, -2) + 210 420 420 - 96 99 51 99 - + ---- DATA(0, 2) - ---- DATA(2, -1) + ---- DATA(-2, 2) - ---- DATA(-2, 1) - 1225 1225 1225 1225 + 11 11 31 17 + - --- DATA(-1, -2) + --- DATA(1, -2) + --- DATA(-2, 2) - --- DATA(-2, 0) + 105 105 420 420 - 99 96 51 - - ---- DATA(-2, -1) + ---- DATA(-2, 0) + ---- DATA(2, -2) - 1225 1225 1225 + \ 99 51 + - 1/84 DATA(-2, 1)| x - ---- DATA(-2, -1) + ---- DATA(2, -2) + / 1225 1225 - 99 96 99 - - ---- DATA(-1, -2) + ---- DATA(0, -2) - ---- DATA(1, -2) - 1225 1225 1225 + 51 99 96 + + ---- DATA(-2, -2) - ---- DATA(-1, -2) + ---- DATA(0, -2) + 1225 1225 1225 - 51 - + ---- DATA(-2, -2) + 99 51 96 + - ---- DATA(1, -2) + ---- DATA(-2, 2) + ---- DATA(-2, 0) + 1225 1225 1225 + + 99 + - ---- DATA(-2, 1) 1225 > # I > coeff_as_lc_of_data(%, posn_list_2d_size5); -bytes used=44033940, alloc=2162292, time=3.85 -bytes used=45039820, alloc=2162292, time=3.91 - 51 3 4 3 2 2 -[COEFF(-2, -2) = ---- + 1/60 x y + 1/120 x - 1/60 y - 1/35 x y - 1/35 x y - 1225 +bytes used=44043980, alloc=2096768, time=3.78 + 3 3 2 2 31 2 31 +[COEFF(-2, -2) = - 1/60 x + 1/60 x y + 1/49 x y + --- y - 1/35 x y + --- x + 420 420 - 4 289 2 2 2 31 3 31 11 - + 1/120 y - ---- x + 1/49 x y + --- y - 1/60 x + --- x - --- x y - 5880 420 420 150 + 289 2 4 4 51 3 3 2 + - ---- y + 1/120 x + 1/120 y + ---- + 1/60 x y - 1/60 y - 1/35 x y + 5880 1225 - 3 289 2 21 2 4 - + 1/60 x y - ---- y , COEFF(-1, -2) = --- x y - 1/70 x y + 1/120 y - 5880 200 + 289 2 11 3 71 2 2 + - ---- x - --- x y, COEFF(-1, -2) = - 1/60 y + ---- y - 1/70 x y + 5880 150 5880 - 3 3 99 113 2 71 2 11 3 - + 1/120 x y + 1/30 x - ---- + --- x + ---- y - --- x - 1/60 y - 1225 735 5880 105 + 11 113 2 21 2 2 3 4 3 + - --- x + --- x + --- x y - 1/98 x y + 1/30 x + 1/120 y - 1/30 x y + 105 735 200 - 4 3 2 2 2 - - 1/30 x - 1/30 x y - 1/84 y - 1/98 x y + 1/70 x y, COEFF(0, -2) = + 4 2 99 3 + - 1/30 x + 1/70 x y - ---- + 1/120 x y - 1/84 y, COEFF(0, -2) = + 1225 - 2 2 2 4 41 2 17 96 4 - 1/35 x y - 1/49 x y + 1/20 x - --- x - --- y + ---- + 1/120 y - 196 420 1225 + 2 2 2 41 2 4 191 2 3 4 + - 1/49 x y + 1/35 x y - --- x + 1/120 y + ---- y - 1/60 y + 1/20 x + 196 5880 - 3 191 2 2 2 99 - - 1/60 y + ---- y , COEFF(1, -2) = - 1/98 x y - ---- - 1/84 y - 5880 1225 + 17 96 3 4 3 + - --- y + ----, COEFF(1, -2) = - 1/60 y - 1/84 y - 1/30 x - 1/120 x y + 420 1225 - 2 113 2 3 4 3 2 - + 1/70 x y + --- x - 1/120 x y + 1/120 y + 1/30 x y + 1/70 x y - 735 + 2 3 113 2 11 4 2 99 + + 1/70 x y - 1/30 x + --- x + --- x + 1/120 y + 1/70 x y - ---- + 735 105 1225 - 21 4 3 71 2 11 3 - - --- x y - 1/30 x - 1/30 x + ---- y + --- x - 1/60 y , COEFF(2, -2) = - 200 5880 105 + 21 71 2 2 2 3 31 + - --- x y + ---- y - 1/98 x y + 1/30 x y, COEFF(2, -2) = - --- x + 200 5880 420 - 2 2 4 3 4 31 31 3 - 1/49 x y + 1/120 y - 1/60 x y + 1/120 x + --- y - --- x + 1/60 x - 420 420 + 11 2 51 289 2 3 2 3 + + --- x y - 1/35 x y + ---- - ---- y - 1/60 y + 1/35 x y + 1/60 x + 150 1225 5880 - 2 51 3 3 11 289 2 2 - - 1/35 x y + ---- - 1/60 x y - 1/60 y + --- x y - ---- y + 1/35 x y - 1225 150 5880 + 3 31 4 4 2 2 289 2 + - 1/60 x y + --- y + 1/120 x + 1/120 y + 1/49 x y - ---- x + 420 5880 - 289 2 2 2 2 4 - - ---- x , COEFF(-2, -1) = - 1/98 x y + 1/70 x y + 1/120 x - 5880 + 3 3 21 2 11 + - 1/60 x y , COEFF(-2, -1) = 1/120 x y + --- x y + 1/70 x y - --- y + 200 105 - 3 11 21 71 2 2 3 - + 1/120 x y - --- y + --- x y + ---- x - 1/70 x y + 1/30 y - 1/84 x - 105 200 5880 + 4 99 113 2 2 2 2 3 + - 1/30 y - ---- + --- y - 1/98 x y - 1/70 x y - 1/30 x y - 1/84 x + 1225 735 - 3 3 113 2 4 99 24 - - 1/60 x - 1/30 x y + --- y - 1/30 y - ----, COEFF(-1, -1) = - ---- - 735 1225 1225 + 71 2 3 4 3 2 + + ---- x - 1/60 x + 1/120 x + 1/30 y , COEFF(-1, -1) = 1/140 x y + 5880 - 31 4 181 2 2 31 3 3 - - --- x - 1/30 y + ---- x + 1/140 x y - --- y - 1/60 x y + 1/30 y - 210 1470 210 + 37 2 2 4 3 181 2 2 + + --- x y + 1/196 x y - 1/30 x - 1/60 x y + ---- x + 1/140 x y + 300 1470 - 4 3 3 181 2 37 2 2 - - 1/30 x + 1/30 x - 1/60 x y + ---- y + --- x y + 1/196 x y - 1470 300 + 3 24 31 31 3 181 2 3 4 + + 1/30 y - ---- - --- x - --- y + 1/30 x + ---- y - 1/60 x y - 1/30 y + 1225 210 210 1470 - 2 246 83 2 3 53 2 17 - + 1/140 x y , COEFF(0, -1) = ---- + --- y + 1/30 y - --- x - --- y - 1225 735 196 105 + 53 2 2 2 2 17 83 2 246 + , COEFF(0, -1) = - --- x + 1/98 x y + 1/70 x y - --- y + --- y + ---- + 196 105 735 1225 - 2 4 2 2 4 181 2 - + 1/70 x y + 1/20 x + 1/98 x y - 1/30 y , COEFF(1, -1) = ---- y - 1470 + 4 3 4 2 37 + - 1/30 y + 1/30 y + 1/20 x , COEFF(1, -1) = 1/140 x y - --- x y + 300 - 4 4 3 3 24 181 2 2 - - 1/30 x - 1/30 y - 1/30 x + 1/60 x y - ---- + ---- x + 1/140 x y - 1225 1470 + 2 3 24 3 31 181 2 181 2 + - 1/140 x y + 1/60 x y - ---- - 1/30 x + --- x + ---- y + ---- x + 1225 210 1470 1470 - 37 31 2 3 3 2 2 31 - - --- x y - --- y - 1/140 x y + 1/30 y + 1/60 x y + 1/196 x y + --- x - 300 210 210 + 4 31 3 4 2 2 3 + - 1/30 x - --- y + 1/30 y - 1/30 y + 1/196 x y + 1/60 x y , + 210 - 3 21 4 2 2 2 - , COEFF(2, -1) = 1/30 x y - --- x y - 1/30 y - 1/70 x y - 1/98 x y - 200 + 3 3 99 3 2 + COEFF(2, -1) = - 1/120 x y + 1/30 x y - ---- + 1/60 x - 1/70 x y + 1225 - 99 11 71 2 113 2 3 2 - - ---- + 1/84 x - --- y + ---- x + --- y + 1/30 y - 1/70 x y - 1225 105 5880 735 + 4 21 2 2 71 2 3 11 + - 1/30 y - --- x y + 1/84 x - 1/98 x y + ---- x + 1/30 y - --- y + 200 5880 105 - 4 3 3 4 3 - + 1/120 x - 1/120 x y + 1/60 x , COEFF(-2, 0) = 1/120 x - 1/60 x + 113 2 2 4 96 41 2 4 + + --- y - 1/70 x y + 1/120 x , COEFF(-2, 0) = ---- - --- y + 1/120 x + 735 1225 196 - 191 2 17 2 2 4 2 41 2 96 - + ---- x - --- x - 1/49 x y + 1/20 y + 1/35 x y - --- y + ----, - 5880 420 196 1225 + 3 191 2 4 2 17 2 2 + - 1/60 x + ---- x + 1/20 y + 1/35 x y - --- x - 1/49 x y , + 5880 420 - 4 17 83 2 246 53 2 4 - COEFF(-1, 0) = 1/20 y - --- x + --- x + ---- - --- y - 1/30 x - 105 735 1225 196 + 53 2 4 83 2 246 3 2 + COEFF(-1, 0) = - --- y - 1/30 x + --- x + ---- + 1/30 x + 1/70 x y + 196 735 1225 - 2 3 2 2 - + 1/70 x y + 1/30 x + 1/98 x y , + 4 2 2 17 + + 1/20 y + 1/98 x y - --- x, + 105 - 57 2 4 4 57 2 2 2 541 - COEFF(0, 0) = - --- x + 1/20 y + 1/20 x - --- y + 1/49 x y + ----, - 196 196 1225 + 541 57 2 4 4 2 2 57 2 + COEFF(0, 0) = ---- - --- y + 1/20 x + 1/20 y + 1/49 x y - --- x , + 1225 196 196 - 246 17 2 53 2 4 4 - COEFF(1, 0) = ---- + --- x - 1/70 x y - --- y - 1/30 x + 1/20 y - 1225 105 196 + 4 2 83 2 2 2 53 2 246 + COEFF(1, 0) = - 1/30 x - 1/70 x y + --- x + 1/98 x y - --- y + ---- + 735 196 1225 - 3 83 2 2 2 2 4 - - 1/30 x + --- x + 1/98 x y , COEFF(2, 0) = - 1/35 x y + 1/20 y - 735 + 3 17 4 17 4 191 2 + - 1/30 x + --- x + 1/20 y , COEFF(2, 0) = --- x + 1/20 y + ---- x + 105 420 5880 - 4 96 3 17 2 2 41 2 191 2 - + 1/120 x + ---- + 1/60 x + --- x - 1/49 x y - --- y + ---- x , - 1225 420 196 5880 + 4 2 96 41 2 2 2 3 + + 1/120 x - 1/35 x y + ---- - --- y - 1/49 x y + 1/60 x , + 1225 196 - 2 2 3 99 3 2 11 - COEFF(-2, 1) = - 1/98 x y - 1/60 x - ---- - 1/30 y + 1/70 x y + --- y - 1225 105 + 113 2 71 2 21 3 2 + COEFF(-2, 1) = --- y + ---- x - 1/84 x - --- x y - 1/60 x + 1/70 x y + 735 5880 200 - 2 4 113 2 3 4 3 - + 1/70 x y - 1/30 y + --- y + 1/30 x y + 1/120 x - 1/120 x y - 735 + 3 11 99 3 3 2 2 4 + - 1/120 x y + --- y - ---- - 1/30 y + 1/30 x y - 1/98 x y + 1/120 x + 105 1225 - 21 71 2 2 2 3 - - 1/84 x - --- x y + ---- x , COEFF(-1, 1) = 1/196 x y + 1/30 x - 200 5880 + 2 4 181 2 3 37 + + 1/70 x y - 1/30 y , COEFF(-1, 1) = ---- y + 1/60 x y - --- x y + 1470 300 - 3 2 4 3 37 31 31 - + 1/60 x y - 1/140 x y - 1/30 x + 1/60 x y - --- x y - --- x + --- y - 300 210 210 + 2 2 2 4 2 3 4 + + 1/196 x y - 1/140 x y - 1/30 x + 1/140 x y + 1/30 x - 1/30 y - 181 2 2 3 24 181 2 4 - + ---- y + 1/140 x y - 1/30 y - ---- + ---- x - 1/30 y , COEFF(0, 1) - 1470 1225 1470 + 181 2 3 31 3 31 24 + + ---- x - 1/30 y - --- x + 1/60 x y + --- y - ----, COEFF(0, 1) = + 1470 210 210 1225 - 3 2 2 53 2 246 4 17 2 - = - 1/30 y + 1/98 x y - --- x + ---- - 1/30 y + --- y - 1/70 x y - 196 1225 105 + 4 2 53 2 83 2 3 246 4 + - 1/30 y - 1/70 x y - --- x + --- y - 1/30 y + ---- + 1/20 x + 196 735 1225 - 4 83 2 3 24 3 - + 1/20 x + --- y , COEFF(1, 1) = - 1/30 y - ---- - 1/60 x y - 735 1225 + 2 2 17 2 31 2 + + 1/98 x y + --- y, COEFF(1, 1) = - 1/140 x y + --- x - 1/140 x y + 105 210 - 2 2 37 3 181 2 31 4 31 - + 1/196 x y + --- x y - 1/60 x y + ---- x + --- y - 1/30 y + --- x - 300 1470 210 210 + 181 2 37 181 2 4 3 31 24 + + ---- x + --- x y + ---- y - 1/30 x - 1/60 x y + --- y - ---- + 1470 300 1470 210 1225 - 4 2 3 181 2 2 - - 1/30 x - 1/140 x y - 1/30 x + ---- y - 1/140 x y, COEFF(2, 1) = - 1470 + 3 2 2 4 3 3 + - 1/30 x + 1/196 x y - 1/30 y - 1/30 y - 1/60 x y , COEFF(2, 1) = - 3 113 2 3 2 2 21 - - 1/30 x y + 1/84 x + --- y + 1/120 x y - 1/98 x y + --- x y - 735 200 + 2 2 2 113 2 4 4 3 + - 1/70 x y - 1/98 x y + --- y - 1/30 y + 1/120 x - 1/30 y + 735 - 2 99 4 71 2 3 11 4 - - 1/70 x y - ---- - 1/30 y + ---- x + 1/60 x + --- y + 1/120 x - 1225 5880 105 + 3 11 2 99 71 2 3 + + 1/120 x y + 1/84 x + --- y + 1/70 x y - ---- + ---- x + 1/60 x + 105 1225 5880 - 3 2 2 3 11 - - 1/30 y + 1/70 x y, COEFF(-2, 2) = 1/35 x y - 1/60 x y + --- x y - 150 + 21 3 4 2 3 + + --- x y - 1/30 x y , COEFF(-2, 2) = 1/120 x - 1/35 x y - 1/60 x + 200 - 2 31 289 2 4 2 2 289 2 31 - - 1/35 x y - --- y - ---- y + 1/120 y + 1/49 x y - ---- x + --- x - 420 5880 5880 420 + 3 11 31 2 2 31 289 2 2 + - 1/60 x y + --- x y + --- x + 1/49 x y - --- y - ---- y + 1/35 x y + 150 420 420 5880 - 3 4 3 51 3 99 - - 1/60 x y + 1/120 x + 1/60 y + ---- - 1/60 x , COEFF(-1, 2) = - ---- - 1225 1225 + 4 3 51 289 2 3 + + 1/120 y - 1/60 x y + ---- - ---- x + 1/60 y , COEFF(-1, 2) = + 1225 5880 - 3 21 71 2 2 2 2 - - 1/120 x y - --- x y + 1/84 y + ---- y - 1/98 x y - 1/70 x y - 200 5880 + 3 99 2 113 2 11 3 2 2 + - 1/120 x y - ---- - 1/70 x y + --- x - --- x + 1/60 y - 1/98 x y + 1225 735 105 - 113 2 4 3 4 3 11 3 - + --- x - 1/30 x + 1/30 x y + 1/120 y + 1/30 x - --- x + 1/60 y - 735 105 + 3 3 71 2 21 2 4 + + 1/30 x + 1/84 y + 1/30 x y + ---- y - --- x y - 1/70 x y - 1/30 x + 5880 200 - 2 4 2 17 41 2 191 2 - - 1/70 x y, COEFF(0, 2) = 1/20 x - 1/35 x y + --- y - --- x + ---- y - 420 196 5880 + 4 96 4 191 2 17 4 + + 1/120 y , COEFF(0, 2) = ---- + 1/120 y + ---- y + --- y + 1/20 x + 1225 5880 420 - 96 4 2 2 3 99 - + ---- + 1/120 y - 1/49 x y + 1/60 y , COEFF(1, 2) = - ---- - 1225 1225 + 2 41 2 3 2 2 99 + - 1/35 x y - --- x + 1/60 y - 1/49 x y , COEFF(1, 2) = - ---- + 196 1225 - 2 2 2 3 71 2 3 - - 1/98 x y - 1/70 x y - 1/30 x y + 1/84 y + ---- y + 1/120 x y - 5880 + 3 71 2 4 3 2 2 + + 1/120 x y + ---- y + 1/120 y + 1/84 y + 1/60 y - 1/98 x y + 5880 - 3 4 4 11 113 2 2 21 - - 1/30 x - 1/30 x + 1/120 y + --- x + --- x + 1/70 x y + --- x y - 105 735 200 + 2 3 4 21 3 11 113 2 + + 1/70 x y - 1/30 x y - 1/30 x + --- x y - 1/30 x + --- x + --- x + 200 105 735 - 3 2 4 2 2 289 2 - + 1/60 y , COEFF(2, 2) = 1/35 x y + 1/120 x + 1/49 x y - ---- y - 5880 + 2 4 289 2 3 289 2 + - 1/70 x y, COEFF(2, 2) = 1/120 y - ---- x + 1/60 y - ---- y + 5880 5880 - 3 3 31 4 289 2 3 2 - + 1/60 x y + 1/60 x y - --- y + 1/120 y - ---- x + 1/60 x + 1/35 x y - 420 5880 + 2 31 4 3 3 51 3 + + 1/35 x y - --- y + 1/120 x + 1/60 x y + 1/60 x + ---- + 1/60 x y + 420 1225 - 11 31 51 3 - - --- x y - --- x + ---- + 1/60 y ] - 150 420 1225 + 11 2 2 31 2 + - --- x y + 1/49 x y - --- x + 1/35 x y] + 150 420 > print_coeff__lc_of_data(%, "coeff_I_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-I.compute.c"); -bytes used=46039980, alloc=2162292, time=4.00 -bytes used=47040144, alloc=2162292, time=4.08 -bytes used=48048756, alloc=2162292, time=4.16 -bytes used=49050036, alloc=2227816, time=4.23 -bytes used=50050424, alloc=2227816, time=4.33 -bytes used=51050604, alloc=2227816, time=4.48 -bytes used=52050764, alloc=2227816, time=4.55 -bytes used=53052936, alloc=2227816, time=4.64 -bytes used=54053412, alloc=2227816, time=4.74 -bytes used=55053604, alloc=2227816, time=4.89 -bytes used=56053828, alloc=2227816, time=4.95 -bytes used=57054040, alloc=2293340, time=5.07 -bytes used=58054312, alloc=2293340, time=5.26 -bytes used=59054740, alloc=2293340, time=5.33 -bytes used=60054904, alloc=2293340, time=5.43 -bytes used=61055148, alloc=2293340, time=5.58 -bytes used=62055404, alloc=2293340, time=5.65 -bytes used=63058408, alloc=2293340, time=5.83 -bytes used=64058672, alloc=2293340, time=5.89 -bytes used=65058956, alloc=2293340, time=6.08 -bytes used=66059172, alloc=2293340, time=6.16 +bytes used=45045780, alloc=2293340, time=3.86 +bytes used=46046060, alloc=2293340, time=3.93 +bytes used=47046296, alloc=2293340, time=4.01 +bytes used=48063992, alloc=2293340, time=4.08 +bytes used=49068776, alloc=2293340, time=4.17 +bytes used=50068940, alloc=2293340, time=4.33 +bytes used=51069184, alloc=2293340, time=4.41 +bytes used=52069472, alloc=2293340, time=4.49 +bytes used=53070464, alloc=2293340, time=4.59 +bytes used=54078496, alloc=2293340, time=4.74 +bytes used=55078844, alloc=2293340, time=4.86 +bytes used=56084964, alloc=2293340, time=4.95 +bytes used=57090392, alloc=2293340, time=5.12 +bytes used=58090872, alloc=2293340, time=5.24 +bytes used=59091028, alloc=2293340, time=5.31 +bytes used=60091208, alloc=2293340, time=5.48 +bytes used=61091384, alloc=2293340, time=5.56 +bytes used=62091584, alloc=2293340, time=5.65 +bytes used=63092040, alloc=2293340, time=5.82 +bytes used=64092228, alloc=2293340, time=5.91 +bytes used=65092808, alloc=2293340, time=6.08 > # d/dx > simplify( diff(interp_2d_cube_order4_smooth0,x) ); -bytes used=67059496, alloc=2293340, time=6.26 -bytes used=68059676, alloc=2293340, time=6.33 -bytes used=69060256, alloc=2358864, time=6.40 -17 31 17 31 ---- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, 0) + --- DATA(1, -1) -105 210 105 210 - - 31 31 11 31 - - --- DATA(-1, -1) - --- DATA(-1, 1) + --- DATA(1, 2) - --- DATA(2, 2) - 210 210 105 420 +bytes used=66093052, alloc=2293340, time=6.20 +bytes used=67093384, alloc=2424388, time=6.26 +bytes used=68093588, alloc=2424388, time=6.34 +bytes used=69093944, alloc=2424388, time=6.40 +17 31 3 3 +--- DATA(1, 0) + --- DATA(1, 1) + 1/30 x DATA(-2, 2) + 1/30 x DATA(-2, 0) +105 210 - 17 11 - + --- DATA(2, 0) + 1/84 DATA(2, 1) - --- DATA(-1, 2) + 1/84 DATA(2, -1) - 420 105 + 3 3 3 + + 1/30 x DATA(-2, 1) + 1/5 x DATA(0, -1) - 2/15 x DATA(1, -1) - 31 2 - + --- DATA(-2, 2) - 1/84 DATA(-2, 1) - 1/70 y DATA(2, 1) - 420 + 3 21 21 + + 1/30 x DATA(-2, -1) + --- y DATA(1, 2) - --- y DATA(-1, 2) + 200 200 - 2 2 2 - - 1/70 y DATA(-1, 2) - 1/70 y DATA(2, -1) - 1/35 y DATA(-2, 2) + 37 2 21 + - --- y DATA(-1, 1) + 2/49 x y DATA(0, 0) + --- y DATA(-1, -2) + 300 200 - 2 2 2 - + 1/70 y DATA(-2, 1) + 1/70 y DATA(-2, -1) + 1/35 y DATA(-2, 0) + 21 11 37 + - --- y DATA(1, -2) + --- y DATA(-2, 2) - --- y DATA(1, -1) + 200 150 300 - 2 2 2 - + 1/35 y DATA(2, -2) - 1/70 y DATA(-1, -2) + 1/35 y DATA(2, 2) + 37 21 21 + + --- y DATA(1, 1) + --- y DATA(2, 1) - --- y DATA(2, -1) + 300 200 200 - 2 2 2 - - 1/70 y DATA(1, 0) - 1/140 y DATA(1, 1) + 1/70 y DATA(-1, 0) + 11 2 3 + - --- y DATA(2, 2) + 1/49 x y DATA(0, 1) + 1/60 y DATA(2, 2) + 150 - 2 2 2 - - 1/140 y DATA(1, -1) + 1/140 y DATA(-1, -1) + 1/140 y DATA(-1, 1) + 3 3 2 + + 1/120 y DATA(1, 2) - 1/120 y DATA(-1, 2) + 1/140 y DATA(-1, 1) - - 1/35 x y DATA(-1, 2) - 2/35 x y DATA(0, 2) - 1/35 x y DATA(0, 1) + 2 2 2 + - 1/70 y DATA(2, -1) + 1/35 y DATA(2, 2) + 1/70 y DATA(1, 2) - 2 2 - - 1/20 x y DATA(-1, -1) - 1/20 x y DATA(1, 1) - 1/35 x y DATA(-2, -1) + 2 2 2 + - 1/70 y DATA(-1, 2) - 1/70 y DATA(1, 0) - 1/140 y DATA(1, 1) - - 2/35 x y DATA(2, -2) + 2/35 x y DATA(2, 2) + 1/35 x y DATA(2, 1) + 2 2 21 + - 1/70 y DATA(2, 1) - 1/35 y DATA(2, 0) - --- y DATA(-2, 1) + 200 - 37 2 2 - + --- y DATA(1, 1) - 1/49 x y DATA(-2, -1) + 2/49 x y DATA(2, -2) - 300 + 37 21 11 + + --- y DATA(-1, -1) + --- y DATA(-2, -1) + --- y DATA(2, -2) + 300 200 150 - 2 2 - - 1/49 x y DATA(-1, -2) - 1/49 x y DATA(1, -2) - 1/35 x y DATA(2, -1) + 11 2 2 + - --- y DATA(-2, -2) + 1/70 y DATA(1, -2) - 1/35 y DATA(-2, 2) + 150 - 21 - + 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1) - --- y DATA(-1, 2) - 200 + 2 2 3 + + 1/35 y DATA(-2, 0) + 1/70 y DATA(-2, 1) - 1/60 y DATA(1, 1) - 21 11 21 - - --- y DATA(2, -1) + --- y DATA(-2, 2) - --- y DATA(-2, 1) - 200 150 200 + 3 3 2 + - 1/30 y DATA(2, 1) + 1/30 y DATA(2, -1) + 1/10 x DATA(-1, 2) - 21 11 21 - + --- y DATA(-2, -1) + --- y DATA(2, -2) + --- y DATA(-1, -2) - 200 150 200 + 3 3 3 + - 1/30 y DATA(-2, -1) - 1/60 y DATA(2, -2) + 1/60 y DATA(-2, -2) - 21 11 37 - - --- y DATA(1, -2) - --- y DATA(-2, -2) - --- y DATA(1, -1) - 200 150 300 + 3 3 3 + + 1/120 y DATA(-1, -2) - 1/120 y DATA(1, -2) - 1/60 y DATA(-2, 2) - 2 2 2 - + 1/70 y DATA(1, -2) - 1/35 y DATA(-2, -2) + 1/70 y DATA(1, 2) + 3 3 3 + + 1/60 y DATA(-1, 1) - 1/60 y DATA(-1, -1) + 1/60 y DATA(1, -1) - 2 2 - - 1/35 y DATA(2, 0) + 1/35 x y DATA(-1, -2) - 2/49 x y DATA(0, 2) + 2 2 2 + + 1/70 y DATA(-1, 0) + 1/140 y DATA(-1, -1) - 1/140 y DATA(1, -1) - 2 2 2 - - 2/49 x y DATA(0, -2) + 1/49 x y DATA(-1, 0) - 2/49 x y DATA(2, 0) + 2 2 2 + + 1/70 y DATA(-2, -1) + 1/35 y DATA(2, -2) - 1/35 y DATA(-2, -2) - 2 - - 2/49 x y DATA(-2, 0) + 2/35 x y DATA(0, -2) + 1/35 x y DATA(1, -2) + 2 2 2 + - 1/70 y DATA(-1, -2) + 1/10 x DATA(-1, 0) - 1/20 x DATA(-2, -2) - 2 2 - - 2/35 x y DATA(-2, -2) - 1/49 x y DATA(2, 1) - 1/49 x y DATA(2, -1) + 2 2 2 + + 1/20 x DATA(2, 1) + 1/20 x DATA(2, 0) + 1/20 x DATA(2, -1) - 2 2 37 - + 2/49 x y DATA(-2, 2) - 1/49 x y DATA(-2, 1) + --- y DATA(-1, -1) - 300 + 2 2 2 + + 1/20 x DATA(2, 2) - 1/10 x DATA(1, 2) + 1/20 x y DATA(2, 2) - 3 3 3 - + 1/30 y DATA(-2, 1) + 1/60 y DATA(-1, 1) - 1/60 y DATA(1, 1) + 2 2 2 + - 1/20 x DATA(-2, -1) + 1/20 x DATA(2, -2) - 1/20 x DATA(-2, 0) - 3 37 21 - + 1/60 y DATA(1, -1) - --- y DATA(-1, 1) + --- y DATA(1, 2) - 300 200 + 3 2 2 + + 1/30 y DATA(-2, 1) - 1/10 x DATA(1, 0) - 1/10 x DATA(1, 1) - 11 21 3 - - --- y DATA(2, 2) + --- y DATA(2, 1) + 1/60 y DATA(-2, -2) - 150 200 + 41 289 191 + - -- x DATA(0, -2) - ---- x DATA(-2, 2) + ---- x DATA(-2, 0) + 98 2940 2940 - 71 289 71 - + ---- x DATA(2, -1) - ---- x DATA(-2, 2) + ---- x DATA(-2, 1) - 2940 2940 2940 + 289 2 2 + - ---- x DATA(2, 2) + 1/10 x DATA(-1, -2) - 1/10 x DATA(1, -2) + 2940 - 71 289 226 - + ---- x DATA(-2, -1) - ---- x DATA(2, -2) + --- x DATA(-1, -2) - 2940 2940 735 + 2 2 57 + - 1/20 x DATA(-2, 2) - 1/20 x DATA(-2, 1) - -- x DATA(0, 0) + 98 - 226 289 53 - + --- x DATA(1, -2) - ---- x DATA(-2, -2) - -- x DATA(0, 1) - 735 2940 98 + 53 71 191 + - -- x DATA(0, 1) + ---- x DATA(2, 1) + ---- x DATA(2, 0) + 98 2940 2940 - 53 41 41 - - -- x DATA(0, -1) - -- x DATA(0, 2) - -- x DATA(0, -2) - 98 98 98 + 2 2 2 + + 1/10 x DATA(-1, 1) + 1/10 x DATA(-1, -1) - 1/10 x DATA(1, -1) - 166 3 3 - + --- x DATA(-1, 0) - 1/60 y DATA(2, -2) - 1/60 y DATA(-1, -1) + 226 3 3 + + --- x DATA(1, -2) - 2/15 x DATA(1, 1) - 2/15 x DATA(-1, -2) 735 - 3 3 3 - + 1/120 y DATA(1, 2) + 1/60 y DATA(2, 2) - 1/30 y DATA(2, 1) + 71 181 71 + + ---- x DATA(-2, 1) + --- x DATA(1, -1) + ---- x DATA(-2, -1) + 2940 735 2940 - 3 3 3 - - 1/120 y DATA(-1, 2) + 1/30 y DATA(2, -1) - 1/60 y DATA(-2, 2) + 289 289 226 + - ---- x DATA(2, -2) - ---- x DATA(-2, -2) + --- x DATA(1, 2) + 2940 2940 735 - 71 191 3 - + ---- x DATA(2, 1) + ---- x DATA(-2, 0) - 1/30 y DATA(-2, -1) - 2940 2940 + 41 226 181 + - -- x DATA(0, 2) + --- x DATA(-1, 2) + --- x DATA(-1, 1) + 98 735 735 - 3 3 191 - + 1/120 y DATA(-1, -2) - 1/120 y DATA(1, -2) + ---- x DATA(2, 0) - 2940 + 53 71 166 + - -- x DATA(0, -1) + ---- x DATA(2, -1) + --- x DATA(1, 0) + 98 2940 735 - 17 3 - - 1/84 DATA(-2, -1) - --- DATA(-2, 0) - 2/15 x DATA(1, -2) - 420 + 181 226 3 + + --- x DATA(1, 1) + --- x DATA(-1, -2) - 2/15 x DATA(-1, 1) + 735 735 - 3 3 3 - + 1/30 x DATA(-2, -2) + 1/5 x DATA(0, 1) + 1/5 x DATA(0, -1) + 3 181 166 + - 2/15 x DATA(-1, 0) + --- x DATA(-1, -1) + --- x DATA(-1, 0) + 735 735 - 3 3 3 - + 1/5 x DATA(0, 2) + 1/5 x DATA(0, -2) - 2/15 x DATA(-1, 0) + 3 3 3 + + 1/5 x DATA(0, 0) + 1/5 x DATA(0, 1) + 1/30 x DATA(2, 1) - 3 3 57 - + 1/30 x DATA(2, 0) + 1/30 x DATA(-2, 0) - -- x DATA(0, 0) - 98 + 3 3 3 + + 1/30 x DATA(2, 0) + 1/30 x DATA(2, -1) + 1/30 x DATA(2, 2) - 226 181 181 - + --- x DATA(-1, 2) + --- x DATA(1, 1) + --- x DATA(1, -1) - 735 735 735 + 3 3 3 + - 2/15 x DATA(1, 0) - 2/15 x DATA(-1, -1) + 1/5 x DATA(0, -2) - 181 181 226 - + --- x DATA(-1, -1) + --- x DATA(-1, 1) + --- x DATA(1, 2) - 735 735 735 + 17 31 + + 1/84 DATA(2, 1) + --- DATA(2, 0) + 1/84 DATA(2, -1) - --- DATA(2, 2) + 420 420 - 289 166 3 - - ---- x DATA(2, 2) + --- x DATA(1, 0) - 2/15 x DATA(-1, 2) - 2940 735 + 11 11 17 31 + + --- DATA(1, 2) - --- DATA(-1, 2) - --- DATA(-1, 0) - --- DATA(-1, 1) + 105 105 105 210 - 3 3 3 - - 2/15 x DATA(1, 1) - 2/15 x DATA(1, -1) - 2/15 x DATA(-1, -1) + 31 31 2 + - --- DATA(-1, -1) + --- DATA(1, -1) + 1/49 x y DATA(0, -1) + 210 210 - 3 3 3 - - 2/15 x DATA(-1, 1) + 1/30 x DATA(2, 1) + 1/30 x DATA(2, -1) + 2 2 2 + - 2/49 x y DATA(-2, 0) - 1/49 x y DATA(1, 2) + 1/98 x y DATA(-1, 1) - 3 3 3 - + 1/30 x DATA(-2, 2) + 1/30 x DATA(-2, 1) + 1/30 x DATA(-2, -1) + 2 2 2 + + 1/40 x y DATA(2, 1) - 1/49 x y DATA(-2, -1) - 1/49 x y DATA(2, -1) - 3 3 2 - + 1/30 x DATA(2, -2) - 2/15 x DATA(-1, -2) - 1/20 x DATA(-2, -2) + 2 2 2 + - 2/49 x y DATA(0, 2) - 1/49 x y DATA(1, -2) + 1/49 x y DATA(1, 0) - 3 3 3 - - 2/15 x DATA(1, 2) + 1/30 x DATA(2, 2) - 2/15 x DATA(1, 0) + 2 2 2 + + 2/49 x y DATA(2, -2) - 1/49 x y DATA(-1, -2) - 2/49 x y DATA(0, -2) - 2 2 2 - - 1/10 x DATA(1, 0) - 1/10 x DATA(1, 1) + 1/10 x DATA(-1, 0) + 2 2 2 + - 1/20 x y DATA(1, 1) - 1/40 x y DATA(2, -1) - 1/49 x y DATA(2, 1) - 2 2 2 - - 1/10 x DATA(1, -1) + 1/10 x DATA(-1, -1) + 1/10 x DATA(-1, 1) + 2 2 2 + - 2/49 x y DATA(2, 0) + 2/49 x y DATA(-2, 2) + 2/49 x y DATA(2, 2) - 3 2 2 - + 1/5 x DATA(0, 0) - 1/10 x y DATA(-1, -2) + 1/20 x y DATA(1, -1) + 2 2 2 + + 1/98 x y DATA(1, -1) + 1/98 x y DATA(1, 1) + 2/49 x y DATA(-2, -2) - 2 2 2 - + 1/40 x y DATA(-2, -1) - 1/49 x y DATA(1, 2) + 2/49 x y DATA(2, 2) + 2 2 2 + + 1/20 x y DATA(1, -1) + 1/40 x y DATA(-2, -1) - 1/20 x y DATA(2, -2) - 2 2 2 - + 1/49 x y DATA(1, 0) + 2/49 x y DATA(0, 0) - 1/49 x y DATA(-1, 2) + 2 2 2 + + 1/20 x y DATA(-2, -2) - 1/10 x y DATA(-1, -2) + 1/10 x y DATA(1, -2) - 2 2 2 - + 1/98 x y DATA(1, 1) + 1/98 x y DATA(1, -1) + 1/98 x y DATA(-1, -1) + 2 2 + - 1/20 x y DATA(-2, 2) - 1/40 x y DATA(-2, 1) - 1/35 x y DATA(0, 1) - 2 2 2 - + 1/98 x y DATA(-1, 1) + 2/49 x y DATA(-2, -2) + 1/49 x y DATA(0, 1) + + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(1, 1) + 1/35 x y DATA(2, 1) - 2 - + 1/49 x y DATA(0, -1) - 1/35 x y DATA(1, 2) + 1/70 x y DATA(1, -1) + - 1/35 x y DATA(2, -1) + 2/35 x y DATA(2, 2) - 1/35 x y DATA(1, 2) - 2 2 - + 1/35 x y DATA(0, -1) + 1/10 x y DATA(1, -2) + 1/10 x y DATA(-1, 2) + 2 + - 2/35 x y DATA(0, 2) - 1/35 x y DATA(-1, 2) - 1/10 x y DATA(1, 2) - 2 31 - - 1/40 x y DATA(-2, 1) - 1/70 x y DATA(1, 1) - --- DATA(2, -2) - 420 + 2 2 2 + + 1/10 x y DATA(-1, 2) + 1/20 x y DATA(-1, 1) - 1/20 x y DATA(-1, -1) - 11 11 2 - - --- DATA(-1, -2) + --- DATA(1, -2) - 1/40 x y DATA(2, -1) - 105 105 + + 1/35 x y DATA(1, -2) + 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1) - 2 2 2 - + 1/20 x y DATA(-2, -2) - 1/10 x y DATA(1, 2) + 1/40 x y DATA(2, 1) + 2 2 + - 1/70 x y DATA(-1, 1) + 1/98 x y DATA(-1, -1) + 1/49 x y DATA(-1, 0) - 2 2 2 - + 1/20 x y DATA(2, 2) - 1/20 x y DATA(2, -2) - 1/20 x y DATA(-2, 2) + + 1/35 x y DATA(0, -1) + 1/70 x y DATA(1, -1) - 1/35 x y DATA(-2, -1) - 2 - + 1/20 x y DATA(-1, 1) + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(-1, 1) + - 2/35 x y DATA(2, -2) - 2/35 x y DATA(-2, -2) + 1/35 x y DATA(-1, -2) - 2 2 2 - - 1/10 x DATA(1, 2) + 1/20 x DATA(2, 0) + 1/20 x DATA(2, 1) + 2 2 + + 2/35 x y DATA(0, -2) - 1/49 x y DATA(-2, 1) - 1/49 x y DATA(-1, 2) - 2 2 2 - + 1/10 x DATA(-1, 2) + 1/20 x DATA(2, -1) + 1/20 x DATA(2, 2) + 31 31 + - 1/84 DATA(-2, -1) - --- DATA(2, -2) + --- DATA(-2, -2) + 420 420 - 2 2 2 - - 1/20 x DATA(-2, 2) - 1/20 x DATA(-2, 1) - 1/20 x DATA(-2, -1) + 11 11 31 17 + - --- DATA(-1, -2) + --- DATA(1, -2) + --- DATA(-2, 2) - --- DATA(-2, 0) + 105 105 420 420 - 2 2 2 - - 1/20 x DATA(-2, 0) + 1/20 x DATA(2, -2) + 1/10 x DATA(-1, -2) + 3 3 + - 1/84 DATA(-2, 1) - 2/15 x DATA(1, -2) + 1/30 x DATA(2, -2) - 2 31 - - 1/10 x DATA(1, -2) + --- DATA(-2, -2) - 420 + 3 3 3 + + 1/30 x DATA(-2, -2) - 2/15 x DATA(1, 2) + 1/5 x DATA(0, 2) + + 3 + - 2/15 x DATA(-1, 2) > coeff_as_lc_of_data(%, posn_list_2d_size5); -bytes used=70063472, alloc=2424388, time=6.47 - 31 3 2 11 3 -[COEFF(-2, -2) = --- + 1/60 y - 2/35 x y + 2/49 x y - --- y + 1/30 x - 420 150 +bytes used=70094424, alloc=2424388, time=6.48 + 2 2 289 2 3 +[COEFF(-2, -2) = 2/49 x y - 2/35 x y - 1/35 y - ---- x + 1/20 x y + 1/30 x + 2940 - 2 2 2 289 2 - - 1/20 x + 1/20 x y - 1/35 y - ---- x, COEFF(-1, -2) = - 1/10 x y - 2940 + 31 11 2 3 2 2 + + --- - --- y - 1/20 x + 1/60 y , COEFF(-1, -2) = - 1/10 x y - 1/70 y + 420 150 - 2 2 3 2 226 11 - - 1/70 y - 1/49 x y + 1/120 y + 1/10 x + --- x - --- + 1/35 x y - 735 105 + 3 3 2 21 2 226 + + 1/120 y - 2/15 x + 1/35 x y + 1/10 x + --- y - 1/49 x y + --- x + 200 735 - 21 3 2 41 3 - + --- y - 2/15 x , COEFF(0, -2) = - 2/49 x y - -- x + 1/5 x + 2/35 x y, - 200 98 + 11 3 41 2 + - ---, COEFF(0, -2) = 1/5 x - -- x + 2/35 x y - 2/49 x y , COEFF(1, -2) + 105 98 - 3 2 3 2 - COEFF(1, -2) = - 2/15 x - 1/49 x y - 1/120 y - 1/10 x + 1/35 x y + 2 2 2 3 2 + = - 1/49 x y + 1/10 x y + 1/35 x y + 1/70 y - 2/15 x - 1/10 x - 21 226 11 2 2 11 - - --- y + --- x + --- + 1/10 x y + 1/70 y , COEFF(2, -2) = --- y - 200 735 105 150 + 3 226 11 21 31 + - 1/120 y + --- x + --- - --- y, COEFF(2, -2) = - 2/35 x y - --- + 735 105 200 420 - 2 2 2 31 289 3 3 - + 2/49 x y + 1/20 x + 1/35 y - --- - ---- x - 1/60 y + 1/30 x - 420 2940 + 3 2 3 2 2 289 2 + + 1/30 x + 1/20 x - 1/60 y - 1/20 x y + 2/49 x y - ---- x + 1/35 y + 2940 - 2 3 21 3 - - 2/35 x y - 1/20 x y, COEFF(-2, -1) = 1/30 x + --- y - 1/30 y - 200 + 11 2 3 2 + + --- y, COEFF(-2, -1) = - 1/49 x y - 1/30 y - 1/35 x y - 1/20 x + 150 - 2 2 2 71 2 - - 1/49 x y - 1/35 x y + 1/40 x y + 1/70 y + ---- x - 1/20 x - 1/84, - 2940 + 2 71 21 3 2 + + 1/70 y + ---- x - 1/84 + --- y + 1/30 x + 1/40 x y, COEFF(-1, -1) = + 2940 200 - 3 31 2 3 2 - COEFF(-1, -1) = - 2/15 x - --- + 1/140 y + 1/70 x y - 1/60 y - 1/20 x y - 210 + 3 2 37 31 2 2 3 + 1/70 x y - 1/60 y + 1/98 x y + --- y - --- + 1/10 x + 1/140 y - 2/15 x + 300 210 - 37 2 2 181 - + --- y + 1/10 x + 1/98 x y + --- x, - 300 735 + 181 2 53 2 3 + + --- x - 1/20 x y, COEFF(0, -1) = - -- x + 1/35 x y + 1/49 x y + 1/5 x , + 735 98 - 3 2 53 3 - COEFF(0, -1) = 1/35 x y + 1/5 x + 1/49 x y - -- x, COEFF(1, -1) = 1/60 y - 98 + 2 181 2 2 2 3 + COEFF(1, -1) = 1/98 x y + --- x + 1/20 x y - 1/140 y - 1/10 x + 1/60 y + 735 - 3 2 2 31 2 181 - - 2/15 x + 1/20 x y - 1/10 x + --- + 1/98 x y + --- x + 1/70 x y - 210 735 + 3 31 37 21 + - 2/15 x + --- - --- y + 1/70 x y, COEFF(2, -1) = - --- y + 1/84 + 210 300 200 - 2 37 2 2 - - 1/140 y - --- y, COEFF(2, -1) = - 1/70 y - 1/49 x y - 1/35 x y - 300 + 3 71 2 2 3 2 + + 1/30 y + ---- x + 1/20 x - 1/70 y - 1/35 x y + 1/30 x - 1/49 x y + 2940 - 21 2 3 3 2 71 - - --- y - 1/40 x y + 1/30 x + 1/30 y + 1/84 + 1/20 x + ---- x, - 200 2940 + 2 + - 1/40 x y, - 2 2 191 3 2 17 - COEFF(-2, 0) = - 2/49 x y + 1/35 y + ---- x + 1/30 x - 1/20 x - ---, - 2940 420 + 2 2 191 17 2 3 + COEFF(-2, 0) = - 1/20 x - 2/49 x y + ---- x - --- + 1/35 y + 1/30 x , + 2940 420 - 2 17 166 2 2 3 - COEFF(-1, 0) = 1/49 x y - --- + --- x + 1/10 x + 1/70 y - 2/15 x , - 105 735 + 2 3 2 166 17 2 + COEFF(-1, 0) = 1/10 x - 2/15 x + 1/49 x y + --- x - --- + 1/70 y , + 735 105 - 57 3 2 - COEFF(0, 0) = - -- x + 1/5 x + 2/49 x y , - 98 + 2 3 57 + COEFF(0, 0) = 2/49 x y + 1/5 x - -- x, + 98 - 2 2 17 2 3 166 - COEFF(1, 0) = 1/49 x y - 1/70 y + --- - 1/10 x - 2/15 x + --- x, - 105 735 + 3 17 2 166 2 2 + COEFF(1, 0) = - 2/15 x + --- - 1/10 x + --- x - 1/70 y + 1/49 x y , + 105 735 - 2 2 17 2 3 191 - COEFF(2, 0) = - 1/35 y - 2/49 x y + --- + 1/20 x + 1/30 x + ---- x, - 420 2940 + 2 191 3 2 17 2 + COEFF(2, 0) = - 2/49 x y + ---- x + 1/30 x + 1/20 x + --- - 1/35 y , + 2940 420 - 3 3 2 2 71 - COEFF(-2, 1) = 1/30 y + 1/30 x - 1/49 x y + 1/35 x y + 1/70 y + ---- x - 2940 + 3 2 2 2 21 + COEFF(-2, 1) = 1/35 x y + 1/30 y - 1/49 x y + 1/70 y - 1/40 x y - --- y + 200 - 2 2 21 2 - - 1/20 x - 1/40 x y - --- y - 1/84, COEFF(-1, 1) = 1/20 x y - 1/70 x y - 200 + 2 71 3 2 3 + - 1/20 x - 1/84 + ---- x + 1/30 x , COEFF(-1, 1) = 1/20 x y + 1/60 y + 2940 - 2 2 2 181 3 3 31 37 - + 1/10 x + 1/98 x y + 1/140 y + --- x - 2/15 x + 1/60 y - --- - --- y - 735 210 300 + 181 37 2 2 3 31 + + --- x - --- y - 1/70 x y + 1/98 x y + 1/10 x - 2/15 x - --- + 735 300 210 - 53 2 3 181 - , COEFF(0, 1) = - -- x + 1/49 x y + 1/5 x - 1/35 x y, COEFF(1, 1) = --- x - 98 735 + 2 53 2 3 + + 1/140 y , COEFF(0, 1) = - -- x + 1/49 x y + 1/5 x - 1/35 x y, + 98 - 2 3 3 31 37 2 - - 1/10 x - 1/60 y - 2/15 x + --- + --- y - 1/140 y - 1/70 x y - 210 300 + 3 37 2 31 3 + COEFF(1, 1) = - 1/60 y + --- y - 1/70 x y - 1/10 x + --- - 2/15 x + 300 210 - 2 2 21 3 - + 1/98 x y - 1/20 x y, COEFF(2, 1) = --- y - 1/30 y + 1/35 x y - 200 + 2 2 181 2 2 + - 1/20 x y + 1/98 x y + --- x - 1/140 y , COEFF(2, 1) = - 1/49 x y + 735 - 2 71 2 3 2 2 - + 1/20 x + ---- x - 1/70 y + 1/30 x + 1/84 + 1/40 x y - 1/49 x y , - 2940 + 71 2 3 3 2 + + ---- x + 1/84 + 1/40 x y + 1/30 x + 1/35 x y - 1/30 y - 1/70 y + 2940 - 2 2 2 11 2 - COEFF(-2, 2) = - 1/20 x - 1/20 x y - 1/35 y + --- y + 2/49 x y - 150 + 2 21 11 3 2 + + 1/20 x + --- y, COEFF(-2, 2) = --- y + 2/35 x y - 1/60 y - 1/20 x y + 200 150 - 3 3 289 31 3 - - 1/60 y + 1/30 x + 2/35 x y - ---- x + ---, COEFF(-1, 2) = - 2/15 x - 2940 420 + 2 289 2 31 2 3 + + 2/49 x y - ---- x - 1/20 x + --- - 1/35 y + 1/30 x , COEFF(-1, 2) = + 2940 420 - 2 3 2 21 2 226 - - 1/35 x y + 1/10 x - 1/120 y + 1/10 x y - --- y - 1/49 x y + --- x - 200 735 + 2 3 2 2 226 11 + 1/10 x y - 1/120 y + 1/10 x - 1/49 x y - 1/35 x y + --- x - --- + 735 105 - 2 11 2 41 3 - - 1/70 y - ---, COEFF(0, 2) = - 2/35 x y - 2/49 x y - -- x + 1/5 x , - 105 98 + 3 21 2 + - 2/15 x - --- y - 1/70 y , + 200 - 11 2 2 3 2 - COEFF(1, 2) = --- - 1/10 x - 1/49 x y - 2/15 x - 1/35 x y + 1/70 y - 105 + 3 2 41 + COEFF(0, 2) = 1/5 x - 2/49 x y - 2/35 x y - -- x, COEFF(1, 2) = + 98 - 21 2 3 226 2 2 - + --- y - 1/10 x y + 1/120 y + --- x, COEFF(2, 2) = 1/20 x y + 1/35 y - 200 735 + 2 2 3 2 11 3 21 + - 1/49 x y - 1/10 x y + 1/120 y + 1/70 y + --- - 2/15 x + --- y + 105 200 - 31 2 11 3 289 2 - + 2/35 x y - --- + 1/20 x - --- y + 1/30 x - ---- x + 2/49 x y - 420 150 2940 + 226 2 2 11 2 + - 1/35 x y + --- x - 1/10 x , COEFF(2, 2) = 1/20 x - --- y + 1/35 y + 735 150 - 3 - + 1/60 y ] + 3 2 289 2 3 31 + + 2/35 x y + 1/30 x + 2/49 x y - ---- x + 1/20 x y + 1/60 y - ---] + 2940 420 > print_coeff__lc_of_data(%, "coeff_dx_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-dx.compute.c"); -bytes used=71064040, alloc=2424388, time=6.54 -bytes used=72064272, alloc=2424388, time=6.62 -bytes used=73075772, alloc=2424388, time=6.70 -bytes used=74075968, alloc=2424388, time=6.88 -bytes used=75076136, alloc=2424388, time=6.95 -bytes used=76076304, alloc=2424388, time=7.04 -bytes used=77076556, alloc=2424388, time=7.20 -bytes used=78076920, alloc=2424388, time=7.29 -bytes used=79077292, alloc=2424388, time=7.46 -bytes used=80077492, alloc=2424388, time=7.59 -bytes used=81077684, alloc=2424388, time=7.72 +bytes used=71095128, alloc=2424388, time=6.56 +bytes used=72109496, alloc=2424388, time=6.63 +bytes used=73109972, alloc=2424388, time=6.71 +bytes used=74110128, alloc=2424388, time=6.86 +bytes used=75111952, alloc=2424388, time=6.95 +bytes used=76112156, alloc=2424388, time=7.14 +bytes used=77115576, alloc=2424388, time=7.22 +bytes used=78115732, alloc=2424388, time=7.40 +bytes used=79116356, alloc=2424388, time=7.47 +bytes used=80116536, alloc=2424388, time=7.66 > # d/dy > simplify( diff(interp_2d_cube_order4_smooth0,y) ); -bytes used=82108412, alloc=2424388, time=7.80 -bytes used=83108600, alloc=2424388, time=7.88 - 17 31 2 -- 2/35 x y DATA(2, 0) + --- DATA(0, 1) + --- DATA(1, 1) + 1/35 x DATA(0, -2) - 105 210 - - 53 166 166 57 - - -- y DATA(1, 0) + --- y DATA(0, 1) + --- y DATA(0, -1) - -- y DATA(0, 0) - 98 735 735 98 - - 191 2 2 - + ---- y DATA(0, -2) + 1/20 y DATA(0, 2) - 1/20 y DATA(0, -2) - 2940 +bytes used=81117572, alloc=2424388, time=7.76 +bytes used=82118060, alloc=2424388, time=7.83 +bytes used=83118724, alloc=2489912, time=7.90 + 2 2 2 +- 1/10 y DATA(0, 1) - 1/20 y DATA(0, -2) + 1/10 y DATA(0, -1) - 3 3 3 - + 1/5 y DATA(-1, 0) + 1/5 y DATA(2, 0) + 1/5 y DATA(-2, 0) + 2 3 3 + + 1/20 y DATA(0, 2) + 1/5 y DATA(2, 0) + 1/5 y DATA(-1, 0) - 53 41 41 - - -- y DATA(-1, 0) - -- y DATA(2, 0) - -- y DATA(-2, 0) - 98 98 98 + 3 53 3 + + 1/5 y DATA(1, 0) - -- y DATA(-1, 0) + 1/30 y DATA(0, -2) + 98 - 191 2 2 - + ---- y DATA(0, 2) - 1/10 y DATA(0, 1) + 1/10 y DATA(0, -1) - 2940 + 3 3 3 + - 2/15 y DATA(0, -1) + 1/30 y DATA(0, 2) - 2/15 y DATA(0, 1) - 2 2 2 - - 2/49 x y DATA(0, -2) + 1/70 x DATA(0, -1) - 1/35 x DATA(0, 2) + 3 3 191 + + 1/5 y DATA(-2, 0) + 1/5 y DATA(0, 0) + ---- y DATA(0, -2) + 2940 - 3 3 3 - + 1/30 y DATA(0, 2) + 1/30 y DATA(0, -2) - 2/15 y DATA(0, -1) + 41 53 2 + - -- y DATA(2, 0) - -- y DATA(1, 0) - 2/49 x y DATA(2, 0) + 98 98 - 3 3 3 - + 1/5 y DATA(0, 0) + 1/5 y DATA(1, 0) - 2/15 y DATA(0, 1) + 166 191 166 + + --- y DATA(0, -1) + ---- y DATA(0, 2) + --- y DATA(0, 1) + 735 2940 735 - 31 17 31 31 - - --- DATA(1, -1) - --- DATA(0, -1) - --- DATA(-1, -1) + --- DATA(-1, 1) - 210 105 210 210 + 2 2 2 + - 1/70 x DATA(0, 1) - 1/35 x DATA(0, 2) + 1/70 x DATA(0, -1) - 31 11 - + 1/84 DATA(1, 2) - --- DATA(2, 2) + --- DATA(2, 1) + 1/84 DATA(-1, 2) - 420 105 + 2 + - 2/35 x y DATA(2, 0) - 1/35 x y DATA(1, 0) + 1/35 x DATA(0, -2) - 17 11 31 11 - + --- DATA(0, 2) - --- DATA(2, -1) - --- DATA(-2, 2) + --- DATA(-2, 1) - 420 105 420 105 + 2 2 2 + + 1/49 x y DATA(1, 0) - 2/49 x y DATA(0, 2) + 2/49 x y DATA(0, 0) - 2 2 2 - - 1/10 y DATA(2, 1) + 1/20 y DATA(-1, 2) + 1/10 y DATA(2, -1) + 2 2 2 + + 1/49 x y DATA(0, -1) - 2/49 x y DATA(0, -2) + 1/49 x y DATA(-1, 0) - 2 2 2 - + 1/20 y DATA(-2, 2) - 1/10 y DATA(-2, 1) + 1/10 y DATA(-2, -1) + 57 41 17 31 + - -- y DATA(0, 0) - -- y DATA(-2, 0) + --- DATA(0, 1) + --- DATA(1, 1) + 98 98 105 210 - 2 2 2 - - 1/20 y DATA(2, -2) - 1/20 y DATA(-1, -2) + 1/20 y DATA(2, 2) + 3 3 3 + - 1/60 x DATA(-2, 2) - 1/120 x DATA(-2, 1) + 1/60 x DATA(1, -1) - 2 2 2 - - 1/10 y DATA(1, 1) + 1/10 y DATA(1, -1) + 1/10 y DATA(-1, -1) + 3 71 71 + + 1/120 x DATA(-2, -1) + ---- y DATA(1, 2) + ---- y DATA(-1, 2) + 2940 2940 - 2 2 - - 1/10 y DATA(-1, 1) - 1/35 x y DATA(-1, 2) + 1/98 x y DATA(-1, -1) + 181 71 71 + + --- y DATA(-1, 1) + ---- y DATA(-1, -2) + ---- y DATA(1, -2) + 735 2940 2940 - 2 - + 1/98 x y DATA(1, 1) + 1/35 x y DATA(-2, -1) + 2/35 x y DATA(2, -2) + 289 181 181 + - ---- y DATA(-2, 2) + --- y DATA(1, -1) + --- y DATA(1, 1) + 2940 735 735 - 181 - + 2/35 x y DATA(2, 2) - 1/35 x y DATA(2, 1) + --- y DATA(1, 1) - 735 + 226 226 289 + + --- y DATA(2, 1) + --- y DATA(2, -1) - ---- y DATA(2, 2) + 735 735 2940 - 2 2 2 - - 1/10 x y DATA(-2, -1) - 1/20 x y DATA(2, -2) + 1/40 x y DATA(-1, -2) + 3 3 3 + + 1/30 y DATA(2, 2) + 1/30 y DATA(1, 2) + 1/30 y DATA(-1, 2) - 2 - - 1/40 x y DATA(1, -2) - 1/35 x y DATA(2, -1) - 2/35 x y DATA(-2, 2) + 2 2 2 + - 1/10 y DATA(-1, 1) + 1/10 y DATA(2, -1) + 1/20 y DATA(2, 2) - 71 226 - + 1/35 x y DATA(-2, 1) + ---- y DATA(-1, 2) + --- y DATA(2, -1) - 2940 735 + 2 2 2 + + 1/20 y DATA(1, 2) + 1/20 y DATA(-1, 2) - 1/10 y DATA(1, 1) - 289 226 226 - - ---- y DATA(-2, 2) + --- y DATA(-2, 1) + --- y DATA(-2, -1) - 2940 735 735 + 2 226 181 + - 1/10 y DATA(2, 1) + --- y DATA(-2, 1) + --- y DATA(-1, -1) + 735 735 - 289 71 71 - - ---- y DATA(2, -2) + ---- y DATA(-1, -2) + ---- y DATA(1, -2) - 2940 2940 2940 + 226 289 289 + + --- y DATA(-2, -1) - ---- y DATA(2, -2) - ---- y DATA(-2, -2) + 735 2940 2940 - 289 181 2 - - ---- y DATA(-2, -2) + --- y DATA(1, -1) - 1/20 y DATA(1, -2) - 2940 735 + 2 2 2 + - 1/20 y DATA(1, -2) + 1/20 y DATA(-2, 2) - 1/10 y DATA(-2, 1) - 2 2 - - 1/20 y DATA(-2, -2) + 1/20 y DATA(1, 2) - 1/35 x y DATA(-1, -2) + 3 3 3 + - 2/15 y DATA(1, 1) - 2/15 y DATA(2, 1) - 2/15 y DATA(2, -1) - 2 - + 1/35 x y DATA(1, -2) - 2/35 x y DATA(-2, -2) - 1/10 x y DATA(2, 1) + 2 3 3 + - 1/70 x DATA(-1, 2) - 2/15 y DATA(-2, -1) + 1/30 y DATA(2, -2) - 2 2 2 - + 1/10 x y DATA(2, -1) - 1/20 x y DATA(-2, 2) + 1/10 x y DATA(-2, 1) + 3 3 3 + + 1/30 y DATA(-2, -2) + 1/30 y DATA(-1, -2) + 1/30 y DATA(1, -2) - 181 3 3 - + --- y DATA(-1, -1) - 2/15 y DATA(-2, 1) - 2/15 y DATA(-1, 1) - 735 + 3 3 3 + + 1/30 y DATA(-2, 2) - 2/15 y DATA(-1, 1) - 2/15 y DATA(-1, -1) - 3 3 181 - - 2/15 y DATA(1, 1) - 2/15 y DATA(1, -1) + --- y DATA(-1, 1) - 735 + 3 2 2 + - 2/15 y DATA(1, -1) + 1/10 y DATA(-1, -1) + 1/10 y DATA(1, -1) - 71 289 226 - + ---- y DATA(1, 2) - ---- y DATA(2, 2) + --- y DATA(2, 1) - 2940 2940 735 + 2 2 2 + + 1/10 y DATA(-2, -1) - 1/20 y DATA(2, -2) - 1/20 y DATA(-2, -2) - 3 21 11 - + 1/30 y DATA(-2, -2) - --- x DATA(2, -1) + --- x DATA(-2, 2) - 200 150 + 2 2 2 + - 1/20 y DATA(-1, -2) - 1/35 x DATA(-2, -2) + 1/70 x DATA(2, 1) - 21 21 11 - - --- x DATA(-2, 1) + --- x DATA(-2, -1) + --- x DATA(2, -2) - 200 200 150 + 2 2 2 + - 1/70 x DATA(2, -1) + 1/35 x DATA(2, 2) - 1/70 x DATA(1, 2) - 21 21 11 - + --- x DATA(-1, -2) - --- x DATA(1, -2) - --- x DATA(-2, -2) - 200 200 150 + 2 2 2 + + 2/49 x y DATA(2, 2) - 1/70 x DATA(-2, -1) - 1/35 x DATA(2, -2) - 3 3 3 - + 1/30 y DATA(2, -2) - 2/15 y DATA(-1, -1) + 1/30 y DATA(1, 2) + 3 2 11 + - 2/15 y DATA(-2, 1) - 1/140 x DATA(1, 1) + --- x DATA(-2, 2) + 150 - 3 3 3 - + 1/30 y DATA(2, 2) - 2/15 y DATA(2, 1) + 1/30 y DATA(-1, 2) + 11 2 2 + - --- x DATA(2, 2) + 1/70 x DATA(-1, -2) + 1/70 x DATA(1, -2) + 150 - 3 3 21 - - 2/15 y DATA(2, -1) + 1/30 y DATA(-2, 2) + --- x DATA(2, 1) + 2 2 21 + + 1/35 x DATA(-2, 2) + 1/70 x DATA(-2, 1) + --- x DATA(2, 1) 200 - 3 3 3 - - 2/15 y DATA(-2, -1) + 1/30 y DATA(-1, -2) + 1/30 y DATA(1, -2) + 2 2 2 + - 1/140 x DATA(-1, 1) + 1/140 x DATA(-1, -1) + 1/140 x DATA(1, -1) - 11 3 3 - - --- DATA(-2, -1) + 1/30 x DATA(1, -2) + 1/60 x DATA(-2, -2) - 105 + 21 3 3 + - --- x DATA(1, -2) - 1/60 x DATA(1, 1) - 1/30 x DATA(-1, -2) + 200 - 21 37 37 - - --- x DATA(-1, 2) + --- x DATA(1, 1) - --- x DATA(1, -1) - 200 300 300 + 21 37 21 + - --- x DATA(-2, 1) - --- x DATA(1, -1) + --- x DATA(-2, -1) + 200 300 200 - 37 37 21 - + --- x DATA(-1, -1) - --- x DATA(-1, 1) + --- x DATA(1, 2) - 300 300 200 + 11 11 21 + + --- x DATA(2, -2) - --- x DATA(-2, -2) + --- x DATA(1, 2) + 150 150 200 - 11 3 3 - - --- x DATA(2, 2) + 1/30 x DATA(-1, 2) - 1/60 x DATA(1, 1) - 150 + 21 37 21 + - --- x DATA(-1, 2) - --- x DATA(-1, 1) - --- x DATA(2, -1) + 200 300 200 - 3 3 3 - + 1/60 x DATA(1, -1) - 1/60 x DATA(-1, -1) + 1/60 x DATA(-1, 1) + 37 21 3 + + --- x DATA(1, 1) + --- x DATA(-1, -2) + 1/60 x DATA(-1, 1) + 300 200 - 3 3 3 - + 1/120 x DATA(2, 1) - 1/120 x DATA(2, -1) - 1/60 x DATA(-2, 2) + 37 3 3 + + --- x DATA(-1, -1) + 1/120 x DATA(2, 1) - 1/120 x DATA(2, -1) + 300 - 3 3 3 - - 1/120 x DATA(-2, 1) + 1/120 x DATA(-2, -1) - 1/60 x DATA(2, -2) + 3 3 11 + + 1/60 x DATA(2, 2) - 1/60 x DATA(-1, -1) + --- DATA(2, 1) + 105 - 3 2 3 - - 1/30 x DATA(-1, -2) - 1/35 x DATA(-2, -2) - 1/30 x DATA(1, 2) + 11 31 17 + - --- DATA(2, -1) - --- DATA(2, 2) + 1/84 DATA(1, 2) + --- DATA(0, 2) + 105 420 420 - 3 2 2 - + 1/60 x DATA(2, 2) - 1/140 x DATA(1, 1) + 1/140 x DATA(1, -1) + 31 31 17 + + 1/84 DATA(-1, 2) + --- DATA(-1, 1) - --- DATA(-1, -1) - --- DATA(0, -1) + 210 210 105 - 2 2 2 - + 1/140 x DATA(-1, -1) - 1/140 x DATA(-1, 1) - 1/49 x y DATA(-1, -2) + 31 2 2 + - --- DATA(1, -1) + 1/40 x y DATA(1, 2) + 1/20 x y DATA(-1, 1) + 210 - 2 2 2 - + 1/98 x y DATA(1, -1) - 1/49 x y DATA(-2, -1) + 1/40 x y DATA(1, 2) + 2 2 2 + - 1/49 x y DATA(2, 1) - 1/10 x y DATA(-2, -1) + 1/10 x y DATA(2, -1) - 2 2 2 - + 1/20 x y DATA(2, 2) - 1/40 x y DATA(-1, 2) - 1/20 x y DATA(1, 1) + 2 2 2 + - 1/40 x y DATA(1, -2) - 1/20 x y DATA(2, -2) + 1/40 x y DATA(-1, -2) - 2 2 2 - + 1/20 x y DATA(1, -1) - 1/20 x y DATA(-1, -1) + 1/20 x y DATA(-1, 1) + 2 2 2 + + 1/98 x y DATA(1, 1) - 1/49 x y DATA(2, -1) - 1/10 x y DATA(2, 1) - 2 - + 1/20 x y DATA(-2, -2) + 1/35 x y DATA(1, 2) - 1/70 x y DATA(1, -1) + 2 2 2 + - 1/20 x y DATA(-2, 2) + 1/20 x y DATA(2, 2) + 1/20 x y DATA(1, -1) - 2 2 2 - - 1/49 x y DATA(1, -2) - 1/49 x y DATA(-1, 2) - 1/49 x y DATA(-2, 1) + 2 2 2 + - 1/20 x y DATA(1, 1) + 1/20 x y DATA(-2, -2) + 1/98 x y DATA(1, -1) - 31 - - 1/70 x y DATA(1, 1) + --- DATA(2, -2) - 1/84 DATA(-1, -2) - 420 + 2 2 2 + - 1/49 x y DATA(-2, -1) + 2/49 x y DATA(2, -2) + 2/49 x y DATA(-2, -2) - 17 2 - - --- DATA(0, -2) - 1/84 DATA(1, -2) - 1/49 x y DATA(2, -1) - 420 + 2 2 2 + - 1/49 x y DATA(-1, -2) - 1/49 x y DATA(1, -2) + 2/49 x y DATA(-2, 2) - 2 2 2 - + 2/49 x y DATA(-2, -2) - 1/49 x y DATA(1, 2) - 1/49 x y DATA(2, 1) + 2 + - 1/49 x y DATA(-2, 1) + 1/70 x y DATA(-1, -1) - 1/70 x y DATA(1, 1) - 2 2 2 - + 2/49 x y DATA(2, 2) + 2/49 x y DATA(2, -2) + 2/49 x y DATA(-2, 2) + - 1/35 x y DATA(2, 1) - 1/35 x y DATA(2, -1) + 2/35 x y DATA(2, 2) - 2 - + 1/98 x y DATA(-1, 1) + 1/70 x y DATA(-1, -1) + 1/70 x y DATA(-1, 1) + 2 + + 1/35 x y DATA(1, 2) - 1/35 x y DATA(-1, 2) - 1/49 x y DATA(1, 2) - 2 2 2 - - 1/70 x DATA(1, 2) + 1/70 x DATA(2, 1) - 1/70 x DATA(-1, 2) + 2 2 2 + - 1/49 x y DATA(-1, 2) + 1/98 x y DATA(-1, 1) + 1/98 x y DATA(-1, -1) - 2 2 2 - - 1/70 x DATA(2, -1) + 1/35 x DATA(2, 2) + 1/35 x DATA(-2, 2) + + 1/35 x y DATA(1, -2) - 2/35 x y DATA(-2, 2) + 1/35 x y DATA(-2, 1) - 2 2 2 - + 1/70 x DATA(-2, 1) - 1/70 x DATA(-2, -1) - 1/35 x DATA(2, -2) + 2 + + 1/70 x y DATA(-1, 1) - 1/20 x y DATA(-1, -1) - 1/70 x y DATA(1, -1) - 2 2 31 - + 1/70 x DATA(-1, -2) + 1/70 x DATA(1, -2) + --- DATA(-2, -2) - 420 + + 1/35 x y DATA(-2, -1) + 2/35 x y DATA(2, -2) - 2/35 x y DATA(-2, -2) - 2 2 - + 2/35 x y DATA(-2, 0) + 1/49 x y DATA(-1, 0) - 2/49 x y DATA(2, 0) + 2 2 + - 1/35 x y DATA(-1, -2) + 1/10 x y DATA(-2, 1) - 1/40 x y DATA(-1, 2) - 2 2 - - 2/49 x y DATA(-2, 0) - 2/49 x y DATA(0, 2) - 1/35 x y DATA(1, 0) + 11 31 31 + - --- DATA(-2, -1) + --- DATA(2, -2) + --- DATA(-2, -2) + 105 420 420 - 2 2 - + 1/35 x y DATA(-1, 0) + 1/49 x y DATA(0, -1) + 2/49 x y DATA(0, 0) + 17 31 + - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 1/84 DATA(1, -2) - --- DATA(-2, 2) + 420 420 - 2 2 2 - + 1/49 x y DATA(1, 0) + 1/49 x y DATA(0, 1) - 1/70 x DATA(0, 1) + 11 3 3 + + --- DATA(-2, 1) + 1/30 x DATA(1, -2) - 1/60 x DATA(2, -2) + 105 -> coeff_as_lc_of_data(%, posn_list_2d_size5); -bytes used=84109804, alloc=2424388, time=7.95 - 31 3 2 2 11 3 -[COEFF(-2, -2) = --- + 1/30 y - 1/35 x - 1/20 y - --- x + 1/60 x - 420 150 + 3 3 3 + + 1/60 x DATA(-2, -2) - 1/30 x DATA(1, 2) + 1/30 x DATA(-1, 2) - 2 2 289 2 - + 2/49 x y + 1/20 x y - ---- y - 2/35 x y, COEFF(-1, -2) = - 1/20 y - 2940 + 2 2 + - 2/49 x y DATA(-2, 0) + 1/49 x y DATA(0, 1) + 2/35 x y DATA(-2, 0) - 21 2 2 2 71 3 - + --- x - 1/49 x y + 1/40 x y + 1/70 x - 1/84 + ---- y - 1/30 x - 200 2940 + + 1/35 x y DATA(-1, 0) - 3 - - 1/35 x y + 1/30 y , +> coeff_as_lc_of_data(%, posn_list_2d_size5); +bytes used=84128420, alloc=2489912, time=7.97 + 11 3 2 2 289 2 +[COEFF(-2, -2) = - --- x + 1/60 x - 1/35 x + 2/49 x y - ---- y - 1/20 y + 150 2940 - 191 17 2 2 3 2 - COEFF(0, -2) = ---- y - --- - 2/49 x y + 1/35 x + 1/30 y - 1/20 y , - 2940 420 + 31 2 3 71 2 + + --- + 1/20 x y + 1/30 y - 2/35 x y, COEFF(-1, -2) = ---- y + 1/40 x y + 420 2940 - 3 2 2 21 - COEFF(1, -2) = 1/35 x y + 1/30 x - 1/49 x y - 1/84 - 1/20 y - --- x - 200 + 3 3 2 2 21 + - 1/30 x + 1/30 y - 1/84 - 1/49 x y + 1/70 x + --- x - 1/35 x y + 200 - 2 2 71 3 3 - + 1/70 x - 1/40 x y + ---- y + 1/30 y , COEFF(2, -2) = - 1/60 x - 2940 + 2 + - 1/20 y , - 2 31 11 289 2 2 - + 2/35 x y - 1/35 x + --- + --- x - ---- y - 1/20 y + 2/49 x y - 420 150 2940 + 2 17 191 2 3 2 + COEFF(0, -2) = 1/35 x - --- + ---- y - 2/49 x y + 1/30 y - 1/20 y , + 420 2940 - 2 3 21 2 3 226 - - 1/20 x y + 1/30 y , COEFF(-2, -1) = --- x - 1/10 x y - 2/15 y + --- y - 200 735 + 2 71 21 2 + COEFF(1, -2) = 1/70 x + 1/35 x y + ---- y - --- x - 1/40 x y - 1/84 + 2940 200 - 3 2 2 11 2 - + 1/120 x + 1/35 x y + 1/10 y - 1/70 x - --- - 1/49 x y, COEFF(-1, -1) - 105 + 2 3 2 3 3 + - 1/20 y + 1/30 x - 1/49 x y + 1/30 y , COEFF(2, -2) = - 1/60 x - 2 37 2 181 2 2 - = - 1/20 x y + 1/70 x y + --- x + 1/10 y + --- y + 1/98 x y + 1/140 x - 300 735 + 2 11 2 289 2 31 3 + - 1/20 y + --- x - 1/20 x y - ---- y + 2/49 x y + --- + 1/30 y + 150 2940 420 - 3 3 31 - - 2/15 y - 1/60 x - ---, - 210 + 2 3 2 21 11 + + 2/35 x y - 1/35 x , COEFF(-2, -1) = 1/120 x - 1/70 x + --- x - --- + 200 105 - 17 2 166 2 2 3 - COEFF(0, -1) = - --- + 1/49 x y + --- y + 1/10 y + 1/70 x - 2/15 y , - 105 735 + 2 2 2 226 3 + + 1/10 y - 1/49 x y - 1/10 x y + --- y + 1/35 x y - 2/15 y , + 735 - 181 2 2 2 31 3 - COEFF(1, -1) = --- y + 1/140 x + 1/98 x y + 1/10 y - --- - 2/15 y - 735 210 + 2 2 181 3 2 + COEFF(-1, -1) = 1/140 x + 1/70 x y + 1/98 x y + --- y - 1/60 x + 1/10 y + 735 - 37 3 2 11 - - --- x + 1/60 x - 1/70 x y + 1/20 x y , COEFF(2, -1) = - 1/35 x y - --- - 300 105 + 31 37 3 2 + - --- + --- x - 2/15 y - 1/20 x y , + 210 300 - 2 21 226 3 3 2 2 - + 1/10 x y - --- x + --- y - 1/120 x - 2/15 y - 1/49 x y + 1/10 y - 200 735 + 2 166 3 2 2 17 + COEFF(0, -1) = 1/49 x y + --- y - 2/15 y + 1/70 x + 1/10 y - ---, + 735 105 - 2 3 41 2 - - 1/70 x , COEFF(-2, 0) = 1/5 y - -- y + 2/35 x y - 2/49 x y, - 98 + 181 2 3 2 31 3 + COEFF(1, -1) = --- y + 1/10 y - 2/15 y + 1/140 x - --- + 1/60 x + 735 210 - 3 53 2 - COEFF(-1, 0) = 1/5 y - -- y + 1/49 x y + 1/35 x y, - 98 + 2 37 2 + + 1/20 x y - --- x + 1/98 x y - 1/70 x y, COEFF(2, -1) = - 1/35 x y + 300 - 2 57 3 - COEFF(0, 0) = 2/49 x y - -- y + 1/5 y , - 98 + 2 3 2 2 11 3 21 + - 1/70 x - 1/120 x + 1/10 x y - 1/49 x y - --- - 2/15 y - --- x + 105 200 - 3 53 2 - COEFF(1, 0) = 1/5 y - -- y + 1/49 x y - 1/35 x y, - 98 + 226 2 3 41 2 + + --- y + 1/10 y , COEFF(-2, 0) = 2/35 x y + 1/5 y - -- y - 2/49 x y, + 735 98 - 3 2 41 - COEFF(2, 0) = 1/5 y - 2/35 x y - 2/49 x y - -- y, COEFF(-2, 1) = - 98 + 2 3 53 + COEFF(-1, 0) = 1/35 x y + 1/49 x y + 1/5 y - -- y, + 98 - 3 3 11 2 2 226 - - 1/120 x - 2/15 y + --- - 1/49 x y + 1/70 x + 1/35 x y + --- y - 105 735 + 57 2 3 + COEFF(0, 0) = - -- y + 2/49 x y + 1/5 y , + 98 - 2 2 21 37 2 - + 1/10 x y - 1/10 y - --- x, COEFF(-1, 1) = - --- x + 1/20 x y - 200 300 + 53 3 2 + COEFF(1, 0) = - -- y + 1/5 y - 1/35 x y + 1/49 x y, + 98 - 3 31 2 2 3 2 - + 1/70 x y + 1/60 x + --- - 1/140 x - 1/10 y - 2/15 y + 1/98 x y - 210 + 3 2 41 2 + COEFF(2, 0) = 1/5 y - 2/49 x y - -- y - 2/35 x y, COEFF(-2, 1) = 1/70 x + 98 - 181 - + --- y, - 735 + 2 2 226 11 2 21 + - 1/10 y - 1/49 x y + --- y + --- + 1/35 x y + 1/10 x y - --- x + 735 105 200 + + 3 3 2 2 37 + - 1/120 x - 2/15 y , COEFF(-1, 1) = 1/20 x y + 1/98 x y - --- x + 300 + + 3 2 31 3 2 181 + + 1/60 x - 1/140 x + 1/70 x y + --- - 2/15 y - 1/10 y + --- y, + 210 735 - 17 3 2 166 2 2 - COEFF(0, 1) = --- - 2/15 y - 1/70 x + --- y - 1/10 y + 1/49 x y, - 105 735 + 2 2 166 2 17 3 + COEFF(0, 1) = - 1/70 x - 1/10 y + --- y + 1/49 x y + --- - 2/15 y , + 735 105 - 31 3 3 2 2 - COEFF(1, 1) = --- - 1/60 x - 2/15 y - 1/70 x y - 1/20 x y - 1/10 y - 210 + 2 2 2 181 + COEFF(1, 1) = - 1/20 x y - 1/10 y - 1/70 x y + 1/98 x y + --- y + 735 - 181 2 37 2 2 21 - + --- y + 1/98 x y + --- x - 1/140 x , COEFF(2, 1) = - 1/49 x y + --- x - 735 300 200 + 3 37 3 2 31 2 + - 2/15 y + --- x - 1/60 x - 1/140 x + ---, COEFF(2, 1) = - 1/49 x y + 300 210 - 226 2 2 11 2 3 - + --- y - 1/10 y + 1/70 x - 1/35 x y + --- - 1/10 x y + 1/120 x - 735 105 + 3 2 226 21 2 2 11 + - 2/15 y + 1/70 x + --- y + --- x - 1/10 y - 1/10 x y - 1/35 x y + --- + 735 200 105 - 3 3 2 289 31 3 - - 2/15 y , COEFF(-2, 2) = - 1/60 x + 1/35 x - ---- y - --- + 1/30 y - 2940 420 + 3 2 3 2 289 31 + + 1/120 x , COEFF(-2, 2) = 1/35 x + 1/30 y + 1/20 y - ---- y - --- + 2940 420 - 11 2 2 2 - + --- x + 2/49 x y - 2/35 x y - 1/20 x y + 1/20 y , COEFF(-1, 2) = + 11 3 2 2 + + --- x - 1/60 x - 2/35 x y + 2/49 x y - 1/20 x y , COEFF(-1, 2) = 150 - 21 2 2 71 2 2 - - --- x - 1/49 x y + 1/20 y + ---- y - 1/40 x y - 1/70 x + 1/84 - 200 2940 + 2 3 21 2 2 3 + 1/20 y + 1/30 x - --- x - 1/40 x y - 1/70 x - 1/35 x y + 1/30 y + 200 - 3 3 - - 1/35 x y + 1/30 x + 1/30 y , + 2 71 + - 1/49 x y + 1/84 + ---- y, + 2940 - 2 17 191 2 3 2 - COEFF(0, 2) = 1/20 y + --- + ---- y - 1/35 x + 1/30 y - 2/49 x y, - 420 2940 + 2 2 3 17 191 2 + COEFF(0, 2) = - 2/49 x y - 1/35 x + 1/30 y + --- + ---- y + 1/20 y , + 420 2940 - 2 2 3 2 21 - COEFF(1, 2) = - 1/70 x + 1/35 x y - 1/49 x y - 1/30 x + 1/20 y + --- x - 200 + 3 2 2 71 3 + COEFF(1, 2) = 1/30 y + 1/40 x y - 1/70 x + ---- y - 1/30 x + 1/35 x y + 2940 - 3 71 2 3 289 - + 1/30 y + ---- y + 1/84 + 1/40 x y , COEFF(2, 2) = 1/60 x - ---- y - 2940 2940 + 21 2 2 3 2 + + --- x - 1/49 x y + 1/84 + 1/20 y , COEFF(2, 2) = 1/30 y + 1/20 x y + 200 - 2 2 3 31 2 2 11 - + 1/35 x + 1/20 y + 1/30 y - --- + 2/49 x y + 1/20 x y - --- x - 420 150 + 2 3 31 289 2 2 + + 2/35 x y + 1/20 y + 1/60 x - --- - ---- y + 2/49 x y + 1/35 x + 420 2940 - + 2/35 x y] + 11 + - --- x] + 150 > print_coeff__lc_of_data(%, "coeff_dy_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-dy.compute.c"); -bytes used=85110104, alloc=2424388, time=8.01 -bytes used=86110296, alloc=2424388, time=8.09 -bytes used=87116120, alloc=2424388, time=8.16 -bytes used=88116280, alloc=2424388, time=8.30 -bytes used=89116760, alloc=2424388, time=8.38 -bytes used=90116912, alloc=2424388, time=8.48 -bytes used=91117288, alloc=2424388, time=8.64 -bytes used=92117484, alloc=2424388, time=8.73 -bytes used=93117892, alloc=2424388, time=8.88 -bytes used=94118116, alloc=2424388, time=8.97 -bytes used=95118268, alloc=2424388, time=9.12 +bytes used=85128740, alloc=2489912, time=8.04 +bytes used=86138952, alloc=2489912, time=8.13 +bytes used=87140216, alloc=2489912, time=8.22 +bytes used=88140840, alloc=2489912, time=8.39 +bytes used=89142228, alloc=2489912, time=8.47 +bytes used=90142420, alloc=2489912, time=8.63 +bytes used=91145772, alloc=2489912, time=8.71 +bytes used=92145948, alloc=2489912, time=8.89 +bytes used=93146116, alloc=2489912, time=8.97 +bytes used=94146456, alloc=2489912, time=9.16 > # d^2/dx^2 > simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); -bytes used=96118472, alloc=2424388, time=9.19 - 57 166 53 181 -- -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) + --- DATA(1, 1) - 98 735 98 735 +bytes used=95147116, alloc=2489912, time=9.28 +bytes used=96147276, alloc=2489912, time=9.35 + 2 2 2 +1/49 y DATA(0, 1) - 2/49 y DATA(0, -2) + 1/49 y DATA(0, -1) - 2 - + 3/5 x DATA(0, -2) - 1/35 y DATA(0, 1) + 1/35 y DATA(0, -1) + 2 + - 2/49 y DATA(0, 2) + 2/35 y DATA(0, -2) + 1/35 y DATA(0, -1) - 2 2 - + 2/35 y DATA(0, -2) - 2/49 y DATA(0, 2) - 2/49 y DATA(0, -2) + 2 + - 2/35 y DATA(0, 2) - 1/35 y DATA(0, 1) + 3/5 x DATA(0, 1) - 2 2 - - 2/35 y DATA(0, 2) + 1/49 y DATA(0, 1) + 1/49 y DATA(0, -1) + 2 2 2 + + 3/5 x DATA(0, 2) + 3/5 x DATA(0, -1) + 3/5 x DATA(0, -2) - 2 2 166 - + 3/5 x DATA(0, -1) + 3/5 x DATA(0, 2) + --- DATA(-1, 0) - 735 + 57 166 53 181 + - -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) + --- DATA(1, 1) + 98 735 98 735 - 181 53 181 181 - + --- DATA(1, -1) - -- DATA(0, -1) + --- DATA(-1, -1) + --- DATA(-1, 1) - 735 98 735 735 + - 1/35 y DATA(1, 2) - 1/35 y DATA(-1, 2) - 1/70 y DATA(-1, 1) - 2 2 - - 2/49 y DATA(-2, 0) - 1/10 x DATA(-2, 0) - 2/49 y DATA(2, 0) + + 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2) + 2/35 y DATA(-2, 2) - 2 2 2 - + 2/49 y DATA(0, 0) + 1/49 y DATA(1, 0) + 1/49 y DATA(-1, 0) + + 1/70 y DATA(1, -1) - 1/70 y DATA(1, 1) + 1/35 y DATA(2, 1) - 2 2 - + 1/10 x DATA(2, 0) + 3/5 x DATA(0, 0) - 2/5 x DATA(1, 0) + 2 + - 1/35 y DATA(2, -1) + 2/35 y DATA(2, 2) + 1/98 y DATA(-1, 1) - 2 2 2 - + 1/10 x DATA(-2, 0) - 2/5 x DATA(-1, 0) + 1/10 x DATA(2, 0) + 2 2 2 + - 1/49 y DATA(2, -1) + 2/49 y DATA(2, 2) - 1/49 y DATA(1, 2) - 226 289 - - 1/5 x DATA(1, 0) + 1/5 x DATA(-1, 0) + --- DATA(1, 2) - ---- DATA(2, 2) - 735 2940 + 2 2 2 + - 1/49 y DATA(-1, 2) + 1/98 y DATA(1, 1) - 1/49 y DATA(2, 1) - 191 71 226 41 - + ---- DATA(2, 0) + ---- DATA(2, 1) + --- DATA(-1, 2) - -- DATA(0, 2) - 2940 2940 735 98 + + 1/35 y DATA(-2, 1) + 1/70 y DATA(-1, -1) - 1/35 y DATA(-2, -1) - 71 289 71 - + ---- DATA(2, -1) - ---- DATA(-2, 2) + ---- DATA(-2, 1) - 2940 2940 2940 + 2 + - 2/35 y DATA(2, -2) - 2/35 y DATA(-2, -2) - 1/49 y DATA(1, -2) - 2 2 2 - - 1/49 y DATA(2, 1) - 1/49 y DATA(-1, 2) - 1/49 y DATA(2, -1) + 2 2 2 + + 2/49 y DATA(-2, 2) - 1/49 y DATA(-2, 1) - 2/5 x DATA(-1, 2) - 2 2 2 - + 2/49 y DATA(-2, 2) - 1/49 y DATA(-2, 1) - 1/49 y DATA(-2, -1) + 2 2 2 + + 1/98 y DATA(-1, -1) + 1/98 y DATA(1, -1) - 1/49 y DATA(-2, -1) 2 2 2 - + 2/49 y DATA(2, -2) - 1/49 y DATA(-1, -2) + 2/49 y DATA(2, 2) + + 2/49 y DATA(2, -2) + 2/49 y DATA(-2, -2) - 1/49 y DATA(-1, -2) - 2 2 2 - + 1/98 y DATA(1, 1) + 1/98 y DATA(1, -1) + 1/98 y DATA(-1, -1) + 2 2 2 + + 1/10 x DATA(-2, -2) + 1/10 x DATA(2, 1) + 1/10 x DATA(2, -1) - 2 - + 1/98 y DATA(-1, 1) + 1/5 x y DATA(-1, 2) + 1/20 x y DATA(-2, -1) + 2 2 2 + + 1/10 x DATA(2, 2) - 2/5 x DATA(1, 2) + 1/10 x DATA(-2, -1) - - 1/10 x y DATA(2, -2) + 1/10 x y DATA(2, 2) + 1/20 x y DATA(2, 1) + 2 2 + + 1/10 x DATA(2, -2) - 2/5 x DATA(1, 1) - 1/10 x DATA(-2, 2) - - 1/70 y DATA(1, 1) - 1/20 x y DATA(2, -1) - 1/10 x y DATA(-2, 2) + 2 2 + + 1/10 x DATA(2, 2) - 2/5 x DATA(-1, -2) - 2/5 x DATA(1, -2) - - 1/20 x y DATA(-2, 1) - 1/35 y DATA(-1, 2) - 1/35 y DATA(2, -1) + 2 2 + + 1/10 x DATA(-2, 2) + 1/10 x DATA(-2, 1) + 1/10 x DATA(2, 1) - + 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1) - 1/35 y DATA(-2, -1) + 2 2 2 + - 2/5 x DATA(-1, 1) - 2/5 x DATA(-1, -1) - 2/5 x DATA(1, -1) - - 2/35 y DATA(2, -2) + 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2) + - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, 1) - 1/5 x DATA(1, -1) - 2 - - 2/35 y DATA(-2, -2) + 1/70 y DATA(1, -1) - 1/49 y DATA(1, -2) + - 1/10 x DATA(-2, -1) + 1/10 x DATA(2, -2) - 1/10 x DATA(-2, -2) - 2 2 - + 2/49 y DATA(-2, -2) - 1/49 y DATA(1, 2) - 1/5 x y DATA(-1, -2) + - 1/5 x DATA(1, 2) + 1/5 x DATA(-1, 2) + 1/5 x DATA(-1, 1) - + 1/5 x y DATA(1, -2) + 1/10 x y DATA(-2, -2) + 1/70 y DATA(-1, -1) + + 1/10 x DATA(2, -1) - 1/5 x DATA(1, 1) + 1/5 x DATA(-1, -2) - - 1/70 y DATA(-1, 1) - 1/35 y DATA(1, 2) + 2/35 y DATA(2, 2) + 71 191 + + 1/5 x DATA(-1, -1) + ---- DATA(2, 1) + ---- DATA(2, 0) + 2940 2940 - + 1/35 y DATA(2, 1) + 1/10 x DATA(2, -1) - 1/10 x DATA(-2, 2) + 71 289 226 41 + + ---- DATA(2, -1) - ---- DATA(2, 2) + --- DATA(1, 2) - -- DATA(0, 2) + 2940 2940 735 98 - - 1/10 x DATA(-2, 1) - 1/10 x DATA(-2, -1) + 1/10 x DATA(2, -2) + 226 166 181 181 + + --- DATA(-1, 2) + --- DATA(-1, 0) + --- DATA(-1, 1) + --- DATA(-1, -1) + 735 735 735 735 - + 1/5 x DATA(-1, -2) - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, -2) + 53 181 2 + - -- DATA(0, -1) + --- DATA(1, -1) - 2/5 x DATA(1, 0) + 98 735 - 71 191 - + 1/10 x DATA(2, 1) + ---- DATA(-2, -1) + ---- DATA(-2, 0) - 2940 2940 + 2 2 2 + + 1/10 x DATA(2, 0) + 1/10 x DATA(-2, 0) + 3/5 x DATA(0, 0) - + 1/5 x DATA(-1, 2) - 1/5 x DATA(1, 1) - 1/5 x DATA(1, -1) + 2 2 + - 2/5 x DATA(-1, 0) - 1/5 x DATA(1, 0) + 1/49 y DATA(-1, 0) - + 1/5 x DATA(-1, -1) + 1/5 x DATA(-1, 1) - 1/5 x DATA(1, 2) + - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) + 1/20 x y DATA(2, 1) - 2 2 - + 1/10 x DATA(2, 2) + 1/10 x DATA(-2, -2) - 2/5 x DATA(1, 1) + - 1/20 x y DATA(2, -1) + 1/10 x y DATA(2, 2) - 1/5 x y DATA(1, 2) - 2 2 2 - - 2/5 x DATA(1, -1) - 2/5 x DATA(-1, -1) - 2/5 x DATA(-1, 1) + + 1/5 x y DATA(-1, 2) + 1/5 x y DATA(1, -2) - 1/10 x y DATA(-2, 2) - - 1/5 x y DATA(1, 2) + 1/10 x y DATA(1, -1) - 1/10 x y DATA(1, 1) + - 1/20 x y DATA(-2, 1) + 1/10 x y DATA(-1, 1) + 1/10 x y DATA(1, -1) - 289 226 41 226 - - ---- DATA(2, -2) + --- DATA(-1, -2) - -- DATA(0, -2) + --- DATA(1, -2) - 2940 735 98 735 + + 1/20 x y DATA(-2, -1) - 1/10 x y DATA(2, -2) + 1/10 x y DATA(-2, -2) - 2 - - 1/10 x y DATA(-1, -1) + 1/10 x y DATA(-1, 1) - 2/5 x DATA(1, 2) + 71 289 + - 1/5 x y DATA(-1, -2) + ---- DATA(-2, -1) - ---- DATA(2, -2) + 2940 2940 - 2 2 2 - + 1/10 x DATA(2, 1) - 2/5 x DATA(-1, 2) + 1/10 x DATA(2, -1) + 289 226 41 226 + - ---- DATA(-2, -2) + --- DATA(-1, -2) - -- DATA(0, -2) + --- DATA(1, -2) + 2940 735 98 735 - 2 2 2 - + 1/10 x DATA(2, 2) + 1/10 x DATA(-2, 2) + 1/10 x DATA(-2, 1) + 289 191 71 + - ---- DATA(-2, 2) + ---- DATA(-2, 0) + ---- DATA(-2, 1) + 2940 2940 2940 - 2 2 2 - + 1/10 x DATA(-2, -1) + 1/10 x DATA(2, -2) - 2/5 x DATA(-1, -2) + 2 2 + + 1/49 y DATA(1, 0) + 1/10 x DATA(2, 0) + 2/49 y DATA(0, 0) - 2 289 2 - - 2/5 x DATA(1, -2) - ---- DATA(-2, -2) + 3/5 x DATA(0, 1) - 2940 + 2 2 + - 2/49 y DATA(-2, 0) - 2/49 y DATA(2, 0) - 1/10 x DATA(-2, 0) + + + 1/5 x DATA(-1, 0) > coeff_as_lc_of_data(%, posn_list_2d_size5); -bytes used=97118648, alloc=2424388, time=9.26 - 2 289 2 -[COEFF(-2, -2) = 1/10 x y - 2/35 y + 2/49 y - ---- + 1/10 x - 1/10 x, - 2940 +bytes used=97147664, alloc=2489912, time=9.43 + 2 2 289 +[COEFF(-2, -2) = 2/49 y - 1/10 x + 1/10 x - 2/35 y + 1/10 x y - ----, + 2940 - 2 226 2 - COEFF(-1, -2) = - 1/5 x y - 2/5 x + 1/35 y + --- + 1/5 x - 1/49 y , - 735 + 2 226 2 + COEFF(-1, -2) = - 1/49 y + 1/5 x + --- - 2/5 x - 1/5 x y + 1/35 y, + 735 - 2 2 41 - COEFF(0, -2) = 2/35 y - 2/49 y + 3/5 x - --, + 2 2 41 + COEFF(0, -2) = 2/35 y + 3/5 x - 2/49 y - --, 98 - 226 2 2 - COEFF(1, -2) = --- - 2/5 x + 1/35 y + 1/5 x y - 1/5 x - 1/49 y , + 226 2 2 + COEFF(1, -2) = --- - 1/5 x - 1/49 y + 1/35 y + 1/5 x y - 2/5 x , 735 - 2 289 2 - COEFF(2, -2) = 2/49 y - ---- - 2/35 y + 1/10 x + 1/10 x - 1/10 x y, - 2940 + 289 2 2 + COEFF(2, -2) = 1/10 x - ---- + 1/10 x - 2/35 y + 2/49 y - 1/10 x y, + 2940 - 71 2 2 - COEFF(-2, -1) = - 1/10 x + ---- - 1/49 y + 1/10 x - 1/35 y + 1/20 x y, - 2940 + 2 71 2 + COEFF(-2, -1) = - 1/49 y + ---- + 1/20 x y - 1/10 x + 1/10 x - 1/35 y, + 2940 - 2 2 181 - COEFF(-1, -1) = - 2/5 x + 1/98 y + 1/5 x + --- - 1/10 x y + 1/70 y, - 735 + 181 2 2 + COEFF(-1, -1) = 1/70 y + --- + 1/5 x - 1/10 x y + 1/98 y - 2/5 x , + 735 - 53 2 2 - COEFF(0, -1) = - -- + 1/35 y + 1/49 y + 3/5 x , + 53 2 2 + COEFF(0, -1) = - -- + 1/35 y + 3/5 x + 1/49 y , 98 - 2 2 181 - COEFF(1, -1) = 1/70 y + 1/98 y - 2/5 x - 1/5 x + 1/10 x y + ---, - 735 + 2 181 2 + COEFF(1, -1) = - 1/5 x + 1/98 y + 1/10 x y + --- + 1/70 y - 2/5 x , + 735 - 2 2 71 - COEFF(2, -1) = 1/10 x - 1/35 y - 1/49 y + 1/10 x + ---- - 1/20 x y, - 2940 + 2 71 2 + COEFF(2, -1) = 1/10 x - 1/35 y + 1/10 x + ---- - 1/49 y - 1/20 x y, + 2940 - 2 2 191 - COEFF(-2, 0) = - 1/10 x + 1/10 x - 2/49 y + ----, - 2940 + 2 191 2 + COEFF(-2, 0) = 1/10 x - 1/10 x + ---- - 2/49 y , + 2940 - 2 2 166 - COEFF(-1, 0) = - 2/5 x + 1/49 y + --- + 1/5 x, - 735 + 2 166 2 + COEFF(-1, 0) = 1/49 y + --- - 2/5 x + 1/5 x, + 735 - 2 57 2 - COEFF(0, 0) = 2/49 y - -- + 3/5 x , - 98 + 57 2 2 + COEFF(0, 0) = - -- + 2/49 y + 3/5 x , + 98 - 2 2 166 - COEFF(1, 0) = - 1/5 x + 1/49 y - 2/5 x + ---, - 735 + 2 166 2 + COEFF(1, 0) = - 1/5 x + 1/49 y + --- - 2/5 x , + 735 - 2 191 2 - COEFF(2, 0) = 1/10 x - 2/49 y + ---- + 1/10 x , - 2940 + 191 2 2 + COEFF(2, 0) = ---- - 2/49 y + 1/10 x + 1/10 x , + 2940 - 71 2 2 - COEFF(-2, 1) = ---- - 1/49 y + 1/10 x + 1/35 y - 1/20 x y - 1/10 x, + 71 2 2 + COEFF(-2, 1) = ---- - 1/49 y - 1/20 x y + 1/35 y + 1/10 x - 1/10 x, 2940 - 181 2 2 - COEFF(-1, 1) = 1/5 x + --- + 1/10 x y - 2/5 x + 1/98 y - 1/70 y, - 735 + 181 2 2 + COEFF(-1, 1) = --- - 1/70 y - 2/5 x + 1/98 y + 1/5 x + 1/10 x y, + 735 - 53 2 2 - COEFF(0, 1) = - -- + 3/5 x + 1/49 y - 1/35 y, - 98 + 2 2 53 + COEFF(0, 1) = 3/5 x - 1/35 y + 1/49 y - --, + 98 - 181 2 2 - COEFF(1, 1) = --- + 1/98 y - 2/5 x - 1/70 y - 1/5 x - 1/10 x y, - 735 + 181 2 2 + COEFF(1, 1) = - 1/70 y + --- - 1/10 x y - 2/5 x - 1/5 x + 1/98 y , + 735 - 2 71 2 - COEFF(2, 1) = 1/10 x + 1/35 y + 1/10 x + ---- + 1/20 x y - 1/49 y , - 2940 + 2 71 2 + COEFF(2, 1) = 1/10 x - 1/49 y + ---- + 1/35 y + 1/10 x + 1/20 x y, + 2940 - 2 289 2 - COEFF(-2, 2) = 2/49 y + 2/35 y - ---- - 1/10 x y - 1/10 x + 1/10 x , + 2 289 2 + COEFF(-2, 2) = 2/35 y + 2/49 y - ---- - 1/10 x y + 1/10 x - 1/10 x, 2940 - 226 2 2 - COEFF(-1, 2) = --- - 2/5 x + 1/5 x + 1/5 x y - 1/49 y - 1/35 y, - 735 + 2 2 226 + COEFF(-1, 2) = - 1/35 y - 1/49 y - 2/5 x + 1/5 x + --- + 1/5 x y, + 735 - 41 2 2 - COEFF(0, 2) = - -- - 2/35 y - 2/49 y + 3/5 x , - 98 + 2 2 41 + COEFF(0, 2) = 3/5 x - 2/49 y - 2/35 y - --, + 98 - 2 226 2 - COEFF(1, 2) = - 1/5 x - 2/5 x - 1/5 x y + --- - 1/49 y - 1/35 y, - 735 + 2 2 226 + COEFF(1, 2) = - 1/49 y - 2/5 x - 1/5 x - 1/5 x y - 1/35 y + ---, + 735 - 2 289 2 - COEFF(2, 2) = 1/10 x + 2/49 y - ---- + 1/10 x + 2/35 y + 1/10 x y] - 2940 + 2 2 289 + COEFF(2, 2) = 2/35 y + 1/10 x + 2/49 y + 1/10 x y + 1/10 x - ----] + 2940 > print_coeff__lc_of_data(%, "coeff_dxx_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-dxx.compute.c"); -bytes used=98118800, alloc=2424388, time=9.34 -bytes used=99118996, alloc=2424388, time=9.43 -bytes used=100119256, alloc=2424388, time=9.58 -bytes used=101122084, alloc=2424388, time=9.74 -bytes used=102122280, alloc=2424388, time=9.85 -bytes used=103122400, alloc=2424388, time=9.97 +bytes used=98147868, alloc=2489912, time=9.52 +bytes used=99148020, alloc=2489912, time=9.68 +bytes used=100148588, alloc=2489912, time=9.76 +bytes used=101148864, alloc=2489912, time=9.92 +bytes used=102149152, alloc=2489912, time=10.09 +bytes used=103149320, alloc=2489912, time=10.25 > # d^2/dxdy > simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); -bytes used=104122552, alloc=2424388, time=10.13 -bytes used=105123136, alloc=2424388, time=10.20 +bytes used=104150048, alloc=2489912, time=10.38 37 ---- DATA(1, 1) - 4/49 x y DATA(-2, 0) - 4/49 x y DATA(0, -2) +--- DATA(1, 1) + 1/35 y DATA(1, 2) - 1/35 y DATA(-1, 2) + 1/70 y DATA(-1, 1) 300 - + 4/49 x y DATA(0, 0) + 2/49 x y DATA(0, -1) - 4/49 x y DATA(0, 2) + - 1/35 y DATA(-1, -2) + 1/35 y DATA(1, -2) - 2/35 y DATA(-2, 2) - + 2/49 x y DATA(0, 1) + 2/49 x y DATA(1, 0) - 4/49 x y DATA(2, 0) + - 1/70 y DATA(1, -1) - 1/70 y DATA(1, 1) - 1/35 y DATA(2, 1) - + 2/49 x y DATA(-1, 0) + 1/35 y DATA(-1, 0) + 2/35 y DATA(-2, 0) + 2 + - 1/35 y DATA(2, -1) + 2/35 y DATA(2, 2) + 1/20 y DATA(-1, 1) - 37 37 37 - - --- DATA(1, -1) + --- DATA(-1, -1) - --- DATA(-1, 1) - 2/35 y DATA(2, 0) - 300 300 300 + 2 2 2 + + 1/10 y DATA(2, -1) + 1/20 y DATA(2, 2) + 1/40 y DATA(1, 2) - 21 11 - - 1/35 y DATA(1, 0) - 1/35 x DATA(0, 1) + --- DATA(1, 2) - --- DATA(2, 2) - 200 150 + 2 2 2 + - 1/40 y DATA(-1, 2) - 1/20 y DATA(1, 1) - 1/10 y DATA(2, 1) - 21 21 21 11 - + --- DATA(2, 1) - --- DATA(-1, 2) - --- DATA(2, -1) + --- DATA(-2, 2) - 200 200 200 150 + + 1/35 y DATA(-2, 1) + 1/70 y DATA(-1, -1) + 1/35 y DATA(-2, -1) - 21 2 2 - - --- DATA(-2, 1) - 1/10 y DATA(2, 1) - 1/40 y DATA(-1, 2) - 200 + 2 + + 2/35 y DATA(2, -2) - 2/35 y DATA(-2, -2) - 1/40 y DATA(1, -2) 2 2 2 - + 1/10 y DATA(2, -1) - 1/20 y DATA(-2, 2) + 1/10 y DATA(-2, 1) + - 1/20 y DATA(-2, 2) + 1/10 y DATA(-2, 1) + 1/10 x DATA(-1, 2) 2 2 2 - - 1/10 y DATA(-2, -1) - 1/20 y DATA(2, -2) + 1/40 y DATA(-1, -2) + - 1/20 y DATA(-1, -1) + 1/20 y DATA(1, -1) - 1/10 y DATA(-2, -1) - 2 2 2 - + 1/20 y DATA(2, 2) - 1/20 y DATA(1, 1) + 1/20 y DATA(1, -1) + 2 2 2 + - 1/20 y DATA(2, -2) + 1/20 y DATA(-2, -2) + 1/40 y DATA(-1, -2) - 2 2 - - 1/20 y DATA(-1, -1) + 1/20 y DATA(-1, 1) - 2/49 x y DATA(-1, 2) + 2 2 2 + + 1/20 x DATA(-2, -2) + 1/40 x DATA(2, 1) - 1/40 x DATA(2, -1) - - 2/49 x y DATA(-2, -1) + 4/49 x y DATA(2, -2) + 4/49 x y DATA(2, 2) + 2 2 2 + + 1/20 x DATA(2, 2) - 1/10 x DATA(1, 2) + 1/40 x DATA(-2, -1) - - 2/49 x y DATA(2, 1) - 1/70 y DATA(1, 1) - 2/49 x y DATA(2, -1) + 2 2 + - 1/20 x DATA(2, -2) - 1/20 x DATA(1, 1) + 2/35 x DATA(-2, 2) - + 4/49 x y DATA(-2, 2) - 2/49 x y DATA(-2, 1) - 1/35 y DATA(-1, 2) + 2 2 + + 2/35 x DATA(2, 2) - 1/10 x DATA(-1, -2) + 1/10 x DATA(1, -2) - - 1/35 y DATA(2, -1) - 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1) + 2 2 + - 1/20 x DATA(-2, 2) - 1/40 x DATA(-2, 1) + 1/35 x DATA(2, 1) - + 1/35 y DATA(-2, -1) + 2/35 y DATA(2, -2) - 1/35 y DATA(-1, -2) + 2 2 2 + + 1/20 x DATA(-1, 1) - 1/20 x DATA(-1, -1) + 1/20 x DATA(1, -1) - + 1/35 y DATA(1, -2) - 2/35 y DATA(-2, -2) - 1/70 y DATA(1, -1) + + 1/35 x DATA(1, -2) + 1/35 x DATA(-2, 1) + 1/70 x DATA(1, -1) - 2 2 2 - - 1/40 y DATA(1, -2) + 1/20 y DATA(-2, -2) + 1/40 y DATA(1, 2) + - 1/35 x DATA(-2, -1) - 2/35 x DATA(2, -2) - 2/35 x DATA(-2, -2) - - 2/49 x y DATA(-1, -2) - 2/49 x y DATA(1, -2) + 4/49 x y DATA(-2, -2) + - 1/35 x DATA(1, 2) - 1/35 x DATA(-1, 2) - 1/70 x DATA(-1, 1) - + 1/70 y DATA(-1, -1) + 1/70 y DATA(-1, 1) + 1/35 y DATA(1, 2) + - 1/35 x DATA(2, -1) - 1/70 x DATA(1, 1) + 1/35 x DATA(-1, -2) - + 2/35 y DATA(2, 2) - 1/35 y DATA(2, 1) - 1/35 x DATA(2, -1) + 21 21 11 + + 1/70 x DATA(-1, -1) + --- DATA(2, 1) - --- DATA(2, -1) - --- DATA(2, 2) + 200 200 150 - + 2/35 x DATA(-2, 2) + 1/35 x DATA(-2, 1) - 1/35 x DATA(-2, -1) + 21 21 37 37 + + --- DATA(1, 2) - --- DATA(-1, 2) - --- DATA(-1, 1) + --- DATA(-1, -1) + 200 200 300 300 - - 2/35 x DATA(2, -2) + 1/35 x DATA(-1, -2) + 1/35 x DATA(1, -2) + 37 + - --- DATA(1, -1) - 4/49 x y DATA(0, 2) + 1/49 x y DATA(-1, -1) + 300 - 21 - - 2/35 x DATA(-2, -2) + 1/35 x DATA(2, 1) + --- DATA(-2, -1) - 200 + + 1/49 x y DATA(1, 1) - 2/49 x y DATA(2, 1) - 2/49 x y DATA(2, -1) - - 1/35 x DATA(-1, 2) - 1/70 x DATA(1, 1) + 1/70 x DATA(1, -1) + + 4/49 x y DATA(2, 2) - 2/49 x y DATA(1, 2) - 2/49 x y DATA(-1, 2) - + 1/70 x DATA(-1, -1) - 1/70 x DATA(-1, 1) - 1/35 x DATA(1, 2) + - 1/35 x DATA(0, 1) - 2/35 x DATA(0, 2) + 1/35 x DATA(0, -1) - 2 2 - + 2/35 x DATA(2, 2) + 1/20 x DATA(-2, -2) - 1/20 x DATA(1, 1) + + 2/35 x DATA(0, -2) + 4/49 x y DATA(0, 0) + 2/49 x y DATA(1, 0) - 2 2 2 - + 1/20 x DATA(1, -1) - 1/20 x DATA(-1, -1) + 1/20 x DATA(-1, 1) + - 4/49 x y DATA(2, 0) + 2/49 x y DATA(-1, 0) - 1/35 y DATA(1, 0) - - 2/49 x y DATA(1, 2) + 1/49 x y DATA(1, -1) + 1/49 x y DATA(1, 1) + + 2/49 x y DATA(0, 1) + 2/49 x y DATA(0, -1) - 4/49 x y DATA(0, -2) - 11 21 21 - + --- DATA(2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) - 150 200 200 + - 2/35 y DATA(2, 0) + 1/35 y DATA(-1, 0) - 4/49 x y DATA(-2, 0) - 2 - + 1/49 x y DATA(-1, -1) + 1/49 x y DATA(-1, 1) - 1/10 x DATA(1, 2) + + 2/35 y DATA(-2, 0) - 2/49 x y DATA(1, -2) + 4/49 x y DATA(-2, 2) - 2 2 2 - + 1/40 x DATA(2, 1) + 1/10 x DATA(-1, 2) - 1/40 x DATA(2, -1) + - 2/49 x y DATA(-2, 1) + 1/49 x y DATA(-1, 1) + 1/49 x y DATA(1, -1) - 2 2 2 - + 1/20 x DATA(2, 2) - 1/20 x DATA(-2, 2) - 1/40 x DATA(-2, 1) + - 2/49 x y DATA(-2, -1) + 4/49 x y DATA(2, -2) + 4/49 x y DATA(-2, -2) - 2 2 2 - + 1/40 x DATA(-2, -1) - 1/20 x DATA(2, -2) - 1/10 x DATA(-1, -2) + 21 11 + - 2/49 x y DATA(-1, -2) + --- DATA(-2, -1) + --- DATA(2, -2) + 200 150 - 2 11 - + 1/10 x DATA(1, -2) - --- DATA(-2, -2) - 2/35 x DATA(0, 2) - 150 + 11 21 21 11 + - --- DATA(-2, -2) + --- DATA(-1, -2) - --- DATA(1, -2) + --- DATA(-2, 2) + 150 200 200 150 - + 1/35 x DATA(0, -1) + 2/35 x DATA(0, -2) + 21 + - --- DATA(-2, 1) + 200 > coeff_as_lc_of_data(%, posn_list_2d_size5); - 2 2 11 -[COEFF(-2, -2) = 4/49 x y + 1/20 x + 1/20 y - 2/35 y - 2/35 x - ---, - 150 +bytes used=105150268, alloc=2489912, time=10.45 + 2 2 11 +[COEFF(-2, -2) = - 2/35 x + 1/20 x + 1/20 y + 4/49 x y - 2/35 y - ---, + 150 - 2 2 21 - COEFF(-1, -2) = - 2/49 x y - 1/35 y + 1/35 x + 1/40 y - 1/10 x + ---, - 200 + 2 2 21 + COEFF(-1, -2) = 1/40 y - 1/10 x + 1/35 x + --- - 2/49 x y - 1/35 y, + 200 COEFF(0, -2) = 2/35 x - 4/49 x y, - 2 21 2 - COEFF(1, -2) = - 2/49 x y + 1/35 x + 1/10 x + 1/35 y - --- - 1/40 y , - 200 + 21 2 2 + COEFF(1, -2) = - 2/49 x y - --- + 1/35 y - 1/40 y + 1/10 x + 1/35 x, + 200 - 11 2 2 - COEFF(2, -2) = --- - 1/20 y - 1/20 x - 2/35 x + 4/49 x y + 2/35 y, - 150 + 2 11 2 + COEFF(2, -2) = - 1/20 x + 2/35 y - 2/35 x + --- - 1/20 y + 4/49 x y, + 150 - 21 2 2 - COEFF(-2, -1) = --- + 1/35 y - 1/10 y - 2/49 x y - 1/35 x + 1/40 x , - 200 + 2 2 21 + COEFF(-2, -1) = - 1/10 y + 1/35 y + 1/40 x - 1/35 x + --- - 2/49 x y, + 200 - 2 2 37 - COEFF(-1, -1) = 1/49 x y - 1/20 y - 1/20 x + 1/70 x + 1/70 y + ---, - 300 + 2 2 37 + COEFF(-1, -1) = - 1/20 x + 1/70 y + 1/70 x + 1/49 x y - 1/20 y + ---, + 300 COEFF(0, -1) = 1/35 x + 2/49 x y, - 37 2 2 - COEFF(1, -1) = - --- + 1/49 x y + 1/20 x - 1/70 y + 1/70 x + 1/20 y , - 300 + 2 37 2 + COEFF(1, -1) = 1/20 y - 1/70 y + 1/70 x - --- + 1/20 x + 1/49 x y, + 300 - 2 2 21 - COEFF(2, -1) = - 1/35 x + 1/10 y - 2/49 x y - 1/35 y - 1/40 x - ---, - 200 + 2 21 2 + COEFF(2, -1) = - 1/35 y - 1/40 x - 1/35 x - --- - 2/49 x y + 1/10 y , + 200 - COEFF(-2, 0) = 2/35 y - 4/49 x y, COEFF(-1, 0) = 1/35 y + 2/49 x y, + COEFF(-2, 0) = - 4/49 x y + 2/35 y, COEFF(-1, 0) = 2/49 x y + 1/35 y, - COEFF(0, 0) = 4/49 x y, COEFF(1, 0) = - 1/35 y + 2/49 x y, + COEFF(0, 0) = 4/49 x y, COEFF(1, 0) = 2/49 x y - 1/35 y, COEFF(2, 0) = - 4/49 x y - 2/35 y, - 2 2 21 - COEFF(-2, 1) = 1/35 y + 1/35 x - 2/49 x y + 1/10 y - 1/40 x - ---, - 200 + 21 2 2 + COEFF(-2, 1) = - --- - 1/40 x + 1/35 x + 1/35 y - 2/49 x y + 1/10 y , + 200 2 37 2 - COEFF(-1, 1) = 1/20 y - --- - 1/70 x + 1/20 x + 1/70 y + 1/49 x y, + COEFF(-1, 1) = 1/20 y - --- + 1/70 y + 1/20 x - 1/70 x + 1/49 x y, 300 - COEFF(0, 1) = - 1/35 x + 2/49 x y, + COEFF(0, 1) = 2/49 x y - 1/35 x, - 37 2 2 - COEFF(1, 1) = 1/49 x y + --- - 1/20 y - 1/70 x - 1/20 x - 1/70 y, - 300 + 37 2 2 + COEFF(1, 1) = --- - 1/20 y - 1/20 x + 1/49 x y - 1/70 y - 1/70 x, + 300 - 21 2 2 - COEFF(2, 1) = --- + 1/40 x - 1/10 y + 1/35 x - 1/35 y - 2/49 x y, - 200 + 2 21 2 + COEFF(2, 1) = 1/40 x + 1/35 x + --- - 1/35 y - 2/49 x y - 1/10 y , + 200 - 2 2 11 - COEFF(-2, 2) = - 1/20 x + 4/49 x y + 2/35 x - 1/20 y - 2/35 y + ---, - 150 + 2 2 11 + COEFF(-2, 2) = - 1/20 x + 2/35 x - 1/20 y + --- - 2/35 y + 4/49 x y, + 150 - 2 2 21 - COEFF(-1, 2) = 1/10 x - 1/35 y - 1/35 x - 1/40 y - --- - 2/49 x y, - 200 + 2 2 21 + COEFF(-1, 2) = - 1/35 y + 1/10 x - 1/40 y - --- - 2/49 x y - 1/35 x, + 200 COEFF(0, 2) = - 2/35 x - 4/49 x y, - 2 2 21 - COEFF(1, 2) = - 1/35 x + 1/40 y - 2/49 x y + 1/35 y - 1/10 x + ---, - 200 + 21 2 2 + COEFF(1, 2) = - 1/35 x - 2/49 x y + --- - 1/10 x + 1/40 y + 1/35 y, + 200 - 2 11 2 - COEFF(2, 2) = 2/35 y + 4/49 x y + 1/20 x - --- + 2/35 x + 1/20 y ] - 150 + 11 2 2 + COEFF(2, 2) = 2/35 y + 2/35 x - --- + 4/49 x y + 1/20 y + 1/20 x ] + 150 > print_coeff__lc_of_data(%, "coeff_dxy_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-dxy.compute.c"); -bytes used=106123844, alloc=2424388, time=10.27 -bytes used=107128472, alloc=2424388, time=10.35 -bytes used=108128708, alloc=2424388, time=10.53 -bytes used=109128920, alloc=2424388, time=10.69 -bytes used=110129208, alloc=2424388, time=10.83 -bytes used=111129472, alloc=2424388, time=11.03 -bytes used=112129776, alloc=2424388, time=11.21 +bytes used=106150484, alloc=2489912, time=10.53 +bytes used=107150764, alloc=2489912, time=10.68 +bytes used=108151004, alloc=2489912, time=10.81 +bytes used=109151492, alloc=2489912, time=10.97 +bytes used=110151712, alloc=2489912, time=11.14 +bytes used=111151948, alloc=2489912, time=11.29 +bytes used=112152148, alloc=2489912, time=11.48 > # d^2/dy^2 > simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); -bytes used=113130192, alloc=2424388, time=11.31 -bytes used=114130376, alloc=2424388, time=11.38 +bytes used=113152336, alloc=2489912, time=11.54 57 53 166 181 - -- DATA(0, 0) - -- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) 98 98 735 735 - 53 181 166 181 - - -- DATA(-1, 0) + --- DATA(1, -1) + --- DATA(0, -1) + --- DATA(-1, -1) - 98 735 735 735 - - 181 71 289 41 - + --- DATA(-1, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - -- DATA(2, 0) - 735 2940 2940 98 + + 1/10 y DATA(1, 2) + 1/10 y DATA(-1, 2) - 1/5 y DATA(-1, 1) - 226 71 191 226 - + --- DATA(2, 1) + ---- DATA(-1, 2) + ---- DATA(0, 2) + --- DATA(2, -1) - 735 2940 2940 735 + - 1/10 y DATA(-1, -2) - 1/10 y DATA(1, -2) + 1/10 y DATA(-2, 2) - 289 226 2 - - ---- DATA(-2, 2) + --- DATA(-2, 1) - 2/5 y DATA(2, 1) - 2940 735 + + 1/5 y DATA(1, -1) - 1/5 y DATA(1, 1) - 1/5 y DATA(2, 1) - 2 2 2 - + 1/10 y DATA(-1, 2) - 2/5 y DATA(2, -1) + 1/10 y DATA(-2, 2) + 2 + + 1/5 y DATA(2, -1) + 1/10 y DATA(2, 2) - 2/5 y DATA(-1, 1) - 2 2 2 - - 2/5 y DATA(-2, 1) - 2/5 y DATA(-2, -1) + 1/10 y DATA(2, -2) + 2 2 2 + - 2/5 y DATA(2, -1) + 1/10 y DATA(2, 2) + 1/10 y DATA(1, 2) - 2 2 2 - + 1/10 y DATA(-1, -2) + 1/10 y DATA(2, 2) - 2/5 y DATA(1, 1) + 2 2 2 + + 1/10 y DATA(-1, 2) - 2/5 y DATA(1, 1) - 2/5 y DATA(2, 1) - 2 2 2 - - 2/5 y DATA(1, -1) - 2/5 y DATA(-1, -1) - 2/5 y DATA(-1, 1) + - 1/5 y DATA(-2, 1) + 1/5 y DATA(-1, -1) + 1/5 y DATA(-2, -1) - - 1/20 x y DATA(-1, 2) - 1/5 x y DATA(-2, -1) - 1/10 x y DATA(2, -2) + 2 + - 1/10 y DATA(2, -2) - 1/10 y DATA(-2, -2) + 1/10 y DATA(1, -2) - + 1/10 x y DATA(2, 2) - 1/5 x y DATA(2, 1) - 1/5 y DATA(1, 1) + 2 2 2 + + 1/10 y DATA(-2, 2) - 2/5 y DATA(-2, 1) - 1/49 x DATA(-1, 2) - + 1/5 x y DATA(2, -1) - 1/10 x y DATA(-2, 2) + 1/5 x y DATA(-2, 1) + 2 2 2 + - 2/5 y DATA(-1, -1) - 2/5 y DATA(1, -1) - 2/5 y DATA(-2, -1) - + 1/10 y DATA(-1, 2) + 1/5 y DATA(2, -1) + 1/10 y DATA(-2, 2) + 2 2 2 + + 1/10 y DATA(2, -2) + 1/10 y DATA(-2, -2) + 1/10 y DATA(-1, -2) - - 1/5 y DATA(-2, 1) + 1/5 y DATA(-2, -1) - 1/10 y DATA(2, -2) + 2 2 2 + + 2/49 x DATA(-2, -2) - 1/49 x DATA(2, 1) - 1/49 x DATA(2, -1) - - 1/10 y DATA(-1, -2) - 1/10 y DATA(1, -2) - 1/10 y DATA(-2, -2) + 2 2 2 + + 2/49 x DATA(2, 2) - 1/49 x DATA(1, 2) - 1/49 x DATA(-2, -1) - 2 2 - + 1/5 y DATA(1, -1) + 1/10 y DATA(1, -2) + 1/10 y DATA(-2, -2) + 2 2 + + 2/49 x DATA(2, -2) + 1/98 x DATA(1, 1) - 2/35 x DATA(-2, 2) - 2 - + 1/10 y DATA(1, 2) + 1/20 x y DATA(-1, -2) - 1/20 x y DATA(1, -2) + 2 2 + + 2/35 x DATA(2, 2) - 1/49 x DATA(-1, -2) - 1/49 x DATA(1, -2) - + 1/10 x y DATA(-2, -2) + 1/5 y DATA(-1, -1) - 1/5 y DATA(-1, 1) + 2 2 + + 2/49 x DATA(-2, 2) - 1/49 x DATA(-2, 1) - 1/35 x DATA(2, 1) - + 1/10 y DATA(1, 2) + 1/10 y DATA(2, 2) - 1/5 y DATA(2, 1) + 2 2 2 + + 1/98 x DATA(-1, 1) + 1/98 x DATA(-1, -1) + 1/98 x DATA(1, -1) - - 1/35 x DATA(2, -1) - 2/35 x DATA(-2, 2) + 1/35 x DATA(-2, 1) + + 1/35 x DATA(1, -2) + 1/35 x DATA(-2, 1) - 1/70 x DATA(1, -1) - + 1/35 x DATA(-2, -1) + 2/35 x DATA(2, -2) - 1/35 x DATA(-1, -2) + + 1/35 x DATA(-2, -1) + 2/35 x DATA(2, -2) - 2/35 x DATA(-2, -2) - + 1/35 x DATA(1, -2) - 2/35 x DATA(-2, -2) - 1/35 x DATA(2, 1) + + 1/35 x DATA(1, 2) - 1/35 x DATA(-1, 2) + 1/70 x DATA(-1, 1) - 226 41 - + --- DATA(-2, -1) - -- DATA(-2, 0) - 1/35 x DATA(-1, 2) - 735 98 + - 1/35 x DATA(2, -1) - 1/70 x DATA(1, 1) - 1/35 x DATA(-1, -2) - - 1/70 x DATA(1, 1) - 1/70 x DATA(1, -1) + 1/70 x DATA(-1, -1) + 226 41 226 + + 1/70 x DATA(-1, -1) + --- DATA(2, 1) - -- DATA(2, 0) + --- DATA(2, -1) + 735 98 735 - + 1/70 x DATA(-1, 1) + 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2) + 289 + + 1/5 y DATA(0, -1) - 1/10 y DATA(0, -2) - ---- DATA(2, 2) + 2940 - 2 2 2 - + 2/49 x DATA(-2, -2) + 1/98 x DATA(1, 1) + 1/98 x DATA(1, -1) + 71 191 71 53 + + ---- DATA(1, 2) + ---- DATA(0, 2) + ---- DATA(-1, 2) - -- DATA(-1, 0) + 2940 2940 2940 98 - 2 2 - + 1/98 x DATA(-1, -1) + 1/98 x DATA(-1, 1) + 1/20 x y DATA(1, 2) + 181 181 166 181 + + --- DATA(-1, 1) + --- DATA(-1, -1) + --- DATA(0, -1) + --- DATA(1, -1) + 735 735 735 735 - 289 - + 1/10 x y DATA(1, -1) - 1/10 x y DATA(1, 1) - ---- DATA(2, -2) - 2940 + 2 2 2 + - 2/49 x DATA(2, 0) + 1/49 x DATA(1, 0) + 1/49 x DATA(0, -1) - 71 191 71 - + ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(1, -2) - 2940 2940 2940 + 2 2 2 + - 2/49 x DATA(-2, 0) - 2/49 x DATA(0, -2) + 1/49 x DATA(-1, 0) - 2 - - 1/10 x y DATA(-1, -1) + 1/10 x y DATA(-1, 1) - 1/49 x DATA(1, 2) + 2 2 2 + - 2/49 x DATA(0, 2) + 1/49 x DATA(0, 1) + 2/49 x DATA(0, 0) - 2 2 2 - - 1/49 x DATA(2, 1) - 1/49 x DATA(-1, 2) - 1/49 x DATA(2, -1) + - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) - 1/5 x y DATA(2, 1) - 2 2 2 - + 2/49 x DATA(2, 2) + 2/49 x DATA(-2, 2) - 1/49 x DATA(-2, 1) + + 1/5 x y DATA(2, -1) + 1/10 x y DATA(2, 2) + 1/20 x y DATA(1, 2) - 2 2 2 - - 1/49 x DATA(-2, -1) + 2/49 x DATA(2, -2) - 1/49 x DATA(-1, -2) + - 1/20 x y DATA(-1, 2) - 1/20 x y DATA(1, -2) - 1/10 x y DATA(-2, 2) - 2 289 - - 1/49 x DATA(1, -2) - ---- DATA(-2, -2) - 1/35 x DATA(1, 0) - 2940 + + 1/5 x y DATA(-2, 1) + 1/10 x y DATA(-1, 1) + 1/35 x DATA(-1, 0) - + 1/35 x DATA(-1, 0) + 1/5 y DATA(0, -1) - 2/35 x DATA(2, 0) + + 1/10 x y DATA(1, -1) - 1/5 x y DATA(-2, -1) - 1/10 x y DATA(2, -2) - 2 - + 1/10 y DATA(0, 2) - 1/10 y DATA(0, -2) + 3/5 y DATA(-2, 0) + + 1/10 x y DATA(-2, -2) + 1/20 x y DATA(-1, -2) - 1/35 x DATA(1, 0) - 2 2 - + 3/5 y DATA(-1, 0) + 3/5 y DATA(1, 0) + 2/35 x DATA(-2, 0) + 226 + - 2/35 x DATA(2, 0) + 2/35 x DATA(-2, 0) + --- DATA(-2, -1) + 735 - 2 2 2 - + 3/5 y DATA(0, 0) - 2/5 y DATA(0, 1) - 2/5 y DATA(0, -1) + 289 289 71 + - ---- DATA(2, -2) - ---- DATA(-2, -2) + ---- DATA(-1, -2) + 2940 2940 2940 - 2 2 2 - + 1/10 y DATA(0, 2) + 1/10 y DATA(0, -2) + 1/49 x DATA(1, 0) + 191 71 2 + + ---- DATA(0, -2) + ---- DATA(1, -2) - 2/5 y DATA(0, -1) + 2940 2940 - 2 2 2 - + 3/5 y DATA(2, 0) - 2/49 x DATA(-2, 0) + 1/49 x DATA(-1, 0) + 2 2 2 + + 3/5 y DATA(-1, 0) + 1/10 y DATA(0, -2) + 3/5 y DATA(-2, 0) - 2 2 - - 1/5 y DATA(0, 1) + 2/49 x DATA(0, 0) + 1/49 x DATA(0, 1) + 289 2 2 + - ---- DATA(-2, 2) - 2/5 y DATA(0, 1) + 1/10 y DATA(0, 2) + 2940 - 2 2 2 - + 1/49 x DATA(0, -1) - 2/49 x DATA(0, 2) - 2/49 x DATA(0, -2) + 2 2 41 226 + + 3/5 y DATA(1, 0) + 3/5 y DATA(2, 0) - -- DATA(-2, 0) + --- DATA(-2, 1) + 98 735 - 2 - - 2/49 x DATA(2, 0) + 2 + + 3/5 y DATA(0, 0) - 1/5 y DATA(0, 1) + 1/10 y DATA(0, 2) > coeff_as_lc_of_data(%, posn_list_2d_size5); - 2 2 289 -[COEFF(-2, -2) = 1/10 y + 1/10 x y - 2/35 x + 2/49 x - 1/10 y - ----, - 2940 - - 71 2 2 - COEFF(-1, -2) = ---- + 1/10 y + 1/20 x y - 1/10 y - 1/35 x - 1/49 x , - 2940 +bytes used=114153352, alloc=2489912, time=11.61 + 289 2 2 +[COEFF(-2, -2) = - 1/10 y - ---- + 2/49 x - 2/35 x + 1/10 y + 1/10 x y, + 2940 - 2 191 2 - COEFF(0, -2) = 1/10 y + ---- - 2/49 x - 1/10 y, - 2940 + 2 71 2 + COEFF(-1, -2) = 1/20 x y - 1/10 y - 1/35 x + 1/10 y + ---- - 1/49 x , + 2940 - 2 2 71 - COEFF(1, -2) = - 1/10 y + 1/35 x - 1/20 x y - 1/49 x + 1/10 y + ----, - 2940 + 191 2 2 + COEFF(0, -2) = - 1/10 y + ---- + 1/10 y - 2/49 x , + 2940 - 2 289 2 - COEFF(2, -2) = 2/49 x - ---- + 1/10 y - 1/10 x y + 2/35 x - 1/10 y, - 2940 + 2 71 2 + COEFF(1, -2) = 1/10 y - 1/20 x y + ---- - 1/10 y + 1/35 x - 1/49 x , + 2940 - 2 2 226 - COEFF(-2, -1) = 1/5 y - 2/5 y - 1/49 x + 1/35 x + --- - 1/5 x y, - 735 + 2 2 289 + COEFF(2, -2) = 2/49 x - 1/10 x y + 1/10 y - ---- - 1/10 y + 2/35 x, + 2940 - 2 181 2 - COEFF(-1, -1) = - 2/5 y - 1/10 x y + 1/5 y + 1/70 x + --- + 1/98 x , + 2 226 2 + COEFF(-2, -1) = - 1/5 x y - 1/49 x + 1/5 y + 1/35 x + --- - 2/5 y , 735 - 2 2 166 - COEFF(0, -1) = 1/49 x - 2/5 y + --- + 1/5 y, - 735 + 181 2 2 + COEFF(-1, -1) = 1/70 x + --- - 1/10 x y + 1/5 y + 1/98 x - 2/5 y , + 735 - 2 2 181 - COEFF(1, -1) = - 1/70 x + 1/5 y - 2/5 y + 1/10 x y + 1/98 x + ---, + 2 166 2 + COEFF(0, -1) = 1/49 x + --- + 1/5 y - 2/5 y , + 735 + + 2 2 181 + COEFF(1, -1) = - 1/70 x + 1/10 x y + 1/5 y + 1/98 x - 2/5 y + ---, 735 - 2 226 2 - COEFF(2, -1) = - 1/35 x - 2/5 y + --- - 1/49 x + 1/5 x y + 1/5 y, - 735 + 2 226 2 + COEFF(2, -1) = 1/5 y + 1/5 x y - 1/35 x - 1/49 x + --- - 2/5 y , + 735 - 41 2 2 - COEFF(-2, 0) = - -- + 2/35 x - 2/49 x + 3/5 y , + 41 2 2 + COEFF(-2, 0) = - -- + 3/5 y + 2/35 x - 2/49 x , 98 - 2 2 53 - COEFF(-1, 0) = 3/5 y + 1/35 x + 1/49 x - --, - 98 - - 2 57 2 - COEFF(0, 0) = 3/5 y - -- + 2/49 x , - 98 - - 2 2 53 - COEFF(1, 0) = 3/5 y + 1/49 x - 1/35 x - --, - 98 + 53 2 2 + COEFF(-1, 0) = 1/35 x - -- + 1/49 x + 3/5 y , + 98 - 41 2 2 - COEFF(2, 0) = - -- - 2/49 x - 2/35 x + 3/5 y , + 57 2 2 + COEFF(0, 0) = - -- + 3/5 y + 2/49 x , 98 - 226 2 2 - COEFF(-2, 1) = 1/35 x - 1/5 y + --- + 1/5 x y - 2/5 y - 1/49 x , - 735 + 2 2 53 + COEFF(1, 0) = - 1/35 x + 3/5 y + 1/49 x - --, + 98 - 2 181 2 - COEFF(-1, 1) = - 1/5 y + 1/70 x + 1/10 x y - 2/5 y + --- + 1/98 x , - 735 + 2 2 41 + COEFF(2, 0) = - 2/49 x - 2/35 x + 3/5 y - --, + 98 - 2 2 166 - COEFF(0, 1) = - 2/5 y + 1/49 x - 1/5 y + ---, - 735 + 2 2 226 + COEFF(-2, 1) = - 1/49 x - 1/5 y + 1/5 x y - 2/5 y + 1/35 x + ---, + 735 - 181 2 2 - COEFF(1, 1) = - 1/70 x + --- - 1/10 x y + 1/98 x - 2/5 y - 1/5 y, - 735 + 2 2 181 + COEFF(-1, 1) = 1/70 x - 2/5 y + 1/10 x y + 1/98 x - 1/5 y + ---, + 735 + + 2 166 2 + COEFF(0, 1) = 1/49 x - 1/5 y + --- - 2/5 y , + 735 - 226 2 2 - COEFF(2, 1) = --- - 1/5 y - 1/49 x - 1/35 x - 2/5 y - 1/5 x y, + 181 2 2 + COEFF(1, 1) = --- - 1/70 x + 1/98 x - 1/5 y - 1/10 x y - 2/5 y , 735 - 2 289 2 - COEFF(-2, 2) = - 2/35 x + 2/49 x - 1/10 x y - ---- + 1/10 y + 1/10 y , - 2940 + 2 226 2 + COEFF(2, 1) = - 1/49 x + --- - 1/35 x - 2/5 y - 1/5 y - 1/5 x y, + 735 - 71 2 2 - COEFF(-1, 2) = ---- - 1/49 x + 1/10 y - 1/35 x + 1/10 y - 1/20 x y, - 2940 + 2 289 2 + COEFF(-2, 2) = - 2/35 x + 2/49 x - ---- + 1/10 y - 1/10 x y + 1/10 y , + 2940 - 2 2 191 - COEFF(0, 2) = - 2/49 x + 1/10 y + 1/10 y + ----, - 2940 + 2 2 71 + COEFF(-1, 2) = 1/10 y - 1/49 x - 1/35 x + 1/10 y + ---- - 1/20 x y, + 2940 + + 191 2 2 + COEFF(0, 2) = ---- + 1/10 y + 1/10 y - 2/49 x , + 2940 - 71 2 2 - COEFF(1, 2) = ---- + 1/10 y + 1/20 x y + 1/10 y + 1/35 x - 1/49 x , + 71 2 2 + COEFF(1, 2) = ---- + 1/10 y - 1/49 x + 1/35 x + 1/10 y + 1/20 x y, 2940 - 289 2 2 - COEFF(2, 2) = - ---- + 1/10 y + 2/49 x + 2/35 x + 1/10 x y + 1/10 y ] + 289 2 2 + COEFF(2, 2) = - ---- + 1/10 y + 2/49 x + 1/10 y + 1/10 x y + 2/35 x] 2940 > print_coeff__lc_of_data(%, "coeff_dyy_", "fp", > "2d.coeffs/2d.cube.order4.smooth0/coeff-dyy.compute.c"); -bytes used=115130604, alloc=2424388, time=11.46 -bytes used=116138968, alloc=2424388, time=11.55 -bytes used=117139208, alloc=2424388, time=11.72 -bytes used=118140008, alloc=2424388, time=11.80 -bytes used=119140212, alloc=2424388, time=12.00 -bytes used=120140404, alloc=2424388, time=12.21 -bytes used=121141040, alloc=2424388, time=12.38 +bytes used=115153616, alloc=2489912, time=11.69 +bytes used=116153852, alloc=2489912, time=11.82 +bytes used=117154004, alloc=2489912, time=11.94 +bytes used=118154188, alloc=2489912, time=12.11 +bytes used=119154664, alloc=2489912, time=12.30 +bytes used=120154836, alloc=2489912, time=12.46 > ################################################################################ > quit -bytes used=121567580, alloc=2424388, time=12.41 +bytes used=121070196, alloc=2489912, time=12.59 |