diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log | 6898 |
1 files changed, 0 insertions, 6898 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log deleted file mode 100644 index 20887a8..0000000 --- a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log +++ /dev/null @@ -1,6898 +0,0 @@ - |\^/| Maple 7 (IBM INTEL LINUX) -._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. - \ MAPLE / All rights reserved. Maple is a registered trademark of - <____ ____> Waterloo Maple Inc. - | Type ? for help. -# util.maple -- misc utility routines -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.5 2002/09/02 10:21:03 jthorn Exp $ -> -# -# fix_rationals - convert numbers to RATIONAL() calls -# nonmatching_names - find names in a list which *don't* have a specified prefix -# sprint_numeric_list - convert a numeric list to a valid C identifier suffix -# print_name_list_dcl - print C declarations for a list of names -# -# hypercube_points - compute all (integer) points in an N-dimensional hypercube -# -# ftruncate - truncate a file to zero length -# -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function converts all {integer, rational} subexpressions of its -# input except integer exponents and -1 factors in products, into function -# calls -# RATIONAL(num,den) -# This is useful in conjunction with the C() library function, since -# -# C( (1/3) * foo * bar ) -# t0 = foo*bar/3; -# -# generates a (slow) division (and runs the risk of mixed-mode-arithmetic -# problems), while -# -# C((1.0/3.0) * foo * bar); -# t0 = 0.3333333333*foo*bar; -# -# suffers from roundoff error. With this function, -# -# fix_rationals((1/3) * foo * bar); -# RATIONAL(1,3) foo bar -# C(%); -# t0 = RATIONAL(1.0,3.0)*foo*bar; -# -# which a C preprocessor macro can easily convert to the desired -# -# t0 = (1.0/3.0)*foo*bar; -# -# Additionally, this function can be told to leave certain types of -# subexpressions unconverged. For example, -# fix_rationals(expr, type, specfunc(integer, DATA)); -# will leave all subexpressions of the form DATA(integer arguments) -# unconverted. -# -# Arguments: -# expr = (in) The expression to be converted. -# inert_fn = (optional in) -# If specified, this argument should be a Boolean procedure -# or the name of a Boolean procedure. This procedure should -# take one or more argument, and return true if and only if -# the first argument should *not* be converted, i.e. if we -# should leave this expression unchanged. See the last -# example above. -# ... = (optional in) -# Any further arguments are passed as additional arguments to -# the inert_fn procedure. -# -> fix_rationals := -> proc( -> expr::{ -> algebraic, name = algebraic, -> list({algebraic, name = algebraic}), -> set ({algebraic, name = algebraic}) -> }, -> inert_fn::{name, procedure} -> ) -> local nn, k, -> base, power, fbase, fpower, -> fn, fn_args_list, -> num, den, mult; -> -# do we want to convert this expression? -> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) -> then return expr; -> end if; -> -# recurse over lists and sets -> if (type(expr, {list,set})) -> then return map(fix_rationals, expr, args[2..nargs]); -> end if; -> -# recurse over equation right hand sides -> if (type(expr, name = algebraic)) -> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); -> end if; -> -# recurse over functions other than RATIONAL() -> if (type(expr, function)) -> then -> fn := op(0, expr); -> if (fn <> 'RATIONAL') -> then -> fn_args_list := [op(expr)]; -> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); -> fn; return '%'( op(fn_args_list) ); -> end if; -> end if; -> -> nn := nops(expr); -> -# recurse over sums -> if (type(expr, `+`)) -> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); -> end if; -> -# recurse over products -# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) -> if (type(expr, `*`)) -> then -> if (op(1, expr) = -1) -> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), -> args[2..nargs]); -> else return product('fix_rationals(op(k,expr), args[2..nargs])', -> 'k'=1..nn); -> end if; -> end if; -> -# recurse over powers -# ... leaving integer exponents intact -> if (type(expr, `^`)) -> then -> base := op(1, expr); -> power := op(2, expr); -> -> fbase := fix_rationals(base, args[2..nargs]); -> if (type(power, integer)) -> then fpower := power; -> else fpower := fix_rationals(power, args[2..nargs]); -> end if; -> return fbase ^ fpower; -> end if; -> -# fix integers and fractions -> if (type(expr, integer)) -> then return 'RATIONAL'(expr, 1); -> end if; -> if (type(expr, fraction)) -> then -> num := op(1, expr); -> den := op(2, expr); -> -> return 'RATIONAL'(num, den); -> end if; -> -# turn Maple floating-point into integer fraction, then recursively fix that -> if (type(expr, float)) -> then -> mult := op(1, expr); -> power := op(2, expr); -> return fix_rationals(mult * 10^power, args[2..nargs]); -> end if; -> -# identity op on names -> if (type(expr, name)) -> then return expr; -> end if; -> -# unknown type -> error "%0", -> "unknown type for expr!", -> " whattype(expr) = ", whattype(expr), -> " expr = ", expr; -> end proc; -fix_rationals := proc(expr::{algebraic, name = algebraic, -list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, -inert_fn::{procedure, name}) -local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; - if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr - end if; - if type(expr, {set, list}) then - return map(fix_rationals, expr, args[2 .. nargs]) - end if; - if type(expr, name = algebraic) then - return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) - end if; - if type(expr, function) then - fn := op(0, expr); - if fn <> 'RATIONAL' then - fn_args_list := [op(expr)]; - fn_args_list := - map(fix_rationals, fn_args_list, args[2 .. nargs]); - fn; - return '%'(op(fn_args_list)) - end if - end if; - nn := nops(expr); - if type(expr, `+`) then return - sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) - end if; - if type(expr, `*`) then - if op(1, expr) = -1 then return -fix_rationals( - remove(type, expr, 'identical(-1)'), args[2 .. nargs]) - else return product('fix_rationals(op(k, expr), args[2 .. nargs])', - 'k' = 1 .. nn) - end if - end if; - if type(expr, `^`) then - base := op(1, expr); - power := op(2, expr); - fbase := fix_rationals(base, args[2 .. nargs]); - if type(power, integer) then fpower := power - else fpower := fix_rationals(power, args[2 .. nargs]) - end if; - return fbase^fpower - end if; - if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; - if type(expr, fraction) then - num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) - end if; - if type(expr, float) then - mult := op(1, expr); - power := op(2, expr); - return fix_rationals(mult*10^power, args[2 .. nargs]) - end if; - if type(expr, name) then return expr end if; - error "%0", "unknown type for expr!", " whattype(expr) = ", - whattype(expr), " expr = ", expr -end proc - -> -################################################################################ -> -# -# This function finds names in a list which *don't* have a specified prefix. -# -# Arguments: -# name_list = A list of the names. -# prefix = The prefix we want to filter out. -# -# Results: -# This function returns the subset list of names which don't have the -# specified prefix. -# -> nonmatching_names := -> proc( name_list::list({name,string}), prefix::{name,string} ) -> -> select( proc(n) -> evalb(not StringTools[IsPrefix](prefix,n)); -> end proc -> , -> name_list -> ); -> end proc; -nonmatching_names := proc( -name_list::list({name, string}), prefix::{name, string}) - select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, - name_list) -end proc - -> -################################################################################ -> -# -# This function converts a numeric list to a string which is a valid -# C identifier suffix: elements are separated by "_", decimal points are -# replaced by "x", and all nonzero values have explicit +/- signs, which -# are replaced by "p"/"m". -# -# For example, [0,-3.5,+4] --> "0_m3x5_p4". -# -> sprint_numeric_list := -> proc(nlist::list(numeric)) -> -# generate preliminary string, eg "+0_-3.5_+4" -> map2(sprintf, "%+a", nlist); -> ListTools[Join](%, "_"); -> cat(op(%)); -> -# fixup bad characters -> StringTools[SubstituteAll](%, "+0", "0"); -> StringTools[CharacterMap](".+-", "xpm", %); -> -> return %; -> end proc; -sprint_numeric_list := proc(nlist::list(numeric)) - map2(sprintf, "%+a", nlist); - ListTools[Join](%, "_"); - cat(op(%)); - StringTools[SubstituteAll](%, "+0", "0"); - StringTools[CharacterMap](".+-", "xpm", %); - return % -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C declarations for a list of names. -# -# Argument: -# name_list = A list of the names. -# type_name = The C type of the names, eg. "double". -# file_name = The file name to write the declaration to. This is -# truncated before writing. -# -> print_name_list_dcl := -> proc( name_list::list({name,string}), -> type_name::string, -> file_name::string ) -> local blanks, separator_string; -> -> ftruncate(file_name); -> -> map( -> proc(var::{name,string}) -> fprintf(file_name, -> "%s %s;\n", -> type_name, var); -> end proc -> , -> name_list -> ); -> -> fclose(file_name); -> NULL; -> end proc; -print_name_list_dcl := proc( -name_list::list({name, string}), type_name::string, file_name::string) -local blanks, separator_string; - ftruncate(file_name); - map(proc(var::{name, string}) - fprintf(file_name, "%s %s;\n", type_name, var) - end proc, name_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes a list of all the (integer) points in an -# N-dimensional hypercube, in lexicographic order. The present -# implementation requires N <= 4. -# -# Arguments: -# cmin,cmax = N-element lists of cube minimum/maximum coordinates. -# -# Results: -# The function returns a set of d-element lists giving the coordinates. -# For example, -# hypercube([0,0], [2,1] -# returns -# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } -> hypercube_points := -> proc(cmin::list(integer), cmax::list(integer)) -> local N, i,j,k,l; -> -> N := nops(cmin); -> if (nops(cmax) <> N) -> then error -> "must have same number of dimensions for min and max coordinates!"; -> fi; -> -> if (N = 1) -> then return [seq([i], i=cmin[1]..cmax[1])]; -> elif (N = 2) -> then return [ -> seq( -> seq([i,j], j=cmin[2]..cmax[2]), -> i=cmin[1]..cmax[1]) -> ]; -> elif (N = 3) -> then return [ -> seq( -> seq( -> seq([i,j,k], k=cmin[3]..cmax[3]), -> j=cmin[2]..cmax[2] ), -> i=cmin[1]..cmax[1]) -> ]; -> elif (N = 4) -> then return [ -> seq( -> seq( -> seq( -> seq([i,j,k,l], l=cmin[4]..cmax[4]), -> k=cmin[3]..cmax[3] ), -> j=cmin[2]..cmax[2]), -> i=cmin[1]..cmax[1]) -> ]; -> else -> error "implementation restriction: must have N <= 4, got %1!", N; -> fi; -> end proc; -hypercube_points := proc(cmin::list(integer), cmax::list(integer)) -local N, i, j, k, l; - N := nops(cmin); - if nops(cmax) <> N then error - "must have same number of dimensions for min and max coordinates!" - end if; - if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] - elif N = 2 then return - [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] - elif N = 3 then return [seq( - seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) - , i = cmin[1] .. cmax[1])] - elif N = 4 then return [seq(seq(seq( - seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), - j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] - else error "implementation restriction: must have N <= 4, got %1!", N - end if -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function truncates a file to 0 length if it exists, or creates -# it at that length if it doesn't exist. -# -# Arguments: -# file_name = (in) The name of the file. -# -> ftruncate := -> proc(file_name::string) -> fopen(file_name, 'WRITE'); -> fclose(%); -> NULL; -> end proc; -ftruncate := - - proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc - -# interpolate.maple -- compute interpolation formulas/coefficients -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.11 2002/09/02 10:21:02 jthorn Exp $ -> -# -# <<<representation of numbers, data values, etc>>> -# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant -# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant -# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) -# -# print_coeffs__lc_of_data - print C code to compute coefficients -# print_fetch_data - print C code to fetch input array chunk into struct data -# print_store_coeffs - print C code to store struct coeffs "somewhere" -# print_interp_cmpt__lc_of_data - print C code for computation of interpolant -# -# coeff_name - name of coefficient of data at a given [m] coordinate -# data_var_name - name of variable storing data value at a given [m] coordinate -# -> -################################################################################ -> -# -# ***** representation of numbers, data values, etc ***** -# -# We use RATIONAL(p.0,q.0) to denote the rational number p/q. -# -# We use DATA(...) to represent the data values being interpolated at a -# specified [m] coordinate, where the arguments are the [m] coordinates. -# -# We use COEFF(...) to represent the molecule coefficient at a specified -# [m] coordinate, where the arguments are the [m] coordinates. -# -# For example, the usual 1-D centered 2nd order 1st derivative molecule -# would be written -# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) -# and its coefficients as -# COEFF(-1) = RATIONAL(-1.0,2.0) -# COEFF(1) = RATIONAL(1.0,2.0) -# -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes a Lagrange polynomial interpolant in any -# number of dimensions. -# -# Arguments: -# fn = The interpolation function. This should be a procedure in the -# coordinates, having the coefficients as global variables. For -# example, -# proc(x,y) c00 + c10*x + c01*y end proc -# coeff_list = A set of the interpolation coefficients (coefficients in -# the interpolation function), for example [c00, c10, c01]. -# coord_list = A list of the coordinates (independent variables in the -# interpolation function), for example [x,y]. -# posn_list = A list of positions (each a list of numeric values) where the -# interpolant is to use data, for example hypercube([0,0], [1,1]). -# Any positions may be used; if they're redundant (as in the -# example) the least-squares interpolant is computed. -# -# Results: -# This function returns the interpolating polynomial, in the form of -# an algebraic expression in the coordinates and the data values. -# -> Lagrange_polynomial_interpolant := -> proc( -> fn::procedure, coeff_list::list(name), -> coord_list::list(name), posn_list::list(list(numeric)) -> ) -> local posn, data_eqns, coeff_eqns; -> -# coefficients of interpolating polynomial -> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; -> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); -> if (has(coeff_eqns, '_t')) -> then error "interpolation coefficients aren't uniquely determined!"; -> end if; -> -# interpolant as a polynomial in the coordinates -> return subs(coeff_eqns, eval(fn))(op(coord_list)); -> end proc; -Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), -coord_list::list(name), posn_list::list(list(numeric))) -local posn, data_eqns, coeff_eqns; - data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; - coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); - if has(coeff_eqns, '_t') then - error "interpolation coefficients aren't uniquely determined!" - end if; - return subs(coeff_eqns, eval(fn))(op(coord_list)) -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_set = 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_set = A set of equations of the form -# {coords} = proc -# giving the derivatives which are to be matched, and the -# procedures to compute their finite-difference approximations. -# 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 -# { -# {x} = proc(i::integer, j::integer) -# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) -# end proc -# , -# {y} = proc(i::integer, j::integer) -# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) -# end proc -# , -# {x,y} = 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_set = A set 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_set = A list of positions (each a list of numeric values) -# where the interpolant is to match the derivatives -# specified by deriv_set , 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_set::set(name), -> coord_list::list(name), -> deriv_set::set(set(name) = procedure), -> fn_posn_set::set(list(numeric)), -> deriv_posn_set::set(list(numeric)) -> ) -> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; -> -> -# -# compute a set of equations -# {fn(posn) = DATA(posn)} -# giving the function values to be matched -# -> fn_eqnset := map( -> # return equation that fn(posn) = DATA(posn) -> proc(posn::list(integer)) -> fn(op(posn)) = 'DATA'(op(posn)); -> end proc -> , -> fn_posn_set -> ); -> -> -# -# compute a set of equations -# { diff(fn,coords)(posn) = DERIV(coords)(posn) } -# giving the derivative values to be matched, where DERIV(coords) -# is a placeholder for the appropriate derivative -# -> map( -> # return set of equations for this particular derivative -> proc(deriv_coords::set(name)) -> local deriv_fn; -> fn(op(coord_list)); -> diff(%, op(deriv_coords)); -> deriv_fn := unapply(%, op(coord_list)); -> map( -> proc(posn::list(integer)) -> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); -> end proc -> , -> deriv_posn_set -> ); -> end proc -> , -> map(lhs, deriv_set) -> ); -> deriv_eqnset := `union`(op(%)); -> -> -# -# solve overall set of equations for coefficients -# in terms of DATA() and DERIV() values -# -> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); -> if (indets(map(rhs,%)) <> {}) -> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", -> nops(fn_eqnset union deriv_eqnset), -> nops(coeff_set); -> fi; -> -> -# -# compute a set of substitution equations -# {'DERIV'(coords) = procedure} -# -> subs_eqnset := map( -> proc(eqn::set(name) = procedure) -> 'DERIV'(op(lhs(eqn))) = rhs(eqn); -> end proc -> , -> deriv_set -> ); -> -> -# -# compute the coefficients in terms of the DATA() values -# -> subs(subs_eqnset, coeff_eqns); -> eval(%); -> -# -# compute the interpolant as a polynomial in the coordinates -# -> subs(%, fn(op(coord_list))); -> end proc; -Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), -coord_list::list(name), deriv_set::set(set(name) = procedure), -fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) -local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; - fn_eqnset := map( - proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, - fn_posn_set); - map(proc(deriv_coords::set(name)) - local deriv_fn; - fn(op(coord_list)); - diff(%, op(deriv_coords)); - deriv_fn := unapply(%, op(coord_list)); - map(proc(posn::list(integer)) - deriv_fn(op(posn)) = - 'DERIV'(op(deriv_coords))(op(posn)) - end proc, deriv_posn_set) - end proc, map(lhs, deriv_set)); - deriv_eqnset := `union`(op(%)); - coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); - if indets(map(rhs, %)) <> {} then error - "no unique solution for coefficients -- %1 eqns for %2 coeffs", - nops(fn_eqnset union deriv_eqnset), nops(coeff_set) - end if; - subs_eqnset := map(proc(eqn::(set(name) = procedure)) - 'DERIV'(op(lhs(eqn))) = rhs(eqn) - end proc, deriv_set); - subs(subs_eqnset, coeff_eqns); - eval(%); - subs(%, 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. -# -# Arguments: -# interpolant = The interpolating polynomial (an algebraic expression -# in the coordinates and the data values). -# 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 -# form COEFF(...) = value , where each value is a polynomial in the -# coordinates. The order of the list matches that of posn_list. -# -> coeffs_as_lc_of_data := -> proc( -> interpolant::algebraic, -> posn_list::list(list(numeric)) -> ) -> local data_list, interpolant_as_lc_of_data; -> -# interpolant as a linear combination of the data values -> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; -> interpolant_as_lc_of_data := collect(interpolant, data_list); -> -# coefficients of the data values in the linear combination -> return map( -> proc(posn::list(numeric)) -> coeff(interpolant_as_lc_of_data, DATA(op(posn))); -> 'COEFF'(op(posn)) = %; -> end proc -> , -> posn_list -> ); -> end proc; -coeffs_as_lc_of_data := proc( -interpolant::algebraic, posn_list::list(list(numeric))) -local data_list, interpolant_as_lc_of_data; - data_list := [seq('DATA'(op(posn)), posn = posn_list)]; - interpolant_as_lc_of_data := collect(interpolant, data_list); - return map(proc(posn::list(numeric)) - coeff(interpolant_as_lc_of_data, DATA(op(posn))); - 'COEFF'(op(posn)) = % - end proc, posn_list) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function prints C expressions for the coefficients of an -# interpolating polynomial. (The polynomial is expressed as linear -# combinations of the data values with coefficients which are -# RATIONAL(p,q) calls.) -# -# Arguments: -# coeff_list = A list of the coefficients, as returned from -# coeffs_as_lc_of_data() . -# coeff_name_prefix = A prefix string for the coefficient names. -# temp_name_type = The C type to be used for Maple-introduced temporary -# names, eg. "double". -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_coeffs__lc_of_data := -> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), -> coeff_name_prefix::string, -> temp_name_type::string, -> file_name::string ) -> global `codegen/C/function/informed`; -> local coeff_list2, cmpt_list, temp_name_list; -> -# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) -# to a Maple/C variable name (eg coeff_I_m1_p1) -> coeff_list2 := map( -> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) -> local posn; -> posn := [op(lhs(coeff_eqn))]; -> coeff_name(posn,coeff_name_prefix); -> convert(%, name); # codegen[C] wants LHS -> # to be an actual Maple *name* -> % = fix_rationals(rhs(coeff_eqn)); -> end proc -> , -> coeff_list -> ); -> -# -# generate the C code -# -> -# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" -# via undocumented :( global table -> `codegen/C/function/informed`['RATIONAL'] := true; -> `codegen/C/function/informed`['DATA'] := true; -> -> ftruncate(file_name); -> -# optimized computation sequence for all the coefficients -# (may use local variables t0,t1,t2,...) -> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; -> -# list of the t0,t1,t2,... local variables -> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); -> -# declare the t0,t1,t2,... local variables (if there are any) -> if (nops(temp_name_list) > 0) -> then print_name_list_dcl(%, temp_name_type, file_name); -> fi; -> -# now print the optimized computation sequence -> codegen[C](cmpt_list, filename=file_name); -> -> fclose(file_name); -> -> NULL; -> end proc; -print_coeffs__lc_of_data := proc( -coeff_list::list(specfunc(numeric, COEFF) = algebraic), -coeff_name_prefix::string, temp_name_type::string, file_name::string) -local coeff_list2, cmpt_list, temp_name_list; -global `codegen/C/function/informed`; - coeff_list2 := map(proc( - coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) - local posn; - posn := [op(lhs(coeff_eqn))]; - coeff_name(posn, coeff_name_prefix); - convert(%, name); - % = fix_rationals(rhs(coeff_eqn)) - end proc, coeff_list); - `codegen/C/function/informed`['RATIONAL'] := true; - `codegen/C/function/informed`['DATA'] := true; - ftruncate(file_name); - cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; - temp_name_list := - nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); - if 0 < nops(temp_name_list) then - print_name_list_dcl(%, temp_name_type, file_name) - end if; - codegen[C](cmpt_list, filename = file_name); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C expression to assign the data-value -# variables, eg -# data->data_m1_p1 = DATA(-1,1); -# -# Arguments: -# posn_list = The same list of positions as was used to compute the -# interpolating polynomial. -# data_var_name_prefix = A prefix string for the data variable names. -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_fetch_data := -> proc( -> posn_list::list(list(numeric)), -> data_var_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> map( -> proc(posn::list(numeric)) -> fprintf(file_name, -> "%s = %a;\n", -> data_var_name(posn,data_var_name_prefix), -> DATA(op(posn))); -> end proc -> , -> posn_list -> ); -> fclose(file_name); -> -> NULL; -> end proc; -print_fetch_data := proc(posn_list::list(list(numeric)), -data_var_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - fprintf(file_name, "%s = %a;\n", - data_var_name(posn, data_var_name_prefix), DATA(op(posn))) - end proc, posn_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C expression to store the interpolation -# coefficients in COEFF(...) expressions, eg -# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; -# -# Arguments: -# posn_list = The list of positions in the molecule. -# coeff_name_prefix = A prefix string for the coefficient names, -# eg "factor * coeffs->coeff_" -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_store_coeffs := -> proc( -> posn_list::list(list(numeric)), -> coeff_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> map( -> proc(posn::list(numeric)) -> fprintf(file_name, -> "%a = %s;\n", -> 'COEFF'(op(posn)), -> coeff_name(posn,coeff_name_prefix)); -> end proc -> , -> posn_list -> ); -> fclose(file_name); -> -> NULL; -> end proc; -print_store_coeffs := proc(posn_list::list(list(numeric)), -coeff_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), - coeff_name(posn, coeff_name_prefix)) - end proc, posn_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a C expression to evaluate a molecule, i.e. -# to compute the molecule as a linear combination of the data values. -# -# Arguments: -# posn_list = The list of positions in the molecule. -# coeff_name_prefix = A prefix string for the coefficient names. -# data_var_name_prefix = A prefix string for the data variable names. -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_evaluate_molecule := -> proc( -> posn_list::list(list(numeric)), -> coeff_name_prefix::string, -> data_var_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> -# list of "coeff*data_var" terms -> map( -> proc(posn::list(numeric)) -> sprintf("%s*%s", -> coeff_name(posn,coeff_name_prefix), -> data_var_name(posn,data_var_name_prefix)); -> end proc -> , -> posn_list -> ); -> -> ListTools[Join](%, "\n + "); -> cat(op(%)); -> fprintf(file_name, " %s;\n", %); -> -> fclose(file_name); -> -> NULL; -> end proc; -print_evaluate_molecule := proc(posn_list::list(list(numeric)), -coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), - data_var_name(posn, data_var_name_prefix)) - end proc, posn_list); - ListTools[Join](%, "\n + "); - cat(op(%)); - fprintf(file_name, " %s;\n", %); - fclose(file_name); - NULL -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes the name of the coefficient of the data at a -# given [m] position, i.e. it encapsulates our naming convention for this. -# -# Arguments: -# posn = (in) The [m] coordinates. -# name_prefix = A prefix string for the coefficient name. -# -# Results: -# The function returns the coefficient, as a Maple string. -# -> coeff_name := -> proc(posn::list(numeric), name_prefix::string) -> cat(name_prefix, sprint_numeric_list(posn)); -> end proc; -coeff_name := proc(posn::list(numeric), name_prefix::string) - cat(name_prefix, sprint_numeric_list(posn)) -end proc - -> -################################################################################ -> -# -# This function computes the name of the variable in which the C code -# will store the input data at a given [m] position, i.e. it encapsulates -# our naming convention for this. -# -# Arguments: -# posn = (in) The [m] coordinates. -# name_prefix = A prefix string for the variable name. -# -# Results: -# The function returns the variable name, as a Maple string. -# -> data_var_name := -> proc(posn::list(numeric), name_prefix::string) -> cat(name_prefix, sprint_numeric_list(posn)); -> end proc; -data_var_name := proc(posn::list(numeric), name_prefix::string) - cat(name_prefix, sprint_numeric_list(posn)) -end proc - -# Maple code to compute lists of point positions in hypercube-shaped molecules -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ -> -################################################################################ -> -# -# 1D interpolation points -# -> posn_list_1d_size2 := hypercube_points([ 0], [+1]); - posn_list_1d_size2 := [[0], [1]] - -> posn_list_1d_size3 := hypercube_points([-1], [+1]); - posn_list_1d_size3 := [[-1], [0], [1]] - -> posn_list_1d_size4 := hypercube_points([-1], [+2]); - posn_list_1d_size4 := [[-1], [0], [1], [2]] - -> posn_list_1d_size5 := hypercube_points([-2], [+2]); - posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] - -> posn_list_1d_size6 := hypercube_points([-2], [+3]); - posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] - -> posn_list_1d_size7 := hypercube_points([-3], [+3]); - posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] - -> -################################################################################ -> -# -# 2D interpolation points (Fortran ordering) -# -> posn_list_2d_size2 := map(ListTools[Reverse], -> hypercube_points([ 0, 0], [+1,+1])); - posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] - -> posn_list_2d_size3 := map(ListTools[Reverse], -> hypercube_points([-1,-1], [+1,+1])); -posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], - - [-1, 1], [0, 1], [1, 1]] - -> posn_list_2d_size4 := map(ListTools[Reverse], -> hypercube_points([-1,-1], [+2,+2])); -posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], - - [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], - - [2, 2]] - -> posn_list_2d_size5 := map(ListTools[Reverse], -> hypercube_points([-2,-2], [+2,+2])); -posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], - - [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], - - [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], - - [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]] - -> -################################################################################ -> -# -# 3D interpolation points (Fortran ordering) -# -> posn_list_3d_size2 := map(ListTools[Reverse], -> hypercube_points([ 0, 0, 0], [+1,+1,+1])); -posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], - - [1, 0, 1], [0, 1, 1], [1, 1, 1]] - -> posn_list_3d_size3 := map(ListTools[Reverse], -> hypercube_points([-1,-1,-1], [+1,+1,+1])); -posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], - - [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], - - [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], - - [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], - - [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] - -> posn_list_3d_size4 := map(ListTools[Reverse], -> hypercube_points([-1,-1,-1], [+2,+2,+2])); -posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], - - [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], - - [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], - - [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], - - [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], - - [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], - - [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], - - [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], - - [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], - - [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], - - [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] - -> posn_list_3d_size5 := map(ListTools[Reverse], -> hypercube_points([-2,-2,-2], [+2,+2,+2])); -posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], - - [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], - - [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], - - [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], - - [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], - - [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], - - [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], - - [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], - - [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], - - [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], - - [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], - - [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], - - [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], - - [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], - - [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], - - [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], - - [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], - - [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], - - [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], - - [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], - - [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 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 -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.3 2002/09/02 10:22:49 jthorn Exp $ -> -################################################################################ -> -# -# 1-D interpolating functions -# -> -> fn_1d_order1 := -> proc(x) -> + c0 + c1*x -> end proc; - fn_1d_order1 := proc(x) c0 + c1*x end proc - -> -> fn_1d_order2 := -> proc(x) -> + c0 + c1*x + c2*x^2 -> end proc; - fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc - -> -> fn_1d_order3 := -> proc(x) -> + c0 + c1*x + c2*x^2 + c3*x^3 -> end proc; - fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc - -> -> fn_1d_order4 := -> proc(x) -> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 -> end; - fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc - -> -> fn_1d_order5 := -> proc(x) -> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 -> end; - fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc - -> -> fn_1d_order6 := -> proc(x) -> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 -> end; -fn_1d_order6 := - - proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc - -> -######################################## -> -# coordinates for 1-D interpolating functions -> coords_list_1d := [x]; - coords_list_1d := [x] - -> -######################################## -> -# -# coefficients in 1-D interpolating functions -# -> -> coeffs_list_1d_order1 := [c0, c1]; - coeffs_list_1d_order1 := [c0, c1] - -> coeffs_list_1d_order2 := [c0, c1, c2]; - coeffs_list_1d_order2 := [c0, c1, c2] - -> coeffs_list_1d_order3 := [c0, c1, c2, c3]; - coeffs_list_1d_order3 := [c0, c1, c2, c3] - -> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; - coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] - -> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; - coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] - -> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; - coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] - -> -################################################################################ -> -# -# 2-D interpolating functions (tensor-product) -# -> -> fn_2d_order1 := -> proc(x,y) -> + c01*y + c11*x*y -> + c00 + c10*x -> end proc; - fn_2d_order1 := proc(x, y) c01*y + c11*x*y + c00 + c10*x end proc - -> -> fn_2d_order2 := -> proc(x,y) -> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 -> + c01*y + c11*x*y + c21*x^2*y -> + c00 + c10*x + c20*x^2 -> end proc; -fn_2d_order2 := proc(x, y) - c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 - + c10*x + c20*x^2 -end proc - -> -> fn_2d_order3 := -> 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; -fn_2d_order3 := 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 - -> -> fn_2d_order4 := -> proc(x,y) -> + c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 -> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 -> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 -> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y -> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 -> end; -fn_2d_order4 := proc(x, y) - c34*x^3*y^4 + c01*y + c10*x + c02*y^2 + c20*x^2 + c03*y^3 + c30*x^3 - + c04*y^4 + c40*x^4 + c11*x*y + c12*x*y^2 + c22*x^2*y^2 + c21*x^2*y - + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c32*x^3*y^2 + c31*x^3*y - + c14*x*y^4 + c24*x^2*y^4 + c44*x^4*y^4 + c00 + c43*x^4*y^3 - + c42*x^4*y^2 + c41*x^4*y -end proc - -> -######################################## -> -# coordinates for 2-D interpolating functions -> coords_list_2d := [x,y]; - coords_list_2d := [x, y] - -> -######################################## -> -# -# coefficients in 2-D interpolating functions (tensor-product) -# -> -> coeffs_list_2d_order1 := [ -> c01, c11, -> c00, c10 -> ]; - coeffs_list_2d_order1 := [c01, c11, c00, c10] - -> coeffs_list_2d_order2 := [ -> c02, c12, c22, -> c01, c11, c21, -> c00, c10, c20 -> ]; - coeffs_list_2d_order2 := [c02, c12, c22, c01, c11, c21, c00, c10, c20] - -> coeffs_list_2d_order3 := [ -> c03, c13, c23, c33, -> c02, c12, c22, c23, -> c01, c11, c21, c13, -> c00, c10, c20, c30 -> ]; -coeffs_list_2d_order3 := [c03, c13, c23, c33, c02, c12, c22, c23, c01, c11, c21, - - c13, c00, c10, c20, c30] - -> coeffs_list_2d_order4 := [ -> c04, c14, c24, c34, c44, -> c03, c13, c23, c33, c43, -> c02, c12, c22, c32, c42, -> c01, c11, c21, c31, c41, -> c00, c10, c20, c30, c40 -> ]; -coeffs_list_2d_order4 := [c04, c14, c24, c34, c44, c03, c13, c23, c33, c43, c02, - - c12, c22, c32, c42, c01, c11, c21, c31, c41, c00, c10, c20, c30, c40] - -> -################################################################################ -> -# -# 3-D interpolating functions (tensor-product) -# -> -> fn_3d_order1 := -> proc(x,y,z) -# z^1 ------------------- -> + c011 *y*z + c111*x*y*z -> + c001 *z + c101*x *z -# z^0 ------------------- -> + c010 *y + c110*x*y -> + c000 + c100*x -> end proc; -fn_3d_order1 := proc(x, y, z) - c011*y*z + c111*x*y*z + c001*z + c101*x*z + c010*y + c110*x*y + c000 - + c100*x -end proc - -> -> fn_3d_order2 := -> proc(x,y,z) -# z^2 -------------------------------------------------- -> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 -> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 -> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 -# z -------------------------------------------------- -> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z -> + c011 *y *z + c111*x *y *z + c211*x^2*y *z -> + c001 *z + c101*x *z + c201*x^2 *z -# z^0 ------------------------------------------------ -> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 -> + c010 *y + c110*x *y + c210*x^2*y -> + c000 + c100*x + c200*x^2 -> end proc; -fn_3d_order2 := proc(x, y, z) - c111*x*y*z + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c112*x*y*z^2 - + c212*x^2*y*z^2 + c121*x*y^2*z + c221*x^2*y^2*z + c211*x^2*y*z - + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + c012*y*z^2 - + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + c120*x*y^2 - + c220*x^2*y^2 + c210*x^2*y + c001*z + c010*y + c000 + c100*x - + c002*z^2 + c020*y^2 + c200*x^2 -end proc - -> -> fn_3d_order3 := -> proc(x,y,z) -# z^3 --------------------------------------------------------------------- -> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 -> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 -> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 -> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 -# z^2 --------------------------------------------------------------------- -> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 -> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 -> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 -> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 -# z --------------------------------------------------------------------- -> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z -> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z -> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z -> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z -# z^0 --------------------------------------------------------------------- -> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 -> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 -> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y -> + c000 + c100*x + c200*x^2 + c300*x^3 -> end proc; -fn_3d_order3 := proc(x, y, z) - c330*x^3*y^3 + c031*y^3*z + c103*x*z^3 + c111*x*y*z + c122*x*y^2*z^2 - + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z - + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 - + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 - + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 - + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 - + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z - + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c011*y*z + c101*x*z - + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 - + c021*y^2*z + c201*x^2*z + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y - + c033*y^3*z^3 + c023*y^2*z^3 + c013*y*z^3 + c203*x^2*z^3 - + c303*x^3*z^3 + c032*y^3*z^2 + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 - + c230*x^2*y^3 + c320*x^3*y^2 + c310*x^3*y + c001*z + c010*y + c000 - + c100*x + c002*z^2 + c020*y^2 + c200*x^2 + c003*z^3 + c030*y^3 - + c300*x^3 -end proc - -> -> fn_3d_order4 := -> proc(x,y,z) -# z^4 ---------------------------------------------------------------------------------------- -> + c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 -> + c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 -> + c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 -> + c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 -> + c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 -# z^3 ---------------------------------------------------------------------------------------- -> + c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 -> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 -> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 -> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 -> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 -# z^2 ---------------------------------------------------------------------------------------- -> + c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 -> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 -> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 -> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 -> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 -# z ---------------------------------------------------------------------------------------- -> + c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z -> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z -> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z -> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z -> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z -# z^0 ---------------------------------------------------------------------------------------- -> + c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 -> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 -> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 -> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y -> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 -> end; -fn_3d_order4 := proc(x, y, z) - c104*x*z^4 + c330*x^3*y^3 + c042*y^4*z^2 + c031*y^3*z + c103*x*z^3 - + c304*x^3*z^4 + c024*y^2*z^4 + c111*x*y*z + c122*x*y^2*z^2 - + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z - + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 - + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 - + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 - + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 - + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z - + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c144*x*y^4*z^4 - + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 - + c134*x*y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 - + c434*x^4*y^3*z^4 + c124*x*y^2*z^4 + c224*x^2*y^2*z^4 - + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 + c114*x*y*z^4 + c214*x^2*y*z^4 - + c314*x^3*y*z^4 + c414*x^4*y*z^4 + c143*x*y^4*z^3 + c243*x^2*y^4*z^3 - + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 + c433*x^4*y^3*z^3 - + c423*x^4*y^2*z^3 + c413*x^4*y*z^3 + c142*x*y^4*z^2 - + c242*x^2*y^4*z^2 + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 - + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z - + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + c033*y^3*z^3 + c023*y^2*z^3 - + c013*y*z^3 + c203*x^2*z^3 + c303*x^3*z^3 + c032*y^3*z^2 - + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + c230*x^2*y^3 + c320*x^3*y^2 - + c310*x^3*y + c001*z + c010*y + c000 + c100*x + c002*z^2 + c020*y^2 - + c200*x^2 + c003*z^3 + c030*y^3 + c300*x^3 + c004*z^4 + c044*y^4*z^4 - + c034*y^3*z^4 + c014*y*z^4 + c204*x^2*z^4 + c404*x^4*z^4 - + c043*y^4*z^3 + c403*x^4*z^3 + c402*x^4*z^2 + c041*y^4*z + c401*x^4*z - + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 - + c430*x^4*y^3 + c420*x^4*y^2 + c410*x^4*y + c342*x^3*y^4*z^2 - + c442*x^4*y^4*z^2 + c432*x^4*y^3*z^2 + c422*x^4*y^2*z^2 - + c412*x^4*y*z^2 + c141*x*y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z - + c441*x^4*y^4*z + c431*x^4*y^3*z + c421*x^4*y^2*z + c411*x^4*y*z - + c040*y^4 + c400*x^4 -end proc - -> -######################################## -> -# coordinates for 3-D interpolating functions -> coords_list_3d := [x,y,z]; - coords_list_3d := [x, y, z] - -> -######################################## -> -# -# coefficients in 3-D interpolating functions -# -> -> coeffs_list_3d_order1 := [ -> # z^1 ----- -> c011, c111, -> c001, c101, -> # z^0 ----- -> c010, c110, -> c000, c100 -> ]; - coeffs_list_3d_order1 := [c011, c111, c001, c101, c010, c110, c000, c100] - -> coeffs_list_3d_order2 := [ -> # z^2 ----------- -> c022, c122, c222, -> c012, c112, c212, -> c002, c102, c202, -> # z^1 ----------- -> c021, c121, c221, -> c011, c111, c211, -> c001, c101, c201, -> # z^0 ----------- -> c020, c120, c220, -> c010, c110, c210, -> c000, c100, c200 -> ]; -coeffs_list_3d_order2 := [c022, c122, c222, c012, c112, c212, c002, c102, c202, - - c021, c121, c221, c011, c111, c211, c001, c101, c201, c020, c120, c220, - - c010, c110, c210, c000, c100, c200] - -> coeffs_list_3d_order3 := [ -> # z^3 ----------------- -> c033, c133, c233, c333, -> c023, c123, c223, c323, -> c013, c113, c213, c313, -> c003, c103, c203, c303, -> # z^2 ----------------- -> c032, c132, c232, c332, -> c022, c122, c222, c322, -> c012, c112, c212, c312, -> c002, c102, c202, c302, -> # z^1 ----------------- -> c031, c131, c231, c331, -> c021, c121, c221, c321, -> c011, c111, c211, c311, -> c001, c101, c201, c301, -> # z^0 ----------------- -> c030, c130, c230, c330, -> c020, c120, c220, c320, -> c010, c110, c210, c310, -> c000, c100, c200, c300 -> ]; -coeffs_list_3d_order3 := [c033, c133, c233, c333, c023, c123, c223, c323, c013, - - c113, c213, c313, c003, c103, c203, c303, c032, c132, c232, c332, c022, - - c122, c222, c322, c012, c112, c212, c312, c002, c102, c202, c302, c031, - - c131, c231, c331, c021, c121, c221, c321, c011, c111, c211, c311, c001, - - c101, c201, c301, c030, c130, c230, c330, c020, c120, c220, c320, c010, - - c110, c210, c310, c000, c100, c200, c300] - -> coeffs_list_3d_order4 := [ -> # z^4 ----------------------- -> c044, c144, c244, c344, c444, -> c034, c134, c234, c334, c434, -> c024, c124, c224, c324, c424, -> c014, c114, c214, c314, c414, -> c004, c104, c204, c304, c404, -> # z^3 ----------------------- -> c043, c143, c243, c343, c443, -> c033, c133, c233, c333, c433, -> c023, c123, c223, c323, c423, -> c013, c113, c213, c313, c413, -> c003, c103, c203, c303, c403, -> # z^2 ----------------------- -> c042, c142, c242, c342, c442, -> c032, c132, c232, c332, c432, -> c022, c122, c222, c322, c422, -> c012, c112, c212, c312, c412, -> c002, c102, c202, c302, c402, -> # z^1 ----------------------- -> c041, c141, c241, c341, c441, -> c031, c131, c231, c331, c431, -> c021, c121, c221, c321, c421, -> c011, c111, c211, c311, c411, -> c001, c101, c201, c301, c401, -> # z^0 ----------------------- -> c040, c140, c240, c340, c440, -> c030, c130, c230, c330, c430, -> c020, c120, c220, c320, c420, -> c010, c110, c210, c310, c410, -> c000, c100, c200, c300, c400 -> ]; -coeffs_list_3d_order4 := [c044, c144, c244, c344, c444, c034, c134, c234, c334, - - c434, c024, c124, c224, c324, c424, c014, c114, c214, c314, c414, c004, - - c104, c204, c304, c404, c043, c143, c243, c343, c443, c033, c133, c233, - - c333, c433, c023, c123, c223, c323, c423, c013, c113, c213, c313, c413, - - c003, c103, c203, c303, c403, c042, c142, c242, c342, c442, c032, c132, - - c232, c332, c432, c022, c122, c222, c322, c422, c012, c112, c212, c312, - - c412, c002, c102, c202, c302, c402, c041, c141, c241, c341, c441, c031, - - c131, c231, c331, c431, c021, c121, c221, c321, c421, c011, c111, c211, - - c311, c411, c001, c101, c201, c301, c401, c040, c140, c240, c340, c440, - - c030, c130, c230, c330, c430, c020, c120, c220, c320, c420, c010, c110, - - c210, c310, c410, c000, c100, c200, c300, c400] - -> -################################################################################ -# 2d.maple -- compute Lagrange interpolation coefficients in 2-D -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple,v 1.3 2002/09/02 10:22:36 jthorn Exp $ -> -################################################################################ -> -# -# 2d, cube, order=1, smoothing=0 (size=2) -# -> -# interpolating polynomial -> interp_2d_cube_order1_smooth0 -> := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, -> coords_list_2d, posn_list_2d_size2); -interp_2d_cube_order1_smooth0 := (-DATA(0, 0) + DATA(0, 1)) y - - + (-DATA(1, 0) + DATA(0, 0) + DATA(1, 1) - DATA(0, 1)) x y + DATA(0, 0) - - + (DATA(1, 0) - DATA(0, 0)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size2); -[COEFF(0, 0) = x y + 1 - y - x, COEFF(1, 0) = x - x y, COEFF(0, 1) = y - x y, - - COEFF(1, 1) = x y] - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); -bytes used=1009312, alloc=917336, time=0.09 -> -# d/dx -> simplify( diff(interp_2d_cube_order1_smooth0,x) ); --y DATA(1, 0) + y DATA(0, 0) + y DATA(1, 1) - y DATA(0, 1) + DATA(1, 0) - - - DATA(0, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size2); - [COEFF(0, 0) = y - 1, COEFF(1, 0) = -y + 1, COEFF(0, 1) = -y, COEFF(1, 1) = y] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); -> -# d/dy -> simplify( diff(interp_2d_cube_order1_smooth0,y) ); --DATA(0, 0) + DATA(0, 1) - x DATA(1, 0) + x DATA(0, 0) + x DATA(1, 1) - - - x DATA(0, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size2); - [COEFF(0, 0) = x - 1, COEFF(1, 0) = -x, COEFF(0, 1) = 1 - x, COEFF(1, 1) = x] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); -> -################################################################################ -> -# -# 2d, cube, order=2, smoothing=0 (size=3) -# -> -# interpolating polynomial -> interp_2d_cube_order2_smooth0 -> := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, -> coords_list_2d, posn_list_2d_size3); -bytes used=2009852, alloc=1376004, time=0.15 -interp_2d_cube_order2_smooth0 := - - 2 - (-DATA(0, 0) + 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + (1/4 DATA(1, 1) - - - 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/2 DATA(-1, 0) - - 2 - - 1/2 DATA(1, 0)) x y + (1/4 DATA(-1, 1) - 1/2 DATA(-1, 0) - - - 1/2 DATA(1, 0) + DATA(0, 0) + 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) - - 2 2 - + 1/4 DATA(1, 1) - 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y - - + (- 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + - - (1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1)) x y - - + (1/4 DATA(1, 1) - 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, 1) - - 2 - + 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y + DATA(0, 0) - - + (- 1/2 DATA(-1, 0) + 1/2 DATA(1, 0)) x - - 2 - + (1/2 DATA(-1, 0) + 1/2 DATA(1, 0) - DATA(0, 0)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 2 2 -[COEFF(-1, -1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , - - 2 2 2 2 - COEFF(0, -1) = 1/2 y - 1/2 x y - 1/2 y + 1/2 x y, - - 2 2 2 2 - COEFF(1, -1) = 1/4 x y - 1/4 x y + 1/4 x y - 1/4 x y, - - 2 2 2 2 - COEFF(-1, 0) = 1/2 x y + 1/2 x - 1/2 x - 1/2 x y , - - 2 2 2 2 - COEFF(0, 0) = -y + x y + 1 - x , - - 2 2 2 2 - COEFF(1, 0) = 1/2 x - 1/2 x y + 1/2 x - 1/2 x y , - - 2 2 2 2 - COEFF(-1, 1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , - - 2 2 2 2 - COEFF(0, 1) = 1/2 y - 1/2 x y - 1/2 x y + 1/2 y, - - 2 2 2 2 - COEFF(1, 1) = 1/4 x y + 1/4 x y + 1/4 x y + 1/4 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); -bytes used=3010044, alloc=1638100, time=0.21 -bytes used=4010200, alloc=1703624, time=0.29 -> -# d/dx -> simplify( diff(interp_2d_cube_order2_smooth0,x) ); -bytes used=5010460, alloc=1703624, time=0.36 - 2 -1/2 DATA(1, 0) + 1/2 x y DATA(-1, -1) + 1/2 x y DATA(1, 1) - - - 1/2 x y DATA(-1, -1) - 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, 1) - - 2 - + x y DATA(0, -1) - x y DATA(0, 1) + 1/2 x y DATA(-1, 1) - - 2 2 2 - - x y DATA(-1, 0) - x y DATA(1, 0) + 2 x y DATA(0, 0) - - 2 2 2 - + 1/2 x y DATA(1, -1) + 1/2 x y DATA(1, 1) - x y DATA(0, -1) - - 2 2 - - x y DATA(0, 1) - 1/2 DATA(-1, 0) - 1/2 y DATA(1, 0) - - + 1/4 y DATA(-1, -1) - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) - - 2 2 - + 1/4 y DATA(1, 1) + 1/4 y DATA(1, 1) - 1/4 y DATA(-1, -1) - - 2 2 2 - + 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + 1/2 y DATA(-1, 0) - - + x DATA(-1, 0) - 2 x DATA(0, 0) + x DATA(1, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 2 -[COEFF(-1, -1) = 1/4 y + 1/2 x y - 1/2 x y - 1/4 y , COEFF(0, -1) = x y - x y , - - 2 2 - COEFF(1, -1) = 1/2 x y + 1/4 y - 1/2 x y - 1/4 y, - - 2 2 2 - COEFF(-1, 0) = x + 1/2 y - x y - 1/2, COEFF(0, 0) = -2 x + 2 x y , - - 2 2 - COEFF(1, 0) = - 1/2 y + x - x y + 1/2, - - 2 2 - COEFF(-1, 1) = - 1/4 y + 1/2 x y - 1/4 y + 1/2 x y , - - 2 - COEFF(0, 1) = -x y - x y , - - 2 2 - COEFF(1, 1) = 1/2 x y + 1/2 x y + 1/4 y + 1/4 y] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); -bytes used=6011072, alloc=1769148, time=0.42 -> -# d/dy -> simplify( diff(interp_2d_cube_order2_smooth0,y) ); -bytes used=7011376, alloc=1769148, time=0.49 -1/2 DATA(0, 1) + 1/2 x y DATA(1, 1) - 1/2 x y DATA(-1, -1) - - + 1/2 x y DATA(1, -1) - 1/2 x y DATA(-1, 1) - 1/2 DATA(0, -1) - - 2 2 2 - - x y DATA(1, 0) + 1/2 x y DATA(1, 1) - x y DATA(0, 1) - - 2 - - x y DATA(0, -1) - x y DATA(1, 0) + x y DATA(-1, 0) + 1/4 x DATA(1, 1) - - + 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) - - 2 2 2 - + 1/4 x DATA(1, 1) - 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) - - 2 2 2 - + 1/4 x DATA(-1, 1) + 1/2 x DATA(0, -1) - 1/2 x DATA(0, 1) - - 2 - - 2 y DATA(0, 0) + y DATA(0, -1) + y DATA(0, 1) + 2 x y DATA(0, 0) - - 2 2 2 - + 1/2 x y DATA(-1, 1) + 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, -1) - - 2 - - x y DATA(-1, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 -[COEFF(-1, -1) = - 1/2 x y + 1/2 x y - 1/4 x + 1/4 x, - - 2 2 - COEFF(0, -1) = -x y - 1/2 + 1/2 x + y, - - 2 2 - COEFF(1, -1) = 1/2 x y + 1/2 x y - 1/4 x - 1/4 x, - - 2 2 - COEFF(-1, 0) = x y - x y, COEFF(0, 0) = -2 y + 2 x y, - - 2 - COEFF(1, 0) = -x y - x y, - - 2 2 - COEFF(-1, 1) = 1/2 x y + 1/4 x - 1/2 x y - 1/4 x, - - 2 2 - COEFF(0, 1) = 1/2 - 1/2 x - x y + y, - - 2 2 - COEFF(1, 1) = 1/4 x + 1/2 x y + 1/2 x y + 1/4 x ] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); -bytes used=8011672, alloc=1769148, time=0.57 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); - 2 2 2 2 -1/2 y DATA(-1, 1) - y DATA(-1, 0) - y DATA(1, 0) + 2 y DATA(0, 0) - - 2 2 2 - + 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) + 1/2 y DATA(1, 1) - - 2 2 - - y DATA(0, -1) - y DATA(0, 1) + 1/2 y DATA(1, 1) - 1/2 y DATA(-1, -1) - - - 1/2 y DATA(1, -1) + 1/2 y DATA(-1, 1) + y DATA(0, -1) - y DATA(0, 1) - - + DATA(-1, 0) + DATA(1, 0) - 2 DATA(0, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 -[COEFF(-1, -1) = - 1/2 y + 1/2 y , COEFF(0, -1) = y - y , - - 2 2 - COEFF(1, -1) = - 1/2 y + 1/2 y , COEFF(-1, 0) = -y + 1, - - 2 2 - COEFF(0, 0) = 2 y - 2, COEFF(1, 0) = -y + 1, - - 2 2 - COEFF(-1, 1) = 1/2 y + 1/2 y, COEFF(0, 1) = -y - y, - - 2 - COEFF(1, 1) = 1/2 y + 1/2 y] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); -bytes used=9011872, alloc=1834672, time=0.66 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); -1/4 DATA(1, 1) - 2 x y DATA(0, -1) - 2 x y DATA(0, 1) + x y DATA(-1, 1) - - - 2 x y DATA(-1, 0) - 2 x y DATA(1, 0) + 4 x y DATA(0, 0) - - + x y DATA(-1, -1) + x y DATA(1, -1) + x y DATA(1, 1) + 1/2 y DATA(1, 1) - - - 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) - 1/2 y DATA(-1, 1) - - + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + x DATA(0, -1) - - - x DATA(0, 1) + 1/2 x DATA(1, 1) - 1/2 x DATA(-1, -1) - 1/2 x DATA(1, -1) - - + 1/2 x DATA(-1, 1) + y DATA(-1, 0) - y DATA(1, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = - 1/2 y + x y - 1/2 x + 1/4, COEFF(0, -1) = -2 x y + x, - - COEFF(1, -1) = - 1/2 x - 1/4 + x y + 1/2 y, COEFF(-1, 0) = -2 x y + y, - - COEFF(0, 0) = 4 x y, COEFF(1, 0) = -y - 2 x y, - - COEFF(-1, 1) = x y - 1/2 y - 1/4 + 1/2 x, COEFF(0, 1) = -2 x y - x, - - COEFF(1, 1) = 1/4 + x y + 1/2 x + 1/2 y] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); -bytes used=10012088, alloc=1834672, time=0.74 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); --2 DATA(0, 0) + DATA(0, -1) + DATA(0, 1) + 1/2 x DATA(1, 1) - - - 1/2 x DATA(-1, -1) + 1/2 x DATA(1, -1) - 1/2 x DATA(-1, 1) - - 2 2 - + x DATA(-1, 0) - x DATA(1, 0) + 1/2 x DATA(-1, 1) - x DATA(-1, 0) - - 2 2 2 - - x DATA(1, 0) + 2 x DATA(0, 0) + 1/2 x DATA(-1, -1) - - 2 2 2 2 - + 1/2 x DATA(1, -1) + 1/2 x DATA(1, 1) - x DATA(0, -1) - x DATA(0, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 -[COEFF(-1, -1) = 1/2 x - 1/2 x, COEFF(0, -1) = 1 - x , - - 2 2 - COEFF(1, -1) = 1/2 x + 1/2 x , COEFF(-1, 0) = -x + x, - - 2 2 - COEFF(0, 0) = 2 x - 2, COEFF(1, 0) = -x - x , - - 2 2 - COEFF(-1, 1) = 1/2 x - 1/2 x, COEFF(0, 1) = 1 - x , - - 2 - COEFF(1, 1) = 1/2 x + 1/2 x ] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); -bytes used=11012264, alloc=1834672, time=0.82 -> -################################################################################ -> -# -# 2d, cube, order=3, smoothing=0 (size=4) -# -> -# interpolating polynomial -> interp_2d_cube_order3_smooth0 -> := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, -> coords_list_2d, posn_list_2d_size4); -bytes used=12012452, alloc=1834672, time=0.88 -bytes used=13012804, alloc=1900196, time=0.94 -bytes used=14014276, alloc=1900196, time=0.99 -bytes used=15014880, alloc=1965720, time=1.05 -bytes used=16015128, alloc=1965720, time=1.12 -bytes used=17015368, alloc=1965720, time=1.18 -bytes used=18015556, alloc=1965720, time=1.25 -bytes used=19016348, alloc=1965720, time=1.31 -bytes used=20016508, alloc=1965720, time=1.38 -bytes used=21016664, alloc=1965720, time=1.44 -bytes used=22016880, alloc=1965720, time=1.51 -bytes used=23019452, alloc=1965720, time=1.57 -bytes used=24021724, alloc=1965720, time=1.63 -bytes used=25022340, alloc=1965720, time=1.69 -interp_2d_cube_order3_smooth0 := (1/8 DATA(2, 1) - 1/4 DATA(2, 0) - - + 1/8 DATA(2, -1) - 3/2 c32 + 1/4 DATA(0, 0) + 1/4 DATA(1, 0) - - - 1/8 DATA(0, 1) - 1/8 DATA(1, 1) + 1/8 DATA(-1, -1) - 1/8 DATA(0, -1) - - 2 2 / - - 1/8 DATA(1, -1) - 1/4 DATA(-1, 0) + 1/8 DATA(-1, 1)) x y + | - \ - - 11 - - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) - 1/40 DATA(0, 2) - 120 - - 13 - + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) - -- c31 - 10 - - - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) - - 11 11 - + -- DATA(-1, -1) - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) - 60 40 - - 11 \ - - -- DATA(-1, 1)| x y + (- 1/24 DATA(2, 2) + 1/24 DATA(1, 2) - 20 / - - - 1/24 DATA(-1, 2) + 1/24 DATA(0, 2) + 1/4 DATA(2, 1) - 1/8 DATA(2, 0) - - - 1/12 DATA(2, -1) - 3/2 c31 + 1/8 DATA(0, 0) + 1/8 DATA(1, 0) - - - 1/4 DATA(0, 1) - 1/4 DATA(1, 1) - 1/12 DATA(-1, -1) + 1/12 DATA(0, -1) - - 2 - + 1/12 DATA(1, -1) - 1/8 DATA(-1, 0) + 1/4 DATA(-1, 1)) x y - - + 3/2000 DATA(2, 2) - 9/2000 DATA(1, 2) - 3/2000 DATA(-1, 2) - - 87 201 111 - + 9/2000 DATA(0, 2) + ---- DATA(2, 1) - ---- DATA(2, 0) + ---- DATA(2, -1) - 2000 2000 2000 - - 3 3 2 / 53 409 - + c31 x y + c32 x y + |- ---- DATA(2, 2) + ---- DATA(1, 2) - \ 3000 3000 - - 197 53 31 101 - - ---- DATA(-1, 2) - ---- DATA(0, 2) - ---- DATA(2, 1) + ---- DATA(2, 0) - 3000 1000 1500 3000 - - 13 91 101 - + 7/1500 DATA(2, -1) + -- c32 + --- c31 + ---- DATA(0, 0) - 25 250 1000 - - 149 31 47 59 - + ---- DATA(1, 0) - --- DATA(0, 1) - --- DATA(1, 1) + --- DATA(-1, -1) - 1000 500 250 750 - - 73 851 203 - + 7/500 DATA(0, -1) - --- DATA(1, -1) - ---- DATA(-1, 0) + --- DATA(-1, 1) - 750 3000 750 - - \ 3 / 29 43 - | x y + |7/600 DATA(2, 2) + --- DATA(1, 2) + --- DATA(-1, 2) - / \ 600 600 - - 79 27 - - --- DATA(0, 2) - 3/25 DATA(2, 1) + --- DATA(2, 0) - 2/75 DATA(2, -1) - 600 200 - - 21 19 31 - + 3/5 c32 + -- c31 - --- DATA(0, 0) - --- DATA(1, 0) + 7/50 DATA(0, 1) - 50 200 200 - - 11 17 13 - + --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - 1/300 DATA(1, -1) - 100 300 150 - - 23 13 \ 2 3 - + --- DATA(-1, 0) - --- DATA(-1, 1)| x y + (1/50 DATA(2, 2) - 200 100 / - - - 3/50 DATA(1, 2) - 1/50 DATA(-1, 2) + 3/50 DATA(0, 2) - 1/300 DATA(2, 1) - - - 1/150 DATA(2, 0) - 1/100 DATA(2, -1) - 2/5 c32 - 7/25 c31 - - - 1/50 DATA(0, 0) + 1/50 DATA(1, 0) - 1/100 DATA(0, 1) + 1/100 DATA(1, 1) - - + 1/100 DATA(-1, -1) - 3/100 DATA(0, -1) + 3/100 DATA(1, -1) - - 3 3 / - + 1/150 DATA(-1, 0) + 1/300 DATA(-1, 1)) x y + |1/40 DATA(2, 1) - \ - - 13 - - 1/20 DATA(2, 0) + 1/40 DATA(2, -1) - -- c32 - 3/20 DATA(0, 0) - 10 - - 11 - - 7/20 DATA(1, 0) + 3/40 DATA(0, 1) + 7/40 DATA(1, 1) - -- DATA(-1, -1) - 40 - - 11 11 \ - + 3/40 DATA(0, -1) + 7/40 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1)| x - 20 40 / - - 2 63 27 1397 603 - y - --- c32 + --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) - 100 500 2000 2000 - - 261 261 / - + ---- DATA(0, 1) - ---- DATA(1, 1) + |- 1/400 DATA(2, 2) - 2000 2000 \ - - 29 - + 3/400 DATA(1, 2) + 1/400 DATA(-1, 2) - 3/400 DATA(0, 2) - --- DATA(2, 1) - 400 - - 67 37 21 199 - + --- DATA(2, 0) - --- DATA(2, -1) + -- c32 - 9/100 c31 - --- DATA(0, 0) - 400 400 20 400 - - 87 87 37 - - 1/400 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(-1, -1) - 400 400 400 - - 111 111 133 29 \ - - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) + --- DATA(-1, 1)| - 400 400 400 400 / - - 2 / - x + |1/600 DATA(2, 2) - 1/200 DATA(1, 2) - 1/600 DATA(-1, 2) - \ - - 29 11 37 - + 1/200 DATA(0, 2) + --- DATA(2, 1) + --- DATA(2, 0) + --- DATA(2, -1) - 600 200 600 - - 33 33 29 - - 7/10 c32 + 3/50 c31 + --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) - 200 200 200 - - 29 37 37 37 - - --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - --- DATA(1, -1) - 200 600 200 200 - - 11 29 \ 3 / - - --- DATA(-1, 0) - --- DATA(-1, 1)| x + |- 3/40 DATA(2, 1) - 200 600 / \ - - 11 - + 3/20 DATA(2, 0) - 3/40 DATA(2, -1) + 9/10 c32 - -- DATA(0, 0) - 20 - - 11 - - 9/20 DATA(1, 0) + -- DATA(0, 1) + 9/40 DATA(1, 1) + 3/40 DATA(-1, -1) - 40 - - 11 \ - + -- DATA(0, -1) + 9/40 DATA(1, -1) - 3/20 DATA(-1, 0) + 3/40 DATA(-1, 1)| - 40 / - - 2 / 21 - y + |- 7/1000 DATA(2, 2) + ---- DATA(1, 2) + 7/1000 DATA(-1, 2) - \ 1000 - - 437 81 - + ---- DATA(0, 2) + 9/125 DATA(2, 1) - ---- DATA(2, 0) + 2/125 DATA(2, -1) - 3000 1000 - - 63 257 243 71 - - 9/25 c32 - --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) - --- DATA(0, 1) - 250 1000 1000 250 - - 27 89 - - --- DATA(1, 1) - 2/125 DATA(-1, -1) - --- DATA(0, -1) - 125 750 - - 81 \ 3 / - - 6/125 DATA(1, -1) + ---- DATA(-1, 0) - 9/125 DATA(-1, 1)| y + | - 1000 / \ - - 13 13 13 13 - - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) - ---- DATA(0, 2) - 6000 2000 6000 2000 - - 377 43 481 91 39 - - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) + --- c32 - --- c31 - 6000 2000 6000 100 500 - - 129 1129 377 377 - - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) - 2000 2000 2000 2000 - - 481 481 481 - + ---- DATA(-1, -1) - ---- DATA(0, -1) + ---- DATA(1, -1) - 6000 2000 2000 - - 957 377 \ / - - ---- DATA(-1, 0) + ---- DATA(-1, 1)| x + |1/40 DATA(2, 2) - 2000 6000 / \ - - 11 - - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) - --- DATA(0, 2) - 3/20 DATA(2, 1) - 120 - - 11 - + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) + 9/10 c31 - -- DATA(0, 0) - 40 - - 11 - - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) - 1/20 DATA(-1, -1) - 20 - - 11 \ - - -- DATA(0, -1) - 3/20 DATA(1, -1) - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1)| - 60 / - - 111 333 333 - y - ---- DATA(-1, -1) + ---- DATA(0, -1) - ---- DATA(1, -1) - 2000 2000 2000 - - 201 87 - + ---- DATA(-1, 0) - ---- DATA(-1, 1) - 2000 2000 - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=26023908, alloc=1965720, time=1.75 - 59 3 37 2 2 37 3 11 -[COEFF(-1, -1) = --- x y + --- x - 1/12 x y - --- x + -- x y - 1/20 y - 750 400 600 60 - - 481 3 3 3 2 2 2 11 2 111 - + ---- x + 1/100 x y - 2/125 y + 1/8 x y + 3/40 y - -- x y - ---- - 6000 40 2000 - - 17 2 3 13 2 3 2 3 333 - - --- x y , COEFF(0, -1) = --- x y + 1/12 x y + 7/500 x y + ---- - 300 150 2000 - - 2 2 2 481 111 2 11 37 3 3 3 - + 3/40 x y - 1/8 x y - ---- x - --- x - -- y + --- x - 3/100 x y - 2000 400 60 200 - - 11 2 89 3 2 2 2 333 - + -- y - 1/20 x y - --- y , COEFF(1, -1) = 1/12 x y - 1/8 x y - ---- - 40 750 2000 - - 2 3 2 3 3 111 2 73 3 - - 1/300 x y + 7/40 x y + 3/100 x y + --- x - 7/60 x y - --- x y - 400 750 - - 3 2 481 37 3 - - 6/125 y - 3/20 y + 9/40 y + ---- x - --- x , COEFF(2, -1) = - 1/60 x y - 2000 200 - - 3 3 2 481 3 37 2 - - 1/100 x y + 1/40 x y - ---- x + 1/20 y + 7/1500 x y - --- x - 6000 400 - - 2 3 2 3 2 111 37 3 2 2 - - 1/12 x y + 2/125 y - 2/75 x y - 3/40 y + ---- + --- x + 1/8 x y , - 2000 600 - - 201 23 2 3 133 2 11 2 2 - COEFF(-1, 0) = ---- + --- x y + --- x + -- x y - 3/40 y - 1/4 x y - 2000 200 400 40 - - 11 3 11 2 957 2 3 3 2 851 3 - - --- x + -- x y - ---- x - 1/8 x y + 1/150 x y - 3/20 y - ---- x y - 200 20 2000 3000 - - 81 3 19 2 3 3 3 11 2 - + ---- y , COEFF(0, 0) = - --- x y - 1/50 x y - 3/40 x y - -- y - 1000 200 20 - - 257 3 11 129 101 3 33 3 2 199 2 - + ---- y - -- y - ---- x + ---- x y + --- x + 1/8 x y - --- x - 1000 40 2000 1000 200 400 - - 2 2 2 1397 2 2 1129 - + 1/4 x y - 3/20 x y + ----, COEFF(1, 0) = 1/4 x y + ---- x - 2000 2000 - - 149 3 2 3 3 2 - - 7/40 x y + ---- x y - 1/400 x + 1/50 x y - 9/40 y - 7/20 x y - 1000 - - 2 603 243 3 33 3 2 31 2 3 - - 9/20 y + ---- + ---- y - --- x + 1/8 x y - --- x y , COEFF(2, 0) = - 2000 1000 200 200 - - 2 2 101 3 11 3 3 3 2 - - 1/4 x y + ---- x y + --- x - 1/150 x y - 1/8 x y + 3/40 y - 3000 200 - - 67 2 2 2 201 81 3 43 - - 1/40 x y + --- x - 1/20 x y + 3/20 y - ---- - ---- y - ---- x - 400 2000 1000 2000 - - 27 2 3 11 2 2 2 29 3 11 - + --- x y , COEFF(-1, 1) = - -- x y + 1/8 x y - --- x - -- x y - 200 40 600 20 - - 377 203 3 13 2 3 29 2 87 2 - + ---- x + --- x y + 3/20 y - --- x y + --- x - ---- + 1/4 x y - 6000 750 100 400 2000 - - 3 3 3 2 261 2 3 - + 1/300 x y - 9/125 y + 3/40 y , COEFF(0, 1) = ---- + 7/50 x y - 2000 - - 2 71 3 2 2 2 11 2 87 2 - - 1/4 x y - --- y + 3/40 x y - 1/8 x y + 3/20 x y + -- y - --- x - 250 40 400 - - 3 3 31 3 377 11 29 3 87 2 - - 1/100 x y - --- x y - ---- x + -- y + --- x , COEFF(1, 1) = --- x - 500 2000 20 200 400 - - 2 27 3 2 3 3 11 2 3 - + 9/40 y + 9/20 y - --- y - 1/4 x y + 1/100 x y + --- x y - 125 100 - - 47 3 2 377 261 29 3 2 2 - - --- x y + 7/40 x y + ---- x - ---- - --- x + 7/20 x y - 1/8 x y , - 250 2000 2000 200 - - 87 29 2 2 31 3 2 2 3 - COEFF(2, 1) = ---- - --- x + 1/4 x y - ---- x y - 3/40 y - 3/25 x y - 2000 400 1500 - - 377 3 29 3 2 3 3 - - 3/20 y - ---- x + 9/125 y + --- x + 1/40 x y + 1/20 x y - 1/300 x y - 6000 600 - - 2 2 2 3 3 3 - + 1/8 x y , COEFF(-1, 2) = 1/400 x - 1/40 y - 1/50 x y + 7/1000 y - - 11 13 2 197 3 3 43 2 3 - + --- x y + ---- x - 1/24 x y - 3/2000 - ---- x y - 1/600 x + --- x y - 120 6000 3000 600 - - 2 11 53 3 2 - , COEFF(0, 2) = - 3/400 x - --- y - 1/40 x y - ---- x y + 1/24 x y - 120 1000 - - 13 3 3 3 437 3 79 2 3 - - ---- x + 9/2000 + 3/50 x y + 1/200 x + ---- y - --- x y , - 2000 3000 600 - - 2 3 3 409 3 3 - COEFF(1, 2) = 3/400 x - 3/40 y - 3/50 x y + ---- x y - 1/200 x - 3000 - - 21 3 2 29 2 3 13 - + ---- y + 1/24 x y + --- x y - 7/120 x y - 9/2000 + ---- x, - 1000 600 2000 - - 2 53 3 3 - COEFF(2, 2) = - 1/400 x + 3/2000 + 1/40 y - ---- x y - 7/1000 y - 3000 - - 3 3 13 2 2 3 3 - + 1/50 x y - ---- x - 1/24 x y + 7/600 x y - 1/120 x y + 1/600 x ] - 6000 - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); -bytes used=27024116, alloc=2031244, time=1.82 -bytes used=28024396, alloc=2031244, time=1.90 -bytes used=29025884, alloc=2162292, time=1.99 -bytes used=30026144, alloc=2162292, time=2.06 -bytes used=31027088, alloc=2162292, time=2.12 -bytes used=32027348, alloc=2162292, time=2.18 -bytes used=33027500, alloc=2162292, time=2.24 -bytes used=34027920, alloc=2162292, time=2.30 -bytes used=35028400, alloc=2162292, time=2.38 -bytes used=36028584, alloc=2162292, time=2.46 -bytes used=37028772, alloc=2162292, time=2.56 -bytes used=38028952, alloc=2162292, time=2.67 -bytes used=39029156, alloc=2162292, time=2.73 -bytes used=40029332, alloc=2162292, time=2.80 -bytes used=41029504, alloc=2162292, time=2.92 -bytes used=42029680, alloc=2162292, time=2.99 -bytes used=43029840, alloc=2162292, time=3.09 -bytes used=44030180, alloc=2162292, time=3.20 -bytes used=45030460, alloc=2162292, time=3.31 -bytes used=46030800, alloc=2162292, time=3.38 -bytes used=47030988, alloc=2162292, time=3.48 -bytes used=48031208, alloc=2162292, time=3.62 -bytes used=49031368, alloc=2162292, time=3.76 -> -# d/dx -> simplify( diff(interp_2d_cube_order3_smooth0,x) ); -bytes used=50031616, alloc=2162292, time=3.86 -bytes used=51059256, alloc=2162292, time=3.92 -bytes used=52059500, alloc=2162292, time=3.99 - 3 13 13 13 -6/5 x y c32 - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) - 6000 2000 6000 - - 13 377 43 481 - - ---- DATA(0, 2) - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) - 2000 6000 2000 6000 - - 2 2 2 91 39 - + 3 c32 x y + 3 c31 x y + 1/20 y DATA(2, 1) + --- c32 - --- c31 - 100 500 - - 129 1129 377 377 - - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) - 2000 2000 2000 2000 - - 2 2 3 21 2 3 13 - - 3 x y c32 - 6/5 x y c32 - -- x y c31 - 3 x y c31 - -- y c31 - 25 10 - - 13 3 91 3 13 2 - + -- y c32 + --- y c31 - -- y c32 - 1/60 y DATA(2, -1) - 25 250 10 - - 21 2 2 - - 3/40 y DATA(0, 0) - 7/40 y DATA(1, 0) - -- x c32 + 9/50 x c31 - 10 - - 2 3 2 3 - + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) - - 2 3 - + 1/100 x y DATA(-1, 1) - 1/12 x y DATA(2, 2) + 1/12 x y DATA(1, 2) - - - 1/12 x y DATA(-1, 2) + 1/12 x y DATA(0, 2) + 1/2 x y DATA(2, 1) - - - 1/4 x y DATA(2, 0) - 1/6 x y DATA(2, -1) + 1/4 x y DATA(0, 0) - - 2 - + 1/4 x y DATA(1, 0) - 1/2 x y DATA(0, 1) + 1/4 x y DATA(2, 1) - - 3 - - 1/150 x y DATA(1, -1) - 1/2 x y DATA(1, 1) - 1/6 x y DATA(-1, -1) - - + 1/6 x y DATA(0, -1) + 1/6 x y DATA(1, -1) - 1/4 x y DATA(-1, 0) - - 11 - + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) + -- y DATA(-1, -1) - 60 - - 11 - - 1/20 y DATA(0, -1) - 7/60 y DATA(1, -1) + -- y DATA(-1, 0) - 40 - - 11 53 3 - - -- y DATA(-1, 1) - 1/40 y DATA(2, 0) - ---- y DATA(2, 2) - 20 3000 - - 409 3 197 3 53 3 - + ---- y DATA(1, 2) - ---- y DATA(-1, 2) - ---- y DATA(0, 2) - 3000 3000 1000 - - 31 3 101 3 3 - - ---- y DATA(2, 1) + ---- y DATA(2, 0) + 7/1500 y DATA(2, -1) - 1500 3000 - - 101 3 149 3 31 3 - + ---- y DATA(0, 0) + ---- y DATA(1, 0) - --- y DATA(0, 1) - 1000 1000 500 - - 47 3 59 3 3 - - --- y DATA(1, 1) + --- y DATA(-1, -1) + 7/500 y DATA(0, -1) - 250 750 - - 73 3 851 3 203 3 - - --- y DATA(1, -1) - ---- y DATA(-1, 0) + --- y DATA(-1, 1) - 750 3000 750 - - 11 - - 1/120 y DATA(2, 2) - 7/120 y DATA(1, 2) + --- y DATA(-1, 2) - 120 - - 2 2 - - 1/40 y DATA(0, 2) + 1/40 y DATA(2, 1) - 1/20 y DATA(2, 0) - - 2 2 2 - + 1/40 y DATA(2, -1) - 3/20 y DATA(0, 0) - 7/20 y DATA(1, 0) - - 3 2 3 - + 7/300 x y DATA(2, 2) + 1/2 x y DATA(0, 0) - 4/75 x y DATA(2, -1) - - 79 3 2 3 2 - - --- x y DATA(0, 2) - 3/50 x y DATA(-1, 2) - 1/4 x y DATA(1, 1) - 300 - - 31 3 3 2 - - --- x y DATA(1, 0) + 7/25 x y DATA(0, 1) - 1/4 x y DATA(0, -1) - 100 - - 2 3 3 2 3 - - 3/100 x y DATA(2, -1) - 6/25 x y DATA(2, 1) - 9/50 x y DATA(1, 2) - - 2 2 3 11 3 - + 1/2 x y DATA(1, 0) - 1/100 x y DATA(2, 1) + -- x y DATA(1, 1) - 50 - - 19 3 21 2 - - --- x y DATA(0, 0) + -- x c32 - 9/50 x c31 + 1/4 x y DATA(-1, 1) - 100 10 - - 2 2 - - 1/2 x y DATA(2, 0) + 1/2 x y DATA(-1, 1) - 1/4 x y DATA(1, -1) - - 23 3 2 3 2 3 - + --- x y DATA(-1, 0) - 1/50 x y DATA(2, 0) - 3/100 x y DATA(0, 1) - 100 - - 2 3 2 3 13 3 - + 9/50 x y DATA(0, 2) - 3/50 x y DATA(0, 0) + -- x y DATA(0, -1) - 75 - - 2 2 29 3 - + 1/4 x y DATA(2, -1) + 1/4 x y DATA(-1, -1) + --- x y DATA(1, 2) - 300 - - 2 2 3 2 3 - - 1/4 x y DATA(0, 1) + 3/50 x y DATA(1, 0) + 3/50 x y DATA(2, 2) - - 17 3 13 3 43 3 - - --- x y DATA(-1, -1) - -- x y DATA(-1, 1) + --- x y DATA(-1, 2) - 150 50 300 - - 27 3 2 2 - + --- x y DATA(2, 0) - 1/2 x y DATA(-1, 0) + 3/40 y DATA(0, 1) - 100 - - 11 2 2 2 - - -- y DATA(-1, -1) + 3/40 y DATA(0, -1) + 7/40 y DATA(1, -1) - 40 - - 11 2 11 2 2 - + -- y DATA(-1, 0) - -- y DATA(-1, 1) + 1/200 x DATA(2, 2) - 20 40 - - 2 2 2 - - 3/200 x DATA(1, 2) - 1/200 x DATA(-1, 2) + 3/200 x DATA(0, 2) - - 29 2 33 2 37 2 - + --- x DATA(2, 1) + --- x DATA(2, 0) + --- x DATA(2, -1) - 200 200 200 - - 99 2 99 2 87 2 - + --- x DATA(0, 0) - --- x DATA(1, 0) + --- x DATA(0, 1) - 200 200 200 - - 87 2 37 2 111 2 - - --- x DATA(1, 1) - --- x DATA(-1, -1) + --- x DATA(0, -1) - 200 200 200 - - 111 2 33 2 29 2 - - --- x DATA(1, -1) - --- x DATA(-1, 0) - --- x DATA(-1, 1) - 200 200 200 - - 2 - - 1/200 x DATA(2, 2) + 3/200 x DATA(1, 2) + 7/40 y DATA(1, 1) - - 29 - + 1/200 x DATA(-1, 2) - 3/200 x DATA(0, 2) - --- x DATA(2, 1) - 200 - - 67 37 199 - + --- x DATA(2, 0) - --- x DATA(2, -1) - --- x DATA(0, 0) - 200 200 200 - - 87 87 - - 1/200 x DATA(1, 0) - --- x DATA(0, 1) + --- x DATA(1, 1) - 200 200 - - 37 111 111 - + --- x DATA(-1, -1) - --- x DATA(0, -1) + --- x DATA(1, -1) - 200 200 200 - - 133 29 21 3 481 - + --- x DATA(-1, 0) + --- x DATA(-1, 1) + -- x y c31 + ---- DATA(-1, -1) - 200 200 25 6000 - - 481 481 957 - - ---- DATA(0, -1) + ---- DATA(1, -1) - ---- DATA(-1, 0) - 2000 2000 2000 - - 377 2 3 2 3 - + ---- DATA(-1, 1) + 3/100 x y DATA(1, 1) + 3/100 x y DATA(-1, -1) - 6000 - - 2 3 - - 9/100 x y DATA(0, -1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=53061376, alloc=2162292, time=4.05 - 37 2 2 481 17 3 37 11 2 11 -[COEFF(-1, -1) = - --- x + 1/4 x y + ---- - --- x y + --- x - -- y + -- y - 200 6000 150 200 40 60 - - 2 3 59 3 3 2 - - 1/6 x y + 3/100 x y + --- y , COEFF(0, -1) = 7/500 y + 3/40 y - 750 - - 13 3 111 2 111 2 481 - + -- x y + 1/6 x y + --- x - --- x - 1/4 x y - 1/20 y - ---- - 75 200 200 2000 - - 2 3 73 3 2 3 3 - - 9/100 x y , COEFF(1, -1) = - --- y + 9/100 x y - 1/150 x y - 7/60 y - 750 - - 2 111 481 111 2 2 - + 1/6 x y + 7/40 y + --- x + ---- - --- x - 1/4 x y , COEFF(2, -1) = - 200 2000 200 - - 3 2 3 3 2 37 2 - - 4/75 x y - 1/6 x y - 3/100 x y - 1/60 y + 7/1500 y + 1/40 y + --- x - 200 - - 2 37 481 33 2 11 851 3 - + 1/4 x y - --- x - ----, COEFF(-1, 0) = - --- x + -- y - ---- y - 200 6000 200 40 3000 - - 2 3 11 2 957 23 3 133 2 - - 1/4 x y + 1/50 x y + -- y - ---- + --- x y + --- x - 1/2 x y , - 20 2000 100 200 - - 129 2 3 101 3 19 3 2 - COEFF(0, 0) = - 3/40 y - ---- - 3/50 x y + ---- y - --- x y + 1/2 x y - 2000 1000 100 - - 2 199 99 2 31 3 - - 3/20 y + 1/4 x y - --- x + --- x , COEFF(1, 0) = - --- x y - 200 200 100 - - 2 3 1129 2 2 99 2 149 3 - + 3/50 x y + ---- + 1/2 x y - 7/40 y - 7/20 y - --- x + ---- y - 2000 200 1000 - - 2 33 2 2 - - 1/200 x + 1/4 x y, COEFF(2, 0) = - 1/40 y - 1/20 y + --- x - 1/2 x y - 200 - - 27 3 101 3 2 3 43 67 - + --- x y + ---- y - 1/50 x y - 1/4 x y - ---- + --- x, COEFF(-1, 1) - 100 3000 2000 200 - - 13 3 11 2 2 377 2 3 203 3 29 - = - -- x y - -- y + 1/4 x y + ---- + 1/100 x y + --- y + --- x - 50 40 6000 750 200 - - 29 2 11 2 3 2 87 2 - - --- x - -- y + 1/2 x y, COEFF(0, 1) = - 3/100 x y - 1/4 x y + --- x - 200 20 200 - - 2 31 3 3 377 87 - + 3/40 y - --- y + 7/25 x y + 3/20 y - ---- - --- x - 1/2 x y, - 500 2000 200 - - 47 3 2 87 2 377 - COEFF(1, 1) = 7/20 y - --- y - 1/2 x y - 1/4 x y - --- x + ---- - 250 200 2000 - - 2 11 3 87 2 3 - + 7/40 y + -- x y + --- x + 3/100 x y , COEFF(2, 1) = 1/20 y - 50 200 - - 2 3 31 3 3 2 2 377 29 2 - - 1/100 x y - ---- y - 6/25 x y + 1/40 y + 1/4 x y - ---- + --- x - 1500 6000 200 - - 29 11 2 13 197 3 - + 1/2 x y - --- x, COEFF(-1, 2) = --- y - 1/200 x + ---- - ---- y - 200 120 6000 3000 - - 43 3 2 3 53 3 - + --- x y - 1/12 x y - 3/50 x y + 1/200 x, COEFF(0, 2) = - ---- y - 300 1000 - - 2 3 13 2 79 3 - - 1/40 y + 9/50 x y - ---- + 3/200 x - --- x y + 1/12 x y - 3/200 x, - 2000 300 - - 409 3 2 - COEFF(1, 2) = 1/12 x y + ---- y - 3/200 x - 7/120 y + 3/200 x - 3000 - - 2 3 13 29 3 53 3 - - 9/50 x y + ---- + --- x y , COEFF(2, 2) = - ---- y - 1/120 y - 2000 300 3000 - - 2 13 2 3 3 - + 1/200 x - ---- - 1/200 x + 3/50 x y + 7/300 x y - 1/12 x y] - 6000 - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); -bytes used=54061732, alloc=2162292, time=4.12 -bytes used=55062064, alloc=2162292, time=4.20 -bytes used=56062456, alloc=2162292, time=4.27 -bytes used=57062648, alloc=2162292, time=4.36 -bytes used=58062912, alloc=2162292, time=4.46 -bytes used=59063180, alloc=2162292, time=4.57 -bytes used=60063412, alloc=2162292, time=4.65 -bytes used=61063624, alloc=2162292, time=4.75 -bytes used=62064392, alloc=2162292, time=4.84 -bytes used=63064556, alloc=2162292, time=4.95 -> -# d/dy -> simplify( diff(interp_2d_cube_order3_smooth0,y) ); -bytes used=64064736, alloc=2162292, time=5.12 -bytes used=65064892, alloc=2162292, time=5.17 - 3 3 -2 c32 x y + c31 x + 1/40 DATA(2, 2) - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) - - 11 - - --- DATA(0, 2) - 3/20 DATA(2, 1) + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) - 120 - - 2 2 3 2 - + 9/5 c32 x y - 3/20 y DATA(2, 1) - 6/5 c32 x y + 9/10 c31 - - 11 11 - - -- DATA(0, 0) - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) - 40 20 - - 39 2 27 2 11 - + -- x y c32 - -- y c32 - 3/20 y DATA(2, -1) - -- y DATA(0, 0) - 25 25 10 - - 2 - - 9/10 y DATA(1, 0) - 3/2 x c31 + 1/20 x y DATA(2, 1) - - - 1/10 x y DATA(2, 0) + 1/20 x y DATA(2, -1) - 3/10 x y DATA(0, 0) - - 31 2 - - 7/10 x y DATA(1, 0) + 3/20 x y DATA(0, 1) - --- x y DATA(2, 1) - 500 - - 11 - + 7/20 x y DATA(1, 1) - -- x y DATA(-1, -1) + 3/20 x y DATA(0, -1) - 20 - - 11 2 - + 7/20 x y DATA(1, -1) + -- x y DATA(-1, 0) + 1/4 x y DATA(2, -1) - 10 - - 2 2 2 - + 1/2 x y DATA(0, 0) + 1/2 x y DATA(1, 0) - 1/4 x y DATA(0, 1) - - 2 2 2 - - 1/4 x y DATA(1, 1) + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(0, -1) - - 2 2 2 - - 1/4 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/4 x y DATA(-1, 1) - - 3 2 3 2 3 2 - - 9/50 x y DATA(1, 2) - 3/50 x y DATA(-1, 2) + 9/50 x y DATA(0, 2) - - 3 2 3 2 3 2 - - 1/100 x y DATA(2, 1) - 1/50 x y DATA(2, 0) + 3/50 x y DATA(2, 2) - - 3 2 3 2 - - 9/100 x y DATA(0, -1) - 3/100 x y DATA(2, -1) - - 3 2 3 2 93 2 2 - - 3/50 x y DATA(0, 0) + 3/50 x y DATA(1, 0) - --- x y DATA(1, 0) - 200 - - 21 2 2 3 2 3 2 - + -- x y DATA(0, 1) - 3/100 x y DATA(0, 1) + 3/100 x y DATA(1, 1) - 50 - - 3 2 2 2 81 2 2 - + 3/100 x y DATA(-1, -1) - 9/25 x y DATA(2, 1) + --- x y DATA(2, 0) - 200 - - 2 2 57 2 2 3 2 - - 2/25 x y DATA(2, -1) - --- x y DATA(0, 0) + 1/100 x y DATA(-1, 1) - 200 - - 29 2 2 43 2 2 79 2 2 - + --- x y DATA(1, 2) + --- x y DATA(-1, 2) - --- x y DATA(0, 2) - 200 200 200 - - 2 2 33 2 2 13 2 2 - + 7/200 x y DATA(2, 2) + --- x y DATA(1, 1) + -- x y DATA(0, -1) - 100 50 - - 2 2 69 2 2 17 2 2 - - 1/100 x y DATA(1, -1) + --- x y DATA(-1, 0) - --- x y DATA(-1, -1) - 200 100 - - 3 2 3 2 53 2 - + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) - ---- x y DATA(2, 2) - 1000 - - 39 2 2 409 2 197 2 - - --- x y DATA(-1, 1) + ---- x y DATA(1, 2) - ---- x y DATA(-1, 2) - 100 1000 1000 - - 159 2 11 - - ---- x y DATA(0, 2) + -- y DATA(0, 1) + 9/20 y DATA(1, 1) - 1000 20 - - 11 - + 3/20 y DATA(-1, -1) + -- y DATA(0, -1) + 9/20 y DATA(1, -1) - 20 - - - 3/10 y DATA(-1, 0) + 3/20 y DATA(-1, 1) + 3/10 y DATA(2, 0) - - 27 2 243 2 2 - + --- y DATA(2, 1) - ---- y DATA(2, 0) + 6/125 y DATA(2, -1) - 125 1000 - - 771 2 729 2 21 2 - + ---- y DATA(0, 0) + ---- y DATA(1, 0) - ---- y DATA(2, 2) - 1000 1000 1000 - - 63 2 21 2 437 2 - + ---- y DATA(1, 2) + ---- y DATA(-1, 2) + ---- y DATA(0, 2) - 1000 1000 1000 - - 2 2 189 2 273 2 - + 1/4 x y DATA(2, 1) - 1/2 x y DATA(2, 0) - --- y c31 + --- x y c31 - 250 250 - - 63 2 2 21 3 2 303 2 - + 9/5 y c32 + -- x y c31 - -- x y c31 + ---- x y DATA(0, 0) - 50 25 1000 - - 141 2 21 2 447 2 - - --- x y DATA(1, 1) + --- x y DATA(0, -1) + ---- x y DATA(1, 0) - 250 500 1000 - - 13 2 203 2 - - 13/5 x y c32 - -- x c31 - 3 x y c32 + --- x y DATA(-1, 1) - 10 250 - - 101 2 11 73 2 - + ---- x y DATA(2, 0) - -- x y DATA(-1, 1) - --- x y DATA(1, -1) - 1000 20 250 - - 2 59 2 93 2 - + 7/500 x y DATA(2, -1) + --- x y DATA(-1, -1) - --- x y DATA(0, 1) - 250 500 - - 851 2 213 2 2 - - ---- x y DATA(-1, 0) - --- y DATA(0, 1) - 6/125 y DATA(-1, -1) - 1000 250 - - 89 2 18 2 243 2 - - --- y DATA(0, -1) - --- y DATA(1, -1) + ---- y DATA(-1, 0) - 250 125 1000 - - 27 2 2 2 - - --- y DATA(-1, 1) - 1/24 x DATA(2, 2) + 1/24 x DATA(1, 2) - 125 - - 2 2 2 - - 1/24 x DATA(-1, 2) + 1/24 x DATA(0, 2) + 1/4 x DATA(2, 1) - - 2 2 2 - - 1/8 x DATA(2, 0) - 1/12 x DATA(2, -1) + 1/8 x DATA(0, 0) - - 2 2 2 - + 1/8 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) - - 2 2 2 - - 1/12 x DATA(-1, -1) + 1/12 x DATA(0, -1) + 1/12 x DATA(1, -1) - - 2 2 - - 1/8 x DATA(-1, 0) + 1/4 x DATA(-1, 1) - 1/120 x DATA(2, 2) - - 81 2 11 - - 7/120 x DATA(1, 2) - --- y DATA(1, 1) + --- x DATA(-1, 2) - 125 120 - - - 1/40 x DATA(0, 2) + 1/20 x DATA(2, 1) - 1/40 x DATA(2, 0) - - - 1/60 x DATA(2, -1) - 3/40 x DATA(0, 0) - 7/40 x DATA(1, 0) - - 11 - + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) + -- x DATA(-1, -1) - 60 - - 11 - - 1/20 x DATA(0, -1) - 7/60 x DATA(1, -1) + -- x DATA(-1, 0) - 40 - - 11 11 - - -- x DATA(-1, 1) - 1/20 DATA(-1, -1) - -- DATA(0, -1) - 3/20 DATA(1, -1) - 20 60 - - - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=66073540, alloc=2162292, time=5.24 - 17 2 2 3 2 11 59 2 -[COEFF(-1, -1) = - --- x y - 1/20 + 3/100 x y + -- x + --- x y + 3/20 y - 100 60 250 - - 2 2 2 11 2 - - 6/125 y - 1/12 x + 1/4 x y - -- x y, COEFF(0, -1) = 1/12 x - 20 - - 2 13 2 2 11 21 2 11 - - 1/4 x y - 1/20 x + -- x y + 3/20 x y + -- y + --- x y - -- - 50 20 500 60 - - 3 2 89 2 2 2 2 - - 9/100 x y - --- y , COEFF(1, -1) = - 3/20 - 1/4 x y - 1/100 x y - 250 - - 18 2 2 3 2 73 2 - + 9/20 y + 7/20 x y - --- y + 1/12 x - 7/60 x + 9/100 x y - --- x y , - 125 250 - - 2 2 2 3 2 - COEFF(2, -1) = 1/4 x y - 1/60 x + 1/20 - 2/25 x y - 3/100 x y - - 2 2 2 - + 7/500 x y + 1/20 x y + 6/125 y - 1/12 x - 3/20 y, COEFF(-1, 0) = - - 11 851 2 2 69 2 2 3 2 - - 3/40 + -- x y - ---- x y - 1/2 x y - 3/10 y + --- x y + 1/50 x y - 10 1000 200 - - 11 2 243 2 2 303 2 11 - + -- x - 1/8 x + ---- y , COEFF(0, 0) = 1/8 x + ---- x y - -- y - 40 1000 1000 10 - - 3 2 11 2 771 2 57 2 2 - - 3/50 x y - -- + 1/2 x y - 3/40 x + ---- y - --- x y - 3/10 x y, - 40 1000 200 - - 93 2 2 3 2 2 - COEFF(1, 0) = - --- x y + 3/50 x y - 7/10 x y - 9/10 y + 1/2 x y - 200 - - 447 2 2 729 2 - + ---- x y + 1/8 x + ---- y - 7/40 x - 9/40, COEFF(2, 0) = 3/40 - 1000 1000 - - 2 81 2 2 2 101 2 243 2 - - 1/2 x y + --- x y - 1/40 x - 1/8 x + ---- x y - ---- y - 1/10 x y - 200 1000 1000 - - 3 2 39 2 2 2 27 2 - + 3/10 y - 1/50 x y , COEFF(-1, 1) = - --- x y + 3/20 + 1/4 x - --- y - 100 125 - - 3 2 11 203 2 11 2 - + 1/100 x y + 3/20 y - -- x + --- x y - -- x y + 1/4 x y, COEFF(0, 1) - 20 250 20 - - 213 2 11 11 21 2 2 93 2 3 2 - = - --- y + -- + -- y + -- x y - --- x y - 3/100 x y + 3/20 x - 250 20 20 50 500 - - 2 2 2 33 2 2 - - 1/4 x y - 1/4 x + 3/20 x y, COEFF(1, 1) = 9/20 y - 1/4 x + --- x y - 100 - - 81 2 2 141 2 3 2 - - --- y + 7/20 x - 1/4 x y - --- x y + 9/20 + 7/20 x y + 3/100 x y , - 125 250 - - 3 2 - COEFF(2, 1) = - 1/100 x y - 3/20 + 1/20 x + 1/20 x y - 3/20 y - - 2 2 31 2 2 2 27 2 - - 9/25 x y - --- x y + 1/4 x + 1/4 x y + --- y , COEFF(-1, 2) = - 500 125 - - 2 197 2 11 3 2 43 2 2 21 2 - - 1/40 - 1/24 x - ---- x y + --- x - 3/50 x y + --- x y + ---- y , - 1000 120 200 1000 - - COEFF(0, 2) = - - 79 2 2 159 2 3 2 2 11 437 2 - - --- x y - 1/40 x - ---- x y + 9/50 x y + 1/24 x - --- + ---- y , - 200 1000 120 1000 - - COEFF(1, 2) = - - 29 2 2 3 2 2 63 2 409 2 - - 3/40 + --- x y - 7/120 x - 9/50 x y + 1/24 x + ---- y + ---- x y , - 200 1000 1000 - - COEFF(2, 2) = - - 21 2 2 2 2 3 2 53 2 - 1/40 - ---- y - 1/24 x + 7/200 x y - 1/120 x + 3/50 x y - ---- x y ] - 1000 1000 - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); -bytes used=67073904, alloc=2162292, time=5.31 -bytes used=68074096, alloc=2162292, time=5.38 -bytes used=69074392, alloc=2162292, time=5.48 -bytes used=70074612, alloc=2162292, time=5.54 -bytes used=71074776, alloc=2162292, time=5.66 -bytes used=72075172, alloc=2162292, time=5.73 -bytes used=73075452, alloc=2162292, time=5.83 -bytes used=74076084, alloc=2162292, time=5.90 -bytes used=75076284, alloc=2162292, time=6.00 -bytes used=76076484, alloc=2162292, time=6.08 -bytes used=77083384, alloc=2162292, time=6.19 -bytes used=78083548, alloc=2162292, time=6.27 -bytes used=79083664, alloc=2162292, time=6.41 -bytes used=80083872, alloc=2162292, time=6.49 -bytes used=81084148, alloc=2162292, time=6.63 -bytes used=82084408, alloc=2162292, time=6.75 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); -bytes used=83085440, alloc=2162292, time=6.83 -6 c31 x y - 1/200 DATA(2, 2) + 3/200 DATA(1, 2) + 1/200 DATA(-1, 2) - - 29 67 37 - - 3/200 DATA(0, 2) - --- DATA(2, 1) + --- DATA(2, 0) - --- DATA(2, -1) - 200 200 200 - - 29 3 3 - + 1/2 y DATA(2, 1) + --- y DATA(1, 2) + 7/300 y DATA(2, 2) - 300 - - 11 3 3 21 - + -- y DATA(1, 1) + 1/25 x y DATA(-1, 0) + -- c32 - 9/50 c31 - 50 10 - - 199 87 87 - - --- DATA(0, 0) - 1/200 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) - 200 200 200 - - 2 2 - + 6 x y c32 - 3 y c32 - 21/5 x c32 - 1/6 y DATA(2, -1) - - + 1/4 y DATA(0, 0) + 1/4 y DATA(1, 0) - 1/2 y DATA(0, 1) - - - 1/2 y DATA(1, 1) - 1/6 y DATA(-1, -1) + 1/6 y DATA(0, -1) - - + 1/6 y DATA(1, -1) - 1/4 y DATA(-1, 0) + 1/2 y DATA(-1, 1) - - 3 19 3 - - 1/4 y DATA(2, 0) + 7/25 y DATA(0, 1) - --- y DATA(0, 0) - 100 - - 3 27 3 3 - - 4/75 y DATA(2, -1) + --- y DATA(2, 0) - 6/25 y DATA(2, 1) - 100 - - 79 3 13 3 23 3 - - --- y DATA(0, 2) - -- y DATA(-1, 1) + --- y DATA(-1, 0) - 300 50 100 - - 3 13 3 17 3 - - 1/150 y DATA(1, -1) + -- y DATA(0, -1) - --- y DATA(-1, -1) - 75 150 - - 31 3 2 2 - - --- y DATA(1, 0) + 1/4 y DATA(2, 1) - 1/2 y DATA(2, 0) - 100 - - 2 2 2 - + 1/4 y DATA(2, -1) + 1/2 y DATA(0, 0) + 1/2 y DATA(1, 0) + 9/25 x c31 - - 2 2 2 - - 3 y c31 - 1/4 y DATA(0, 1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(0, -1) - - 2 2 2 - - 1/4 y DATA(1, -1) - 1/2 y DATA(-1, 0) + 1/4 y DATA(-1, 1) - - 2 - + 1/100 x DATA(2, 2) - 3/100 x DATA(1, 2) - 1/4 y DATA(1, 1) - - 29 - - 1/100 x DATA(-1, 2) + 3/100 x DATA(0, 2) + --- x DATA(2, 1) - 100 - - 33 37 99 - + --- x DATA(2, 0) + --- x DATA(2, -1) + --- x DATA(0, 0) - 100 100 100 - - 99 87 87 - - --- x DATA(1, 0) + --- x DATA(0, 1) - --- x DATA(1, 1) - 100 100 100 - - 37 111 111 - - --- x DATA(-1, -1) + --- x DATA(0, -1) - --- x DATA(1, -1) - 100 100 100 - - 33 29 21 3 3 - - --- x DATA(-1, 0) - --- x DATA(-1, 1) + -- y c31 + 6/5 y c32 - 100 100 25 - - 37 111 111 133 - + --- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) - 200 200 200 200 - - 29 42 3 3 3 - + --- DATA(-1, 1) - -- x y c31 - 12/5 x y c32 - 9/50 x y DATA(0, -1) - 200 25 - - 3 3 3 - + 9/50 x y DATA(1, -1) + 1/50 x y DATA(-1, 1) + 3/25 x y DATA(2, 2) - - 3 3 3 - - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) - - 3 3 3 - - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) - - 3 3 3 - - 3/25 x y DATA(0, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) - - 3 3 - + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) - 1/12 y DATA(2, 2) - - + 1/12 y DATA(1, 2) - 1/12 y DATA(-1, 2) + 1/12 y DATA(0, 2) - - 43 3 - + --- y DATA(-1, 2) - 300 - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 37 2 17 3 3 37 -[COEFF(-1, -1) = - --- x + 1/4 y - --- y + 3/50 x y - 1/6 y + ---, - 100 150 200 - - 111 2 13 3 3 111 - COEFF(0, -1) = - --- - 1/4 y + 1/6 y + -- y - 9/50 x y + --- x, - 200 75 100 - - 3 111 111 2 3 - COEFF(1, -1) = 9/50 x y + --- - --- x - 1/4 y - 1/150 y + 1/6 y, - 200 100 - - 37 2 3 3 37 - COEFF(2, -1) = - --- + 1/4 y - 1/6 y - 4/75 y - 3/50 x y + --- x, - 200 100 - - 23 3 133 2 33 3 - COEFF(-1, 0) = --- y + --- - 1/4 y - 1/2 y - --- x + 1/25 x y , - 100 200 100 - - 199 19 3 99 2 3 - COEFF(0, 0) = 1/4 y - --- - --- y + --- x + 1/2 y - 3/25 x y , - 200 100 100 - - 2 3 99 31 3 - COEFF(1, 0) = 1/4 y + 1/2 y + 3/25 x y - --- x - 1/200 - --- y , - 100 100 - - 33 67 3 2 27 3 - COEFF(2, 0) = --- x + --- - 1/25 x y - 1/2 y - 1/4 y + --- y , - 100 200 100 - - 29 13 3 3 29 2 - COEFF(-1, 1) = - --- x - -- y + 1/50 x y + --- + 1/4 y + 1/2 y, - 100 50 200 - - 2 87 3 87 3 - COEFF(0, 1) = - 1/4 y - --- - 1/2 y - 3/50 x y + --- x + 7/25 y , - 200 100 - - 87 3 2 87 11 3 - COEFF(1, 1) = - --- x + 3/50 x y - 1/4 y + --- - 1/2 y + -- y , - 100 200 50 - - 3 29 2 3 29 - COEFF(2, 1) = - 6/25 y + --- x + 1/4 y - 1/50 x y - --- + 1/2 y, - 100 200 - - 43 3 3 - COEFF(-1, 2) = --- y - 1/100 x - 3/25 x y - 1/12 y + 1/200, - 300 - - 79 3 3 - COEFF(0, 2) = 3/100 x - --- y - 3/200 + 1/12 y + 9/25 x y , - 300 - - 29 3 3 - COEFF(1, 2) = - 3/100 x + --- y + 3/200 - 9/25 x y + 1/12 y, - 300 - - 3 3 - COEFF(2, 2) = 1/100 x - 1/200 + 3/25 x y + 7/300 y - 1/12 y] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); -bytes used=84085660, alloc=2162292, time=6.91 -bytes used=85085812, alloc=2162292, time=6.99 -bytes used=86086048, alloc=2162292, time=7.09 -bytes used=87086364, alloc=2162292, time=7.18 -bytes used=88086596, alloc=2162292, time=7.29 -bytes used=89086816, alloc=2162292, time=7.43 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); -bytes used=90086976, alloc=2162292, time=7.50 - 2 2 11 -3 c31 x + 6 c32 x y - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) - 120 - - - 1/40 DATA(0, 2) + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) - - 13 - + 1/20 y DATA(2, 1) - -- c31 - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) - 10 - - 2 39 2 - + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) + 18/5 x y c32 + -- y c32 - 25 - - + 1/2 x y DATA(2, -1) + 1/20 y DATA(2, -1) - 3/10 y DATA(0, 0) - - - 7/10 y DATA(1, 0) + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) - - 11 - - -- y DATA(-1, -1) + 3/20 y DATA(0, -1) + 7/20 y DATA(1, -1) - 20 - - 11 11 - + -- y DATA(-1, 0) - -- y DATA(-1, 1) - 1/10 y DATA(2, 0) - 10 20 - - 31 2 101 2 2 - - --- y DATA(2, 1) + ---- y DATA(2, 0) + 7/500 y DATA(2, -1) - 500 1000 - - 303 2 447 2 93 2 - + ---- y DATA(0, 0) + ---- y DATA(1, 0) - 3 x c31 - --- y DATA(0, 1) - 1000 1000 500 - - 59 2 21 2 73 2 - + --- y DATA(-1, -1) + --- y DATA(0, -1) - --- y DATA(1, -1) - 250 500 250 - - 851 2 203 2 - - ---- y DATA(-1, 0) + --- y DATA(-1, 1) - 1/12 x DATA(2, 2) - 1000 250 - - 141 2 - + 1/12 x DATA(1, 2) - --- y DATA(1, 1) - 1/12 x DATA(-1, 2) - 250 - - + 1/12 x DATA(0, 2) + 1/2 x DATA(2, 1) - 1/4 x DATA(2, 0) - - - 1/6 x DATA(2, -1) + 1/4 x DATA(0, 0) + 1/4 x DATA(1, 0) - - - 1/2 x DATA(0, 1) - 1/2 x DATA(1, 1) - 1/6 x DATA(-1, -1) - - + 1/6 x DATA(0, -1) + 1/6 x DATA(1, -1) - 1/4 x DATA(-1, 0) - - 2 2 2 2 - + 1/2 x DATA(-1, 1) + 3/100 x y DATA(-1, 1) + 3/50 x y DATA(-1, 0) - - 27 2 2 2 2 2 - + --- x y DATA(1, -1) + 7/100 x y DATA(2, 2) - 3/100 x y DATA(2, 1) - 100 - - 2 2 2 2 2 2 - - 9/50 x y DATA(0, 0) + 9/100 x y DATA(1, 1) - 9/100 x y DATA(0, 1) - - 27 2 2 2 2 2 2 - - --- x y DATA(0, -1) + 9/100 x y DATA(-1, -1) + 9/50 x y DATA(1, 0) - 100 - - 43 2 79 2 18 2 - + --- x y DATA(-1, 2) - --- x y DATA(0, 2) - -- x y DATA(2, 1) - 100 100 25 - - 2 2 27 2 2 2 2 - + 9/50 x y DATA(2, 2) + -- x y DATA(0, 2) - 9/50 x y DATA(-1, 2) - 50 - - 27 2 2 2 2 2 2 - - -- x y DATA(1, 2) - 9/100 x y DATA(2, -1) - 3/50 x y DATA(2, 0) - 50 - - 13 2 81 2 2 - + -- x y DATA(0, -1) + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) - 25 100 - - 57 2 29 2 2 - - --- x y DATA(0, 0) + --- x y DATA(1, 2) - 1/50 x y DATA(1, -1) - 100 100 - - 69 2 39 2 - + --- x y DATA(-1, 0) - -- x y DATA(-1, 1) + 1/2 x y DATA(2, 1) - 100 50 - - 93 2 21 2 - - x y DATA(2, 0) - --- x y DATA(1, 0) + -- x y DATA(0, 1) - 100 25 - - 33 2 17 2 - + -- x y DATA(1, 1) - -- x y DATA(-1, -1) + 1/2 x y DATA(-1, -1) - 50 50 - - - 1/2 x y DATA(1, -1) - x y DATA(-1, 0) + 1/2 x y DATA(-1, 1) - - - 1/2 x y DATA(0, -1) + x y DATA(0, 0) + x y DATA(1, 0) - - 159 2 - - 1/2 x y DATA(0, 1) - 1/2 x y DATA(1, 1) - ---- y DATA(0, 2) - 1000 - - 409 2 53 2 197 2 - + ---- y DATA(1, 2) - ---- y DATA(2, 2) - ---- y DATA(-1, 2) - 1000 1000 1000 - - 63 2 273 2 2 2 11 - - 6 x y c32 + -- x y c31 + --- y c31 - 18/5 c32 x y + -- DATA(-1, -1) - 25 250 60 - - 11 11 - - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1) - 40 20 - - 63 2 2 - - 13/5 y c32 - -- x y c31 - 25 - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 11 17 2 59 2 2 2 11 -[COEFF(-1, -1) = - -- y - 1/6 x - -- x y + 1/2 x y + --- y + 9/100 x y + -- - 20 50 250 60 - - , COEFF(0, -1) = - - 21 2 13 2 27 2 2 - - 1/20 + 1/6 x - 1/2 x y + --- y + -- x y + 3/20 y - --- x y , - 500 25 100 - - COEFF(1, -1) = - - 2 73 2 27 2 2 - - 1/2 x y - 1/50 x y + 1/6 x - 7/60 - --- y + --- x y + 7/20 y, - 250 100 - - COEFF(2, -1) = - - 2 2 2 2 - 1/2 x y + 1/20 y - 9/100 x y - 4/25 x y - 1/6 x - 1/60 + 7/500 y , - - 851 2 2 2 11 11 69 2 - COEFF(-1, 0) = -x y - ---- y + 3/50 x y - 1/4 x + -- + -- y + --- x y , - 1000 40 10 100 - - COEFF(0, 0) = - - 57 2 2 2 303 2 - - --- x y - 9/50 x y + x y + ---- y + 1/4 x - 3/10 y - 3/40, - 100 1000 - - 447 2 93 2 2 2 - COEFF(1, 0) = 1/4 x + ---- y - --- x y + 9/50 x y + x y - 7/10 y - 7/40 - 1000 100 - - , COEFF(2, 0) = - - 101 2 2 2 81 2 - -x y + ---- y - 1/4 x - 1/40 - 3/50 x y + --- x y - 1/10 y, - 1000 100 - - 203 2 11 11 39 2 2 2 - COEFF(-1, 1) = --- y - -- + 1/2 x - -- y - -- x y + 3/100 x y + 1/2 x y - 250 20 20 50 - - , COEFF(0, 1) = - - 93 2 21 2 2 2 - 3/20 + 3/20 y - 1/2 x y - --- y + -- x y - 1/2 x - 9/100 x y , - 500 25 - - COEFF(1, 1) = - - 33 2 141 2 2 2 - - 1/2 x + -- x y - --- y + 7/20 - 1/2 x y + 7/20 y + 9/100 x y , - 50 250 - - COEFF(2, 1) = - - 2 2 31 2 18 2 - - 3/100 x y + 1/2 x y + 1/20 + 1/2 x - --- y + 1/20 y - -- x y , - 500 25 - - 197 2 43 2 11 2 2 - COEFF(-1, 2) = - 1/12 x - ---- y + --- x y + --- - 9/50 x y , - 1000 100 120 - - 159 2 27 2 2 79 2 - COEFF(0, 2) = - 1/40 - ---- y + -- x y + 1/12 x - --- x y , - 1000 50 100 - - 27 2 2 29 2 409 2 - COEFF(1, 2) = 1/12 x - -- x y + --- x y + ---- y - 7/120, - 50 100 1000 - - 53 2 2 2 2 - COEFF(2, 2) = - ---- y - 1/12 x - 1/120 + 9/50 x y + 7/100 x y ] - 1000 - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); -bytes used=91087448, alloc=2162292, time=7.56 -bytes used=92087608, alloc=2162292, time=7.64 -bytes used=93087776, alloc=2162292, time=7.70 -bytes used=94088036, alloc=2162292, time=7.82 -bytes used=95088216, alloc=2162292, time=7.92 -bytes used=96088436, alloc=2162292, time=8.04 -bytes used=97088696, alloc=2162292, time=8.16 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); -bytes used=98091880, alloc=2162292, time=8.28 - 2 -18/5 c32 x y - 3/20 DATA(2, 1) + 3/10 DATA(2, 0) - 3/20 DATA(2, -1) - - 3 54 42 3 3 - - 12/5 c32 x y + --- y DATA(2, 1) - -- c31 x y + 2 c32 x + 9/5 c32 - 125 25 - - 11 11 - - -- DATA(0, 0) - 9/10 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) - 10 20 - - 63 2 273 189 2 - - 13/5 x c32 + -- x y c31 + --- x y c31 - --- y c31 - 3 x c32 - 25 125 125 - - 81 2 2 57 2 - + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) - --- x y DATA(0, 0) - 100 100 - - 93 2 21 2 33 2 - - --- x y DATA(1, 0) + -- x y DATA(0, 1) + -- x y DATA(1, 1) - 100 25 50 - - 17 2 13 2 2 - - -- x y DATA(-1, -1) + -- x y DATA(0, -1) - 1/50 x y DATA(1, -1) - 50 25 - - 53 409 - + 7/250 x y DATA(2, -1) - --- x y DATA(2, 2) + --- x y DATA(1, 2) - 500 500 - - 197 159 3 - - --- x y DATA(-1, 2) - --- x y DATA(0, 2) + 3/25 x y DATA(2, 2) - 500 500 - - 3 3 3 - - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) - - 3 3 3 - - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) - - 3 437 12 - - 3/25 x y DATA(0, 0) + --- y DATA(0, 2) + --- y DATA(2, -1) - 500 125 - - 771 729 213 - + --- y DATA(0, 0) + --- y DATA(1, 0) - --- y DATA(0, 1) - 500 500 125 - - 162 12 89 - - --- y DATA(1, 1) - --- y DATA(-1, -1) - --- y DATA(0, -1) - 125 125 125 - - 36 243 54 - - --- y DATA(1, -1) + --- y DATA(-1, 0) - --- y DATA(-1, 1) - 125 500 125 - - 243 3 3 - - --- y DATA(2, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) - 500 - - 3 3 3 - + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) + 9/50 x y DATA(1, -1) - - 3 3 3 - + 1/25 x y DATA(-1, 0) + 1/50 x y DATA(-1, 1) - 9/50 x y DATA(0, -1) - - 29 2 2 79 2 - + --- x y DATA(1, 2) + 7/100 x y DATA(2, 2) - --- x y DATA(0, 2) - 100 100 - - 43 2 18 2 2 - + --- x y DATA(-1, 2) - -- x y DATA(2, 1) + 1/4 x DATA(2, 1) - 100 25 - - 2 2 2 - - 1/2 x DATA(2, 0) + 1/4 x DATA(2, -1) + 1/2 x DATA(0, 0) - - 2 2 2 - + 1/2 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) - - 2 21 63 - + 1/4 x DATA(-1, -1) - --- y DATA(2, 2) + --- y DATA(1, 2) - 500 500 - - 21 2 2 - + --- y DATA(-1, 2) + 1/4 x DATA(-1, 1) - 1/4 x DATA(0, -1) - 500 - - 2 2 69 2 - - 1/2 x DATA(-1, 0) - 1/4 x DATA(1, -1) + --- x y DATA(-1, 0) - 100 - - 39 2 - - -- x y DATA(-1, 1) + 1/20 x DATA(2, 1) - 1/10 x DATA(2, 0) - 50 - - + 1/20 x DATA(2, -1) - 3/10 x DATA(0, 0) - 7/10 x DATA(1, 0) - - 11 - + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) - -- x DATA(-1, -1) - 20 - - 11 - + 3/20 x DATA(0, -1) + 7/20 x DATA(1, -1) + -- x DATA(-1, 0) - 10 - - 11 31 101 - - -- x DATA(-1, 1) - --- x y DATA(2, 1) + --- x y DATA(2, 0) - 20 250 500 - - 59 73 851 - + --- x y DATA(-1, -1) - --- x y DATA(1, -1) - --- x y DATA(-1, 0) - 125 125 500 - - 203 21 303 - + --- x y DATA(-1, 1) + --- x y DATA(0, -1) + --- x y DATA(0, 0) - 125 250 500 - - 447 93 141 - + --- x y DATA(1, 0) - --- x y DATA(0, 1) - --- x y DATA(1, 1) - 500 250 125 - - 78 11 - + -- x y c32 + 3/20 DATA(-1, -1) + -- DATA(0, -1) + 9/20 DATA(1, -1) - 25 20 - - 54 - - 3/10 DATA(-1, 0) + 3/20 DATA(-1, 1) - -- y c32 - 25 - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=99092352, alloc=2227816, time=8.34 - 2 12 3 59 11 17 2 -[COEFF(-1, -1) = 1/4 x - --- y + 3/50 y x + --- x y - -- x + 3/20 - -- y x , - 125 125 20 50 - - 21 13 2 3 89 11 2 - COEFF(0, -1) = --- x y + -- y x - 9/50 y x - --- y + -- + 3/20 x - 1/4 x - 250 25 125 20 - - , COEFF(1, -1) = - - 73 2 36 2 3 - 7/20 x - --- x y - 1/50 y x - --- y - 1/4 x + 9/50 y x + 9/20, - 125 125 - - COEFF(2, -1) = - - 12 2 2 3 - - 3/20 + --- y + 1/4 x - 4/25 y x - 3/50 y x + 7/250 x y + 1/20 x, - 125 - - COEFF(-1, 0) = - - 11 69 2 2 243 3 851 - -- x + --- y x - 1/2 x + --- y + 1/25 y x - 3/10 - --- x y, COEFF(0, 0) - 10 100 500 500 - - 57 2 771 3 11 2 303 - = - --- y x + --- y - 3/25 y x - -- + 1/2 x - 3/10 x + --- x y, - 100 500 10 500 - - COEFF(1, 0) = - - 3 729 2 93 2 447 - 3/25 y x + --- y + 1/2 x - 9/10 - --- y x + --- x y - 7/10 x, - 500 100 500 - - COEFF(2, 0) = - - 243 2 101 81 2 3 - - --- y - 1/2 x + 3/10 + --- x y + --- y x - 1/10 x - 1/25 y x , - 500 500 100 - - COEFF(-1, 1) = - - 11 203 3 54 2 39 2 - - -- x + --- x y + 1/50 y x - --- y + 1/4 x + 3/20 - -- y x , - 20 125 125 50 - - 11 3 213 21 2 2 93 - COEFF(0, 1) = -- - 3/50 y x - --- y + -- y x + 3/20 x - 1/4 x - --- x y, - 20 125 25 250 - - COEFF(1, 1) = - - 141 3 33 2 2 162 - 9/20 + 7/20 x - --- x y + 3/50 y x + -- y x - 1/4 x - --- y, COEFF(2, 1) - 125 50 125 - - 54 2 18 2 31 3 - = - 3/20 + --- y + 1/4 x - -- y x - --- x y - 1/50 y x + 1/20 x, - 125 25 250 - - 3 21 197 43 2 - COEFF(-1, 2) = - 3/25 y x + --- y - --- x y + --- y x , - 500 500 100 - - 3 159 79 2 437 - COEFF(0, 2) = 9/25 y x - --- x y - --- y x + --- y, - 500 100 500 - - 29 2 3 63 409 - COEFF(1, 2) = --- y x - 9/25 y x + --- y + --- x y, - 100 500 500 - - 2 53 3 21 - COEFF(2, 2) = 7/100 y x - --- x y + 3/25 y x - --- y] - 500 500 - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); -bytes used=100092548, alloc=2227816, time=8.41 -bytes used=101092996, alloc=2227816, time=8.49 -bytes used=102093148, alloc=2227816, time=8.61 -bytes used=103093312, alloc=2227816, time=8.69 -bytes used=104093644, alloc=2227816, time=8.84 -bytes used=105093832, alloc=2227816, time=8.92 -bytes used=106093996, alloc=2227816, time=9.05 -> -################################################################################ -> -# -# 2d, cube, order=4, smoothing=0 (size=5) -# -> -# interpolating polynomial -> interp_2d_cube_order4_smooth0 -> := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, -> coords_list_2d, posn_list_2d_size5); -bytes used=107094420, alloc=2227816, time=9.13 -bytes used=108095396, alloc=2227816, time=9.19 -bytes used=109095660, alloc=2227816, time=9.25 -bytes used=110095928, alloc=2227816, time=9.31 -bytes used=111096132, alloc=2227816, time=9.36 -bytes used=112096424, alloc=2227816, time=9.43 -bytes used=113096732, alloc=2227816, time=9.50 -bytes used=114097080, alloc=2227816, time=9.57 -bytes used=115097268, alloc=2227816, time=9.64 -bytes used=116097436, alloc=2227816, time=9.71 -bytes used=117097712, alloc=2227816, time=9.77 -bytes used=118100480, alloc=2227816, time=9.84 -bytes used=119101300, alloc=2227816, time=9.90 -bytes used=120101536, alloc=2227816, time=9.96 -bytes used=121102272, alloc=2227816, time=10.03 -bytes used=122103488, alloc=2227816, time=10.09 -bytes used=123103664, alloc=2227816, time=10.14 -bytes used=124103840, alloc=2227816, time=10.21 -bytes used=125104372, alloc=2227816, time=10.28 -interp_2d_cube_order4_smooth0 := (- 1/24 DATA(0, 2) - 5/4 DATA(0, 0) - - 2 - + 2/3 DATA(0, 1) - 1/24 DATA(0, -2) + 2/3 DATA(0, -1)) y + DATA(0, 0) + ( - - - 1/576 DATA(2, 2) + 1/144 DATA(1, 2) + 1/144 DATA(-1, 2) - 1/96 DATA(0, 2) - - + 1/36 DATA(2, 1) - 5/96 DATA(2, 0) + 1/36 DATA(2, -1) - 5/16 DATA(0, 0) - - + 5/24 DATA(1, 0) + 1/6 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) - - + 1/36 DATA(-2, 1) - 5/96 DATA(-2, 0) + 1/36 DATA(-2, -1) - - - 1/576 DATA(2, -2) + 1/144 DATA(1, -2) - 1/96 DATA(0, -2) - - + 1/144 DATA(-1, -2) - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) - - + 1/6 DATA(0, -1) - 1/9 DATA(1, -1) + 5/24 DATA(-1, 0) - 1/9 DATA(-1, 1)) - - 4 2 - x y + (- 1/288 DATA(2, 2) + 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) - - - 1/48 DATA(0, 2) + 1/36 DATA(2, 1) - 1/36 DATA(2, -1) + 1/6 DATA(0, 1) - - - 1/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/36 DATA(-2, 1) - - - 1/36 DATA(-2, -1) + 1/288 DATA(2, -2) - 1/72 DATA(1, -2) - - + 1/48 DATA(0, -2) - 1/72 DATA(-1, -2) + 1/288 DATA(-2, -2) - - + 1/9 DATA(-1, -1) - 1/6 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) - - 4 - x y + (1/144 DATA(2, 2) - 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) - - - 1/72 DATA(2, 1) + 1/72 DATA(2, -1) - 1/72 DATA(-2, -1) + 1/36 DATA(1, 1) - - - 1/144 DATA(-2, 2) + 1/72 DATA(-2, 1) + 1/144 DATA(-2, -2) - - - 1/144 DATA(2, -2) + 1/72 DATA(1, -2) - 1/72 DATA(-1, -2) - - 3 3 - + 1/36 DATA(-1, -1) - 1/36 DATA(1, -1) - 1/36 DATA(-1, 1)) x y + ( - - - 1/288 DATA(2, 2) + 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/18 DATA(2, 1) - - - 5/48 DATA(2, 0) + 1/18 DATA(2, -1) + 5/24 DATA(1, 0) - 1/9 DATA(1, 1) - - + 1/288 DATA(-2, 2) - 1/18 DATA(-2, 1) + 5/48 DATA(-2, 0) - - - 1/18 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/144 DATA(1, -2) - - - 1/144 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) - - 3 2 - - 1/9 DATA(1, -1) - 5/24 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + ( - - - 1/144 DATA(2, 2) + 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) + 1/18 DATA(2, 1) - - - 1/18 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) - 1/18 DATA(-2, 1) - - + 1/18 DATA(-2, -1) + 1/144 DATA(2, -2) - 1/72 DATA(1, -2) - - + 1/72 DATA(-1, -2) - 1/144 DATA(-2, -2) - 1/9 DATA(-1, -1) - - 3 - + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + (- 1/288 DATA(2, 2) - - + 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) + 1/72 DATA(2, 1) - 1/48 DATA(2, 0) - - + 1/72 DATA(2, -1) + 1/6 DATA(1, 0) - 1/9 DATA(1, 1) + 1/288 DATA(-2, 2) - - - 1/72 DATA(-2, 1) + 1/48 DATA(-2, 0) - 1/72 DATA(-2, -1) - - - 1/288 DATA(2, -2) + 1/36 DATA(1, -2) - 1/36 DATA(-1, -2) - - + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) - 1/9 DATA(1, -1) - - 4 - - 1/6 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + (- 1/576 DATA(2, 2) - - + 1/36 DATA(1, 2) + 1/36 DATA(-1, 2) - 5/96 DATA(0, 2) + 1/144 DATA(2, 1) - - - 1/96 DATA(2, 0) + 1/144 DATA(2, -1) - 5/16 DATA(0, 0) + 1/6 DATA(1, 0) - - + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) + 1/144 DATA(-2, 1) - - - 1/96 DATA(-2, 0) + 1/144 DATA(-2, -1) - 1/576 DATA(2, -2) - - + 1/36 DATA(1, -2) - 5/96 DATA(0, -2) + 1/36 DATA(-1, -2) - - - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) + 5/24 DATA(0, -1) - - 2 4 - - 1/9 DATA(1, -1) + 1/6 DATA(-1, 0) - 1/9 DATA(-1, 1)) x y + ( - - 1/576 DATA(2, 2) - 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/96 DATA(0, 2) - - - 1/144 DATA(2, 1) + 1/96 DATA(2, 0) - 1/144 DATA(2, -1) + 1/16 DATA(0, 0) - - - 1/24 DATA(1, 0) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/576 DATA(-2, 2) - - - 1/144 DATA(-2, 1) + 1/96 DATA(-2, 0) - 1/144 DATA(-2, -1) - - + 1/576 DATA(2, -2) - 1/144 DATA(1, -2) + 1/96 DATA(0, -2) - - - 1/144 DATA(-1, -2) + 1/576 DATA(-2, -2) + 1/36 DATA(-1, -1) - - - 1/24 DATA(0, -1) + 1/36 DATA(1, -1) - 1/24 DATA(-1, 0) - - 4 4 - + 1/36 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/144 DATA(1, 2) - - + 1/144 DATA(-1, 2) - 1/72 DATA(2, 1) + 1/48 DATA(2, 0) - 1/72 DATA(2, -1) - - + 1/24 DATA(-1, 0) - 1/24 DATA(1, 0) + 1/36 DATA(1, 1) - 1/288 DATA(-2, 2) - - + 1/72 DATA(-2, 1) - 1/48 DATA(-2, 0) + 1/72 DATA(-2, -1) - - + 1/288 DATA(2, -2) - 1/144 DATA(1, -2) + 1/144 DATA(-1, -2) - - - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/36 DATA(1, -1) - - 3 4 - - 1/36 DATA(-1, 1)) x y + (1/144 DATA(2, 2) - 1/18 DATA(1, 2) - - + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) - - - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) - 1/18 DATA(-2, -1) - - - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - 1/18 DATA(-1, -2) - - + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) - 4/9 DATA(1, -1) - - - 4/9 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/36 DATA(1, 2) - - + 1/36 DATA(-1, 2) - 1/18 DATA(2, 1) + 5/48 DATA(2, 0) - 1/18 DATA(2, -1) - - - 5/6 DATA(1, 0) + 4/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/18 DATA(-2, 1) - - - 5/48 DATA(-2, 0) + 1/18 DATA(-2, -1) + 1/288 DATA(2, -2) - - - 1/36 DATA(1, -2) + 1/36 DATA(-1, -2) - 1/288 DATA(-2, -2) - - - 4/9 DATA(-1, -1) + 4/9 DATA(1, -1) + 5/6 DATA(-1, 0) - 4/9 DATA(-1, 1)) - - 2 / - x y + |1/576 DATA(2, 2) - 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) - \ - - + 5/96 DATA(0, 2) - 1/36 DATA(2, 1) + 5/96 DATA(2, 0) - 1/36 DATA(2, -1) - - 25 - + -- DATA(0, 0) - 5/6 DATA(1, 0) - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) - 16 - - + 1/576 DATA(-2, 2) - 1/36 DATA(-2, 1) + 5/96 DATA(-2, 0) - - - 1/36 DATA(-2, -1) + 1/576 DATA(2, -2) - 1/36 DATA(1, -2) - - + 5/96 DATA(0, -2) - 1/36 DATA(-1, -2) + 1/576 DATA(-2, -2) - - + 4/9 DATA(-1, -1) - 5/6 DATA(0, -1) + 4/9 DATA(1, -1) - 5/6 DATA(-1, 0) - - \ 2 2 - + 4/9 DATA(-1, 1)| x y + (1/288 DATA(2, 2) - 1/18 DATA(1, 2) - / - - - 1/18 DATA(-1, 2) + 5/48 DATA(0, 2) - 1/36 DATA(2, 1) + 1/36 DATA(2, -1) - - - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) + 1/288 DATA(-2, 2) - 1/36 DATA(-2, 1) - - + 1/36 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/18 DATA(1, -2) - - - 5/48 DATA(0, -2) + 1/18 DATA(-1, -2) - 1/288 DATA(-2, -2) - - - 4/9 DATA(-1, -1) + 5/6 DATA(0, -1) - 4/9 DATA(1, -1) + 4/9 DATA(-1, 1)) - - 2 - x y + (1/288 DATA(2, 2) - 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) - - + 1/48 DATA(0, 2) - 1/144 DATA(2, 1) + 1/144 DATA(2, -1) - - - 1/36 DATA(1, -1) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/288 DATA(-2, 2) - - - 1/144 DATA(-2, 1) + 1/144 DATA(-2, -1) - 1/288 DATA(2, -2) - - + 1/72 DATA(1, -2) - 1/48 DATA(0, -2) + 1/72 DATA(-1, -2) - - - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/24 DATA(0, -1) - - 4 3 - + 1/36 DATA(-1, 1)) x y + (1/24 DATA(0, 2) + 1/4 DATA(0, 0) - - 4 - - 1/6 DATA(0, 1) + 1/24 DATA(0, -2) - 1/6 DATA(0, -1)) y + ( - - 1/24 DATA(2, 0) + 1/4 DATA(0, 0) - 1/6 DATA(1, 0) + 1/24 DATA(-2, 0) - - 4 - - 1/6 DATA(-1, 0)) x + - - (- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0)) x - - + (- 1/24 DATA(2, 0) - 5/4 DATA(0, 0) + 2/3 DATA(1, 0) - 1/24 DATA(-2, 0) - - 2 - + 2/3 DATA(-1, 0)) x + - - 3 - (1/12 DATA(0, 2) - 1/6 DATA(0, 1) - 1/12 DATA(0, -2) + 1/6 DATA(0, -1)) y - - + - - (- 1/12 DATA(0, 2) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) - 2/3 DATA(0, -1)) y - - + (- 1/144 DATA(2, 2) + 1/18 DATA(1, 2) - 1/18 DATA(-1, 2) - - + 1/72 DATA(2, 1) - 1/72 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) - - - 1/72 DATA(-2, 1) + 1/72 DATA(-2, -1) + 1/144 DATA(2, -2) - - - 1/18 DATA(1, -2) + 1/18 DATA(-1, -2) - 1/144 DATA(-2, -2) - - 3 - - 1/9 DATA(-1, -1) + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + ( - - - 1/288 DATA(2, 2) + 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 5/48 DATA(0, 2) - - + 1/144 DATA(2, 1) - 1/144 DATA(2, -1) + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) - - - 1/288 DATA(-2, 2) + 1/144 DATA(-2, 1) - 1/144 DATA(-2, -1) - - + 1/288 DATA(2, -2) - 1/18 DATA(1, -2) + 5/48 DATA(0, -2) - - - 1/18 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) - - 2 3 - - 5/24 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) x y + - - 3 - (1/12 DATA(2, 0) - 1/6 DATA(1, 0) - 1/12 DATA(-2, 0) + 1/6 DATA(-1, 0)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=126126424, alloc=2227816, time=10.34 -bytes used=127129732, alloc=2227816, time=10.40 - 4 2 3 3 2 -[COEFF(-2, -2) = 1/288 x y + 1/288 x y - 1/144 x y - 1/288 y x - - 2 4 4 3 4 2 2 3 - - 1/576 x y - 1/288 x y + 1/288 x y + 1/576 x y - 1/144 y x - - 2 3 2 3 3 3 4 - - 1/288 x y + 1/288 x y + 1/144 x y + 1/144 x y - 1/288 x y - - 4 2 4 4 2 2 4 3 - - 1/576 x y + 1/576 x y , COEFF(-1, -2) = - 1/36 x y + 1/72 x y - - 4 2 4 3 2 2 4 - - 1/72 x y + 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y - - 4 2 4 4 3 3 4 2 3 - + 1/144 x y - 1/144 x y + 1/18 x y + 1/144 x y - 1/18 x y - - 3 3 2 3 3 - - 1/18 x y - 1/72 x y + 1/36 x y + 1/72 y x , COEFF(0, -2) = - 1/12 y - - 4 4 4 2 2 3 2 - + 1/24 y + 1/48 x y - 1/96 x y + 5/48 x y + 1/12 y - 5/48 y x - - 2 4 4 3 4 4 2 2 2 - - 5/96 x y - 1/48 x y + 1/96 x y + 5/96 x y - 1/24 y , - - 4 3 3 2 2 4 - COEFF(1, -2) = 1/18 x y + 1/72 x y + 1/144 x y + 1/18 y x + 1/36 x y - - 4 2 3 4 3 3 4 4 - + 1/144 x y - 1/72 y x - 1/72 x y + 1/72 x y - 1/144 x y - - 3 2 3 2 2 4 3 4 - - 1/18 x y - 1/18 x y - 1/36 x y + 1/36 x y - 1/144 x y - - 2 2 2 4 2 2 3 - - 1/36 x y , COEFF(2, -2) = - 1/576 x y - 1/288 y x + 1/288 x y - - 4 4 3 3 4 4 2 - + 1/576 x y + 1/144 y x + 1/288 x y - 1/144 x y - 1/576 x y - - 4 3 2 3 2 3 4 - - 1/288 x y + 1/288 x y - 1/288 x y + 1/144 x y - 1/288 x y - - 3 3 2 2 4 4 - - 1/144 x y + 1/576 x y + 1/288 x y, COEFF(-2, -1) = - 1/36 x y - - 2 2 3 2 2 3 3 3 - + 1/36 y x - 1/144 x y - 1/36 x y + 1/18 y x - 1/72 x y - - 2 4 3 4 2 4 3 - + 1/144 x y + 1/72 x y - 1/18 x y + 1/36 x y + 1/144 x y - - 2 3 2 4 4 4 3 4 - + 1/18 x y - 1/18 x y - 1/144 x y - 1/72 x y + 1/72 x y , - - 2 4 3 3 3 4 - COEFF(-1, -1) = - 1/9 x y + 4/9 x y - 1/9 x y + 1/36 x y + 1/9 x y - - 2 2 4 2 3 2 2 2 4 4 - + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y - 4/9 y x + 1/36 x y - - 4 3 4 3 4 3 2 3 - + 1/9 x y - 1/36 x y - 1/9 y x - 1/36 x y + 1/9 x y , COEFF(0, -1) - - 4 4 4 2 4 3 2 2 - = - 1/24 x y + 1/6 x y - 1/6 y + 1/6 y + 5/6 y x - 2/3 y + 2/3 y - - 2 3 2 4 4 4 3 2 2 - - 5/24 x y + 5/24 x y - 1/6 x y + 1/24 x y - 5/6 x y , - - 3 3 2 4 2 2 4 2 4 - COEFF(1, -1) = - 1/36 x y - 1/9 x y + 4/9 x y - 1/9 x y + 1/9 x y - - 2 3 3 2 2 3 4 3 - - 4/9 x y + 1/9 x y - 1/9 x y - 4/9 y x + 1/9 x y - 1/36 x y - - 2 4 4 3 4 4 3 - + 4/9 x y + 1/36 x y + 1/36 x y - 1/9 x y + 1/9 y x , COEFF(2, -1) - - 4 4 4 4 2 4 2 2 - = 1/18 x y - 1/144 x y - 1/36 x y + 1/36 x y + 1/72 x y - 1/36 x y - - 3 3 3 4 3 3 4 2 4 - + 1/72 x y - 1/18 y x + 1/144 x y - 1/72 x y + 1/144 x y - - 2 2 3 2 3 3 2 - - 1/18 x y + 1/36 y x - 1/72 x y - 1/144 x y + 1/18 x y , - - 4 2 3 3 4 2 2 4 - COEFF(-2, 0) = - 5/96 x y - 1/12 x - 1/48 x y + 5/96 x y + 1/24 x - - 4 2 4 4 4 2 2 3 2 - + 1/48 x y - 1/96 x y + 1/96 x y - 5/48 x y - 1/24 x + 5/48 x y - - 4 4 4 2 4 2 - + 1/12 x, COEFF(-1, 0) = - 1/24 x y - 1/6 x y + 5/6 x y + 5/24 x y - - 3 4 3 2 2 3 4 2 2 - + 1/24 x y - 5/24 x y + 2/3 x + 1/6 x - 1/6 x - 2/3 x - 5/6 x y - - 2 4 4 2 4 2 4 25 2 2 - + 1/6 x y , COEFF(0, 0) = - 5/16 x y + 1/4 x - 5/16 x y + -- x y - 16 - - 4 4 4 2 2 2 2 - + 1/16 x y + 1/4 y + 1 - 5/4 y - 5/4 x , COEFF(1, 0) = - 5/6 x y - - 2 4 2 4 4 4 4 3 4 - + 1/6 x y + 2/3 x - 1/24 x y + 1/6 x y - 1/6 x - 1/24 x y + 2/3 x - - 3 2 2 3 4 2 4 - + 5/24 x y - 5/6 x y - 1/6 x + 5/24 x y , COEFF(2, 0) = - 1/48 x y - - 4 2 4 4 2 4 4 2 - + 1/24 x + 5/48 x y - 1/12 x + 1/96 x y - 1/96 x y - 5/96 x y - - 3 2 3 4 3 2 2 2 - + 1/12 x - 1/24 x + 1/48 x y - 5/48 x y + 5/96 x y , COEFF(-2, 1) - - 3 4 2 3 2 3 2 - = - 1/72 x y + 1/36 x y + 1/144 x y - 1/36 y x - 1/18 x y - - 2 4 4 3 3 3 3 4 - + 1/18 x y + 1/144 x y - 1/144 x y + 1/72 x y + 1/72 x y - - 2 3 2 2 4 4 4 2 - + 1/18 x y - 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y - - 4 3 3 3 3 4 2 - - 1/72 x y , COEFF(-1, 1) = 1/9 x y - 1/36 x y + 1/9 y x - 1/9 x y - - 3 4 4 4 3 4 4 2 4 2 - - 1/36 x y - 1/9 x y + 1/36 x y + 1/36 x y - 1/9 x y - 4/9 x y - - 2 2 2 2 3 3 2 4 - + 4/9 y x + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y + 1/9 x y , - - 4 2 2 3 2 4 4 4 - COEFF(0, 1) = 1/6 x y + 5/24 x y + 2/3 y + 2/3 y - 1/24 x y - 1/6 y - - 4 4 3 2 2 2 2 4 3 - + 1/6 x y - 1/24 x y - 5/6 x y - 5/6 y x + 5/24 x y - 1/6 y , - - 2 4 3 3 4 3 - COEFF(1, 1) = 4/9 x y + 1/36 x y - 1/9 x y - 1/9 x y - 1/9 y x - - 3 2 3 3 2 2 2 4 4 4 - - 1/9 x y + 1/36 x y + 4/9 x y - 1/9 x y + 1/36 x y + 4/9 x y - - 2 3 4 2 4 2 3 4 - - 1/9 x y - 1/9 x y - 1/9 x y + 4/9 y x + 1/36 x y , COEFF(2, 1) = - - 4 2 3 4 3 2 2 3 - 1/36 x y - 1/18 x y + 1/18 y x + 1/36 x y + 1/18 x y + 1/144 x y - - 2 4 3 2 4 4 2 4 - - 1/18 x y - 1/144 x y - 1/36 y x - 1/144 x y + 1/144 x y - - 3 4 3 2 2 3 3 4 - - 1/72 x y + 1/72 x y - 1/36 x y - 1/72 x y + 1/72 x y , - - 4 2 4 4 2 4 - COEFF(-2, 2) = - 1/288 x y + 1/288 y x + 1/576 x y - 1/576 x y - - 3 3 4 4 3 2 2 - + 1/144 x y - 1/288 x y - 1/144 x y + 1/288 x y + 1/576 x y - - 2 3 2 4 2 4 3 3 - - 1/288 x y - 1/288 x y - 1/576 x y + 1/288 x y - 1/144 x y - - 3 2 3 4 3 4 2 - + 1/288 x y + 1/144 y x , COEFF(-1, 2) = - 1/72 x y + 1/144 x y - - 4 4 4 3 3 3 2 4 - - 1/144 x y + 1/72 x y - 1/72 y x + 1/72 x y + 1/36 x y - - 2 2 2 3 2 3 2 2 - - 1/36 x y + 1/18 x y + 1/18 x y - 1/18 y x - 1/144 x y + 1/36 x y - - 3 4 3 4 4 2 - - 1/18 x y - 1/36 x y + 1/144 x y , COEFF(0, 2) = - 1/96 x y - - 2 4 3 2 4 4 2 - - 1/24 y + 1/48 x y - 5/96 x y + 1/24 y + 5/48 y x - 1/12 y - - 4 4 2 2 3 4 2 3 - + 1/96 x y + 5/96 x y + 1/12 y - 1/48 x y - 5/48 x y , COEFF(1, 2) - - 4 3 4 4 2 3 4 - = - 1/72 x y - 1/144 x y - 1/36 x y - 1/144 x y - 1/18 x y - - 3 2 3 2 4 3 3 - + 1/18 x y - 1/18 y x + 1/144 x y + 1/36 x y - 1/72 x y - - 2 4 2 3 4 2 2 2 4 - + 1/36 x y + 1/18 x y + 1/144 x y - 1/36 x y + 1/72 x y - - 3 4 3 4 2 4 4 - + 1/72 y x , COEFF(2, 2) = 1/288 x y - 1/576 x y + 1/576 x y - - 4 2 3 4 3 - - 1/288 x y + 1/288 x y + 1/288 x y + 1/144 x y - 1/144 x y - - 2 3 2 4 3 3 2 4 - + 1/288 y x - 1/288 x y - 1/288 x y + 1/144 x y - 1/576 x y - - 2 3 2 2 3 - - 1/288 x y + 1/576 x y - 1/144 y x ] - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); -bytes used=128130292, alloc=2227816, time=10.47 -bytes used=129130448, alloc=2227816, time=10.54 -bytes used=130130628, alloc=2227816, time=10.63 -bytes used=131157976, alloc=2227816, time=10.72 -bytes used=132170256, alloc=2227816, time=10.79 -bytes used=133182936, alloc=2227816, time=10.85 -bytes used=134184444, alloc=2227816, time=10.93 -bytes used=135184740, alloc=2227816, time=11.04 -bytes used=136185208, alloc=2227816, time=11.13 -bytes used=137185504, alloc=2227816, time=11.19 -bytes used=138185676, alloc=2227816, time=11.39 -bytes used=139186008, alloc=2227816, time=11.46 -bytes used=140186252, alloc=2227816, time=11.53 -bytes used=141186616, alloc=2227816, time=11.59 -bytes used=142186928, alloc=2227816, time=11.65 -bytes used=143187140, alloc=2227816, time=11.71 -bytes used=144187292, alloc=2227816, time=11.79 -bytes used=145187476, alloc=2424388, time=11.88 -bytes used=146187724, alloc=2424388, time=11.96 -bytes used=147188072, alloc=2424388, time=12.05 -bytes used=148188276, alloc=2424388, time=12.14 -bytes used=149188548, alloc=2424388, time=12.24 -bytes used=150189040, alloc=2424388, time=12.35 -bytes used=151189584, alloc=2424388, time=12.44 -bytes used=152189776, alloc=2424388, time=12.71 -bytes used=153190128, alloc=2424388, time=12.86 -bytes used=154190356, alloc=2424388, time=12.92 -bytes used=155198184, alloc=2424388, time=13.02 -bytes used=156199352, alloc=2424388, time=13.15 -bytes used=157206092, alloc=2424388, time=13.34 -bytes used=158206320, alloc=2424388, time=13.51 -bytes used=159206528, alloc=2424388, time=13.63 -bytes used=160206828, alloc=2424388, time=13.70 -bytes used=161207036, alloc=2424388, time=13.81 -bytes used=162207248, alloc=2424388, time=13.91 -bytes used=163207460, alloc=2424388, time=14.15 -bytes used=164207736, alloc=2424388, time=14.23 -bytes used=165207896, alloc=2424388, time=14.31 -bytes used=166208088, alloc=2424388, time=14.42 -bytes used=167208332, alloc=2424388, time=14.63 -bytes used=168208740, alloc=2424388, time=14.73 -bytes used=169208984, alloc=2424388, time=14.80 -bytes used=170209144, alloc=2424388, time=14.91 -bytes used=171209480, alloc=2424388, time=15.13 -bytes used=172209780, alloc=2424388, time=15.24 -> -# d/dx -> simplify( diff(interp_2d_cube_order4_smooth0,x) ); -bytes used=173210092, alloc=2424388, time=15.39 -bytes used=174210336, alloc=2424388, time=15.44 -bytes used=175210520, alloc=2424388, time=15.51 -bytes used=176210708, alloc=2424388, time=15.57 -bytes used=177210968, alloc=2489912, time=15.65 -bytes used=178211200, alloc=2620960, time=15.71 -- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0) - - 3 3 2 - - 1/18 y DATA(-1, 2) - 1/72 y DATA(2, -1) + 8/9 x y DATA(-1, -1) - - 2 2 2 2 2 2 - + 5/8 x y DATA(1, 0) - 1/3 x y DATA(1, 1) + 1/96 x y DATA(-2, 2) - - 3 3 3 - - 1/9 y DATA(1, 1) + 1/144 y DATA(-2, 2) - 1/72 y DATA(-2, 1) - - 3 3 - + 1/72 y DATA(2, 1) - 2/3 x DATA(-1, 0) - 1/12 x DATA(2, 0) - - - 5/2 x DATA(0, 0) + 4/3 x DATA(1, 0) - 1/12 x DATA(-2, 0) - - 3 3 - + 4/3 x DATA(-1, 0) - 1/144 y DATA(2, 2) + 1/18 y DATA(1, 2) - - 3 3 3 - + 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 1/18 y DATA(1, -2) - - 2 2 2 2 - - 1/96 x y DATA(2, -2) + 1/48 x y DATA(1, -2) - - 2 2 2 2 - - 1/48 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) - - 2 2 2 2 2 2 - + 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, -1) - 5/8 x y DATA(-1, 0) - - 2 2 2 2 - + 1/3 x y DATA(-1, 1) + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) - - 2 2 2 2 2 - + 1/6 y x DATA(2, 1) + 5/16 x y DATA(-2, 0) - 1/6 x y DATA(-2, -1) - - 2 2 2 - - 1/24 y x DATA(1, -2) + 1/24 y x DATA(-1, -2) - 1/48 y x DATA(-2, -2) - - 2 2 2 - - 1/48 y x DATA(2, 2) - 1/3 y x DATA(1, 1) + 1/48 y x DATA(-2, 2) - - 2 2 2 - - 1/6 y x DATA(-2, 1) + 1/6 y x DATA(-2, -1) + 1/48 y x DATA(2, -2) - - 4 4 4 - - 1/9 y DATA(1, -1) - 1/288 y DATA(2, 2) + 1/36 y DATA(1, 2) - - 4 4 4 - - 1/36 y DATA(-1, 2) + 1/72 y DATA(2, 1) - 1/288 x y DATA(-2, 2) - - 4 4 4 - - 2/9 x y DATA(-1, -1) + 5/12 x y DATA(0, -1) - 2/9 x y DATA(1, -1) - - 4 4 4 - + 1/3 x y DATA(-1, 0) - 2/9 x y DATA(-1, 1) + 1/72 x y DATA(-2, -1) - - 4 4 4 - - 1/288 x y DATA(2, -2) + 1/18 x y DATA(1, -2) - 1/288 x y DATA(-2, -2) - - 2 2 2 - - 1/3 y x DATA(-1, -1) + 1/3 y x DATA(1, -1) + 1/3 y x DATA(-1, 1) - - 2 4 4 - - 1/6 y x DATA(2, -1) + 1/18 x y DATA(1, 2) + 1/72 x y DATA(2, -1) - - 4 4 4 - - 5/8 x y DATA(0, 0) + 1/3 x y DATA(1, 0) + 5/12 x y DATA(0, 1) - - 4 3 4 4 - - 1/288 x y DATA(2, 2) + 1/144 x y DATA(-2, -2) - 5/48 x y DATA(0, -2) - - 4 4 4 - + 1/18 x y DATA(-1, -2) - 2/9 x y DATA(1, 1) + 1/72 x y DATA(-2, 1) - - 4 4 4 - - 1/48 x y DATA(-2, 0) - 1/6 y DATA(-1, 0) + 1/18 x y DATA(-1, 2) - - 4 4 4 - - 5/48 x y DATA(0, 2) + 1/72 x y DATA(2, 1) - 1/48 x y DATA(2, 0) - - 4 3 4 3 4 - + 1/9 y DATA(-1, 1) - 1/36 x y DATA(1, -2) - 1/36 x y DATA(-1, -2) - - 3 4 3 4 3 4 - + 1/9 x y DATA(1, 1) - 1/36 x y DATA(-2, 1) - 1/36 x y DATA(-2, -1) - - 3 4 3 4 3 4 - + 1/9 x y DATA(-1, -1) - 1/6 x y DATA(0, -1) + 1/9 x y DATA(1, -1) - - 3 4 3 4 3 4 - - 1/6 x y DATA(-1, 0) + 1/24 x y DATA(0, -2) + 1/24 x y DATA(0, 2) - - 3 4 3 4 3 4 - - 1/36 x y DATA(2, 1) + 1/24 x y DATA(2, 0) - 1/36 x y DATA(2, -1) - - 3 4 3 4 3 4 - + 1/4 x y DATA(0, 0) - 1/6 x y DATA(1, 0) + 1/9 x y DATA(-1, 1) - - 3 4 2 4 - + 1/144 x y DATA(2, -2) + 1/24 x y DATA(-2, -1) - - 2 4 3 4 3 4 - + 1/96 x y DATA(2, 2) - 1/6 x y DATA(0, 1) + 1/144 x y DATA(2, 2) - - 2 4 2 4 2 4 - - 1/48 x y DATA(1, 2) + 1/48 x y DATA(-1, 2) - 1/24 x y DATA(2, 1) - - 2 4 3 4 3 4 - + 1/16 x y DATA(2, 0) + 1/24 x y DATA(-2, 0) + 1/144 x y DATA(-2, 2) - - 3 4 3 4 2 4 - - 1/36 x y DATA(1, 2) - 1/36 x y DATA(-1, 2) + 1/96 x y DATA(2, -2) - - 2 4 2 4 2 4 - - 1/24 x y DATA(2, -1) + 1/8 x y DATA(-1, 0) - 1/8 x y DATA(1, 0) - - 2 4 2 4 2 4 - + 1/12 x y DATA(1, 1) - 1/96 x y DATA(-2, 2) + 1/24 x y DATA(-2, 1) - - 2 4 2 4 - - 1/16 x y DATA(-2, 0) + 1/48 x y DATA(-1, -2) - - 2 4 2 4 - - 1/96 x y DATA(-2, -2) - 1/12 x y DATA(-1, -1) - - 2 4 2 4 2 - + 1/12 x y DATA(1, -1) - 1/12 x y DATA(-1, 1) + 8/9 x y DATA(1, -1) - - 2 2 2 - - 5/3 x y DATA(-1, 0) + 8/9 x y DATA(-1, 1) - 1/18 x y DATA(-2, -1) - - 2 2 2 - + 1/288 x y DATA(2, -2) - 1/18 x y DATA(1, -2) + 5/48 x y DATA(0, -2) - - 2 - - 1/18 x y DATA(-1, -2) - 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) - - + 4/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) + 1/144 y DATA(2, 2) - - 4 4 - - 1/18 y DATA(1, 2) - 1/48 y DATA(2, 0) + 1/72 y DATA(2, -1) - - 4 4 4 - + 1/6 y DATA(1, 0) - 1/9 y DATA(1, 1) + 1/288 y DATA(-2, 2) - - 4 4 4 - - 1/72 y DATA(-2, 1) + 1/48 y DATA(-2, 0) - 1/72 y DATA(-2, -1) - - 4 4 4 - - 1/288 y DATA(2, -2) + 1/36 y DATA(1, -2) - 1/36 y DATA(-1, -2) - - 4 4 2 - + 1/288 y DATA(-2, -2) + 1/9 y DATA(-1, -1) - 5/3 x y DATA(0, -1) - - 2 - - 5/6 y DATA(1, 0) + 1/18 y DATA(-2, 1) - 1/18 y DATA(-2, -1) - - - 1/144 y DATA(2, -2) + 1/18 y DATA(1, -2) - 1/18 y DATA(-1, -2) - - + 1/144 y DATA(-2, -2) + 4/9 y DATA(-1, -1) - 4/9 y DATA(1, -1) - - 2 2 - - 4/9 y DATA(-1, 1) + 1/288 y DATA(2, 2) - 1/36 y DATA(1, 2) - - 2 2 - + 1/18 y DATA(-1, 2) + 5/6 y DATA(-1, 0) + 1/36 y DATA(-1, 2) - - 2 2 2 - - 1/18 y DATA(2, 1) + 5/48 y DATA(2, 0) - 1/18 y DATA(2, -1) - - 2 2 2 - - 4/9 y DATA(-1, 1) + 4/9 y DATA(1, 1) - 1/288 y DATA(-2, 2) - - 2 2 2 - + 1/18 y DATA(-2, 1) - 5/48 y DATA(-2, 0) + 1/18 y DATA(-2, -1) - - 2 2 2 - + 1/288 y DATA(2, -2) - 1/36 y DATA(1, -2) + 1/36 y DATA(-1, -2) - - 2 2 2 - - 1/288 y DATA(-2, -2) - 4/9 y DATA(-1, -1) + 4/9 y DATA(1, -1) - - 2 4 2 2 - - 1/48 x y DATA(1, -2) - 1/18 x y DATA(1, 2) - 1/18 x y DATA(-1, 2) - - 2 2 2 - + 5/48 x y DATA(0, 2) - 1/18 x y DATA(2, 1) + 5/48 x y DATA(2, 0) - - 2 - + 1/288 x y DATA(-2, -2) - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) - - + 5/24 x y DATA(0, 2) - 1/18 x y DATA(2, 1) + 1/18 x y DATA(2, -1) - - - 5/3 x y DATA(0, 1) + 8/9 x y DATA(1, 1) + 1/144 x y DATA(-2, 2) - - - 1/18 x y DATA(-2, 1) + 1/18 x y DATA(-2, -1) - 1/144 x y DATA(2, -2) - - 2 2 2 - + 8/9 x y DATA(1, 1) - 1/18 x y DATA(-2, 1) + 5/48 x y DATA(-2, 0) - - 2 2 2 - + 1/288 x y DATA(-2, 2) - 1/18 x y DATA(2, -1) + 25/8 x y DATA(0, 0) - - 2 2 2 - - 5/3 x y DATA(1, 0) - 5/3 x y DATA(0, 1) + 1/288 x y DATA(2, 2) - - 3 3 3 3 - + 8/9 x y DATA(-1, 1) + 1/72 x y DATA(2, 2) - 1/18 x y DATA(1, 2) - - 3 3 3 3 3 3 - - 1/18 x y DATA(-1, 2) + 1/12 x y DATA(0, 2) - 1/36 x y DATA(2, 1) - - 3 3 3 3 - + 1/36 x y DATA(2, -1) - 1/9 x y DATA(1, -1) + 1/144 x y DATA(2, 2) - - 3 3 - - 1/72 x y DATA(2, -2) + 1/9 x y DATA(1, -2) - 5/24 x y DATA(0, -2) - - + 1/9 x y DATA(-1, -2) - 1/144 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) - - 3 3 - + 5/3 x y DATA(0, -1) - 8/9 x y DATA(1, -1) + 1/18 x y DATA(-1, -2) - - 3 3 3 3 3 3 - - 1/72 x y DATA(-2, -2) - 1/9 x y DATA(-1, -1) + 1/6 x y DATA(0, -1) - - 3 3 3 3 3 - + 1/9 x y DATA(-1, 1) - 1/144 x y DATA(2, 2) - 1/6 x y DATA(0, 1) - - 3 3 3 3 3 3 - + 1/9 x y DATA(1, 1) + 1/72 x y DATA(-2, 2) - 1/36 x y DATA(-2, 1) - - 3 3 3 3 - + 1/36 x y DATA(-2, -1) + 1/18 y DATA(-1, -2) - 1/144 y DATA(-2, -2) - - 3 3 3 - - 1/9 y DATA(-1, -1) + 1/9 y DATA(1, -1) + 1/9 y DATA(-1, 1) - - 3 3 3 - + 1/6 x DATA(2, 0) + x DATA(0, 0) - 2/3 x DATA(1, 0) - - 3 3 3 - + 1/6 x DATA(-2, 0) - 1/72 x y DATA(2, -1) + 5/12 x y DATA(0, 1) - - 3 3 3 - - 2/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) + 1/72 x y DATA(-2, 1) - - 3 3 3 3 3 - + 1/18 x y DATA(1, -2) - 1/12 x y DATA(0, -2) - 2/9 x y DATA(-1, 1) - - 3 3 3 - + 1/9 x y DATA(1, 2) + 1/9 x y DATA(-1, 2) - 5/24 x y DATA(0, 2) - - 3 3 2 3 - + 1/72 x y DATA(2, 1) - 4/9 x y DATA(1, -1) - 1/72 x y DATA(-2, -1) - - 3 3 3 - + 1/144 x y DATA(2, -2) - 1/9 x y DATA(1, -2) + 5/24 x y DATA(0, -2) - - 3 3 3 - - 1/9 x y DATA(-1, -2) + 1/144 x y DATA(-2, -2) + 2/9 x y DATA(-1, -1) - - 3 3 3 2 - - 5/12 x y DATA(0, -1) + 2/9 x y DATA(1, -1) + 5/6 x y DATA(1, 0) - - 3 2 3 2 3 - + 2/3 x y DATA(0, 1) - 1/144 x y DATA(2, 2) - 1/72 y x DATA(2, 2) - - 3 2 3 2 3 2 - + 5/6 x y DATA(-1, 0) - 4/9 x y DATA(-1, 1) + 1/9 x y DATA(-2, -1) - - 3 2 3 2 - - 1/144 x y DATA(2, -2) + 1/36 x y DATA(1, -2) - - 3 2 3 2 - - 1/24 x y DATA(0, -2) + 1/36 x y DATA(-1, -2) - - 3 2 3 2 - - 1/144 x y DATA(-2, -2) - 4/9 x y DATA(-1, -1) - - 3 2 2 3 2 - + 2/3 x y DATA(0, -1) + 1/4 x DATA(2, 0) - 1/24 x y DATA(0, 2) - - 3 2 3 2 3 2 - + 1/9 x y DATA(2, 1) - 5/24 x y DATA(2, 0) + 1/9 x y DATA(2, -1) - - 3 2 2 3 - - 5/4 x y DATA(0, 0) - 1/2 x DATA(1, 0) - 1/12 y x DATA(0, 2) - - 3 3 3 - + 1/9 y x DATA(2, 1) - 1/9 y x DATA(2, -1) + 2/3 y x DATA(0, 1) - - 3 2 3 2 3 2 - - 4/9 x y DATA(1, 1) + 1/9 x y DATA(-2, 1) - 5/24 x y DATA(-2, 0) - - 3 2 3 2 3 2 - - 1/144 x y DATA(-2, 2) + 1/36 x y DATA(1, 2) + 1/36 x y DATA(-1, 2) - - 2 3 3 - - 1/4 x DATA(-2, 0) - 2/3 y x DATA(0, -1) - 4/9 y x DATA(-1, 1) - - 3 3 3 - - 4/9 y x DATA(1, 1) - 1/72 y x DATA(-2, 2) + 1/9 y x DATA(-2, 1) - - 3 3 3 - - 1/9 y x DATA(-2, -1) + 1/72 y x DATA(2, -2) + 1/18 y x DATA(1, 2) - - 3 3 3 - + 1/18 y x DATA(-1, 2) + 4/9 y x DATA(1, -1) - 1/18 y x DATA(1, -2) - - 3 3 3 - - 1/18 y x DATA(-1, -2) + 1/72 y x DATA(-2, -2) + 4/9 y x DATA(-1, -1) - - 3 2 3 2 3 - + 1/12 y x DATA(0, -2) + 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, -2) - - 2 3 2 3 2 3 - - 1/48 x y DATA(2, -2) + 1/24 x y DATA(1, -2) + 1/24 x y DATA(2, -1) - - 2 3 2 3 2 3 - - 1/24 x y DATA(-2, -1) + 1/12 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) - - 2 3 2 3 2 3 - + 1/48 x y DATA(2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) - - 2 3 2 2 2 - - 1/24 x y DATA(2, 1) + 1/2 x DATA(-1, 0) - 1/6 x y DATA(-2, 1) - - 2 2 2 2 2 2 - + 1/48 x y DATA(1, 2) - 1/48 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) - - 2 2 2 2 2 2 - - 5/16 x y DATA(2, 0) + 1/6 x y DATA(2, -1) - 1/96 x y DATA(2, 2) - - 2 3 2 3 - - 1/24 x y DATA(-1, -2) + 1/12 x y DATA(-1, -1) - - 2 3 2 3 - - 1/12 x y DATA(1, -1) - 1/12 x y DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=179213692, alloc=2620960, time=15.78 -bytes used=180223192, alloc=2620960, time=15.84 - 2 2 2 4 -[COEFF(-2, -2) = - 1/144 x y + 1/288 x y - 1/288 y + 1/144 y - 1/96 x y - - 3 2 2 3 4 3 3 - + 1/72 y x + 1/96 x y + 1/144 x y + 1/144 x y - 1/144 y - - 2 3 2 4 3 2 4 - + 1/48 x y - 1/48 y x - 1/288 x y - 1/144 x y + 1/288 y - - 3 3 2 4 3 4 3 2 - - 1/72 x y , COEFF(-1, -2) = 1/48 x y - 1/36 x y + 1/36 x y - - 2 2 2 3 3 3 3 - - 1/48 x y + 1/36 y + 1/18 x y - 1/9 x y + 1/18 y - 1/18 y - - 4 2 2 3 2 3 - - 1/36 y + 1/24 y x - 1/18 x y - 1/18 y x - 1/24 x y + 1/9 x y - - 4 3 3 3 3 2 - + 1/18 x y , COEFF(0, -2) = 1/12 y x - 1/12 x y - 1/24 x y - - 2 4 3 3 4 - + 5/48 x y - 5/24 x y - 5/48 x y + 5/24 x y + 1/24 x y , COEFF(1, -2) - - 2 3 2 2 3 3 4 - = - 1/18 x y - 1/18 y x - 1/24 y x + 1/24 x y - 1/36 x y + 1/18 y - - 3 2 2 3 3 2 4 3 2 2 - + 1/36 x y - 1/36 y + 1/18 x y - 1/48 x y - 1/18 y + 1/48 x y - - 3 4 4 4 - + 1/9 x y - 1/9 x y + 1/36 y + 1/18 x y , COEFF(2, -2) = - 1/288 y - - 2 3 3 2 3 4 - + 1/288 x y - 1/72 x y - 1/48 x y - 1/288 x y - 1/144 x y - 1/144 y - - 2 4 2 3 4 3 2 3 - + 1/96 x y + 1/48 y x + 1/144 x y - 1/144 x y + 1/144 x y - - 2 2 3 3 2 - - 1/96 x y + 1/144 y + 1/72 y x + 1/288 y , COEFF(-2, -1) = - - 3 4 4 2 3 2 2 - - 1/72 x y - 1/72 y + 1/72 x y - 1/24 x y + 1/18 y - 1/18 x y - - 3 4 2 4 2 3 3 - - 1/36 x y + 1/24 x y + 1/6 y x + 1/18 x y + 1/36 x y - 1/18 y - - 3 3 2 3 2 2 2 3 - - 1/9 y x + 1/9 x y + 1/72 y - 1/6 x y , COEFF(-1, -1) = 1/12 x y - - 2 2 4 3 3 3 4 - - 4/9 y - 8/9 x y - 1/12 x y - 1/9 y + 2/9 x y + 4/9 y x + 1/9 y - - 3 3 3 4 2 2 2 3 2 - - 1/9 x y + 4/9 y + 1/9 x y + 1/3 x y + 8/9 x y - 4/9 x y - - 2 4 3 3 3 3 4 - - 1/3 y x - 2/9 x y , COEFF(0, -1) = 1/6 x y - 2/3 y x - 1/6 x y - - 3 2 2 3 4 - + 2/3 x y - 5/3 x y + 5/3 x y - 5/12 x y + 5/12 x y , COEFF(1, -1) = - - 2 2 3 3 4 2 3 3 3 - - 1/3 x y + 4/9 y x + 1/9 x y + 4/9 y + 2/9 x y - 1/9 x y - - 2 2 4 4 2 3 2 - - 8/9 x y + 8/9 x y + 1/12 x y - 2/9 x y + 1/3 y x - 4/9 x y - - 3 4 2 3 2 2 - + 1/9 y - 4/9 y - 1/9 y - 1/12 x y , COEFF(2, -1) = 1/6 x y - - 2 3 2 4 4 4 2 3 - - 1/6 y x - 1/72 y - 1/24 x y + 1/72 y + 1/72 x y + 1/24 x y - - 3 2 2 3 4 2 3 3 - + 1/9 x y - 1/18 y - 1/36 x y + 1/18 x y - 1/18 x y + 1/36 x y - - 3 3 3 2 - + 1/18 y - 1/9 y x - 1/72 x y , COEFF(-2, 0) = 1/12 - 5/24 x y - - 4 2 4 2 2 3 4 3 - + 1/48 y - 1/16 x y + 5/48 x y - 1/4 x + 1/24 x y + 1/6 x - - 2 2 4 2 4 - + 5/16 x y - 1/48 x y - 5/48 y - 1/12 x, COEFF(-1, 0) = 1/3 x y - 2/3 - - 2 2 4 3 2 2 3 4 2 - - 5/3 x y + 1/8 x y + 5/6 x y + 1/2 x - 2/3 x - 1/6 y + 5/6 y - - 2 2 3 4 - - 5/8 x y + 4/3 x - 1/6 x y , - - 2 3 3 4 4 3 2 - COEFF(0, 0) = 25/8 x y + x + 1/4 x y - 5/2 x - 5/8 x y - 5/4 x y , - - 3 2 3 4 2 2 2 2 - COEFF(1, 0) = 5/6 x y - 1/6 x y - 5/3 x y - 5/6 y + 2/3 + 5/8 x y - - 2 2 4 3 4 4 - - 1/2 x - 1/8 x y - 2/3 x + 1/3 x y + 1/6 y + 4/3 x, COEFF(2, 0) = - - 2 2 3 2 3 4 - - 1/12 x + 1/4 x + 5/48 x y - 5/24 x y + 1/6 x - 1/12 - 1/48 y - - 4 2 2 2 2 4 3 4 - - 1/48 x y + 5/48 y - 5/16 x y + 1/16 x y + 1/24 x y , COEFF(-2, 1) - - 3 2 2 2 3 4 - = - 1/72 y - 1/18 x y + 1/18 y - 1/6 y x + 1/18 y - 1/36 x y - - 2 4 4 3 3 3 2 2 2 - + 1/24 x y - 1/72 y - 1/36 x y + 1/9 x y - 1/6 x y - 1/18 x y - - 3 4 2 3 3 4 - + 1/9 y x + 1/72 x y + 1/24 x y + 1/72 x y , COEFF(-1, 1) = - 2/9 x y - - 2 3 3 3 2 2 3 - + 8/9 x y - 4/9 y + 1/9 x y - 4/9 x y + 1/3 y x - 2/9 x y - - 3 2 4 4 3 4 2 2 2 - - 4/9 y x - 1/12 x y + 1/9 y + 1/9 x y + 8/9 x y + 1/3 x y - - 3 2 3 2 - + 1/9 y - 1/12 x y - 4/9 y, COEFF(0, 1) = - 5/3 x y - 5/3 x y - - 3 4 3 4 3 3 3 3 2 - - 1/6 x y + 5/12 x y + 5/12 x y - 1/6 x y + 2/3 y x + 2/3 x y , - - 2 2 3 3 3 4 3 - COEFF(1, 1) = - 1/3 y x + 1/12 x y + 1/9 x y - 2/9 x y - 2/9 x y - - 2 3 3 2 2 4 - + 4/9 y - 1/9 y + 8/9 x y + 4/9 y - 4/9 y x - 1/3 x y - 1/9 y - - 3 4 2 4 3 2 2 2 - + 1/9 x y + 1/12 x y - 4/9 x y + 8/9 x y , COEFF(2, 1) = 1/6 y x - - 4 3 2 3 2 4 2 - + 1/72 x y + 1/72 x y - 1/18 y + 1/9 y x - 1/24 x y - 1/18 x y - - 3 4 3 2 2 2 3 - - 1/36 x y + 1/9 x y + 1/6 x y + 1/72 y - 1/18 y - 1/18 x y - - 4 2 3 3 3 2 - + 1/72 y - 1/24 x y - 1/36 x y , COEFF(-2, 2) = 1/144 x y + 1/48 y x - - 3 3 3 2 3 2 4 2 3 - + 1/72 x y + 1/144 y + 1/288 x y - 1/144 x y + 1/288 y - 1/48 x y - - 2 2 2 3 4 3 4 - - 1/144 y + 1/96 x y - 1/288 y - 1/144 x y - 1/288 x y + 1/144 x y - - 2 4 3 2 4 2 - - 1/96 x y - 1/72 y x , COEFF(-1, 2) = 1/48 x y - 1/9 x y - 1/18 x y - - 3 3 2 2 2 3 4 2 3 - - 1/18 x y + 1/36 y - 1/48 x y + 1/18 y - 1/36 x y + 1/24 x y - - 3 2 3 2 3 4 4 - - 1/18 y - 1/24 y x + 1/36 x y + 1/18 y x + 1/18 x y - 1/36 y - - 3 2 3 3 3 2 - + 1/9 x y , COEFF(0, 2) = 5/48 x y + 1/12 x y - 1/24 x y + 5/24 x y - - 4 3 4 3 3 - - 5/48 x y + 1/24 x y - 1/12 y x - 5/24 x y , COEFF(1, 2) = - - 3 4 2 2 3 2 3 - - 1/36 x y - 1/9 x y + 1/48 x y + 1/18 y x + 1/24 y x + 1/9 x y - - 4 2 4 2 3 2 3 2 2 - + 1/18 x y - 1/48 x y - 1/24 x y - 1/36 y + 1/36 x y - 1/18 x y - - 3 3 4 3 3 - - 1/18 y - 1/18 x y + 1/36 y + 1/18 y , COEFF(2, 2) = - 1/144 y - - 2 2 2 3 4 3 3 2 - - 1/96 x y + 1/48 x y - 1/288 y + 1/72 x y + 1/288 x y - - 3 2 4 3 3 2 - - 1/144 x y - 1/48 y x - 1/288 x y - 1/72 y x - 1/144 x y - - 3 4 2 4 2 - + 1/144 x y + 1/96 x y + 1/144 y + 1/144 x y + 1/288 y ] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); -bytes used=181223344, alloc=2620960, time=15.90 -bytes used=182223500, alloc=2620960, time=15.97 -bytes used=183223664, alloc=2620960, time=16.07 -bytes used=184244420, alloc=2620960, time=16.17 -bytes used=185261976, alloc=2620960, time=16.24 -bytes used=186262132, alloc=2620960, time=16.32 -bytes used=187271400, alloc=2620960, time=16.41 -bytes used=188271672, alloc=2620960, time=16.50 -bytes used=189271940, alloc=2620960, time=16.57 -bytes used=190272092, alloc=2620960, time=16.84 -bytes used=191272872, alloc=2620960, time=16.90 -bytes used=192273040, alloc=2620960, time=16.96 -bytes used=193273564, alloc=2620960, time=17.03 -bytes used=194283560, alloc=2620960, time=17.13 -bytes used=195283924, alloc=2620960, time=17.24 -bytes used=196288796, alloc=2620960, time=17.34 -bytes used=197290992, alloc=2620960, time=17.43 -bytes used=198291176, alloc=2620960, time=17.52 -bytes used=199291660, alloc=2620960, time=17.61 -bytes used=200292092, alloc=2620960, time=17.89 -bytes used=201292244, alloc=2620960, time=18.05 -bytes used=202292640, alloc=2620960, time=18.12 -bytes used=203294780, alloc=2620960, time=18.22 -bytes used=204295016, alloc=2620960, time=18.34 -bytes used=205295216, alloc=2620960, time=18.44 -bytes used=206305080, alloc=2620960, time=18.68 -bytes used=207305332, alloc=2620960, time=18.84 -bytes used=208305696, alloc=2620960, time=18.90 -bytes used=209306900, alloc=2620960, time=19.00 -bytes used=210308068, alloc=2620960, time=19.12 -bytes used=211308248, alloc=2620960, time=19.34 -bytes used=212308496, alloc=2620960, time=19.47 -bytes used=213308676, alloc=2620960, time=19.54 -bytes used=214312144, alloc=2620960, time=19.67 -bytes used=215319752, alloc=2620960, time=19.92 -bytes used=216319980, alloc=2620960, time=20.07 -bytes used=217320236, alloc=2620960, time=20.15 -bytes used=218320488, alloc=2620960, time=20.29 -bytes used=219320656, alloc=2620960, time=20.59 -bytes used=220320808, alloc=2620960, time=20.75 -> -# d/dy -> simplify( diff(interp_2d_cube_order4_smooth0,y) ); -bytes used=221321332, alloc=2620960, time=20.87 -bytes used=222321548, alloc=2620960, time=20.93 -bytes used=223321736, alloc=2620960, time=21.00 -bytes used=224321912, alloc=2620960, time=21.06 - 4 2 4 2 -- 1/12 DATA(0, 2) - 1/12 x y DATA(-1, -1) + 1/8 x y DATA(0, -1) - - 4 2 4 2 - + 1/12 x y DATA(-1, 1) - 1/96 x y DATA(-2, -2) - - 4 2 3 3 - - 1/48 x y DATA(-2, 1) + 1/6 y DATA(0, 2) + y DATA(0, 0) - - 3 3 3 - - 2/3 y DATA(0, 1) + 1/6 y DATA(0, -2) - 2/3 y DATA(0, -1) - - 4 2 2 2 2 2 - + 1/24 x y DATA(-1, -2) - 5/16 x y DATA(0, 2) + 5/16 x y DATA(0, -2) - - 2 2 3 2 2 - + 5/8 x y DATA(0, 1) - 2/3 x y DATA(-1, 0) - 5/8 x y DATA(0, -1) - - 3 2 3 2 3 - + 1/12 x y DATA(-2, 0) + 2/3 x y DATA(-1, 0) + 2/3 x y DATA(1, 0) - - 2 3 2 3 2 3 - - 1/24 x y DATA(-2, 0) + 5/6 x y DATA(0, -1) - 1/24 x y DATA(2, 0) - - 2 3 4 3 4 3 - - 5/24 x y DATA(0, 2) - 1/6 x y DATA(-1, 0) - 1/36 x y DATA(-2, -1) - - 4 3 4 3 - + 1/144 x y DATA(2, -2) - 1/36 x y DATA(1, -2) - - 4 3 4 3 2 3 - - 1/36 x y DATA(-1, -2) + 1/24 x y DATA(2, 0) + 5/6 x y DATA(0, 1) - - 2 3 4 3 - - 5/24 x y DATA(0, -2) + 1/9 x y DATA(-1, 1) - - 4 3 4 3 2 3 - + 1/144 x y DATA(-2, -2) + 1/9 x y DATA(-1, -1) - 5/4 x y DATA(0, 0) - - 4 3 - + 1/9 x y DATA(1, -1) - 1/12 y DATA(0, 2) - 5/2 y DATA(0, 0) - - 4 3 - + 4/3 y DATA(0, 1) - 1/12 y DATA(0, -2) + 1/144 x y DATA(2, 2) - - 4 3 4 3 4 3 - - 1/36 x y DATA(-1, 2) - 1/6 x y DATA(0, 1) + 1/24 x y DATA(0, -2) - - 4 3 4 3 4 3 - - 1/6 x y DATA(0, -1) + 1/24 x y DATA(0, 2) - 1/36 x y DATA(1, 2) - - 4 3 4 3 4 3 - - 1/36 x y DATA(2, 1) - 1/6 x y DATA(1, 0) + 1/9 x y DATA(1, 1) - - 4 3 4 3 - - 1/36 x y DATA(-2, 1) + 1/24 x y DATA(-2, 0) - - 4 3 4 3 - + 1/144 x y DATA(-2, 2) - 1/36 x y DATA(2, -1) + 4/3 y DATA(0, -1) - - 2 2 2 - - 1/4 y DATA(0, -2) + 1/2 y DATA(0, -1) - 1/2 y DATA(0, 1) - - 2 3 3 - + 1/4 y DATA(0, 2) + 2/3 x y DATA(1, 0) - 1/12 x y DATA(2, 0) - - 3 3 3 - - 5/12 y x DATA(-1, 0) + 5/24 y x DATA(-2, 0) - 5/24 y x DATA(2, 0) - - 3 3 3 - + 5/12 y x DATA(1, 0) - 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) - - 3 3 3 - - 1/144 x DATA(2, 2) + 1/144 x DATA(2, -2) + 1/18 x DATA(-2, -1) - - 3 3 3 - - 1/18 x DATA(-2, 1) + 1/144 x DATA(-2, 2) - 1/9 x DATA(1, 1) - - 3 3 4 - - 1/18 x DATA(2, -1) + 1/18 x DATA(2, 1) + 1/18 x y DATA(2, 1) - - 4 4 4 - + 1/72 x y DATA(-1, -2) + 1/72 x y DATA(1, -2) - 1/288 x y DATA(2, -2) - - 4 4 4 - - 5/48 x y DATA(2, 0) - 5/8 x y DATA(0, 0) + 1/3 x y DATA(0, -1) - - 4 4 4 - - 1/48 x y DATA(0, -2) + 1/3 x y DATA(0, 1) + 1/72 x y DATA(-1, 2) - - 4 4 4 - + 1/72 x y DATA(1, 2) - 1/288 x y DATA(2, 2) - 1/288 x y DATA(-2, 2) - - 4 4 4 - - 5/48 x y DATA(-2, 0) + 1/18 x y DATA(-2, 1) - 2/9 x y DATA(1, 1) - - 4 4 4 - + 5/12 x y DATA(1, 0) + 1/18 x y DATA(2, -1) - 1/48 x y DATA(0, 2) - - 4 4 4 - - 2/9 x y DATA(-1, 1) - 2/9 x y DATA(1, -1) - 2/9 x y DATA(-1, -1) - - 4 4 4 - - 1/288 x y DATA(-2, -2) + 5/12 x y DATA(-1, 0) - 1/288 x DATA(-2, 2) - - 3 3 3 - + 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) - 1/9 x DATA(-1, -1) - - 3 3 3 - - 1/144 x DATA(-2, -2) + 1/72 x DATA(-1, -2) - 1/72 x DATA(1, -2) - - 4 4 4 - - 1/9 x DATA(1, 1) - 1/6 x DATA(0, -1) + 1/9 x DATA(-1, -1) - - 4 4 4 - + 1/288 x DATA(-2, -2) - 1/72 x DATA(-1, -2) + 1/48 x DATA(0, -2) - - 4 4 4 - - 1/72 x DATA(1, -2) + 1/288 x DATA(2, -2) - 1/36 x DATA(-2, -1) - - 4 4 - + 1/36 x DATA(-2, 1) + 1/18 x DATA(2, -1) + 1/6 x DATA(0, 1) - - 4 4 4 - - 1/36 x DATA(2, -1) + 1/36 x DATA(2, 1) - 1/48 x DATA(0, 2) - - 4 4 4 - + 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) - 1/288 x DATA(2, 2) - - 4 4 - - 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) + 5/24 x y DATA(2, 0) - - 4 3 3 3 - - 5/3 x y DATA(1, 0) + 1/4 x y DATA(0, 0) + 1/12 x y DATA(2, 0) - - 3 3 3 3 4 - + 1/6 x y DATA(-1, 0) - 1/6 x y DATA(1, 0) + 1/18 x y DATA(-2, -1) - - 3 3 2 2 - - 1/12 x y DATA(-2, 0) + 1/36 x DATA(-2, -1) + 1/18 x DATA(1, -2) - - 2 2 2 - - 5/48 x DATA(0, -2) + 1/18 x DATA(-1, -2) - 1/288 x DATA(-2, -2) - - - 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/18 x DATA(-2, 1) - - - 1/144 x DATA(2, -2) + 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) - - + 1/144 x DATA(-2, -2) + 4/9 x DATA(-1, -1) - 1/18 x DATA(-2, -1) - - + 4/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/144 x DATA(2, 2) - - - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) - - 2 - - 1/288 x DATA(2, -2) + 5/3 x y DATA(-1, 0) - 5/24 x y DATA(-2, 0) - - 2 2 2 - + 5/48 y x DATA(-2, 0) - 5/3 y x DATA(-1, 0) - 5/3 y x DATA(0, 1) - - 2 2 2 - + 5/48 y x DATA(0, -2) - 5/3 y x DATA(0, -1) + 5/48 y x DATA(0, 2) - - 2 4 2 4 2 - + 25/8 y x DATA(0, 0) - 1/24 x y DATA(1, 2) - 1/24 x y DATA(-1, 2) - - 4 2 4 2 2 - + 1/16 x y DATA(0, 2) - 1/48 x y DATA(2, 1) + 5/48 y x DATA(2, 0) - - 2 2 2 - - 5/3 y x DATA(1, 0) + 5/6 x DATA(0, -1) - 4/9 x DATA(1, -1) - - 2 2 2 - + 4/9 x DATA(-1, 1) + 1/288 x DATA(2, 2) - 1/18 x DATA(1, 2) - - 2 2 2 - - 1/18 x DATA(-1, 2) + 5/48 x DATA(0, 2) - 1/36 x DATA(2, 1) - - 2 2 2 - + 1/36 x DATA(2, -1) - 5/6 x DATA(0, 1) + 4/9 x DATA(1, 1) - - 2 2 4 2 - + 1/288 x DATA(-2, 2) - 1/36 x DATA(-2, 1) + 1/12 x y DATA(1, 1) - - 4 2 4 2 4 2 - + 1/96 x y DATA(-2, 2) - 1/12 x y DATA(1, -1) + 1/96 x y DATA(2, 2) - - 4 2 4 2 4 2 - - 1/96 x y DATA(2, -2) + 1/24 x y DATA(1, -2) - 1/16 x y DATA(0, -2) - - 4 2 4 2 4 2 - + 1/48 x y DATA(-2, -1) + 1/48 x y DATA(2, -1) - 1/8 x y DATA(0, 1) - - 2 - - 4/9 x DATA(-1, -1) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) - - 2 2 2 - - 2/3 DATA(0, -1) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, 1) - - 2 2 2 2 2 2 - - 1/96 x y DATA(-2, 2) + 1/96 x y DATA(2, -2) - 1/6 x y DATA(1, -2) - - 2 2 2 2 - - 1/6 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) - - 2 2 2 2 2 2 - + 1/3 x y DATA(-1, -1) + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) - - 2 2 2 - - 1/18 y x DATA(1, 2) - 1/18 y x DATA(-1, 2) - 1/18 y x DATA(2, 1) - - 2 2 2 2 - - 1/48 x y DATA(-2, -1) - 1/18 y x DATA(1, -2) - 1/18 y x DATA(-1, -2) - - 2 2 2 - + 1/288 y x DATA(-2, -2) + 1/288 y x DATA(2, 2) + 8/9 y x DATA(1, 1) - - 2 2 2 - + 1/288 y x DATA(-2, 2) - 1/18 y x DATA(-2, 1) - 1/18 y x DATA(-2, -1) - - 2 2 2 - + 1/288 y x DATA(2, -2) + 8/9 y x DATA(-1, -1) + 8/9 y x DATA(1, -1) - - 2 2 2 - + 8/9 y x DATA(-1, 1) - 1/18 y x DATA(2, -1) + 1/3 x y DATA(1, -1) - - 2 2 2 - + 1/3 x y DATA(-1, 1) + 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) - - 2 2 2 - - 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) + 1/6 x y DATA(1, 2) - - 2 2 2 - - 1/6 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) - 1/48 x y DATA(-2, -2) - - - 1/18 x y DATA(1, 2) + 1/18 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) - - - 1/9 x y DATA(2, -1) + 8/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) - - + 1/9 x y DATA(-2, 1) + 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) - - 2 2 2 - - 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) - - 2 2 - - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) - 8/9 x y DATA(-1, 1) - - 3 3 3 3 3 3 - + 1/72 x y DATA(2, 2) - 1/36 x y DATA(1, 2) + 1/36 x y DATA(-1, 2) - - 3 3 3 3 3 3 - - 1/18 x y DATA(2, 1) - 1/18 x y DATA(2, -1) + 1/9 x y DATA(1, -1) - - 3 3 - + 1/144 x y DATA(2, 2) + 1/72 x y DATA(2, -2) - 1/18 x y DATA(1, -2) - - + 1/18 x y DATA(-1, -2) - 1/144 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) - - 3 3 3 3 - + 8/9 x y DATA(1, -1) + 1/36 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) - - 3 3 3 3 3 - - 1/9 x y DATA(-1, -1) - 1/9 x y DATA(-1, 1) - 1/72 x y DATA(2, 2) - - 3 3 3 3 3 3 - + 1/9 x y DATA(1, 1) - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) - - 3 3 3 3 - + 1/18 x y DATA(-2, -1) + 1/18 x y DATA(2, -1) - 4/9 x y DATA(1, 1) - - 3 3 3 3 - + 1/72 x y DATA(-2, 2) - 1/18 x y DATA(-2, 1) - 1/36 x y DATA(1, -2) - - 3 3 3 - + 4/9 x y DATA(-1, 1) + 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) - - 3 3 2 3 - + 1/18 x y DATA(2, 1) - 1/12 x y DATA(1, -1) - 1/18 x y DATA(-2, -1) - - 3 3 3 - - 1/72 x y DATA(2, -2) + 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) - - 3 3 3 - + 1/72 x y DATA(-2, -2) + 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) - - 3 2 3 3 2 - + 1/48 x y DATA(2, 2) - 1/144 y x DATA(2, 2) - 1/12 x y DATA(-1, 1) - - 3 2 3 2 - - 1/24 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) - - 3 2 3 2 - + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) - - 3 2 3 2 - + 1/48 x y DATA(-2, -2) + 1/12 x y DATA(-1, -1) - - 3 2 3 2 3 - - 1/24 x y DATA(2, 1) + 1/24 x y DATA(2, -1) + 1/9 y x DATA(2, 1) - - 3 3 2 3 2 - + 1/9 y x DATA(2, -1) + 1/12 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) - - 3 2 3 2 3 2 - - 1/48 x y DATA(-2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) - - 3 3 3 - + 2/9 y x DATA(-1, 1) - 2/9 y x DATA(1, 1) + 1/144 y x DATA(-2, 2) - - 3 3 3 - - 1/9 y x DATA(-2, 1) - 1/9 y x DATA(-2, -1) - 1/144 y x DATA(2, -2) - - 3 3 3 - + 1/72 y x DATA(1, 2) - 1/72 y x DATA(-1, 2) - 2/9 y x DATA(1, -1) - - 3 3 3 - + 1/72 y x DATA(1, -2) - 1/72 y x DATA(-1, -2) + 1/144 y x DATA(-2, -2) - - 3 2 3 - + 2/9 y x DATA(-1, -1) + 1/36 x y DATA(-2, 1) - - 2 3 2 3 - - 1/144 x y DATA(-2, -2) - 1/144 x y DATA(2, -2) - - 2 3 2 3 2 3 - + 1/9 x y DATA(1, -2) + 1/36 x y DATA(2, -1) + 1/36 x y DATA(-2, -1) - - 2 3 2 3 2 3 - - 4/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) - 1/144 x y DATA(2, 2) - - 2 3 2 3 2 3 - + 1/9 x y DATA(1, 2) + 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 1) - - 2 2 2 2 2 2 - + 1/48 x y DATA(-2, 1) + 1/6 x y DATA(1, 2) + 1/6 x y DATA(-1, 2) - - 2 2 2 2 2 2 - + 1/48 x y DATA(2, 1) - 1/48 x y DATA(2, -1) - 1/96 x y DATA(2, 2) - - 2 3 2 3 2 3 - + 1/9 x y DATA(-1, -2) - 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) - - 2 3 - - 4/9 x y DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=225340376, alloc=2752008, time=21.13 -bytes used=226340564, alloc=2752008, time=21.19 - 2 3 3 4 3 3 -[COEFF(-2, -2) = - 1/288 x - 1/72 x y + 1/144 x + 1/144 x y - 1/144 x - - 2 3 3 2 2 3 2 4 2 - - 1/144 x y + 1/72 x y + 1/96 x y + 1/48 x y - 1/96 x y - - 2 4 3 4 2 - + 1/288 y x - 1/288 x y + 1/144 y x + 1/288 x - 1/144 x y - 1/48 x y , - - 2 4 3 3 2 2 - COEFF(-1, -2) = 1/18 x - 1/36 x y - 1/72 y x - 1/18 y x + 1/6 x y - - 2 3 3 3 2 4 2 - + 1/9 x y + 1/72 x - 1/24 x y + 1/24 x y - 1/18 x + 1/18 x y - - 4 3 3 3 4 2 2 - - 1/72 x - 1/9 x y + 1/36 x y + 1/72 x y - 1/6 x y , COEFF(0, -2) = - - 4 2 2 4 2 3 - - 1/48 x y - 5/48 x + 5/48 y x + 1/48 x + 1/12 - 1/12 y - 5/24 x y - - 3 2 2 2 4 3 4 2 - + 1/6 y + 5/16 x y - 1/4 y + 1/24 x y - 1/16 x y , COEFF(1, -2) = - - 3 2 2 2 3 2 4 3 - - 1/18 x y + 1/24 x y - 1/6 x y - 1/72 x - 1/6 x y - 1/36 x y - - 4 3 3 2 4 2 3 3 - - 1/72 x + 1/9 x y + 1/72 y x + 1/18 x + 1/24 x y - 1/36 x y - - 2 3 2 4 3 - + 1/9 x y - 1/18 y x + 1/18 x + 1/72 x y, COEFF(2, -2) = - 1/144 y x - - 2 4 3 2 2 2 - + 1/288 y x + 1/144 x y + 1/96 x y + 1/144 x y - 1/144 x - 1/288 x - - 4 3 3 2 3 3 2 3 - - 1/288 x y + 1/144 x - 1/48 x y + 1/72 x y + 1/48 x y - 1/72 x y - - 4 2 3 4 2 2 - + 1/288 x - 1/144 x y - 1/96 x y , COEFF(-2, -1) = 1/24 x y - - 3 2 2 2 2 4 2 3 - - 1/24 x y + 1/9 x y - 1/48 x y - 1/18 y x + 1/48 x y - 1/18 x y - - 4 2 3 4 3 3 3 2 - + 1/18 x y + 1/36 x y - 1/36 x + 1/18 x y + 1/18 x + 1/36 x - - 3 4 3 3 2 - - 1/18 x - 1/9 y x - 1/36 x y , COEFF(-1, -1) = 1/12 x y - 8/9 x y - - 3 3 3 2 4 4 3 2 2 - + 4/9 x y - 1/9 x y - 4/9 x - 2/9 x y + 1/9 x y + 1/3 x y - - 4 2 3 2 3 2 4 2 - + 1/9 x - 4/9 x y + 8/9 y x + 2/9 y x + 4/9 x - 1/3 x y - 1/12 x y - - 3 4 2 2 2 2 - - 1/9 x , COEFF(0, -1) = 1/3 x y - 5/3 y x + 5/6 x - 2/3 - 5/8 x y - - 3 4 4 3 2 3 2 4 2 - + 4/3 y - 2/3 y - 1/6 x - 1/6 x y + 5/6 x y + 1/2 y + 1/8 x y , - - 3 2 2 3 4 3 - COEFF(1, -1) = 1/9 x + 8/9 x y + 1/3 x y - 4/9 x y + 1/9 x y - - 4 3 2 4 2 2 3 3 - - 2/9 x y - 1/12 x y - 1/12 x y + 8/9 y x - 4/9 x + 1/9 x y - - 2 2 3 4 2 3 - + 1/3 x y - 4/9 x - 2/9 y x + 1/9 x - 4/9 x y , COEFF(2, -1) = - - 4 3 2 3 3 2 2 4 2 - - 1/36 x + 1/9 y x + 1/36 x - 1/18 x y - 1/48 x y + 1/48 x y - - 2 4 3 2 3 2 3 - - 1/18 y x + 1/18 x - 1/36 x y - 1/24 x y + 1/24 x y + 1/18 x y - - 2 3 4 3 3 3 - + 1/36 x y + 1/18 x y - 1/18 x - 1/9 x y, COEFF(-2, 0) = - 1/12 x y - - 4 2 2 3 3 3 - - 5/48 x y + 5/48 y x - 1/24 x y + 5/24 y x + 1/12 x y - 5/24 x y - - 4 3 2 3 4 3 3 3 - + 1/24 x y , COEFF(-1, 0) = 2/3 x y - 1/6 x y + 1/6 x y + 5/3 x y - - 3 2 4 3 - - 5/12 y x - 5/3 y x + 5/12 x y - 2/3 x y , - - 2 3 4 2 3 4 3 - COEFF(0, 0) = 25/8 y x + y - 5/8 x y - 5/4 x y + 1/4 x y - 5/2 y, - - 2 3 4 4 3 3 3 - COEFF(1, 0) = 2/3 x y + 5/12 x y - 5/3 x y - 1/6 x y - 1/6 x y - - 2 3 3 3 3 - - 5/3 y x + 5/12 y x + 2/3 x y , COEFF(2, 0) = 5/24 x y + 1/12 x y - - 4 3 2 2 3 3 3 4 - + 1/24 x y + 5/48 y x - 1/24 x y - 1/12 x y - 5/24 y x - 5/48 x y, - - 3 3 2 4 3 4 2 - COEFF(-2, 1) = - 1/18 x + 1/24 x y + 1/18 x y - 1/9 y x - 1/48 x y - - 3 3 2 4 3 2 2 - + 1/9 x y + 1/18 x y - 1/24 x y + 1/36 x - 1/18 x y + 1/48 x y - - 2 3 4 3 2 2 - + 1/36 x y + 1/18 x - 1/36 x y - 1/36 x - 1/18 y x , COEFF(-1, 1) = - - 3 3 4 3 2 2 2 3 4 3 - - 1/9 x y - 1/9 x + 4/9 x y + 1/3 x y - 1/3 x y + 1/9 x + 1/9 x y - - 2 3 2 2 2 3 4 - + 8/9 y x - 1/12 x y + 4/9 x - 4/9 x y - 4/9 x - 2/9 x y - 8/9 x y - - 4 2 3 4 4 2 2 - + 1/12 x y + 2/9 y x , COEFF(0, 1) = 1/6 x - 1/8 x y - 1/2 y + 2/3 - - 2 3 4 3 2 2 2 2 4 - + 5/6 x y + 4/3 y - 1/6 x y - 5/6 x + 5/8 x y - 5/3 y x + 1/3 x y - - 3 2 3 4 2 4 - - 2/3 y , COEFF(1, 1) = - 1/3 x y - 4/9 x y + 1/12 x y - 1/9 x - - 3 2 3 3 2 2 2 3 4 - + 1/12 x y + 1/9 x y + 4/9 x - 1/3 x y - 2/9 y x - 2/9 x y - - 2 3 4 3 3 2 - + 4/9 x + 8/9 x y - 4/9 x y + 1/9 x y - 1/9 x + 8/9 y x , COEFF(2, 1) - - 3 2 2 2 2 2 2 3 - = 1/18 x y - 1/18 y x - 1/36 x + 1/48 x y + 1/24 x y + 1/36 x y - - 3 2 3 3 4 2 3 - - 1/24 x y - 1/18 x y - 1/9 x y - 1/48 x y - 1/18 x + 1/9 y x - - 3 4 3 4 4 - + 1/18 x - 1/36 x y + 1/36 x + 1/18 x y, COEFF(-2, 2) = - 1/144 x - - 2 2 4 2 4 2 2 3 - + 1/288 y x + 1/288 x + 1/96 x y - 1/288 x - 1/96 x y + 1/72 x y - - 2 3 3 4 3 2 2 - - 1/144 x y - 1/144 x y + 1/144 x - 1/288 x y - 1/48 x y + 1/48 x y - - 3 3 3 4 3 4 - - 1/72 x y + 1/144 y x + 1/144 x y , COEFF(-1, 2) = 1/72 x - - 3 3 3 4 2 3 2 - + 1/36 x y - 1/72 x - 1/24 x y + 1/18 x y - 1/72 y x - 1/18 x - - 3 2 2 3 2 2 2 2 3 - + 1/24 x y + 1/9 x y + 1/6 x y - 1/6 x y - 1/18 y x - 1/9 x y - - 4 3 4 2 - - 1/36 x y + 1/18 x + 1/72 x y, COEFF(0, 2) = - 1/12 - 1/12 y + 5/48 x - - 4 2 4 2 4 2 2 2 3 - + 1/16 x y - 1/48 x + 5/48 y x - 1/48 x y - 5/16 x y - 5/24 x y - - 3 4 3 2 - + 1/6 y + 1/24 x y + 1/4 y , COEFF(1, 2) = - 1/18 x - 1/18 x y - - 3 3 3 4 2 2 4 - - 1/36 x y + 1/72 x + 1/72 x y + 1/6 x y - 1/18 y x + 1/72 x - - 2 3 2 3 4 2 2 3 2 2 - - 1/18 x - 1/24 x y + 1/9 x y - 1/24 x y + 1/9 x y + 1/6 x y - - 3 4 3 3 4 2 - + 1/72 y x - 1/36 x y , COEFF(2, 2) = 1/144 x y - 1/144 x + 1/96 x y - - 4 4 2 2 2 3 - - 1/288 x + 1/144 x - 1/288 x y + 1/288 x - 1/96 x y - 1/72 x y - - 2 3 3 3 2 3 2 - - 1/48 x y + 1/72 x y - 1/144 y x - 1/144 x y + 1/288 y x - - 4 3 3 2 - + 1/144 x y + 1/48 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); -bytes used=227340944, alloc=2817532, time=21.27 -bytes used=228341108, alloc=2817532, time=21.34 -bytes used=229341284, alloc=2817532, time=21.43 -bytes used=230364276, alloc=2817532, time=21.51 -bytes used=231366896, alloc=2817532, time=21.59 -bytes used=232387828, alloc=2817532, time=21.65 -bytes used=233410164, alloc=2817532, time=21.73 -bytes used=234411164, alloc=2817532, time=21.82 -bytes used=235411816, alloc=2817532, time=21.89 -bytes used=236412028, alloc=2817532, time=22.25 -bytes used=237412372, alloc=2817532, time=22.32 -bytes used=238412628, alloc=2817532, time=22.39 -bytes used=239412864, alloc=2817532, time=22.45 -bytes used=240413072, alloc=2817532, time=22.53 -bytes used=241413260, alloc=2817532, time=22.64 -bytes used=242415104, alloc=2817532, time=22.74 -bytes used=243422528, alloc=2817532, time=22.84 -bytes used=244422796, alloc=2817532, time=22.92 -bytes used=245434308, alloc=2817532, time=23.25 -bytes used=246434640, alloc=2817532, time=23.47 -bytes used=247434804, alloc=2817532, time=23.55 -bytes used=248445404, alloc=2817532, time=23.66 -bytes used=249445736, alloc=2817532, time=23.79 -bytes used=250454324, alloc=2817532, time=24.11 -bytes used=251454648, alloc=2817532, time=24.31 -bytes used=252454820, alloc=2817532, time=24.38 -bytes used=253455412, alloc=2817532, time=24.47 -bytes used=254455864, alloc=2817532, time=24.59 -bytes used=255456212, alloc=2817532, time=24.96 -bytes used=256456488, alloc=2817532, time=25.03 -bytes used=257456656, alloc=2817532, time=25.12 -bytes used=258456848, alloc=2817532, time=25.35 -bytes used=259457064, alloc=2817532, time=25.61 -bytes used=260457280, alloc=2817532, time=25.69 -bytes used=261457952, alloc=2817532, time=25.80 -bytes used=262458396, alloc=2817532, time=26.10 -bytes used=263458644, alloc=2817532, time=26.17 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); -bytes used=264458908, alloc=2817532, time=26.30 -bytes used=265459400, alloc=2817532, time=26.38 -bytes used=266459604, alloc=2817532, time=26.45 - 3 3 -- 1/12 DATA(2, 0) - 5/24 y DATA(0, 2) + 5/12 y DATA(0, 1) - - 3 3 2 2 - + 5/24 y DATA(0, -2) - 5/12 y DATA(0, -1) - 1/8 x y DATA(0, 2) - - 2 2 2 2 2 2 - - 1/8 x y DATA(0, -2) + 2 x y DATA(0, 1) + 2 x y DATA(0, -1) - - 2 3 2 3 2 3 - + 1/2 x y DATA(0, -1) + 1/4 x y DATA(0, 2) - 1/2 x y DATA(0, 1) - - 2 3 - - 1/4 x y DATA(0, -2) + 5/24 y DATA(0, 2) - 5/3 y DATA(0, 1) - - 2 - - 5/24 y DATA(0, -2) + 5/3 y DATA(0, -1) + 5/48 y DATA(0, -2) - - 2 2 2 - - 5/3 y DATA(0, -1) - 5/3 y DATA(0, 1) + 5/48 y DATA(0, 2) - - 2 2 2 - + 2 y x DATA(0, 1) + 1/4 y x DATA(0, -2) - 2 y x DATA(0, -1) - - 2 - - 1/4 y x DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(1, 0) - 1/12 DATA(-2, 0) - - 2 2 2 - + 4/3 DATA(-1, 0) + 2/3 x y DATA(-1, -1) - 4/3 x y DATA(1, 1) - - 2 2 2 2 2 2 - - 1/48 x y DATA(-2, 2) - 1/48 x y DATA(2, -2) + 1/12 x y DATA(1, -2) - - 2 2 2 2 - + 1/12 x y DATA(-1, -2) - 1/48 x y DATA(-2, -2) - - 2 2 2 2 2 2 - - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) - 4/3 x y DATA(-1, 1) - - 2 2 2 - + 1/6 y x DATA(1, 2) + 1/6 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) - - 2 2 2 2 - + 1/3 x y DATA(-2, -1) - 1/6 y x DATA(1, -2) - 1/6 y x DATA(-1, -2) - - 2 2 2 - + 1/24 y x DATA(-2, -2) - 1/24 y x DATA(2, 2) - 4/3 y x DATA(1, 1) - - 2 2 2 - - 1/24 y x DATA(-2, 2) + 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) - - 2 2 2 - + 1/24 y x DATA(2, -2) + 4/3 y x DATA(-1, -1) + 4/3 y x DATA(1, -1) - - 2 2 2 - - 4/3 y x DATA(-1, 1) - 1/3 y x DATA(2, -1) - 2/3 x y DATA(1, -1) - - 2 2 2 - + 2/3 x y DATA(-1, 1) - 1/3 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) - - 2 2 2 - + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) + 1/24 x y DATA(1, 2) - - 2 2 2 - - 1/24 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) - - + 1/12 x y DATA(1, 2) - 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) - - - 1/3 x y DATA(2, -1) - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) - - - 1/3 x y DATA(-2, 1) + 1/3 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) - - 2 2 2 - - 2/3 x y DATA(1, 1) - 1/3 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) - - 2 2 - + 1/3 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 2/3 x y DATA(-1, 1) - - - 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) - - - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) + 2/3 x y DATA(1, -1) - - 3 3 3 - + 1/24 x y DATA(2, 2) + 1/12 x y DATA(2, -1) + 1/6 x y DATA(1, 1) - - 3 3 3 - - 1/24 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) - 1/6 x y DATA(-1, 1) - - 3 3 3 - - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) - - 3 3 3 - - 1/12 x y DATA(-2, -1) - 1/24 x y DATA(2, -2) + 1/12 x y DATA(1, -2) - - 3 3 3 - - 1/12 x y DATA(-1, -2) + 1/24 x y DATA(-2, -2) + 1/6 x y DATA(-1, -1) - - 3 2 3 2 3 - - 1/6 x y DATA(1, -1) - 1/12 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) - - 2 3 2 3 2 3 - - 1/24 x y DATA(2, -2) + 1/6 x y DATA(1, -2) + 1/12 x y DATA(2, -1) - - 2 3 2 3 2 3 - + 1/12 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) - - 2 3 2 3 2 3 - + 1/24 x y DATA(2, 2) - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) - - 2 3 2 2 2 2 - - 1/12 x y DATA(2, 1) + 1/3 x y DATA(-2, 1) + 1/12 x y DATA(1, 2) - - 2 2 2 2 2 2 - + 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/3 x y DATA(2, -1) - - 2 2 2 3 2 3 - - 1/48 x y DATA(2, 2) + 1/6 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) - - 2 3 2 3 4 - - 1/3 x y DATA(1, -1) + 1/3 x y DATA(-1, 1) - 1/8 x y DATA(-2, 0) - - 4 4 4 - + 1/48 x y DATA(2, -2) - 1/24 x y DATA(1, -2) + 1/24 x y DATA(-1, -2) - - 4 4 4 - - 1/48 x y DATA(-2, -2) - 1/6 x y DATA(-1, -1) + 1/6 x y DATA(1, -1) - - 3 3 2 - - 1/9 y DATA(-1, -2) + 1/9 y DATA(-1, 2) + 1/2 x DATA(2, 0) - - 2 2 2 - + 3 x DATA(0, 0) - 2 x DATA(1, 0) + 1/2 x DATA(-2, 0) - - 2 3 - - 2 x DATA(-1, 0) - 1/144 y DATA(2, 2) - 1/18 y DATA(-2, 1) - - 2 2 - + 1/18 y DATA(-2, -1) - 1/144 y DATA(2, -2) + 5/2 x y DATA(1, 0) - - 2 2 2 2 2 2 - + 5/2 x y DATA(-1, 0) - 5/8 x y DATA(2, 0) - 15/4 x y DATA(0, 0) - - 2 2 2 3 - - 5/8 x y DATA(-2, 0) - 5/8 x y DATA(2, 0) + 2/9 y DATA(1, -1) - - 3 - - 2/9 y DATA(-1, 1) + 1/2 x DATA(2, 0) - x DATA(1, 0) - 1/2 x DATA(-2, 0) - - 3 3 3 - + 2/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) + 1/72 y DATA(2, 1) - - 3 3 3 - - 1/72 y DATA(2, -1) - 2/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) - - 3 3 3 - + 1/72 y DATA(-2, 1) - 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) - - 3 2 4 4 - - 1/9 y DATA(1, -2) - 1/2 x y DATA(1, 0) + 1/18 y DATA(-1, 2) - - 4 4 4 - - 1/288 y DATA(-2, -2) + 5/12 y DATA(0, -1) - 2/9 y DATA(1, -1) - - 4 4 4 - + 1/3 y DATA(-1, 0) - 2/9 y DATA(-1, 1) - 2/9 y DATA(-1, -1) - - 4 4 4 - + 5/12 y DATA(0, 1) - 1/288 y DATA(-2, 2) + 1/72 y DATA(-2, 1) - - 4 4 4 - - 2/9 y DATA(1, 1) + 1/72 y DATA(-2, -1) - 1/288 y DATA(2, -2) - - 4 2 4 4 - + 1/18 y DATA(1, -2) - 1/12 x y DATA(1, 2) - 5/48 y DATA(0, -2) - - 4 4 4 - + 1/18 y DATA(-1, -2) - 1/48 y DATA(-2, 0) - 5/48 y DATA(0, 2) - - 4 4 4 - + 1/72 y DATA(2, 1) - 1/48 y DATA(2, 0) + 1/72 y DATA(2, -1) - - 4 4 4 - - 5/8 y DATA(0, 0) + 1/3 y DATA(1, 0) - 1/288 y DATA(2, 2) - - 4 2 4 2 4 - + 1/18 y DATA(1, 2) - 1/12 x y DATA(-1, 2) - 1/2 x y DATA(0, -1) - - 2 4 2 4 2 4 - + 1/3 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/48 x y DATA(-2, -2) - - 2 4 2 4 2 4 - + 1/48 x y DATA(2, 2) + 1/8 x y DATA(0, 2) - 1/12 x y DATA(2, 1) - - 2 4 2 4 2 4 - + 1/8 x y DATA(2, 0) - 1/12 x y DATA(2, -1) - 1/12 x y DATA(-2, -1) - - 2 4 2 4 2 4 - + 1/48 x y DATA(2, -2) - 1/12 x y DATA(1, -2) + 1/8 x y DATA(0, -2) - - 2 4 2 4 4 - - 1/12 x y DATA(-1, -2) + 1/8 x y DATA(-2, 0) - 1/12 x y DATA(2, -1) - - 4 4 4 - + 1/4 x y DATA(-1, 0) - 1/4 x y DATA(1, 0) + 1/6 x y DATA(1, 1) - - 4 4 2 4 - - 1/48 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) + 3/4 x y DATA(0, 0) - - 2 4 2 4 4 - + 1/3 x y DATA(-1, 1) + 1/3 x y DATA(-1, -1) - 1/6 x y DATA(-1, 1) - - 4 4 4 - + 1/12 x y DATA(-2, -1) - 1/24 x y DATA(1, 2) + 1/48 x y DATA(2, 2) - - 4 4 4 - + 1/24 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) + 1/8 x y DATA(2, 0) - - 2 2 2 - - 1/18 y DATA(1, 2) - 1/18 y DATA(-1, 2) + 1/288 y DATA(-2, -2) - - 2 2 2 - + 8/9 y DATA(1, -1) - 5/3 y DATA(-1, 0) + 8/9 y DATA(-1, 1) - - 2 2 2 - + 8/9 y DATA(-1, -1) + 1/288 y DATA(-2, 2) - 1/18 y DATA(-2, 1) - - 2 2 2 - + 8/9 y DATA(1, 1) - 1/18 y DATA(-2, -1) + 1/288 y DATA(2, -2) - - 2 2 - + 1/288 y DATA(2, 2) + 1/144 y DATA(2, 2) - 1/18 y DATA(2, 1) - - 2 2 2 - + 5/48 y DATA(2, 0) - 1/18 y DATA(2, -1) + 25/8 y DATA(0, 0) - - 2 - - 5/3 y DATA(1, 0) - 1/9 y DATA(1, 2) - 1/9 y DATA(-1, 2) - - - 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) + 8/9 y DATA(1, 1) - - 2 2 - + 1/144 y DATA(-2, 2) - 1/18 y DATA(1, -2) - 1/18 y DATA(-1, -2) - - 2 - + 5/48 y DATA(-2, 0) + 1/9 y DATA(1, -2) + 1/9 y DATA(-1, -2) - - - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) - 8/9 y DATA(1, -1) - - 2 4 2 4 - + 8/9 y DATA(-1, 1) - 1/2 x y DATA(0, 1) + 1/48 x y DATA(-2, 2) - - 2 4 2 4 2 - - 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 1) - 5/4 x y DATA(-1, 0) - - 2 2 3 - + 5/4 x y DATA(1, 0) + 5/8 x y DATA(-2, 0) + 1/144 y DATA(-2, -2) - - + x DATA(-1, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=267463800, alloc=2817532, time=26.51 - 2 4 2 2 4 2 2 -[COEFF(-2, -2) = 1/48 x y + 1/48 x y + 1/288 y - 1/288 y - 1/48 x y - - 2 3 4 3 2 3 - + 1/24 y x + 1/24 x y - 1/48 x y + 1/144 y - 1/144 y - 1/24 x y - - 4 2 2 2 - - 1/24 x y, COEFF(-1, -2) = 1/24 x y + 1/12 x y - 1/24 x y + 1/12 x y - - 3 2 4 3 2 4 2 - - 1/9 y + 1/9 y - 1/12 x y - 1/12 x y - 1/18 y + 1/18 y - 1/6 y x - - 2 3 2 2 3 - + 1/6 x y , COEFF(0, -2) = - 5/24 y + 5/48 y + 1/4 y x + 5/24 y - - 2 2 2 3 4 2 4 2 - - 1/8 x y - 1/4 x y - 5/48 y + 1/8 x y , COEFF(1, -2) = 1/24 x y - - 2 3 2 2 4 2 - - 1/12 x y - 1/6 y x - 1/9 y + 1/12 x y + 1/18 y - 1/18 y - - 3 2 3 4 2 4 - + 1/12 x y + 1/6 x y + 1/9 y - 1/24 x y - 1/12 x y , COEFF(2, -2) = - - 2 4 4 2 2 4 - - 1/48 x y - 1/288 y + 1/48 x y + 1/24 y x + 1/24 x y + 1/48 x y - - 3 2 2 2 2 3 3 - - 1/144 y + 1/144 y - 1/48 x y + 1/288 y - 1/24 x y - 1/24 x y , - - 2 2 3 2 2 3 - COEFF(-2, -1) = 1/3 x y + 1/3 x y - 1/72 y - 1/18 y + 1/12 x y - - 4 3 2 4 2 2 - + 1/18 y + 1/12 x y - 1/12 x y - 1/12 x y - 1/3 y x - 1/3 x y - - 4 4 2 2 4 - + 1/72 y , COEFF(-1, -1) = - 1/6 x y + 2/3 x y - 8/9 y + 1/3 x y - - 2 2 2 2 3 3 4 2 3 - + 8/9 y - 4/3 x y + 4/3 y x + 2/9 y + 1/6 x y - 2/9 y - 1/3 x y - - 2 3 2 2 4 2 - - 2/3 x y, COEFF(0, -1) = 1/2 x y + 2 x y + 5/12 y - 5/3 y - - 2 4 2 3 2 4 - - 1/2 x y - 2 y x - 5/12 y + 5/3 y, COEFF(1, -1) = 1/3 x y + 2/3 x y - - 4 3 2 2 2 4 2 3 - + 1/6 x y + 2/9 y - 4/3 x y - 8/9 y - 2/3 x y - 2/9 y - 1/3 x y - - 3 2 2 2 2 4 - - 1/6 x y + 8/9 y + 4/3 y x , COEFF(2, -1) = - 1/18 y - 1/12 x y - - 4 2 2 2 2 3 - - 1/12 x y + 1/3 x y + 1/3 x y + 1/18 y - 1/3 x y + 1/12 x y - - 3 3 4 2 2 - - 1/72 y + 1/12 x y + 1/72 y - 1/3 y x , COEFF(-2, 0) = 1/2 x - - 2 4 2 4 2 2 2 - + 1/8 x y + 5/8 x y - 1/48 y - 1/12 + 5/48 y - 5/8 x y - 1/2 x - - 4 2 2 2 4 4 - - 1/8 x y , COEFF(-1, 0) = 4/3 + 5/2 x y - 2 x + 1/4 x y + 1/3 y + x - - 2 4 2 2 - - 1/2 x y - 5/4 x y - 5/3 y , - - 2 4 2 4 2 2 2 - COEFF(0, 0) = 3 x - 5/8 y + 3/4 x y - 5/2 - 15/4 x y + 25/8 y , - - 4 2 2 2 2 2 4 - COEFF(1, 0) = - 1/4 x y + 5/2 x y + 5/4 x y - 5/3 y - 2 x + 1/3 y - - 2 4 2 2 2 4 - - 1/2 x y + 4/3 - x, COEFF(2, 0) = - 5/8 x y + 1/2 x + 1/8 x y - - 2 4 2 2 4 - + 1/8 x y - 5/8 x y + 1/2 x - 1/12 + 5/48 y - 1/48 y , COEFF(-2, 1) = - - 4 2 2 2 2 2 4 - - 1/18 y + 1/12 x y + 1/3 y x - 1/3 x y + 1/3 x y - 1/12 x y - - 3 3 2 4 2 3 - + 1/12 x y + 1/72 y - 1/18 y + 1/72 y - 1/3 x y - 1/12 x y , - - 3 2 4 2 4 - COEFF(-1, 1) = - 2/9 y - 4/3 y x - 1/6 x y + 2/3 x y + 1/3 x y - - 2 2 3 2 3 2 2 4 - + 2/3 x y + 1/3 x y + 8/9 y - 1/6 x y - 4/3 x y + 8/9 y - 2/9 y , - - 3 2 2 2 2 4 4 - COEFF(0, 1) = 5/12 y + 2 x y - 5/3 y - 1/2 x y - 5/3 y + 5/12 y - - 2 3 2 4 2 4 3 - - 1/2 x y + 2 y x , COEFF(1, 1) = - 2/9 y + 1/3 x y + 1/6 x y - - 3 4 2 2 2 2 3 2 - - 2/9 y + 8/9 y + 1/6 x y - 2/3 x y - 4/3 x y + 1/3 x y + 8/9 y - - 2 3 2 - - 4/3 y x - 2/3 x y, COEFF(2, 1) = 1/3 x y - 1/18 y + 1/72 y + 1/3 x y - - 2 3 2 4 2 2 2 2 4 - - 1/12 x y + 1/3 y x + 1/72 y + 1/3 x y - 1/18 y - 1/12 x y - - 4 3 2 2 3 - - 1/12 x y - 1/12 x y , COEFF(-2, 2) = 1/48 x y - 1/24 y x - 1/24 x y - - 2 2 2 2 3 2 4 3 - - 1/48 x y + 1/288 y + 1/144 y + 1/24 x y + 1/48 x y - 1/144 y - - 4 4 3 - + 1/24 x y - 1/288 y - 1/48 x y , COEFF(-1, 2) = - 1/12 x y + 1/9 y - - 4 2 4 2 2 2 4 2 - + 1/24 x y - 1/12 x y - 1/18 y + 1/12 x y + 1/18 y - 1/24 x y - - 2 2 3 3 2 - + 1/6 y x - 1/6 x y - 1/9 y + 1/12 x y , COEFF(0, 2) = 5/48 y - - 2 2 3 4 2 4 2 3 - - 1/8 x y - 5/24 y + 5/24 y - 5/48 y + 1/8 x y + 1/4 x y - - 2 4 2 - - 1/4 y x , COEFF(1, 2) = 1/12 x y + 1/18 y + 1/24 x y - 1/9 y - - 2 2 3 2 2 2 4 2 4 - + 1/6 y x - 1/6 x y + 1/12 x y - 1/18 y - 1/24 x y - 1/12 x y - - 3 3 4 4 2 2 - - 1/12 x y + 1/9 y , COEFF(2, 2) = - 1/288 y + 1/48 x y - 1/48 x y - - 2 2 3 2 4 - + 1/144 y + 1/288 y - 1/48 x y - 1/24 x y - 1/144 y + 1/48 x y - - 2 3 3 2 - + 1/24 x y + 1/24 x y - 1/24 y x ] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); -bytes used=268463952, alloc=2817532, time=26.58 -bytes used=269464108, alloc=2817532, time=26.64 -bytes used=270464264, alloc=2817532, time=26.72 -bytes used=271468824, alloc=2817532, time=26.79 -bytes used=272470884, alloc=2817532, time=26.86 -bytes used=273471272, alloc=2817532, time=26.94 -bytes used=274471420, alloc=2817532, time=27.14 -bytes used=275471752, alloc=2817532, time=27.42 -bytes used=276472040, alloc=2817532, time=27.49 -bytes used=277475512, alloc=2817532, time=27.55 -bytes used=278475700, alloc=2817532, time=27.65 -bytes used=279484180, alloc=2817532, time=27.75 -bytes used=280484464, alloc=2817532, time=27.86 -bytes used=281491584, alloc=2817532, time=28.19 -bytes used=282491764, alloc=2817532, time=28.39 -bytes used=283493688, alloc=2817532, time=28.47 -bytes used=284493880, alloc=2817532, time=28.62 -bytes used=285503016, alloc=2817532, time=28.93 -bytes used=286503156, alloc=2817532, time=29.13 -bytes used=287503572, alloc=2817532, time=29.21 -bytes used=288504456, alloc=2817532, time=29.36 -bytes used=289504572, alloc=2817532, time=29.68 -bytes used=290504728, alloc=2817532, time=29.75 -bytes used=291504932, alloc=2817532, time=30.12 -bytes used=292505132, alloc=2817532, time=30.26 -bytes used=293505260, alloc=2817532, time=30.36 -bytes used=294505412, alloc=2817532, time=30.69 -bytes used=295505644, alloc=2817532, time=30.79 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); -bytes used=296505980, alloc=2817532, time=30.89 -bytes used=297506132, alloc=2817532, time=30.96 -bytes used=298506352, alloc=2817532, time=31.03 -1/144 DATA(2, 2) - 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) - - + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) - - - 1/18 DATA(-2, -1) - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - - - 1/18 DATA(-1, -2) + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) - - 3 3 - - 4/9 DATA(1, -1) - 4/9 DATA(-1, 1) - 2/3 x y DATA(1, 0) - - 3 3 3 3 3 3 - + 1/6 x y DATA(-2, 0) - 2/3 x y DATA(-1, 0) + 4/9 x y DATA(-1, 1) - - 3 3 3 3 3 3 - + x y DATA(0, 0) - 1/9 x y DATA(2, 1) - 1/9 x y DATA(2, -1) - - + 8/9 x DATA(-1, 1) + 5/24 y DATA(2, 0) - 5/3 y DATA(1, 0) - - - 8/9 x DATA(-1, -1) + 5/3 x DATA(0, -1) - 8/9 x DATA(1, -1) - - 3 3 - + 5/3 y DATA(-1, 0) - 1/72 x DATA(2, 2) + 1/18 x DATA(1, 2) - - 3 3 3 - + 1/18 x DATA(-1, 2) - 1/12 x DATA(0, 2) + 1/72 x DATA(2, -2) - - 3 3 3 - - 1/18 x DATA(1, -2) + 1/12 x DATA(0, -2) - 1/18 x DATA(-1, -2) - - 3 3 3 - + 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) + 2/3 x DATA(0, 1) - - 3 3 - - 4/9 x DATA(1, 1) - 1/72 x DATA(-2, 2) - 5/24 y DATA(-2, 0) - - 3 3 3 3 3 3 - - 2/3 x y DATA(0, 1) + 1/36 x y DATA(-2, 2) - 1/9 x y DATA(-2, 1) - - 3 3 3 3 3 3 - + 4/9 x y DATA(1, 1) + 1/36 x y DATA(2, -2) - 1/9 x y DATA(1, -2) - - 3 3 3 3 3 3 - + 1/6 x y DATA(0, -2) - 1/9 x y DATA(-1, -2) + 1/36 x y DATA(-2, -2) - - 2 2 2 2 2 - + 2/3 x y DATA(-1, -1) + 1/4 x y DATA(1, 1) - 1/16 x y DATA(-2, 2) - - 3 3 3 3 3 3 - - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 2) - - 3 3 3 - + 4/3 x y DATA(1, 0) - 1/12 x y DATA(-2, 0) + 4/3 x y DATA(-1, 0) - - 3 3 3 3 3 - - 5/2 x y DATA(0, 0) + 1/6 x y DATA(2, 0) - 1/9 x y DATA(-2, -1) - - 3 3 3 - + 1/72 x DATA(-2, -2) + 5/3 x y DATA(0, -1) - 5/12 x y DATA(0, 2) - - 3 3 3 3 - + 5/3 x y DATA(0, 1) - 1/12 x y DATA(2, 0) + 4/9 x y DATA(-1, -1) - - 3 3 3 3 - - 2/3 x y DATA(0, -1) - 5/12 x y DATA(0, -2) + 4/9 x DATA(-1, -1) - - 2 2 2 - + 5/4 y x DATA(1, 0) + 5/8 y x DATA(-2, 0) - 5/8 y x DATA(2, 0) - - 2 3 3 - - 5/4 y x DATA(-1, 0) - 5/2 y x DATA(0, 0) - 5/12 y x DATA(2, 0) - - 3 3 3 - + 2/9 y x DATA(-2, 1) + 2/9 y x DATA(-2, -1) - 1/72 y x DATA(2, -2) - - 3 3 3 - - 8/9 y x DATA(1, -1) + 5/3 y x DATA(1, 0) - 5/12 y x DATA(-2, 0) - - 3 3 3 - + 5/3 y x DATA(-1, 0) - 8/9 y x DATA(-1, 1) + 2/9 y x DATA(2, -1) - - 3 3 3 - - 1/12 y x DATA(0, 2) + 4/3 y x DATA(0, 1) - 8/9 y x DATA(1, 1) - - 3 3 3 - - 1/72 y x DATA(-2, 2) - 1/72 y x DATA(-2, -2) - 8/9 y x DATA(-1, -1) - - 3 3 3 - + 4/3 y x DATA(0, -1) + 1/18 y x DATA(1, 2) + 1/18 y x DATA(-1, 2) - - 3 3 2 - - 1/72 y x DATA(2, 2) + 2/9 y x DATA(2, 1) - 1/6 x DATA(2, -1) - - 2 2 2 - - 1/3 x DATA(1, 1) + 1/48 x DATA(-2, 2) - 1/6 x DATA(-2, 1) - - 2 2 2 - + 1/6 x DATA(-2, -1) + 1/48 x DATA(2, -2) - 1/24 x DATA(1, -2) - - 2 2 2 - + 1/24 x DATA(-1, -2) - 1/48 x DATA(-2, -2) - 1/3 x DATA(-1, -1) - - 2 2 2 - + 1/3 x DATA(1, -1) + 1/24 x DATA(1, 2) - 1/24 x DATA(-1, 2) - - 2 2 3 - + 1/6 x DATA(2, 1) - 1/48 x DATA(2, 2) - 2/3 x DATA(0, -1) - - 3 3 3 - + 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/9 x DATA(-2, 1) - - 3 - - 1/9 x DATA(-2, -1) + 5/24 x DATA(0, 2) - 1/18 x DATA(2, 1) - - + 1/18 x DATA(2, -1) - 5/3 x DATA(0, 1) + 8/9 x DATA(1, 1) - - + 1/144 x DATA(-2, 2) - 1/18 x DATA(-2, 1) + 1/18 x DATA(-2, -1) - - - 1/144 x DATA(2, -2) + 1/9 x DATA(1, -2) - 5/24 x DATA(0, -2) - - 2 3 3 - + 5/4 x y DATA(0, 1) + 1/18 y x DATA(1, -2) - 1/12 y x DATA(0, -2) - - 3 2 - + 1/18 y x DATA(-1, -2) - 5/8 x y DATA(0, 2) + 1/9 x DATA(-1, -2) - - 3 2 3 2 3 2 - - 1/2 x y DATA(0, 1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) - - 3 2 3 2 - - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) - - 3 2 2 2 - - 1/24 x y DATA(2, -2) + 5/8 x y DATA(0, -2) - 5/4 x y DATA(0, -1) - - 3 2 3 2 - - 1/144 x DATA(-2, -2) - 1/4 x y DATA(0, -2) + 1/24 x y DATA(2, 2) - - 3 2 3 2 3 2 - - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) + 1/4 x y DATA(0, 2) - - 3 2 3 2 3 2 - - 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) - 1/3 x y DATA(1, -1) - - 2 - + 1/3 x DATA(-1, 1) + 5/24 x y DATA(-2, 0) - 10/3 x y DATA(-1, 0) - - 3 2 3 2 3 2 - + 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) - - 3 2 3 2 3 2 - - 1/3 x y DATA(-1, -1) + 1/2 x y DATA(0, -1) + 1/3 x y DATA(-1, 1) - - + 5/24 x y DATA(2, 0) - 10/3 x y DATA(1, 0) + 1/144 x DATA(2, 2) - - + 25/4 x y DATA(0, 0) + 5/24 x y DATA(0, 2) - 10/3 x y DATA(0, 1) - - 2 3 - + 5/24 x y DATA(0, -2) + 1/4 x y DATA(2, 0) - 10/3 x y DATA(0, -1) - - 2 3 2 3 3 - + 1/2 x y DATA(-1, 0) - 1/2 x y DATA(1, 0) - 2/3 y DATA(-1, 0) - - 3 3 - - 1/9 x DATA(1, 2) - 1/9 x DATA(-1, 2) + 1/6 x y DATA(0, 2) - - 2 3 3 3 - - 1/4 x y DATA(-2, 0) - 1/12 y DATA(2, 0) + 2/3 y DATA(1, 0) - - 3 3 3 2 2 - + 1/12 y DATA(-2, 0) + 4/9 x y DATA(1, -1) - 1/16 x y DATA(2, -2) - - 2 2 2 2 2 2 - + 1/8 x y DATA(1, -2) - 1/8 x y DATA(-1, -2) + 1/16 x y DATA(-2, -2) - - 2 2 2 2 2 2 - + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(1, -1) - 1/4 x y DATA(-1, 1) - - 2 2 2 - + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) - - 2 2 2 2 - - 1/8 x y DATA(-2, -1) + 1/24 y x DATA(1, -2) - 1/24 y x DATA(-1, -2) - - 2 2 2 - + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) - 2/3 y x DATA(1, 1) - - 2 2 2 - + 1/48 y x DATA(-2, 2) - 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) - - 2 2 2 - - 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) - 2/3 y x DATA(1, -1) - - 2 2 2 - + 2/3 y x DATA(-1, 1) + 1/3 y x DATA(2, -1) + 2/3 x y DATA(1, -1) - - 2 2 2 - - 2/3 x y DATA(-1, 1) - 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) - - 2 2 2 - - 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) + 1/3 x y DATA(1, 2) - - 2 2 2 - + 1/3 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) - - - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) - - - 1/9 x y DATA(2, -1) + 16/9 x y DATA(1, 1) + 1/144 x y DATA(-2, 2) - - - 1/9 x y DATA(-2, 1) - 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) - - 2 2 2 - - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) - 1/48 x y DATA(-2, 2) - - 2 2 - - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 16/9 x y DATA(-1, 1) - - + 1/144 x y DATA(2, 2) - 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) - - + 1/144 x y DATA(-2, -2) + 16/9 x y DATA(-1, -1) + 16/9 x y DATA(1, -1) - - 3 3 3 - - 1/72 x y DATA(2, 2) + 1/18 x y DATA(2, -1) - 8/9 x y DATA(1, 1) - - 3 3 3 - - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) - 8/9 x y DATA(-1, 1) - - 3 3 3 - + 2/9 x y DATA(1, 2) + 2/9 x y DATA(-1, 2) + 1/18 x y DATA(2, 1) - - 3 3 3 - + 1/18 x y DATA(-2, -1) - 1/72 x y DATA(2, -2) + 2/9 x y DATA(1, -2) - - 3 3 3 - + 2/9 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) - - 3 2 3 2 3 - - 8/9 x y DATA(1, -1) + 1/6 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) - - 2 3 2 3 2 3 - + 1/24 x y DATA(2, -2) - 1/12 x y DATA(1, -2) - 1/6 x y DATA(2, -1) - - 2 3 2 3 2 3 - + 1/6 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) - - 2 3 2 3 2 3 - + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) - - 2 3 2 2 2 2 - - 1/6 x y DATA(2, 1) + 1/8 x y DATA(-2, 1) - 1/8 x y DATA(1, 2) - - 2 2 2 2 2 2 - + 1/8 x y DATA(-1, 2) - 1/8 x y DATA(2, 1) + 1/8 x y DATA(2, -1) - - 2 2 2 3 2 3 - + 1/16 x y DATA(2, 2) + 1/12 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) - - 2 3 2 3 3 - + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) - 1/9 y DATA(-1, -2) - - 3 3 - - 1/9 y DATA(-1, 2) - 1/72 y DATA(2, 2) + 1/9 y DATA(-2, 1) - - 3 - + 1/9 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 4/9 y DATA(1, -1) - - 3 3 3 - + 4/9 y DATA(-1, 1) + 4/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) - - 3 3 3 - + 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) - 4/9 y DATA(1, 1) - - 3 3 3 - + 1/72 y DATA(-2, 2) - 1/18 y DATA(-2, 1) - 1/18 y DATA(-2, -1) - - 3 3 2 - - 1/72 y DATA(2, -2) + 1/9 y DATA(1, -2) + 1/6 y DATA(1, 2) - - 2 2 2 - - 1/6 y DATA(-1, 2) - 1/48 y DATA(-2, -2) + 1/3 y DATA(1, -1) - - 2 2 2 - + 1/3 y DATA(-1, 1) - 1/3 y DATA(-1, -1) + 1/48 y DATA(-2, 2) - - 2 2 2 - - 1/24 y DATA(-2, 1) - 1/3 y DATA(1, 1) + 1/24 y DATA(-2, -1) - - 2 2 - + 1/48 y DATA(2, -2) - 1/48 y DATA(2, 2) + 1/144 y DATA(2, 2) - - 2 2 - + 1/24 y DATA(2, 1) - 1/24 y DATA(2, -1) - 1/18 y DATA(1, 2) - - + 1/18 y DATA(-1, 2) - 1/9 y DATA(2, 1) - 1/9 y DATA(2, -1) - - 2 - + 8/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) - 1/6 y DATA(1, -2) - - 2 - + 1/6 y DATA(-1, -2) - 1/18 y DATA(1, -2) + 1/18 y DATA(-1, -2) - - - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) + 8/9 y DATA(1, -1) - - 3 - - 8/9 y DATA(-1, 1) + 1/72 y DATA(-2, -2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=299534960, alloc=2817532, time=31.10 -bytes used=300538760, alloc=2817532, time=31.17 - 3 3 2 2 2 3 -[COEFF(-2, -2) = 1/36 x y - 1/144 y + 1/16 x y + 1/144 x y - 1/24 x y - - 2 2 3 2 3 3 - + 1/48 x y + 1/48 y x - 1/24 x y + 1/72 y + 1/72 x - 1/144 x - - 2 3 3 2 - - 1/48 y - 1/72 x y + 1/144 - 1/72 y x - 1/48 x , COEFF(-1, -2) = - - 2 3 2 2 3 3 - 1/24 x + 1/9 x + 1/6 x y + 1/18 y + 1/12 x y - 1/18 + 2/9 x y - - 2 2 2 2 3 3 3 - - 1/24 y x - 1/9 x y - 1/8 x y - 1/3 x y - 1/9 y - 1/9 x y - - 3 2 3 2 3 - - 1/18 x + 1/6 y + 1/18 y x , COEFF(0, -2) = 5/8 x y - 1/12 y x - - 3 3 3 3 2 3 - - 5/12 x y + 5/24 x y + 1/6 x y - 5/24 x - 1/4 x y + 1/12 x , - - 2 3 2 2 - COEFF(1, -2) = - 1/3 x y + 1/6 x y - 1/6 y - 1/18 y + 1/9 x - - 2 3 2 3 3 3 2 2 - - 1/12 x y + 1/24 y x + 1/18 + 1/18 y x + 1/9 y - 1/18 x + 1/8 x y - - 3 3 2 3 2 2 - - 1/9 x y - 1/24 x - 1/9 x y + 2/9 x y , COEFF(2, -2) = - 1/16 x y - - 3 2 3 2 2 - - 1/72 x y + 1/48 x y + 1/144 x y - 1/24 x y - 1/48 y x - 1/144 x - - 3 2 3 2 3 3 3 - - 1/72 y x + 1/24 x y + 1/48 y - 1/144 - 1/72 y + 1/36 x y - - 3 2 3 3 3 - + 1/72 x + 1/144 y + 1/48 x , COEFF(-2, -1) = - 1/18 - 1/9 x y - 1/9 x - - 3 2 3 2 3 2 3 - - 1/18 y + 1/6 x y + 1/6 x + 1/12 x y - 1/9 x y + 2/9 y x + 1/9 y - - 2 2 3 2 2 2 - - 1/8 x y + 1/18 x y + 1/24 y - 1/24 x y + 1/18 x - 1/3 y x , - - 3 3 3 2 3 - COEFF(-1, -1) = 4/9 x y - 8/9 y x + 16/9 x y + 4/9 - 1/3 x - 8/9 x y - - 3 2 2 3 2 2 - - 1/3 x y - 8/9 x + 2/3 x y + 4/9 x - 8/9 y + 2/3 y x - 1/3 y - - 2 3 3 2 2 3 3 3 - - 1/3 x y + 4/9 y + 1/4 x y , COEFF(0, -1) = - 2/3 x y + 4/3 y x - - 3 3 2 2 3 - + 5/3 x y + 1/2 x y + 5/3 x - 5/4 x y - 10/3 x y - 2/3 x , - - 3 3 3 3 3 3 - COEFF(1, -1) = - 4/9 y - 8/9 x y + 4/9 x - 8/9 x + 4/9 x y - 8/9 y x - - 2 3 2 2 3 2 2 2 - + 1/3 x y + 16/9 x y - 1/4 x y - 1/3 x y + 1/3 y + 1/3 x + 8/9 y - - 2 2 2 3 2 - - 2/3 y x - 4/9 + 2/3 x y , COEFF(2, -1) = 1/3 y x + 1/12 x y - - 3 3 2 2 3 3 - + 2/9 y x + 1/18 y - 1/6 x - 1/9 x y + 1/18 x - 1/24 y - 1/9 x y - - 2 2 2 3 2 3 3 - + 1/18 + 1/8 x y - 1/9 y - 1/6 x y - 1/24 x y + 1/18 x y - 1/9 x , - - 3 3 3 3 2 3 - COEFF(-2, 0) = 1/6 x y - 5/24 y - 5/12 y x - 1/12 x y - 1/4 x y - - 2 3 2 2 3 - + 5/24 x y + 5/8 y x + 1/12 y , COEFF(-1, 0) = - 5/4 y x + 1/2 x y - - 3 3 3 3 3 - + 4/3 x y + 5/3 y x - 10/3 x y - 2/3 y - 2/3 x y + 5/3 y, - - 3 3 3 3 - COEFF(0, 0) = 25/4 x y - 5/2 y x - 5/2 x y + x y , COEFF(1, 0) = - - 2 3 2 3 3 3 3 - - 1/2 x y + 5/4 y x - 5/3 y - 2/3 x y + 5/3 y x + 2/3 y - 10/3 x y - - 3 3 3 2 3 - + 4/3 x y , COEFF(2, 0) = 5/24 y + 1/6 x y + 5/24 x y + 1/4 x y - - 2 3 3 3 2 - - 5/8 y x - 5/12 y x - 1/12 y - 1/12 x y , COEFF(-2, 1) = 1/24 x y - - 2 3 2 2 3 2 3 3 - - 1/3 y x + 2/9 y x + 1/8 x y - 1/12 x y + 1/18 x y - 1/18 y - - 2 2 3 2 3 3 - - 1/9 x y - 1/6 x + 1/18 + 1/6 x y - 1/24 y - 1/9 x y + 1/9 y - - 3 2 2 - + 1/9 x - 1/18 x, COEFF(-1, 1) = 2/3 y x - 4/9 - 8/9 y - 2/3 x y - - 3 2 3 3 3 3 3 2 - - 8/9 x y + 1/3 x + 4/9 y + 16/9 x y - 4/9 x + 4/9 x y + 1/3 x y - - 3 2 2 3 2 2 - - 8/9 y x + 8/9 x + 1/3 y - 1/3 x y - 1/4 x y , COEFF(0, 1) = - - 3 3 2 3 3 3 3 - 4/3 y x - 1/2 x y + 5/3 x y - 2/3 x y - 10/3 x y - 5/3 x + 2/3 x - - 2 3 2 3 2 2 3 - + 5/4 x y , COEFF(1, 1) = - 4/9 x + 1/3 x y + 1/4 x y - 4/9 y - - 2 2 3 2 3 - - 1/3 y + 8/9 y - 1/3 x - 8/9 x y - 2/3 x y - 8/9 y x + 8/9 x - - 2 3 2 3 3 - - 2/3 y x + 1/3 x y + 4/9 x y + 16/9 x y + 4/9, COEFF(2, 1) = - 1/18 - - 3 2 3 2 3 2 2 - + 1/9 x - 1/18 x + 1/24 y - 1/12 x y + 2/9 y x + 1/6 x + 1/24 x y - - 2 3 3 2 2 3 3 3 - - 1/6 x y + 1/18 x y - 1/9 y - 1/8 x y - 1/9 x y + 1/18 y - - 2 2 2 2 - - 1/9 x y + 1/3 y x , COEFF(-2, 2) = - 1/48 x y + 1/48 x + 1/48 y x - - 2 2 2 2 3 - - 1/144 + 1/144 x y + 1/48 y - 1/16 x y - 1/24 x y + 1/144 x - - 3 3 3 3 3 3 2 - - 1/72 x y - 1/144 y - 1/72 x - 1/72 y x + 1/36 x y + 1/24 x y - - 3 2 3 3 2 - + 1/72 y , COEFF(-1, 2) = 1/3 x y - 1/9 y + 1/18 x - 1/24 y x + 1/18 - - 2 2 3 2 2 3 2 3 3 - - 1/24 x + 1/12 x y + 1/8 x y + 2/9 x y - 1/6 y - 1/9 x y - - 3 2 3 - - 1/6 x y - 1/9 x y + 1/18 y - 1/9 x + 1/18 y x , COEFF(0, 2) = 5/24 x - - 2 3 2 3 3 3 3 - - 5/8 x y + 5/24 x y + 1/4 x y + 1/6 x y - 5/12 x y - 1/12 y x - - 3 2 3 2 3 3 - - 1/12 x , COEFF(1, 2) = - 1/12 x y - 1/18 + 1/24 x + 1/18 x + 1/9 y - - 2 3 2 3 2 2 - + 1/6 y + 2/9 x y + 1/24 y x - 1/18 y + 1/18 y x - 1/8 x y - 1/9 x y - - 3 2 3 3 2 3 - - 1/6 x y - 1/9 x y + 1/3 x y - 1/9 x, COEFF(2, 2) = - 1/72 y x - - 3 2 2 2 3 - - 1/72 x - 1/48 x + 1/144 x y + 1/144 - 1/48 y + 1/144 x + 1/24 x y - - 2 3 2 2 2 3 2 3 - - 1/48 y x - 1/72 x y + 1/16 x y - 1/48 x y + 1/24 x y - 1/72 y - - 3 3 - + 1/36 x y + 1/144 y] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); -bytes used=301539208, alloc=2817532, time=31.25 -bytes used=302539400, alloc=2817532, time=31.32 -bytes used=303539592, alloc=2817532, time=31.40 -bytes used=304557648, alloc=2817532, time=31.44 -bytes used=305571464, alloc=2817532, time=31.54 -bytes used=306581776, alloc=2817532, time=31.63 -bytes used=307582028, alloc=2817532, time=31.71 -bytes used=308582248, alloc=2817532, time=31.78 -bytes used=309582476, alloc=2817532, time=32.18 -bytes used=310582696, alloc=2817532, time=32.25 -bytes used=311582884, alloc=2817532, time=32.32 -bytes used=312583056, alloc=2817532, time=32.42 -bytes used=313583260, alloc=2817532, time=32.51 -bytes used=314583428, alloc=2817532, time=32.60 -bytes used=315583596, alloc=2817532, time=32.70 -bytes used=316593332, alloc=2817532, time=33.09 -bytes used=317593536, alloc=2817532, time=33.32 -bytes used=318593748, alloc=2817532, time=33.39 -bytes used=319593964, alloc=2817532, time=33.51 -bytes used=320594120, alloc=2817532, time=33.69 -bytes used=321594408, alloc=2817532, time=34.06 -bytes used=322594856, alloc=2817532, time=34.26 -bytes used=323595080, alloc=2817532, time=34.33 -bytes used=324595308, alloc=2817532, time=34.46 -bytes used=325595460, alloc=2817532, time=34.65 -bytes used=326595828, alloc=2817532, time=35.02 -bytes used=327596080, alloc=2817532, time=35.09 -bytes used=328596388, alloc=2817532, time=35.22 -bytes used=329596548, alloc=2817532, time=35.63 -bytes used=330596860, alloc=2817532, time=35.76 -bytes used=331597036, alloc=2817532, time=35.86 -bytes used=332597196, alloc=2817532, time=36.29 -bytes used=333597480, alloc=2817532, time=36.41 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); -bytes used=334597656, alloc=2817532, time=36.56 -bytes used=335597820, alloc=2817532, time=36.64 -bytes used=336597976, alloc=2817532, time=36.70 -- 1/12 DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(0, 1) - 1/12 DATA(0, -2) - - 3 4 4 - + 5/12 x DATA(1, 0) - 5/8 x DATA(0, 0) + 5/12 x DATA(-1, 0) - - 4 4 4 - - 5/48 x DATA(2, 0) + 5/12 x DATA(1, 0) + 1/72 x DATA(1, 2) - - 4 4 4 - + 1/72 x DATA(-1, 2) + 1/18 x DATA(2, 1) - 1/48 x DATA(0, 2) - - 3 3 - - 5/12 x DATA(-1, 0) + 5/24 x DATA(-2, 0) + 1/2 y DATA(0, 2) - - 4 4 4 - + 1/3 x DATA(0, -1) - 1/48 x DATA(0, -2) + 1/3 x DATA(0, 1) - - 4 4 4 - + 1/72 x DATA(1, -2) - 1/288 x DATA(2, -2) + 1/18 x DATA(-2, -1) - - 4 3 2 4 - - 5/48 x DATA(-2, 0) - 5/24 x DATA(2, 0) - 1/2 y x DATA(0, -1) - - 2 4 2 4 2 4 - - 1/2 y x DATA(0, 1) + 1/8 y x DATA(0, -2) + 1/48 y x DATA(2, -2) - - 2 4 2 4 2 4 - - 1/12 y x DATA(-2, -1) + 1/8 y x DATA(-2, 0) - 1/12 y x DATA(1, -2) - - 3 2 3 2 - + 1/4 x y DATA(2, 0) + 5/24 x DATA(2, 0) - 1/2 x y DATA(1, 0) - - 3 2 2 2 2 2 - + 1/2 x y DATA(-1, 0) - 5/8 x y DATA(0, 2) - 5/8 x y DATA(0, -2) - - 2 2 2 2 2 2 - - 15/4 x y DATA(0, 0) + 5/2 x y DATA(0, 1) - 1/8 x y DATA(-2, 0) - - 2 2 2 4 2 4 - + 5/2 x y DATA(0, -1) + 1/3 y x DATA(-1, -1) - 1/12 y x DATA(-1, -2) - - 2 4 2 4 2 4 - + 1/3 y x DATA(-1, 1) + 1/48 y x DATA(-2, -2) - 1/2 y x DATA(-1, 0) - - 2 4 2 4 2 4 - + 1/3 y x DATA(1, -1) + 1/3 y x DATA(1, 1) - 1/2 y x DATA(1, 0) - - 2 4 2 4 2 4 - + 1/8 y x DATA(2, 0) - 1/12 y x DATA(-2, 1) + 1/48 y x DATA(-2, 2) - - 2 2 4 2 4 - - 2 x y DATA(-1, 0) + 1/48 y x DATA(2, 2) - 1/12 y x DATA(2, -1) - - 2 2 2 2 2 2 - + 2 x y DATA(-1, 0) + 2 x y DATA(1, 0) - 1/8 x y DATA(2, 0) - - 2 - - 5/3 x DATA(1, 0) + 4/3 DATA(0, -1) + 2 x y DATA(1, 0) - - 2 2 4 - + 1/4 x y DATA(-2, 0) - 1/4 x y DATA(2, 0) - 2/9 x DATA(-1, -1) - - 2 4 4 - - 5/4 y x DATA(0, -1) - 1/288 x DATA(2, 2) + 1/72 x DATA(-1, -2) - - 4 4 4 - - 2/9 x DATA(1, -1) - 2/9 x DATA(-1, 1) - 2/9 x DATA(1, 1) - - 4 4 2 - - 1/288 x DATA(-2, 2) - 1/288 x DATA(-2, -2) + 5/8 y x DATA(0, -2) - - 2 - + 5/4 y x DATA(0, 1) - 1/2 y DATA(0, -2) - y DATA(0, 1) - - 2 2 - - 5/8 y x DATA(0, 2) + y DATA(0, -1) + 1/2 y DATA(0, 2) - - 2 2 2 - + 1/2 y DATA(0, -2) - 2 y DATA(0, 1) - 2 y DATA(0, -1) - - 4 4 4 - + 1/6 y x DATA(-1, 1) + 1/12 y x DATA(-1, -2) - 1/8 y x DATA(0, -2) - - 2 2 2 - + 3 y DATA(0, 0) - 5/3 x DATA(1, 0) + 5/48 x DATA(0, 2) - - 2 2 2 - - 5/3 x DATA(0, -1) + 5/48 x DATA(0, -2) - 5/3 x DATA(0, 1) - - 2 4 4 - + 25/8 x DATA(0, 0) - 1/6 y x DATA(-1, -1) - 1/48 y x DATA(-2, -2) - - 2 4 4 - + 5/48 x DATA(-2, 0) + 1/48 y x DATA(-2, 2) + 1/6 y x DATA(1, 1) - - 4 4 4 - + 1/4 y x DATA(0, -1) + 1/24 y x DATA(-2, -1) + 1/12 y x DATA(1, -2) - - 2 2 4 - - 5/3 x DATA(-1, 0) + 5/48 x DATA(2, 0) - 1/48 y x DATA(2, -2) - - 4 3 2 - - 1/24 y x DATA(-2, 1) - 1/4 x y DATA(-2, 0) - 5/24 x DATA(-2, 0) - - 4 4 4 - + 1/48 y x DATA(2, 2) + 1/18 x DATA(-2, 1) + 1/18 x DATA(2, -1) - - 4 4 4 - - 1/24 y x DATA(2, 1) + 1/8 y x DATA(0, 2) - 1/4 y x DATA(0, 1) - - 4 4 2 4 - + 1/24 y x DATA(2, -1) - 1/6 y x DATA(1, -1) - 1/12 y x DATA(-1, 2) - - 2 4 2 4 - - 1/12 y x DATA(1, 2) + 5/3 x DATA(-1, 0) + 3/4 y x DATA(0, 0) - - 2 4 2 4 4 - + 1/8 y x DATA(0, 2) - 1/12 y x DATA(2, 1) - 1/12 y x DATA(-1, 2) - - 4 - - 1/12 y x DATA(1, 2) - 8/9 x DATA(-1, 1) - 8/9 x DATA(-1, -1) - - 3 3 - + 8/9 x DATA(1, -1) - 1/144 x DATA(2, 2) + 1/72 x DATA(1, 2) - - 3 3 3 - - 1/72 x DATA(-1, 2) - 1/144 x DATA(2, -2) + 1/72 x DATA(1, -2) - - 3 3 3 - - 1/72 x DATA(-1, -2) + 1/9 x DATA(2, 1) + 1/9 x DATA(2, -1) - - 3 3 2 - - 2/9 x DATA(1, 1) + 1/144 x DATA(-2, 2) + 4/3 x y DATA(-1, -1) - - 2 2 2 2 3 - - 4/3 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) + 1/144 x DATA(-2, -2) - - 3 3 3 - + 2/9 x DATA(-1, -1) + 1/12 y x DATA(-2, 1) - 1/12 y x DATA(-2, -1) - - 3 3 3 - - 1/24 y x DATA(2, -2) - 1/6 y x DATA(1, -1) - 1/6 y x DATA(-1, 1) - - 3 3 3 - + 1/12 y x DATA(2, -1) + 1/6 y x DATA(1, 1) - 1/24 y x DATA(-2, 2) - - 3 3 3 - + 1/24 y x DATA(-2, -2) + 1/6 y x DATA(-1, -1) - 1/12 y x DATA(1, 2) - - 3 3 3 - + 1/12 y x DATA(-1, 2) + 1/24 y x DATA(2, 2) - 1/12 y x DATA(2, 1) - - 2 2 2 - - 1/18 x DATA(2, -1) + 8/9 x DATA(1, 1) + 1/288 x DATA(-2, 2) - - 2 2 2 - - 1/18 x DATA(-2, 1) - 1/18 x DATA(-2, -1) + 1/288 x DATA(2, -2) - - 2 2 2 - - 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) + 1/288 x DATA(-2, -2) - - 2 2 2 - + 8/9 x DATA(-1, -1) + 8/9 x DATA(1, -1) - 1/18 x DATA(1, 2) - - 2 2 2 - - 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + 1/288 x DATA(2, 2) - - 3 3 3 - - 2/9 x DATA(1, -1) + 2/9 x DATA(-1, 1) - 1/9 x DATA(-2, 1) - - 3 - - 1/9 x DATA(-2, -1) - 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) - - + 8/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/9 x DATA(-2, 1) - - + 1/9 x DATA(-2, -1) + 1/144 x DATA(2, -2) - 1/18 x DATA(1, -2) - - 3 3 - + 1/12 y x DATA(1, -2) - 1/12 y x DATA(-1, -2) + 1/18 x DATA(-1, -2) - - 3 2 3 2 3 2 - + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) + 1/6 x y DATA(-2, 1) - - 3 2 3 2 - + 1/6 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) - 1/144 x DATA(-2, -2) - - 3 2 3 2 3 2 - + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) - - 3 2 3 2 3 2 - - 1/6 x y DATA(2, 1) - 1/6 x y DATA(2, -1) + 1/3 x y DATA(1, -1) - - 2 3 2 3 2 - + 8/9 x DATA(-1, 1) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) - - 3 2 3 2 3 2 - - 1/24 x y DATA(-2, -2) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(-1, 1) - - + 1/144 x DATA(2, 2) - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) - - 2 2 2 2 2 2 - - 1/48 x y DATA(2, -2) + 1/3 x y DATA(1, -2) + 1/3 x y DATA(-1, -2) - - 2 2 2 2 2 2 - - 1/48 x y DATA(-2, -2) - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) - - 2 2 2 2 - - 4/3 x y DATA(-1, 1) + 1/3 y x DATA(1, 2) + 1/3 y x DATA(-1, 2) - - 2 2 2 2 - + 1/24 y x DATA(2, 1) + 1/12 x y DATA(-2, -1) - 1/3 y x DATA(1, -2) - - 2 2 2 - - 1/3 y x DATA(-1, -2) + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) - - 2 2 2 - - 2/3 y x DATA(1, 1) - 1/48 y x DATA(-2, 2) + 1/24 y x DATA(-2, 1) - - 2 2 2 - - 1/24 y x DATA(-2, -1) + 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) - - 2 2 2 - + 2/3 y x DATA(1, -1) - 2/3 y x DATA(-1, 1) - 1/24 y x DATA(2, -1) - - 2 2 2 - - 4/3 x y DATA(1, -1) + 4/3 x y DATA(-1, 1) - 1/6 x y DATA(-2, -1) - - 2 2 2 - - 1/24 x y DATA(2, -2) + 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) - - 2 2 2 - + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) - - 2 - + 1/24 x y DATA(-2, -2) + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) - - + 1/12 x y DATA(2, 1) - 1/12 x y DATA(2, -1) - 2/3 x y DATA(1, 1) - - + 1/24 x y DATA(-2, 2) - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) - - 2 2 - + 1/24 x y DATA(2, -2) - 4/3 x y DATA(1, 1) - 1/6 x y DATA(-2, 1) - - 2 2 2 - + 1/24 x y DATA(-2, 2) + 1/6 x y DATA(2, -1) - 1/24 x y DATA(2, 2) - - + 2/3 x y DATA(-1, 1) - 1/24 x y DATA(2, 2) - 1/3 x y DATA(1, -2) - - + 1/3 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) - - 2 2 2 2 - + 2/3 x y DATA(1, -1) + 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 2) - - 2 2 2 2 2 2 - + 1/3 x y DATA(-1, 2) + 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) - - 2 2 - - 1/48 x y DATA(2, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=337598236, alloc=2817532, time=36.76 -bytes used=338598536, alloc=2817532, time=36.83 - 3 2 2 4 -[COEFF(-2, -2) = 1/144 x - 1/48 x y - 1/24 x y - 1/144 x - 1/48 y x - - 2 2 3 2 2 2 4 3 - + 1/48 y x + 1/288 x - 1/24 x y + 1/24 x y + 1/48 y x + 1/24 y x - - 4 3 2 4 2 2 - - 1/288 x , COEFF(-1, -2) = - 1/72 x - 1/3 y x + 1/72 x + 1/3 x y - - 3 2 2 3 2 2 4 - - 1/12 y x - 1/18 x + 1/3 x y - 1/3 x y + 1/12 x y - 1/12 y x - - 4 2 2 4 4 - + 1/18 x + 1/12 y x , COEFF(0, -2) = 5/8 y x + 1/8 y x - 1/8 y x - - 4 2 2 2 2 - - 1/48 x + 5/48 x + 1/2 y - 5/8 x y - 1/12 - 1/2 y, COEFF(1, -2) = - - 2 4 2 2 3 3 - - 1/18 x + 1/72 x + 1/3 x y - 1/3 x y + 1/12 y x - 1/18 x + 1/72 x - - 2 4 2 3 2 2 4 - - 1/12 y x - 1/3 y x - 1/12 x y + 1/3 x y + 1/12 y x , COEFF(2, -2) - - 2 4 2 2 2 - = - 1/24 x y - 1/48 y x + 1/288 x + 1/144 x - 1/48 x y + 1/24 x y - - 3 3 2 3 2 2 4 4 - - 1/144 x - 1/24 y x + 1/48 y x + 1/24 x y + 1/48 y x - 1/288 x , - - 4 3 2 2 2 - COEFF(-2, -1) = 1/12 x y + 1/18 x - 1/9 x + 1/12 x y - 1/24 y x - - 4 2 4 2 3 3 2 - + 1/24 y x - 1/12 y x - 1/18 x - 1/12 y x + 1/6 x y + 1/9 x - - 2 4 3 2 2 2 - - 1/6 x y , COEFF(-1, -1) = - 2/9 x - 1/3 x y + 8/9 x + 2/3 y x - - 4 2 4 3 3 2 2 2 - - 1/6 y x + 1/3 y x + 1/6 y x + 2/9 x - 4/3 x y - 8/9 x + 4/3 x y - - 2 4 2 2 2 - - 2/3 x y, COEFF(0, -1) = 4/3 - 1/2 y x + y - 5/3 x - 5/4 y x - 2 y - - 4 4 2 2 4 4 - + 1/4 y x + 1/3 x + 5/2 x y , COEFF(1, -1) = 8/9 x - 1/6 y x - 2/9 x - - 2 4 2 2 3 2 3 - + 1/3 y x - 4/3 x y + 2/3 y x + 1/3 x y - 2/9 x + 2/3 x y - - 2 2 2 3 3 2 - - 4/3 x y + 8/9 x - 1/6 y x , COEFF(2, -1) = 1/9 x + 1/6 x y - 1/9 x - - 2 3 4 2 2 3 2 - - 1/18 x + 1/12 y x + 1/24 y x + 1/12 x y - 1/6 x y - 1/12 x y - - 4 2 4 2 2 2 3 2 - + 1/18 x - 1/12 y x - 1/24 y x , COEFF(-2, 0) = - 1/8 x y - 1/4 x y - - 3 2 4 2 4 2 - + 5/24 x + 1/8 y x + 1/4 x y - 5/48 x - 5/24 x + 5/48 x , - - 3 2 2 2 2 4 2 4 - COEFF(-1, 0) = 1/2 x y + 2 x y + 5/3 x - 5/3 x + 5/12 x - 1/2 y x - - 3 2 - - 5/12 x - 2 x y , - - 2 2 4 2 4 2 2 - COEFF(0, 0) = 25/8 x - 5/2 + 3 y - 5/8 x + 3/4 y x - 15/4 x y , - - 2 4 2 2 2 2 3 2 3 - COEFF(1, 0) = - 1/2 y x + 2 x y + 2 x y - 5/3 x - 1/2 x y + 5/12 x - - 4 4 3 2 2 4 - + 5/12 x - 5/3 x, COEFF(2, 0) = - 5/48 x + 1/4 x y + 1/8 y x - - 2 2 2 2 3 - - 1/8 x y - 1/4 x y + 5/48 x - 5/24 x + 5/24 x, COEFF(-2, 1) = - - 3 2 2 4 3 - - 1/9 x + 1/12 x y - 1/12 x y + 1/9 x - 1/24 y x + 1/12 y x - - 2 2 2 4 2 4 3 2 - + 1/24 y x - 1/18 x - 1/12 y x - 1/6 x y + 1/18 x + 1/6 x y , - - 4 2 3 4 - COEFF(-1, 1) = 2/3 x y + 1/6 y x - 2/3 y x - 1/6 y x - 2/9 x - - 2 4 3 2 2 3 2 2 2 - + 1/3 y x + 2/9 x + 8/9 x - 8/9 x + 4/3 x y - 1/3 x y - 4/3 x y , - - 2 2 4 2 4 4 - COEFF(0, 1) = -2 y + 4/3 - 1/2 y x + 5/4 y x + 1/3 x - 1/4 y x - y - - 2 2 2 2 3 4 - + 5/2 x y - 5/3 x , COEFF(1, 1) = - 2/3 y x - 2/3 x y - 2/9 x - 2/9 x - - 4 2 2 2 3 2 4 - + 8/9 x + 1/6 y x - 4/3 x y - 4/3 x y + 1/6 y x + 1/3 y x - - 3 2 2 2 2 4 2 - + 1/3 x y + 8/9 x , COEFF(2, 1) = 1/12 x y + 1/18 x - 1/18 x - - 2 4 2 4 3 3 2 - - 1/12 y x + 1/6 x y - 1/24 y x + 1/12 x y + 1/9 x - 1/6 x y - - 3 2 2 2 - - 1/9 x - 1/12 y x + 1/24 y x , COEFF(-2, 2) = 1/24 x y + 1/288 x - - 3 2 4 4 3 - + 1/24 x y + 1/144 x + 1/48 y x - 1/144 x + 1/48 y x - 1/24 y x - - 4 2 2 2 3 2 - - 1/288 x - 1/48 y x - 1/48 x y - 1/24 x y , COEFF(-1, 2) = - 1/3 x y - - 2 2 2 3 2 2 2 4 3 - - 1/3 x y + 1/3 x y + 1/12 x y + 1/3 y x - 1/12 y x - 1/72 x - - 2 4 3 4 - + 1/18 x - 1/18 x + 1/72 x + 1/12 y x - 1/12 y x , COEFF(0, 2) = - - 4 2 4 2 2 4 2 2 - - 1/48 x - 5/8 y x + 1/2 y + 1/8 y x + 1/2 y + 1/8 y x - 5/8 x y - - 2 3 2 2 2 - + 5/48 x - 1/12, COEFF(1, 2) = - 1/12 x y + 1/3 x y + 1/3 x y - - 2 4 4 3 3 2 - + 1/3 x y + 1/72 x - 1/12 y x - 1/12 y x + 1/72 x - 1/18 x - - 2 2 4 3 - + 1/3 y x - 1/18 x - 1/12 y x , COEFF(2, 2) = - 1/24 x y - 1/144 x - - 2 2 3 2 4 2 3 2 - - 1/48 x y + 1/24 x y - 1/288 x - 1/48 y x + 1/24 y x + 1/288 x - - 4 2 2 4 - + 1/48 y x + 1/144 x - 1/24 x y + 1/48 y x ] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); -bytes used=339598688, alloc=2817532, time=36.92 -bytes used=340598856, alloc=2817532, time=36.99 -bytes used=341599544, alloc=2817532, time=37.04 -bytes used=342609588, alloc=2817532, time=37.12 -bytes used=343617792, alloc=2817532, time=37.21 -bytes used=344618020, alloc=2817532, time=37.30 -bytes used=345618228, alloc=2817532, time=37.79 -bytes used=346618720, alloc=2817532, time=37.87 -bytes used=347618880, alloc=2817532, time=37.94 -bytes used=348623292, alloc=2817532, time=38.03 -bytes used=349623484, alloc=2817532, time=38.12 -bytes used=350623648, alloc=2817532, time=38.22 -bytes used=351625036, alloc=2817532, time=38.32 -bytes used=352625232, alloc=2817532, time=38.73 -bytes used=353625668, alloc=2817532, time=38.91 -bytes used=354625832, alloc=2817532, time=38.99 -bytes used=355626060, alloc=2817532, time=39.14 -bytes used=356630912, alloc=2817532, time=39.56 -bytes used=357631128, alloc=2817532, time=39.78 -bytes used=358631348, alloc=2817532, time=39.86 -bytes used=359632096, alloc=2817532, time=40.02 -bytes used=360632268, alloc=2817532, time=40.42 -bytes used=361632468, alloc=2817532, time=40.49 -bytes used=362632652, alloc=2817532, time=40.71 -bytes used=363633064, alloc=2817532, time=41.09 -bytes used=364633244, alloc=2817532, time=41.18 -bytes used=365633400, alloc=2817532, time=41.60 -bytes used=366633640, alloc=2817532, time=41.81 -> -################################################################################ -> quit -bytes used=367598444, alloc=2817532, time=41.95 |