diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Hermite/2d.log')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Hermite/2d.log | 5631 |
1 files changed, 0 insertions, 5631 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/2d.log b/src/GeneralizedPolynomial-Uniform/Hermite/2d.log deleted file mode 100644 index b177297..0000000 --- a/src/GeneralizedPolynomial-Uniform/Hermite/2d.log +++ /dev/null @@ -1,5631 +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 1.4 2002/08/20 16:46:06 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 1.10 2002/08/28 11:31:09 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 Hermite interpolating functions/coords/coeffs/mols -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Hermite/fns.maple,v 1.2 2002/09/01 18:33:34 jthorn Exp $ -> -# -# Note: -# interpolation order 2 <==> fn order 3, 3-point (2nd order) derivative mols -# interpolation order 3 <==> fn order 3, 5-point (4th order) derivative mols -# interpolation order 4 <==> fn order 5, 5-point (4th order) derivative mols -# -> -################################################################################ -################################################################################ -################################################################################ -> -# -# derivative primitives -# (argument is a procedure which should map m into the DATA() reference) -# -> -> dx_3point := -> proc(f::procedure(integer)) -> (1/2) * (-f(-1) + f(+1)) -> end proc; - dx_3point := proc(f::procedure(integer)) -1/2*f(-1) + 1/2*f(1) end proc - -> -> dx_5point := -> proc(f::procedure(integer)) -> (1/12) * (f(-2) - 8*f(-1) + 8*f(+1) - f(+2)) -> end proc; -dx_5point := proc(f::procedure(integer)) - 1/12*f(-2) - 2/3*f(-1) + 2/3*f(1) - 1/12*f(2) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# 1-D interpolating functions -# -> -> 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_order5 := -> proc(x) -> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 -> end proc; - fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc - -> -################################################################################ -> -# coordinates for 1-D interpolating functions -> coord_list_1d := [x]; - coord_list_1d := [x] - -> -################################################################################ -> -# -# coefficients in 1-D interpolating functions -# -> -> coeffs_set_1d_order3 := {c0, c1, c2, c3}; - coeffs_set_1d_order3 := {c0, c1, c2, c3} - -> coeffs_set_1d_order5 := {c0, c1, c2, c3, c4, c5}; - coeffs_set_1d_order5 := {c0, c1, c2, c3, c4, c5} - -> -################################################################################ -> -# -# 1-D derivative molecules (argument = molecule center) -# -> -> deriv_1d_dx_3point := proc(i::integer) -> dx_3point(proc(mi::integer) DATA(i+mi) end proc) -> end proc; -deriv_1d_dx_3point := proc(i::integer) - dx_3point(proc(mi::integer) DATA(i + mi) end proc) -end proc - -> deriv_1d_dx_5point := proc(i::integer) -> dx_5point(proc(mi::integer) DATA(i+mi) end proc) -> end proc; -deriv_1d_dx_5point := proc(i::integer) - dx_5point(proc(mi::integer) DATA(i + mi) end proc) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# 2-D interpolating functions -# -> -> 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_order5 := -> proc(x,y) -> + c05*y^5 + c15*x*y^5 + c25*x^2*y^5 + c35*x^3*y^5 + c45*x^4*y^5 + c55*x^5*y^5 -> + c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 + c54*x^5*y^4 -> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 + c53*x^5*y^3 -> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 + c52*x^5*y^2 -> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y + c51*x^5*y -> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 + c50*x^5 -> end proc; -fn_2d_order5 := proc(x, y) - c34*x^3*y^4 + c14*x*y^4 + c03*y^3 + c02*y^2 + c01*y + c10*x + c20*x^2 - + c30*x^3 + c05*y^5 + c04*y^4 + c40*x^4 + c50*x^5 + c13*x*y^3 - + c23*x^2*y^3 + c33*x^3*y^3 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 - + c11*x*y + c21*x^2*y + c31*x^3*y + c15*x*y^5 + c25*x^2*y^5 - + c35*x^3*y^5 + c45*x^4*y^5 + c55*x^5*y^5 + c24*x^2*y^4 + c44*x^4*y^4 - + c54*x^5*y^4 + c43*x^4*y^3 + c53*x^5*y^3 + c42*x^4*y^2 + c52*x^5*y^2 - + c00 + c41*x^4*y + c51*x^5*y -end proc - -> -################################################################################ -> -# coordinates for 2-D interpolating functions -> coord_list_2d := [x,y]; - coord_list_2d := [x, y] - -> -################################################################################ -> -# -# coefficients in 2-D interpolating functions -# -> -> coeffs_set_2d_order3 := { -> c03, c13, c23, c33, -> c02, c12, c22, c32, -> c01, c11, c21, c31, -> c00, c10, c20, c30 -> }; -coeffs_set_2d_order3 := {c03, c13, c23, c33, c02, c12, c22, c32, c01, c11, c21, - - c31, c00, c10, c20, c30} - -> -> coeffs_set_2d_order5 := { -> c05, c15, c25, c35, c45, c55, -> c04, c14, c24, c34, c44, c54, -> c03, c13, c23, c33, c43, c53, -> c02, c12, c22, c32, c42, c52, -> c01, c11, c21, c31, c41, c51, -> c00, c10, c20, c30, c40, c50 -> }; -coeffs_set_2d_order5 := {c03, c13, c23, c33, c02, c12, c22, c32, c01, c11, c21, - - c31, c00, c10, c20, c30, c05, c15, c25, c35, c45, c55, c04, c14, c24, c34, - - c44, c54, c43, c53, c42, c52, c41, c51, c40, c50} - -> -################################################################################ -> -# -# 2-D derivative molecules (arguments = molecule center) -# -> -> deriv_2d_dx_3point := proc(i::integer, j::integer) -> dx_3point( -> proc(mi::integer) DATA(i+mi,j) end proc -> ) -> end proc; -deriv_2d_dx_3point := proc(i::integer, j::integer) - dx_3point(proc(mi::integer) DATA(i + mi, j) end proc) -end proc - -> deriv_2d_dy_3point := proc(i::integer, j::integer) -> dx_3point( -> proc(mj::integer) DATA(i,j+mj) end proc -> ) -> end proc; -deriv_2d_dy_3point := proc(i::integer, j::integer) - dx_3point(proc(mj::integer) DATA(i, j + mj) end proc) -end proc - -> deriv_2d_dxy_3point := proc(i::integer, j::integer) -> dx_3point( -> proc(mi::integer) -> dx_3point(proc(mj::integer) DATA(i+mi,j+mj) end proc) -> end proc -> ) -> end proc; -deriv_2d_dxy_3point := proc(i::integer, j::integer) - dx_3point(proc(mi::integer) - dx_3point(proc(mj::integer) DATA(i + mi, j + mj) end proc) - end proc) -end proc - -> -> deriv_2d_dx_5point := proc(i::integer, j::integer) -> dx_5point( -> proc(mi::integer) DATA(i+mi,j) end proc -> ) -> end proc; -deriv_2d_dx_5point := proc(i::integer, j::integer) - dx_5point(proc(mi::integer) DATA(i + mi, j) end proc) -end proc - -> deriv_2d_dy_5point := proc(i::integer, j::integer) -> dx_5point( -> proc(mj::integer) DATA(i,j+mj) end proc -> ) -> end proc; -deriv_2d_dy_5point := proc(i::integer, j::integer) - dx_5point(proc(mj::integer) DATA(i, j + mj) end proc) -end proc - -> deriv_2d_dxy_5point := proc(i::integer, j::integer) -> dx_5point( -> proc(mi::integer) -> dx_5point(proc(mj::integer) DATA(i+mi,j+mj) end proc) -> end proc -> ) -> end proc; -deriv_2d_dxy_5point := proc(i::integer, j::integer) - dx_5point(proc(mi::integer) - dx_5point(proc(mj::integer) DATA(i + mi, j + mj) end proc) - end proc) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# 3-D interpolating functions -# -> -> 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^1 --------------------------------------------------------------- -> + 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 + c022*y^2*z^2 + c301*x^3*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 + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 - + c322*x^3*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*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 + c121*x*y^2*z - + c221*x^2*y^2*z + c321*x^3*y^2*z + c111*x*y*z + c211*x^2*y*z - + c311*x^3*y*z + 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 + c012*y*z^2 + c102*x*z^2 - + c202*x^2*z^2 + c302*x^3*z^2 + c021*y^2*z + c011*y*z + c101*x*z - + c201*x^2*z + c130*x*y^3 + c230*x^2*y^3 + c120*x*y^2 + c220*x^2*y^2 - + c320*x^3*y^2 + c110*x*y + c210*x^2*y + c310*x^3*y + c003*z^3 - + c002*z^2 + c001*z + c030*y^3 + c020*y^2 + c010*y + c000 + c100*x - + c200*x^2 + c300*x^3 -end proc - -> -> fn_3d_order5 := -> proc(x,y,z) -# z^5 -> + c055*y^5*z^5 + c155*x*y^5*z^5 + c255*x^2*y^5*z^5 + c355*x^3*y^5*z^5 + c455*x^4*y^5*z^5 + c555*x^5*y^5*z^5 -> + c045*y^4*z^5 + c145*x*y^4*z^5 + c245*x^2*y^4*z^5 + c345*x^3*y^4*z^5 + c445*x^4*y^4*z^5 + c545*x^5*y^4*z^5 -> + c035*y^3*z^5 + c135*x*y^3*z^5 + c235*x^2*y^3*z^5 + c335*x^3*y^3*z^5 + c435*x^4*y^3*z^5 + c535*x^5*y^3*z^5 -> + c025*y^2*z^5 + c125*x*y^2*z^5 + c225*x^2*y^2*z^5 + c325*x^3*y^2*z^5 + c425*x^4*y^2*z^5 + c525*x^5*y^2*z^5 -> + c015*y *z^5 + c115*x*y *z^5 + c215*x^2*y *z^5 + c315*x^3*y *z^5 + c415*x^4*y *z^5 + c515*x^5*y *z^5 -> + c005 *z^5 + c105*x *z^5 + c205*x^2 *z^5 + c305*x^3 *z^5 + c405*x^4 *z^5 + c505*x^5 *z^5 -# z^4 -> + c054*y^5*z^4 + c154*x*y^5*z^4 + c254*x^2*y^5*z^4 + c354*x^3*y^5*z^4 + c454*x^4*y^5*z^4 + c554*x^5*y^5*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 + c544*x^5*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 + c534*x^5*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 + c524*x^5*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 + c514*x^5*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 + c504*x^5 *z^4 -# z^3 -> + c053*y^5*z^3 + c153*x*y^5*z^3 + c253*x^2*y^5*z^3 + c353*x^3*y^5*z^3 + c453*x^4*y^5*z^3 + c553*x^5*y^5*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 + c543*x^5*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 + c533*x^5*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 + c523*x^5*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 + c513*x^5*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 + c503*x^5 *z^3 -# z^2 -> + c052*y^5*z^2 + c152*x*y^5*z^2 + c252*x^2*y^5*z^2 + c352*x^3*y^5*z^2 + c452*x^4*y^5*z^2 + c552*x^5*y^5*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 + c542*x^5*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 + c532*x^5*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 + c522*x^5*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 + c512*x^5*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 + c502*x^5 *z^2 -# z^1 -> + c051*y^5*z + c151*x*y^5*z + c251*x^2*y^5*z + c351*x^3*y^5*z + c451*x^4*y^5*z + c551*x^5*y^5*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 + c541*x^5*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 + c531*x^5*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 + c521*x^5*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 + c511*x^5*y *z -> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z + c501*x^5 *z -# z^0 -> + c050*y^5 + c150*x*y^5 + c250*x^2*y^5 + c350*x^3*y^5 + c450*x^4*y^5 + c550*x^5*y^5 -> + c040*y^4 + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 + c540*x^5*y^4 -> + c030*y^3 + c130*x*y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 + c530*x^5*y^3 -> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 + c520*x^5*y^2 -> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y + c410*x^4*y + c510*x^5*y -> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 + c500*x^5 -> end proc; -fn_3d_order5 := proc(x, y, z) - c043*y^4*z^3 + c104*x*z^4 + c330*x^3*y^3 + c503*x^5*z^3 + c250*x^2*y^5 - + c031*y^3*z + c103*x*z^3 + c540*x^5*y^4 + c052*y^5*z^2 + c051*y^5*z - + c550*x^5*y^5 + c204*x^2*z^4 + c340*x^3*y^4 + c304*x^3*z^4 - + c042*y^4*z^2 + c140*x*y^4 + c022*y^2*z^2 + c205*x^2*z^5 + c150*x*y^5 - + c301*x^3*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 + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 - + c322*x^3*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*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 + c121*x*y^2*z - + c221*x^2*y^2*z + c321*x^3*y^2*z + c111*x*y*z + c211*x^2*y*z - + c311*x^3*y*z + c155*x*y^5*z^5 + c255*x^2*y^5*z^5 + c355*x^3*y^5*z^5 - + c455*x^4*y^5*z^5 + c555*x^5*y^5*z^5 + c145*x*y^4*z^5 - + c245*x^2*y^4*z^5 + c345*x^3*y^4*z^5 + c445*x^4*y^4*z^5 - + c545*x^5*y^4*z^5 + c135*x*y^3*z^5 + c235*x^2*y^3*z^5 - + c335*x^3*y^3*z^5 + c435*x^4*y^3*z^5 + c535*x^5*y^3*z^5 - + c125*x*y^2*z^5 + c225*x^2*y^2*z^5 + c325*x^3*y^2*z^5 - + c425*x^4*y^2*z^5 + c525*x^5*y^2*z^5 + c115*x*y*z^5 + c215*x^2*y*z^5 - + c315*x^3*y*z^5 + c415*x^4*y*z^5 + c515*x^5*y*z^5 + c154*x*y^5*z^4 - + c254*x^2*y^5*z^4 + c354*x^3*y^5*z^4 + c454*x^4*y^5*z^4 - + c554*x^5*y^5*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 + c544*x^5*y^4*z^4 - + c134*x*y^3*z^4 + c035*y^3*z^5 + 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 + c012*y*z^2 - + c102*x*z^2 + c202*x^2*z^2 + c302*x^3*z^2 + c021*y^2*z + c011*y*z - + c101*x*z + c201*x^2*z + c130*x*y^3 + c230*x^2*y^3 + c120*x*y^2 - + c220*x^2*y^2 + c320*x^3*y^2 + c110*x*y + c210*x^2*y + c310*x^3*y - + c003*z^3 + c002*z^2 + c001*z + c030*y^3 + c020*y^2 + c010*y + c000 - + c100*x + c200*x^2 + c300*x^3 + c005*z^5 + c055*y^5*z^5 - + c045*y^4*z^5 + c025*y^2*z^5 + c015*y*z^5 + c105*x*z^5 + c305*x^3*z^5 - + c405*x^4*z^5 + c505*x^5*z^5 + c054*y^5*z^4 + c044*y^4*z^4 - + c034*y^3*z^4 + c024*y^2*z^4 + c014*y*z^4 + c404*x^4*z^4 - + c504*x^5*z^4 + c053*y^5*z^3 + c403*x^4*z^3 + c402*x^4*z^2 - + c502*x^5*z^2 + c041*y^4*z + c401*x^4*z + c501*x^5*z + c350*x^3*y^5 - + c450*x^4*y^5 + c240*x^2*y^4 + c440*x^4*y^4 + c430*x^4*y^3 - + c530*x^5*y^3 + c420*x^4*y^2 + c520*x^5*y^2 + c234*x^2*y^3*z^4 - + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 + c534*x^5*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 + c524*x^5*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 + c514*x^5*y*z^4 + c153*x*y^5*z^3 - + c253*x^2*y^5*z^3 + c353*x^3*y^5*z^3 + c453*x^4*y^5*z^3 - + c553*x^5*y^5*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 + c543*x^5*y^4*z^3 - + c433*x^4*y^3*z^3 + c533*x^5*y^3*z^3 + c004*z^4 + c050*y^5 + c040*y^4 - + c400*x^4 + c500*x^5 + c423*x^4*y^2*z^3 + c523*x^5*y^2*z^3 - + c413*x^4*y*z^3 + c513*x^5*y*z^3 + c152*x*y^5*z^2 + c252*x^2*y^5*z^2 - + c352*x^3*y^5*z^2 + c452*x^4*y^5*z^2 + c552*x^5*y^5*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 + c542*x^5*y^4*z^2 + c432*x^4*y^3*z^2 - + c532*x^5*y^3*z^2 + c422*x^4*y^2*z^2 + c522*x^5*y^2*z^2 - + c412*x^4*y*z^2 + c512*x^5*y*z^2 + c151*x*y^5*z + c251*x^2*y^5*z - + c351*x^3*y^5*z + c451*x^4*y^5*z + c551*x^5*y^5*z + c141*x*y^4*z - + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z + c541*x^5*y^4*z - + c431*x^4*y^3*z + c531*x^5*y^3*z + c421*x^4*y^2*z + c521*x^5*y^2*z - + c411*x^4*y*z + c511*x^5*y*z + c410*x^4*y + c510*x^5*y -end proc - -> -################################################################################ -> -# coordinates for 3-D interpolating functions -> coord_list_3d := [x,y,z]; - coord_list_3d := [x, y, z] - -> -################################################################################ -> -# -# coefficients in 3-D interpolating functions -# -> -> coeffs_set_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_set_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_set_3d_order5 := { -> # z^5 -> c055, c155, c255, c355, c455, c555, -> c045, c145, c245, c345, c445, c545, -> c035, c135, c235, c335, c435, c535, -> c025, c125, c225, c325, c425, c525, -> c015, c115, c215, c315, c415, c515, -> c005, c105, c205, c305, c405, c505, -> # z^4 -> c054, c154, c254, c354, c454, c554, -> c044, c144, c244, c344, c444, c544, -> c034, c134, c234, c334, c434, c534, -> c024, c124, c224, c324, c424, c524, -> c014, c114, c214, c314, c414, c514, -> c004, c104, c204, c304, c404, c504, -> # z^3 -> c053, c153, c253, c353, c453, c553, -> c043, c143, c243, c343, c443, c543, -> c033, c133, c233, c333, c433, c533, -> c023, c123, c223, c323, c423, c523, -> c013, c113, c213, c313, c413, c513, -> c003, c103, c203, c303, c403, c503, -> # z^2 -> c052, c152, c252, c352, c452, c552, -> c042, c142, c242, c342, c442, c542, -> c032, c132, c232, c332, c432, c532, -> c022, c122, c222, c322, c422, c522, -> c012, c112, c212, c312, c412, c512, -> c002, c102, c202, c302, c402, c502, -> # z^1 -> c051, c151, c251, c351, c451, c551, -> c041, c141, c241, c341, c441, c541, -> c031, c131, c231, c331, c431, c531, -> c021, c121, c221, c321, c421, c521, -> c011, c111, c211, c311, c411, c511, -> c001, c101, c201, c301, c401, c501, -> # z^0 -> c050, c150, c250, c350, c450, c550, -> c040, c140, c240, c340, c440, c540, -> c030, c130, c230, c330, c430, c530, -> c020, c120, c220, c320, c420, c520, -> c010, c110, c210, c310, c410, c510, -> c000, c100, c200, c300, c400, c500 -> }; -coeffs_set_3d_order5 := {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, c055, c155, c255, c355, c455, - - c555, c045, c145, c245, c345, c445, c545, c035, c135, c235, c335, c435, - - c535, c025, c125, c225, c325, c425, c525, c015, c115, c215, c315, c415, - - c515, c005, c105, c205, c305, c405, c505, c054, c154, c254, c354, c454, - - c554, c044, c144, c244, c344, c444, c544, c034, c134, c234, c334, c434, - - c534, c024, c124, c224, c324, c424, c524, c014, c114, c214, c314, c414, - - c514, c004, c104, c204, c304, c404, c504, c053, c153, c253, c353, c453, - - c553, c043, c143, c243, c343, c443, c543, c433, c533, c423, c523, c413, - - c513, c403, c503, c052, c152, c252, c352, c452, c552, c042, c142, c242, - - c342, c442, c542, c432, c532, c422, c522, c412, c512, c402, c502, c051, - - c151, c251, c351, c451, c551, c041, c141, c241, c341, c441, c541, c431, - - c531, c421, c521, c411, c511, c401, c501, c050, c150, c250, c350, c450, - - c550, c040, c140, c240, c340, c440, c540, c430, c530, c420, c520, c410, - - c510, c400, c500} - -> -################################################################################ -> -# -# 3-D derivative molecules (arguments = molecule center) -# -> -> deriv_3d_dx_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mi::integer) DATA(i+mi,j,k) end proc -> ) -> end proc; -deriv_3d_dx_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mi::integer) DATA(i + mi, j, k) end proc) -end proc - -> deriv_3d_dy_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mj::integer) DATA(i,j+mj,k) end proc -> ) -> end proc; -deriv_3d_dy_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mj::integer) DATA(i, j + mj, k) end proc) -end proc - -> deriv_3d_dz_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mk::integer) DATA(i,j,k+mk) end proc -> ) -> end proc; -deriv_3d_dz_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mk::integer) DATA(i, j, k + mk) end proc) -end proc - -> deriv_3d_dxy_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mi::integer) -> dx_3point( -> proc(mj::integer) DATA(i+mi,j+mj,k) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxy_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mi::integer) - dx_3point(proc(mj::integer) DATA(i + mi, j + mj, k) end proc) - end proc) -end proc - -> deriv_3d_dxz_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mi::integer) -> dx_3point( -> proc(mk::integer) DATA(i+mi,j,k+mk) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxz_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mi::integer) - dx_3point(proc(mk::integer) DATA(i + mi, j, k + mk) end proc) - end proc) -end proc - -> deriv_3d_dyz_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mj::integer) -> dx_3point( -> proc(mk::integer) DATA(i,j+mj,k+mk) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dyz_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mj::integer) - dx_3point(proc(mk::integer) DATA(i, j + mj, k + mk) end proc) - end proc) -end proc - -> deriv_3d_dxyz_3point := proc(i::integer, j::integer, k::integer) -> dx_3point( -> proc(mi::integer) -> dx_3point( -> proc(mj::integer) -> dx_3point( -> proc(mk::integer) -> DATA(i+mi,j+mj,k+mk) -> end proc -> ) -> end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxyz_3point := proc(i::integer, j::integer, k::integer) - dx_3point(proc(mi::integer) - dx_3point(proc(mj::integer) - dx_3point( - proc(mk::integer) DATA(i + mi, j + mj, k + mk) end proc) - end proc) - end proc) -end proc - -> -> deriv_3d_dx_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mi::integer) DATA(i+mi,j,k) end proc -> ) -> end proc; -deriv_3d_dx_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mi::integer) DATA(i + mi, j, k) end proc) -end proc - -> deriv_3d_dy_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mj::integer) DATA(i,j+mj,k) end proc -> ) -> end proc; -deriv_3d_dy_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mj::integer) DATA(i, j + mj, k) end proc) -end proc - -> deriv_3d_dz_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mk::integer) DATA(i,j,k+mk) end proc -> ) -> end proc; -deriv_3d_dz_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mk::integer) DATA(i, j, k + mk) end proc) -end proc - -> deriv_3d_dxy_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mi::integer) -> dx_5point( -> proc(mj::integer) DATA(i+mi,j+mj,k) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxy_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mi::integer) - dx_5point(proc(mj::integer) DATA(i + mi, j + mj, k) end proc) - end proc) -end proc - -> deriv_3d_dxz_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mi::integer) -> dx_5point( -> proc(mk::integer) DATA(i+mi,j,k+mk) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxz_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mi::integer) - dx_5point(proc(mk::integer) DATA(i + mi, j, k + mk) end proc) - end proc) -end proc - -> deriv_3d_dyz_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mj::integer) -> dx_5point( -> proc(mk::integer) DATA(i,j+mj,k+mk) end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dyz_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mj::integer) - dx_5point(proc(mk::integer) DATA(i, j + mj, k + mk) end proc) - end proc) -end proc - -> deriv_3d_dxyz_5point := proc(i::integer, j::integer, k::integer) -> dx_5point( -> proc(mi::integer) -> dx_5point( -> proc(mj::integer) -> dx_5point( -> proc(mk::integer) -> DATA(i+mi,j+mj,k+mk) -> end proc -> ) -> end proc -> ) -> end proc -> ) -> end proc; -deriv_3d_dxyz_5point := proc(i::integer, j::integer, k::integer) - dx_5point(proc(mi::integer) - dx_5point(proc(mj::integer) - dx_5point( - proc(mk::integer) DATA(i + mi, j + mj, k + mk) end proc) - end proc) - end proc) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -# 2d.maple -- compute Hermite interpolation coefficients in 2-D -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Hermite/2d.maple,v 1.2 2002/09/01 18:33:34 jthorn Exp $ -> -################################################################################ -> -# -# 2d, cube, polynomial order=3, derivatives via 3-point order=2 formula -# ==> overall order=2, 4-point molecule -# -> -# interpolating polynomial -> interp_2d_cube_order2 -> := Hermite_polynomial_interpolant(fn_2d_order3, -> coeffs_set_2d_order3, -> [x,y], -> { -> {x} = deriv_2d_dx_3point, -> {y} = deriv_2d_dy_3point, -> {x,y} = deriv_2d_dxy_3point -> }, -> {op(posn_list_2d_size2)}, -> {op(posn_list_2d_size2)}); -bytes used=1000484, alloc=917336, time=0.10 -bytes used=2000792, alloc=1376004, time=0.18 -interp_2d_cube_order2 := - - 3 - (- 1/2 DATA(0, -1) - 3/2 DATA(0, 1) + 3/2 DATA(0, 0) + 1/2 DATA(0, 2)) y - - + (1/4 DATA(-1, -1) + 3/4 DATA(-1, 1) - 1/4 DATA(1, -1) - 3/4 DATA(1, 1) - - - 3/4 DATA(-1, 0) - 1/4 DATA(-1, 2) + 3/4 DATA(1, 0) + 1/4 DATA(1, 2)) x - - 3 - y + (- 15/4 DATA(0, 0) - 3 DATA(1, 1) + 15/4 DATA(0, 1) + 3 DATA(1, 0) - - + 1/4 DATA(2, -1) + 3/4 DATA(2, 1) - DATA(1, -1) - 1/2 DATA(-1, -1) - - - 3/2 DATA(-1, 1) + 3/2 DATA(-1, 0) - 3/4 DATA(2, 0) - 1/4 DATA(2, 2) - - 2 3 - + 1/2 DATA(-1, 2) + 5/4 DATA(0, -1) - 5/4 DATA(0, 2) + DATA(1, 2)) x y - - + (9/4 DATA(0, 0) + 9/4 DATA(1, 1) - 9/4 DATA(0, 1) - 9/4 DATA(1, 0) - - - 1/4 DATA(2, -1) - 3/4 DATA(2, 1) + 3/4 DATA(1, -1) + 1/4 DATA(-1, -1) - - + 3/4 DATA(-1, 1) - 3/4 DATA(-1, 0) + 3/4 DATA(2, 0) + 1/4 DATA(2, 2) - - 3 - - 1/4 DATA(-1, 2) - 3/4 DATA(0, -1) + 3/4 DATA(0, 2) - 3/4 DATA(1, 2)) x - - 3 2 - y + (DATA(0, -1) + 2 DATA(0, 1) - 5/2 DATA(0, 0) - 1/2 DATA(0, 2)) y + ( - - - 1/2 DATA(-1, -1) - DATA(-1, 1) + 1/2 DATA(1, -1) + DATA(1, 1) - - + 5/4 DATA(-1, 0) + 1/4 DATA(-1, 2) - 5/4 DATA(1, 0) - 1/4 DATA(1, 2)) x - - 2 - y + (25/4 DATA(0, 0) + 4 DATA(1, 1) - 5 DATA(0, 1) - 5 DATA(1, 0) - - - 1/2 DATA(2, -1) - DATA(2, 1) + 2 DATA(1, -1) + DATA(-1, -1) - - + 2 DATA(-1, 1) - 5/2 DATA(-1, 0) + 5/4 DATA(2, 0) + 1/4 DATA(2, 2) - - 2 2 - - 1/2 DATA(-1, 2) - 5/2 DATA(0, -1) + 5/4 DATA(0, 2) - DATA(1, 2)) x y - - + (- 15/4 DATA(0, 0) - 3 DATA(1, 1) + 3 DATA(0, 1) + 15/4 DATA(1, 0) - - + 1/2 DATA(2, -1) + DATA(2, 1) - 3/2 DATA(1, -1) - 1/2 DATA(-1, -1) - - - DATA(-1, 1) + 5/4 DATA(-1, 0) - 5/4 DATA(2, 0) - 1/4 DATA(2, 2) - - 3 - + 1/4 DATA(-1, 2) + 3/2 DATA(0, -1) - 3/4 DATA(0, 2) + 3/4 DATA(1, 2)) x - - 2 - 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 - - + (- 1/2 DATA(-1, -1) + 1/2 DATA(-1, 1) - DATA(1, -1) + DATA(1, 1) - - 2 - + 5/4 DATA(0, -1) - 5/4 DATA(0, 1) + 1/4 DATA(2, -1) - 1/4 DATA(2, 1)) x - - y + (- 3/4 DATA(0, -1) + 3/4 DATA(0, 1) + 1/4 DATA(-1, -1) - - - 1/4 DATA(-1, 1) + 3/4 DATA(1, -1) - 3/4 DATA(1, 1) - 1/4 DATA(2, -1) - - 3 - + 1/4 DATA(2, 1)) x y + DATA(0, 0) - - + (- 1/2 DATA(-1, 0) + 1/2 DATA(1, 0)) x - - 2 - + (DATA(-1, 0) + 2 DATA(1, 0) - 5/2 DATA(0, 0) - 1/2 DATA(2, 0)) x - - 3 - + (3/2 DATA(0, 0) - 1/2 DATA(-1, 0) - 3/2 DATA(1, 0) + 1/2 DATA(2, 0)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=3001112, alloc=1507052, time=0.24 - 3 2 2 3 3 -[COEFF(-1, -1) = 1/4 x y - 1/2 x y - 1/2 x y + 1/4 x y + 1/4 x y - - 2 3 2 3 3 2 2 3 2 - - 1/2 x y - 1/2 x y + 1/4 x y + x y , COEFF(0, -1) = - 1/2 y + y - - 2 3 2 3 2 2 2 3 3 - + 5/4 x y + 5/4 x y + 3/2 x y - 5/2 x y - 3/4 x y - 1/2 y - - 3 2 3 3 3 2 - - 3/4 x y, COEFF(1, -1) = -x y + 3/4 x y + 3/4 x y + 1/2 x y - - 3 2 3 3 2 2 2 - - 1/4 x y - x y - 3/2 x y - 1/4 x y + 2 x y , COEFF(2, -1) = - - 2 3 2 2 2 3 2 3 3 3 - 1/4 x y - 1/2 x y + 1/4 x y + 1/2 x y - 1/4 x y - 1/4 x y, - - 3 2 2 3 3 3 2 2 2 - COEFF(-1, 0) = - 3/4 x y + x + 3/2 x y - 1/2 x + 5/4 x y - 5/2 x y - - 3 3 2 3 3 3 2 - - 3/4 x y + 5/4 x y - 1/2 x, COEFF(0, 0) = 9/4 x y + 3/2 y - 5/2 x - - 2 2 2 2 3 3 2 3 - - 5/2 y + 25/4 x y - 15/4 x y + 1 - 15/4 x y + 3/2 x , COEFF(1, 0) - - 3 2 3 2 2 2 3 2 3 3 - = 15/4 x y - 3/2 x - 5 x y - 5/4 x y + 3/4 x y + 2 x - 9/4 x y - - 2 3 - + 1/2 x + 3 x y , COEFF(2, 0) = - - 2 3 2 2 3 2 3 2 3 3 - - 3/4 x y + 5/4 x y + 1/2 x - 1/2 x - 5/4 x y + 3/4 x y , - - 3 2 2 3 3 3 2 2 2 2 - COEFF(-1, 1) = -x y - 3/2 x y + 3/4 x y - x y + 1/2 x y + 2 x y - - 3 3 3 3 2 - + 3/4 x y - 1/4 x y - 1/4 x y, COEFF(0, 1) = - 3/2 y + 3 x y - - 2 2 3 3 3 3 2 2 2 - - 5/4 x y + 15/4 x y + 3/4 x y - 9/4 x y + 1/2 y + 2 y - 5 x y , - - 2 3 2 2 3 3 3 3 2 - COEFF(1, 1) = -3 x y + 4 x y - 3/4 x y + 9/4 x y - 3 x y - - 3 2 2 - - 3/4 x y + x y + x y + 1/4 x y, - - 3 3 3 2 3 2 2 2 3 2 - COEFF(2, 1) = - 3/4 x y + 1/4 x y + 3/4 x y - 1/4 x y - x y + x y - - , COEFF(-1, 2) = - - 2 3 3 3 2 2 3 3 2 2 - 1/2 x y - 1/4 x y - 1/2 x y - 1/4 x y + 1/4 x y + 1/4 x y , - - COEFF(0, 2) = - - 3 2 3 2 2 3 3 3 2 2 - 1/2 y - 5/4 x y + 5/4 x y + 3/4 x y - 3/4 x y - 1/2 y , - - 3 3 2 3 3 3 2 2 2 2 - COEFF(1, 2) = - 3/4 x y + x y + 1/4 x y + 3/4 x y - 1/4 x y - x y - - 3 3 2 3 2 2 3 2 - , COEFF(2, 2) = 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/coeffs-I.compute.c"); -bytes used=4001272, alloc=1572576, time=0.30 -bytes used=5003880, alloc=1638100, time=0.35 -bytes used=6004196, alloc=1703624, time=0.41 -bytes used=7004508, alloc=1769148, time=0.47 -bytes used=8004988, alloc=1769148, time=0.54 -bytes used=9005768, alloc=1769148, time=0.62 -bytes used=10011040, alloc=1834672, time=0.69 -bytes used=11011304, alloc=1834672, time=0.77 -bytes used=12011544, alloc=1834672, time=0.85 -bytes used=13011832, alloc=1834672, time=0.92 -> -# d/dx -> simplify( diff(interp_2d_cube_order2,x) ); -bytes used=14012040, alloc=1900196, time=0.99 -bytes used=15012196, alloc=1965720, time=1.05 - 2 2 2 3 -9 x y DATA(0, 1) + 1/2 DATA(1, 0) - 9/4 x y DATA(-1, 0) - - 2 3 2 3 2 3 - + 9/4 x y DATA(2, 0) + 3/4 x y DATA(2, 2) - 3/4 x y DATA(-1, 2) - - 2 3 2 3 3 - - 9/4 x y DATA(0, -1) + 9/4 x y DATA(0, 2) - 6 x y DATA(1, 1) - - 3 3 3 - + 15/2 x y DATA(0, 1) + 6 x y DATA(1, 0) + 1/2 x y DATA(2, -1) - - 3 3 3 - + 3/2 x y DATA(2, 1) - 2 x y DATA(1, -1) - x y DATA(-1, -1) - - 3 3 3 - - 3 x y DATA(-1, 1) + 3 x y DATA(-1, 0) - 3/2 x y DATA(2, 0) - - 2 3 2 3 2 3 - - 9/4 x y DATA(2, 1) + 9/4 x y DATA(1, -1) + 3/4 x y DATA(-1, -1) - - 2 3 3 3 - + 9/4 x y DATA(-1, 1) + 5/2 x y DATA(0, -1) - 5/2 x y DATA(0, 2) - - 3 2 3 2 3 - + 2 x y DATA(1, 2) - 27/4 x y DATA(1, 0) - 3/4 x y DATA(2, -1) - - 2 2 2 2 2 - - 2 x y DATA(1, 2) + 45/4 x y DATA(1, 0) + 3/2 x y DATA(2, -1) - - 3 3 2 - - 1/2 x y DATA(2, 2) + x y DATA(-1, 2) + 4 x y DATA(1, -1) - - 2 2 2 - + 2 x y DATA(-1, -1) + 4 x y DATA(-1, 1) - 5 x y DATA(-1, 0) - - 2 2 2 - + 5/2 x y DATA(2, 0) + 1/2 x y DATA(2, 2) - x y DATA(-1, 2) - - 2 2 2 - - 5 x y DATA(0, -1) + 5/2 x y DATA(0, 2) - 3/4 x y DATA(2, -1) - - 2 2 3 2 - + 3/4 x y DATA(2, 1) - 9/4 x y DATA(1, 2) - 10 x y DATA(0, 1) - - 2 2 2 - - 10 x y DATA(1, 0) - x y DATA(2, -1) - 2 x y DATA(2, 1) - - 2 2 - - 1/2 x y DATA(2, 1) + 9/4 x y DATA(0, 1) + 3/4 x y DATA(-1, -1) - - 2 2 2 - - 3/4 x y DATA(-1, 1) + 9/4 x y DATA(1, -1) - 9/4 x y DATA(1, 1) - - 2 2 - - 5/2 x y DATA(0, 1) + 1/2 x y DATA(2, -1) - 9/4 x y DATA(0, 2) - - 2 2 - + 9/4 x y DATA(1, 2) + 2 x y DATA(1, 1) + 5/2 x y DATA(0, -1) - - 2 2 2 2 2 2 - + 3 x y DATA(2, 1) - 9/2 x y DATA(1, -1) - 3/2 x y DATA(-1, -1) - - 2 2 2 2 2 2 - - 3 x y DATA(-1, 1) + 15/4 x y DATA(-1, 0) - 15/4 x y DATA(2, 0) - - 2 2 2 2 2 2 - - 3/4 x y DATA(2, 2) + 3/4 x y DATA(-1, 2) + 9/2 x y DATA(0, -1) - - 3 2 3 2 3 - - 15/2 x y DATA(0, 0) - 27/4 x y DATA(0, 1) + 27/4 x y DATA(1, 1) - - 2 3 2 - + 27/4 x y DATA(0, 0) - 2 x y DATA(1, -1) - 9/4 x y DATA(0, -1) - - 2 2 - - 1/2 DATA(-1, 0) + 8 x y DATA(1, 1) + 25/2 x y DATA(0, 0) - - 2 2 - - 9 x y DATA(1, 1) + x y DATA(-1, 1) - x y DATA(-1, -1) - - 3 3 2 - - 3/4 y DATA(1, 1) - 3/4 y DATA(-1, 0) + y DATA(1, 1) - - 2 2 2 - - 1/2 y DATA(-1, -1) + 5/4 y DATA(-1, 0) - 1/4 y DATA(1, 2) - - 2 2 - - y DATA(-1, 1) + 1/2 y DATA(1, -1) - 1/4 y DATA(1, -1) - - 2 2 - + 1/4 y DATA(1, 1) + 1/4 y DATA(-1, 2) - 5/4 y DATA(1, 0) - - 2 2 - - 45/4 x y DATA(0, 0) - 5 x DATA(0, 0) + 1/4 y DATA(-1, -1) - - 2 - - 1/4 y DATA(-1, 1) - x DATA(2, 0) + 9/2 x DATA(0, 0) + 2 x DATA(-1, 0) - - 3 2 - + 4 x DATA(1, 0) + 3/4 y DATA(-1, 1) - 3/2 x DATA(-1, 0) - - 2 2 3 - + 3/2 x DATA(2, 0) - 9/2 x DATA(1, 0) - 1/4 y DATA(-1, 2) - - 3 3 3 - + 3/4 y DATA(1, 0) + 1/4 y DATA(1, 2) + 1/4 y DATA(-1, -1) - - 3 - - 1/4 y DATA(1, -1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 2 2 2 3 2 2 3 -[COEFF(-1, -1) = - 3/2 x y + 3/4 x y - x y + 2 x y + 3/4 x y + 1/4 y - - 3 2 - + 1/4 y - x y - 1/2 y , COEFF(0, -1) = - - 2 2 2 2 3 2 3 - - 9/4 x y + 9/2 x y - 5 x y + 5/2 x y - 9/4 x y + 5/2 x y, - - 2 2 3 2 3 - COEFF(1, -1) = 4 x y + 1/2 y - 1/4 y - 1/4 y + 9/4 x y - 2 x y - 2 x y - - 2 2 2 3 - - 9/2 x y + 9/4 x y , COEFF(2, -1) = - - 2 2 2 3 3 2 2 - -x y - 3/4 x y - 3/4 x y + 1/2 x y + 3/2 x y + 1/2 x y, COEFF(-1, 0) - - 2 2 3 2 3 2 2 2 - = 2 x - 5 x y - 3/2 x + 3 x y - 1/2 - 9/4 x y + 15/4 x y + 5/4 y - - 3 - - 3/4 y , COEFF(0, 0) = - - 3 2 3 2 2 2 2 - - 15/2 x y - 5 x + 27/4 x y + 25/2 x y + 9/2 x - 45/4 x y , - - 2 2 2 2 3 3 2 - COEFF(1, 0) = - 5/4 y + 45/4 x y - 27/4 x y + 4 x + 6 x y - 10 x y - - 3 2 - + 3/4 y + 1/2 - 9/2 x , - - 2 2 2 2 3 3 2 - COEFF(2, 0) = 3/2 x - 15/4 x y + 9/4 x y - 3/2 x y + 5/2 x y - x, - - 2 3 2 3 2 3 - COEFF(-1, 1) = x y - 1/4 y + 9/4 x y - y + 3/4 y - 3/4 x y - 3 x y - - 2 2 2 - + 4 x y - 3 x y , COEFF(0, 1) = - - 2 3 3 2 2 2 2 - - 27/4 x y - 5/2 x y + 15/2 x y + 9/4 x y + 9 x y - 10 x y , - - 2 2 2 2 2 3 3 - COEFF(1, 1) = 8 x y + y + 1/4 y - 9 x y + 2 x y + 27/4 x y - 6 x y - - 2 3 - - 9/4 x y - 3/4 y , - - 2 2 2 2 3 2 3 - COEFF(2, 1) = 3 x y + 3/4 x y - 2 x y + 3/2 x y - 9/4 x y - 1/2 x y, - - 2 2 3 2 3 3 2 2 - COEFF(-1, 2) = 3/4 x y + x y - 3/4 x y - 1/4 y - x y + 1/4 y , - - 2 2 2 2 3 3 - COEFF(0, 2) = - 9/4 x y + 5/2 x y + 9/4 x y - 5/2 x y , - - 2 3 2 3 2 3 2 2 - COEFF(1, 2) = -2 x y + 1/4 y - 9/4 x y - 1/4 y + 2 x y + 9/4 x y , - - 2 2 3 3 2 2 - COEFF(2, 2) = 1/2 x y + 3/4 x y - 1/2 x y - 3/4 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2/coeffs-dx.compute.c"); -bytes used=16012348, alloc=2096768, time=1.13 -bytes used=17014736, alloc=2096768, time=1.19 -bytes used=18015700, alloc=2096768, time=1.27 -bytes used=19015872, alloc=2096768, time=1.35 -bytes used=20016312, alloc=2096768, time=1.42 -bytes used=21016692, alloc=2096768, time=1.50 -bytes used=22016864, alloc=2096768, time=1.57 -bytes used=23017148, alloc=2096768, time=1.67 -> -# d/dy -> simplify( diff(interp_2d_cube_order2,y) ); -bytes used=24017500, alloc=2096768, time=1.75 - 2 2 2 -45/4 x y DATA(0, 1) + 1/2 DATA(0, 1) + 3/4 x y DATA(1, 2) - - 2 2 2 2 2 - + 9 x y DATA(1, 0) + 3/4 x y DATA(2, -1) - 3/4 x y DATA(1, -1) - - 2 2 2 - + 3/4 x y DATA(-1, -1) + 9/4 x y DATA(-1, 1) - 9/4 x y DATA(-1, 0) - - 2 2 2 - - 3/4 x y DATA(-1, 2) + 25/2 x y DATA(0, 0) - 10 x y DATA(1, 0) - - 2 2 2 - - 5 x y DATA(-1, 0) + 5/2 x y DATA(2, 0) + 1/2 x y DATA(2, 2) - - 2 2 - - x y DATA(-1, 2) + 1/4 x DATA(1, 1) - 1/2 x DATA(-1, -1) - - 2 2 2 2 - + 1/2 x DATA(-1, 1) - x DATA(1, -1) + x DATA(1, 1) + 5/4 x DATA(0, -1) - - 2 2 2 - - 5/4 x DATA(0, 1) + 1/4 x DATA(2, -1) - 1/4 x DATA(2, 1) - - 3 3 3 - - 3/4 x DATA(0, -1) + 3/4 x DATA(0, 1) + 1/4 x DATA(-1, -1) - - 3 3 3 - - 1/4 x DATA(-1, 1) + 3/4 x DATA(1, -1) - 3/4 x DATA(1, 1) - - 3 3 2 - - 1/4 x DATA(2, -1) + 1/4 x DATA(2, 1) - x y DATA(2, -1) - - 2 3 3 - - 2 x y DATA(2, 1) + 5/2 x y DATA(-1, 0) - 1/2 x y DATA(2, 2) - - 3 3 3 - + 1/2 x y DATA(-1, 2) + 3 x y DATA(0, -1) - 3/2 x y DATA(0, 2) - - 3 3 2 - + 3/2 x y DATA(1, 2) - 5/2 x y DATA(2, 0) + 5/2 x y DATA(0, 2) - - 2 3 3 - - 2 x y DATA(1, 2) - 15/2 x y DATA(0, 0) - 6 x y DATA(1, 1) - - 3 3 3 - + 6 x y DATA(0, 1) + 15/2 x y DATA(1, 0) + x y DATA(2, -1) - - 3 3 3 - + 2 x y DATA(2, 1) - 3 x y DATA(1, -1) - x y DATA(-1, -1) - - 3 - - 2 x y DATA(-1, 1) + 5/2 x y DATA(-1, 0) + 1/2 x y DATA(-1, 2) - - 2 - - 5/2 x y DATA(1, 0) - 1/2 x y DATA(1, 2) + 9/4 x y DATA(1, 0) - - 3 2 3 2 3 2 - + 27/4 x y DATA(0, 0) + 27/4 x y DATA(1, 1) - 27/4 x y DATA(0, 1) - - 3 2 3 2 3 2 - - 27/4 x y DATA(1, 0) - 3/4 x y DATA(2, -1) - 9/4 x y DATA(2, 1) - - 3 2 3 2 3 2 - + 9/4 x y DATA(1, -1) + 3/4 x y DATA(-1, -1) + 9/4 x y DATA(-1, 1) - - 3 2 3 2 3 2 - - 9/4 x y DATA(-1, 0) + 9/4 x y DATA(2, 0) + 3/4 x y DATA(2, 2) - - 3 2 3 2 3 2 - - 3/4 x y DATA(-1, 2) - 9/4 x y DATA(0, -1) + 9/4 x y DATA(0, 2) - - 3 2 2 2 - - 9/4 x y DATA(1, 2) + 9/2 y DATA(0, 0) + 3/2 y DATA(0, 2) - - 2 - - 3/2 y DATA(0, -1) + 2 y DATA(0, -1) + 4 y DATA(0, 1) - 5 y DATA(0, 0) - - 2 - - y DATA(0, 2) - 9/2 y DATA(0, 1) + 1/4 x DATA(-1, -1) - - 2 - - 1/4 x DATA(-1, 1) - 1/4 x DATA(1, -1) - 10 x y DATA(0, 1) - - 2 2 2 - + 2 x y DATA(-1, -1) + 4 x y DATA(-1, 1) + 4 x y DATA(1, -1) - - 2 2 2 2 2 - + 8 x y DATA(1, 1) - 15/4 x y DATA(0, 2) + 3 x y DATA(1, 2) - - 2 2 2 2 - + 2 x y DATA(1, 1) + 9/4 x y DATA(2, 1) - 3 x y DATA(1, -1) - - 2 2 2 2 2 2 - - 3/2 x y DATA(-1, -1) - 9/2 x y DATA(-1, 1) + 9/2 x y DATA(-1, 0) - - 2 2 2 2 2 2 - - 9/4 x y DATA(2, 0) - 3/4 x y DATA(2, 2) + 3/2 x y DATA(-1, 2) - - 2 2 2 - + 15/4 x y DATA(0, -1) + x y DATA(1, -1) - 5 x y DATA(0, -1) - - 2 2 2 - - 1/2 DATA(0, -1) - 9/4 x y DATA(1, 1) - 9 x y DATA(1, 1) - - 2 2 - - 2 x y DATA(-1, 1) - x y DATA(-1, -1) - 45/4 x y DATA(0, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=25017764, alloc=2096768, time=1.81 - 2 3 2 2 2 3 2 -[COEFF(-1, -1) = 2 x y + 1/4 x - 1/2 x - 3/2 x y + 1/4 x + 3/4 x y - - 2 3 2 2 2 3 - + 3/4 x y - x y - x y, COEFF(0, -1) = 2 y - 5 x y + 15/4 x y - 3/4 x - - 3 2 3 2 2 - - 9/4 x y + 3 x y - 1/2 - 3/2 y + 5/4 x , COEFF(1, -1) = - 1/4 x + x y - - 2 2 2 3 2 2 3 2 3 - + 4 x y - 3 x y - 3 x y - x - 3/4 x y + 9/4 x y + 3/4 x , - - 3 2 2 3 3 2 2 2 - COEFF(2, -1) = - 3/4 x y + 1/4 x - 1/4 x + x y - x y + 3/4 x y , - - COEFF(-1, 0) = - - 3 2 2 2 2 3 2 - 5/2 x y - 9/4 x y + 9/2 x y - 5 x y - 9/4 x y + 5/2 x y, COEFF(0, 0) - - 2 3 2 3 2 2 2 - = 9/2 y + 27/4 x y - 15/2 x y + 25/2 x y - 5 y - 45/4 x y , - - COEFF(1, 0) = - - 3 3 2 2 2 2 2 - 15/2 x y - 5/2 x y - 27/4 x y + 9/4 x y - 10 x y + 9 x y , - - 2 3 3 2 2 2 - COEFF(2, 0) = 5/2 x y - 5/2 x y + 9/4 x y - 9/4 x y , COEFF(-1, 1) = - - 2 3 2 3 3 2 2 - 4 x y + 9/4 x y - 1/4 x - 2 x y + 9/4 x y + 1/2 x - 1/4 x - - 2 2 2 3 2 3 3 - - 9/2 x y - 2 x y, COEFF(0, 1) = - 9/2 y - 27/4 x y + 3/4 x + 6 x y - - 2 2 2 2 3 - + 45/4 x y + 4 y - 10 x y + 1/2 - 5/4 x , COEFF(1, 1) = -6 x y - - 2 2 3 2 3 2 2 2 - - 9 x y - 3/4 x + 2 x y - 9/4 x y + 27/4 x y + 1/4 x + 8 x y + x , - - 3 2 3 2 2 2 2 3 - COEFF(2, 1) = 2 x y - 1/4 x - 9/4 x y - 2 x y + 9/4 x y + 1/4 x , - - 2 2 3 2 3 2 2 - COEFF(-1, 2) = 1/2 x y + 3/2 x y + 1/2 x y - 3/4 x y - 3/4 x y - x y - - 3 2 2 2 2 3 2 - , COEFF(0, 2) = 9/4 x y + 3/2 y - 15/4 x y - y - 3/2 x y + 5/2 x y, - - 2 2 3 2 2 2 3 - COEFF(1, 2) = 3 x y - 1/2 x y - 9/4 x y - 2 x y + 3/4 x y + 3/2 x y, - - 3 2 3 2 2 2 - COEFF(2, 2) = - 1/2 x y + 1/2 x y + 3/4 x y - 3/4 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2/coeffs-dy.compute.c"); -bytes used=26018428, alloc=2096768, time=1.90 -bytes used=27018688, alloc=2096768, time=1.96 -bytes used=28018936, alloc=2096768, time=2.03 -bytes used=29019200, alloc=2096768, time=2.12 -bytes used=30019840, alloc=2096768, time=2.20 -bytes used=31020164, alloc=2096768, time=2.29 -bytes used=32020368, alloc=2096768, time=2.39 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order2,x,x) ); -bytes used=33020816, alloc=2096768, time=2.51 - 3 -- 27/2 x y DATA(1, 0) + 9/2 x y DATA(0, 1) - 3/2 x y DATA(2, -1) - - 3 3 - + 3/2 x y DATA(2, 1) + 27/2 x y DATA(0, 0) + 27/2 x y DATA(1, 1) - - 3 3 3 - - 27/2 x y DATA(0, 1) - 9/2 x y DATA(2, 1) + 9/2 x y DATA(1, -1) - - 3 3 3 - + 3/2 x y DATA(-1, -1) + 9/2 x y DATA(-1, 1) - 9/2 x y DATA(-1, 0) - - 3 3 3 - + 3/2 x y DATA(2, 2) - 3/2 x y DATA(-1, 2) - 9/2 x y DATA(0, -1) - - 3 3 2 - + 9/2 x y DATA(0, 2) - 9/2 x y DATA(1, 2) - 45/2 x y DATA(0, 0) - - 2 2 2 - + 18 x y DATA(0, 1) + 3 x y DATA(2, -1) + 6 x y DATA(2, 1) - - 2 2 2 - - 15/2 x y DATA(2, 0) - 3/2 x y DATA(2, 2) + 9 x y DATA(0, -1) - - 2 3 - - 9/2 x y DATA(0, 2) - 9/2 x y DATA(0, -1) + 9/2 x y DATA(2, 0) - - 3 2 - - 3/2 x y DATA(2, -1) - 5 DATA(0, 0) + 4 DATA(1, 0) + 9/2 x y DATA(1, 2) - - 2 2 2 - - y DATA(2, -1) - 2 y DATA(2, 1) - 9 x y DATA(1, -1) - - 2 2 2 - - 3 x y DATA(-1, -1) + 4 y DATA(1, -1) + 2 y DATA(-1, -1) - - 2 2 2 - - 6 x y DATA(-1, 1) + 15/2 x y DATA(-1, 0) + 3/2 x y DATA(-1, 2) - - 2 2 - + 4 y DATA(-1, 1) - 5 y DATA(-1, 0) + 2 y DATA(1, 1) + 1/2 y DATA(2, -1) - - 2 - + 45/2 x y DATA(1, 0) - 1/2 y DATA(2, 1) - y DATA(-1, -1) - - 2 2 2 - + 25/2 y DATA(0, 0) + 5/2 y DATA(0, 2) - 5 y DATA(0, -1) - - 2 - + 5/2 y DATA(0, -1) - 5/2 y DATA(0, 1) - 10 y DATA(0, 1) - - 2 2 2 2 - + 8 y DATA(1, 1) - 10 y DATA(1, 0) - 2 y DATA(1, 2) - y DATA(-1, 2) - - 2 2 - - 9 x DATA(1, 0) + 3 x DATA(2, 0) + 1/2 y DATA(2, 2) + 5/2 y DATA(2, 0) - - 3 - + 9 x DATA(0, 0) + y DATA(-1, 1) - 2 y DATA(1, -1) + y DATA(-1, 2) - - 3 3 3 - - 1/2 y DATA(2, 2) - 3/2 y DATA(2, 0) + 3 y DATA(-1, 0) - - 3 3 3 - - 3 y DATA(-1, 1) - y DATA(-1, -1) - 2 y DATA(1, -1) - - 3 3 - + 3/2 y DATA(2, 1) - 3 x DATA(-1, 0) - 6 y DATA(1, 1) - - 3 3 - - 15/2 y DATA(0, 0) + 2 y DATA(1, 2) - 9/2 x y DATA(1, 1) - - 3 3 3 - - 5/2 y DATA(0, 2) + 5/2 y DATA(0, -1) + 1/2 y DATA(2, -1) - - 3 3 - + 6 y DATA(1, 0) + 15/2 y DATA(0, 1) + 9/2 x y DATA(1, -1) - - 2 - + 2 DATA(-1, 0) - DATA(2, 0) - 18 x y DATA(1, 1) - 3/2 x y DATA(-1, 1) - - + 3/2 x y DATA(-1, -1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=34021072, alloc=2096768, time=2.56 - 3 2 2 3 -[COEFF(-1, -1) = 3/2 x y - y + 3/2 x y + 2 y - 3 x y - y , - - 2 3 2 3 - COEFF(0, -1) = -5 y + 5/2 y + 5/2 y + 9 x y - 9/2 x y - 9/2 x y , - - 2 2 3 3 - COEFF(1, -1) = -9 x y - 2 y + 4 y + 9/2 x y + 9/2 x y - 2 y , - - 2 3 2 3 - COEFF(2, -1) = - 3/2 x y + 3 x y + 1/2 y - 3/2 x y - y + 1/2 y , - - 3 2 2 3 - COEFF(-1, 0) = -3 x + 3 y + 2 + 15/2 x y - 5 y - 9/2 x y , - - 3 2 3 2 - COEFF(0, 0) = -5 + 9 x - 15/2 y + 25/2 y + 27/2 x y - 45/2 x y , - - 2 3 2 3 - COEFF(1, 0) = 45/2 x y + 4 - 27/2 x y - 9 x - 10 y + 6 y , - - 2 3 3 2 - COEFF(2, 0) = - 15/2 x y - 1 - 3/2 y + 3 x + 9/2 x y + 5/2 y , - - 3 2 3 2 - COEFF(-1, 1) = 9/2 x y + y - 6 x y - 3 y - 3/2 x y + 4 y , - - 3 2 2 3 - COEFF(0, 1) = - 27/2 x y + 18 x y - 5/2 y + 9/2 x y - 10 y + 15/2 y , - - 2 2 3 3 - COEFF(1, 1) = 8 y - 9/2 x y - 18 x y + 2 y + 27/2 x y - 6 y , - - 3 2 2 3 - COEFF(2, 1) = 3/2 x y - 1/2 y + 3/2 y - 2 y + 6 x y - 9/2 x y , - - 2 3 2 3 - COEFF(-1, 2) = 3/2 x y + y - y - 3/2 x y , - - 2 3 2 3 - COEFF(0, 2) = - 9/2 x y + 9/2 x y + 5/2 y - 5/2 y , - - 3 3 2 2 - COEFF(1, 2) = 2 y - 9/2 x y - 2 y + 9/2 x y , - - 3 2 2 3 - COEFF(2, 2) = 3/2 x y + 1/2 y - 3/2 x y - 1/2 y ] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2/coeffs-dxx.compute.c"); -bytes used=35021308, alloc=2096768, time=2.64 -bytes used=36021476, alloc=2096768, time=2.71 -bytes used=37021788, alloc=2096768, time=2.81 -bytes used=38021992, alloc=2096768, time=2.91 -bytes used=39022164, alloc=2096768, time=2.99 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order2,x,y) ); -bytes used=40022344, alloc=2096768, time=3.07 --20 x y DATA(0, 1) - 2 x y DATA(2, -1) - 4 x y DATA(2, 1) - - 2 2 2 - - 45/2 x y DATA(0, 0) + 45/2 x y DATA(0, 1) + 3/2 x y DATA(2, -1) - - 2 2 2 - + 9/2 x y DATA(2, 1) - 9/2 x y DATA(2, 0) - 3/2 x y DATA(2, 2) - - 2 2 - + 15/2 x y DATA(0, -1) - 15/2 x y DATA(0, 2) - 10 x y DATA(0, -1) - - 2 2 - - 9 x y DATA(1, -1) + 1/4 DATA(1, 1) + 6 x y DATA(1, 2) - - 2 2 2 - - 6 x y DATA(1, -1) - 3 x y DATA(-1, -1) - 3/4 y DATA(1, -1) - - 2 2 2 - + 3/4 y DATA(-1, -1) - 9 x y DATA(-1, 1) + 9 x y DATA(-1, 0) - - 2 2 2 - + 3 x y DATA(-1, 2) + 9/4 y DATA(-1, 1) - 9/4 y DATA(-1, 0) - - 2 2 - + 2 y DATA(1, 1) + 18 x y DATA(1, 0) - y DATA(-1, -1) - 9/4 y DATA(1, 1) - - 2 2 2 - + 9/4 y DATA(1, 0) + 3/4 y DATA(1, 2) - 3/4 y DATA(-1, 2) - - - 2 y DATA(-1, 1) + y DATA(1, -1) + 16 x y DATA(1, 1) - - 2 2 2 - - 3 x y DATA(-1, -1) - 6 x y DATA(-1, 1) + 15/2 x y DATA(-1, 0) - - - x DATA(-1, -1) - 2 x DATA(1, -1) + 2 x DATA(1, 1) + 5/2 x DATA(0, -1) - - - 5/2 x DATA(0, 1) + x DATA(-1, 1) + 1/2 x DATA(2, -1) - 1/4 DATA(1, -1) - - + 1/4 DATA(-1, -1) - 1/4 DATA(-1, 1) + 8 x y DATA(1, -1) - - + 5 x y DATA(2, 0) - 4 x y DATA(1, 2) + 5 x y DATA(0, 2) - - - 5/2 y DATA(1, 0) - 10 x y DATA(-1, 0) - 2 x y DATA(-1, 2) - - 2 2 2 2 - + x y DATA(2, 2) + 27/4 x y DATA(0, 2) - 27/4 x y DATA(0, -1) - - 2 2 - + 25 x y DATA(0, 0) - 27/4 x y DATA(1, 2) - 20 x y DATA(1, 0) - - 2 2 2 2 2 2 - + 27/4 x y DATA(1, -1) - 9/4 x y DATA(-1, 2) + 9/4 x y DATA(2, 2) - - 2 2 2 2 2 2 - + 27/4 x y DATA(2, 0) - 27/4 x y DATA(2, 1) + 81/4 x y DATA(0, 0) - - 2 2 2 2 2 2 - - 9/4 x y DATA(2, -1) - 81/4 x y DATA(1, 0) - 81/4 x y DATA(0, 1) - - 2 2 2 2 2 2 - + 81/4 x y DATA(1, 1) - 27/4 x y DATA(-1, 0) + 27/4 x y DATA(-1, 1) - - 2 2 - + 9/4 x y DATA(-1, -1) + 1/2 y DATA(-1, 2) + 5/2 y DATA(-1, 0) - - 2 2 - - 1/2 y DATA(1, 2) + 18 x y DATA(0, 1) + 45/2 x y DATA(1, 0) - - 2 2 2 - + 3 x y DATA(2, -1) + 6 x y DATA(2, 1) - 9/2 x y DATA(0, 2) - - 2 2 2 - + 9/2 x y DATA(1, 2) - 45/2 x y DATA(0, 0) - 18 x y DATA(1, 1) - - 2 2 2 - - 15/2 x y DATA(2, 0) - 3/2 x y DATA(2, 2) + 3/2 x y DATA(-1, 2) - - 2 2 2 - + 9 x y DATA(0, -1) - 9/4 x DATA(0, -1) + 9/4 x DATA(0, 1) - - 2 2 2 - + 3/4 x DATA(-1, -1) - 3/4 x DATA(-1, 1) + 9/4 x DATA(1, -1) - - 2 2 2 - - 9/4 x DATA(1, 1) - 3/4 x DATA(2, -1) + 3/4 x DATA(2, 1) - - 2 - - 1/2 x DATA(2, 1) - 18 x y DATA(1, 1) + 8 x y DATA(-1, 1) - - + 4 x y DATA(-1, -1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -[COEFF(-1, -1) = - - 2 2 2 2 2 2 - 4 x y + 1/4 - 3 x y + 3/4 x + 9/4 x y - 3 x y - x - y + 3/4 y , - - 2 2 2 2 2 - COEFF(0, -1) = -10 x y + 9 x y + 5/2 x - 9/4 x - 27/4 x y + 15/2 x y , - - COEFF(1, -1) = - - 2 2 2 2 2 2 - 8 x y - 2 x - 9 x y + y + 27/4 x y + 9/4 x - 1/4 - 6 x y - 3/4 y , - - 2 2 2 2 2 - COEFF(2, -1) = 3/2 x y - 9/4 x y + 1/2 x - 2 x y - 3/4 x + 3 x y, - - 2 2 2 2 2 - COEFF(-1, 0) = 9 x y + 15/2 x y - 10 x y - 27/4 x y + 5/2 y - 9/4 y , - - 2 2 2 2 - COEFF(0, 0) = 81/4 x y + 25 x y - 45/2 x y - 45/2 x y , - - 2 2 2 2 2 - COEFF(1, 0) = 45/2 x y + 18 x y + 9/4 y - 81/4 x y - 20 x y - 5/2 y, - - 2 2 2 2 - COEFF(2, 0) = - 15/2 x y - 9/2 x y + 5 x y + 27/4 x y , COEFF(-1, 1) = - - 2 2 2 2 2 2 - -2 y + 27/4 x y + 9/4 y - 9 x y + x + 8 x y - 1/4 - 3/4 x - 6 x y, - - 2 2 2 2 2 - COEFF(0, 1) = - 81/4 x y + 9/4 x + 18 x y + 45/2 x y - 20 x y - 5/2 x, - - 2 2 2 2 - COEFF(1, 1) = - 9/4 y - 18 x y + 1/4 - 9/4 x - 18 x y + 2 y - - 2 2 - + 81/4 x y + 16 x y + 2 x, - - 2 2 2 2 2 - COEFF(2, 1) = - 27/4 x y + 6 x y + 3/4 x - 1/2 x + 9/2 x y - 4 x y, - - 2 2 2 2 2 - COEFF(-1, 2) = 3/2 x y + 1/2 y + 3 x y - 3/4 y - 9/4 x y - 2 x y, - - 2 2 2 2 - COEFF(0, 2) = 5 x y - 9/2 x y + 27/4 x y - 15/2 x y , - - 2 2 2 2 2 - COEFF(1, 2) = - 1/2 y - 27/4 x y + 6 x y + 3/4 y + 9/2 x y - 4 x y, - - 2 2 2 2 - COEFF(2, 2) = x y + 9/4 x y - 3/2 x y - 3/2 x y] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2/coeffs-dxy.compute.c"); -bytes used=41022772, alloc=2096768, time=3.14 -bytes used=42026380, alloc=2096768, time=3.22 -bytes used=43026852, alloc=2096768, time=3.30 -bytes used=44027040, alloc=2096768, time=3.41 -bytes used=45027196, alloc=2096768, time=3.49 -bytes used=46027416, alloc=2096768, time=3.59 -bytes used=47027724, alloc=2096768, time=3.70 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order2,y,y) ); -bytes used=48028176, alloc=2096768, time=3.78 - 2 --6 x y DATA(1, -1) - 5 DATA(0, 0) + 4 DATA(0, 1) - 9/2 x y DATA(1, 1) - - 2 2 2 - - 3 x y DATA(-1, -1) - 9 x y DATA(-1, 1) + 9 x y DATA(-1, 0) - - - x DATA(-1, -1) + x DATA(1, -1) + 2 x DATA(1, 1) - 2 x DATA(-1, 1) - - - 3/2 x y DATA(1, -1) + 2 DATA(0, -1) + 3/2 x y DATA(1, 2) - - - 9/2 x y DATA(-1, 0) - 3/2 x y DATA(-1, 2) + 9/2 x y DATA(1, 0) - - 2 2 2 - + 45/2 x y DATA(0, 1) + 18 x y DATA(1, 0) + 3/2 x y DATA(2, -1) - - 2 2 2 - + 9/2 x y DATA(2, 1) - 15/2 x y DATA(0, 2) + 6 x y DATA(1, 2) - - 2 2 2 - - 45/2 x y DATA(0, 0) - 18 x y DATA(1, 1) - 9/2 x y DATA(2, 0) - - 2 2 2 - - 3/2 x y DATA(2, 2) + 3 x y DATA(-1, 2) + 15/2 x y DATA(0, -1) - - 2 2 2 - - 5 x DATA(0, -1) - 10 x DATA(0, 1) + 2 x DATA(-1, -1) - - 2 2 2 2 - + 4 x DATA(-1, 1) + 4 x DATA(1, -1) + 8 x DATA(1, 1) - x DATA(2, -1) - - 2 - - 2 x DATA(2, 1) + 9/2 x y DATA(-1, 1) + 3/2 x y DATA(-1, -1) - - 3 3 3 - - DATA(0, 2) - 5/2 x DATA(2, 0) + 1/2 x DATA(-1, 2) - 1/2 x DATA(2, 2) - - 3 3 3 - + 3 x DATA(0, -1) - 3/2 x DATA(0, 2) + 3/2 x DATA(1, 2) - - 3 - + 5/2 x DATA(-1, 0) + 5/2 x DATA(-1, 0) + 1/2 x DATA(-1, 2) - - 2 - - 5/2 x DATA(1, 0) - 1/2 x DATA(1, 2) + 25/2 x DATA(0, 0) - - 2 2 2 - - 10 x DATA(1, 0) - 5 x DATA(-1, 0) + 5/2 x DATA(2, 0) - - 2 2 2 - + 1/2 x DATA(2, 2) + 5/2 x DATA(0, 2) - 2 x DATA(1, 2) - - 3 3 3 - - 15/2 x DATA(0, 0) - 6 x DATA(1, 1) + 6 x DATA(0, 1) - - 3 3 3 3 - + 15/2 x DATA(1, 0) + x DATA(2, -1) + 2 x DATA(2, 1) - 3 x DATA(1, -1) - - 3 3 - - x DATA(-1, -1) - 2 x DATA(-1, 1) - 9 y DATA(0, 1) + 9 y DATA(0, 0) - - 2 3 - + 3 y DATA(0, 2) - 3 y DATA(0, -1) - x DATA(-1, 2) - 9/2 y x DATA(2, 1) - - 3 3 3 - - 3/2 y x DATA(2, -1) - 27/2 y x DATA(1, 0) - 9/2 y x DATA(-1, 0) - - 3 3 3 - + 9/2 y x DATA(-1, 1) + 3/2 y x DATA(-1, -1) + 9/2 y x DATA(1, -1) - - 3 3 3 - - 9/2 y x DATA(1, 2) + 9/2 y x DATA(0, 2) - 9/2 y x DATA(0, -1) - - 3 3 3 - - 3/2 y x DATA(-1, 2) + 3/2 y x DATA(2, 2) + 9/2 y x DATA(2, 0) - - 3 3 3 - + 27/2 y x DATA(0, 0) - 27/2 y x DATA(0, 1) + 27/2 y x DATA(1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=49033200, alloc=2162292, time=3.85 - 3 3 2 2 -[COEFF(-1, -1) = 3/2 y x - x - 3 x y + 3/2 x y - x + 2 x , - - 3 2 2 3 - COEFF(0, -1) = - 9/2 y x + 2 - 5 x - 3 y + 15/2 x y + 3 x , - - 3 2 3 2 - COEFF(1, -1) = -3 x - 3/2 x y + x - 6 x y + 9/2 y x + 4 x , - - 2 3 3 2 - COEFF(2, -1) = 3/2 x y + x - 3/2 y x - x , - - 2 2 3 3 - COEFF(-1, 0) = -5 x + 9 x y - 9/2 y x + 5/2 x - 9/2 x y + 5/2 x , - - 3 3 2 2 - COEFF(0, 0) = 27/2 y x - 5 - 15/2 x - 45/2 x y + 9 y + 25/2 x , - - 3 2 3 2 - COEFF(1, 0) = - 5/2 x - 27/2 y x + 9/2 x y - 10 x + 15/2 x + 18 x y, - - 2 2 3 3 - COEFF(2, 0) = - 9/2 x y + 5/2 x - 5/2 x + 9/2 y x , - - 3 2 3 2 - COEFF(-1, 1) = -2 x - 9 x y - 2 x + 9/2 y x + 4 x + 9/2 x y, - - 2 3 2 3 - COEFF(0, 1) = -10 x - 9 y + 6 x + 45/2 x y - 27/2 y x + 4, - - 2 2 3 3 - COEFF(1, 1) = 8 x - 18 x y - 6 x + 27/2 y x + 2 x - 9/2 x y, - - 3 2 3 2 - COEFF(2, 1) = - 9/2 y x + 9/2 x y + 2 x - 2 x , - - 2 2 3 3 - COEFF(-1, 2) = -x + 1/2 x + 3 x y + 1/2 x - 3/2 y x - 3/2 x y, - - 2 2 3 3 - COEFF(0, 2) = 5/2 x + 3 y - 15/2 x y - 1 - 3/2 x + 9/2 y x , - - 2 3 2 3 - COEFF(1, 2) = 6 x y + 3/2 x - 2 x - 1/2 x + 3/2 x y - 9/2 y x , - - 3 3 2 2 - COEFF(2, 2) = 3/2 y x - 1/2 x + 1/2 x - 3/2 x y] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2/coeffs-dyy.compute.c"); -bytes used=50035368, alloc=2162292, time=3.93 -bytes used=51035560, alloc=2162292, time=4.03 -bytes used=52035720, alloc=2162292, time=4.10 -bytes used=53035872, alloc=2162292, time=4.19 -bytes used=54036040, alloc=2162292, time=4.31 -> -################################################################################ -> -# -# 2d, cube, polynomial order=3, derivatives via 5-point order=4 formula -# ==> overall order=3, 6-point molecule -# -> -# interpolating polynomial -> interp_2d_cube_order3 -> := Hermite_polynomial_interpolant(fn_2d_order3, -> coeffs_set_2d_order3, -> [x,y], -> { -> {x} = deriv_2d_dx_5point, -> {y} = deriv_2d_dy_5point, -> {x,y} = deriv_2d_dxy_5point -> }, -> {op(posn_list_2d_size2)}, -> {op(posn_list_2d_size2)}); -bytes used=55037056, alloc=2162292, time=4.40 -bytes used=56037560, alloc=2162292, time=4.50 -interp_2d_cube_order3 := (1/12 DATA(0, -2) - 7/12 DATA(0, -1) - 4/3 DATA(0, 1) - - 3 - + 7/12 DATA(0, 2) + 4/3 DATA(0, 0) - 1/12 DATA(0, 3)) y + ( - - - 8/9 DATA(1, 1) + 8/9 DATA(1, 0) - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - - - 1/18 DATA(-1, -2) + 1/144 DATA(-2, -2) - 7/144 DATA(-2, -1) - - + 7/144 DATA(-2, 2) - 1/9 DATA(-2, 1) + 1/144 DATA(2, 3) - 1/18 DATA(1, 3) - - + 1/18 DATA(-1, 3) - 1/144 DATA(-2, 3) + 1/9 DATA(-2, 0) - - + 7/144 DATA(2, -1) + 1/9 DATA(2, 1) - 7/18 DATA(1, -1) - - + 7/18 DATA(-1, -1) + 8/9 DATA(-1, 1) - 8/9 DATA(-1, 0) - 1/9 DATA(2, 0) - - 3 / - - 7/144 DATA(2, 2) - 7/18 DATA(-1, 2) + 7/18 DATA(1, 2)) x y + | - \ - - - 28/9 DATA(0, 0) - 20/9 DATA(1, 1) + 28/9 DATA(0, 1) + 20/9 DATA(1, 0) - - - 1/24 DATA(2, -2) + 5/36 DATA(1, -2) + 5/48 DATA(-1, -2) - - - 1/72 DATA(-2, -2) + 7/72 DATA(-2, -1) - 7/72 DATA(-2, 2) - - + 2/9 DATA(-2, 1) - 7/36 DATA(0, -2) + 7/36 DATA(0, 3) + 1/24 DATA(2, 3) - - - 5/36 DATA(1, 3) - 5/48 DATA(-1, 3) + 1/72 DATA(-2, 3) - 2/9 DATA(-2, 0) - - + 1/144 DATA(3, -2) - 7/144 DATA(3, -1) - 1/9 DATA(3, 1) - - + 7/144 DATA(3, 2) + 1/9 DATA(3, 0) - 1/144 DATA(3, 3) + 7/24 DATA(2, -1) - - 35 35 - + 2/3 DATA(2, 1) - -- DATA(1, -1) - -- DATA(-1, -1) - 5/3 DATA(-1, 1) - 36 48 - - 35 - + 5/3 DATA(-1, 0) - 2/3 DATA(2, 0) - 7/24 DATA(2, 2) + -- DATA(-1, 2) - 48 - - 49 49 35 \ 2 3 / - + -- DATA(0, -1) - -- DATA(0, 2) + -- DATA(1, 2)| x y + |16/9 DATA(0, 0) - 36 36 36 / \ - - + 16/9 DATA(1, 1) - 16/9 DATA(0, 1) - 16/9 DATA(1, 0) + 7/144 DATA(2, -2) - - - 1/9 DATA(1, -2) - 7/144 DATA(-1, -2) + 1/144 DATA(-2, -2) - - - 7/144 DATA(-2, -1) + 7/144 DATA(-2, 2) - 1/9 DATA(-2, 1) - - + 1/9 DATA(0, -2) - 1/9 DATA(0, 3) - 7/144 DATA(2, 3) + 1/9 DATA(1, 3) - - + 7/144 DATA(-1, 3) - 1/144 DATA(-2, 3) + 1/9 DATA(-2, 0) - - - 1/144 DATA(3, -2) + 7/144 DATA(3, -1) + 1/9 DATA(3, 1) - - 49 - - 7/144 DATA(3, 2) - 1/9 DATA(3, 0) + 1/144 DATA(3, 3) - --- DATA(2, -1) - 144 - - 49 - - 7/9 DATA(2, 1) + 7/9 DATA(1, -1) + --- DATA(-1, -1) + 7/9 DATA(-1, 1) - 144 - - 49 49 - - 7/9 DATA(-1, 0) + 7/9 DATA(2, 0) + --- DATA(2, 2) - --- DATA(-1, 2) - 144 144 - - \ 3 3 - - 7/9 DATA(0, -1) + 7/9 DATA(0, 2) - 7/9 DATA(1, 2)| x y + ( - / - - - 1/6 DATA(0, -2) + 5/4 DATA(0, -1) + 5/3 DATA(0, 1) - 1/2 DATA(0, 2) - - 2 - - 7/3 DATA(0, 0) + 1/12 DATA(0, 3)) y + (10/9 DATA(1, 1) - - - 14/9 DATA(1, 0) + 1/72 DATA(2, -2) - 1/9 DATA(1, -2) + 1/9 DATA(-1, -2) - - - 1/72 DATA(-2, -2) + 5/48 DATA(-2, -1) - 1/24 DATA(-2, 2) - - + 5/36 DATA(-2, 1) - 1/144 DATA(2, 3) + 1/18 DATA(1, 3) - 1/18 DATA(-1, 3) - - + 1/144 DATA(-2, 3) - 7/36 DATA(-2, 0) - 5/48 DATA(2, -1) - - - 5/36 DATA(2, 1) + 5/6 DATA(1, -1) - 5/6 DATA(-1, -1) - 10/9 DATA(-1, 1) - - + 14/9 DATA(-1, 0) + 7/36 DATA(2, 0) + 1/24 DATA(2, 2) + 1/3 DATA(-1, 2) - - 2 / - - 1/3 DATA(1, 2)) x y + |49/9 DATA(0, 0) + 25/9 DATA(1, 1) - \ - - - 35/9 DATA(0, 1) - 35/9 DATA(1, 0) + 1/12 DATA(2, -2) - 5/18 DATA(1, -2) - - - 5/24 DATA(-1, -2) + 1/36 DATA(-2, -2) - 5/24 DATA(-2, -1) - - + 1/12 DATA(-2, 2) - 5/18 DATA(-2, 1) + 7/18 DATA(0, -2) - 7/36 DATA(0, 3) - - - 1/24 DATA(2, 3) + 5/36 DATA(1, 3) + 5/48 DATA(-1, 3) - 1/72 DATA(-2, 3) - - + 7/18 DATA(-2, 0) - 1/72 DATA(3, -2) + 5/48 DATA(3, -1) + 5/36 DATA(3, 1) - - - 1/24 DATA(3, 2) - 7/36 DATA(3, 0) + 1/144 DATA(3, 3) - 5/8 DATA(2, -1) - - 25 25 25 - - 5/6 DATA(2, 1) + -- DATA(1, -1) + -- DATA(-1, -1) + -- DATA(-1, 1) - 12 16 12 - - 35 - - -- DATA(-1, 0) + 7/6 DATA(2, 0) + 1/4 DATA(2, 2) - 5/8 DATA(-1, 2) - 12 - - 35 \ 2 2 / - - -- DATA(0, -1) + 7/6 DATA(0, 2) - 5/6 DATA(1, 2)| x y + | - 12 / \ - - - 28/9 DATA(0, 0) - 20/9 DATA(1, 1) + 20/9 DATA(0, 1) + 28/9 DATA(1, 0) - - - 7/72 DATA(2, -2) + 2/9 DATA(1, -2) + 7/72 DATA(-1, -2) - - - 1/72 DATA(-2, -2) + 5/48 DATA(-2, -1) - 1/24 DATA(-2, 2) - - + 5/36 DATA(-2, 1) - 2/9 DATA(0, -2) + 1/9 DATA(0, 3) + 7/144 DATA(2, 3) - - - 1/9 DATA(1, 3) - 7/144 DATA(-1, 3) + 1/144 DATA(-2, 3) - - - 7/36 DATA(-2, 0) + 1/72 DATA(3, -2) - 5/48 DATA(3, -1) - 5/36 DATA(3, 1) - - 35 - + 1/24 DATA(3, 2) + 7/36 DATA(3, 0) - 1/144 DATA(3, 3) + -- DATA(2, -1) - 48 - - 35 35 35 - + -- DATA(2, 1) - 5/3 DATA(1, -1) - -- DATA(-1, -1) - -- DATA(-1, 1) - 36 48 36 - - 49 49 - + -- DATA(-1, 0) - -- DATA(2, 0) - 7/24 DATA(2, 2) + 7/24 DATA(-1, 2) - 36 36 - - \ 3 2 - + 5/3 DATA(0, -1) - 2/3 DATA(0, 2) + 2/3 DATA(1, 2)| x y + - / - - (1/12 DATA(0, -2) - 2/3 DATA(0, -1) + 2/3 DATA(0, 1) - 1/12 DATA(0, 2)) y - - + (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) + 4/9 DATA(-1, -1) - - - 4/9 DATA(-1, 1) + 1/18 DATA(-1, 2) + 1/18 DATA(1, -2) - 4/9 DATA(1, -1) - - + 4/9 DATA(1, 1) - 1/18 DATA(1, 2) - 1/144 DATA(2, -2) + 1/18 DATA(2, -1) - - - 1/18 DATA(2, 1) + 1/144 DATA(2, 2)) x y + (10/9 DATA(1, 1) - - - 14/9 DATA(0, 1) - 1/24 DATA(2, -2) + 5/36 DATA(1, -2) - - + 5/48 DATA(-1, -2) - 1/72 DATA(-2, -2) + 1/9 DATA(-2, -1) - - + 1/72 DATA(-2, 2) - 1/9 DATA(-2, 1) - 7/36 DATA(0, -2) - - + 1/144 DATA(3, -2) - 1/18 DATA(3, -1) + 1/18 DATA(3, 1) - - - 1/144 DATA(3, 2) + 1/3 DATA(2, -1) - 1/3 DATA(2, 1) - 10/9 DATA(1, -1) - - - 5/6 DATA(-1, -1) + 5/6 DATA(-1, 1) + 1/24 DATA(2, 2) - 5/48 DATA(-1, 2) - - 2 - + 14/9 DATA(0, -1) + 7/36 DATA(0, 2) - 5/36 DATA(1, 2)) x y + ( - - - 8/9 DATA(1, 1) + 8/9 DATA(0, 1) + 7/144 DATA(2, -2) - 1/9 DATA(1, -2) - - - 7/144 DATA(-1, -2) + 1/144 DATA(-2, -2) - 1/18 DATA(-2, -1) - - - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) + 1/9 DATA(0, -2) - - - 1/144 DATA(3, -2) + 1/18 DATA(3, -1) - 1/18 DATA(3, 1) - - + 1/144 DATA(3, 2) - 7/18 DATA(2, -1) + 7/18 DATA(2, 1) + 8/9 DATA(1, -1) - - + 7/18 DATA(-1, -1) - 7/18 DATA(-1, 1) - 7/144 DATA(2, 2) - - + 7/144 DATA(-1, 2) - 8/9 DATA(0, -1) - 1/9 DATA(0, 2) + 1/9 DATA(1, 2)) - - 3 - x y + DATA(0, 0) + - - (1/12 DATA(-2, 0) - 2/3 DATA(-1, 0) + 2/3 DATA(1, 0) - 1/12 DATA(2, 0)) x - - + (- 1/6 DATA(-2, 0) + 5/4 DATA(-1, 0) + 5/3 DATA(1, 0) - 1/2 DATA(2, 0) - - 2 - - 7/3 DATA(0, 0) + 1/12 DATA(3, 0)) x + (4/3 DATA(0, 0) - - + 1/12 DATA(-2, 0) - 7/12 DATA(-1, 0) - 4/3 DATA(1, 0) + 7/12 DATA(2, 0) - - 3 - - 1/12 DATA(3, 0)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=57037728, alloc=2162292, time=4.59 -bytes used=58038024, alloc=2162292, time=4.65 - 3 2 2 3 3 -[COEFF(-2, -2) = 1/144 x y - 1/72 x y - 1/72 x y + 1/144 x y + 1/144 y x - - 2 3 2 3 3 2 2 - - 1/72 x y - 1/72 x y + 1/144 x y + 1/36 x y , COEFF(-1, -2) = - - 2 3 2 3 2 3 2 - 1/9 x y - 1/18 x y - 1/18 x y + 5/48 x y + 5/48 x y + 7/72 x y - - 2 2 3 3 3 3 - - 5/24 x y - 7/144 x y - 7/144 y x , COEFF(0, -2) = 1/12 y - - 3 3 3 2 2 2 2 3 2 - + 1/9 x y + 1/9 y x + 7/18 x y - 7/36 x y - 7/36 x y - 1/6 y - - 3 2 2 3 2 - + 1/12 y - 2/9 x y , COEFF(1, -2) = 1/18 x y + 5/36 x y + 5/36 x y - - 3 2 2 3 2 2 3 3 3 - + 2/9 x y - 1/9 x y + 1/18 x y - 5/18 x y - 1/9 x y - 1/9 y x , - - 3 3 3 2 2 2 3 - COEFF(2, -2) = 7/144 x y - 7/72 x y + 1/12 x y + 7/144 y x - - 2 2 3 3 2 - + 1/72 x y - 1/24 x y - 1/144 x y - 1/144 x y - 1/24 x y, - - 2 3 3 3 2 2 2 - COEFF(3, -2) = 1/144 x y - 1/144 x y + 1/144 x y - 1/72 x y - - 3 3 2 2 2 3 - - 1/144 y x + 1/72 x y , COEFF(-2, -1) = 1/9 x y + 7/72 x y - - 3 3 2 3 3 2 3 - - 7/144 x y - 1/18 x y + 5/48 x y - 7/144 x y + 5/48 x y - 1/18 y x - - 2 2 3 2 2 49 3 3 - - 5/24 x y , COEFF(-1, -1) = 7/18 x y - 5/6 x y - 5/6 x y + --- x y - 144 - - 3 35 2 3 25 2 2 35 3 2 - + 7/18 y x - -- x y + 4/9 x y + -- x y - -- x y , COEFF(0, -1) = - 48 16 48 - - 3 3 2 2 49 2 3 3 3 2 - - 7/12 y + 5/3 x y + 14/9 x y + -- x y - 7/9 x y + 5/4 y - 36 - - 3 35 2 2 2 3 3 - - 8/9 y x - -- x y - 2/3 y, COEFF(1, -1) = - 10/9 x y + 7/9 x y - 12 - - 2 3 2 3 25 2 2 35 2 3 - + 5/6 x y - 5/3 x y + 8/9 y x - 4/9 x y + -- x y - -- x y - 12 36 - - 3 2 2 2 35 3 2 - - 7/18 x y , COEFF(2, -1) = 1/18 x y - 5/8 x y + 1/3 x y + -- x y - 48 - - 49 3 3 2 3 3 2 3 - - --- x y + 7/24 x y - 7/18 y x - 5/48 x y + 7/144 x y , - 144 - - COEFF(3, -1) = - - 3 3 2 2 3 2 3 2 2 3 - 7/144 x y + 5/48 x y - 5/48 x y + 1/18 y x - 1/18 x y - 7/144 x y - - 3 3 2 2 3 3 3 - , COEFF(-2, 0) = 1/12 x + 1/9 x y - 1/6 x - 2/9 x y + 1/9 x y - - 3 2 2 2 2 3 - - 7/36 x y + 7/18 x y + 1/12 x - 7/36 x y , COEFF(-1, 0) = - 7/12 x - - 2 3 3 3 3 35 2 2 2 49 3 2 - + 5/3 x y - 8/9 x y - 7/9 x y - -- x y + 5/4 x - 2/3 x + -- x y - 12 36 - - 2 2 2 2 3 3 - + 14/9 x y , COEFF(0, 0) = - 7/3 x + 49/9 x y + 4/3 x + 4/3 y + 1 - - 2 3 3 3 2 2 3 2 - - 7/3 y + 16/9 x y - 28/9 x y - 28/9 x y , COEFF(1, 0) = 5/3 x - - 3 3 3 3 2 2 3 - + 8/9 x y - 16/9 x y + 28/9 x y + 2/3 x - 14/9 x y - 4/3 x - - 2 3 2 2 2 49 3 2 2 - + 20/9 x y - 35/9 x y , COEFF(2, 0) = - 1/2 x - -- x y + 7/36 x y - 36 - - 3 3 3 2 3 2 2 3 - + 7/12 x - 1/12 x + 7/9 x y - 2/3 x y + 7/6 x y - 1/9 x y , - - COEFF(3, 0) = - - 3 3 3 2 2 2 2 3 2 3 - - 1/9 x y + 7/36 x y - 7/36 x y + 1/12 x - 1/12 x + 1/9 x y , - - 2 2 2 3 3 2 2 - COEFF(-2, 1) = - 5/18 x y + 1/18 x y + 2/9 x y + 5/36 x y - 1/9 x y - - 3 3 3 2 3 3 3 - - 1/9 x y + 1/18 y x + 5/36 x y - 1/9 x y , COEFF(-1, 1) = 7/9 x y - - 3 2 35 3 2 3 2 - - 7/18 y x - 10/9 x y - -- x y + 8/9 x y + 5/6 x y - 4/9 x y - 36 - - 25 2 2 2 3 2 2 2 3 - + -- x y - 5/3 x y , COEFF(0, 1) = 5/3 y - 35/9 x y - 4/3 y - 12 - - 3 3 3 2 2 3 3 2 - - 16/9 x y + 20/9 x y + 2/3 y + 28/9 x y + 8/9 y x - 14/9 x y, - - 2 2 3 2 3 3 - COEFF(1, 1) = 10/9 x y - 20/9 x y + 4/9 x y + 10/9 x y + 16/9 x y - - 3 2 3 3 2 2 2 3 - - 20/9 x y - 8/9 x y - 8/9 y x + 25/9 x y , COEFF(2, 1) = 2/3 x y - - 2 2 3 2 3 3 2 35 3 2 - - 5/6 x y + 7/18 y x - 5/36 x y - 7/9 x y - 1/3 x y + -- x y - 36 - - 3 - - 1/18 x y + 1/9 x y , COEFF(3, 1) = - - 3 3 3 2 2 3 2 2 2 3 - 1/9 x y - 5/36 x y + 1/18 x y - 1/18 y x + 5/36 x y - 1/9 x y , - - 3 3 2 2 3 3 2 - COEFF(-2, 2) = 7/144 x y + 1/12 x y + 7/144 x y - 1/24 x y - - 2 2 3 3 2 - - 1/24 x y - 7/72 x y - 1/144 x y - 1/144 y x + 1/72 x y, - - 49 3 3 2 2 3 2 35 2 3 3 - COEFF(-1, 2) = - --- x y - 5/8 x y + 7/24 x y + -- x y - 7/18 x y - 144 48 - - 2 3 2 - + 1/3 x y + 1/18 x y + 7/144 y x - 5/48 x y, COEFF(0, 2) = - 1/12 y - - 49 2 3 3 3 2 2 3 2 3 2 - - -- x y + 7/9 x y + 7/6 x y - 2/3 x y - 1/9 y x - 1/2 y - 36 - - 3 2 3 2 - + 7/12 y + 7/36 x y, COEFF(1, 2) = 7/18 x y - 1/3 x y - 1/18 x y - - 35 2 3 3 3 3 2 2 3 2 2 - + -- x y - 7/9 x y + 1/9 y x - 5/6 x y + 2/3 x y - 5/36 x y, - 36 - - 3 2 2 3 49 3 3 - COEFF(2, 2) = - 7/144 y x + 1/24 x y + 1/144 x y - 7/24 x y + --- x y - 144 - - 3 2 2 2 3 2 - - 7/24 x y + 1/4 x y - 7/144 x y + 1/24 x y, COEFF(3, 2) = - - 3 2 3 2 2 3 2 2 - 1/24 x y + 1/144 y x - 1/144 x y + 7/144 x y - 1/24 x y - - 3 3 3 2 2 3 2 2 - - 7/144 x y , COEFF(-2, 3) = 1/144 x y + 1/72 x y - 1/72 x y - - 2 3 3 3 3 2 - + 1/144 x y - 1/144 x y - 1/144 x y , COEFF(-1, 3) = - 7/144 x y - - 2 3 2 2 2 3 3 3 - - 5/48 x y + 5/48 x y - 1/18 x y + 1/18 x y + 7/144 x y , - - COEFF(0, 3) = - - 3 2 3 2 2 2 3 3 3 2 - 1/9 x y - 1/12 y - 7/36 x y + 7/36 x y - 1/9 x y + 1/12 y , - - COEFF(1, 3) = - - 3 3 2 2 3 2 2 2 3 3 - - 1/18 x y - 1/9 x y - 5/36 x y + 5/36 x y + 1/18 x y + 1/9 x y , - - 3 2 3 2 2 2 - COEFF(2, 3) = 7/144 x y + 1/144 x y - 1/24 x y - 1/144 x y - - 2 3 3 3 - + 1/24 x y - 7/144 x y , - - 3 3 3 2 2 3 2 2 - COEFF(3, 3) = 1/144 x y - 1/144 x y - 1/144 x y + 1/144 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-I.compute.c"); -bytes used=59038308, alloc=2358864, time=4.72 -bytes used=60038764, alloc=2358864, time=4.79 -bytes used=61038968, alloc=2358864, time=4.87 -bytes used=62039132, alloc=2358864, time=4.94 -bytes used=63054592, alloc=2358864, time=5.01 -bytes used=64055828, alloc=2358864, time=5.07 -bytes used=65062288, alloc=2358864, time=5.14 -bytes used=66062588, alloc=2358864, time=5.21 -bytes used=67062780, alloc=2358864, time=5.28 -bytes used=68063356, alloc=2358864, time=5.34 -bytes used=69063752, alloc=2358864, time=5.41 -bytes used=70064360, alloc=2358864, time=5.48 -bytes used=71064576, alloc=2358864, time=5.70 -bytes used=72064888, alloc=2358864, time=5.76 -bytes used=73065092, alloc=2358864, time=5.83 -bytes used=74065284, alloc=2358864, time=5.89 -bytes used=75065500, alloc=2555436, time=5.99 -bytes used=76065692, alloc=2555436, time=6.10 -bytes used=77065892, alloc=2555436, time=6.18 -bytes used=78066280, alloc=2555436, time=6.27 -bytes used=79066596, alloc=2555436, time=6.36 -bytes used=80066840, alloc=2555436, time=6.45 -bytes used=81067304, alloc=2555436, time=6.53 -bytes used=82067900, alloc=2555436, time=6.60 -bytes used=83068232, alloc=2555436, time=6.82 -bytes used=84068472, alloc=2555436, time=6.89 -bytes used=85068740, alloc=2555436, time=6.98 -bytes used=86068968, alloc=2555436, time=7.11 -bytes used=87069148, alloc=2555436, time=7.21 -bytes used=88069444, alloc=2555436, time=7.44 -bytes used=89069696, alloc=2555436, time=7.51 -bytes used=90069884, alloc=2555436, time=7.60 -bytes used=91070132, alloc=2555436, time=7.73 -bytes used=92070372, alloc=2555436, time=7.83 -bytes used=93070840, alloc=2555436, time=8.08 -bytes used=94071232, alloc=2555436, time=8.17 -> -# d/dx -> simplify( diff(interp_2d_cube_order3,x) ); -bytes used=95071420, alloc=2555436, time=8.28 -bytes used=96072108, alloc=2555436, time=8.34 -bytes used=97072268, alloc=2555436, time=8.40 -bytes used=98072440, alloc=2555436, time=8.47 -bytes used=99072940, alloc=2555436, time=8.53 -2/3 DATA(1, 0) + 1/12 DATA(-2, 0) + 2/9 x y DATA(-2, -1) + 1/36 x y DATA(-2, 2) - - - 2/9 x y DATA(-2, 1) - 7/18 x y DATA(0, -2) + 1/72 x y DATA(3, -2) - - - 1/9 x y DATA(3, -1) - 28/9 x y DATA(0, 1) - 1/12 x y DATA(2, -2) - - + 5/18 x y DATA(1, -2) + 5/24 x y DATA(-1, -2) - 1/36 x y DATA(-2, -2) - - + 1/144 y DATA(2, 2) + 1/18 y DATA(-2, 1) - 1/144 y DATA(-2, 2) - - - 1/18 y DATA(-1, -2) + 4/9 y DATA(-1, -1) - 4/9 y DATA(-1, 1) - - + 1/18 y DATA(-1, 2) + 1/18 y DATA(1, -2) - 4/9 y DATA(1, -1) - - + 4/9 y DATA(1, 1) - 1/18 y DATA(1, 2) - 1/144 y DATA(2, -2) - - + 1/144 y DATA(-2, -2) - 1/18 y DATA(-2, -1) - 1/18 y DATA(2, 1) - - - 2/3 x y DATA(2, 1) - 20/9 x y DATA(1, -1) - 5/3 x y DATA(-1, -1) - - 2 2 - + 5/3 x y DATA(-1, 1) + 1/12 x y DATA(2, 2) + 2/3 x y DATA(1, -2) - - 2 2 - + 7/24 x y DATA(-1, -2) + 20/9 x y DATA(1, 1) + 7/18 x y DATA(0, 2) - - - 5/18 x y DATA(1, 2) + 28/9 x y DATA(0, -1) + 2/3 x y DATA(2, -1) - - 2 2 2 - - 1/3 x y DATA(1, -2) - 7/48 x y DATA(-1, -2) + 1/48 x y DATA(-2, -2) - - 2 - - 1/6 x y DATA(-2, -1) - 5/24 x y DATA(-1, 2) - 1/3 x DATA(-2, 0) - - 2 2 2 - - 1/48 x y DATA(-2, 2) + 1/6 x y DATA(-2, 1) + 1/3 x y DATA(0, -2) - - 2 2 2 - - 1/48 x y DATA(3, -2) + 1/6 x y DATA(3, -1) - 1/6 x y DATA(3, 1) - - 2 2 2 - + 1/48 x y DATA(3, 2) - 8/3 x y DATA(1, 1) + 8/3 x y DATA(0, 1) - - 2 2 2 - + 7/48 x y DATA(2, -2) + 7/48 x y DATA(-1, 2) - 8/3 x y DATA(0, -1) - - 2 2 2 - - 1/3 x y DATA(0, 2) + 1/3 x y DATA(1, 2) - 7/6 x y DATA(2, -1) - - 2 2 2 - + 7/6 x y DATA(2, 1) + 8/3 x y DATA(1, -1) + 7/6 x y DATA(-1, -1) - - 3 3 3 - - 1/144 y DATA(2, -2) - 1/18 y DATA(-1, -2) + 1/144 y DATA(-2, -2) - - 3 3 3 - - 7/144 y DATA(-2, -1) + 7/144 y DATA(-2, 2) - 1/9 y DATA(-2, 1) - - 3 3 3 - + 1/144 y DATA(2, 3) - 1/18 y DATA(1, 3) + 1/18 y DATA(-1, 3) - - 2 2 2 - + 4 x DATA(0, 0) + 1/4 x DATA(-2, 0) - 7/4 x DATA(-1, 0) - - 2 2 2 - - 4 x DATA(1, 0) + 7/4 x DATA(2, 0) - 1/4 x DATA(3, 0) - - + 5/2 x DATA(-1, 0) + 10/3 x DATA(1, 0) - x DATA(2, 0) - 14/3 x DATA(0, 0) - - 3 - + 1/6 x DATA(3, 0) + 1/18 y DATA(2, -1) + 7/144 y DATA(2, -1) - - 3 3 3 - - 7/18 y DATA(1, -1) + 1/9 y DATA(-2, 0) - 8/9 y DATA(1, 1) - - 3 3 2 3 - + 8/9 y DATA(1, 0) + 1/9 y DATA(2, 1) - 16/3 x y DATA(0, 1) - - 2 3 2 3 49 2 3 - - 7/3 x y DATA(2, 1) + 7/3 x y DATA(1, -1) + -- x y DATA(-1, -1) - 48 - - 2 3 2 3 2 3 - + 7/3 x y DATA(-1, 1) - 7/3 x y DATA(-1, 0) + 1/48 x y DATA(-2, -2) - - 2 3 2 3 3 - - 7/48 x y DATA(-2, -1) + 7/48 x y DATA(-2, 2) - 40/9 x y DATA(1, 1) - - 3 2 2 - - 10/3 x y DATA(-1, 1) - 7/6 x y DATA(-1, 1) - 7/48 x y DATA(2, 2) - - 2 3 49 2 3 2 3 - + 1/3 x y DATA(-2, 0) - -- x y DATA(2, -1) + 16/3 x y DATA(1, 1) - 48 - - 2 3 2 3 2 3 - - 7/3 x y DATA(1, 2) + 16/3 x y DATA(0, 0) - 1/3 x y DATA(1, -2) - - 2 3 2 2 - - 7/48 x y DATA(-1, -2) + 5/18 x y DATA(3, 1) - 1/12 x y DATA(3, 2) - - 2 2 3 2 3 - - 7/18 x y DATA(3, 0) - 1/3 x y DATA(-2, 1) - 7/48 x y DATA(2, 3) - - 2 3 2 3 2 3 - + 1/3 x y DATA(1, 3) + 7/48 x y DATA(-1, 3) - 1/48 x y DATA(-2, 3) - - 2 2 2 - - 7/36 y DATA(-2, 0) - 5/48 y DATA(2, -1) - 5/36 y DATA(2, 1) - - 2 2 2 - + 10/9 y DATA(1, 1) - 14/9 y DATA(1, 0) + 1/72 y DATA(2, -2) - - 3 3 3 - - 7/18 y DATA(-1, 2) + 7/18 y DATA(1, 2) + 7/18 y DATA(-1, -1) - - 3 3 3 - + 8/9 y DATA(-1, 1) - 8/9 y DATA(-1, 0) - 1/9 y DATA(2, 0) - - 3 3 2 3 - - 7/144 y DATA(2, 2) - 1/144 y DATA(-2, 3) - 16/3 x y DATA(1, 0) - - 2 2 2 - + 1/9 y DATA(-1, -2) - 1/144 y DATA(2, 3) + 1/18 y DATA(1, 3) - - 2 2 2 3 - - 1/18 y DATA(-1, 3) + 1/144 y DATA(-2, 3) + 7/48 x y DATA(2, -2) - - 3 3 2 3 - - 5/24 x y DATA(-1, 3) - 7/36 x y DATA(-2, 2) + 1/3 x y DATA(3, 1) - - 3 3 3 - - 56/9 x y DATA(0, 0) + 7/18 x y DATA(0, 3) - 7/72 x y DATA(3, -1) - - 3 3 49 3 - - 2/9 x y DATA(3, 1) + 2/9 x y DATA(3, 0) - -- x y DATA(0, 2) - 18 - - 3 49 3 2 - - 1/72 x y DATA(3, 3) + -- x y DATA(0, -1) + 5/24 x y DATA(3, -1) - 18 - - 3 2 3 35 3 - + 7/12 x y DATA(2, -1) + 7/3 x y DATA(0, 2) - -- x y DATA(-1, -1) - 24 - - 3 3 35 3 - - 7/12 x y DATA(2, 2) - 1/12 x y DATA(2, -2) + -- x y DATA(-1, 2) - 24 - - 3 3 2 3 - + 10/3 x y DATA(-1, 0) + 40/9 x y DATA(1, 0) - 1/3 x y DATA(3, 0) - - 3 3 3 - - 7/18 x y DATA(0, -2) - 4/3 x y DATA(2, 0) - 1/36 x y DATA(-2, -2) - - 2 3 2 3 3 - - 1/48 x y DATA(3, -2) + 1/48 x y DATA(3, 3) - 5/18 x y DATA(1, 3) - - 2 3 3 2 - - 1/3 x y DATA(0, 3) + 1/12 x y DATA(2, 3) + 5/6 y DATA(1, -1) - - 2 2 2 - - 5/6 y DATA(-1, -1) - 10/9 y DATA(-1, 1) + 14/9 y DATA(-1, 0) - - 2 2 2 - + 7/36 y DATA(2, 0) + 1/24 y DATA(2, 2) + 1/3 y DATA(-1, 2) - - 2 2 2 - - 1/3 y DATA(1, 2) - 1/9 y DATA(1, -2) - 1/72 y DATA(-2, -2) - - 2 2 2 - + 5/48 y DATA(-2, -1) - 1/24 y DATA(-2, 2) + 5/36 y DATA(-2, 1) - - 3 3 - + 4/9 x y DATA(-2, 1) + 4/3 x y DATA(2, 1) - 2/3 DATA(-1, 0) - - 2 2 - - 1/12 DATA(2, 0) + 1/2 x y DATA(2, 2) - 5/4 x y DATA(-1, 2) - - 3 35 3 49 2 3 - + 5/18 x y DATA(1, -2) - -- x y DATA(1, -1) - -- x y DATA(-1, 2) - 18 48 - - 3 2 3 49 2 3 - + 7/36 x y DATA(-2, -1) + 7/3 x y DATA(2, 0) + -- x y DATA(2, 2) - 48 - - 3 2 3 - + 1/18 y DATA(1, -2) - 7/18 x y DATA(0, 3) - 4/9 x y DATA(-2, 0) - - 2 2 2 - + 7/9 x y DATA(0, -2) + 7/3 x y DATA(2, 0) - 5/3 x y DATA(1, 2) - - 2 2 2 - + 98/9 x y DATA(0, 0) - 70/9 x y DATA(0, 1) - 5/3 x y DATA(2, 1) - - 2 2 2 - + 25/6 x y DATA(1, -1) + 25/8 x y DATA(-1, -1) + 25/6 x y DATA(-1, 1) - - 2 2 2 - + 1/72 x y DATA(3, 3) - 35/6 x y DATA(0, -1) + 7/3 x y DATA(0, 2) - - 2 2 2 - - 1/36 x y DATA(3, -2) + 1/6 x y DATA(-2, 2) - 5/9 x y DATA(-2, 1) - - 2 2 35 2 2 - - 1/12 x y DATA(2, 3) + 5/18 x y DATA(1, 3) + -- x y DATA(2, 1) - 12 - - 2 2 2 2 2 2 - + 1/3 x y DATA(0, 3) - 5/16 x y DATA(3, -1) - 5/12 x y DATA(3, 1) - - 2 2 2 - + 5/24 x y DATA(-1, 3) - 1/36 x y DATA(-2, 3) + 7/9 x y DATA(-2, 0) - - 2 2 2 - - 5/4 x y DATA(2, -1) + 50/9 x y DATA(1, 1) - 70/9 x y DATA(1, 0) - - 2 2 2 - + 1/6 x y DATA(2, -2) - 5/9 x y DATA(1, -2) - 5/12 x y DATA(-1, -2) - - 2 2 2 - - 35/6 x y DATA(-1, 0) + 1/18 x y DATA(-2, -2) - 5/12 x y DATA(-2, -1) - - 2 2 2 2 2 2 - + 7/8 x y DATA(-1, 2) + 2 x y DATA(1, 2) - 28/3 x y DATA(0, 0) - - 2 2 2 2 2 2 - + 20/3 x y DATA(0, 1) + 1/24 x y DATA(3, -2) - 2/3 x y DATA(0, -2) - - 49 2 2 2 2 2 2 - - -- x y DATA(2, 0) - 7/8 x y DATA(2, 2) + 1/8 x y DATA(3, 2) - 12 - - 2 2 2 2 2 2 - - 1/48 x y DATA(3, 3) + 5 x y DATA(0, -1) - 2 x y DATA(0, 2) - - 2 2 35 2 2 35 2 2 - + 7/12 x y DATA(3, 0) - -- x y DATA(-1, -1) - -- x y DATA(-1, 1) - 16 12 - - 49 2 2 2 2 - + -- x y DATA(-1, 0) - 1/24 x y DATA(-2, -2) + 1/9 x y DATA(3, 1) - 12 - - 2 2 35 2 2 - - 1/72 x y DATA(3, 2) - 7/12 x y DATA(-2, 0) + -- x y DATA(2, -1) - 16 - - 2 2 2 2 2 2 - - 20/3 x y DATA(1, 1) + 28/3 x y DATA(1, 0) - 7/24 x y DATA(2, -2) - - 2 2 2 2 2 2 - + 5/16 x y DATA(-2, -1) + 5/12 x y DATA(-2, 1) + 7/48 x y DATA(2, 3) - - 2 2 2 2 2 2 - - 1/3 x y DATA(1, 3) - 7/48 x y DATA(-1, 3) + 1/48 x y DATA(-2, 3) - - 2 2 2 2 3 - - 1/8 x y DATA(-2, 2) - 5 x y DATA(1, -1) + 1/72 x y DATA(3, -2) - - 3 3 2 3 - + 1/36 x y DATA(-2, 3) + 5/24 x y DATA(-1, -2) + 7/48 x y DATA(3, -1) - - 35 3 2 3 3 - + -- x y DATA(1, 2) - 7/3 x y DATA(0, -1) + 7/72 x y DATA(3, 2) - 18 - - 2 3 3 2 3 - + 1/3 x y DATA(0, -2) + 56/9 x y DATA(0, 1) - 7/48 x y DATA(3, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=100082336, alloc=2620960, time=8.59 -bytes used=101100524, alloc=2620960, time=8.66 - 2 2 3 2 2 -[COEFF(-2, -2) = - 1/72 y + 1/48 x y + 1/144 y - 1/24 x y - 1/36 x y - - 2 3 2 3 2 2 - + 1/48 x y + 1/18 x y - 1/36 x y + 1/144 y, COEFF(-1, -2) = 7/24 x y - - 2 2 2 3 3 3 - - 7/48 x y - 5/12 x y - 7/48 x y + 5/24 x y + 5/24 x y - 1/18 y - - 2 - - 1/18 y + 1/9 y , COEFF(0, -2) = - - 2 2 2 2 2 3 3 - - 2/3 x y + 1/3 x y + 7/9 x y + 1/3 x y - 7/18 x y - 7/18 x y, - - 2 3 3 3 2 - COEFF(1, -2) = - 1/3 x y + 1/18 y + 5/18 x y + 1/18 y - 5/9 x y - - 2 2 2 2 3 - - 1/9 y + 5/18 x y - 1/3 x y + 2/3 x y , COEFF(2, -2) = - 1/12 x y - - 2 3 2 2 3 2 2 - + 1/72 y - 1/144 y + 1/6 x y + 7/48 x y - 7/24 x y - 1/12 x y - - 2 - + 7/48 x y - 1/144 y, COEFF(3, -2) = - - 3 2 2 2 3 2 2 - 1/72 x y + 1/72 x y + 1/24 x y - 1/48 x y - 1/36 x y - 1/48 x y, - - 2 3 3 2 2 - COEFF(-2, -1) = - 7/48 x y - 7/144 y + 5/48 y - 1/6 x y - 1/18 y - - 2 2 2 3 35 3 - + 2/9 x y - 5/12 x y + 5/16 x y + 7/36 x y , COEFF(-1, -1) = - -- x y - 24 - - 49 2 3 3 2 35 2 2 2 - - 5/3 x y + 4/9 y + -- x y + 7/18 y - 5/6 y - -- x y + 7/6 x y - 48 16 - - 2 - + 25/8 x y , COEFF(0, -1) = - - 2 2 2 49 3 2 3 2 - - 35/6 x y + 5 x y + -- x y - 7/3 x y + 28/9 x y - 8/3 x y, - 18 - - 35 3 2 3 2 - COEFF(1, -1) = - -- x y - 20/9 x y - 4/9 y + 7/3 x y + 8/3 x y - 18 - - 2 2 2 3 2 - + 25/6 x y - 5 x y - 7/18 y + 5/6 y , COEFF(2, -1) = 2/3 x y - - 2 3 3 2 49 2 3 2 - - 5/4 x y + 7/12 x y + 7/144 y - 5/48 y - -- x y - 7/6 x y - 48 - - 35 2 2 - + -- x y + 1/18 y, COEFF(3, -1) = - 16 - - 2 3 2 2 2 2 3 - 1/6 x y - 7/72 x y - 5/16 x y - 1/9 x y + 5/24 x y + 7/48 x y , - - 2 3 3 2 2 2 - COEFF(-2, 0) = - 7/36 y + 1/9 y - 4/9 x y + 1/12 + 1/4 x - 7/12 x y - - 2 3 2 2 3 - + 1/3 x y - 1/3 x + 7/9 x y , COEFF(-1, 0) = - 2/3 - 35/6 x y - 8/9 y - - 2 2 3 2 3 49 2 2 - + 5/2 x + 14/9 y - 7/3 x y - 7/4 x + 10/3 x y + -- x y , COEFF(0, 0) - 12 - - 2 2 3 2 2 3 2 - = 4 x + 16/3 x y - 28/3 x y - 14/3 x - 56/9 x y + 98/9 x y , - - 2 2 2 3 3 3 - COEFF(1, 0) = 28/3 x y + 2/3 - 16/3 x y + 40/9 x y + 8/9 y - - 2 2 2 3 49 2 2 - - 70/9 x y - 4 x - 14/9 y + 10/3 x, COEFF(2, 0) = - 1/9 y - -- x y - 12 - - 2 3 2 3 2 2 - + 7/3 x y - x - 1/12 + 7/4 x - 4/3 x y + 7/36 y + 7/3 x y , - - COEFF(3, 0) = - - 2 2 2 3 3 2 2 - 7/12 x y - 1/3 x y + 2/9 x y - 7/18 x y + 1/6 x - 1/4 x , - - 2 3 2 2 2 2 - COEFF(-2, 1) = 1/6 x y + 4/9 x y + 5/12 x y - 5/9 x y + 5/36 y - - 3 2 3 2 3 - - 2/9 x y + 1/18 y - 1/9 y - 1/3 x y , COEFF(-1, 1) = - 10/9 y + 8/9 y - - 3 2 2 35 2 2 - - 10/3 x y - 7/6 x y - 4/9 y + 5/3 x y + 25/6 x y - -- x y - 12 - - 2 3 - + 7/3 x y , COEFF(0, 1) = - - 2 3 2 2 2 2 3 - - 16/3 x y + 8/3 x y + 20/3 x y - 70/9 x y + 56/9 x y - 28/9 x y, - - 3 3 2 2 2 2 - COEFF(1, 1) = - 40/9 x y - 8/9 y - 20/3 x y + 50/9 x y + 10/9 y - - 2 3 2 2 3 - + 20/9 x y + 16/3 x y + 4/9 y - 8/3 x y, COEFF(2, 1) = - 7/3 x y - - 35 2 2 2 2 3 2 - + -- x y - 2/3 x y - 5/3 x y - 5/36 y + 1/9 y + 7/6 x y - 1/18 y - 12 - - 3 - + 4/3 x y , COEFF(3, 1) = - - 2 2 3 2 3 2 2 - 5/18 x y + 1/3 x y + 1/9 x y - 1/6 x y - 2/9 x y - 5/12 x y , - - 2 3 3 2 - COEFF(-2, 2) = 7/48 x y - 1/144 y + 1/36 x y - 7/36 x y - 1/24 y - - 2 2 3 2 2 2 2 - - 1/48 x y + 1/6 x y + 7/144 y - 1/8 x y , COEFF(-1, 2) = 7/8 x y - - 2 35 3 2 2 3 49 2 3 - + 1/18 y + 7/48 x y + -- x y - 5/4 x y + 1/3 y - 7/18 y - -- x y - 24 48 - - - 5/24 x y, COEFF(0, 2) = - - 2 49 3 2 2 2 3 2 - 7/3 x y + 7/18 x y - -- x y - 2 x y + 7/3 x y - 1/3 x y, COEFF(1, 2) - 18 - - 2 2 2 3 2 35 3 - = 1/3 x y - 5/18 x y - 5/3 x y - 7/3 x y - 1/3 y - 1/18 y + -- x y - 18 - - 3 2 2 2 3 - + 7/18 y + 2 x y , COEFF(2, 2) = - 7/48 x y - 7/12 x y + 1/144 y - - 3 2 2 2 2 49 2 3 - - 7/144 y + 1/12 x y + 1/24 y + 1/2 x y - 7/8 x y + -- x y , - 48 - - COEFF(3, 2) = - - 2 2 2 2 3 2 3 - - 1/72 x y - 1/12 x y + 1/48 x y + 1/8 x y + 7/72 x y - 7/48 x y , - - COEFF(-2, 3) = - - 2 2 3 3 2 2 2 3 - - 1/36 x y - 1/48 x y - 1/144 y + 1/144 y + 1/48 x y + 1/36 x y , - - COEFF(-1, 3) = - - 2 3 2 2 3 3 2 2 - - 1/18 y + 1/18 y + 5/24 x y + 7/48 x y - 5/24 x y - 7/48 x y , - - 2 2 2 3 2 3 - COEFF(0, 3) = - 7/18 x y + 1/3 x y + 7/18 x y - 1/3 x y , COEFF(1, 3) - - 2 3 2 2 2 3 3 2 - = 1/18 y - 5/18 x y - 1/3 x y + 1/3 x y - 1/18 y + 5/18 x y , - - COEFF(2, 3) = - - 3 2 2 2 3 2 3 2 - 1/144 y + 7/48 x y - 1/12 x y + 1/12 x y - 7/48 x y - 1/144 y , - - 2 3 3 2 2 2 - COEFF(3, 3) = 1/48 x y - 1/72 x y - 1/48 x y + 1/72 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-dx.compute.c"); -bytes used=102100840, alloc=2620960, time=8.73 -bytes used=103101096, alloc=2620960, time=8.80 -bytes used=104101348, alloc=2620960, time=8.88 -bytes used=105101516, alloc=2620960, time=8.96 -bytes used=106101724, alloc=2620960, time=9.03 -bytes used=107102800, alloc=2620960, time=9.12 -bytes used=108103400, alloc=2620960, time=9.19 -bytes used=109103604, alloc=2620960, time=9.26 -bytes used=110104636, alloc=2620960, time=9.33 -bytes used=111108460, alloc=2620960, time=9.40 -bytes used=112108632, alloc=2620960, time=9.64 -bytes used=113108800, alloc=2620960, time=9.71 -bytes used=114116948, alloc=2620960, time=9.77 -bytes used=115117148, alloc=2620960, time=9.86 -bytes used=116117316, alloc=2620960, time=9.96 -bytes used=117117532, alloc=2620960, time=10.05 -bytes used=118118796, alloc=2620960, time=10.14 -bytes used=119118996, alloc=2620960, time=10.24 -bytes used=120119228, alloc=2620960, time=10.32 -bytes used=121119432, alloc=2620960, time=10.41 -bytes used=122119736, alloc=2620960, time=10.49 -bytes used=123119932, alloc=2620960, time=10.75 -bytes used=124120204, alloc=2620960, time=10.85 -bytes used=125120408, alloc=2620960, time=10.91 -bytes used=126120620, alloc=2620960, time=11.04 -bytes used=127120800, alloc=2620960, time=11.15 -bytes used=128121240, alloc=2620960, time=11.24 -bytes used=129121648, alloc=2620960, time=11.50 -bytes used=130122020, alloc=2620960, time=11.56 -> -# d/dy -> simplify( diff(interp_2d_cube_order3,y) ); -bytes used=131122288, alloc=2620960, time=11.69 -bytes used=132122572, alloc=2620960, time=11.76 -bytes used=133123056, alloc=2620960, time=11.83 - 2 -1/18 x DATA(1, -2) + 4 y DATA(0, 0) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) - - 2 2 2 - + 1/4 y DATA(0, -2) - 4 y DATA(0, 1) + 7/4 y DATA(0, 2) - - 3 - - 7/12 y x DATA(2, 2) + 5/24 x y DATA(-2, -1) - 1/12 x y DATA(-2, 2) - - 2 - + 5/18 x y DATA(-2, 1) - 7/4 y DATA(0, -1) + 1/36 x y DATA(2, -2) - - - 2/9 x y DATA(1, -2) + 2/9 x y DATA(-1, -2) - 1/36 x y DATA(-2, -2) - - 35 3 49 3 3 - + -- y x DATA(2, -1) + -- y x DATA(-1, 0) + 1/36 y x DATA(3, -2) - 24 18 - - 3 3 3 - - 7/72 y x DATA(-1, 3) - 10/3 y x DATA(1, -1) - 1/36 y x DATA(-2, -2) - - 3 3 3 - + 7/72 y x DATA(2, 3) - 2/9 y x DATA(1, 3) + 5/18 y x DATA(-2, 1) - - 3 3 - + 5/24 y x DATA(-2, -1) + 1/72 y x DATA(-2, 3) - 5/18 x y DATA(2, 1) - - + 5/3 x y DATA(1, -1) - 5/3 x y DATA(-1, -1) - 20/9 x y DATA(-1, 1) - - 2 2 2 2 - + 1/12 x y DATA(2, 2) + 5/12 x y DATA(1, -2) + 5/16 x y DATA(-1, -2) - - + 20/9 x y DATA(1, 1) - 2/3 x y DATA(1, 2) - 5/24 x y DATA(2, -1) - - 2 2 2 - - 5/9 x y DATA(1, -2) - 5/12 x y DATA(-1, -2) + 1/18 x y DATA(-2, -2) - - 2 2 - - 5/12 x y DATA(-2, -1) + 2/3 x y DATA(-1, 2) + 1/6 x y DATA(-2, 2) - - 2 2 2 - - 5/9 x y DATA(-2, 1) + 7/9 x y DATA(0, -2) - 1/36 x y DATA(3, -2) - - 2 2 2 - + 5/24 x y DATA(3, -1) + 5/18 x y DATA(3, 1) - 1/12 x y DATA(3, 2) - - 2 2 2 - + 50/9 x y DATA(1, 1) - 70/9 x y DATA(0, 1) + 1/6 x y DATA(2, -2) - - 2 2 2 - - 5/4 x y DATA(-1, 2) - 35/6 x y DATA(0, -1) + 7/3 x y DATA(0, 2) - - 2 2 2 - - 5/3 x y DATA(1, 2) - 5/4 x y DATA(2, -1) - 5/3 x y DATA(2, 1) - - 2 2 3 - + 25/6 x y DATA(1, -1) + 25/8 x y DATA(-1, -1) + 2/9 y x DATA(0, 3) - - 3 3 2 - + 56/9 y x DATA(1, 0) - 40/9 y x DATA(1, 1) + 25/6 x y DATA(-1, 1) - - 2 3 3 - + 1/2 x y DATA(2, 2) - 4/9 y x DATA(0, -2) + 4/9 y x DATA(1, -2) - - 3 3 3 - - 56/9 y x DATA(0, 0) + 10/3 y x DATA(0, -1) - 7/36 y x DATA(2, -2) - - 3 3 35 3 - - 4/3 y x DATA(0, 2) + 40/9 y x DATA(0, 1) - -- y x DATA(-1, -1) - 24 - - 35 3 3 3 - - -- y x DATA(-1, 1) - 1/72 y x DATA(3, 3) + 1/12 y x DATA(3, 2) - 18 - - 3 3 3 - + 7/18 y x DATA(3, 0) + 7/36 y x DATA(-1, -2) - 1/12 y x DATA(-2, 2) - - 3 3 - + 1/144 x DATA(-2, -2) - 7/18 y x DATA(-2, 0) - 5/18 y x DATA(3, 1) - - 3 3 35 3 - - 5/24 y x DATA(3, -1) + 7/12 y x DATA(-1, 2) + -- y x DATA(2, 1) - 18 - - 49 3 - - -- y x DATA(2, 0) + 1/6 y DATA(0, 3) - 14/3 y DATA(0, 0) - 18 - - + 10/3 y DATA(0, 1) + 5/2 y DATA(0, -1) - 1/3 y DATA(0, -2) - - 2 3 2 - - 7/18 x y DATA(3, 0) + 4/3 y x DATA(1, 2) + 1/72 x y DATA(3, 3) - - 2 2 2 - + 98/9 x y DATA(0, 0) - 70/9 x y DATA(1, 0) - 7/18 x y DATA(0, 3) - - 2 2 2 - + 5/18 x y DATA(1, 3) - 1/36 x y DATA(-2, 3) + 5/24 x y DATA(-1, 3) - - 2 2 3 - + 7/9 x y DATA(-2, 0) - 1/12 x y DATA(2, 3) + 7/18 x DATA(-1, -1) - - 3 3 3 - + 1/9 x DATA(1, 2) + 8/9 x DATA(1, -1) + 7/144 x DATA(-1, 2) - - 3 3 2 - - 7/144 x DATA(2, 2) - 7/18 x DATA(-1, 1) - 35/6 x y DATA(-1, 0) - - 3 3 3 - - 7/144 x DATA(-1, -2) - 1/9 x DATA(0, 2) - 8/9 x DATA(0, -1) - - 3 3 3 - - 1/9 x DATA(1, -2) - 1/144 x DATA(-2, 2) - 1/18 x DATA(-2, -1) - - 3 3 3 - + 1/144 x DATA(-2, -2) + 1/9 x DATA(0, -2) + 1/18 x DATA(-2, 1) - - 2 3 - - 2/3 DATA(0, -1) + 7/3 x y DATA(2, 0) - 7/18 x DATA(2, -1) - - 3 3 3 - + 1/144 x DATA(3, 2) - 1/18 x DATA(3, 1) + 1/18 x DATA(3, -1) - - 3 3 - - 1/144 x DATA(3, -2) + 28/9 x y DATA(-1, 0) - 8/9 x DATA(1, 1) - - 3 - + 7/18 x DATA(2, 1) - 1/72 x y DATA(2, 3) + 7/18 x y DATA(2, 0) - - 2 2 3 - - 5/6 x DATA(-1, -1) - 10/9 x DATA(1, -1) + 7/144 x DATA(2, -2) - - 3 - + 8/9 x DATA(0, 1) + 1/72 x y DATA(-2, 3) - 1/9 x y DATA(-1, 3) - - + 1/9 x y DATA(1, 3) - 7/18 x y DATA(-2, 0) - 28/9 x y DATA(1, 0) - - 3 2 3 2 - + 1/48 x y DATA(-2, -2) + 7/48 x y DATA(-2, 2) - - 3 2 3 2 3 2 - - 7/48 x y DATA(-1, -2) - 1/3 x y DATA(0, 3) - 1/3 x y DATA(-2, 1) - - 3 2 3 2 3 2 - - 7/48 x y DATA(-2, -1) - 16/3 x y DATA(1, 0) + 16/3 x y DATA(1, 1) - - 3 2 3 2 3 2 - - 1/3 x y DATA(1, -2) + 7/48 x y DATA(2, -2) + 7/3 x y DATA(0, 2) - - 3 2 3 2 49 3 2 - + 1/3 x y DATA(0, -2) - 7/3 x y DATA(0, -1) + -- x y DATA(-1, -1) - 48 - - 3 2 3 2 3 2 - + 16/3 x y DATA(0, 0) - 16/3 x y DATA(0, 1) - 1/3 x y DATA(3, 0) - - 3 2 3 2 3 2 - + 1/48 x y DATA(3, 3) + 7/3 x y DATA(-1, 1) - 7/48 x y DATA(3, 2) - - 3 2 49 3 2 3 2 - + 1/3 x y DATA(3, 1) - -- x y DATA(-1, 2) - 7/3 x y DATA(-1, 0) - 48 - - 3 2 49 3 2 49 3 2 - - 1/48 x y DATA(3, -2) + -- x y DATA(2, 2) - -- x y DATA(2, -1) - 48 48 - - 3 2 3 2 3 2 - + 7/3 x y DATA(1, -1) - 7/3 x y DATA(2, 1) + 1/3 x y DATA(1, 3) - - 3 2 3 2 3 2 - - 7/48 x y DATA(2, 3) - 1/48 x y DATA(-2, 3) + 7/48 x y DATA(-1, 3) - - 3 2 3 2 - - 1/144 x DATA(2, -2) + 7/48 x y DATA(3, -1) - 7/3 x y DATA(1, 2) - - 2 2 - + 4/9 x DATA(1, 1) - 7/48 x y DATA(2, 2) - 7/6 x y DATA(-1, 2) - - 2 2 - - 1/3 x y DATA(2, 0) - 4/9 x DATA(1, -1) + 7/6 x y DATA(1, 2) - - 2 2 2 - + 1/3 x y DATA(2, 1) - 7/6 x y DATA(1, -1) + 7/6 x y DATA(-1, -1) - - 2 2 2 - + 8/3 x y DATA(-1, 1) + 7/48 x y DATA(-2, 2) - 1/3 x y DATA(-2, 1) - - 2 2 2 2 - + 1/48 x y DATA(2, 3) - 1/6 x y DATA(1, 3) + 2 x y DATA(2, 1) - - 2 2 2 2 2 2 - + 7/12 x y DATA(0, 3) - 7/48 x y DATA(3, -1) - 1/3 x y DATA(3, 1) - - 2 2 2 - + 1/6 x y DATA(-1, 3) - 1/48 x y DATA(-2, 3) + 1/3 x y DATA(-2, 0) - - 2 2 2 - + 7/48 x y DATA(2, -1) - 8/3 x y DATA(1, 1) + 8/3 x y DATA(1, 0) - - 2 2 2 - - 1/48 x y DATA(2, -2) + 1/6 x y DATA(1, -2) - 1/6 x y DATA(-1, -2) - - 2 2 2 - - 8/3 x y DATA(-1, 0) + 1/48 x y DATA(-2, -2) - 7/48 x y DATA(-2, -1) - - 35 2 2 35 2 2 2 2 - + -- x y DATA(-1, 2) + -- x y DATA(1, 2) - 28/3 x y DATA(0, 0) - 16 12 - - 2 2 2 2 2 2 - + 28/3 x y DATA(0, 1) + 1/48 x y DATA(3, -2) - 7/12 x y DATA(0, -2) - - 2 2 2 2 2 2 - - 2 x y DATA(2, 0) - 7/8 x y DATA(2, 2) + 7/48 x y DATA(3, 2) - - 2 2 49 2 2 49 2 2 - - 1/48 x y DATA(3, 3) + -- x y DATA(0, -1) - -- x y DATA(0, 2) - 12 12 - - 2 2 35 2 2 2 2 - + 1/3 x y DATA(3, 0) - -- x y DATA(-1, -1) - 5 x y DATA(-1, 1) - 16 - - 2 2 2 2 2 2 - + 5 x y DATA(-1, 0) - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-2, 0) - - 2 2 2 2 2 2 - + 7/8 x y DATA(2, -1) - 20/3 x y DATA(1, 1) + 20/3 x y DATA(1, 0) - - 2 2 2 2 2 2 - - 1/8 x y DATA(2, -2) + 7/24 x y DATA(-2, -1) + 2/3 x y DATA(-2, 1) - - 2 2 2 2 2 2 - + 1/8 x y DATA(2, 3) - 5/12 x y DATA(1, 3) - 5/16 x y DATA(-1, 3) - - 2 2 2 2 35 2 2 - + 1/24 x y DATA(-2, 3) - 7/24 x y DATA(-2, 2) - -- x y DATA(1, -1) - 12 - - 3 2 3 2 - + 1/3 x y DATA(-2, 0) + 7/3 x y DATA(2, 0) - 1/12 DATA(0, 2) - - - y DATA(0, 2) + 1/18 x DATA(-2, 1) - 1/144 x DATA(-2, 2) - - - 1/18 x DATA(-1, -2) + 4/9 x DATA(-1, -1) - 4/9 x DATA(-1, 1) - - + 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + 1/144 x DATA(2, 2) - - 2 2 2 - + 10/9 x DATA(1, 1) - 14/9 x DATA(0, 1) - 1/24 x DATA(2, -2) - - 2 2 2 - + 5/36 x DATA(1, -2) + 5/48 x DATA(-1, -2) - 1/72 x DATA(-2, -2) - - 2 - - 1/18 x DATA(1, 2) - 1/18 x DATA(-2, -1) + 1/3 x DATA(2, -1) - - 2 2 - - 1/3 x DATA(2, 1) + 1/18 x DATA(2, -1) - 7/36 x DATA(0, -2) - - 2 2 2 - + 1/144 x DATA(3, -2) - 1/18 x DATA(3, -1) + 1/18 x DATA(3, 1) - - 2 2 2 - - 1/144 x DATA(3, 2) - 5/36 x DATA(1, 2) + 1/9 x DATA(-2, -1) - - 2 2 2 - + 1/72 x DATA(-2, 2) - 1/9 x DATA(-2, 1) + 14/9 x DATA(0, -1) - - 2 2 2 - + 7/36 x DATA(0, 2) - 5/48 x DATA(-1, 2) - 1/4 y DATA(0, 3) - - 2 2 - + 1/24 x DATA(2, 2) + 5/6 x DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=134162200, alloc=2620960, time=11.90 -bytes used=135162664, alloc=2620960, time=11.96 -bytes used=136163612, alloc=2620960, time=12.03 - 3 2 2 3 -[COEFF(-2, -2) = 1/144 x + 1/18 x y + 1/48 x y - 1/36 x y - 1/36 y x - - 2 2 2 3 2 3 - - 1/24 x y + 1/144 x - 1/72 x + 1/48 x y , COEFF(-1, -2) = 7/36 y x - - 2 2 2 2 2 - - 5/12 x y + 5/48 x + 2/9 x y - 1/18 x - 1/6 x y + 5/16 x y - - 3 3 2 2 3 2 - - 7/144 x - 7/48 x y , COEFF(0, -2) = 1/4 y + 1/12 + 1/3 x y - - 2 2 3 2 2 3 - - 7/36 x + 7/9 x y - 4/9 y x - 7/12 x y + 1/9 x - 1/3 y, - - 3 2 2 2 2 3 - COEFF(1, -2) = - 1/9 x + 5/12 x y + 5/36 x + 1/6 x y + 4/9 y x - - 2 3 2 2 2 - - 5/9 x y + 1/18 x - 2/9 x y - 1/3 x y , COEFF(2, -2) = - 1/8 x y - - 2 3 2 3 2 2 - + 1/36 x y + 1/6 x y + 7/144 x - 1/48 x y + 7/48 x y - 1/24 x - - 3 - - 1/144 x - 7/36 y x , COEFF(3, -2) = - - 3 2 2 3 2 2 3 2 - 1/36 y x - 1/36 x y + 1/144 x - 1/144 x + 1/48 x y - 1/48 x y , - - 2 2 2 3 2 - COEFF(-2, -1) = 1/9 x + 7/24 x y - 7/48 x y - 1/18 x + 5/24 x y - - 3 3 2 2 2 - + 5/24 y x - 1/18 x - 5/12 x y - 7/48 x y , COEFF(-1, -1) = - 5/6 x - - 35 2 2 2 2 3 35 3 - - -- x y + 4/9 x + 25/8 x y + 7/6 x y - 5/3 x y + 7/18 x - -- y x - 16 24 - - 49 3 2 2 3 2 2 2 - + -- x y , COEFF(0, -1) = - 35/6 x y - 7/3 x y - 7/4 y + 14/9 x - 48 - - 49 2 2 3 3 2 - + -- x y + 5/2 y - 2/3 - 8/9 x + 10/3 y x , COEFF(1, -1) = - 7/6 x y - 12 - - 3 3 2 3 2 35 2 2 - - 10/3 y x + 7/3 x y + 8/9 x + 25/6 x y - -- x y + 5/3 x y - 4/9 x - 12 - - 2 2 2 3 - - 10/9 x , COEFF(2, -1) = - 5/24 x y + 1/18 x + 7/8 x y - 7/18 x - - 35 3 2 49 3 2 2 2 - + -- y x + 7/48 x y - -- x y + 1/3 x - 5/4 x y, COEFF(3, -1) = - 24 48 - - 2 3 2 2 3 3 2 2 - - 1/18 x + 7/48 x y + 5/24 x y + 1/18 x - 5/24 y x - 7/48 x y , - - COEFF(-2, 0) = - - 2 2 3 3 2 2 2 - - 2/3 x y - 7/18 x y - 7/18 y x + 1/3 x y + 1/3 x y + 7/9 x y, - - COEFF(-1, 0) = - - 3 2 2 2 2 2 49 3 - - 7/3 x y + 28/9 x y - 35/6 x y + 5 x y - 8/3 x y + -- y x , - 18 - - COEFF(0, 0) = - - 2 2 2 3 2 3 2 - 4 y - 28/3 x y - 14/3 y + 16/3 x y - 56/9 y x + 98/9 x y, - - COEFF(1, 0) = - - 2 2 3 3 2 2 2 - - 70/9 x y - 28/9 x y + 8/3 x y + 56/9 y x - 16/3 x y + 20/3 x y , - - COEFF(2, 0) = - - 2 49 3 2 2 2 3 2 - - 1/3 x y - -- y x - 2 x y + 7/3 x y + 7/3 x y + 7/18 x y, - 18 - - 2 3 2 2 3 2 - COEFF(3, 0) = - 7/18 x y + 7/18 y x + 1/3 x y - 1/3 x y , COEFF(-2, 1) - - 3 3 2 3 2 - = 5/18 x y + 1/18 x + 5/18 y x - 5/9 x y - 1/3 x y + 1/18 x - - 2 2 2 2 3 2 2 - + 2/3 x y - 1/3 x y - 1/9 x , COEFF(-1, 1) = 7/3 x y + 8/3 x y - - 2 2 2 2 3 35 3 - + 5/6 x + 25/6 x y - 5 x y - 7/18 x - 4/9 x - -- y x - 20/9 x y, - 18 - - 3 2 2 3 2 - COEFF(0, 1) = 40/9 y x - 4 y - 70/9 x y - 16/3 x y + 10/3 y - - 2 2 3 2 3 - + 28/3 x y + 8/9 x + 2/3 - 14/9 x , COEFF(1, 1) = 4/9 x - 8/9 x - - 2 2 2 3 2 3 2 - - 20/3 x y + 20/9 x y + 50/9 x y + 16/3 x y - 40/9 y x - 8/3 x y - - 2 35 3 2 3 2 - + 10/9 x , COEFF(2, 1) = -- y x - 5/3 x y - 7/3 x y - 1/18 x - 18 - - 3 2 2 2 2 - - 5/18 x y + 7/18 x + 1/3 x y - 1/3 x + 2 x y , COEFF(3, 1) = - - 3 2 2 2 3 2 3 2 - 1/3 x y - 1/3 x y - 1/18 x + 5/18 x y - 5/18 y x + 1/18 x , - - 2 3 2 2 - COEFF(-2, 2) = 1/6 x y - 1/12 x y - 1/12 y x + 1/72 x + 7/48 x y - - 3 2 2 3 2 - - 1/144 x - 1/144 x - 7/24 x y + 7/48 x y , COEFF(-1, 2) = 2/3 x y - - 2 35 2 2 2 49 3 2 3 3 - - 5/48 x + -- x y + 1/18 x - 7/6 x y - -- x y + 7/144 x + 7/12 y x - 16 48 - - 2 2 2 3 49 2 2 - - 5/4 x y, COEFF(0, 2) = - 1/12 + 7/4 y + 7/36 x - 1/9 x - -- x y - 12 - - 3 3 2 2 3 - - 4/3 y x + 7/3 x y + 7/3 x y - y, COEFF(1, 2) = 4/3 y x - 2/3 x y - - 35 2 2 2 3 2 2 2 3 - + -- x y - 5/36 x - 7/3 x y + 7/6 x y - 5/3 x y + 1/9 x - 1/18 x, - 12 - - 3 2 2 2 2 - COEFF(2, 2) = - 7/12 y x - 7/8 x y + 1/144 x + 1/2 x y + 1/24 x - - 49 3 2 3 2 - + 1/12 x y + -- x y - 7/144 x - 7/48 x y , COEFF(3, 2) = - 48 - - 2 2 2 3 3 3 2 2 - 7/48 x y - 1/144 x + 1/144 x + 1/12 y x - 7/48 x y - 1/12 x y, - - COEFF(-2, 3) = - - 2 3 2 2 3 2 2 - - 1/36 x y - 1/48 x y + 1/72 x y - 1/48 x y + 1/72 y x + 1/24 x y , - - COEFF(-1, 3) = - - 3 2 2 2 3 2 2 - 7/48 x y + 1/6 x y + 5/24 x y - 7/72 y x - 1/9 x y - 5/16 x y , - - COEFF(0, 3) = - - 2 2 2 2 3 3 2 - 7/12 x y - 1/4 y - 7/18 x y + 2/9 y x - 1/3 x y + 1/6 y, COEFF(1, 3) - - 2 3 3 2 2 2 2 - = 5/18 x y + 1/9 x y - 2/9 y x + 1/3 x y - 5/12 x y - 1/6 x y , - - COEFF(2, 3) = - - 3 2 3 2 2 2 2 - 7/72 y x + 1/48 x y - 7/48 x y - 1/12 x y - 1/72 x y + 1/8 x y , - - 3 2 2 2 3 2 - COEFF(3, 3) = 1/48 x y - 1/48 x y - 1/72 y x + 1/72 x y] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-dy.compute.c"); -bytes used=137163792, alloc=3014104, time=12.11 -bytes used=138163952, alloc=3014104, time=12.19 -bytes used=139164132, alloc=3014104, time=12.26 -bytes used=140175232, alloc=3014104, time=12.33 -bytes used=141178452, alloc=3014104, time=12.41 -bytes used=142178916, alloc=3014104, time=12.49 -bytes used=143179088, alloc=3014104, time=12.56 -bytes used=144179384, alloc=3014104, time=12.63 -bytes used=145179768, alloc=3014104, time=12.70 -bytes used=146179932, alloc=3014104, time=12.95 -bytes used=147180108, alloc=3014104, time=13.02 -bytes used=148180528, alloc=3014104, time=13.09 -bytes used=149180772, alloc=3014104, time=13.16 -bytes used=150180980, alloc=3014104, time=13.27 -bytes used=151181932, alloc=3014104, time=13.36 -bytes used=152182144, alloc=3014104, time=13.48 -bytes used=153193564, alloc=3014104, time=13.57 -bytes used=154193736, alloc=3014104, time=13.66 -bytes used=155194144, alloc=3014104, time=13.74 -bytes used=156194356, alloc=3014104, time=14.04 -bytes used=157194740, alloc=3014104, time=14.13 -bytes used=158194908, alloc=3014104, time=14.19 -bytes used=159195132, alloc=3014104, time=14.32 -bytes used=160195316, alloc=3014104, time=14.45 -bytes used=161195616, alloc=3014104, time=14.74 -bytes used=162195916, alloc=3014104, time=14.79 -bytes used=163196160, alloc=3014104, time=14.94 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order3,x,x) ); -bytes used=164196448, alloc=3014104, time=15.02 -bytes used=165207068, alloc=3014104, time=15.09 - 2 -98/9 y DATA(0, 0) + 1/24 x y DATA(3, 2) - 2/3 x y DATA(0, 2) - - 2 2 - - 16/3 x y DATA(0, -1) - 1/24 x y DATA(3, 3) + 7/6 x y DATA(3, 0) - - - 1/3 x y DATA(3, 1) + 1/3 x y DATA(3, -1) - 1/24 x y DATA(3, -2) - - 2 2 - + 2/3 x y DATA(0, -2) - 4 x y DATA(0, 2) + 10 x y DATA(0, -1) - - 2 2 - + 16/3 x y DATA(0, 1) + 1/4 x y DATA(3, 2) - 5/6 x y DATA(3, 1) - - 2 2 2 - - 5/8 x y DATA(3, -1) - 4/3 x y DATA(0, -2) + 2/3 x y DATA(0, 3) - - 2 2 3 - + 40/3 x y DATA(0, 1) - 56/3 x y DATA(0, 0) + 14/3 x y DATA(1, -1) - - 3 3 49 3 - + 14/3 x y DATA(0, 2) - 14/3 x y DATA(0, -1) - -- x y DATA(-1, 2) - 24 - - 3 2 - - 14/3 x y DATA(2, 1) + 1/2 x DATA(-2, 0) + 5/18 y DATA(3, 1) - - 2 2 - + 8 x DATA(0, 0) - 5/12 y DATA(-2, -1) - 1/12 y DATA(3, 2) - - 2 2 - + 1/18 y DATA(-2, -2) - 5/9 y DATA(1, -2) - 14/3 DATA(0, 0) - - 2 2 - + 10/3 DATA(1, 0) + 5/24 y DATA(-1, 3) + 7/9 y DATA(-2, 0) - - 2 2 3 - - 1/36 y DATA(3, -2) + 5/24 y DATA(3, -1) + 2/9 y DATA(3, 0) - - 2 2 2 - + 25/6 y DATA(-1, 1) - 35/6 y DATA(-1, 0) - 1/12 y DATA(2, 3) - - 3 2 3 - + 7/12 y DATA(2, -1) + 5/18 y DATA(1, 3) - 1/72 y DATA(3, 3) - - 3 2 2 - + 4/3 y DATA(2, 1) - 5/3 y DATA(1, 2) + 7/3 y DATA(2, 0) - - 2 2 - + 1/2 y DATA(2, 2) - 5/4 y DATA(-1, 2) - 1/3 DATA(-2, 0) - - 49 3 2 2 - - -- y DATA(0, 2) - 1/36 y DATA(-2, 3) - 5/12 y DATA(-1, -2) - 18 - - 2 35 3 2 - - 5/9 y DATA(-2, 1) - -- y DATA(-1, -1) + 50/9 y DATA(1, 1) - 24 - - 35 3 2 - + 1/6 DATA(3, 0) - -- y DATA(1, -1) - 70/9 y DATA(1, 0) - 18 - - 2 3 3 - + 1/6 y DATA(2, -2) - 1/12 y DATA(2, -2) + 40/9 y DATA(1, 0) - - 3 3 3 - + 56/9 y DATA(0, 1) - 56/9 y DATA(0, 0) - 40/9 y DATA(1, 1) - - 3 3 3 - - 7/18 y DATA(0, -2) + 4/9 y DATA(-2, 1) + 5/24 y DATA(-1, -2) - - 3 2 2 - - 7/36 y DATA(-2, 2) + 1/72 y DATA(3, 3) - 5/4 y DATA(2, -1) - - 3 3 2 - + 7/36 y DATA(-2, -1) - 1/36 y DATA(-2, -2) + 1/6 y DATA(-2, 2) - - 2 3 3 - + 7/9 y DATA(0, -2) + 7/72 y DATA(3, 2) - 2/9 y DATA(3, 1) - - 3 2 - - 7/72 y DATA(3, -1) - 70/9 y DATA(0, 1) + 20/9 y DATA(1, 1) - - 2 2 49 3 - + 7/3 y DATA(0, 2) - 5/3 y DATA(2, 1) + -- y DATA(0, -1) - 18 - - 35 3 2 2 - + -- y DATA(-1, 2) + 25/6 y DATA(1, -1) + 25/8 y DATA(-1, -1) - 24 - - 3 3 35 3 - - 7/12 y DATA(2, 2) - 4/3 y DATA(2, 0) + -- y DATA(1, 2) - 18 - - 2 - - 7/18 y DATA(3, 0) - 1/3 x y DATA(-2, -1) - 1/24 x y DATA(-2, 2) - - 2 - + 1/3 x y DATA(-2, 1) - 35/6 y DATA(0, -1) + 7/24 x y DATA(2, -2) - - - 2/3 x y DATA(1, -2) - 7/24 x y DATA(-1, -2) + 1/24 x y DATA(-2, -2) - - + 7/3 x y DATA(2, 1) + 16/3 x y DATA(1, -1) + 7/3 x y DATA(-1, -1) - - - 7/3 x y DATA(-1, 1) - 7/24 x y DATA(2, 2) - 16/3 x y DATA(1, 1) - - + 2/3 x y DATA(1, 2) - 7/3 x y DATA(2, -1) + 7/24 x y DATA(-1, 2) - - - 1/72 y DATA(3, 2) + 2/3 y DATA(2, -1) - 28/9 y DATA(0, 1) - - + 28/9 y DATA(0, -1) - 2/3 y DATA(2, 1) - 7/18 y DATA(0, -2) - - 3 - + 5/18 y DATA(1, -2) - 5/18 y DATA(1, 2) - 20/9 y DATA(1, -1) - - - 5/3 y DATA(-1, -1) + 5/3 y DATA(-1, 1) + 1/12 y DATA(2, 2) - - - 5/24 y DATA(-1, 2) + 5/2 DATA(-1, 0) - DATA(2, 0) - 1/12 y DATA(2, -2) - - + 5/18 y DATA(1, -2) + 5/24 y DATA(-1, -2) - 1/36 y DATA(-2, -2) - - + 2/9 y DATA(-2, -1) + 1/36 y DATA(-2, 2) - 2/9 y DATA(-2, 1) - - 2 - + 1/72 y DATA(3, -2) - 1/9 y DATA(3, -1) - 7/4 x y DATA(2, 2) - - 2 2 2 - + 7/4 x y DATA(-1, 2) - 49/6 x y DATA(2, 0) + 4 x y DATA(1, 2) - - 2 2 2 - + 35/6 x y DATA(2, 1) - 10 x y DATA(1, -1) - 35/8 x y DATA(-1, -1) - - 2 2 2 - - 35/6 x y DATA(-1, 1) - 1/4 x y DATA(-2, 2) + 5/6 x y DATA(-2, 1) - - 2 2 2 - + 7/24 x y DATA(2, 3) - 2/3 x y DATA(1, 3) - 7/24 x y DATA(-1, 3) - - 2 2 2 - + 1/24 x y DATA(-2, 3) - 7/6 x y DATA(-2, 0) + 35/8 x y DATA(2, -1) - - 2 2 2 - - 40/3 x y DATA(1, 1) + 56/3 x y DATA(1, 0) - 7/12 x y DATA(2, -2) - - 2 2 2 - + 4/3 x y DATA(1, -2) + 7/12 x y DATA(-1, -2) + 49/6 x y DATA(-1, 0) - - 2 2 - - 1/12 x y DATA(-2, -2) + 5/8 x y DATA(-2, -1) + 1/9 y DATA(3, 1) - - 3 3 - - 10/3 y DATA(-1, 1) + 1/36 y DATA(-2, 3) + 7/2 x DATA(2, 0) - - - 1/2 x DATA(3, 0) - 7/2 x DATA(-1, 0) - 8 x DATA(1, 0) - - 3 3 3 - + 10/3 y DATA(-1, 0) + 7/18 y DATA(0, 3) + 1/12 y DATA(2, 3) - - 3 3 3 - - 4/9 y DATA(-2, 0) - 5/24 y DATA(-1, 3) - 5/18 y DATA(1, 3) - - 3 3 - + 1/72 y DATA(3, -2) + 7/18 y DATA(0, 2) + 2/3 x y DATA(1, 3) - - 3 3 3 - - 1/24 x y DATA(-2, 3) + 14/3 x y DATA(-1, 1) - 14/3 x y DATA(-1, 0) - - 3 3 3 - - 2/3 x y DATA(0, 3) - 7/24 x y DATA(2, 3) - 7/24 x y DATA(-2, -1) - - 3 3 3 - + 7/24 x y DATA(-2, 2) - 7/24 x y DATA(-1, -2) - 2/3 x y DATA(-2, 1) - - 3 3 3 - + 2/3 x y DATA(0, -2) - 7/24 x y DATA(3, 2) - 2/3 x y DATA(1, -2) - - 3 3 3 - + 1/24 x y DATA(-2, -2) + 2/3 x y DATA(-2, 0) - 1/24 x y DATA(3, -2) - - 3 3 3 - + 7/24 x y DATA(3, -1) + 2/3 x y DATA(3, 1) + 7/24 x y DATA(-1, 3) - - 3 49 3 2 - + 1/24 x y DATA(3, 3) - -- x y DATA(2, -1) - 7/18 y DATA(0, 3) - 24 - - 49 3 3 3 - + -- x y DATA(2, 2) + 14/3 x y DATA(2, 0) - 14/3 x y DATA(1, 2) - 24 - - 3 3 3 - + 7/24 x y DATA(2, -2) - 32/3 x y DATA(1, 0) - 32/3 x y DATA(0, 1) - - 3 3 2 - + 32/3 x y DATA(0, 0) + 32/3 x y DATA(1, 1) + 1/12 x y DATA(3, -2) - - 49 3 3 - + -- x y DATA(-1, -1) - 2/3 x y DATA(3, 0) - 24 - -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=166207496, alloc=3014104, time=15.17 -bytes used=167207668, alloc=3014104, time=15.23 -[COEFF(-2, -2) = - - 2 3 2 3 - - 1/12 x y + 1/24 x y - 1/36 y - 1/36 y + 1/18 y + 1/24 x y , - - COEFF(-1, -2) = - - 2 3 2 3 - - 7/24 x y + 5/24 y + 7/12 x y - 7/24 x y - 5/12 y + 5/24 y , - - 3 2 3 2 - COEFF(0, -2) = - 7/18 y + 2/3 x y - 4/3 x y - 7/18 y + 2/3 x y + 7/9 y , - - 2 2 3 3 - COEFF(1, -2) = 5/18 y - 5/9 y - 2/3 x y + 4/3 x y - 2/3 x y + 5/18 y , - - COEFF(2, -2) = - - 2 2 3 3 - - 7/12 x y + 7/24 x y + 1/6 y - 1/12 y - 1/12 y + 7/24 x y , - - COEFF(3, -2) = - - 3 2 3 2 - 1/72 y + 1/12 x y - 1/24 x y - 1/36 y + 1/72 y - 1/24 x y, - - 2 3 2 3 - COEFF(-2, -1) = 2/9 y - 5/12 y + 7/36 y + 5/8 x y - 7/24 x y - 1/3 x y, - - 2 49 3 2 35 3 - COEFF(-1, -1) = - 35/8 x y + -- x y + 7/3 x y + 25/8 y - -- y - 5/3 y, - 24 24 - - 3 2 49 3 2 - COEFF(0, -1) = 28/9 y - 16/3 x y - 14/3 x y - 35/6 y + -- y + 10 x y , - 18 - - 2 2 3 35 3 - COEFF(1, -1) = 16/3 x y + 25/6 y - 10 x y + 14/3 x y - 20/9 y - -- y , - 18 - - 2 2 49 3 3 - COEFF(2, -1) = 35/8 x y + 2/3 y - 7/3 x y - 5/4 y - -- x y + 7/12 y , - 24 - - 3 3 2 2 - COEFF(3, -1) = 7/24 x y - 7/72 y - 1/9 y + 1/3 x y + 5/24 y - 5/8 x y , - - 3 2 3 2 - COEFF(-2, 0) = - 4/9 y + 7/9 y - 1/3 + 1/2 x + 2/3 x y - 7/6 x y , - - 3 3 2 2 - COEFF(-1, 0) = - 7/2 x + 10/3 y - 14/3 x y - 35/6 y + 49/6 x y + 5/2, - - 3 2 2 3 - COEFF(0, 0) = - 56/9 y - 14/3 + 8 x - 56/3 x y + 98/9 y + 32/3 x y , - - 3 3 2 2 - COEFF(1, 0) = 10/3 - 32/3 x y + 40/9 y + 56/3 x y - 70/9 y - 8 x, - - 3 2 3 2 - COEFF(2, 0) = - 4/3 y + 7/3 y - 1 + 14/3 x y + 7/2 x - 49/6 x y , - - 2 2 3 3 - COEFF(3, 0) = - 7/18 y + 7/6 x y + 2/9 y - 1/2 x + 1/6 - 2/3 x y , - - 3 2 2 3 - COEFF(-2, 1) = - 2/3 x y + 5/6 x y - 5/9 y + 4/9 y + 1/3 x y - 2/9 y, - - 2 3 2 3 - COEFF(-1, 1) = 25/6 y + 5/3 y - 10/3 y - 7/3 x y - 35/6 x y + 14/3 x y , - - 3 2 2 3 - COEFF(0, 1) = 56/9 y - 28/9 y + 40/3 x y - 70/9 y - 32/3 x y + 16/3 x y - - , - - 2 3 2 3 - COEFF(1, 1) = 50/9 y + 32/3 x y - 40/3 x y + 20/9 y - 16/3 x y - 40/9 y - - 3 2 2 3 - , COEFF(2, 1) = - 14/3 x y - 5/3 y + 7/3 x y + 35/6 x y + 4/3 y - 2/3 y, - - 3 2 3 2 - COEFF(3, 1) = - 1/3 x y - 2/9 y + 1/9 y - 5/6 x y + 2/3 x y + 5/18 y , - - COEFF(-2, 2) = - - 3 2 3 2 - - 7/36 y - 1/24 x y - 1/4 x y + 7/24 x y + 1/6 y + 1/36 y, - - 2 35 3 49 3 2 - COEFF(-1, 2) = - 5/24 y - 5/4 y + -- y - -- x y + 7/4 x y + 7/24 x y, - 24 24 - - 3 49 3 2 2 - COEFF(0, 2) = 14/3 x y - -- y + 7/18 y - 2/3 x y + 7/3 y - 4 x y , - 18 - - 2 3 2 35 3 - COEFF(1, 2) = 2/3 x y + 4 x y - 14/3 x y - 5/3 y - 5/18 y + -- y , - 18 - - 3 2 2 49 3 - COEFF(2, 2) = - 7/12 y + 1/12 y + 1/2 y - 7/24 x y - 7/4 x y + -- x y , - 24 - - COEFF(3, 2) = - - 3 3 2 2 - - 7/24 x y + 7/72 y - 1/72 y + 1/24 x y - 1/12 y + 1/4 x y , - - 2 3 2 3 - COEFF(-2, 3) = - 1/36 y - 1/24 x y + 1/24 x y + 1/36 y , - - 2 3 3 2 - COEFF(-1, 3) = 5/24 y - 5/24 y + 7/24 x y - 7/24 x y , - - 3 3 2 2 - COEFF(0, 3) = - 2/3 x y + 7/18 y + 2/3 x y - 7/18 y , - - 2 2 3 3 - COEFF(1, 3) = 5/18 y - 2/3 x y - 5/18 y + 2/3 x y , - - 2 2 3 3 - COEFF(2, 3) = 7/24 x y - 1/12 y - 7/24 x y + 1/12 y , - - 3 3 2 2 - COEFF(3, 3) = - 1/72 y + 1/24 x y + 1/72 y - 1/24 x y ] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-dxx.compute.c"); -bytes used=168207836, alloc=3014104, time=15.32 -bytes used=169208044, alloc=3014104, time=15.40 -bytes used=170221676, alloc=3014104, time=15.47 -bytes used=171222016, alloc=3014104, time=15.56 -bytes used=172222280, alloc=3014104, time=15.72 -bytes used=173222532, alloc=3014104, time=15.85 -bytes used=174222932, alloc=3014104, time=15.91 -bytes used=175223152, alloc=3014104, time=15.99 -bytes used=176223420, alloc=3014104, time=16.08 -bytes used=177225428, alloc=3014104, time=16.18 -bytes used=178225976, alloc=3014104, time=16.26 -bytes used=179226200, alloc=3014104, time=16.52 -bytes used=180226432, alloc=3014104, time=16.59 -bytes used=181227272, alloc=3014104, time=16.70 -bytes used=182227520, alloc=3014104, time=16.97 -bytes used=183227776, alloc=3014104, time=17.07 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order3,x,y) ); -bytes used=184227964, alloc=3014104, time=17.15 -bytes used=185228324, alloc=3014104, time=17.22 -bytes used=186228720, alloc=3014104, time=17.29 -- 1/6 x y DATA(3, 2) + 14/3 x y DATA(0, 2) - 35/3 x y DATA(0, -1) - - 2 2 - - 1/24 x y DATA(3, 3) + 2/3 x y DATA(3, 0) + 5/9 x y DATA(3, 1) - - + 5/12 x y DATA(3, -1) - 1/18 x y DATA(3, -2) + 14/9 x y DATA(0, -2) - - 2 2 - - 49/6 x y DATA(0, 2) + 49/6 x y DATA(0, -1) - 140/9 x y DATA(0, 1) - - 2 2 2 - + 7/24 x y DATA(3, 2) - 2/3 x y DATA(3, 1) - 7/24 x y DATA(3, -1) - - 2 2 2 - - 7/6 x y DATA(0, -2) + 7/6 x y DATA(0, 3) + 56/3 x y DATA(0, 1) - - 2 2 2 - - 56/3 x y DATA(0, 0) - 7/48 y DATA(-2, -1) + 1/48 y DATA(-2, -2) - - 2 2 - + 1/6 y DATA(1, -2) + 4/9 DATA(1, 1) + 1/6 y DATA(-1, 3) - - 2 - + 1/3 y DATA(-2, 0) - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - - - 1/18 DATA(-1, -2) + 1/144 DATA(-2, -2) - 1/18 DATA(-2, -1) - - 2 - - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) + 8/3 y DATA(-1, 1) - - 2 2 2 - - 8/3 y DATA(-1, 0) + 1/48 y DATA(2, 3) - 1/6 y DATA(1, 3) - - 2 2 2 - + 7/6 y DATA(1, 2) - 1/3 y DATA(2, 0) - 7/48 y DATA(2, 2) - - 2 2 2 - - 7/6 y DATA(-1, 2) - 1/48 y DATA(-2, 3) - 1/6 y DATA(-1, -2) - - 2 2 2 - - 1/3 y DATA(-2, 1) - 8/3 y DATA(1, 1) + 8/3 y DATA(1, 0) - - 2 2 2 - - 1/48 y DATA(2, -2) + 7/48 y DATA(2, -1) + 7/48 y DATA(-2, 2) - - 2 2 - + 20/9 y DATA(1, 1) + 1/3 y DATA(2, 1) - 7/6 y DATA(1, -1) - - 2 - + 7/6 y DATA(-1, -1) - 5/6 x y DATA(-2, -1) + 1/3 x y DATA(-2, 2) - - 2 2 - - 10/9 x y DATA(-2, 1) + 7/48 x DATA(-1, 2) - 1/3 x DATA(0, 2) - - 2 2 2 - + 1/3 x DATA(1, 2) - 8/3 x DATA(0, -1) - 8/3 x DATA(1, 1) - - 2 2 2 - + 8/3 x DATA(0, 1) + 7/48 x DATA(2, -2) - 1/3 x DATA(1, -2) - - 2 - + 4/3 x y DATA(1, -2) + 1/3 x y DATA(2, -2) - 10/9 x y DATA(1, -2) - - 2 - - 5/6 x y DATA(-1, -2) + 1/9 x y DATA(-2, -2) + 7/12 x y DATA(-1, -2) - - 2 2 2 - + 7/24 x y DATA(2, 3) + 5/8 x y DATA(-2, -1) - 7/24 x y DATA(-1, 3) - - 2 2 2 2 - + x y DATA(0, -2) + x y DATA(-2, 0) - 10/3 x y DATA(2, 1) - - + 25/3 x y DATA(1, -1) + 25/4 x y DATA(-1, -1) + 25/3 x y DATA(-1, 1) - - + x y DATA(2, 2) + 100/9 x y DATA(1, 1) - 10/3 x y DATA(1, 2) - - 2 2 - - 5/2 x y DATA(2, -1) - 5/2 x y DATA(-1, 2) + 7 x y DATA(0, 2) - - 2 2 2 2 - + 16 x y DATA(0, 0) - 7 x y DATA(0, -1) - 5/24 y DATA(2, -1) - - - 5/18 y DATA(2, 1) - 2/3 y DATA(1, 2) + 5/3 y DATA(1, -1) - - - 5/3 y DATA(-1, -1) - 20/9 y DATA(-1, 1) + 1/18 DATA(2, -1) - - - 1/18 DATA(2, 1) + 1/12 y DATA(2, 2) - 4/9 DATA(1, -1) + 4/9 DATA(-1, -1) - - - 4/9 DATA(-1, 1) + 2/3 y DATA(-1, 2) + 1/144 DATA(2, 2) - - + 1/18 DATA(-1, 2) + 1/36 y DATA(2, -2) - 2/9 y DATA(1, -2) - - + 2/9 y DATA(-1, -2) - 1/36 y DATA(-2, -2) + 5/24 y DATA(-2, -1) - - 2 2 49 2 2 - - 1/12 y DATA(-2, 2) + 7 x y DATA(1, -1) + -- x y DATA(-1, -1) - 16 - - 2 2 2 2 - + 7 x y DATA(-1, 1) - 28/9 y DATA(1, 0) - 7 x y DATA(2, 1) - - 49 2 2 49 2 2 2 2 - + -- x y DATA(2, 2) - -- x y DATA(-1, 2) - 7 x y DATA(1, 2) - 16 16 - - 49 2 2 2 2 - - -- x y DATA(2, -1) + 5/18 y DATA(-2, 1) - 1/16 x y DATA(3, -2) - 16 - - 2 2 2 2 2 2 - + 7/16 x y DATA(3, -1) + x y DATA(3, 1) - 7/16 x y DATA(3, 2) - - 2 2 2 2 2 2 - - x y DATA(3, 0) - 7 x y DATA(-1, 0) + 7/16 x y DATA(2, -2) - - 2 2 2 2 2 2 - - 7/16 x y DATA(-1, -2) - 7/16 x y DATA(2, 3) + 1/16 x y DATA(3, 3) - - 2 2 2 2 2 2 - + 7 x y DATA(2, 0) + 1/16 x y DATA(-2, -2) + 7/16 x y DATA(-2, 2) - - 2 2 2 2 2 2 - - x y DATA(-2, 1) - 7/16 x y DATA(-2, -1) + 7/16 x y DATA(-1, 3) - - 2 2 2 2 2 2 - - x y DATA(0, 3) - 16 x y DATA(0, 1) - x y DATA(1, -2) - - - 1/9 y DATA(-1, 3) + 1/72 y DATA(-2, 3) - 7/18 y DATA(-2, 0) - - + 28/9 y DATA(-1, 0) + 7/18 y DATA(2, 0) - 1/72 y DATA(2, 3) - - 2 2 - + 1/9 y DATA(1, 3) - 140/9 x y DATA(1, 0) + x y DATA(1, 3) - - 2 2 2 2 - + 196/9 x y DATA(0, 0) - 1/16 x y DATA(-2, 3) + 16 x y DATA(1, 1) - - 2 2 - - 16 x y DATA(1, 0) + 14/9 x y DATA(-2, 0) - 35/3 x y DATA(-1, 0) - - + 5/12 x y DATA(-1, 3) - 1/18 x y DATA(-2, 3) - 7/9 x y DATA(3, 0) - - 2 - - 4 x y DATA(0, 2) - 1/6 x y DATA(2, 3) + 5/9 x y DATA(1, 3) - - 2 - - 56/3 x y DATA(0, 0) + 1/36 x y DATA(3, 3) - 7/9 x y DATA(0, 3) - - + 14/3 x y DATA(2, 0) - 28/9 x DATA(0, 1) - 1/12 x DATA(2, -2) - - 2 - + 5/18 x DATA(1, -2) + 5/24 x DATA(-1, -2) + 35/8 x y DATA(2, -1) - - 2 2 2 - + 40/3 x y DATA(0, 1) + 1/12 x y DATA(3, -2) - 5/8 x y DATA(3, -1) - - 2 2 2 - - 35/8 x y DATA(-1, -1) - 35/6 x y DATA(-1, 1) + 49/6 x y DATA(-1, 0) - - 2 2 2 - - 7/4 x y DATA(2, 2) + 7/4 x y DATA(-1, 2) + 4 x y DATA(1, 2) - - 2 2 - + 20/9 x DATA(1, 1) - 4/3 x y DATA(0, -2) - 7/6 x y DATA(-2, 0) - - 2 2 2 - + 35/6 x y DATA(2, 1) - 10 x y DATA(1, -1) + 1/24 x y DATA(-2, 3) - - 2 2 2 - - 40/3 x y DATA(1, 1) - 5/6 x y DATA(3, 1) + 1/4 x y DATA(3, 2) - - 2 2 2 - + 7/6 x y DATA(3, 0) - 1/24 x y DATA(3, 3) + 2/3 x y DATA(0, 3) - - 2 2 2 - - 49/6 x y DATA(2, 0) - 1/12 x y DATA(-2, -2) - 1/4 x y DATA(-2, 2) - - 2 2 2 - + 5/6 x y DATA(-2, 1) + 10 x y DATA(0, -1) - 7/4 x y DATA(2, 2) - - 2 - + 35/8 x y DATA(-1, 2) - 5/18 x DATA(1, 2) - 5/24 x DATA(-1, 2) - - + 1/36 x DATA(-2, 2) - 7/18 x DATA(0, -2) + 1/72 x DATA(3, -2) - - - 1/9 x DATA(3, -1) + 1/9 x DATA(3, 1) - 1/72 x DATA(3, 2) - - + 2/3 x DATA(2, -1) - 2/3 x DATA(2, 1) - 20/9 x DATA(1, -1) - - - 5/3 x DATA(-1, -1) + 5/3 x DATA(-1, 1) - 2/9 x DATA(-2, 1) - - 2 - - 1/36 x DATA(-2, -2) + 2/9 x DATA(-2, -1) - 2/3 x y DATA(1, 3) - - 2 2 2 - - 4 x y DATA(2, 0) + 35/6 x y DATA(1, 2) + 4 x y DATA(2, 1) - - 2 2 2 - - 35/6 x y DATA(1, -1) - 35/8 x y DATA(-1, -1) - 10 x y DATA(-1, 1) - - 2 2 2 - - 7/12 x y DATA(-2, 2) + 4/3 x y DATA(-2, 1) + 1/4 x y DATA(2, 3) - - 2 2 2 - - 5/6 x y DATA(1, 3) - 5/8 x y DATA(-1, 3) + 1/12 x y DATA(-2, 3) - - 2 2 2 - - 4/3 x y DATA(-2, 0) + 7/4 x y DATA(2, -1) - 40/3 x y DATA(1, 1) - - 2 2 2 - + 40/3 x y DATA(1, 0) - 1/4 x y DATA(2, -2) + 5/6 x y DATA(1, -2) - - 2 2 2 - + 5/8 x y DATA(-1, -2) + 10 x y DATA(-1, 0) - 1/12 x y DATA(-2, -2) - - 2 2 2 - + 7/12 x y DATA(-2, -1) + 8/3 x DATA(1, -1) + 7/6 x DATA(-1, -1) - - 2 2 - - 7/6 x DATA(-1, 1) - 7/48 x DATA(2, 2) + 1/12 x DATA(2, 2) - - 2 - + 28/9 x DATA(0, -1) + 7/18 x DATA(0, 2) + 56/3 x y DATA(1, 0) - - 2 2 2 - - 7/48 x DATA(-1, -2) + 1/48 x DATA(-2, -2) - 1/6 x DATA(-2, -1) - - 2 2 2 - - 1/48 x DATA(-2, 2) + 1/6 x DATA(-2, 1) + 1/3 x DATA(0, -2) - - 2 2 2 - - 1/48 x DATA(3, -2) + 1/6 x DATA(3, -1) - 1/6 x DATA(3, 1) - - 2 2 2 - + 1/48 x DATA(3, 2) - 7/6 x DATA(2, -1) + 7/6 x DATA(2, 1) - - 2 2 - - 7/12 x y DATA(2, -2) - 1/18 DATA(1, 2) + 1/24 x y DATA(3, -2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=187238408, alloc=3014104, time=17.36 -bytes used=188238568, alloc=3014104, time=17.43 - 2 2 2 2 -[COEFF(-2, -2) = 1/48 x - 1/12 x y + 1/48 y - 1/12 x y - 1/36 y + 1/9 x y - - 2 2 2 - - 1/36 x + 1/16 x y + 1/144, COEFF(-1, -2) = - 7/48 x + 5/24 x - - 2 2 2 2 2 - - 7/16 x y - 1/18 - 5/6 x y + 2/9 y - 1/6 y + 5/8 x y + 7/12 x y, - - 2 2 2 2 2 - COEFF(0, -2) = - 7/18 x + x y + 14/9 x y - 4/3 x y + 1/3 x - 7/6 x y , - - 2 2 2 2 2 - COEFF(1, -2) = 1/6 y + 5/6 x y + 1/18 - 2/9 y - 1/3 x + 5/18 x - x y - - 2 2 2 - - 10/9 x y + 4/3 x y, COEFF(2, -2) = 1/36 y - 1/48 y + 7/48 x + 1/3 x y - - 2 2 2 2 - - 1/4 x y + 7/16 x y - 1/144 - 7/12 x y - 1/12 x, COEFF(3, -2) = - - 2 2 2 2 2 - - 1/18 x y + 1/24 x y + 1/12 x y - 1/16 x y + 1/72 x - 1/48 x , - - 2 2 2 2 2 - COEFF(-2, -1) = 7/12 x y - 7/48 y - 7/16 x y + 5/8 x y + 5/24 y - - 2 2 - + 2/9 x - 1/6 x - 5/6 x y - 1/18, COEFF(-1, -1) = 4/9 - 35/8 x y - - 2 2 2 49 2 2 - + 25/4 x y + 7/6 x - 35/8 x y - 5/3 x + 7/6 y - 5/3 y + -- x y , - 16 - - 2 2 2 2 2 - COEFF(0, -1) = - 35/3 x y + 28/9 x + 49/6 x y - 8/3 x - 7 x y + 10 x y - - 2 2 2 2 - , COEFF(1, -1) = -10 x y - 20/9 x - 35/6 x y - 4/9 + 25/3 x y + 7 x y - - 2 2 2 2 - - 7/6 y + 8/3 x + 5/3 y, COEFF(2, -1) = - 7/6 x + 2/3 x + 7/48 y - - 49 2 2 2 2 - - -- x y - 5/24 y + 7/4 x y - 5/2 x y + 35/8 x y + 1/18, COEFF(3, -1) - 16 - - 2 2 2 2 2 - = - 7/24 x y + 7/16 x y - 5/8 x y + 5/12 x y - 1/9 x + 1/6 x , - - 2 2 2 2 2 - COEFF(-2, 0) = 14/9 x y + 1/3 y - 7/18 y - 7/6 x y + x y - 4/3 x y , - - 2 2 2 2 2 - COEFF(-1, 0) = - 35/3 x y + 28/9 y + 49/6 x y - 8/3 y - 7 x y + 10 x y - - 2 2 2 2 - , COEFF(0, 0) = 16 x y - 56/3 x y - 56/3 x y + 196/9 x y, COEFF(1, 0) - - 2 2 2 2 2 - = - 140/9 x y - 28/9 y + 8/3 y + 56/3 x y - 16 x y + 40/3 x y , - - 2 2 2 2 2 - COEFF(2, 0) = 7 x y - 49/6 x y + 7/18 y - 1/3 y - 4 x y + 14/3 x y, - - 2 2 2 2 2 - COEFF(3, 0) = 2/3 x y - x y - 7/9 x y + 7/6 x y, COEFF(-2, 1) = 1/6 x - - 2 2 2 2 2 - - x y + 5/6 x y - 2/9 x + 5/18 y + 4/3 x y + 1/18 - 10/9 x y - 1/3 y , - - 2 2 2 - COEFF(-1, 1) = - 7/6 x - 4/9 + 8/3 y - 10 x y + 25/3 x y + 5/3 x - - 2 2 2 - - 35/6 x y - 20/9 y + 7 x y , COEFF(0, 1) = - - 2 2 2 2 2 - 40/3 x y + 56/3 x y + 8/3 x - 28/9 x - 140/9 x y - 16 x y , COEFF(1, 1) - - 2 2 2 2 - = - 40/3 x y + 20/9 y - 8/3 x + 4/9 + 20/9 x - 8/3 y - 40/3 x y - - 2 2 2 2 2 2 - + 100/9 x y + 16 x y , COEFF(2, 1) = 35/6 x y + 7/6 x - 7 x y - - 2 2 - - 10/3 x y - 2/3 x + 4 x y - 5/18 y - 1/18 + 1/3 y , - - 2 2 2 2 2 - COEFF(3, 1) = x y + 5/9 x y + 1/9 x - 1/6 x - 5/6 x y - 2/3 x y , - - 2 2 2 2 - COEFF(-2, 2) = 7/16 x y + 1/3 x y - 1/48 x - 7/12 x y + 1/36 x - - 2 2 - + 7/48 y - 1/4 x y - 1/12 y - 1/144, COEFF(-1, 2) = 1/18 - 5/24 x - - 2 49 2 2 2 2 2 - - 5/2 x y + 7/4 x y - -- x y + 2/3 y + 7/48 x + 35/8 x y - 7/6 y , - 16 - - 2 2 2 2 2 - COEFF(0, 2) = 7/18 x + 14/3 x y - 49/6 x y + 7 x y - 4 x y - 1/3 x , - - 2 2 2 2 2 2 - COEFF(1, 2) = 4 x y - 7 x y - 1/18 + 35/6 x y + 7/6 y + 1/3 x - 2/3 y - - 49 2 2 2 - - 5/18 x - 10/3 x y, COEFF(2, 2) = -- x y - 7/4 x y + 1/12 x + x y - 16 - - 2 2 2 - - 7/4 x y - 7/48 y + 1/12 y - 7/48 x + 1/144, COEFF(3, 2) = - - 2 2 2 2 2 - 1/48 x + 1/4 x y - 7/16 x y - 1/6 x y + 7/24 x y - 1/72 x, - - COEFF(-2, 3) = - - 2 2 2 2 2 - - 1/16 x y + 1/72 y - 1/18 x y + 1/24 x y + 1/12 x y - 1/48 y , - - COEFF(-1, 3) = - - 2 2 2 2 2 - 1/6 y + 5/12 x y - 1/9 y - 5/8 x y + 7/16 x y - 7/24 x y, - - 2 2 2 2 - COEFF(0, 3) = -x y - 7/9 x y + 2/3 x y + 7/6 x y , - - 2 2 2 2 2 - COEFF(1, 3) = x y - 1/6 y + 1/9 y - 5/6 x y + 5/9 x y - 2/3 x y, - - COEFF(2, 3) = - - 2 2 2 2 2 - 1/48 y - 7/16 x y + 7/24 x y + 1/4 x y - 1/6 x y - 1/72 y, - - 2 2 2 2 - COEFF(3, 3) = - 1/24 x y - 1/24 x y + 1/16 x y + 1/36 x y] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-dxy.compute.c"); -bytes used=189239064, alloc=3014104, time=17.51 -bytes used=190239412, alloc=3014104, time=17.59 -bytes used=191239964, alloc=3014104, time=17.66 -bytes used=192242180, alloc=3014104, time=17.74 -bytes used=193247692, alloc=3014104, time=17.84 -bytes used=194247960, alloc=3014104, time=17.91 -bytes used=195248140, alloc=3014104, time=17.98 -bytes used=196248344, alloc=3014104, time=18.13 -bytes used=197263428, alloc=3014104, time=18.39 -bytes used=198263684, alloc=3014104, time=18.46 -bytes used=199263864, alloc=3014104, time=18.53 -bytes used=200264028, alloc=3014104, time=18.62 -bytes used=201264204, alloc=3014104, time=18.72 -bytes used=202267576, alloc=3014104, time=18.82 -bytes used=203267724, alloc=3014104, time=18.91 -bytes used=204267872, alloc=3014104, time=18.99 -bytes used=205268028, alloc=3014104, time=19.07 -bytes used=206268200, alloc=3014104, time=19.37 -bytes used=207268400, alloc=3014104, time=19.46 -bytes used=208268576, alloc=3014104, time=19.53 -bytes used=209268756, alloc=3014104, time=19.66 -bytes used=210268952, alloc=3014104, time=19.75 -bytes used=211269132, alloc=3014104, time=20.07 -bytes used=212269444, alloc=3014104, time=20.19 -bytes used=213269748, alloc=3014104, time=20.33 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order3,y,y) ); -bytes used=214270188, alloc=3014104, time=20.41 -bytes used=215270624, alloc=3014104, time=20.48 - 3 -- 14/3 DATA(0, 0) + 10/3 DATA(0, 1) - 14/3 y x DATA(0, -1) - - 3 3 3 - + 2/3 y x DATA(0, -2) + 7/24 y x DATA(-1, 3) + 2/3 y x DATA(1, 3) - - 3 3 3 - - 7/24 y x DATA(2, 3) - 2/3 y x DATA(-2, 1) + 7/24 y x DATA(-2, 2) - - 3 3 3 - - 7/24 y x DATA(-2, -1) + 1/24 y x DATA(-2, -2) - 7/24 y x DATA(-1, -2) - - 3 49 3 3 - + 14/3 y x DATA(1, -1) - -- y x DATA(2, -1) + 2/3 y x DATA(-2, 0) - 24 - - 3 3 3 - - 1/24 y x DATA(-2, 3) - 14/3 y x DATA(1, 2) - 2/3 y x DATA(1, -2) - - 3 3 3 - + 7/24 y x DATA(2, -2) - 32/3 y x DATA(1, 0) + 32/3 y x DATA(1, 1) - - 3 3 3 - - 2/3 y x DATA(0, 3) + 32/3 y x DATA(0, 0) + 14/3 y x DATA(0, 2) - - 3 3 49 3 - - 32/3 y x DATA(0, 1) - 14/3 y x DATA(2, 1) + -- y x DATA(-1, -1) - 24 - - 3 3 3 - - 4/9 x DATA(0, -2) - 2/9 x DATA(1, 3) + 7/72 x DATA(2, 3) - - 3 49 3 49 3 - - 7/72 x DATA(-1, 3) - -- y x DATA(-1, 2) + -- y x DATA(2, 2) - 24 24 - - 3 3 3 - + 14/3 y x DATA(2, 0) - 14/3 y x DATA(-1, 0) + 2/9 x DATA(0, 3) - - 3 3 3 - - 1/36 x DATA(-2, -2) + 4/9 x DATA(1, -2) - 7/36 x DATA(2, -2) - - 3 3 3 - + 56/9 x DATA(1, 0) - 40/9 x DATA(1, 1) - 56/9 x DATA(0, 0) - - 3 3 3 - + 10/3 x DATA(0, -1) + 7/36 x DATA(-1, -2) + 14/3 y x DATA(-1, 1) - - 3 3 3 - + 7/24 y x DATA(3, -1) + 1/24 y x DATA(3, 3) - 2/3 y x DATA(3, 0) - - 3 3 3 - - 7/24 y x DATA(3, 2) + 2/3 y x DATA(3, 1) - 1/24 y x DATA(3, -2) - - 3 3 35 3 - - 5/24 x DATA(3, -1) + 40/9 x DATA(0, 1) + -- x DATA(2, 1) - 18 - - 35 3 3 35 3 - - -- x DATA(-1, -1) - 10/3 x DATA(1, -1) + -- x DATA(2, -1) - 24 24 - - 3 3 3 - - 7/18 x DATA(-2, 0) + 1/72 x DATA(-2, 3) + 5/18 x DATA(-2, 1) - - 3 3 3 - - 1/12 x DATA(-2, 2) + 5/24 x DATA(-2, -1) - 4/3 x DATA(0, 2) - - 2 - - 1/12 x DATA(2, 3) - 1/2 y DATA(0, 3) + 8 y DATA(0, 0) - - + 7/2 y DATA(0, 2) - 8 y DATA(0, 1) - 1/3 DATA(0, -2) + 1/6 DATA(0, 3) - - - 7/24 x y DATA(-2, -1) + 7/24 x y DATA(-2, 2) - 2/3 x y DATA(-2, 1) - - 2 2 2 - - 5/4 x DATA(-1, 2) + 7/3 x DATA(0, 2) - 5/3 x DATA(1, 2) - - 2 2 2 - - 35/6 x DATA(0, -1) + 50/9 x DATA(1, 1) - 70/9 x DATA(0, 1) - - 2 2 2 - + 1/6 x DATA(2, -2) - 5/9 x DATA(1, -2) + 5/6 x y DATA(1, -2) - - - 1/24 x y DATA(2, -2) + 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) - - 2 2 - + 1/24 x y DATA(-2, -2) + 5/8 x y DATA(-1, -2) + 1/4 x y DATA(2, 3) - - 2 2 - + 7/12 x y DATA(-2, -1) - 5/8 x y DATA(-1, 3) + 2/3 x y DATA(2, 1) - - - 7/3 x y DATA(1, -1) + 7/3 x y DATA(-1, -1) + 16/3 x y DATA(-1, 1) - - - 7/24 x y DATA(2, 2) - 16/3 x y DATA(1, 1) + 7/3 x y DATA(1, 2) - - + 7/24 x y DATA(2, -1) - 7/3 x y DATA(-1, 2) + 5/2 DATA(0, -1) - - + 16/3 x y DATA(1, 0) + 2/3 x y DATA(-2, 0) - 16/3 x y DATA(-1, 0) - - 2 - + 1/3 x y DATA(-1, 3) - 1/24 x y DATA(-2, 3) - 49/6 x y DATA(0, 2) - - 2 - + 1/24 x y DATA(2, 3) - 1/3 x y DATA(1, 3) - 56/3 x y DATA(0, 0) - - - 2/3 x y DATA(2, 0) + 1/36 x DATA(2, -2) - 2/9 x DATA(1, -2) - - 2 2 - + 2/9 x DATA(-1, -2) + 7/4 x y DATA(2, -1) + 56/3 x y DATA(0, 1) - - 2 2 2 - + 1/24 x y DATA(3, -2) - 7/24 x y DATA(3, -1) - 35/8 x y DATA(-1, -1) - - 2 2 2 - - 10 x y DATA(-1, 1) + 10 x y DATA(-1, 0) - 7/4 x y DATA(2, 2) - - 2 2 - + 35/8 x y DATA(-1, 2) + 35/6 x y DATA(1, 2) + 20/9 x DATA(1, 1) - - 2 2 2 - - 7/6 x y DATA(0, -2) - 4/3 x y DATA(-2, 0) + 4 x y DATA(2, 1) - - 2 2 2 - - 35/6 x y DATA(1, -1) + 1/12 x y DATA(-2, 3) - 40/3 x y DATA(1, 1) - - 2 2 2 - - 2/3 x y DATA(3, 1) + 7/24 x y DATA(3, 2) + 2/3 x y DATA(3, 0) - - 2 2 2 - - 1/24 x y DATA(3, 3) + 7/6 x y DATA(0, 3) - 4 x y DATA(2, 0) - - 2 2 2 - - 1/12 x y DATA(-2, -2) - 7/12 x y DATA(-2, 2) + 4/3 x y DATA(-2, 1) - - 2 - + 49/6 x y DATA(0, -1) - 2/3 x DATA(1, 2) + 2/3 x DATA(-1, 2) - - - 1/12 x DATA(-2, 2) - 5/24 x DATA(2, -1) - 5/18 x DATA(2, 1) - - + 5/3 x DATA(1, -1) - 5/3 x DATA(-1, -1) - 20/9 x DATA(-1, 1) - - + 5/18 x DATA(-2, 1) - 1/36 x DATA(-2, -2) + 5/24 x DATA(-2, -1) - - 2 2 2 - - 5/6 x y DATA(1, 3) + 25/6 x DATA(1, -1) + 25/8 x DATA(-1, -1) - - 2 2 - + 25/6 x DATA(-1, 1) + 1/2 x DATA(2, 2) + 1/12 x DATA(2, 2) - - 2 2 2 - + 40/3 x y DATA(1, 0) - 5/12 x DATA(-1, -2) + 1/18 x DATA(-2, -2) - - 2 2 2 - - 5/12 x DATA(-2, -1) + 1/6 x DATA(-2, 2) - 5/9 x DATA(-2, 1) - - 2 2 2 - + 7/9 x DATA(0, -2) - 1/36 x DATA(3, -2) + 5/24 x DATA(3, -1) - - 2 2 2 - + 5/18 x DATA(3, 1) - 1/12 x DATA(3, 2) - 5/4 x DATA(2, -1) - - 2 2 - - 5/3 x DATA(2, 1) - 1/4 x y DATA(2, -2) - DATA(0, 2) - - - 1/9 x DATA(-1, 3) + 1/72 x DATA(-2, 3) - 7/18 x DATA(-2, 0) - - + 1/2 y DATA(0, -2) - 1/72 x DATA(2, 3) + 1/9 x DATA(1, 3) - - + 28/9 x DATA(-1, 0) + 7/18 x DATA(2, 0) - 28/9 x DATA(1, 0) - - 2 2 2 - + 1/72 x DATA(3, 3) - 7/18 x DATA(3, 0) - 1/36 x DATA(-2, 3) - - 2 2 2 - + 7/9 x DATA(-2, 0) - 7/18 x DATA(0, 3) + 98/9 x DATA(0, 0) - - 3 3 3 - - 1/72 x DATA(3, 3) + 7/18 x DATA(3, 0) + 1/12 x DATA(3, 2) - - 3 3 2 - - 5/18 x DATA(3, 1) + 1/36 x DATA(3, -2) + 5/24 x DATA(-1, 3) - - 2 3 3 - + 5/18 x DATA(1, 3) + 4/3 x DATA(1, 2) + 7/12 x DATA(-1, 2) - - 3 49 3 49 3 - - 7/12 x DATA(2, 2) - -- x DATA(2, 0) + -- x DATA(-1, 0) - 18 18 - - 35 3 2 - - -- x DATA(-1, 1) - 7/2 y DATA(0, -1) + 7/3 x DATA(2, 0) - 18 - - 2 2 - - 35/6 x DATA(-1, 0) - 70/9 x DATA(1, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size6); -bytes used=216271092, alloc=3014104, time=20.54 -bytes used=217272568, alloc=3014104, time=20.61 - 3 2 3 2 -[COEFF(-2, -2) = 1/24 x y - 1/36 x - 1/12 x y + 1/24 y x + 1/18 x - 1/36 x, - - 2 3 3 2 - COEFF(-1, -2) = 5/8 x y - 7/24 y x + 7/36 x - 1/3 x y + 2/9 x - 5/12 x , - - 2 3 2 3 - COEFF(0, -2) = - 7/6 x y - 1/3 + 2/3 y x + 1/2 y + 7/9 x - 4/9 x , - - 2 3 3 2 - COEFF(1, -2) = 5/6 x y + 1/3 x y + 4/9 x - 2/3 y x - 2/9 x - 5/9 x , - - COEFF(2, -2) = - - 2 3 2 3 - - 1/24 x y - 1/4 x y + 1/36 x + 7/24 y x + 1/6 x - 7/36 x , - - 3 2 2 3 - COEFF(3, -2) = - 1/24 y x + 1/24 x y - 1/36 x + 1/36 x , COEFF(-2, -1) - - 2 2 3 3 - = 7/12 x y + 5/24 x - 5/12 x - 7/24 y x - 7/24 x y + 5/24 x , - - 49 3 2 35 3 2 - COEFF(-1, -1) = -- y x + 25/8 x - 5/3 x - -- x - 35/8 x y + 7/3 x y, - 24 24 - - 2 3 2 3 - COEFF(0, -1) = - 35/6 x - 14/3 y x + 49/6 x y + 5/2 + 10/3 x - 7/2 y, - - 3 3 2 2 - COEFF(1, -1) = 14/3 y x + 5/3 x - 7/3 x y - 10/3 x - 35/6 x y + 25/6 x , - - 2 49 3 2 35 3 - COEFF(2, -1) = 7/4 x y - 5/24 x - -- y x - 5/4 x + -- x + 7/24 x y, - 24 24 - - 2 3 2 3 - COEFF(3, -1) = - 7/24 x y + 7/24 y x + 5/24 x - 5/24 x , - - 2 3 2 3 - COEFF(-2, 0) = - 7/18 x + 2/3 x y - 4/3 x y + 2/3 y x + 7/9 x - 7/18 x , - - 2 3 2 49 3 - COEFF(-1, 0) = 10 x y - 14/3 y x + 28/9 x - 35/6 x - 16/3 x y + -- x , - 18 - - 3 2 3 2 - COEFF(0, 0) = - 14/3 - 56/9 x + 98/9 x + 32/3 y x - 56/3 x y + 8 y, - - 3 3 2 2 - COEFF(1, 0) = 16/3 x y - 28/9 x + 56/9 x - 32/3 y x - 70/9 x + 40/3 x y - - 2 49 3 2 3 - , COEFF(2, 0) = 7/3 x - 2/3 x y - -- x + 7/18 x - 4 x y + 14/3 y x , - 18 - - 2 3 2 3 - COEFF(3, 0) = - 7/18 x + 7/18 x + 2/3 x y - 2/3 y x , - - 3 3 2 2 - COEFF(-2, 1) = 5/18 x - 2/3 y x - 5/9 x - 2/3 x y + 4/3 x y + 5/18 x, - - 35 3 2 3 2 - COEFF(-1, 1) = - -- x + 25/6 x - 20/9 x + 16/3 x y + 14/3 y x - 10 x y, - 18 - - 2 3 3 2 - COEFF(0, 1) = - 70/9 x - 32/3 y x + 10/3 + 40/9 x + 56/3 x y - 8 y, - - 3 3 2 2 - COEFF(1, 1) = 32/3 y x - 16/3 x y + 20/9 x - 40/9 x + 50/9 x - 40/3 x y - - 3 35 3 2 2 - , COEFF(2, 1) = - 14/3 y x + 2/3 x y + -- x + 4 x y - 5/3 x - 5/18 x, - 18 - - 2 2 3 3 - COEFF(3, 1) = 5/18 x - 2/3 x y - 5/18 x + 2/3 y x , COEFF(-2, 2) = - - 2 3 2 3 - - 7/12 x y - 1/12 x - 1/12 x + 1/6 x + 7/24 y x + 7/24 x y, - - 49 3 2 2 3 - COEFF(-1, 2) = - -- y x - 5/4 x + 35/8 x y - 7/3 x y + 2/3 x + 7/12 x , - 24 - - 2 3 3 2 - COEFF(0, 2) = - 49/6 x y + 14/3 y x - 4/3 x + 7/3 x + 7/2 y - 1, - - 2 3 3 2 - COEFF(1, 2) = 35/6 x y + 4/3 x - 2/3 x - 14/3 y x + 7/3 x y - 5/3 x , - - 49 3 2 3 2 - COEFF(2, 2) = -- y x - 7/24 x y - 7/4 x y - 7/12 x + 1/2 x + 1/12 x, - 24 - - 3 3 2 2 - COEFF(3, 2) = 1/12 x - 7/24 y x - 1/12 x + 7/24 x y, COEFF(-2, 3) = - - 2 2 3 3 - 1/72 x - 1/36 x + 1/12 x y - 1/24 y x + 1/72 x - 1/24 x y, - - 2 3 3 2 - COEFF(-1, 3) = 5/24 x - 7/72 x + 1/3 x y - 1/9 x + 7/24 y x - 5/8 x y, - - 2 2 3 3 - COEFF(0, 3) = 7/6 x y - 1/2 y - 7/18 x + 1/6 + 2/9 x - 2/3 y x , - - 2 3 2 3 - COEFF(1, 3) = 1/9 x + 5/18 x - 2/9 x - 5/6 x y - 1/3 x y + 2/3 y x , - - 2 3 3 2 - COEFF(2, 3) = 1/24 x y + 1/4 x y - 1/72 x - 7/24 y x + 7/72 x - 1/12 x , - - 2 2 3 3 - COEFF(3, 3) = - 1/24 x y + 1/72 x - 1/72 x + 1/24 y x ] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3/coeffs-dyy.compute.c"); -bytes used=218272828, alloc=3014104, time=20.68 -bytes used=219273052, alloc=3014104, time=20.76 -bytes used=220288464, alloc=3014104, time=20.83 -bytes used=221288776, alloc=3014104, time=20.92 -bytes used=222289116, alloc=3014104, time=20.99 -bytes used=223289304, alloc=3014104, time=21.26 -bytes used=224289712, alloc=3014104, time=21.32 -bytes used=225289876, alloc=3014104, time=21.40 -bytes used=226290080, alloc=3014104, time=21.49 -bytes used=227296984, alloc=3014104, time=21.59 -bytes used=228297136, alloc=3014104, time=21.66 -bytes used=229297344, alloc=3014104, time=21.95 -bytes used=230297508, alloc=3014104, time=22.10 -bytes used=231298100, alloc=3014104, time=22.19 -bytes used=232298384, alloc=3014104, time=22.46 -bytes used=233298544, alloc=3014104, time=22.60 -> -################################################################################ -> quit -bytes used=234141912, alloc=3014104, time=22.71 |