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diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log new file mode 100644 index 0000000..20887a8 --- /dev/null +++ b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/2d.log @@ -0,0 +1,6898 @@ + |\^/| Maple 7 (IBM INTEL LINUX) +._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. + \ MAPLE / All rights reserved. Maple is a registered trademark of + <____ ____> Waterloo Maple Inc. + | Type ? for help. +# util.maple -- misc utility routines +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.5 2002/09/02 10:21:03 jthorn Exp $ +> +# +# fix_rationals - convert numbers to RATIONAL() calls +# nonmatching_names - find names in a list which *don't* have a specified prefix +# sprint_numeric_list - convert a numeric list to a valid C identifier suffix +# print_name_list_dcl - print C declarations for a list of names +# +# hypercube_points - compute all (integer) points in an N-dimensional hypercube +# +# ftruncate - truncate a file to zero length +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function converts all {integer, rational} subexpressions of its +# input except integer exponents and -1 factors in products, into function +# calls +# RATIONAL(num,den) +# This is useful in conjunction with the C() library function, since +# +# C( (1/3) * foo * bar ) +# t0 = foo*bar/3; +# +# generates a (slow) division (and runs the risk of mixed-mode-arithmetic +# problems), while +# +# C((1.0/3.0) * foo * bar); +# t0 = 0.3333333333*foo*bar; +# +# suffers from roundoff error. With this function, +# +# fix_rationals((1/3) * foo * bar); +# RATIONAL(1,3) foo bar +# C(%); +# t0 = RATIONAL(1.0,3.0)*foo*bar; +# +# which a C preprocessor macro can easily convert to the desired +# +# t0 = (1.0/3.0)*foo*bar; +# +# Additionally, this function can be told to leave certain types of +# subexpressions unconverged. For example, +# fix_rationals(expr, type, specfunc(integer, DATA)); +# will leave all subexpressions of the form DATA(integer arguments) +# unconverted. +# +# Arguments: +# expr = (in) The expression to be converted. +# inert_fn = (optional in) +# If specified, this argument should be a Boolean procedure +# or the name of a Boolean procedure. This procedure should +# take one or more argument, and return true if and only if +# the first argument should *not* be converted, i.e. if we +# should leave this expression unchanged. See the last +# example above. +# ... = (optional in) +# Any further arguments are passed as additional arguments to +# the inert_fn procedure. +# +> fix_rationals := +> proc( +> expr::{ +> algebraic, name = algebraic, +> list({algebraic, name = algebraic}), +> set ({algebraic, name = algebraic}) +> }, +> inert_fn::{name, procedure} +> ) +> local nn, k, +> base, power, fbase, fpower, +> fn, fn_args_list, +> num, den, mult; +> +# do we want to convert this expression? +> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) +> then return expr; +> end if; +> +# recurse over lists and sets +> if (type(expr, {list,set})) +> then return map(fix_rationals, expr, args[2..nargs]); +> end if; +> +# recurse over equation right hand sides +> if (type(expr, name = algebraic)) +> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); +> end if; +> +# recurse over functions other than RATIONAL() +> if (type(expr, function)) +> then +> fn := op(0, expr); +> if (fn <> 'RATIONAL') +> then +> fn_args_list := [op(expr)]; +> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); +> fn; return '%'( op(fn_args_list) ); +> end if; +> end if; +> +> nn := nops(expr); +> +# recurse over sums +> if (type(expr, `+`)) +> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); +> end if; +> +# recurse over products +# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) +> if (type(expr, `*`)) +> then +> if (op(1, expr) = -1) +> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), +> args[2..nargs]); +> else return product('fix_rationals(op(k,expr), args[2..nargs])', +> 'k'=1..nn); +> end if; +> end if; +> +# recurse over powers +# ... leaving integer exponents intact +> if (type(expr, `^`)) +> then +> base := op(1, expr); +> power := op(2, expr); +> +> fbase := fix_rationals(base, args[2..nargs]); +> if (type(power, integer)) +> then fpower := power; +> else fpower := fix_rationals(power, args[2..nargs]); +> end if; +> return fbase ^ fpower; +> end if; +> +# fix integers and fractions +> if (type(expr, integer)) +> then return 'RATIONAL'(expr, 1); +> end if; +> if (type(expr, fraction)) +> then +> num := op(1, expr); +> den := op(2, expr); +> +> return 'RATIONAL'(num, den); +> end if; +> +# turn Maple floating-point into integer fraction, then recursively fix that +> if (type(expr, float)) +> then +> mult := op(1, expr); +> power := op(2, expr); +> return fix_rationals(mult * 10^power, args[2..nargs]); +> end if; +> +# identity op on names +> if (type(expr, name)) +> then return expr; +> end if; +> +# unknown type +> error "%0", +> "unknown type for expr!", +> " whattype(expr) = ", whattype(expr), +> " expr = ", expr; +> end proc; +fix_rationals := proc(expr::{algebraic, name = algebraic, +list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, +inert_fn::{procedure, name}) +local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; + if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr + end if; + if type(expr, {set, list}) then + return map(fix_rationals, expr, args[2 .. nargs]) + end if; + if type(expr, name = algebraic) then + return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) + end if; + if type(expr, function) then + fn := op(0, expr); + if fn <> 'RATIONAL' then + fn_args_list := [op(expr)]; + fn_args_list := + map(fix_rationals, fn_args_list, args[2 .. nargs]); + fn; + return '%'(op(fn_args_list)) + end if + end if; + nn := nops(expr); + if type(expr, `+`) then return + sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) + end if; + if type(expr, `*`) then + if op(1, expr) = -1 then return -fix_rationals( + remove(type, expr, 'identical(-1)'), args[2 .. nargs]) + else return product('fix_rationals(op(k, expr), args[2 .. nargs])', + 'k' = 1 .. nn) + end if + end if; + if type(expr, `^`) then + base := op(1, expr); + power := op(2, expr); + fbase := fix_rationals(base, args[2 .. nargs]); + if type(power, integer) then fpower := power + else fpower := fix_rationals(power, args[2 .. nargs]) + end if; + return fbase^fpower + end if; + if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; + if type(expr, fraction) then + num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) + end if; + if type(expr, float) then + mult := op(1, expr); + power := op(2, expr); + return fix_rationals(mult*10^power, args[2 .. nargs]) + end if; + if type(expr, name) then return expr end if; + error "%0", "unknown type for expr!", " whattype(expr) = ", + whattype(expr), " expr = ", expr +end proc + +> +################################################################################ +> +# +# This function finds names in a list which *don't* have a specified prefix. +# +# Arguments: +# name_list = A list of the names. +# prefix = The prefix we want to filter out. +# +# Results: +# This function returns the subset list of names which don't have the +# specified prefix. +# +> nonmatching_names := +> proc( name_list::list({name,string}), prefix::{name,string} ) +> +> select( proc(n) +> evalb(not StringTools[IsPrefix](prefix,n)); +> end proc +> , +> name_list +> ); +> end proc; +nonmatching_names := proc( +name_list::list({name, string}), prefix::{name, string}) + select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, + name_list) +end proc + +> +################################################################################ +> +# +# This function converts a numeric list to a string which is a valid +# C identifier suffix: elements are separated by "_", decimal points are +# replaced by "x", and all nonzero values have explicit +/- signs, which +# are replaced by "p"/"m". +# +# For example, [0,-3.5,+4] --> "0_m3x5_p4". +# +> sprint_numeric_list := +> proc(nlist::list(numeric)) +> +# generate preliminary string, eg "+0_-3.5_+4" +> map2(sprintf, "%+a", nlist); +> ListTools[Join](%, "_"); +> cat(op(%)); +> +# fixup bad characters +> StringTools[SubstituteAll](%, "+0", "0"); +> StringTools[CharacterMap](".+-", "xpm", %); +> +> return %; +> end proc; +sprint_numeric_list := proc(nlist::list(numeric)) + map2(sprintf, "%+a", nlist); + ListTools[Join](%, "_"); + cat(op(%)); + StringTools[SubstituteAll](%, "+0", "0"); + StringTools[CharacterMap](".+-", "xpm", %); + return % +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C declarations for a list of names. +# +# Argument: +# name_list = A list of the names. +# type_name = The C type of the names, eg. "double". +# file_name = The file name to write the declaration to. This is +# truncated before writing. +# +> print_name_list_dcl := +> proc( name_list::list({name,string}), +> type_name::string, +> file_name::string ) +> local blanks, separator_string; +> +> ftruncate(file_name); +> +> map( +> proc(var::{name,string}) +> fprintf(file_name, +> "%s %s;\n", +> type_name, var); +> end proc +> , +> name_list +> ); +> +> fclose(file_name); +> NULL; +> end proc; +print_name_list_dcl := proc( +name_list::list({name, string}), type_name::string, file_name::string) +local blanks, separator_string; + ftruncate(file_name); + map(proc(var::{name, string}) + fprintf(file_name, "%s %s;\n", type_name, var) + end proc, name_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a list of all the (integer) points in an +# N-dimensional hypercube, in lexicographic order. The present +# implementation requires N <= 4. +# +# Arguments: +# cmin,cmax = N-element lists of cube minimum/maximum coordinates. +# +# Results: +# The function returns a set of d-element lists giving the coordinates. +# For example, +# hypercube([0,0], [2,1] +# returns +# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } +> hypercube_points := +> proc(cmin::list(integer), cmax::list(integer)) +> local N, i,j,k,l; +> +> N := nops(cmin); +> if (nops(cmax) <> N) +> then error +> "must have same number of dimensions for min and max coordinates!"; +> fi; +> +> if (N = 1) +> then return [seq([i], i=cmin[1]..cmax[1])]; +> elif (N = 2) +> then return [ +> seq( +> seq([i,j], j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 3) +> then return [ +> seq( +> seq( +> seq([i,j,k], k=cmin[3]..cmax[3]), +> j=cmin[2]..cmax[2] ), +> i=cmin[1]..cmax[1]) +> ]; +> elif (N = 4) +> then return [ +> seq( +> seq( +> seq( +> seq([i,j,k,l], l=cmin[4]..cmax[4]), +> k=cmin[3]..cmax[3] ), +> j=cmin[2]..cmax[2]), +> i=cmin[1]..cmax[1]) +> ]; +> else +> error "implementation restriction: must have N <= 4, got %1!", N; +> fi; +> end proc; +hypercube_points := proc(cmin::list(integer), cmax::list(integer)) +local N, i, j, k, l; + N := nops(cmin); + if nops(cmax) <> N then error + "must have same number of dimensions for min and max coordinates!" + end if; + if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] + elif N = 2 then return + [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + elif N = 3 then return [seq( + seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) + , i = cmin[1] .. cmax[1])] + elif N = 4 then return [seq(seq(seq( + seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), + j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] + else error "implementation restriction: must have N <= 4, got %1!", N + end if +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function truncates a file to 0 length if it exists, or creates +# it at that length if it doesn't exist. +# +# Arguments: +# file_name = (in) The name of the file. +# +> ftruncate := +> proc(file_name::string) +> fopen(file_name, 'WRITE'); +> fclose(%); +> NULL; +> end proc; +ftruncate := + + proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc + +# interpolate.maple -- compute interpolation formulas/coefficients +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.11 2002/09/02 10:21:02 jthorn Exp $ +> +# +# <<<representation of numbers, data values, etc>>> +# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant +# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant +# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) +# +# print_coeffs__lc_of_data - print C code to compute coefficients +# print_fetch_data - print C code to fetch input array chunk into struct data +# print_store_coeffs - print C code to store struct coeffs "somewhere" +# print_interp_cmpt__lc_of_data - print C code for computation of interpolant +# +# coeff_name - name of coefficient of data at a given [m] coordinate +# data_var_name - name of variable storing data value at a given [m] coordinate +# +> +################################################################################ +> +# +# ***** representation of numbers, data values, etc ***** +# +# We use RATIONAL(p.0,q.0) to denote the rational number p/q. +# +# We use DATA(...) to represent the data values being interpolated at a +# specified [m] coordinate, where the arguments are the [m] coordinates. +# +# We use COEFF(...) to represent the molecule coefficient at a specified +# [m] coordinate, where the arguments are the [m] coordinates. +# +# For example, the usual 1-D centered 2nd order 1st derivative molecule +# would be written +# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) +# and its coefficients as +# COEFF(-1) = RATIONAL(-1.0,2.0) +# COEFF(1) = RATIONAL(1.0,2.0) +# +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes a Lagrange polynomial interpolant in any +# number of dimensions. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) c00 + c10*x + c01*y end proc +# coeff_list = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example [c00, c10, c01]. +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# posn_list = A list of positions (each a list of numeric values) where the +# interpolant is to use data, for example hypercube([0,0], [1,1]). +# Any positions may be used; if they're redundant (as in the +# example) the least-squares interpolant is computed. +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Lagrange_polynomial_interpolant := +> proc( +> fn::procedure, coeff_list::list(name), +> coord_list::list(name), posn_list::list(list(numeric)) +> ) +> local posn, data_eqns, coeff_eqns; +> +# coefficients of interpolating polynomial +> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; +> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); +> if (has(coeff_eqns, '_t')) +> then error "interpolation coefficients aren't uniquely determined!"; +> end if; +> +# interpolant as a polynomial in the coordinates +> return subs(coeff_eqns, eval(fn))(op(coord_list)); +> end proc; +Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), +coord_list::list(name), posn_list::list(list(numeric))) +local posn, data_eqns, coeff_eqns; + data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; + coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); + if has(coeff_eqns, '_t') then + error "interpolation coefficients aren't uniquely determined!" + end if; + return subs(coeff_eqns, eval(fn))(op(coord_list)) +end proc + +> +################################################################################ +> +# +# This function computes a Hermite polynomial interpolant in any +# number of dimensions. This is a polynomial which +# * has values which match the given data DATA() at a specified set of +# points, and +# * has derivatives which match the specified finite-difference derivatives +# of the given data DATA() at a specified set of points +# +# For the derivative matching, we actually match all possible products +# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we +# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. +# +# Arguments: +# fn = The interpolation function. This should be a procedure in the +# coordinates, having the coefficients as global variables. For +# example, +# proc(x,y) +# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +# + c00 + c10*x + c20*x^2 + c30*x^3 +# end proc; +# coeff_set = A set of the interpolation coefficients (coefficients in +# the interpolation function), for example +# { +# c03, c13, c23, c33, +# c02, c12, c22, c32, +# c01, c11, c21, c31, +# c00, c10, c20, c30 +# } +# coord_list = A list of the coordinates (independent variables in the +# interpolation function), for example [x,y]. +# deriv_set = A set of equations of the form +# {coords} = proc +# giving the derivatives which are to be matched, and the +# procedures to compute their finite-difference approximations. +# Each procedure should take N_dims integer arguments specifying +# an evaluation point, and return a suitable linear combination +# of the DATA() for the derivative at that point. For example +# { +# {x} = proc(i::integer, j::integer) +# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) +# end proc +# , +# {y} = proc(i::integer, j::integer) +# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) +# end proc +# , +# {x,y} = proc(i::integer, j::integer) +# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) +# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) +# end proc +# } +# fn_posn_set = A set of positions (each a list of numeric values) +# where the interpolant is to match the given data DATA(), +# for example +# {[0,0], [0,1], [1,0], [1,1]} +# deriv_posn_set = A list of positions (each a list of numeric values) +# where the interpolant is to match the derivatives +# specified by deriv_set , for example +# {[0,0], [0,1], [1,0], [1,1]} +# +# Results: +# This function returns the interpolating polynomial, in the form of +# an algebraic expression in the coordinates and the data values. +# +> Hermite_polynomial_interpolant := +> proc( +> fn::procedure, +> coeff_set::set(name), +> coord_list::list(name), +> deriv_set::set(set(name) = procedure), +> fn_posn_set::set(list(numeric)), +> deriv_posn_set::set(list(numeric)) +> ) +> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; +> +> +# +# compute a set of equations +# {fn(posn) = DATA(posn)} +# giving the function values to be matched +# +> fn_eqnset := map( +> # return equation that fn(posn) = DATA(posn) +> proc(posn::list(integer)) +> fn(op(posn)) = 'DATA'(op(posn)); +> end proc +> , +> fn_posn_set +> ); +> +> +# +# compute a set of equations +# { diff(fn,coords)(posn) = DERIV(coords)(posn) } +# giving the derivative values to be matched, where DERIV(coords) +# is a placeholder for the appropriate derivative +# +> map( +> # return set of equations for this particular derivative +> proc(deriv_coords::set(name)) +> local deriv_fn; +> fn(op(coord_list)); +> diff(%, op(deriv_coords)); +> deriv_fn := unapply(%, op(coord_list)); +> map( +> proc(posn::list(integer)) +> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); +> end proc +> , +> deriv_posn_set +> ); +> end proc +> , +> map(lhs, deriv_set) +> ); +> deriv_eqnset := `union`(op(%)); +> +> +# +# solve overall set of equations for coefficients +# in terms of DATA() and DERIV() values +# +> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); +> if (indets(map(rhs,%)) <> {}) +> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", +> nops(fn_eqnset union deriv_eqnset), +> nops(coeff_set); +> fi; +> +> +# +# compute a set of substitution equations +# {'DERIV'(coords) = procedure} +# +> subs_eqnset := map( +> proc(eqn::set(name) = procedure) +> 'DERIV'(op(lhs(eqn))) = rhs(eqn); +> end proc +> , +> deriv_set +> ); +> +> +# +# compute the coefficients in terms of the DATA() values +# +> subs(subs_eqnset, coeff_eqns); +> eval(%); +> +# +# compute the interpolant as a polynomial in the coordinates +# +> subs(%, fn(op(coord_list))); +> end proc; +Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), +coord_list::list(name), deriv_set::set(set(name) = procedure), +fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) +local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; + fn_eqnset := map( + proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, + fn_posn_set); + map(proc(deriv_coords::set(name)) + local deriv_fn; + fn(op(coord_list)); + diff(%, op(deriv_coords)); + deriv_fn := unapply(%, op(coord_list)); + map(proc(posn::list(integer)) + deriv_fn(op(posn)) = + 'DERIV'(op(deriv_coords))(op(posn)) + end proc, deriv_posn_set) + end proc, map(lhs, deriv_set)); + deriv_eqnset := `union`(op(%)); + coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); + if indets(map(rhs, %)) <> {} then error + "no unique solution for coefficients -- %1 eqns for %2 coeffs", + nops(fn_eqnset union deriv_eqnset), nops(coeff_set) + end if; + subs_eqnset := map(proc(eqn::(set(name) = procedure)) + 'DERIV'(op(lhs(eqn))) = rhs(eqn) + end proc, deriv_set); + subs(subs_eqnset, coeff_eqns); + eval(%); + subs(%, fn(op(coord_list))) +end proc + +> +################################################################################ +> +# +# This function takes as input an interpolating polynomial, expresses +# it as a linear combination of the data values, and returns the coefficeints +# of that form. +# +# Arguments: +# interpolant = The interpolating polynomial (an algebraic expression +# in the coordinates and the data values). +# posn_list = The same list of data positions used in the interpolant. +# +# Results: +# This function returns the coefficients, as a list of equations of the +# form COEFF(...) = value , where each value is a polynomial in the +# coordinates. The order of the list matches that of posn_list. +# +> coeffs_as_lc_of_data := +> proc( +> interpolant::algebraic, +> posn_list::list(list(numeric)) +> ) +> local data_list, interpolant_as_lc_of_data; +> +# interpolant as a linear combination of the data values +> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; +> interpolant_as_lc_of_data := collect(interpolant, data_list); +> +# coefficients of the data values in the linear combination +> return map( +> proc(posn::list(numeric)) +> coeff(interpolant_as_lc_of_data, DATA(op(posn))); +> 'COEFF'(op(posn)) = %; +> end proc +> , +> posn_list +> ); +> end proc; +coeffs_as_lc_of_data := proc( +interpolant::algebraic, posn_list::list(list(numeric))) +local data_list, interpolant_as_lc_of_data; + data_list := [seq('DATA'(op(posn)), posn = posn_list)]; + interpolant_as_lc_of_data := collect(interpolant, data_list); + return map(proc(posn::list(numeric)) + coeff(interpolant_as_lc_of_data, DATA(op(posn))); + 'COEFF'(op(posn)) = % + end proc, posn_list) +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function prints C expressions for the coefficients of an +# interpolating polynomial. (The polynomial is expressed as linear +# combinations of the data values with coefficients which are +# RATIONAL(p,q) calls.) +# +# Arguments: +# coeff_list = A list of the coefficients, as returned from +# coeffs_as_lc_of_data() . +# coeff_name_prefix = A prefix string for the coefficient names. +# temp_name_type = The C type to be used for Maple-introduced temporary +# names, eg. "double". +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_coeffs__lc_of_data := +> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), +> coeff_name_prefix::string, +> temp_name_type::string, +> file_name::string ) +> global `codegen/C/function/informed`; +> local coeff_list2, cmpt_list, temp_name_list; +> +# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) +# to a Maple/C variable name (eg coeff_I_m1_p1) +> coeff_list2 := map( +> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) +> local posn; +> posn := [op(lhs(coeff_eqn))]; +> coeff_name(posn,coeff_name_prefix); +> convert(%, name); # codegen[C] wants LHS +> # to be an actual Maple *name* +> % = fix_rationals(rhs(coeff_eqn)); +> end proc +> , +> coeff_list +> ); +> +# +# generate the C code +# +> +# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" +# via undocumented :( global table +> `codegen/C/function/informed`['RATIONAL'] := true; +> `codegen/C/function/informed`['DATA'] := true; +> +> ftruncate(file_name); +> +# optimized computation sequence for all the coefficients +# (may use local variables t0,t1,t2,...) +> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; +> +# list of the t0,t1,t2,... local variables +> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); +> +# declare the t0,t1,t2,... local variables (if there are any) +> if (nops(temp_name_list) > 0) +> then print_name_list_dcl(%, temp_name_type, file_name); +> fi; +> +# now print the optimized computation sequence +> codegen[C](cmpt_list, filename=file_name); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_coeffs__lc_of_data := proc( +coeff_list::list(specfunc(numeric, COEFF) = algebraic), +coeff_name_prefix::string, temp_name_type::string, file_name::string) +local coeff_list2, cmpt_list, temp_name_list; +global `codegen/C/function/informed`; + coeff_list2 := map(proc( + coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) + local posn; + posn := [op(lhs(coeff_eqn))]; + coeff_name(posn, coeff_name_prefix); + convert(%, name); + % = fix_rationals(rhs(coeff_eqn)) + end proc, coeff_list); + `codegen/C/function/informed`['RATIONAL'] := true; + `codegen/C/function/informed`['DATA'] := true; + ftruncate(file_name); + cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; + temp_name_list := + nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); + if 0 < nops(temp_name_list) then + print_name_list_dcl(%, temp_name_type, file_name) + end if; + codegen[C](cmpt_list, filename = file_name); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to assign the data-value +# variables, eg +# data->data_m1_p1 = DATA(-1,1); +# +# Arguments: +# posn_list = The same list of positions as was used to compute the +# interpolating polynomial. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_fetch_data := +> proc( +> posn_list::list(list(numeric)), +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%s = %a;\n", +> data_var_name(posn,data_var_name_prefix), +> DATA(op(posn))); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_fetch_data := proc(posn_list::list(list(numeric)), +data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%s = %a;\n", + data_var_name(posn, data_var_name_prefix), DATA(op(posn))) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a sequence of C expression to store the interpolation +# coefficients in COEFF(...) expressions, eg +# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names, +# eg "factor * coeffs->coeff_" +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_store_coeffs := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> map( +> proc(posn::list(numeric)) +> fprintf(file_name, +> "%a = %s;\n", +> 'COEFF'(op(posn)), +> coeff_name(posn,coeff_name_prefix)); +> end proc +> , +> posn_list +> ); +> fclose(file_name); +> +> NULL; +> end proc; +print_store_coeffs := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), + coeff_name(posn, coeff_name_prefix)) + end proc, posn_list); + fclose(file_name); + NULL +end proc + +> +################################################################################ +> +# +# This function prints a C expression to evaluate a molecule, i.e. +# to compute the molecule as a linear combination of the data values. +# +# Arguments: +# posn_list = The list of positions in the molecule. +# coeff_name_prefix = A prefix string for the coefficient names. +# data_var_name_prefix = A prefix string for the data variable names. +# file_name = The file name to write the coefficients to. This is +# truncated before writing. +# +> print_evaluate_molecule := +> proc( +> posn_list::list(list(numeric)), +> coeff_name_prefix::string, +> data_var_name_prefix::string, +> file_name::string +> ) +> +> ftruncate(file_name); +> +# list of "coeff*data_var" terms +> map( +> proc(posn::list(numeric)) +> sprintf("%s*%s", +> coeff_name(posn,coeff_name_prefix), +> data_var_name(posn,data_var_name_prefix)); +> end proc +> , +> posn_list +> ); +> +> ListTools[Join](%, "\n + "); +> cat(op(%)); +> fprintf(file_name, " %s;\n", %); +> +> fclose(file_name); +> +> NULL; +> end proc; +print_evaluate_molecule := proc(posn_list::list(list(numeric)), +coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) + ftruncate(file_name); + map(proc(posn::list(numeric)) + sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), + data_var_name(posn, data_var_name_prefix)) + end proc, posn_list); + ListTools[Join](%, "\n + "); + cat(op(%)); + fprintf(file_name, " %s;\n", %); + fclose(file_name); + NULL +end proc + +> +################################################################################ +################################################################################ +################################################################################ +> +# +# This function computes the name of the coefficient of the data at a +# given [m] position, i.e. it encapsulates our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the coefficient name. +# +# Results: +# The function returns the coefficient, as a Maple string. +# +> coeff_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +coeff_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +> +################################################################################ +> +# +# This function computes the name of the variable in which the C code +# will store the input data at a given [m] position, i.e. it encapsulates +# our naming convention for this. +# +# Arguments: +# posn = (in) The [m] coordinates. +# name_prefix = A prefix string for the variable name. +# +# Results: +# The function returns the variable name, as a Maple string. +# +> data_var_name := +> proc(posn::list(numeric), name_prefix::string) +> cat(name_prefix, sprint_numeric_list(posn)); +> end proc; +data_var_name := proc(posn::list(numeric), name_prefix::string) + cat(name_prefix, sprint_numeric_list(posn)) +end proc + +# Maple code to compute lists of point positions in hypercube-shaped molecules +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ +> +################################################################################ +> +# +# 1D interpolation points +# +> posn_list_1d_size2 := hypercube_points([ 0], [+1]); + posn_list_1d_size2 := [[0], [1]] + +> posn_list_1d_size3 := hypercube_points([-1], [+1]); + posn_list_1d_size3 := [[-1], [0], [1]] + +> posn_list_1d_size4 := hypercube_points([-1], [+2]); + posn_list_1d_size4 := [[-1], [0], [1], [2]] + +> posn_list_1d_size5 := hypercube_points([-2], [+2]); + posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] + +> posn_list_1d_size6 := hypercube_points([-2], [+3]); + posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] + +> posn_list_1d_size7 := hypercube_points([-3], [+3]); + posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] + +> +################################################################################ +> +# +# 2D interpolation points (Fortran ordering) +# +> posn_list_2d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0], [+1,+1])); + posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] + +> posn_list_2d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+1,+1])); +posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], + + [-1, 1], [0, 1], [1, 1]] + +> posn_list_2d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1], [+2,+2])); +posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], + + [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], + + [2, 2]] + +> posn_list_2d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+2,+2])); +posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], + + [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], + + [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], + + [1, 2], [2, 2]] + +> posn_list_2d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2], [+3,+3])); +posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], + + [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], + + [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], + + [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], + + [0, 3], [1, 3], [2, 3], [3, 3]] + +> +################################################################################ +> +# +# 3D interpolation points (Fortran ordering) +# +> posn_list_3d_size2 := map(ListTools[Reverse], +> hypercube_points([ 0, 0, 0], [+1,+1,+1])); +posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], + + [1, 0, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size3 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+1,+1,+1])); +posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], + + [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], + + [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], + + [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], + + [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] + +> posn_list_3d_size4 := map(ListTools[Reverse], +> hypercube_points([-1,-1,-1], [+2,+2,+2])); +posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], + + [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], + + [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], + + [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], + + [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size5 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+2,+2,+2])); +posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], + + [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], + + [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], + + [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], + + [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], + + [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], + + [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], + + [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], + + [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], + + [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], + + [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], + + [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], + + [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], + + [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], + + [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], + + [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], + + [0, 2, 2], [1, 2, 2], [2, 2, 2]] + +> posn_list_3d_size6 := map(ListTools[Reverse], +> hypercube_points([-2,-2,-2], [+3,+3,+3])); +posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], + + [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], + + [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], + + [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], + + [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], + + [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], + + [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], + + [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], + + [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], + + [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], + + [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], + + [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], + + [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], + + [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], + + [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], + + [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], + + [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], + + [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], + + [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], + + [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], + + [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], + + [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], + + [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], + + [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], + + [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], + + [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], + + [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], + + [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], + + [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], + + [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], + + [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], + + [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], + + [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], + + [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], + + [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], + + [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], + + [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] + +# Maple code to define Lagrange interpolating functions/coords/coeffs +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.3 2002/09/02 10:22:49 jthorn Exp $ +> +################################################################################ +> +# +# 1-D interpolating functions +# +> +> fn_1d_order1 := +> proc(x) +> + c0 + c1*x +> end proc; + fn_1d_order1 := proc(x) c0 + c1*x end proc + +> +> fn_1d_order2 := +> proc(x) +> + c0 + c1*x + c2*x^2 +> end proc; + fn_1d_order2 := proc(x) c0 + c1*x + c2*x^2 end proc + +> +> fn_1d_order3 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 +> end proc; + fn_1d_order3 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 end proc + +> +> fn_1d_order4 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 +> end; + fn_1d_order4 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 end proc + +> +> fn_1d_order5 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 +> end; + fn_1d_order5 := proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 end proc + +> +> fn_1d_order6 := +> proc(x) +> + c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 +> end; +fn_1d_order6 := + + proc(x) c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 + c6*x^6 end proc + +> +######################################## +> +# coordinates for 1-D interpolating functions +> coords_list_1d := [x]; + coords_list_1d := [x] + +> +######################################## +> +# +# coefficients in 1-D interpolating functions +# +> +> coeffs_list_1d_order1 := [c0, c1]; + coeffs_list_1d_order1 := [c0, c1] + +> coeffs_list_1d_order2 := [c0, c1, c2]; + coeffs_list_1d_order2 := [c0, c1, c2] + +> coeffs_list_1d_order3 := [c0, c1, c2, c3]; + coeffs_list_1d_order3 := [c0, c1, c2, c3] + +> coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; + coeffs_list_1d_order4 := [c0, c1, c2, c3, c4] + +> coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; + coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5] + +> coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; + coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6] + +> +################################################################################ +> +# +# 2-D interpolating functions (tensor-product) +# +> +> fn_2d_order1 := +> proc(x,y) +> + c01*y + c11*x*y +> + c00 + c10*x +> end proc; + fn_2d_order1 := proc(x, y) c01*y + c11*x*y + c00 + c10*x end proc + +> +> fn_2d_order2 := +> proc(x,y) +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 +> + c01*y + c11*x*y + c21*x^2*y +> + c00 + c10*x + c20*x^2 +> end proc; +fn_2d_order2 := proc(x, y) + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 + + c10*x + c20*x^2 +end proc + +> +> fn_2d_order3 := +> proc(x,y) +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y +> + c00 + c10*x + c20*x^2 + c30*x^3 +> end proc; +fn_2d_order3 := proc(x, y) + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c02*y^2 + c12*x*y^2 + + c22*x^2*y^2 + c32*x^3*y^2 + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + + c00 + c10*x + c20*x^2 + c30*x^3 +end proc + +> +> fn_2d_order4 := +> proc(x,y) +> + c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 +> + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 +> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 +> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y +> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 +> end; +fn_2d_order4 := proc(x, y) + c34*x^3*y^4 + c01*y + c10*x + c02*y^2 + c20*x^2 + c03*y^3 + c30*x^3 + + c04*y^4 + c40*x^4 + c11*x*y + c12*x*y^2 + c22*x^2*y^2 + c21*x^2*y + + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c32*x^3*y^2 + c31*x^3*y + + c14*x*y^4 + c24*x^2*y^4 + c44*x^4*y^4 + c00 + c43*x^4*y^3 + + c42*x^4*y^2 + c41*x^4*y +end proc + +> +######################################## +> +# coordinates for 2-D interpolating functions +> coords_list_2d := [x,y]; + coords_list_2d := [x, y] + +> +######################################## +> +# +# coefficients in 2-D interpolating functions (tensor-product) +# +> +> coeffs_list_2d_order1 := [ +> c01, c11, +> c00, c10 +> ]; + coeffs_list_2d_order1 := [c01, c11, c00, c10] + +> coeffs_list_2d_order2 := [ +> c02, c12, c22, +> c01, c11, c21, +> c00, c10, c20 +> ]; + coeffs_list_2d_order2 := [c02, c12, c22, c01, c11, c21, c00, c10, c20] + +> coeffs_list_2d_order3 := [ +> c03, c13, c23, c33, +> c02, c12, c22, c23, +> c01, c11, c21, c13, +> c00, c10, c20, c30 +> ]; +coeffs_list_2d_order3 := [c03, c13, c23, c33, c02, c12, c22, c23, c01, c11, c21, + + c13, c00, c10, c20, c30] + +> coeffs_list_2d_order4 := [ +> c04, c14, c24, c34, c44, +> c03, c13, c23, c33, c43, +> c02, c12, c22, c32, c42, +> c01, c11, c21, c31, c41, +> c00, c10, c20, c30, c40 +> ]; +coeffs_list_2d_order4 := [c04, c14, c24, c34, c44, c03, c13, c23, c33, c43, c02, + + c12, c22, c32, c42, c01, c11, c21, c31, c41, c00, c10, c20, c30, c40] + +> +################################################################################ +> +# +# 3-D interpolating functions (tensor-product) +# +> +> fn_3d_order1 := +> proc(x,y,z) +# z^1 ------------------- +> + c011 *y*z + c111*x*y*z +> + c001 *z + c101*x *z +# z^0 ------------------- +> + c010 *y + c110*x*y +> + c000 + c100*x +> end proc; +fn_3d_order1 := proc(x, y, z) + c011*y*z + c111*x*y*z + c001*z + c101*x*z + c010*y + c110*x*y + c000 + + c100*x +end proc + +> +> fn_3d_order2 := +> proc(x,y,z) +# z^2 -------------------------------------------------- +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 +# z -------------------------------------------------- +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z +> + c001 *z + c101*x *z + c201*x^2 *z +# z^0 ------------------------------------------------ +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 +> + c010 *y + c110*x *y + c210*x^2*y +> + c000 + c100*x + c200*x^2 +> end proc; +fn_3d_order2 := proc(x, y, z) + c111*x*y*z + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c112*x*y*z^2 + + c212*x^2*y*z^2 + c121*x*y^2*z + c221*x^2*y^2*z + c211*x^2*y*z + + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + c120*x*y^2 + + c220*x^2*y^2 + c210*x^2*y + c001*z + c010*y + c000 + c100*x + + c002*z^2 + c020*y^2 + c200*x^2 +end proc + +> +> fn_3d_order3 := +> proc(x,y,z) +# z^3 --------------------------------------------------------------------- +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 +# z^2 --------------------------------------------------------------------- +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 +# z --------------------------------------------------------------------- +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z +# z^0 --------------------------------------------------------------------- +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y +> + c000 + c100*x + c200*x^2 + c300*x^3 +> end proc; +fn_3d_order3 := proc(x, y, z) + c330*x^3*y^3 + c031*y^3*z + c103*x*z^3 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c011*y*z + c101*x*z + + c110*x*y + c022*y^2*z^2 + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + + c021*y^2*z + c201*x^2*z + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + + c033*y^3*z^3 + c023*y^2*z^3 + c013*y*z^3 + c203*x^2*z^3 + + c303*x^3*z^3 + c032*y^3*z^2 + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + + c230*x^2*y^3 + c320*x^3*y^2 + c310*x^3*y + c001*z + c010*y + c000 + + c100*x + c002*z^2 + c020*y^2 + c200*x^2 + c003*z^3 + c030*y^3 + + c300*x^3 +end proc + +> +> fn_3d_order4 := +> proc(x,y,z) +# z^4 ---------------------------------------------------------------------------------------- +> + c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 +> + c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 +> + c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 +> + c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 +> + c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 +# z^3 ---------------------------------------------------------------------------------------- +> + c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 +> + c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 +> + c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 +> + c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 +> + c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 +# z^2 ---------------------------------------------------------------------------------------- +> + c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 +> + c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 +> + c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 +> + c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 +> + c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 +# z ---------------------------------------------------------------------------------------- +> + c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z +> + c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z +> + c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z +> + c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z +> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z +# z^0 ---------------------------------------------------------------------------------------- +> + c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 +> + c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 +> + c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 +> + c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y +> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 +> end; +fn_3d_order4 := proc(x, y, z) + c104*x*z^4 + c330*x^3*y^3 + c042*y^4*z^2 + c031*y^3*z + c103*x*z^3 + + c304*x^3*z^4 + c024*y^2*z^4 + c111*x*y*z + c122*x*y^2*z^2 + + c222*x^2*y^2*z^2 + c112*x*y*z^2 + c212*x^2*y*z^2 + c121*x*y^2*z + + c221*x^2*y^2*z + c211*x^2*y*z + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + + c333*x^3*y^3*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + + c323*x^3*y^2*z^3 + c113*x*y*z^3 + c213*x^2*y*z^3 + c313*x^3*y*z^3 + + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + + c322*x^3*y^2*z^2 + c312*x^3*y*z^2 + c131*x*y^3*z + c231*x^2*y^3*z + + c331*x^3*y^3*z + c321*x^3*y^2*z + c311*x^3*y*z + c144*x*y^4*z^4 + + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 + + c134*x*y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + + c434*x^4*y^3*z^4 + c124*x*y^2*z^4 + c224*x^2*y^2*z^4 + + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 + c114*x*y*z^4 + c214*x^2*y*z^4 + + c314*x^3*y*z^4 + c414*x^4*y*z^4 + c143*x*y^4*z^3 + c243*x^2*y^4*z^3 + + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 + c433*x^4*y^3*z^3 + + c423*x^4*y^2*z^3 + c413*x^4*y*z^3 + c142*x*y^4*z^2 + + c242*x^2*y^4*z^2 + c011*y*z + c101*x*z + c110*x*y + c022*y^2*z^2 + + c012*y*z^2 + c102*x*z^2 + c202*x^2*z^2 + c021*y^2*z + c201*x^2*z + + c120*x*y^2 + c220*x^2*y^2 + c210*x^2*y + c033*y^3*z^3 + c023*y^2*z^3 + + c013*y*z^3 + c203*x^2*z^3 + c303*x^3*z^3 + c032*y^3*z^2 + + c302*x^3*z^2 + c301*x^3*z + c130*x*y^3 + c230*x^2*y^3 + c320*x^3*y^2 + + c310*x^3*y + c001*z + c010*y + c000 + c100*x + c002*z^2 + c020*y^2 + + c200*x^2 + c003*z^3 + c030*y^3 + c300*x^3 + c004*z^4 + c044*y^4*z^4 + + c034*y^3*z^4 + c014*y*z^4 + c204*x^2*z^4 + c404*x^4*z^4 + + c043*y^4*z^3 + c403*x^4*z^3 + c402*x^4*z^2 + c041*y^4*z + c401*x^4*z + + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 + + c430*x^4*y^3 + c420*x^4*y^2 + c410*x^4*y + c342*x^3*y^4*z^2 + + c442*x^4*y^4*z^2 + c432*x^4*y^3*z^2 + c422*x^4*y^2*z^2 + + c412*x^4*y*z^2 + c141*x*y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + + c441*x^4*y^4*z + c431*x^4*y^3*z + c421*x^4*y^2*z + c411*x^4*y*z + + c040*y^4 + c400*x^4 +end proc + +> +######################################## +> +# coordinates for 3-D interpolating functions +> coords_list_3d := [x,y,z]; + coords_list_3d := [x, y, z] + +> +######################################## +> +# +# coefficients in 3-D interpolating functions +# +> +> coeffs_list_3d_order1 := [ +> # z^1 ----- +> c011, c111, +> c001, c101, +> # z^0 ----- +> c010, c110, +> c000, c100 +> ]; + coeffs_list_3d_order1 := [c011, c111, c001, c101, c010, c110, c000, c100] + +> coeffs_list_3d_order2 := [ +> # z^2 ----------- +> c022, c122, c222, +> c012, c112, c212, +> c002, c102, c202, +> # z^1 ----------- +> c021, c121, c221, +> c011, c111, c211, +> c001, c101, c201, +> # z^0 ----------- +> c020, c120, c220, +> c010, c110, c210, +> c000, c100, c200 +> ]; +coeffs_list_3d_order2 := [c022, c122, c222, c012, c112, c212, c002, c102, c202, + + c021, c121, c221, c011, c111, c211, c001, c101, c201, c020, c120, c220, + + c010, c110, c210, c000, c100, c200] + +> coeffs_list_3d_order3 := [ +> # z^3 ----------------- +> c033, c133, c233, c333, +> c023, c123, c223, c323, +> c013, c113, c213, c313, +> c003, c103, c203, c303, +> # z^2 ----------------- +> c032, c132, c232, c332, +> c022, c122, c222, c322, +> c012, c112, c212, c312, +> c002, c102, c202, c302, +> # z^1 ----------------- +> c031, c131, c231, c331, +> c021, c121, c221, c321, +> c011, c111, c211, c311, +> c001, c101, c201, c301, +> # z^0 ----------------- +> c030, c130, c230, c330, +> c020, c120, c220, c320, +> c010, c110, c210, c310, +> c000, c100, c200, c300 +> ]; +coeffs_list_3d_order3 := [c033, c133, c233, c333, c023, c123, c223, c323, c013, + + c113, c213, c313, c003, c103, c203, c303, c032, c132, c232, c332, c022, + + c122, c222, c322, c012, c112, c212, c312, c002, c102, c202, c302, c031, + + c131, c231, c331, c021, c121, c221, c321, c011, c111, c211, c311, c001, + + c101, c201, c301, c030, c130, c230, c330, c020, c120, c220, c320, c010, + + c110, c210, c310, c000, c100, c200, c300] + +> coeffs_list_3d_order4 := [ +> # z^4 ----------------------- +> c044, c144, c244, c344, c444, +> c034, c134, c234, c334, c434, +> c024, c124, c224, c324, c424, +> c014, c114, c214, c314, c414, +> c004, c104, c204, c304, c404, +> # z^3 ----------------------- +> c043, c143, c243, c343, c443, +> c033, c133, c233, c333, c433, +> c023, c123, c223, c323, c423, +> c013, c113, c213, c313, c413, +> c003, c103, c203, c303, c403, +> # z^2 ----------------------- +> c042, c142, c242, c342, c442, +> c032, c132, c232, c332, c432, +> c022, c122, c222, c322, c422, +> c012, c112, c212, c312, c412, +> c002, c102, c202, c302, c402, +> # z^1 ----------------------- +> c041, c141, c241, c341, c441, +> c031, c131, c231, c331, c431, +> c021, c121, c221, c321, c421, +> c011, c111, c211, c311, c411, +> c001, c101, c201, c301, c401, +> # z^0 ----------------------- +> c040, c140, c240, c340, c440, +> c030, c130, c230, c330, c430, +> c020, c120, c220, c320, c420, +> c010, c110, c210, c310, c410, +> c000, c100, c200, c300, c400 +> ]; +coeffs_list_3d_order4 := [c044, c144, c244, c344, c444, c034, c134, c234, c334, + + c434, c024, c124, c224, c324, c424, c014, c114, c214, c314, c414, c004, + + c104, c204, c304, c404, c043, c143, c243, c343, c443, c033, c133, c233, + + c333, c433, c023, c123, c223, c323, c423, c013, c113, c213, c313, c413, + + c003, c103, c203, c303, c403, c042, c142, c242, c342, c442, c032, c132, + + c232, c332, c432, c022, c122, c222, c322, c422, c012, c112, c212, c312, + + c412, c002, c102, c202, c302, c402, c041, c141, c241, c341, c441, c031, + + c131, c231, c331, c431, c021, c121, c221, c321, c421, c011, c111, c211, + + c311, c411, c001, c101, c201, c301, c401, c040, c140, c240, c340, c440, + + c030, c130, c230, c330, c430, c020, c120, c220, c320, c420, c010, c110, + + c210, c310, c410, c000, c100, c200, c300, c400] + +> +################################################################################ +# 2d.maple -- compute Lagrange interpolation coefficients in 2-D +# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple,v 1.3 2002/09/02 10:22:36 jthorn Exp $ +> +################################################################################ +> +# +# 2d, cube, order=1, smoothing=0 (size=2) +# +> +# interpolating polynomial +> interp_2d_cube_order1_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order1, coeffs_list_2d_order1, +> coords_list_2d, posn_list_2d_size2); +interp_2d_cube_order1_smooth0 := (-DATA(0, 0) + DATA(0, 1)) y + + + (-DATA(1, 0) + DATA(0, 0) + DATA(1, 1) - DATA(0, 1)) x y + DATA(0, 0) + + + (DATA(1, 0) - DATA(0, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size2); +[COEFF(0, 0) = x y + 1 - y - x, COEFF(1, 0) = x - x y, COEFF(0, 1) = y - x y, + + COEFF(1, 1) = x y] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); +bytes used=1009312, alloc=917336, time=0.09 +> +# d/dx +> simplify( diff(interp_2d_cube_order1_smooth0,x) ); +-y DATA(1, 0) + y DATA(0, 0) + y DATA(1, 1) - y DATA(0, 1) + DATA(1, 0) + + - DATA(0, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); + [COEFF(0, 0) = y - 1, COEFF(1, 0) = -y + 1, COEFF(0, 1) = -y, COEFF(1, 1) = y] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dx.compute.c"); +> +# d/dy +> simplify( diff(interp_2d_cube_order1_smooth0,y) ); +-DATA(0, 0) + DATA(0, 1) - x DATA(1, 0) + x DATA(0, 0) + x DATA(1, 1) + + - x DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size2); + [COEFF(0, 0) = x - 1, COEFF(1, 0) = -x, COEFF(0, 1) = 1 - x, COEFF(1, 1) = x] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order1.smooth0/coeffs-dy.compute.c"); +> +################################################################################ +> +# +# 2d, cube, order=2, smoothing=0 (size=3) +# +> +# interpolating polynomial +> interp_2d_cube_order2_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order2, coeffs_list_2d_order2, +> coords_list_2d, posn_list_2d_size3); +bytes used=2009852, alloc=1376004, time=0.15 +interp_2d_cube_order2_smooth0 := + + 2 + (-DATA(0, 0) + 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + (1/4 DATA(1, 1) + + - 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + 1/2 DATA(-1, 0) + + 2 + - 1/2 DATA(1, 0)) x y + (1/4 DATA(-1, 1) - 1/2 DATA(-1, 0) + + - 1/2 DATA(1, 0) + DATA(0, 0) + 1/4 DATA(-1, -1) + 1/4 DATA(1, -1) + + 2 2 + + 1/4 DATA(1, 1) - 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y + + + (- 1/2 DATA(0, -1) + 1/2 DATA(0, 1)) y + + + (1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1)) x y + + + (1/4 DATA(1, 1) - 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) + 1/4 DATA(-1, 1) + + 2 + + 1/2 DATA(0, -1) - 1/2 DATA(0, 1)) x y + DATA(0, 0) + + + (- 1/2 DATA(-1, 0) + 1/2 DATA(1, 0)) x + + 2 + + (1/2 DATA(-1, 0) + 1/2 DATA(1, 0) - DATA(0, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 2 2 +[COEFF(-1, -1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , + + 2 2 2 2 + COEFF(0, -1) = 1/2 y - 1/2 x y - 1/2 y + 1/2 x y, + + 2 2 2 2 + COEFF(1, -1) = 1/4 x y - 1/4 x y + 1/4 x y - 1/4 x y, + + 2 2 2 2 + COEFF(-1, 0) = 1/2 x y + 1/2 x - 1/2 x - 1/2 x y , + + 2 2 2 2 + COEFF(0, 0) = -y + x y + 1 - x , + + 2 2 2 2 + COEFF(1, 0) = 1/2 x - 1/2 x y + 1/2 x - 1/2 x y , + + 2 2 2 2 + COEFF(-1, 1) = - 1/4 x y - 1/4 x y + 1/4 x y + 1/4 x y , + + 2 2 2 2 + COEFF(0, 1) = 1/2 y - 1/2 x y - 1/2 x y + 1/2 y, + + 2 2 2 2 + COEFF(1, 1) = 1/4 x y + 1/4 x y + 1/4 x y + 1/4 x y ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-I.compute.c"); +bytes used=3010044, alloc=1638100, time=0.21 +bytes used=4010200, alloc=1703624, time=0.29 +> +# d/dx +> simplify( diff(interp_2d_cube_order2_smooth0,x) ); +bytes used=5010460, alloc=1703624, time=0.36 + 2 +1/2 DATA(1, 0) + 1/2 x y DATA(-1, -1) + 1/2 x y DATA(1, 1) + + - 1/2 x y DATA(-1, -1) - 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, 1) + + 2 + + x y DATA(0, -1) - x y DATA(0, 1) + 1/2 x y DATA(-1, 1) + + 2 2 2 + - x y DATA(-1, 0) - x y DATA(1, 0) + 2 x y DATA(0, 0) + + 2 2 2 + + 1/2 x y DATA(1, -1) + 1/2 x y DATA(1, 1) - x y DATA(0, -1) + + 2 2 + - x y DATA(0, 1) - 1/2 DATA(-1, 0) - 1/2 y DATA(1, 0) + + + 1/4 y DATA(-1, -1) - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + + 2 2 + + 1/4 y DATA(1, 1) + 1/4 y DATA(1, 1) - 1/4 y DATA(-1, -1) + + 2 2 2 + + 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) + 1/2 y DATA(-1, 0) + + + x DATA(-1, 0) - 2 x DATA(0, 0) + x DATA(1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 2 +[COEFF(-1, -1) = 1/4 y + 1/2 x y - 1/2 x y - 1/4 y , COEFF(0, -1) = x y - x y , + + 2 2 + COEFF(1, -1) = 1/2 x y + 1/4 y - 1/2 x y - 1/4 y, + + 2 2 2 + COEFF(-1, 0) = x + 1/2 y - x y - 1/2, COEFF(0, 0) = -2 x + 2 x y , + + 2 2 + COEFF(1, 0) = - 1/2 y + x - x y + 1/2, + + 2 2 + COEFF(-1, 1) = - 1/4 y + 1/2 x y - 1/4 y + 1/2 x y , + + 2 + COEFF(0, 1) = -x y - x y , + + 2 2 + COEFF(1, 1) = 1/2 x y + 1/2 x y + 1/4 y + 1/4 y] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); +bytes used=6011072, alloc=1769148, time=0.42 +> +# d/dy +> simplify( diff(interp_2d_cube_order2_smooth0,y) ); +bytes used=7011376, alloc=1769148, time=0.49 +1/2 DATA(0, 1) + 1/2 x y DATA(1, 1) - 1/2 x y DATA(-1, -1) + + + 1/2 x y DATA(1, -1) - 1/2 x y DATA(-1, 1) - 1/2 DATA(0, -1) + + 2 2 2 + - x y DATA(1, 0) + 1/2 x y DATA(1, 1) - x y DATA(0, 1) + + 2 + - x y DATA(0, -1) - x y DATA(1, 0) + x y DATA(-1, 0) + 1/4 x DATA(1, 1) + + + 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) + + 2 2 2 + + 1/4 x DATA(1, 1) - 1/4 x DATA(-1, -1) - 1/4 x DATA(1, -1) + + 2 2 2 + + 1/4 x DATA(-1, 1) + 1/2 x DATA(0, -1) - 1/2 x DATA(0, 1) + + 2 + - 2 y DATA(0, 0) + y DATA(0, -1) + y DATA(0, 1) + 2 x y DATA(0, 0) + + 2 2 2 + + 1/2 x y DATA(-1, 1) + 1/2 x y DATA(1, -1) + 1/2 x y DATA(-1, -1) + + 2 + - x y DATA(-1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = - 1/2 x y + 1/2 x y - 1/4 x + 1/4 x, + + 2 2 + COEFF(0, -1) = -x y - 1/2 + 1/2 x + y, + + 2 2 + COEFF(1, -1) = 1/2 x y + 1/2 x y - 1/4 x - 1/4 x, + + 2 2 + COEFF(-1, 0) = x y - x y, COEFF(0, 0) = -2 y + 2 x y, + + 2 + COEFF(1, 0) = -x y - x y, + + 2 2 + COEFF(-1, 1) = 1/2 x y + 1/4 x - 1/2 x y - 1/4 x, + + 2 2 + COEFF(0, 1) = 1/2 - 1/2 x - x y + y, + + 2 2 + COEFF(1, 1) = 1/4 x + 1/2 x y + 1/2 x y + 1/4 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); +bytes used=8011672, alloc=1769148, time=0.57 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); + 2 2 2 2 +1/2 y DATA(-1, 1) - y DATA(-1, 0) - y DATA(1, 0) + 2 y DATA(0, 0) + + 2 2 2 + + 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) + 1/2 y DATA(1, 1) + + 2 2 + - y DATA(0, -1) - y DATA(0, 1) + 1/2 y DATA(1, 1) - 1/2 y DATA(-1, -1) + + - 1/2 y DATA(1, -1) + 1/2 y DATA(-1, 1) + y DATA(0, -1) - y DATA(0, 1) + + + DATA(-1, 0) + DATA(1, 0) - 2 DATA(0, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = - 1/2 y + 1/2 y , COEFF(0, -1) = y - y , + + 2 2 + COEFF(1, -1) = - 1/2 y + 1/2 y , COEFF(-1, 0) = -y + 1, + + 2 2 + COEFF(0, 0) = 2 y - 2, COEFF(1, 0) = -y + 1, + + 2 2 + COEFF(-1, 1) = 1/2 y + 1/2 y, COEFF(0, 1) = -y - y, + + 2 + COEFF(1, 1) = 1/2 y + 1/2 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); +bytes used=9011872, alloc=1834672, time=0.66 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); +1/4 DATA(1, 1) - 2 x y DATA(0, -1) - 2 x y DATA(0, 1) + x y DATA(-1, 1) + + - 2 x y DATA(-1, 0) - 2 x y DATA(1, 0) + 4 x y DATA(0, 0) + + + x y DATA(-1, -1) + x y DATA(1, -1) + x y DATA(1, 1) + 1/2 y DATA(1, 1) + + - 1/2 y DATA(-1, -1) + 1/2 y DATA(1, -1) - 1/2 y DATA(-1, 1) + + + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) + x DATA(0, -1) + + - x DATA(0, 1) + 1/2 x DATA(1, 1) - 1/2 x DATA(-1, -1) - 1/2 x DATA(1, -1) + + + 1/2 x DATA(-1, 1) + y DATA(-1, 0) - y DATA(1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); +[COEFF(-1, -1) = - 1/2 y + x y - 1/2 x + 1/4, COEFF(0, -1) = -2 x y + x, + + COEFF(1, -1) = - 1/2 x - 1/4 + x y + 1/2 y, COEFF(-1, 0) = -2 x y + y, + + COEFF(0, 0) = 4 x y, COEFF(1, 0) = -y - 2 x y, + + COEFF(-1, 1) = x y - 1/2 y - 1/4 + 1/2 x, COEFF(0, 1) = -2 x y - x, + + COEFF(1, 1) = 1/4 + x y + 1/2 x + 1/2 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); +bytes used=10012088, alloc=1834672, time=0.74 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); +-2 DATA(0, 0) + DATA(0, -1) + DATA(0, 1) + 1/2 x DATA(1, 1) + + - 1/2 x DATA(-1, -1) + 1/2 x DATA(1, -1) - 1/2 x DATA(-1, 1) + + 2 2 + + x DATA(-1, 0) - x DATA(1, 0) + 1/2 x DATA(-1, 1) - x DATA(-1, 0) + + 2 2 2 + - x DATA(1, 0) + 2 x DATA(0, 0) + 1/2 x DATA(-1, -1) + + 2 2 2 2 + + 1/2 x DATA(1, -1) + 1/2 x DATA(1, 1) - x DATA(0, -1) - x DATA(0, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size3); + 2 2 +[COEFF(-1, -1) = 1/2 x - 1/2 x, COEFF(0, -1) = 1 - x , + + 2 2 + COEFF(1, -1) = 1/2 x + 1/2 x , COEFF(-1, 0) = -x + x, + + 2 2 + COEFF(0, 0) = 2 x - 2, COEFF(1, 0) = -x - x , + + 2 2 + COEFF(-1, 1) = 1/2 x - 1/2 x, COEFF(0, 1) = 1 - x , + + 2 + COEFF(1, 1) = 1/2 x + 1/2 x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); +bytes used=11012264, alloc=1834672, time=0.82 +> +################################################################################ +> +# +# 2d, cube, order=3, smoothing=0 (size=4) +# +> +# interpolating polynomial +> interp_2d_cube_order3_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order3, coeffs_list_2d_order3, +> coords_list_2d, posn_list_2d_size4); +bytes used=12012452, alloc=1834672, time=0.88 +bytes used=13012804, alloc=1900196, time=0.94 +bytes used=14014276, alloc=1900196, time=0.99 +bytes used=15014880, alloc=1965720, time=1.05 +bytes used=16015128, alloc=1965720, time=1.12 +bytes used=17015368, alloc=1965720, time=1.18 +bytes used=18015556, alloc=1965720, time=1.25 +bytes used=19016348, alloc=1965720, time=1.31 +bytes used=20016508, alloc=1965720, time=1.38 +bytes used=21016664, alloc=1965720, time=1.44 +bytes used=22016880, alloc=1965720, time=1.51 +bytes used=23019452, alloc=1965720, time=1.57 +bytes used=24021724, alloc=1965720, time=1.63 +bytes used=25022340, alloc=1965720, time=1.69 +interp_2d_cube_order3_smooth0 := (1/8 DATA(2, 1) - 1/4 DATA(2, 0) + + + 1/8 DATA(2, -1) - 3/2 c32 + 1/4 DATA(0, 0) + 1/4 DATA(1, 0) + + - 1/8 DATA(0, 1) - 1/8 DATA(1, 1) + 1/8 DATA(-1, -1) - 1/8 DATA(0, -1) + + 2 2 / + - 1/8 DATA(1, -1) - 1/4 DATA(-1, 0) + 1/8 DATA(-1, 1)) x y + | + \ + + 11 + - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) - 1/40 DATA(0, 2) + 120 + + 13 + + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) - -- c31 + 10 + + - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) + + 11 11 + + -- DATA(-1, -1) - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) + 60 40 + + 11 \ + - -- DATA(-1, 1)| x y + (- 1/24 DATA(2, 2) + 1/24 DATA(1, 2) + 20 / + + - 1/24 DATA(-1, 2) + 1/24 DATA(0, 2) + 1/4 DATA(2, 1) - 1/8 DATA(2, 0) + + - 1/12 DATA(2, -1) - 3/2 c31 + 1/8 DATA(0, 0) + 1/8 DATA(1, 0) + + - 1/4 DATA(0, 1) - 1/4 DATA(1, 1) - 1/12 DATA(-1, -1) + 1/12 DATA(0, -1) + + 2 + + 1/12 DATA(1, -1) - 1/8 DATA(-1, 0) + 1/4 DATA(-1, 1)) x y + + + 3/2000 DATA(2, 2) - 9/2000 DATA(1, 2) - 3/2000 DATA(-1, 2) + + 87 201 111 + + 9/2000 DATA(0, 2) + ---- DATA(2, 1) - ---- DATA(2, 0) + ---- DATA(2, -1) + 2000 2000 2000 + + 3 3 2 / 53 409 + + c31 x y + c32 x y + |- ---- DATA(2, 2) + ---- DATA(1, 2) + \ 3000 3000 + + 197 53 31 101 + - ---- DATA(-1, 2) - ---- DATA(0, 2) - ---- DATA(2, 1) + ---- DATA(2, 0) + 3000 1000 1500 3000 + + 13 91 101 + + 7/1500 DATA(2, -1) + -- c32 + --- c31 + ---- DATA(0, 0) + 25 250 1000 + + 149 31 47 59 + + ---- DATA(1, 0) - --- DATA(0, 1) - --- DATA(1, 1) + --- DATA(-1, -1) + 1000 500 250 750 + + 73 851 203 + + 7/500 DATA(0, -1) - --- DATA(1, -1) - ---- DATA(-1, 0) + --- DATA(-1, 1) + 750 3000 750 + + \ 3 / 29 43 + | x y + |7/600 DATA(2, 2) + --- DATA(1, 2) + --- DATA(-1, 2) + / \ 600 600 + + 79 27 + - --- DATA(0, 2) - 3/25 DATA(2, 1) + --- DATA(2, 0) - 2/75 DATA(2, -1) + 600 200 + + 21 19 31 + + 3/5 c32 + -- c31 - --- DATA(0, 0) - --- DATA(1, 0) + 7/50 DATA(0, 1) + 50 200 200 + + 11 17 13 + + --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - 1/300 DATA(1, -1) + 100 300 150 + + 23 13 \ 2 3 + + --- DATA(-1, 0) - --- DATA(-1, 1)| x y + (1/50 DATA(2, 2) + 200 100 / + + - 3/50 DATA(1, 2) - 1/50 DATA(-1, 2) + 3/50 DATA(0, 2) - 1/300 DATA(2, 1) + + - 1/150 DATA(2, 0) - 1/100 DATA(2, -1) - 2/5 c32 - 7/25 c31 + + - 1/50 DATA(0, 0) + 1/50 DATA(1, 0) - 1/100 DATA(0, 1) + 1/100 DATA(1, 1) + + + 1/100 DATA(-1, -1) - 3/100 DATA(0, -1) + 3/100 DATA(1, -1) + + 3 3 / + + 1/150 DATA(-1, 0) + 1/300 DATA(-1, 1)) x y + |1/40 DATA(2, 1) + \ + + 13 + - 1/20 DATA(2, 0) + 1/40 DATA(2, -1) - -- c32 - 3/20 DATA(0, 0) + 10 + + 11 + - 7/20 DATA(1, 0) + 3/40 DATA(0, 1) + 7/40 DATA(1, 1) - -- DATA(-1, -1) + 40 + + 11 11 \ + + 3/40 DATA(0, -1) + 7/40 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1)| x + 20 40 / + + 2 63 27 1397 603 + y - --- c32 + --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) + 100 500 2000 2000 + + 261 261 / + + ---- DATA(0, 1) - ---- DATA(1, 1) + |- 1/400 DATA(2, 2) + 2000 2000 \ + + 29 + + 3/400 DATA(1, 2) + 1/400 DATA(-1, 2) - 3/400 DATA(0, 2) - --- DATA(2, 1) + 400 + + 67 37 21 199 + + --- DATA(2, 0) - --- DATA(2, -1) + -- c32 - 9/100 c31 - --- DATA(0, 0) + 400 400 20 400 + + 87 87 37 + - 1/400 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + --- DATA(-1, -1) + 400 400 400 + + 111 111 133 29 \ + - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) + --- DATA(-1, 1)| + 400 400 400 400 / + + 2 / + x + |1/600 DATA(2, 2) - 1/200 DATA(1, 2) - 1/600 DATA(-1, 2) + \ + + 29 11 37 + + 1/200 DATA(0, 2) + --- DATA(2, 1) + --- DATA(2, 0) + --- DATA(2, -1) + 600 200 600 + + 33 33 29 + - 7/10 c32 + 3/50 c31 + --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + 200 200 200 + + 29 37 37 37 + - --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(0, -1) - --- DATA(1, -1) + 200 600 200 200 + + 11 29 \ 3 / + - --- DATA(-1, 0) - --- DATA(-1, 1)| x + |- 3/40 DATA(2, 1) + 200 600 / \ + + 11 + + 3/20 DATA(2, 0) - 3/40 DATA(2, -1) + 9/10 c32 - -- DATA(0, 0) + 20 + + 11 + - 9/20 DATA(1, 0) + -- DATA(0, 1) + 9/40 DATA(1, 1) + 3/40 DATA(-1, -1) + 40 + + 11 \ + + -- DATA(0, -1) + 9/40 DATA(1, -1) - 3/20 DATA(-1, 0) + 3/40 DATA(-1, 1)| + 40 / + + 2 / 21 + y + |- 7/1000 DATA(2, 2) + ---- DATA(1, 2) + 7/1000 DATA(-1, 2) + \ 1000 + + 437 81 + + ---- DATA(0, 2) + 9/125 DATA(2, 1) - ---- DATA(2, 0) + 2/125 DATA(2, -1) + 3000 1000 + + 63 257 243 71 + - 9/25 c32 - --- c31 + ---- DATA(0, 0) + ---- DATA(1, 0) - --- DATA(0, 1) + 250 1000 1000 250 + + 27 89 + - --- DATA(1, 1) - 2/125 DATA(-1, -1) - --- DATA(0, -1) + 125 750 + + 81 \ 3 / + - 6/125 DATA(1, -1) + ---- DATA(-1, 0) - 9/125 DATA(-1, 1)| y + | + 1000 / \ + + 13 13 13 13 + - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) - ---- DATA(0, 2) + 6000 2000 6000 2000 + + 377 43 481 91 39 + - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) + --- c32 - --- c31 + 6000 2000 6000 100 500 + + 129 1129 377 377 + - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) + 2000 2000 2000 2000 + + 481 481 481 + + ---- DATA(-1, -1) - ---- DATA(0, -1) + ---- DATA(1, -1) + 6000 2000 2000 + + 957 377 \ / + - ---- DATA(-1, 0) + ---- DATA(-1, 1)| x + |1/40 DATA(2, 2) + 2000 6000 / \ + + 11 + - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) - --- DATA(0, 2) - 3/20 DATA(2, 1) + 120 + + 11 + + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) + 9/10 c31 - -- DATA(0, 0) + 40 + + 11 + - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) - 1/20 DATA(-1, -1) + 20 + + 11 \ + - -- DATA(0, -1) - 3/20 DATA(1, -1) - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1)| + 60 / + + 111 333 333 + y - ---- DATA(-1, -1) + ---- DATA(0, -1) - ---- DATA(1, -1) + 2000 2000 2000 + + 201 87 + + ---- DATA(-1, 0) - ---- DATA(-1, 1) + 2000 2000 + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=26023908, alloc=1965720, time=1.75 + 59 3 37 2 2 37 3 11 +[COEFF(-1, -1) = --- x y + --- x - 1/12 x y - --- x + -- x y - 1/20 y + 750 400 600 60 + + 481 3 3 3 2 2 2 11 2 111 + + ---- x + 1/100 x y - 2/125 y + 1/8 x y + 3/40 y - -- x y - ---- + 6000 40 2000 + + 17 2 3 13 2 3 2 3 333 + - --- x y , COEFF(0, -1) = --- x y + 1/12 x y + 7/500 x y + ---- + 300 150 2000 + + 2 2 2 481 111 2 11 37 3 3 3 + + 3/40 x y - 1/8 x y - ---- x - --- x - -- y + --- x - 3/100 x y + 2000 400 60 200 + + 11 2 89 3 2 2 2 333 + + -- y - 1/20 x y - --- y , COEFF(1, -1) = 1/12 x y - 1/8 x y - ---- + 40 750 2000 + + 2 3 2 3 3 111 2 73 3 + - 1/300 x y + 7/40 x y + 3/100 x y + --- x - 7/60 x y - --- x y + 400 750 + + 3 2 481 37 3 + - 6/125 y - 3/20 y + 9/40 y + ---- x - --- x , COEFF(2, -1) = - 1/60 x y + 2000 200 + + 3 3 2 481 3 37 2 + - 1/100 x y + 1/40 x y - ---- x + 1/20 y + 7/1500 x y - --- x + 6000 400 + + 2 3 2 3 2 111 37 3 2 2 + - 1/12 x y + 2/125 y - 2/75 x y - 3/40 y + ---- + --- x + 1/8 x y , + 2000 600 + + 201 23 2 3 133 2 11 2 2 + COEFF(-1, 0) = ---- + --- x y + --- x + -- x y - 3/40 y - 1/4 x y + 2000 200 400 40 + + 11 3 11 2 957 2 3 3 2 851 3 + - --- x + -- x y - ---- x - 1/8 x y + 1/150 x y - 3/20 y - ---- x y + 200 20 2000 3000 + + 81 3 19 2 3 3 3 11 2 + + ---- y , COEFF(0, 0) = - --- x y - 1/50 x y - 3/40 x y - -- y + 1000 200 20 + + 257 3 11 129 101 3 33 3 2 199 2 + + ---- y - -- y - ---- x + ---- x y + --- x + 1/8 x y - --- x + 1000 40 2000 1000 200 400 + + 2 2 2 1397 2 2 1129 + + 1/4 x y - 3/20 x y + ----, COEFF(1, 0) = 1/4 x y + ---- x + 2000 2000 + + 149 3 2 3 3 2 + - 7/40 x y + ---- x y - 1/400 x + 1/50 x y - 9/40 y - 7/20 x y + 1000 + + 2 603 243 3 33 3 2 31 2 3 + - 9/20 y + ---- + ---- y - --- x + 1/8 x y - --- x y , COEFF(2, 0) = + 2000 1000 200 200 + + 2 2 101 3 11 3 3 3 2 + - 1/4 x y + ---- x y + --- x - 1/150 x y - 1/8 x y + 3/40 y + 3000 200 + + 67 2 2 2 201 81 3 43 + - 1/40 x y + --- x - 1/20 x y + 3/20 y - ---- - ---- y - ---- x + 400 2000 1000 2000 + + 27 2 3 11 2 2 2 29 3 11 + + --- x y , COEFF(-1, 1) = - -- x y + 1/8 x y - --- x - -- x y + 200 40 600 20 + + 377 203 3 13 2 3 29 2 87 2 + + ---- x + --- x y + 3/20 y - --- x y + --- x - ---- + 1/4 x y + 6000 750 100 400 2000 + + 3 3 3 2 261 2 3 + + 1/300 x y - 9/125 y + 3/40 y , COEFF(0, 1) = ---- + 7/50 x y + 2000 + + 2 71 3 2 2 2 11 2 87 2 + - 1/4 x y - --- y + 3/40 x y - 1/8 x y + 3/20 x y + -- y - --- x + 250 40 400 + + 3 3 31 3 377 11 29 3 87 2 + - 1/100 x y - --- x y - ---- x + -- y + --- x , COEFF(1, 1) = --- x + 500 2000 20 200 400 + + 2 27 3 2 3 3 11 2 3 + + 9/40 y + 9/20 y - --- y - 1/4 x y + 1/100 x y + --- x y + 125 100 + + 47 3 2 377 261 29 3 2 2 + - --- x y + 7/40 x y + ---- x - ---- - --- x + 7/20 x y - 1/8 x y , + 250 2000 2000 200 + + 87 29 2 2 31 3 2 2 3 + COEFF(2, 1) = ---- - --- x + 1/4 x y - ---- x y - 3/40 y - 3/25 x y + 2000 400 1500 + + 377 3 29 3 2 3 3 + - 3/20 y - ---- x + 9/125 y + --- x + 1/40 x y + 1/20 x y - 1/300 x y + 6000 600 + + 2 2 2 3 3 3 + + 1/8 x y , COEFF(-1, 2) = 1/400 x - 1/40 y - 1/50 x y + 7/1000 y + + 11 13 2 197 3 3 43 2 3 + + --- x y + ---- x - 1/24 x y - 3/2000 - ---- x y - 1/600 x + --- x y + 120 6000 3000 600 + + 2 11 53 3 2 + , COEFF(0, 2) = - 3/400 x - --- y - 1/40 x y - ---- x y + 1/24 x y + 120 1000 + + 13 3 3 3 437 3 79 2 3 + - ---- x + 9/2000 + 3/50 x y + 1/200 x + ---- y - --- x y , + 2000 3000 600 + + 2 3 3 409 3 3 + COEFF(1, 2) = 3/400 x - 3/40 y - 3/50 x y + ---- x y - 1/200 x + 3000 + + 21 3 2 29 2 3 13 + + ---- y + 1/24 x y + --- x y - 7/120 x y - 9/2000 + ---- x, + 1000 600 2000 + + 2 53 3 3 + COEFF(2, 2) = - 1/400 x + 3/2000 + 1/40 y - ---- x y - 7/1000 y + 3000 + + 3 3 13 2 2 3 3 + + 1/50 x y - ---- x - 1/24 x y + 7/600 x y - 1/120 x y + 1/600 x ] + 6000 + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); +bytes used=27024116, alloc=2031244, time=1.82 +bytes used=28024396, alloc=2031244, time=1.90 +bytes used=29025884, alloc=2162292, time=1.99 +bytes used=30026144, alloc=2162292, time=2.06 +bytes used=31027088, alloc=2162292, time=2.12 +bytes used=32027348, alloc=2162292, time=2.18 +bytes used=33027500, alloc=2162292, time=2.24 +bytes used=34027920, alloc=2162292, time=2.30 +bytes used=35028400, alloc=2162292, time=2.38 +bytes used=36028584, alloc=2162292, time=2.46 +bytes used=37028772, alloc=2162292, time=2.56 +bytes used=38028952, alloc=2162292, time=2.67 +bytes used=39029156, alloc=2162292, time=2.73 +bytes used=40029332, alloc=2162292, time=2.80 +bytes used=41029504, alloc=2162292, time=2.92 +bytes used=42029680, alloc=2162292, time=2.99 +bytes used=43029840, alloc=2162292, time=3.09 +bytes used=44030180, alloc=2162292, time=3.20 +bytes used=45030460, alloc=2162292, time=3.31 +bytes used=46030800, alloc=2162292, time=3.38 +bytes used=47030988, alloc=2162292, time=3.48 +bytes used=48031208, alloc=2162292, time=3.62 +bytes used=49031368, alloc=2162292, time=3.76 +> +# d/dx +> simplify( diff(interp_2d_cube_order3_smooth0,x) ); +bytes used=50031616, alloc=2162292, time=3.86 +bytes used=51059256, alloc=2162292, time=3.92 +bytes used=52059500, alloc=2162292, time=3.99 + 3 13 13 13 +6/5 x y c32 - ---- DATA(2, 2) + ---- DATA(1, 2) + ---- DATA(-1, 2) + 6000 2000 6000 + + 13 377 43 481 + - ---- DATA(0, 2) - ---- DATA(2, 1) - ---- DATA(2, 0) - ---- DATA(2, -1) + 2000 6000 2000 6000 + + 2 2 2 91 39 + + 3 c32 x y + 3 c31 x y + 1/20 y DATA(2, 1) + --- c32 - --- c31 + 100 500 + + 129 1129 377 377 + - ---- DATA(0, 0) + ---- DATA(1, 0) - ---- DATA(0, 1) + ---- DATA(1, 1) + 2000 2000 2000 2000 + + 2 2 3 21 2 3 13 + - 3 x y c32 - 6/5 x y c32 - -- x y c31 - 3 x y c31 - -- y c31 + 25 10 + + 13 3 91 3 13 2 + + -- y c32 + --- y c31 - -- y c32 - 1/60 y DATA(2, -1) + 25 250 10 + + 21 2 2 + - 3/40 y DATA(0, 0) - 7/40 y DATA(1, 0) - -- x c32 + 9/50 x c31 + 10 + + 2 3 2 3 + + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) + + 2 3 + + 1/100 x y DATA(-1, 1) - 1/12 x y DATA(2, 2) + 1/12 x y DATA(1, 2) + + - 1/12 x y DATA(-1, 2) + 1/12 x y DATA(0, 2) + 1/2 x y DATA(2, 1) + + - 1/4 x y DATA(2, 0) - 1/6 x y DATA(2, -1) + 1/4 x y DATA(0, 0) + + 2 + + 1/4 x y DATA(1, 0) - 1/2 x y DATA(0, 1) + 1/4 x y DATA(2, 1) + + 3 + - 1/150 x y DATA(1, -1) - 1/2 x y DATA(1, 1) - 1/6 x y DATA(-1, -1) + + + 1/6 x y DATA(0, -1) + 1/6 x y DATA(1, -1) - 1/4 x y DATA(-1, 0) + + 11 + + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) + -- y DATA(-1, -1) + 60 + + 11 + - 1/20 y DATA(0, -1) - 7/60 y DATA(1, -1) + -- y DATA(-1, 0) + 40 + + 11 53 3 + - -- y DATA(-1, 1) - 1/40 y DATA(2, 0) - ---- y DATA(2, 2) + 20 3000 + + 409 3 197 3 53 3 + + ---- y DATA(1, 2) - ---- y DATA(-1, 2) - ---- y DATA(0, 2) + 3000 3000 1000 + + 31 3 101 3 3 + - ---- y DATA(2, 1) + ---- y DATA(2, 0) + 7/1500 y DATA(2, -1) + 1500 3000 + + 101 3 149 3 31 3 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - --- y DATA(0, 1) + 1000 1000 500 + + 47 3 59 3 3 + - --- y DATA(1, 1) + --- y DATA(-1, -1) + 7/500 y DATA(0, -1) + 250 750 + + 73 3 851 3 203 3 + - --- y DATA(1, -1) - ---- y DATA(-1, 0) + --- y DATA(-1, 1) + 750 3000 750 + + 11 + - 1/120 y DATA(2, 2) - 7/120 y DATA(1, 2) + --- y DATA(-1, 2) + 120 + + 2 2 + - 1/40 y DATA(0, 2) + 1/40 y DATA(2, 1) - 1/20 y DATA(2, 0) + + 2 2 2 + + 1/40 y DATA(2, -1) - 3/20 y DATA(0, 0) - 7/20 y DATA(1, 0) + + 3 2 3 + + 7/300 x y DATA(2, 2) + 1/2 x y DATA(0, 0) - 4/75 x y DATA(2, -1) + + 79 3 2 3 2 + - --- x y DATA(0, 2) - 3/50 x y DATA(-1, 2) - 1/4 x y DATA(1, 1) + 300 + + 31 3 3 2 + - --- x y DATA(1, 0) + 7/25 x y DATA(0, 1) - 1/4 x y DATA(0, -1) + 100 + + 2 3 3 2 3 + - 3/100 x y DATA(2, -1) - 6/25 x y DATA(2, 1) - 9/50 x y DATA(1, 2) + + 2 2 3 11 3 + + 1/2 x y DATA(1, 0) - 1/100 x y DATA(2, 1) + -- x y DATA(1, 1) + 50 + + 19 3 21 2 + - --- x y DATA(0, 0) + -- x c32 - 9/50 x c31 + 1/4 x y DATA(-1, 1) + 100 10 + + 2 2 + - 1/2 x y DATA(2, 0) + 1/2 x y DATA(-1, 1) - 1/4 x y DATA(1, -1) + + 23 3 2 3 2 3 + + --- x y DATA(-1, 0) - 1/50 x y DATA(2, 0) - 3/100 x y DATA(0, 1) + 100 + + 2 3 2 3 13 3 + + 9/50 x y DATA(0, 2) - 3/50 x y DATA(0, 0) + -- x y DATA(0, -1) + 75 + + 2 2 29 3 + + 1/4 x y DATA(2, -1) + 1/4 x y DATA(-1, -1) + --- x y DATA(1, 2) + 300 + + 2 2 3 2 3 + - 1/4 x y DATA(0, 1) + 3/50 x y DATA(1, 0) + 3/50 x y DATA(2, 2) + + 17 3 13 3 43 3 + - --- x y DATA(-1, -1) - -- x y DATA(-1, 1) + --- x y DATA(-1, 2) + 150 50 300 + + 27 3 2 2 + + --- x y DATA(2, 0) - 1/2 x y DATA(-1, 0) + 3/40 y DATA(0, 1) + 100 + + 11 2 2 2 + - -- y DATA(-1, -1) + 3/40 y DATA(0, -1) + 7/40 y DATA(1, -1) + 40 + + 11 2 11 2 2 + + -- y DATA(-1, 0) - -- y DATA(-1, 1) + 1/200 x DATA(2, 2) + 20 40 + + 2 2 2 + - 3/200 x DATA(1, 2) - 1/200 x DATA(-1, 2) + 3/200 x DATA(0, 2) + + 29 2 33 2 37 2 + + --- x DATA(2, 1) + --- x DATA(2, 0) + --- x DATA(2, -1) + 200 200 200 + + 99 2 99 2 87 2 + + --- x DATA(0, 0) - --- x DATA(1, 0) + --- x DATA(0, 1) + 200 200 200 + + 87 2 37 2 111 2 + - --- x DATA(1, 1) - --- x DATA(-1, -1) + --- x DATA(0, -1) + 200 200 200 + + 111 2 33 2 29 2 + - --- x DATA(1, -1) - --- x DATA(-1, 0) - --- x DATA(-1, 1) + 200 200 200 + + 2 + - 1/200 x DATA(2, 2) + 3/200 x DATA(1, 2) + 7/40 y DATA(1, 1) + + 29 + + 1/200 x DATA(-1, 2) - 3/200 x DATA(0, 2) - --- x DATA(2, 1) + 200 + + 67 37 199 + + --- x DATA(2, 0) - --- x DATA(2, -1) - --- x DATA(0, 0) + 200 200 200 + + 87 87 + - 1/200 x DATA(1, 0) - --- x DATA(0, 1) + --- x DATA(1, 1) + 200 200 + + 37 111 111 + + --- x DATA(-1, -1) - --- x DATA(0, -1) + --- x DATA(1, -1) + 200 200 200 + + 133 29 21 3 481 + + --- x DATA(-1, 0) + --- x DATA(-1, 1) + -- x y c31 + ---- DATA(-1, -1) + 200 200 25 6000 + + 481 481 957 + - ---- DATA(0, -1) + ---- DATA(1, -1) - ---- DATA(-1, 0) + 2000 2000 2000 + + 377 2 3 2 3 + + ---- DATA(-1, 1) + 3/100 x y DATA(1, 1) + 3/100 x y DATA(-1, -1) + 6000 + + 2 3 + - 9/100 x y DATA(0, -1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=53061376, alloc=2162292, time=4.05 + 37 2 2 481 17 3 37 11 2 11 +[COEFF(-1, -1) = - --- x + 1/4 x y + ---- - --- x y + --- x - -- y + -- y + 200 6000 150 200 40 60 + + 2 3 59 3 3 2 + - 1/6 x y + 3/100 x y + --- y , COEFF(0, -1) = 7/500 y + 3/40 y + 750 + + 13 3 111 2 111 2 481 + + -- x y + 1/6 x y + --- x - --- x - 1/4 x y - 1/20 y - ---- + 75 200 200 2000 + + 2 3 73 3 2 3 3 + - 9/100 x y , COEFF(1, -1) = - --- y + 9/100 x y - 1/150 x y - 7/60 y + 750 + + 2 111 481 111 2 2 + + 1/6 x y + 7/40 y + --- x + ---- - --- x - 1/4 x y , COEFF(2, -1) = + 200 2000 200 + + 3 2 3 3 2 37 2 + - 4/75 x y - 1/6 x y - 3/100 x y - 1/60 y + 7/1500 y + 1/40 y + --- x + 200 + + 2 37 481 33 2 11 851 3 + + 1/4 x y - --- x - ----, COEFF(-1, 0) = - --- x + -- y - ---- y + 200 6000 200 40 3000 + + 2 3 11 2 957 23 3 133 2 + - 1/4 x y + 1/50 x y + -- y - ---- + --- x y + --- x - 1/2 x y , + 20 2000 100 200 + + 129 2 3 101 3 19 3 2 + COEFF(0, 0) = - 3/40 y - ---- - 3/50 x y + ---- y - --- x y + 1/2 x y + 2000 1000 100 + + 2 199 99 2 31 3 + - 3/20 y + 1/4 x y - --- x + --- x , COEFF(1, 0) = - --- x y + 200 200 100 + + 2 3 1129 2 2 99 2 149 3 + + 3/50 x y + ---- + 1/2 x y - 7/40 y - 7/20 y - --- x + ---- y + 2000 200 1000 + + 2 33 2 2 + - 1/200 x + 1/4 x y, COEFF(2, 0) = - 1/40 y - 1/20 y + --- x - 1/2 x y + 200 + + 27 3 101 3 2 3 43 67 + + --- x y + ---- y - 1/50 x y - 1/4 x y - ---- + --- x, COEFF(-1, 1) + 100 3000 2000 200 + + 13 3 11 2 2 377 2 3 203 3 29 + = - -- x y - -- y + 1/4 x y + ---- + 1/100 x y + --- y + --- x + 50 40 6000 750 200 + + 29 2 11 2 3 2 87 2 + - --- x - -- y + 1/2 x y, COEFF(0, 1) = - 3/100 x y - 1/4 x y + --- x + 200 20 200 + + 2 31 3 3 377 87 + + 3/40 y - --- y + 7/25 x y + 3/20 y - ---- - --- x - 1/2 x y, + 500 2000 200 + + 47 3 2 87 2 377 + COEFF(1, 1) = 7/20 y - --- y - 1/2 x y - 1/4 x y - --- x + ---- + 250 200 2000 + + 2 11 3 87 2 3 + + 7/40 y + -- x y + --- x + 3/100 x y , COEFF(2, 1) = 1/20 y + 50 200 + + 2 3 31 3 3 2 2 377 29 2 + - 1/100 x y - ---- y - 6/25 x y + 1/40 y + 1/4 x y - ---- + --- x + 1500 6000 200 + + 29 11 2 13 197 3 + + 1/2 x y - --- x, COEFF(-1, 2) = --- y - 1/200 x + ---- - ---- y + 200 120 6000 3000 + + 43 3 2 3 53 3 + + --- x y - 1/12 x y - 3/50 x y + 1/200 x, COEFF(0, 2) = - ---- y + 300 1000 + + 2 3 13 2 79 3 + - 1/40 y + 9/50 x y - ---- + 3/200 x - --- x y + 1/12 x y - 3/200 x, + 2000 300 + + 409 3 2 + COEFF(1, 2) = 1/12 x y + ---- y - 3/200 x - 7/120 y + 3/200 x + 3000 + + 2 3 13 29 3 53 3 + - 9/50 x y + ---- + --- x y , COEFF(2, 2) = - ---- y - 1/120 y + 2000 300 3000 + + 2 13 2 3 3 + + 1/200 x - ---- - 1/200 x + 3/50 x y + 7/300 x y - 1/12 x y] + 6000 + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); +bytes used=54061732, alloc=2162292, time=4.12 +bytes used=55062064, alloc=2162292, time=4.20 +bytes used=56062456, alloc=2162292, time=4.27 +bytes used=57062648, alloc=2162292, time=4.36 +bytes used=58062912, alloc=2162292, time=4.46 +bytes used=59063180, alloc=2162292, time=4.57 +bytes used=60063412, alloc=2162292, time=4.65 +bytes used=61063624, alloc=2162292, time=4.75 +bytes used=62064392, alloc=2162292, time=4.84 +bytes used=63064556, alloc=2162292, time=4.95 +> +# d/dy +> simplify( diff(interp_2d_cube_order3_smooth0,y) ); +bytes used=64064736, alloc=2162292, time=5.12 +bytes used=65064892, alloc=2162292, time=5.17 + 3 3 +2 c32 x y + c31 x + 1/40 DATA(2, 2) - 3/40 DATA(1, 2) - 1/40 DATA(-1, 2) + + 11 + - --- DATA(0, 2) - 3/20 DATA(2, 1) + 3/40 DATA(2, 0) + 1/20 DATA(2, -1) + 120 + + 2 2 3 2 + + 9/5 c32 x y - 3/20 y DATA(2, 1) - 6/5 c32 x y + 9/10 c31 + + 11 11 + - -- DATA(0, 0) - 9/40 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) + 40 20 + + 39 2 27 2 11 + + -- x y c32 - -- y c32 - 3/20 y DATA(2, -1) - -- y DATA(0, 0) + 25 25 10 + + 2 + - 9/10 y DATA(1, 0) - 3/2 x c31 + 1/20 x y DATA(2, 1) + + - 1/10 x y DATA(2, 0) + 1/20 x y DATA(2, -1) - 3/10 x y DATA(0, 0) + + 31 2 + - 7/10 x y DATA(1, 0) + 3/20 x y DATA(0, 1) - --- x y DATA(2, 1) + 500 + + 11 + + 7/20 x y DATA(1, 1) - -- x y DATA(-1, -1) + 3/20 x y DATA(0, -1) + 20 + + 11 2 + + 7/20 x y DATA(1, -1) + -- x y DATA(-1, 0) + 1/4 x y DATA(2, -1) + 10 + + 2 2 2 + + 1/2 x y DATA(0, 0) + 1/2 x y DATA(1, 0) - 1/4 x y DATA(0, 1) + + 2 2 2 + - 1/4 x y DATA(1, 1) + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(0, -1) + + 2 2 2 + - 1/4 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/4 x y DATA(-1, 1) + + 3 2 3 2 3 2 + - 9/50 x y DATA(1, 2) - 3/50 x y DATA(-1, 2) + 9/50 x y DATA(0, 2) + + 3 2 3 2 3 2 + - 1/100 x y DATA(2, 1) - 1/50 x y DATA(2, 0) + 3/50 x y DATA(2, 2) + + 3 2 3 2 + - 9/100 x y DATA(0, -1) - 3/100 x y DATA(2, -1) + + 3 2 3 2 93 2 2 + - 3/50 x y DATA(0, 0) + 3/50 x y DATA(1, 0) - --- x y DATA(1, 0) + 200 + + 21 2 2 3 2 3 2 + + -- x y DATA(0, 1) - 3/100 x y DATA(0, 1) + 3/100 x y DATA(1, 1) + 50 + + 3 2 2 2 81 2 2 + + 3/100 x y DATA(-1, -1) - 9/25 x y DATA(2, 1) + --- x y DATA(2, 0) + 200 + + 2 2 57 2 2 3 2 + - 2/25 x y DATA(2, -1) - --- x y DATA(0, 0) + 1/100 x y DATA(-1, 1) + 200 + + 29 2 2 43 2 2 79 2 2 + + --- x y DATA(1, 2) + --- x y DATA(-1, 2) - --- x y DATA(0, 2) + 200 200 200 + + 2 2 33 2 2 13 2 2 + + 7/200 x y DATA(2, 2) + --- x y DATA(1, 1) + -- x y DATA(0, -1) + 100 50 + + 2 2 69 2 2 17 2 2 + - 1/100 x y DATA(1, -1) + --- x y DATA(-1, 0) - --- x y DATA(-1, -1) + 200 100 + + 3 2 3 2 53 2 + + 9/100 x y DATA(1, -1) + 1/50 x y DATA(-1, 0) - ---- x y DATA(2, 2) + 1000 + + 39 2 2 409 2 197 2 + - --- x y DATA(-1, 1) + ---- x y DATA(1, 2) - ---- x y DATA(-1, 2) + 100 1000 1000 + + 159 2 11 + - ---- x y DATA(0, 2) + -- y DATA(0, 1) + 9/20 y DATA(1, 1) + 1000 20 + + 11 + + 3/20 y DATA(-1, -1) + -- y DATA(0, -1) + 9/20 y DATA(1, -1) + 20 + + - 3/10 y DATA(-1, 0) + 3/20 y DATA(-1, 1) + 3/10 y DATA(2, 0) + + 27 2 243 2 2 + + --- y DATA(2, 1) - ---- y DATA(2, 0) + 6/125 y DATA(2, -1) + 125 1000 + + 771 2 729 2 21 2 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - ---- y DATA(2, 2) + 1000 1000 1000 + + 63 2 21 2 437 2 + + ---- y DATA(1, 2) + ---- y DATA(-1, 2) + ---- y DATA(0, 2) + 1000 1000 1000 + + 2 2 189 2 273 2 + + 1/4 x y DATA(2, 1) - 1/2 x y DATA(2, 0) - --- y c31 + --- x y c31 + 250 250 + + 63 2 2 21 3 2 303 2 + + 9/5 y c32 + -- x y c31 - -- x y c31 + ---- x y DATA(0, 0) + 50 25 1000 + + 141 2 21 2 447 2 + - --- x y DATA(1, 1) + --- x y DATA(0, -1) + ---- x y DATA(1, 0) + 250 500 1000 + + 13 2 203 2 + - 13/5 x y c32 - -- x c31 - 3 x y c32 + --- x y DATA(-1, 1) + 10 250 + + 101 2 11 73 2 + + ---- x y DATA(2, 0) - -- x y DATA(-1, 1) - --- x y DATA(1, -1) + 1000 20 250 + + 2 59 2 93 2 + + 7/500 x y DATA(2, -1) + --- x y DATA(-1, -1) - --- x y DATA(0, 1) + 250 500 + + 851 2 213 2 2 + - ---- x y DATA(-1, 0) - --- y DATA(0, 1) - 6/125 y DATA(-1, -1) + 1000 250 + + 89 2 18 2 243 2 + - --- y DATA(0, -1) - --- y DATA(1, -1) + ---- y DATA(-1, 0) + 250 125 1000 + + 27 2 2 2 + - --- y DATA(-1, 1) - 1/24 x DATA(2, 2) + 1/24 x DATA(1, 2) + 125 + + 2 2 2 + - 1/24 x DATA(-1, 2) + 1/24 x DATA(0, 2) + 1/4 x DATA(2, 1) + + 2 2 2 + - 1/8 x DATA(2, 0) - 1/12 x DATA(2, -1) + 1/8 x DATA(0, 0) + + 2 2 2 + + 1/8 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) + + 2 2 2 + - 1/12 x DATA(-1, -1) + 1/12 x DATA(0, -1) + 1/12 x DATA(1, -1) + + 2 2 + - 1/8 x DATA(-1, 0) + 1/4 x DATA(-1, 1) - 1/120 x DATA(2, 2) + + 81 2 11 + - 7/120 x DATA(1, 2) - --- y DATA(1, 1) + --- x DATA(-1, 2) + 125 120 + + - 1/40 x DATA(0, 2) + 1/20 x DATA(2, 1) - 1/40 x DATA(2, 0) + + - 1/60 x DATA(2, -1) - 3/40 x DATA(0, 0) - 7/40 x DATA(1, 0) + + 11 + + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) + -- x DATA(-1, -1) + 60 + + 11 + - 1/20 x DATA(0, -1) - 7/60 x DATA(1, -1) + -- x DATA(-1, 0) + 40 + + 11 11 + - -- x DATA(-1, 1) - 1/20 DATA(-1, -1) - -- DATA(0, -1) - 3/20 DATA(1, -1) + 20 60 + + - 3/40 DATA(-1, 0) + 3/20 DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=66073540, alloc=2162292, time=5.24 + 17 2 2 3 2 11 59 2 +[COEFF(-1, -1) = - --- x y - 1/20 + 3/100 x y + -- x + --- x y + 3/20 y + 100 60 250 + + 2 2 2 11 2 + - 6/125 y - 1/12 x + 1/4 x y - -- x y, COEFF(0, -1) = 1/12 x + 20 + + 2 13 2 2 11 21 2 11 + - 1/4 x y - 1/20 x + -- x y + 3/20 x y + -- y + --- x y - -- + 50 20 500 60 + + 3 2 89 2 2 2 2 + - 9/100 x y - --- y , COEFF(1, -1) = - 3/20 - 1/4 x y - 1/100 x y + 250 + + 18 2 2 3 2 73 2 + + 9/20 y + 7/20 x y - --- y + 1/12 x - 7/60 x + 9/100 x y - --- x y , + 125 250 + + 2 2 2 3 2 + COEFF(2, -1) = 1/4 x y - 1/60 x + 1/20 - 2/25 x y - 3/100 x y + + 2 2 2 + + 7/500 x y + 1/20 x y + 6/125 y - 1/12 x - 3/20 y, COEFF(-1, 0) = + + 11 851 2 2 69 2 2 3 2 + - 3/40 + -- x y - ---- x y - 1/2 x y - 3/10 y + --- x y + 1/50 x y + 10 1000 200 + + 11 2 243 2 2 303 2 11 + + -- x - 1/8 x + ---- y , COEFF(0, 0) = 1/8 x + ---- x y - -- y + 40 1000 1000 10 + + 3 2 11 2 771 2 57 2 2 + - 3/50 x y - -- + 1/2 x y - 3/40 x + ---- y - --- x y - 3/10 x y, + 40 1000 200 + + 93 2 2 3 2 2 + COEFF(1, 0) = - --- x y + 3/50 x y - 7/10 x y - 9/10 y + 1/2 x y + 200 + + 447 2 2 729 2 + + ---- x y + 1/8 x + ---- y - 7/40 x - 9/40, COEFF(2, 0) = 3/40 + 1000 1000 + + 2 81 2 2 2 101 2 243 2 + - 1/2 x y + --- x y - 1/40 x - 1/8 x + ---- x y - ---- y - 1/10 x y + 200 1000 1000 + + 3 2 39 2 2 2 27 2 + + 3/10 y - 1/50 x y , COEFF(-1, 1) = - --- x y + 3/20 + 1/4 x - --- y + 100 125 + + 3 2 11 203 2 11 2 + + 1/100 x y + 3/20 y - -- x + --- x y - -- x y + 1/4 x y, COEFF(0, 1) + 20 250 20 + + 213 2 11 11 21 2 2 93 2 3 2 + = - --- y + -- + -- y + -- x y - --- x y - 3/100 x y + 3/20 x + 250 20 20 50 500 + + 2 2 2 33 2 2 + - 1/4 x y - 1/4 x + 3/20 x y, COEFF(1, 1) = 9/20 y - 1/4 x + --- x y + 100 + + 81 2 2 141 2 3 2 + - --- y + 7/20 x - 1/4 x y - --- x y + 9/20 + 7/20 x y + 3/100 x y , + 125 250 + + 3 2 + COEFF(2, 1) = - 1/100 x y - 3/20 + 1/20 x + 1/20 x y - 3/20 y + + 2 2 31 2 2 2 27 2 + - 9/25 x y - --- x y + 1/4 x + 1/4 x y + --- y , COEFF(-1, 2) = + 500 125 + + 2 197 2 11 3 2 43 2 2 21 2 + - 1/40 - 1/24 x - ---- x y + --- x - 3/50 x y + --- x y + ---- y , + 1000 120 200 1000 + + COEFF(0, 2) = + + 79 2 2 159 2 3 2 2 11 437 2 + - --- x y - 1/40 x - ---- x y + 9/50 x y + 1/24 x - --- + ---- y , + 200 1000 120 1000 + + COEFF(1, 2) = + + 29 2 2 3 2 2 63 2 409 2 + - 3/40 + --- x y - 7/120 x - 9/50 x y + 1/24 x + ---- y + ---- x y , + 200 1000 1000 + + COEFF(2, 2) = + + 21 2 2 2 2 3 2 53 2 + 1/40 - ---- y - 1/24 x + 7/200 x y - 1/120 x + 3/50 x y - ---- x y ] + 1000 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); +bytes used=67073904, alloc=2162292, time=5.31 +bytes used=68074096, alloc=2162292, time=5.38 +bytes used=69074392, alloc=2162292, time=5.48 +bytes used=70074612, alloc=2162292, time=5.54 +bytes used=71074776, alloc=2162292, time=5.66 +bytes used=72075172, alloc=2162292, time=5.73 +bytes used=73075452, alloc=2162292, time=5.83 +bytes used=74076084, alloc=2162292, time=5.90 +bytes used=75076284, alloc=2162292, time=6.00 +bytes used=76076484, alloc=2162292, time=6.08 +bytes used=77083384, alloc=2162292, time=6.19 +bytes used=78083548, alloc=2162292, time=6.27 +bytes used=79083664, alloc=2162292, time=6.41 +bytes used=80083872, alloc=2162292, time=6.49 +bytes used=81084148, alloc=2162292, time=6.63 +bytes used=82084408, alloc=2162292, time=6.75 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); +bytes used=83085440, alloc=2162292, time=6.83 +6 c31 x y - 1/200 DATA(2, 2) + 3/200 DATA(1, 2) + 1/200 DATA(-1, 2) + + 29 67 37 + - 3/200 DATA(0, 2) - --- DATA(2, 1) + --- DATA(2, 0) - --- DATA(2, -1) + 200 200 200 + + 29 3 3 + + 1/2 y DATA(2, 1) + --- y DATA(1, 2) + 7/300 y DATA(2, 2) + 300 + + 11 3 3 21 + + -- y DATA(1, 1) + 1/25 x y DATA(-1, 0) + -- c32 - 9/50 c31 + 50 10 + + 199 87 87 + - --- DATA(0, 0) - 1/200 DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) + 200 200 200 + + 2 2 + + 6 x y c32 - 3 y c32 - 21/5 x c32 - 1/6 y DATA(2, -1) + + + 1/4 y DATA(0, 0) + 1/4 y DATA(1, 0) - 1/2 y DATA(0, 1) + + - 1/2 y DATA(1, 1) - 1/6 y DATA(-1, -1) + 1/6 y DATA(0, -1) + + + 1/6 y DATA(1, -1) - 1/4 y DATA(-1, 0) + 1/2 y DATA(-1, 1) + + 3 19 3 + - 1/4 y DATA(2, 0) + 7/25 y DATA(0, 1) - --- y DATA(0, 0) + 100 + + 3 27 3 3 + - 4/75 y DATA(2, -1) + --- y DATA(2, 0) - 6/25 y DATA(2, 1) + 100 + + 79 3 13 3 23 3 + - --- y DATA(0, 2) - -- y DATA(-1, 1) + --- y DATA(-1, 0) + 300 50 100 + + 3 13 3 17 3 + - 1/150 y DATA(1, -1) + -- y DATA(0, -1) - --- y DATA(-1, -1) + 75 150 + + 31 3 2 2 + - --- y DATA(1, 0) + 1/4 y DATA(2, 1) - 1/2 y DATA(2, 0) + 100 + + 2 2 2 + + 1/4 y DATA(2, -1) + 1/2 y DATA(0, 0) + 1/2 y DATA(1, 0) + 9/25 x c31 + + 2 2 2 + - 3 y c31 - 1/4 y DATA(0, 1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(0, -1) + + 2 2 2 + - 1/4 y DATA(1, -1) - 1/2 y DATA(-1, 0) + 1/4 y DATA(-1, 1) + + 2 + + 1/100 x DATA(2, 2) - 3/100 x DATA(1, 2) - 1/4 y DATA(1, 1) + + 29 + - 1/100 x DATA(-1, 2) + 3/100 x DATA(0, 2) + --- x DATA(2, 1) + 100 + + 33 37 99 + + --- x DATA(2, 0) + --- x DATA(2, -1) + --- x DATA(0, 0) + 100 100 100 + + 99 87 87 + - --- x DATA(1, 0) + --- x DATA(0, 1) - --- x DATA(1, 1) + 100 100 100 + + 37 111 111 + - --- x DATA(-1, -1) + --- x DATA(0, -1) - --- x DATA(1, -1) + 100 100 100 + + 33 29 21 3 3 + - --- x DATA(-1, 0) - --- x DATA(-1, 1) + -- y c31 + 6/5 y c32 + 100 100 25 + + 37 111 111 133 + + --- DATA(-1, -1) - --- DATA(0, -1) + --- DATA(1, -1) + --- DATA(-1, 0) + 200 200 200 200 + + 29 42 3 3 3 + + --- DATA(-1, 1) - -- x y c31 - 12/5 x y c32 - 9/50 x y DATA(0, -1) + 200 25 + + 3 3 3 + + 9/50 x y DATA(1, -1) + 1/50 x y DATA(-1, 1) + 3/25 x y DATA(2, 2) + + 3 3 3 + - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) + + 3 3 3 + - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) + + 3 3 3 + - 3/25 x y DATA(0, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) + + 3 3 + + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) - 1/12 y DATA(2, 2) + + + 1/12 y DATA(1, 2) - 1/12 y DATA(-1, 2) + 1/12 y DATA(0, 2) + + 43 3 + + --- y DATA(-1, 2) + 300 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 37 2 17 3 3 37 +[COEFF(-1, -1) = - --- x + 1/4 y - --- y + 3/50 x y - 1/6 y + ---, + 100 150 200 + + 111 2 13 3 3 111 + COEFF(0, -1) = - --- - 1/4 y + 1/6 y + -- y - 9/50 x y + --- x, + 200 75 100 + + 3 111 111 2 3 + COEFF(1, -1) = 9/50 x y + --- - --- x - 1/4 y - 1/150 y + 1/6 y, + 200 100 + + 37 2 3 3 37 + COEFF(2, -1) = - --- + 1/4 y - 1/6 y - 4/75 y - 3/50 x y + --- x, + 200 100 + + 23 3 133 2 33 3 + COEFF(-1, 0) = --- y + --- - 1/4 y - 1/2 y - --- x + 1/25 x y , + 100 200 100 + + 199 19 3 99 2 3 + COEFF(0, 0) = 1/4 y - --- - --- y + --- x + 1/2 y - 3/25 x y , + 200 100 100 + + 2 3 99 31 3 + COEFF(1, 0) = 1/4 y + 1/2 y + 3/25 x y - --- x - 1/200 - --- y , + 100 100 + + 33 67 3 2 27 3 + COEFF(2, 0) = --- x + --- - 1/25 x y - 1/2 y - 1/4 y + --- y , + 100 200 100 + + 29 13 3 3 29 2 + COEFF(-1, 1) = - --- x - -- y + 1/50 x y + --- + 1/4 y + 1/2 y, + 100 50 200 + + 2 87 3 87 3 + COEFF(0, 1) = - 1/4 y - --- - 1/2 y - 3/50 x y + --- x + 7/25 y , + 200 100 + + 87 3 2 87 11 3 + COEFF(1, 1) = - --- x + 3/50 x y - 1/4 y + --- - 1/2 y + -- y , + 100 200 50 + + 3 29 2 3 29 + COEFF(2, 1) = - 6/25 y + --- x + 1/4 y - 1/50 x y - --- + 1/2 y, + 100 200 + + 43 3 3 + COEFF(-1, 2) = --- y - 1/100 x - 3/25 x y - 1/12 y + 1/200, + 300 + + 79 3 3 + COEFF(0, 2) = 3/100 x - --- y - 3/200 + 1/12 y + 9/25 x y , + 300 + + 29 3 3 + COEFF(1, 2) = - 3/100 x + --- y + 3/200 - 9/25 x y + 1/12 y, + 300 + + 3 3 + COEFF(2, 2) = 1/100 x - 1/200 + 3/25 x y + 7/300 y - 1/12 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); +bytes used=84085660, alloc=2162292, time=6.91 +bytes used=85085812, alloc=2162292, time=6.99 +bytes used=86086048, alloc=2162292, time=7.09 +bytes used=87086364, alloc=2162292, time=7.18 +bytes used=88086596, alloc=2162292, time=7.29 +bytes used=89086816, alloc=2162292, time=7.43 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); +bytes used=90086976, alloc=2162292, time=7.50 + 2 2 11 +3 c31 x + 6 c32 x y - 1/120 DATA(2, 2) - 7/120 DATA(1, 2) + --- DATA(-1, 2) + 120 + + - 1/40 DATA(0, 2) + 1/20 DATA(2, 1) - 1/40 DATA(2, 0) - 1/60 DATA(2, -1) + + 13 + + 1/20 y DATA(2, 1) - -- c31 - 3/40 DATA(0, 0) - 7/40 DATA(1, 0) + 10 + + 2 39 2 + + 3/20 DATA(0, 1) + 7/20 DATA(1, 1) + 18/5 x y c32 + -- y c32 + 25 + + + 1/2 x y DATA(2, -1) + 1/20 y DATA(2, -1) - 3/10 y DATA(0, 0) + + - 7/10 y DATA(1, 0) + 3/20 y DATA(0, 1) + 7/20 y DATA(1, 1) + + 11 + - -- y DATA(-1, -1) + 3/20 y DATA(0, -1) + 7/20 y DATA(1, -1) + 20 + + 11 11 + + -- y DATA(-1, 0) - -- y DATA(-1, 1) - 1/10 y DATA(2, 0) + 10 20 + + 31 2 101 2 2 + - --- y DATA(2, 1) + ---- y DATA(2, 0) + 7/500 y DATA(2, -1) + 500 1000 + + 303 2 447 2 93 2 + + ---- y DATA(0, 0) + ---- y DATA(1, 0) - 3 x c31 - --- y DATA(0, 1) + 1000 1000 500 + + 59 2 21 2 73 2 + + --- y DATA(-1, -1) + --- y DATA(0, -1) - --- y DATA(1, -1) + 250 500 250 + + 851 2 203 2 + - ---- y DATA(-1, 0) + --- y DATA(-1, 1) - 1/12 x DATA(2, 2) + 1000 250 + + 141 2 + + 1/12 x DATA(1, 2) - --- y DATA(1, 1) - 1/12 x DATA(-1, 2) + 250 + + + 1/12 x DATA(0, 2) + 1/2 x DATA(2, 1) - 1/4 x DATA(2, 0) + + - 1/6 x DATA(2, -1) + 1/4 x DATA(0, 0) + 1/4 x DATA(1, 0) + + - 1/2 x DATA(0, 1) - 1/2 x DATA(1, 1) - 1/6 x DATA(-1, -1) + + + 1/6 x DATA(0, -1) + 1/6 x DATA(1, -1) - 1/4 x DATA(-1, 0) + + 2 2 2 2 + + 1/2 x DATA(-1, 1) + 3/100 x y DATA(-1, 1) + 3/50 x y DATA(-1, 0) + + 27 2 2 2 2 2 + + --- x y DATA(1, -1) + 7/100 x y DATA(2, 2) - 3/100 x y DATA(2, 1) + 100 + + 2 2 2 2 2 2 + - 9/50 x y DATA(0, 0) + 9/100 x y DATA(1, 1) - 9/100 x y DATA(0, 1) + + 27 2 2 2 2 2 2 + - --- x y DATA(0, -1) + 9/100 x y DATA(-1, -1) + 9/50 x y DATA(1, 0) + 100 + + 43 2 79 2 18 2 + + --- x y DATA(-1, 2) - --- x y DATA(0, 2) - -- x y DATA(2, 1) + 100 100 25 + + 2 2 27 2 2 2 2 + + 9/50 x y DATA(2, 2) + -- x y DATA(0, 2) - 9/50 x y DATA(-1, 2) + 50 + + 27 2 2 2 2 2 2 + - -- x y DATA(1, 2) - 9/100 x y DATA(2, -1) - 3/50 x y DATA(2, 0) + 50 + + 13 2 81 2 2 + + -- x y DATA(0, -1) + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) + 25 100 + + 57 2 29 2 2 + - --- x y DATA(0, 0) + --- x y DATA(1, 2) - 1/50 x y DATA(1, -1) + 100 100 + + 69 2 39 2 + + --- x y DATA(-1, 0) - -- x y DATA(-1, 1) + 1/2 x y DATA(2, 1) + 100 50 + + 93 2 21 2 + - x y DATA(2, 0) - --- x y DATA(1, 0) + -- x y DATA(0, 1) + 100 25 + + 33 2 17 2 + + -- x y DATA(1, 1) - -- x y DATA(-1, -1) + 1/2 x y DATA(-1, -1) + 50 50 + + - 1/2 x y DATA(1, -1) - x y DATA(-1, 0) + 1/2 x y DATA(-1, 1) + + - 1/2 x y DATA(0, -1) + x y DATA(0, 0) + x y DATA(1, 0) + + 159 2 + - 1/2 x y DATA(0, 1) - 1/2 x y DATA(1, 1) - ---- y DATA(0, 2) + 1000 + + 409 2 53 2 197 2 + + ---- y DATA(1, 2) - ---- y DATA(2, 2) - ---- y DATA(-1, 2) + 1000 1000 1000 + + 63 2 273 2 2 2 11 + - 6 x y c32 + -- x y c31 + --- y c31 - 18/5 c32 x y + -- DATA(-1, -1) + 25 250 60 + + 11 11 + - 1/20 DATA(0, -1) - 7/60 DATA(1, -1) + -- DATA(-1, 0) - -- DATA(-1, 1) + 40 20 + + 63 2 2 + - 13/5 y c32 - -- x y c31 + 25 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); + 11 17 2 59 2 2 2 11 +[COEFF(-1, -1) = - -- y - 1/6 x - -- x y + 1/2 x y + --- y + 9/100 x y + -- + 20 50 250 60 + + , COEFF(0, -1) = + + 21 2 13 2 27 2 2 + - 1/20 + 1/6 x - 1/2 x y + --- y + -- x y + 3/20 y - --- x y , + 500 25 100 + + COEFF(1, -1) = + + 2 73 2 27 2 2 + - 1/2 x y - 1/50 x y + 1/6 x - 7/60 - --- y + --- x y + 7/20 y, + 250 100 + + COEFF(2, -1) = + + 2 2 2 2 + 1/2 x y + 1/20 y - 9/100 x y - 4/25 x y - 1/6 x - 1/60 + 7/500 y , + + 851 2 2 2 11 11 69 2 + COEFF(-1, 0) = -x y - ---- y + 3/50 x y - 1/4 x + -- + -- y + --- x y , + 1000 40 10 100 + + COEFF(0, 0) = + + 57 2 2 2 303 2 + - --- x y - 9/50 x y + x y + ---- y + 1/4 x - 3/10 y - 3/40, + 100 1000 + + 447 2 93 2 2 2 + COEFF(1, 0) = 1/4 x + ---- y - --- x y + 9/50 x y + x y - 7/10 y - 7/40 + 1000 100 + + , COEFF(2, 0) = + + 101 2 2 2 81 2 + -x y + ---- y - 1/4 x - 1/40 - 3/50 x y + --- x y - 1/10 y, + 1000 100 + + 203 2 11 11 39 2 2 2 + COEFF(-1, 1) = --- y - -- + 1/2 x - -- y - -- x y + 3/100 x y + 1/2 x y + 250 20 20 50 + + , COEFF(0, 1) = + + 93 2 21 2 2 2 + 3/20 + 3/20 y - 1/2 x y - --- y + -- x y - 1/2 x - 9/100 x y , + 500 25 + + COEFF(1, 1) = + + 33 2 141 2 2 2 + - 1/2 x + -- x y - --- y + 7/20 - 1/2 x y + 7/20 y + 9/100 x y , + 50 250 + + COEFF(2, 1) = + + 2 2 31 2 18 2 + - 3/100 x y + 1/2 x y + 1/20 + 1/2 x - --- y + 1/20 y - -- x y , + 500 25 + + 197 2 43 2 11 2 2 + COEFF(-1, 2) = - 1/12 x - ---- y + --- x y + --- - 9/50 x y , + 1000 100 120 + + 159 2 27 2 2 79 2 + COEFF(0, 2) = - 1/40 - ---- y + -- x y + 1/12 x - --- x y , + 1000 50 100 + + 27 2 2 29 2 409 2 + COEFF(1, 2) = 1/12 x - -- x y + --- x y + ---- y - 7/120, + 50 100 1000 + + 53 2 2 2 2 + COEFF(2, 2) = - ---- y - 1/12 x - 1/120 + 9/50 x y + 7/100 x y ] + 1000 + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); +bytes used=91087448, alloc=2162292, time=7.56 +bytes used=92087608, alloc=2162292, time=7.64 +bytes used=93087776, alloc=2162292, time=7.70 +bytes used=94088036, alloc=2162292, time=7.82 +bytes used=95088216, alloc=2162292, time=7.92 +bytes used=96088436, alloc=2162292, time=8.04 +bytes used=97088696, alloc=2162292, time=8.16 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); +bytes used=98091880, alloc=2162292, time=8.28 + 2 +18/5 c32 x y - 3/20 DATA(2, 1) + 3/10 DATA(2, 0) - 3/20 DATA(2, -1) + + 3 54 42 3 3 + - 12/5 c32 x y + --- y DATA(2, 1) - -- c31 x y + 2 c32 x + 9/5 c32 + 125 25 + + 11 11 + - -- DATA(0, 0) - 9/10 DATA(1, 0) + -- DATA(0, 1) + 9/20 DATA(1, 1) + 10 20 + + 63 2 273 189 2 + - 13/5 x c32 + -- x y c31 + --- x y c31 - --- y c31 - 3 x c32 + 25 125 125 + + 81 2 2 57 2 + + --- x y DATA(2, 0) - 4/25 x y DATA(2, -1) - --- x y DATA(0, 0) + 100 100 + + 93 2 21 2 33 2 + - --- x y DATA(1, 0) + -- x y DATA(0, 1) + -- x y DATA(1, 1) + 100 25 50 + + 17 2 13 2 2 + - -- x y DATA(-1, -1) + -- x y DATA(0, -1) - 1/50 x y DATA(1, -1) + 50 25 + + 53 409 + + 7/250 x y DATA(2, -1) - --- x y DATA(2, 2) + --- x y DATA(1, 2) + 500 500 + + 197 159 3 + - --- x y DATA(-1, 2) - --- x y DATA(0, 2) + 3/25 x y DATA(2, 2) + 500 500 + + 3 3 3 + - 9/25 x y DATA(1, 2) - 3/25 x y DATA(-1, 2) + 9/25 x y DATA(0, 2) + + 3 3 3 + - 1/50 x y DATA(2, 1) - 1/25 x y DATA(2, 0) - 3/50 x y DATA(2, -1) + + 3 437 12 + - 3/25 x y DATA(0, 0) + --- y DATA(0, 2) + --- y DATA(2, -1) + 500 125 + + 771 729 213 + + --- y DATA(0, 0) + --- y DATA(1, 0) - --- y DATA(0, 1) + 500 500 125 + + 162 12 89 + - --- y DATA(1, 1) - --- y DATA(-1, -1) - --- y DATA(0, -1) + 125 125 125 + + 36 243 54 + - --- y DATA(1, -1) + --- y DATA(-1, 0) - --- y DATA(-1, 1) + 125 500 125 + + 243 3 3 + - --- y DATA(2, 0) + 3/25 x y DATA(1, 0) - 3/50 x y DATA(0, 1) + 500 + + 3 3 3 + + 3/50 x y DATA(1, 1) + 3/50 x y DATA(-1, -1) + 9/50 x y DATA(1, -1) + + 3 3 3 + + 1/25 x y DATA(-1, 0) + 1/50 x y DATA(-1, 1) - 9/50 x y DATA(0, -1) + + 29 2 2 79 2 + + --- x y DATA(1, 2) + 7/100 x y DATA(2, 2) - --- x y DATA(0, 2) + 100 100 + + 43 2 18 2 2 + + --- x y DATA(-1, 2) - -- x y DATA(2, 1) + 1/4 x DATA(2, 1) + 100 25 + + 2 2 2 + - 1/2 x DATA(2, 0) + 1/4 x DATA(2, -1) + 1/2 x DATA(0, 0) + + 2 2 2 + + 1/2 x DATA(1, 0) - 1/4 x DATA(0, 1) - 1/4 x DATA(1, 1) + + 2 21 63 + + 1/4 x DATA(-1, -1) - --- y DATA(2, 2) + --- y DATA(1, 2) + 500 500 + + 21 2 2 + + --- y DATA(-1, 2) + 1/4 x DATA(-1, 1) - 1/4 x DATA(0, -1) + 500 + + 2 2 69 2 + - 1/2 x DATA(-1, 0) - 1/4 x DATA(1, -1) + --- x y DATA(-1, 0) + 100 + + 39 2 + - -- x y DATA(-1, 1) + 1/20 x DATA(2, 1) - 1/10 x DATA(2, 0) + 50 + + + 1/20 x DATA(2, -1) - 3/10 x DATA(0, 0) - 7/10 x DATA(1, 0) + + 11 + + 3/20 x DATA(0, 1) + 7/20 x DATA(1, 1) - -- x DATA(-1, -1) + 20 + + 11 + + 3/20 x DATA(0, -1) + 7/20 x DATA(1, -1) + -- x DATA(-1, 0) + 10 + + 11 31 101 + - -- x DATA(-1, 1) - --- x y DATA(2, 1) + --- x y DATA(2, 0) + 20 250 500 + + 59 73 851 + + --- x y DATA(-1, -1) - --- x y DATA(1, -1) - --- x y DATA(-1, 0) + 125 125 500 + + 203 21 303 + + --- x y DATA(-1, 1) + --- x y DATA(0, -1) + --- x y DATA(0, 0) + 125 250 500 + + 447 93 141 + + --- x y DATA(1, 0) - --- x y DATA(0, 1) - --- x y DATA(1, 1) + 500 250 125 + + 78 11 + + -- x y c32 + 3/20 DATA(-1, -1) + -- DATA(0, -1) + 9/20 DATA(1, -1) + 25 20 + + 54 + - 3/10 DATA(-1, 0) + 3/20 DATA(-1, 1) - -- y c32 + 25 + +> coeffs_as_lc_of_data(%, posn_list_2d_size4); +bytes used=99092352, alloc=2227816, time=8.34 + 2 12 3 59 11 17 2 +[COEFF(-1, -1) = 1/4 x - --- y + 3/50 y x + --- x y - -- x + 3/20 - -- y x , + 125 125 20 50 + + 21 13 2 3 89 11 2 + COEFF(0, -1) = --- x y + -- y x - 9/50 y x - --- y + -- + 3/20 x - 1/4 x + 250 25 125 20 + + , COEFF(1, -1) = + + 73 2 36 2 3 + 7/20 x - --- x y - 1/50 y x - --- y - 1/4 x + 9/50 y x + 9/20, + 125 125 + + COEFF(2, -1) = + + 12 2 2 3 + - 3/20 + --- y + 1/4 x - 4/25 y x - 3/50 y x + 7/250 x y + 1/20 x, + 125 + + COEFF(-1, 0) = + + 11 69 2 2 243 3 851 + -- x + --- y x - 1/2 x + --- y + 1/25 y x - 3/10 - --- x y, COEFF(0, 0) + 10 100 500 500 + + 57 2 771 3 11 2 303 + = - --- y x + --- y - 3/25 y x - -- + 1/2 x - 3/10 x + --- x y, + 100 500 10 500 + + COEFF(1, 0) = + + 3 729 2 93 2 447 + 3/25 y x + --- y + 1/2 x - 9/10 - --- y x + --- x y - 7/10 x, + 500 100 500 + + COEFF(2, 0) = + + 243 2 101 81 2 3 + - --- y - 1/2 x + 3/10 + --- x y + --- y x - 1/10 x - 1/25 y x , + 500 500 100 + + COEFF(-1, 1) = + + 11 203 3 54 2 39 2 + - -- x + --- x y + 1/50 y x - --- y + 1/4 x + 3/20 - -- y x , + 20 125 125 50 + + 11 3 213 21 2 2 93 + COEFF(0, 1) = -- - 3/50 y x - --- y + -- y x + 3/20 x - 1/4 x - --- x y, + 20 125 25 250 + + COEFF(1, 1) = + + 141 3 33 2 2 162 + 9/20 + 7/20 x - --- x y + 3/50 y x + -- y x - 1/4 x - --- y, COEFF(2, 1) + 125 50 125 + + 54 2 18 2 31 3 + = - 3/20 + --- y + 1/4 x - -- y x - --- x y - 1/50 y x + 1/20 x, + 125 25 250 + + 3 21 197 43 2 + COEFF(-1, 2) = - 3/25 y x + --- y - --- x y + --- y x , + 500 500 100 + + 3 159 79 2 437 + COEFF(0, 2) = 9/25 y x - --- x y - --- y x + --- y, + 500 100 500 + + 29 2 3 63 409 + COEFF(1, 2) = --- y x - 9/25 y x + --- y + --- x y, + 100 500 500 + + 2 53 3 21 + COEFF(2, 2) = 7/100 y x - --- x y + 3/25 y x - --- y] + 500 500 + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); +bytes used=100092548, alloc=2227816, time=8.41 +bytes used=101092996, alloc=2227816, time=8.49 +bytes used=102093148, alloc=2227816, time=8.61 +bytes used=103093312, alloc=2227816, time=8.69 +bytes used=104093644, alloc=2227816, time=8.84 +bytes used=105093832, alloc=2227816, time=8.92 +bytes used=106093996, alloc=2227816, time=9.05 +> +################################################################################ +> +# +# 2d, cube, order=4, smoothing=0 (size=5) +# +> +# interpolating polynomial +> interp_2d_cube_order4_smooth0 +> := Lagrange_polynomial_interpolant(fn_2d_order4, coeffs_list_2d_order4, +> coords_list_2d, posn_list_2d_size5); +bytes used=107094420, alloc=2227816, time=9.13 +bytes used=108095396, alloc=2227816, time=9.19 +bytes used=109095660, alloc=2227816, time=9.25 +bytes used=110095928, alloc=2227816, time=9.31 +bytes used=111096132, alloc=2227816, time=9.36 +bytes used=112096424, alloc=2227816, time=9.43 +bytes used=113096732, alloc=2227816, time=9.50 +bytes used=114097080, alloc=2227816, time=9.57 +bytes used=115097268, alloc=2227816, time=9.64 +bytes used=116097436, alloc=2227816, time=9.71 +bytes used=117097712, alloc=2227816, time=9.77 +bytes used=118100480, alloc=2227816, time=9.84 +bytes used=119101300, alloc=2227816, time=9.90 +bytes used=120101536, alloc=2227816, time=9.96 +bytes used=121102272, alloc=2227816, time=10.03 +bytes used=122103488, alloc=2227816, time=10.09 +bytes used=123103664, alloc=2227816, time=10.14 +bytes used=124103840, alloc=2227816, time=10.21 +bytes used=125104372, alloc=2227816, time=10.28 +interp_2d_cube_order4_smooth0 := (- 1/24 DATA(0, 2) - 5/4 DATA(0, 0) + + 2 + + 2/3 DATA(0, 1) - 1/24 DATA(0, -2) + 2/3 DATA(0, -1)) y + DATA(0, 0) + ( + + - 1/576 DATA(2, 2) + 1/144 DATA(1, 2) + 1/144 DATA(-1, 2) - 1/96 DATA(0, 2) + + + 1/36 DATA(2, 1) - 5/96 DATA(2, 0) + 1/36 DATA(2, -1) - 5/16 DATA(0, 0) + + + 5/24 DATA(1, 0) + 1/6 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) + + + 1/36 DATA(-2, 1) - 5/96 DATA(-2, 0) + 1/36 DATA(-2, -1) + + - 1/576 DATA(2, -2) + 1/144 DATA(1, -2) - 1/96 DATA(0, -2) + + + 1/144 DATA(-1, -2) - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) + + + 1/6 DATA(0, -1) - 1/9 DATA(1, -1) + 5/24 DATA(-1, 0) - 1/9 DATA(-1, 1)) + + 4 2 + x y + (- 1/288 DATA(2, 2) + 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) + + - 1/48 DATA(0, 2) + 1/36 DATA(2, 1) - 1/36 DATA(2, -1) + 1/6 DATA(0, 1) + + - 1/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/36 DATA(-2, 1) + + - 1/36 DATA(-2, -1) + 1/288 DATA(2, -2) - 1/72 DATA(1, -2) + + + 1/48 DATA(0, -2) - 1/72 DATA(-1, -2) + 1/288 DATA(-2, -2) + + + 1/9 DATA(-1, -1) - 1/6 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) + + 4 + x y + (1/144 DATA(2, 2) - 1/72 DATA(1, 2) + 1/72 DATA(-1, 2) + + - 1/72 DATA(2, 1) + 1/72 DATA(2, -1) - 1/72 DATA(-2, -1) + 1/36 DATA(1, 1) + + - 1/144 DATA(-2, 2) + 1/72 DATA(-2, 1) + 1/144 DATA(-2, -2) + + - 1/144 DATA(2, -2) + 1/72 DATA(1, -2) - 1/72 DATA(-1, -2) + + 3 3 + + 1/36 DATA(-1, -1) - 1/36 DATA(1, -1) - 1/36 DATA(-1, 1)) x y + ( + + - 1/288 DATA(2, 2) + 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/18 DATA(2, 1) + + - 5/48 DATA(2, 0) + 1/18 DATA(2, -1) + 5/24 DATA(1, 0) - 1/9 DATA(1, 1) + + + 1/288 DATA(-2, 2) - 1/18 DATA(-2, 1) + 5/48 DATA(-2, 0) + + - 1/18 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/144 DATA(1, -2) + + - 1/144 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) + + 3 2 + - 1/9 DATA(1, -1) - 5/24 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + ( + + - 1/144 DATA(2, 2) + 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) + 1/18 DATA(2, 1) + + - 1/18 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) - 1/18 DATA(-2, 1) + + + 1/18 DATA(-2, -1) + 1/144 DATA(2, -2) - 1/72 DATA(1, -2) + + + 1/72 DATA(-1, -2) - 1/144 DATA(-2, -2) - 1/9 DATA(-1, -1) + + 3 + + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + (- 1/288 DATA(2, 2) + + + 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) + 1/72 DATA(2, 1) - 1/48 DATA(2, 0) + + + 1/72 DATA(2, -1) + 1/6 DATA(1, 0) - 1/9 DATA(1, 1) + 1/288 DATA(-2, 2) + + - 1/72 DATA(-2, 1) + 1/48 DATA(-2, 0) - 1/72 DATA(-2, -1) + + - 1/288 DATA(2, -2) + 1/36 DATA(1, -2) - 1/36 DATA(-1, -2) + + + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) - 1/9 DATA(1, -1) + + 4 + - 1/6 DATA(-1, 0) + 1/9 DATA(-1, 1)) x y + (- 1/576 DATA(2, 2) + + + 1/36 DATA(1, 2) + 1/36 DATA(-1, 2) - 5/96 DATA(0, 2) + 1/144 DATA(2, 1) + + - 1/96 DATA(2, 0) + 1/144 DATA(2, -1) - 5/16 DATA(0, 0) + 1/6 DATA(1, 0) + + + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) - 1/576 DATA(-2, 2) + 1/144 DATA(-2, 1) + + - 1/96 DATA(-2, 0) + 1/144 DATA(-2, -1) - 1/576 DATA(2, -2) + + + 1/36 DATA(1, -2) - 5/96 DATA(0, -2) + 1/36 DATA(-1, -2) + + - 1/576 DATA(-2, -2) - 1/9 DATA(-1, -1) + 5/24 DATA(0, -1) + + 2 4 + - 1/9 DATA(1, -1) + 1/6 DATA(-1, 0) - 1/9 DATA(-1, 1)) x y + ( + + 1/576 DATA(2, 2) - 1/144 DATA(1, 2) - 1/144 DATA(-1, 2) + 1/96 DATA(0, 2) + + - 1/144 DATA(2, 1) + 1/96 DATA(2, 0) - 1/144 DATA(2, -1) + 1/16 DATA(0, 0) + + - 1/24 DATA(1, 0) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/576 DATA(-2, 2) + + - 1/144 DATA(-2, 1) + 1/96 DATA(-2, 0) - 1/144 DATA(-2, -1) + + + 1/576 DATA(2, -2) - 1/144 DATA(1, -2) + 1/96 DATA(0, -2) + + - 1/144 DATA(-1, -2) + 1/576 DATA(-2, -2) + 1/36 DATA(-1, -1) + + - 1/24 DATA(0, -1) + 1/36 DATA(1, -1) - 1/24 DATA(-1, 0) + + 4 4 + + 1/36 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/144 DATA(1, 2) + + + 1/144 DATA(-1, 2) - 1/72 DATA(2, 1) + 1/48 DATA(2, 0) - 1/72 DATA(2, -1) + + + 1/24 DATA(-1, 0) - 1/24 DATA(1, 0) + 1/36 DATA(1, 1) - 1/288 DATA(-2, 2) + + + 1/72 DATA(-2, 1) - 1/48 DATA(-2, 0) + 1/72 DATA(-2, -1) + + + 1/288 DATA(2, -2) - 1/144 DATA(1, -2) + 1/144 DATA(-1, -2) + + - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/36 DATA(1, -1) + + 3 4 + - 1/36 DATA(-1, 1)) x y + (1/144 DATA(2, 2) - 1/18 DATA(1, 2) + + + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) + + - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) - 1/18 DATA(-2, -1) + + - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) - 1/18 DATA(-1, -2) + + + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) - 4/9 DATA(1, -1) + + - 4/9 DATA(-1, 1)) x y + (1/288 DATA(2, 2) - 1/36 DATA(1, 2) + + + 1/36 DATA(-1, 2) - 1/18 DATA(2, 1) + 5/48 DATA(2, 0) - 1/18 DATA(2, -1) + + - 5/6 DATA(1, 0) + 4/9 DATA(1, 1) - 1/288 DATA(-2, 2) + 1/18 DATA(-2, 1) + + - 5/48 DATA(-2, 0) + 1/18 DATA(-2, -1) + 1/288 DATA(2, -2) + + - 1/36 DATA(1, -2) + 1/36 DATA(-1, -2) - 1/288 DATA(-2, -2) + + - 4/9 DATA(-1, -1) + 4/9 DATA(1, -1) + 5/6 DATA(-1, 0) - 4/9 DATA(-1, 1)) + + 2 / + x y + |1/576 DATA(2, 2) - 1/36 DATA(1, 2) - 1/36 DATA(-1, 2) + \ + + + 5/96 DATA(0, 2) - 1/36 DATA(2, 1) + 5/96 DATA(2, 0) - 1/36 DATA(2, -1) + + 25 + + -- DATA(0, 0) - 5/6 DATA(1, 0) - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) + 16 + + + 1/576 DATA(-2, 2) - 1/36 DATA(-2, 1) + 5/96 DATA(-2, 0) + + - 1/36 DATA(-2, -1) + 1/576 DATA(2, -2) - 1/36 DATA(1, -2) + + + 5/96 DATA(0, -2) - 1/36 DATA(-1, -2) + 1/576 DATA(-2, -2) + + + 4/9 DATA(-1, -1) - 5/6 DATA(0, -1) + 4/9 DATA(1, -1) - 5/6 DATA(-1, 0) + + \ 2 2 + + 4/9 DATA(-1, 1)| x y + (1/288 DATA(2, 2) - 1/18 DATA(1, 2) + / + + - 1/18 DATA(-1, 2) + 5/48 DATA(0, 2) - 1/36 DATA(2, 1) + 1/36 DATA(2, -1) + + - 5/6 DATA(0, 1) + 4/9 DATA(1, 1) + 1/288 DATA(-2, 2) - 1/36 DATA(-2, 1) + + + 1/36 DATA(-2, -1) - 1/288 DATA(2, -2) + 1/18 DATA(1, -2) + + - 5/48 DATA(0, -2) + 1/18 DATA(-1, -2) - 1/288 DATA(-2, -2) + + - 4/9 DATA(-1, -1) + 5/6 DATA(0, -1) - 4/9 DATA(1, -1) + 4/9 DATA(-1, 1)) + + 2 + x y + (1/288 DATA(2, 2) - 1/72 DATA(1, 2) - 1/72 DATA(-1, 2) + + + 1/48 DATA(0, 2) - 1/144 DATA(2, 1) + 1/144 DATA(2, -1) + + - 1/36 DATA(1, -1) - 1/24 DATA(0, 1) + 1/36 DATA(1, 1) + 1/288 DATA(-2, 2) + + - 1/144 DATA(-2, 1) + 1/144 DATA(-2, -1) - 1/288 DATA(2, -2) + + + 1/72 DATA(1, -2) - 1/48 DATA(0, -2) + 1/72 DATA(-1, -2) + + - 1/288 DATA(-2, -2) - 1/36 DATA(-1, -1) + 1/24 DATA(0, -1) + + 4 3 + + 1/36 DATA(-1, 1)) x y + (1/24 DATA(0, 2) + 1/4 DATA(0, 0) + + 4 + - 1/6 DATA(0, 1) + 1/24 DATA(0, -2) - 1/6 DATA(0, -1)) y + ( + + 1/24 DATA(2, 0) + 1/4 DATA(0, 0) - 1/6 DATA(1, 0) + 1/24 DATA(-2, 0) + + 4 + - 1/6 DATA(-1, 0)) x + + + (- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0)) x + + + (- 1/24 DATA(2, 0) - 5/4 DATA(0, 0) + 2/3 DATA(1, 0) - 1/24 DATA(-2, 0) + + 2 + + 2/3 DATA(-1, 0)) x + + + 3 + (1/12 DATA(0, 2) - 1/6 DATA(0, 1) - 1/12 DATA(0, -2) + 1/6 DATA(0, -1)) y + + + + + (- 1/12 DATA(0, 2) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) - 2/3 DATA(0, -1)) y + + + (- 1/144 DATA(2, 2) + 1/18 DATA(1, 2) - 1/18 DATA(-1, 2) + + + 1/72 DATA(2, 1) - 1/72 DATA(2, -1) - 1/9 DATA(1, 1) + 1/144 DATA(-2, 2) + + - 1/72 DATA(-2, 1) + 1/72 DATA(-2, -1) + 1/144 DATA(2, -2) + + - 1/18 DATA(1, -2) + 1/18 DATA(-1, -2) - 1/144 DATA(-2, -2) + + 3 + - 1/9 DATA(-1, -1) + 1/9 DATA(1, -1) + 1/9 DATA(-1, 1)) x y + ( + + - 1/288 DATA(2, 2) + 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 5/48 DATA(0, 2) + + + 1/144 DATA(2, 1) - 1/144 DATA(2, -1) + 5/24 DATA(0, 1) - 1/9 DATA(1, 1) + + - 1/288 DATA(-2, 2) + 1/144 DATA(-2, 1) - 1/144 DATA(-2, -1) + + + 1/288 DATA(2, -2) - 1/18 DATA(1, -2) + 5/48 DATA(0, -2) + + - 1/18 DATA(-1, -2) + 1/288 DATA(-2, -2) + 1/9 DATA(-1, -1) + + 2 3 + - 5/24 DATA(0, -1) + 1/9 DATA(1, -1) - 1/9 DATA(-1, 1)) x y + + + 3 + (1/12 DATA(2, 0) - 1/6 DATA(1, 0) - 1/12 DATA(-2, 0) + 1/6 DATA(-1, 0)) x + +> +# I +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=126126424, alloc=2227816, time=10.34 +bytes used=127129732, alloc=2227816, time=10.40 + 4 2 3 3 2 +[COEFF(-2, -2) = 1/288 x y + 1/288 x y - 1/144 x y - 1/288 y x + + 2 4 4 3 4 2 2 3 + - 1/576 x y - 1/288 x y + 1/288 x y + 1/576 x y - 1/144 y x + + 2 3 2 3 3 3 4 + - 1/288 x y + 1/288 x y + 1/144 x y + 1/144 x y - 1/288 x y + + 4 2 4 4 2 2 4 3 + - 1/576 x y + 1/576 x y , COEFF(-1, -2) = - 1/36 x y + 1/72 x y + + 4 2 4 3 2 2 4 + - 1/72 x y + 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y + + 4 2 4 4 3 3 4 2 3 + + 1/144 x y - 1/144 x y + 1/18 x y + 1/144 x y - 1/18 x y + + 3 3 2 3 3 + - 1/18 x y - 1/72 x y + 1/36 x y + 1/72 y x , COEFF(0, -2) = - 1/12 y + + 4 4 4 2 2 3 2 + + 1/24 y + 1/48 x y - 1/96 x y + 5/48 x y + 1/12 y - 5/48 y x + + 2 4 4 3 4 4 2 2 2 + - 5/96 x y - 1/48 x y + 1/96 x y + 5/96 x y - 1/24 y , + + 4 3 3 2 2 4 + COEFF(1, -2) = 1/18 x y + 1/72 x y + 1/144 x y + 1/18 y x + 1/36 x y + + 4 2 3 4 3 3 4 4 + + 1/144 x y - 1/72 y x - 1/72 x y + 1/72 x y - 1/144 x y + + 3 2 3 2 2 4 3 4 + - 1/18 x y - 1/18 x y - 1/36 x y + 1/36 x y - 1/144 x y + + 2 2 2 4 2 2 3 + - 1/36 x y , COEFF(2, -2) = - 1/576 x y - 1/288 y x + 1/288 x y + + 4 4 3 3 4 4 2 + + 1/576 x y + 1/144 y x + 1/288 x y - 1/144 x y - 1/576 x y + + 4 3 2 3 2 3 4 + - 1/288 x y + 1/288 x y - 1/288 x y + 1/144 x y - 1/288 x y + + 3 3 2 2 4 4 + - 1/144 x y + 1/576 x y + 1/288 x y, COEFF(-2, -1) = - 1/36 x y + + 2 2 3 2 2 3 3 3 + + 1/36 y x - 1/144 x y - 1/36 x y + 1/18 y x - 1/72 x y + + 2 4 3 4 2 4 3 + + 1/144 x y + 1/72 x y - 1/18 x y + 1/36 x y + 1/144 x y + + 2 3 2 4 4 4 3 4 + + 1/18 x y - 1/18 x y - 1/144 x y - 1/72 x y + 1/72 x y , + + 2 4 3 3 3 4 + COEFF(-1, -1) = - 1/9 x y + 4/9 x y - 1/9 x y + 1/36 x y + 1/9 x y + + 2 2 4 2 3 2 2 2 4 4 + + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y - 4/9 y x + 1/36 x y + + 4 3 4 3 4 3 2 3 + + 1/9 x y - 1/36 x y - 1/9 y x - 1/36 x y + 1/9 x y , COEFF(0, -1) + + 4 4 4 2 4 3 2 2 + = - 1/24 x y + 1/6 x y - 1/6 y + 1/6 y + 5/6 y x - 2/3 y + 2/3 y + + 2 3 2 4 4 4 3 2 2 + - 5/24 x y + 5/24 x y - 1/6 x y + 1/24 x y - 5/6 x y , + + 3 3 2 4 2 2 4 2 4 + COEFF(1, -1) = - 1/36 x y - 1/9 x y + 4/9 x y - 1/9 x y + 1/9 x y + + 2 3 3 2 2 3 4 3 + - 4/9 x y + 1/9 x y - 1/9 x y - 4/9 y x + 1/9 x y - 1/36 x y + + 2 4 4 3 4 4 3 + + 4/9 x y + 1/36 x y + 1/36 x y - 1/9 x y + 1/9 y x , COEFF(2, -1) + + 4 4 4 4 2 4 2 2 + = 1/18 x y - 1/144 x y - 1/36 x y + 1/36 x y + 1/72 x y - 1/36 x y + + 3 3 3 4 3 3 4 2 4 + + 1/72 x y - 1/18 y x + 1/144 x y - 1/72 x y + 1/144 x y + + 2 2 3 2 3 3 2 + - 1/18 x y + 1/36 y x - 1/72 x y - 1/144 x y + 1/18 x y , + + 4 2 3 3 4 2 2 4 + COEFF(-2, 0) = - 5/96 x y - 1/12 x - 1/48 x y + 5/96 x y + 1/24 x + + 4 2 4 4 4 2 2 3 2 + + 1/48 x y - 1/96 x y + 1/96 x y - 5/48 x y - 1/24 x + 5/48 x y + + 4 4 4 2 4 2 + + 1/12 x, COEFF(-1, 0) = - 1/24 x y - 1/6 x y + 5/6 x y + 5/24 x y + + 3 4 3 2 2 3 4 2 2 + + 1/24 x y - 5/24 x y + 2/3 x + 1/6 x - 1/6 x - 2/3 x - 5/6 x y + + 2 4 4 2 4 2 4 25 2 2 + + 1/6 x y , COEFF(0, 0) = - 5/16 x y + 1/4 x - 5/16 x y + -- x y + 16 + + 4 4 4 2 2 2 2 + + 1/16 x y + 1/4 y + 1 - 5/4 y - 5/4 x , COEFF(1, 0) = - 5/6 x y + + 2 4 2 4 4 4 4 3 4 + + 1/6 x y + 2/3 x - 1/24 x y + 1/6 x y - 1/6 x - 1/24 x y + 2/3 x + + 3 2 2 3 4 2 4 + + 5/24 x y - 5/6 x y - 1/6 x + 5/24 x y , COEFF(2, 0) = - 1/48 x y + + 4 2 4 4 2 4 4 2 + + 1/24 x + 5/48 x y - 1/12 x + 1/96 x y - 1/96 x y - 5/96 x y + + 3 2 3 4 3 2 2 2 + + 1/12 x - 1/24 x + 1/48 x y - 5/48 x y + 5/96 x y , COEFF(-2, 1) + + 3 4 2 3 2 3 2 + = - 1/72 x y + 1/36 x y + 1/144 x y - 1/36 y x - 1/18 x y + + 2 4 4 3 3 3 3 4 + + 1/18 x y + 1/144 x y - 1/144 x y + 1/72 x y + 1/72 x y + + 2 3 2 2 4 4 4 2 + + 1/18 x y - 1/18 y x - 1/36 x y - 1/144 x y + 1/36 x y + + 4 3 3 3 3 4 2 + - 1/72 x y , COEFF(-1, 1) = 1/9 x y - 1/36 x y + 1/9 y x - 1/9 x y + + 3 4 4 4 3 4 4 2 4 2 + - 1/36 x y - 1/9 x y + 1/36 x y + 1/36 x y - 1/9 x y - 4/9 x y + + 2 2 2 2 3 3 2 4 + + 4/9 y x + 4/9 x y - 1/9 x y + 1/9 x y - 4/9 x y + 1/9 x y , + + 4 2 2 3 2 4 4 4 + COEFF(0, 1) = 1/6 x y + 5/24 x y + 2/3 y + 2/3 y - 1/24 x y - 1/6 y + + 4 4 3 2 2 2 2 4 3 + + 1/6 x y - 1/24 x y - 5/6 x y - 5/6 y x + 5/24 x y - 1/6 y , + + 2 4 3 3 4 3 + COEFF(1, 1) = 4/9 x y + 1/36 x y - 1/9 x y - 1/9 x y - 1/9 y x + + 3 2 3 3 2 2 2 4 4 4 + - 1/9 x y + 1/36 x y + 4/9 x y - 1/9 x y + 1/36 x y + 4/9 x y + + 2 3 4 2 4 2 3 4 + - 1/9 x y - 1/9 x y - 1/9 x y + 4/9 y x + 1/36 x y , COEFF(2, 1) = + + 4 2 3 4 3 2 2 3 + 1/36 x y - 1/18 x y + 1/18 y x + 1/36 x y + 1/18 x y + 1/144 x y + + 2 4 3 2 4 4 2 4 + - 1/18 x y - 1/144 x y - 1/36 y x - 1/144 x y + 1/144 x y + + 3 4 3 2 2 3 3 4 + - 1/72 x y + 1/72 x y - 1/36 x y - 1/72 x y + 1/72 x y , + + 4 2 4 4 2 4 + COEFF(-2, 2) = - 1/288 x y + 1/288 y x + 1/576 x y - 1/576 x y + + 3 3 4 4 3 2 2 + + 1/144 x y - 1/288 x y - 1/144 x y + 1/288 x y + 1/576 x y + + 2 3 2 4 2 4 3 3 + - 1/288 x y - 1/288 x y - 1/576 x y + 1/288 x y - 1/144 x y + + 3 2 3 4 3 4 2 + + 1/288 x y + 1/144 y x , COEFF(-1, 2) = - 1/72 x y + 1/144 x y + + 4 4 4 3 3 3 2 4 + - 1/144 x y + 1/72 x y - 1/72 y x + 1/72 x y + 1/36 x y + + 2 2 2 3 2 3 2 2 + - 1/36 x y + 1/18 x y + 1/18 x y - 1/18 y x - 1/144 x y + 1/36 x y + + 3 4 3 4 4 2 + - 1/18 x y - 1/36 x y + 1/144 x y , COEFF(0, 2) = - 1/96 x y + + 2 4 3 2 4 4 2 + - 1/24 y + 1/48 x y - 5/96 x y + 1/24 y + 5/48 y x - 1/12 y + + 4 4 2 2 3 4 2 3 + + 1/96 x y + 5/96 x y + 1/12 y - 1/48 x y - 5/48 x y , COEFF(1, 2) + + 4 3 4 4 2 3 4 + = - 1/72 x y - 1/144 x y - 1/36 x y - 1/144 x y - 1/18 x y + + 3 2 3 2 4 3 3 + + 1/18 x y - 1/18 y x + 1/144 x y + 1/36 x y - 1/72 x y + + 2 4 2 3 4 2 2 2 4 + + 1/36 x y + 1/18 x y + 1/144 x y - 1/36 x y + 1/72 x y + + 3 4 3 4 2 4 4 + + 1/72 y x , COEFF(2, 2) = 1/288 x y - 1/576 x y + 1/576 x y + + 4 2 3 4 3 + - 1/288 x y + 1/288 x y + 1/288 x y + 1/144 x y - 1/144 x y + + 2 3 2 4 3 3 2 4 + + 1/288 y x - 1/288 x y - 1/288 x y + 1/144 x y - 1/576 x y + + 2 3 2 2 3 + - 1/288 x y + 1/576 x y - 1/144 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); +bytes used=128130292, alloc=2227816, time=10.47 +bytes used=129130448, alloc=2227816, time=10.54 +bytes used=130130628, alloc=2227816, time=10.63 +bytes used=131157976, alloc=2227816, time=10.72 +bytes used=132170256, alloc=2227816, time=10.79 +bytes used=133182936, alloc=2227816, time=10.85 +bytes used=134184444, alloc=2227816, time=10.93 +bytes used=135184740, alloc=2227816, time=11.04 +bytes used=136185208, alloc=2227816, time=11.13 +bytes used=137185504, alloc=2227816, time=11.19 +bytes used=138185676, alloc=2227816, time=11.39 +bytes used=139186008, alloc=2227816, time=11.46 +bytes used=140186252, alloc=2227816, time=11.53 +bytes used=141186616, alloc=2227816, time=11.59 +bytes used=142186928, alloc=2227816, time=11.65 +bytes used=143187140, alloc=2227816, time=11.71 +bytes used=144187292, alloc=2227816, time=11.79 +bytes used=145187476, alloc=2424388, time=11.88 +bytes used=146187724, alloc=2424388, time=11.96 +bytes used=147188072, alloc=2424388, time=12.05 +bytes used=148188276, alloc=2424388, time=12.14 +bytes used=149188548, alloc=2424388, time=12.24 +bytes used=150189040, alloc=2424388, time=12.35 +bytes used=151189584, alloc=2424388, time=12.44 +bytes used=152189776, alloc=2424388, time=12.71 +bytes used=153190128, alloc=2424388, time=12.86 +bytes used=154190356, alloc=2424388, time=12.92 +bytes used=155198184, alloc=2424388, time=13.02 +bytes used=156199352, alloc=2424388, time=13.15 +bytes used=157206092, alloc=2424388, time=13.34 +bytes used=158206320, alloc=2424388, time=13.51 +bytes used=159206528, alloc=2424388, time=13.63 +bytes used=160206828, alloc=2424388, time=13.70 +bytes used=161207036, alloc=2424388, time=13.81 +bytes used=162207248, alloc=2424388, time=13.91 +bytes used=163207460, alloc=2424388, time=14.15 +bytes used=164207736, alloc=2424388, time=14.23 +bytes used=165207896, alloc=2424388, time=14.31 +bytes used=166208088, alloc=2424388, time=14.42 +bytes used=167208332, alloc=2424388, time=14.63 +bytes used=168208740, alloc=2424388, time=14.73 +bytes used=169208984, alloc=2424388, time=14.80 +bytes used=170209144, alloc=2424388, time=14.91 +bytes used=171209480, alloc=2424388, time=15.13 +bytes used=172209780, alloc=2424388, time=15.24 +> +# d/dx +> simplify( diff(interp_2d_cube_order4_smooth0,x) ); +bytes used=173210092, alloc=2424388, time=15.39 +bytes used=174210336, alloc=2424388, time=15.44 +bytes used=175210520, alloc=2424388, time=15.51 +bytes used=176210708, alloc=2424388, time=15.57 +bytes used=177210968, alloc=2489912, time=15.65 +bytes used=178211200, alloc=2620960, time=15.71 +- 1/12 DATA(2, 0) + 2/3 DATA(1, 0) + 1/12 DATA(-2, 0) - 2/3 DATA(-1, 0) + + 3 3 2 + - 1/18 y DATA(-1, 2) - 1/72 y DATA(2, -1) + 8/9 x y DATA(-1, -1) + + 2 2 2 2 2 2 + + 5/8 x y DATA(1, 0) - 1/3 x y DATA(1, 1) + 1/96 x y DATA(-2, 2) + + 3 3 3 + - 1/9 y DATA(1, 1) + 1/144 y DATA(-2, 2) - 1/72 y DATA(-2, 1) + + 3 3 + + 1/72 y DATA(2, 1) - 2/3 x DATA(-1, 0) - 1/12 x DATA(2, 0) + + - 5/2 x DATA(0, 0) + 4/3 x DATA(1, 0) - 1/12 x DATA(-2, 0) + + 3 3 + + 4/3 x DATA(-1, 0) - 1/144 y DATA(2, 2) + 1/18 y DATA(1, 2) + + 3 3 3 + + 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 1/18 y DATA(1, -2) + + 2 2 2 2 + - 1/96 x y DATA(2, -2) + 1/48 x y DATA(1, -2) + + 2 2 2 2 + - 1/48 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, -1) - 5/8 x y DATA(-1, 0) + + 2 2 2 2 + + 1/3 x y DATA(-1, 1) + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) + + 2 2 2 2 2 + + 1/6 y x DATA(2, 1) + 5/16 x y DATA(-2, 0) - 1/6 x y DATA(-2, -1) + + 2 2 2 + - 1/24 y x DATA(1, -2) + 1/24 y x DATA(-1, -2) - 1/48 y x DATA(-2, -2) + + 2 2 2 + - 1/48 y x DATA(2, 2) - 1/3 y x DATA(1, 1) + 1/48 y x DATA(-2, 2) + + 2 2 2 + - 1/6 y x DATA(-2, 1) + 1/6 y x DATA(-2, -1) + 1/48 y x DATA(2, -2) + + 4 4 4 + - 1/9 y DATA(1, -1) - 1/288 y DATA(2, 2) + 1/36 y DATA(1, 2) + + 4 4 4 + - 1/36 y DATA(-1, 2) + 1/72 y DATA(2, 1) - 1/288 x y DATA(-2, 2) + + 4 4 4 + - 2/9 x y DATA(-1, -1) + 5/12 x y DATA(0, -1) - 2/9 x y DATA(1, -1) + + 4 4 4 + + 1/3 x y DATA(-1, 0) - 2/9 x y DATA(-1, 1) + 1/72 x y DATA(-2, -1) + + 4 4 4 + - 1/288 x y DATA(2, -2) + 1/18 x y DATA(1, -2) - 1/288 x y DATA(-2, -2) + + 2 2 2 + - 1/3 y x DATA(-1, -1) + 1/3 y x DATA(1, -1) + 1/3 y x DATA(-1, 1) + + 2 4 4 + - 1/6 y x DATA(2, -1) + 1/18 x y DATA(1, 2) + 1/72 x y DATA(2, -1) + + 4 4 4 + - 5/8 x y DATA(0, 0) + 1/3 x y DATA(1, 0) + 5/12 x y DATA(0, 1) + + 4 3 4 4 + - 1/288 x y DATA(2, 2) + 1/144 x y DATA(-2, -2) - 5/48 x y DATA(0, -2) + + 4 4 4 + + 1/18 x y DATA(-1, -2) - 2/9 x y DATA(1, 1) + 1/72 x y DATA(-2, 1) + + 4 4 4 + - 1/48 x y DATA(-2, 0) - 1/6 y DATA(-1, 0) + 1/18 x y DATA(-1, 2) + + 4 4 4 + - 5/48 x y DATA(0, 2) + 1/72 x y DATA(2, 1) - 1/48 x y DATA(2, 0) + + 4 3 4 3 4 + + 1/9 y DATA(-1, 1) - 1/36 x y DATA(1, -2) - 1/36 x y DATA(-1, -2) + + 3 4 3 4 3 4 + + 1/9 x y DATA(1, 1) - 1/36 x y DATA(-2, 1) - 1/36 x y DATA(-2, -1) + + 3 4 3 4 3 4 + + 1/9 x y DATA(-1, -1) - 1/6 x y DATA(0, -1) + 1/9 x y DATA(1, -1) + + 3 4 3 4 3 4 + - 1/6 x y DATA(-1, 0) + 1/24 x y DATA(0, -2) + 1/24 x y DATA(0, 2) + + 3 4 3 4 3 4 + - 1/36 x y DATA(2, 1) + 1/24 x y DATA(2, 0) - 1/36 x y DATA(2, -1) + + 3 4 3 4 3 4 + + 1/4 x y DATA(0, 0) - 1/6 x y DATA(1, 0) + 1/9 x y DATA(-1, 1) + + 3 4 2 4 + + 1/144 x y DATA(2, -2) + 1/24 x y DATA(-2, -1) + + 2 4 3 4 3 4 + + 1/96 x y DATA(2, 2) - 1/6 x y DATA(0, 1) + 1/144 x y DATA(2, 2) + + 2 4 2 4 2 4 + - 1/48 x y DATA(1, 2) + 1/48 x y DATA(-1, 2) - 1/24 x y DATA(2, 1) + + 2 4 3 4 3 4 + + 1/16 x y DATA(2, 0) + 1/24 x y DATA(-2, 0) + 1/144 x y DATA(-2, 2) + + 3 4 3 4 2 4 + - 1/36 x y DATA(1, 2) - 1/36 x y DATA(-1, 2) + 1/96 x y DATA(2, -2) + + 2 4 2 4 2 4 + - 1/24 x y DATA(2, -1) + 1/8 x y DATA(-1, 0) - 1/8 x y DATA(1, 0) + + 2 4 2 4 2 4 + + 1/12 x y DATA(1, 1) - 1/96 x y DATA(-2, 2) + 1/24 x y DATA(-2, 1) + + 2 4 2 4 + - 1/16 x y DATA(-2, 0) + 1/48 x y DATA(-1, -2) + + 2 4 2 4 + - 1/96 x y DATA(-2, -2) - 1/12 x y DATA(-1, -1) + + 2 4 2 4 2 + + 1/12 x y DATA(1, -1) - 1/12 x y DATA(-1, 1) + 8/9 x y DATA(1, -1) + + 2 2 2 + - 5/3 x y DATA(-1, 0) + 8/9 x y DATA(-1, 1) - 1/18 x y DATA(-2, -1) + + 2 2 2 + + 1/288 x y DATA(2, -2) - 1/18 x y DATA(1, -2) + 5/48 x y DATA(0, -2) + + 2 + - 1/18 x y DATA(-1, -2) - 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) + + + 4/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) + 1/144 y DATA(2, 2) + + 4 4 + - 1/18 y DATA(1, 2) - 1/48 y DATA(2, 0) + 1/72 y DATA(2, -1) + + 4 4 4 + + 1/6 y DATA(1, 0) - 1/9 y DATA(1, 1) + 1/288 y DATA(-2, 2) + + 4 4 4 + - 1/72 y DATA(-2, 1) + 1/48 y DATA(-2, 0) - 1/72 y DATA(-2, -1) + + 4 4 4 + - 1/288 y DATA(2, -2) + 1/36 y DATA(1, -2) - 1/36 y DATA(-1, -2) + + 4 4 2 + + 1/288 y DATA(-2, -2) + 1/9 y DATA(-1, -1) - 5/3 x y DATA(0, -1) + + 2 + - 5/6 y DATA(1, 0) + 1/18 y DATA(-2, 1) - 1/18 y DATA(-2, -1) + + - 1/144 y DATA(2, -2) + 1/18 y DATA(1, -2) - 1/18 y DATA(-1, -2) + + + 1/144 y DATA(-2, -2) + 4/9 y DATA(-1, -1) - 4/9 y DATA(1, -1) + + 2 2 + - 4/9 y DATA(-1, 1) + 1/288 y DATA(2, 2) - 1/36 y DATA(1, 2) + + 2 2 + + 1/18 y DATA(-1, 2) + 5/6 y DATA(-1, 0) + 1/36 y DATA(-1, 2) + + 2 2 2 + - 1/18 y DATA(2, 1) + 5/48 y DATA(2, 0) - 1/18 y DATA(2, -1) + + 2 2 2 + - 4/9 y DATA(-1, 1) + 4/9 y DATA(1, 1) - 1/288 y DATA(-2, 2) + + 2 2 2 + + 1/18 y DATA(-2, 1) - 5/48 y DATA(-2, 0) + 1/18 y DATA(-2, -1) + + 2 2 2 + + 1/288 y DATA(2, -2) - 1/36 y DATA(1, -2) + 1/36 y DATA(-1, -2) + + 2 2 2 + - 1/288 y DATA(-2, -2) - 4/9 y DATA(-1, -1) + 4/9 y DATA(1, -1) + + 2 4 2 2 + - 1/48 x y DATA(1, -2) - 1/18 x y DATA(1, 2) - 1/18 x y DATA(-1, 2) + + 2 2 2 + + 5/48 x y DATA(0, 2) - 1/18 x y DATA(2, 1) + 5/48 x y DATA(2, 0) + + 2 + + 1/288 x y DATA(-2, -2) - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + + + 5/24 x y DATA(0, 2) - 1/18 x y DATA(2, 1) + 1/18 x y DATA(2, -1) + + - 5/3 x y DATA(0, 1) + 8/9 x y DATA(1, 1) + 1/144 x y DATA(-2, 2) + + - 1/18 x y DATA(-2, 1) + 1/18 x y DATA(-2, -1) - 1/144 x y DATA(2, -2) + + 2 2 2 + + 8/9 x y DATA(1, 1) - 1/18 x y DATA(-2, 1) + 5/48 x y DATA(-2, 0) + + 2 2 2 + + 1/288 x y DATA(-2, 2) - 1/18 x y DATA(2, -1) + 25/8 x y DATA(0, 0) + + 2 2 2 + - 5/3 x y DATA(1, 0) - 5/3 x y DATA(0, 1) + 1/288 x y DATA(2, 2) + + 3 3 3 3 + + 8/9 x y DATA(-1, 1) + 1/72 x y DATA(2, 2) - 1/18 x y DATA(1, 2) + + 3 3 3 3 3 3 + - 1/18 x y DATA(-1, 2) + 1/12 x y DATA(0, 2) - 1/36 x y DATA(2, 1) + + 3 3 3 3 + + 1/36 x y DATA(2, -1) - 1/9 x y DATA(1, -1) + 1/144 x y DATA(2, 2) + + 3 3 + - 1/72 x y DATA(2, -2) + 1/9 x y DATA(1, -2) - 5/24 x y DATA(0, -2) + + + 1/9 x y DATA(-1, -2) - 1/144 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) + + 3 3 + + 5/3 x y DATA(0, -1) - 8/9 x y DATA(1, -1) + 1/18 x y DATA(-1, -2) + + 3 3 3 3 3 3 + - 1/72 x y DATA(-2, -2) - 1/9 x y DATA(-1, -1) + 1/6 x y DATA(0, -1) + + 3 3 3 3 3 + + 1/9 x y DATA(-1, 1) - 1/144 x y DATA(2, 2) - 1/6 x y DATA(0, 1) + + 3 3 3 3 3 3 + + 1/9 x y DATA(1, 1) + 1/72 x y DATA(-2, 2) - 1/36 x y DATA(-2, 1) + + 3 3 3 3 + + 1/36 x y DATA(-2, -1) + 1/18 y DATA(-1, -2) - 1/144 y DATA(-2, -2) + + 3 3 3 + - 1/9 y DATA(-1, -1) + 1/9 y DATA(1, -1) + 1/9 y DATA(-1, 1) + + 3 3 3 + + 1/6 x DATA(2, 0) + x DATA(0, 0) - 2/3 x DATA(1, 0) + + 3 3 3 + + 1/6 x DATA(-2, 0) - 1/72 x y DATA(2, -1) + 5/12 x y DATA(0, 1) + + 3 3 3 + - 2/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) + 1/72 x y DATA(-2, 1) + + 3 3 3 3 3 + + 1/18 x y DATA(1, -2) - 1/12 x y DATA(0, -2) - 2/9 x y DATA(-1, 1) + + 3 3 3 + + 1/9 x y DATA(1, 2) + 1/9 x y DATA(-1, 2) - 5/24 x y DATA(0, 2) + + 3 3 2 3 + + 1/72 x y DATA(2, 1) - 4/9 x y DATA(1, -1) - 1/72 x y DATA(-2, -1) + + 3 3 3 + + 1/144 x y DATA(2, -2) - 1/9 x y DATA(1, -2) + 5/24 x y DATA(0, -2) + + 3 3 3 + - 1/9 x y DATA(-1, -2) + 1/144 x y DATA(-2, -2) + 2/9 x y DATA(-1, -1) + + 3 3 3 2 + - 5/12 x y DATA(0, -1) + 2/9 x y DATA(1, -1) + 5/6 x y DATA(1, 0) + + 3 2 3 2 3 + + 2/3 x y DATA(0, 1) - 1/144 x y DATA(2, 2) - 1/72 y x DATA(2, 2) + + 3 2 3 2 3 2 + + 5/6 x y DATA(-1, 0) - 4/9 x y DATA(-1, 1) + 1/9 x y DATA(-2, -1) + + 3 2 3 2 + - 1/144 x y DATA(2, -2) + 1/36 x y DATA(1, -2) + + 3 2 3 2 + - 1/24 x y DATA(0, -2) + 1/36 x y DATA(-1, -2) + + 3 2 3 2 + - 1/144 x y DATA(-2, -2) - 4/9 x y DATA(-1, -1) + + 3 2 2 3 2 + + 2/3 x y DATA(0, -1) + 1/4 x DATA(2, 0) - 1/24 x y DATA(0, 2) + + 3 2 3 2 3 2 + + 1/9 x y DATA(2, 1) - 5/24 x y DATA(2, 0) + 1/9 x y DATA(2, -1) + + 3 2 2 3 + - 5/4 x y DATA(0, 0) - 1/2 x DATA(1, 0) - 1/12 y x DATA(0, 2) + + 3 3 3 + + 1/9 y x DATA(2, 1) - 1/9 y x DATA(2, -1) + 2/3 y x DATA(0, 1) + + 3 2 3 2 3 2 + - 4/9 x y DATA(1, 1) + 1/9 x y DATA(-2, 1) - 5/24 x y DATA(-2, 0) + + 3 2 3 2 3 2 + - 1/144 x y DATA(-2, 2) + 1/36 x y DATA(1, 2) + 1/36 x y DATA(-1, 2) + + 2 3 3 + - 1/4 x DATA(-2, 0) - 2/3 y x DATA(0, -1) - 4/9 y x DATA(-1, 1) + + 3 3 3 + - 4/9 y x DATA(1, 1) - 1/72 y x DATA(-2, 2) + 1/9 y x DATA(-2, 1) + + 3 3 3 + - 1/9 y x DATA(-2, -1) + 1/72 y x DATA(2, -2) + 1/18 y x DATA(1, 2) + + 3 3 3 + + 1/18 y x DATA(-1, 2) + 4/9 y x DATA(1, -1) - 1/18 y x DATA(1, -2) + + 3 3 3 + - 1/18 y x DATA(-1, -2) + 1/72 y x DATA(-2, -2) + 4/9 y x DATA(-1, -1) + + 3 2 3 2 3 + + 1/12 y x DATA(0, -2) + 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, -2) + + 2 3 2 3 2 3 + - 1/48 x y DATA(2, -2) + 1/24 x y DATA(1, -2) + 1/24 x y DATA(2, -1) + + 2 3 2 3 2 3 + - 1/24 x y DATA(-2, -1) + 1/12 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/48 x y DATA(2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) + + 2 3 2 2 2 + - 1/24 x y DATA(2, 1) + 1/2 x DATA(-1, 0) - 1/6 x y DATA(-2, 1) + + 2 2 2 2 2 2 + + 1/48 x y DATA(1, 2) - 1/48 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) + + 2 2 2 2 2 2 + - 5/16 x y DATA(2, 0) + 1/6 x y DATA(2, -1) - 1/96 x y DATA(2, 2) + + 2 3 2 3 + - 1/24 x y DATA(-1, -2) + 1/12 x y DATA(-1, -1) + + 2 3 2 3 + - 1/12 x y DATA(1, -1) - 1/12 x y DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=179213692, alloc=2620960, time=15.78 +bytes used=180223192, alloc=2620960, time=15.84 + 2 2 2 4 +[COEFF(-2, -2) = - 1/144 x y + 1/288 x y - 1/288 y + 1/144 y - 1/96 x y + + 3 2 2 3 4 3 3 + + 1/72 y x + 1/96 x y + 1/144 x y + 1/144 x y - 1/144 y + + 2 3 2 4 3 2 4 + + 1/48 x y - 1/48 y x - 1/288 x y - 1/144 x y + 1/288 y + + 3 3 2 4 3 4 3 2 + - 1/72 x y , COEFF(-1, -2) = 1/48 x y - 1/36 x y + 1/36 x y + + 2 2 2 3 3 3 3 + - 1/48 x y + 1/36 y + 1/18 x y - 1/9 x y + 1/18 y - 1/18 y + + 4 2 2 3 2 3 + - 1/36 y + 1/24 y x - 1/18 x y - 1/18 y x - 1/24 x y + 1/9 x y + + 4 3 3 3 3 2 + + 1/18 x y , COEFF(0, -2) = 1/12 y x - 1/12 x y - 1/24 x y + + 2 4 3 3 4 + + 5/48 x y - 5/24 x y - 5/48 x y + 5/24 x y + 1/24 x y , COEFF(1, -2) + + 2 3 2 2 3 3 4 + = - 1/18 x y - 1/18 y x - 1/24 y x + 1/24 x y - 1/36 x y + 1/18 y + + 3 2 2 3 3 2 4 3 2 2 + + 1/36 x y - 1/36 y + 1/18 x y - 1/48 x y - 1/18 y + 1/48 x y + + 3 4 4 4 + + 1/9 x y - 1/9 x y + 1/36 y + 1/18 x y , COEFF(2, -2) = - 1/288 y + + 2 3 3 2 3 4 + + 1/288 x y - 1/72 x y - 1/48 x y - 1/288 x y - 1/144 x y - 1/144 y + + 2 4 2 3 4 3 2 3 + + 1/96 x y + 1/48 y x + 1/144 x y - 1/144 x y + 1/144 x y + + 2 2 3 3 2 + - 1/96 x y + 1/144 y + 1/72 y x + 1/288 y , COEFF(-2, -1) = + + 3 4 4 2 3 2 2 + - 1/72 x y - 1/72 y + 1/72 x y - 1/24 x y + 1/18 y - 1/18 x y + + 3 4 2 4 2 3 3 + - 1/36 x y + 1/24 x y + 1/6 y x + 1/18 x y + 1/36 x y - 1/18 y + + 3 3 2 3 2 2 2 3 + - 1/9 y x + 1/9 x y + 1/72 y - 1/6 x y , COEFF(-1, -1) = 1/12 x y + + 2 2 4 3 3 3 4 + - 4/9 y - 8/9 x y - 1/12 x y - 1/9 y + 2/9 x y + 4/9 y x + 1/9 y + + 3 3 3 4 2 2 2 3 2 + - 1/9 x y + 4/9 y + 1/9 x y + 1/3 x y + 8/9 x y - 4/9 x y + + 2 4 3 3 3 3 4 + - 1/3 y x - 2/9 x y , COEFF(0, -1) = 1/6 x y - 2/3 y x - 1/6 x y + + 3 2 2 3 4 + + 2/3 x y - 5/3 x y + 5/3 x y - 5/12 x y + 5/12 x y , COEFF(1, -1) = + + 2 2 3 3 4 2 3 3 3 + - 1/3 x y + 4/9 y x + 1/9 x y + 4/9 y + 2/9 x y - 1/9 x y + + 2 2 4 4 2 3 2 + - 8/9 x y + 8/9 x y + 1/12 x y - 2/9 x y + 1/3 y x - 4/9 x y + + 3 4 2 3 2 2 + + 1/9 y - 4/9 y - 1/9 y - 1/12 x y , COEFF(2, -1) = 1/6 x y + + 2 3 2 4 4 4 2 3 + - 1/6 y x - 1/72 y - 1/24 x y + 1/72 y + 1/72 x y + 1/24 x y + + 3 2 2 3 4 2 3 3 + + 1/9 x y - 1/18 y - 1/36 x y + 1/18 x y - 1/18 x y + 1/36 x y + + 3 3 3 2 + + 1/18 y - 1/9 y x - 1/72 x y , COEFF(-2, 0) = 1/12 - 5/24 x y + + 4 2 4 2 2 3 4 3 + + 1/48 y - 1/16 x y + 5/48 x y - 1/4 x + 1/24 x y + 1/6 x + + 2 2 4 2 4 + + 5/16 x y - 1/48 x y - 5/48 y - 1/12 x, COEFF(-1, 0) = 1/3 x y - 2/3 + + 2 2 4 3 2 2 3 4 2 + - 5/3 x y + 1/8 x y + 5/6 x y + 1/2 x - 2/3 x - 1/6 y + 5/6 y + + 2 2 3 4 + - 5/8 x y + 4/3 x - 1/6 x y , + + 2 3 3 4 4 3 2 + COEFF(0, 0) = 25/8 x y + x + 1/4 x y - 5/2 x - 5/8 x y - 5/4 x y , + + 3 2 3 4 2 2 2 2 + COEFF(1, 0) = 5/6 x y - 1/6 x y - 5/3 x y - 5/6 y + 2/3 + 5/8 x y + + 2 2 4 3 4 4 + - 1/2 x - 1/8 x y - 2/3 x + 1/3 x y + 1/6 y + 4/3 x, COEFF(2, 0) = + + 2 2 3 2 3 4 + - 1/12 x + 1/4 x + 5/48 x y - 5/24 x y + 1/6 x - 1/12 - 1/48 y + + 4 2 2 2 2 4 3 4 + - 1/48 x y + 5/48 y - 5/16 x y + 1/16 x y + 1/24 x y , COEFF(-2, 1) + + 3 2 2 2 3 4 + = - 1/72 y - 1/18 x y + 1/18 y - 1/6 y x + 1/18 y - 1/36 x y + + 2 4 4 3 3 3 2 2 2 + + 1/24 x y - 1/72 y - 1/36 x y + 1/9 x y - 1/6 x y - 1/18 x y + + 3 4 2 3 3 4 + + 1/9 y x + 1/72 x y + 1/24 x y + 1/72 x y , COEFF(-1, 1) = - 2/9 x y + + 2 3 3 3 2 2 3 + + 8/9 x y - 4/9 y + 1/9 x y - 4/9 x y + 1/3 y x - 2/9 x y + + 3 2 4 4 3 4 2 2 2 + - 4/9 y x - 1/12 x y + 1/9 y + 1/9 x y + 8/9 x y + 1/3 x y + + 3 2 3 2 + + 1/9 y - 1/12 x y - 4/9 y, COEFF(0, 1) = - 5/3 x y - 5/3 x y + + 3 4 3 4 3 3 3 3 2 + - 1/6 x y + 5/12 x y + 5/12 x y - 1/6 x y + 2/3 y x + 2/3 x y , + + 2 2 3 3 3 4 3 + COEFF(1, 1) = - 1/3 y x + 1/12 x y + 1/9 x y - 2/9 x y - 2/9 x y + + 2 3 3 2 2 4 + + 4/9 y - 1/9 y + 8/9 x y + 4/9 y - 4/9 y x - 1/3 x y - 1/9 y + + 3 4 2 4 3 2 2 2 + + 1/9 x y + 1/12 x y - 4/9 x y + 8/9 x y , COEFF(2, 1) = 1/6 y x + + 4 3 2 3 2 4 2 + + 1/72 x y + 1/72 x y - 1/18 y + 1/9 y x - 1/24 x y - 1/18 x y + + 3 4 3 2 2 2 3 + - 1/36 x y + 1/9 x y + 1/6 x y + 1/72 y - 1/18 y - 1/18 x y + + 4 2 3 3 3 2 + + 1/72 y - 1/24 x y - 1/36 x y , COEFF(-2, 2) = 1/144 x y + 1/48 y x + + 3 3 3 2 3 2 4 2 3 + + 1/72 x y + 1/144 y + 1/288 x y - 1/144 x y + 1/288 y - 1/48 x y + + 2 2 2 3 4 3 4 + - 1/144 y + 1/96 x y - 1/288 y - 1/144 x y - 1/288 x y + 1/144 x y + + 2 4 3 2 4 2 + - 1/96 x y - 1/72 y x , COEFF(-1, 2) = 1/48 x y - 1/9 x y - 1/18 x y + + 3 3 2 2 2 3 4 2 3 + - 1/18 x y + 1/36 y - 1/48 x y + 1/18 y - 1/36 x y + 1/24 x y + + 3 2 3 2 3 4 4 + - 1/18 y - 1/24 y x + 1/36 x y + 1/18 y x + 1/18 x y - 1/36 y + + 3 2 3 3 3 2 + + 1/9 x y , COEFF(0, 2) = 5/48 x y + 1/12 x y - 1/24 x y + 5/24 x y + + 4 3 4 3 3 + - 5/48 x y + 1/24 x y - 1/12 y x - 5/24 x y , COEFF(1, 2) = + + 3 4 2 2 3 2 3 + - 1/36 x y - 1/9 x y + 1/48 x y + 1/18 y x + 1/24 y x + 1/9 x y + + 4 2 4 2 3 2 3 2 2 + + 1/18 x y - 1/48 x y - 1/24 x y - 1/36 y + 1/36 x y - 1/18 x y + + 3 3 4 3 3 + - 1/18 y - 1/18 x y + 1/36 y + 1/18 y , COEFF(2, 2) = - 1/144 y + + 2 2 2 3 4 3 3 2 + - 1/96 x y + 1/48 x y - 1/288 y + 1/72 x y + 1/288 x y + + 3 2 4 3 3 2 + - 1/144 x y - 1/48 y x - 1/288 x y - 1/72 y x - 1/144 x y + + 3 4 2 4 2 + + 1/144 x y + 1/96 x y + 1/144 y + 1/144 x y + 1/288 y ] + +> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); +bytes used=181223344, alloc=2620960, time=15.90 +bytes used=182223500, alloc=2620960, time=15.97 +bytes used=183223664, alloc=2620960, time=16.07 +bytes used=184244420, alloc=2620960, time=16.17 +bytes used=185261976, alloc=2620960, time=16.24 +bytes used=186262132, alloc=2620960, time=16.32 +bytes used=187271400, alloc=2620960, time=16.41 +bytes used=188271672, alloc=2620960, time=16.50 +bytes used=189271940, alloc=2620960, time=16.57 +bytes used=190272092, alloc=2620960, time=16.84 +bytes used=191272872, alloc=2620960, time=16.90 +bytes used=192273040, alloc=2620960, time=16.96 +bytes used=193273564, alloc=2620960, time=17.03 +bytes used=194283560, alloc=2620960, time=17.13 +bytes used=195283924, alloc=2620960, time=17.24 +bytes used=196288796, alloc=2620960, time=17.34 +bytes used=197290992, alloc=2620960, time=17.43 +bytes used=198291176, alloc=2620960, time=17.52 +bytes used=199291660, alloc=2620960, time=17.61 +bytes used=200292092, alloc=2620960, time=17.89 +bytes used=201292244, alloc=2620960, time=18.05 +bytes used=202292640, alloc=2620960, time=18.12 +bytes used=203294780, alloc=2620960, time=18.22 +bytes used=204295016, alloc=2620960, time=18.34 +bytes used=205295216, alloc=2620960, time=18.44 +bytes used=206305080, alloc=2620960, time=18.68 +bytes used=207305332, alloc=2620960, time=18.84 +bytes used=208305696, alloc=2620960, time=18.90 +bytes used=209306900, alloc=2620960, time=19.00 +bytes used=210308068, alloc=2620960, time=19.12 +bytes used=211308248, alloc=2620960, time=19.34 +bytes used=212308496, alloc=2620960, time=19.47 +bytes used=213308676, alloc=2620960, time=19.54 +bytes used=214312144, alloc=2620960, time=19.67 +bytes used=215319752, alloc=2620960, time=19.92 +bytes used=216319980, alloc=2620960, time=20.07 +bytes used=217320236, alloc=2620960, time=20.15 +bytes used=218320488, alloc=2620960, time=20.29 +bytes used=219320656, alloc=2620960, time=20.59 +bytes used=220320808, alloc=2620960, time=20.75 +> +# d/dy +> simplify( diff(interp_2d_cube_order4_smooth0,y) ); +bytes used=221321332, alloc=2620960, time=20.87 +bytes used=222321548, alloc=2620960, time=20.93 +bytes used=223321736, alloc=2620960, time=21.00 +bytes used=224321912, alloc=2620960, time=21.06 + 4 2 4 2 +- 1/12 DATA(0, 2) - 1/12 x y DATA(-1, -1) + 1/8 x y DATA(0, -1) + + 4 2 4 2 + + 1/12 x y DATA(-1, 1) - 1/96 x y DATA(-2, -2) + + 4 2 3 3 + - 1/48 x y DATA(-2, 1) + 1/6 y DATA(0, 2) + y DATA(0, 0) + + 3 3 3 + - 2/3 y DATA(0, 1) + 1/6 y DATA(0, -2) - 2/3 y DATA(0, -1) + + 4 2 2 2 2 2 + + 1/24 x y DATA(-1, -2) - 5/16 x y DATA(0, 2) + 5/16 x y DATA(0, -2) + + 2 2 3 2 2 + + 5/8 x y DATA(0, 1) - 2/3 x y DATA(-1, 0) - 5/8 x y DATA(0, -1) + + 3 2 3 2 3 + + 1/12 x y DATA(-2, 0) + 2/3 x y DATA(-1, 0) + 2/3 x y DATA(1, 0) + + 2 3 2 3 2 3 + - 1/24 x y DATA(-2, 0) + 5/6 x y DATA(0, -1) - 1/24 x y DATA(2, 0) + + 2 3 4 3 4 3 + - 5/24 x y DATA(0, 2) - 1/6 x y DATA(-1, 0) - 1/36 x y DATA(-2, -1) + + 4 3 4 3 + + 1/144 x y DATA(2, -2) - 1/36 x y DATA(1, -2) + + 4 3 4 3 2 3 + - 1/36 x y DATA(-1, -2) + 1/24 x y DATA(2, 0) + 5/6 x y DATA(0, 1) + + 2 3 4 3 + - 5/24 x y DATA(0, -2) + 1/9 x y DATA(-1, 1) + + 4 3 4 3 2 3 + + 1/144 x y DATA(-2, -2) + 1/9 x y DATA(-1, -1) - 5/4 x y DATA(0, 0) + + 4 3 + + 1/9 x y DATA(1, -1) - 1/12 y DATA(0, 2) - 5/2 y DATA(0, 0) + + 4 3 + + 4/3 y DATA(0, 1) - 1/12 y DATA(0, -2) + 1/144 x y DATA(2, 2) + + 4 3 4 3 4 3 + - 1/36 x y DATA(-1, 2) - 1/6 x y DATA(0, 1) + 1/24 x y DATA(0, -2) + + 4 3 4 3 4 3 + - 1/6 x y DATA(0, -1) + 1/24 x y DATA(0, 2) - 1/36 x y DATA(1, 2) + + 4 3 4 3 4 3 + - 1/36 x y DATA(2, 1) - 1/6 x y DATA(1, 0) + 1/9 x y DATA(1, 1) + + 4 3 4 3 + - 1/36 x y DATA(-2, 1) + 1/24 x y DATA(-2, 0) + + 4 3 4 3 + + 1/144 x y DATA(-2, 2) - 1/36 x y DATA(2, -1) + 4/3 y DATA(0, -1) + + 2 2 2 + - 1/4 y DATA(0, -2) + 1/2 y DATA(0, -1) - 1/2 y DATA(0, 1) + + 2 3 3 + + 1/4 y DATA(0, 2) + 2/3 x y DATA(1, 0) - 1/12 x y DATA(2, 0) + + 3 3 3 + - 5/12 y x DATA(-1, 0) + 5/24 y x DATA(-2, 0) - 5/24 y x DATA(2, 0) + + 3 3 3 + + 5/12 y x DATA(1, 0) - 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) + + 3 3 3 + - 1/144 x DATA(2, 2) + 1/144 x DATA(2, -2) + 1/18 x DATA(-2, -1) + + 3 3 3 + - 1/18 x DATA(-2, 1) + 1/144 x DATA(-2, 2) - 1/9 x DATA(1, 1) + + 3 3 4 + - 1/18 x DATA(2, -1) + 1/18 x DATA(2, 1) + 1/18 x y DATA(2, 1) + + 4 4 4 + + 1/72 x y DATA(-1, -2) + 1/72 x y DATA(1, -2) - 1/288 x y DATA(2, -2) + + 4 4 4 + - 5/48 x y DATA(2, 0) - 5/8 x y DATA(0, 0) + 1/3 x y DATA(0, -1) + + 4 4 4 + - 1/48 x y DATA(0, -2) + 1/3 x y DATA(0, 1) + 1/72 x y DATA(-1, 2) + + 4 4 4 + + 1/72 x y DATA(1, 2) - 1/288 x y DATA(2, 2) - 1/288 x y DATA(-2, 2) + + 4 4 4 + - 5/48 x y DATA(-2, 0) + 1/18 x y DATA(-2, 1) - 2/9 x y DATA(1, 1) + + 4 4 4 + + 5/12 x y DATA(1, 0) + 1/18 x y DATA(2, -1) - 1/48 x y DATA(0, 2) + + 4 4 4 + - 2/9 x y DATA(-1, 1) - 2/9 x y DATA(1, -1) - 2/9 x y DATA(-1, -1) + + 4 4 4 + - 1/288 x y DATA(-2, -2) + 5/12 x y DATA(-1, 0) - 1/288 x DATA(-2, 2) + + 3 3 3 + + 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) - 1/9 x DATA(-1, -1) + + 3 3 3 + - 1/144 x DATA(-2, -2) + 1/72 x DATA(-1, -2) - 1/72 x DATA(1, -2) + + 4 4 4 + - 1/9 x DATA(1, 1) - 1/6 x DATA(0, -1) + 1/9 x DATA(-1, -1) + + 4 4 4 + + 1/288 x DATA(-2, -2) - 1/72 x DATA(-1, -2) + 1/48 x DATA(0, -2) + + 4 4 4 + - 1/72 x DATA(1, -2) + 1/288 x DATA(2, -2) - 1/36 x DATA(-2, -1) + + 4 4 + + 1/36 x DATA(-2, 1) + 1/18 x DATA(2, -1) + 1/6 x DATA(0, 1) + + 4 4 4 + - 1/36 x DATA(2, -1) + 1/36 x DATA(2, 1) - 1/48 x DATA(0, 2) + + 4 4 4 + + 1/72 x DATA(-1, 2) + 1/72 x DATA(1, 2) - 1/288 x DATA(2, 2) + + 4 4 + - 1/9 x DATA(-1, 1) + 1/9 x DATA(1, -1) + 5/24 x y DATA(2, 0) + + 4 3 3 3 + - 5/3 x y DATA(1, 0) + 1/4 x y DATA(0, 0) + 1/12 x y DATA(2, 0) + + 3 3 3 3 4 + + 1/6 x y DATA(-1, 0) - 1/6 x y DATA(1, 0) + 1/18 x y DATA(-2, -1) + + 3 3 2 2 + - 1/12 x y DATA(-2, 0) + 1/36 x DATA(-2, -1) + 1/18 x DATA(1, -2) + + 2 2 2 + - 5/48 x DATA(0, -2) + 1/18 x DATA(-1, -2) - 1/288 x DATA(-2, -2) + + - 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/18 x DATA(-2, 1) + + - 1/144 x DATA(2, -2) + 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) + + + 1/144 x DATA(-2, -2) + 4/9 x DATA(-1, -1) - 1/18 x DATA(-2, -1) + + + 4/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/144 x DATA(2, 2) + + - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + + 2 + - 1/288 x DATA(2, -2) + 5/3 x y DATA(-1, 0) - 5/24 x y DATA(-2, 0) + + 2 2 2 + + 5/48 y x DATA(-2, 0) - 5/3 y x DATA(-1, 0) - 5/3 y x DATA(0, 1) + + 2 2 2 + + 5/48 y x DATA(0, -2) - 5/3 y x DATA(0, -1) + 5/48 y x DATA(0, 2) + + 2 4 2 4 2 + + 25/8 y x DATA(0, 0) - 1/24 x y DATA(1, 2) - 1/24 x y DATA(-1, 2) + + 4 2 4 2 2 + + 1/16 x y DATA(0, 2) - 1/48 x y DATA(2, 1) + 5/48 y x DATA(2, 0) + + 2 2 2 + - 5/3 y x DATA(1, 0) + 5/6 x DATA(0, -1) - 4/9 x DATA(1, -1) + + 2 2 2 + + 4/9 x DATA(-1, 1) + 1/288 x DATA(2, 2) - 1/18 x DATA(1, 2) + + 2 2 2 + - 1/18 x DATA(-1, 2) + 5/48 x DATA(0, 2) - 1/36 x DATA(2, 1) + + 2 2 2 + + 1/36 x DATA(2, -1) - 5/6 x DATA(0, 1) + 4/9 x DATA(1, 1) + + 2 2 4 2 + + 1/288 x DATA(-2, 2) - 1/36 x DATA(-2, 1) + 1/12 x y DATA(1, 1) + + 4 2 4 2 4 2 + + 1/96 x y DATA(-2, 2) - 1/12 x y DATA(1, -1) + 1/96 x y DATA(2, 2) + + 4 2 4 2 4 2 + - 1/96 x y DATA(2, -2) + 1/24 x y DATA(1, -2) - 1/16 x y DATA(0, -2) + + 4 2 4 2 4 2 + + 1/48 x y DATA(-2, -1) + 1/48 x y DATA(2, -1) - 1/8 x y DATA(0, 1) + + 2 + - 4/9 x DATA(-1, -1) + 2/3 DATA(0, 1) + 1/12 DATA(0, -2) + + 2 2 2 + - 2/3 DATA(0, -1) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(1, 1) + + 2 2 2 2 2 2 + - 1/96 x y DATA(-2, 2) + 1/96 x y DATA(2, -2) - 1/6 x y DATA(1, -2) + + 2 2 2 2 + - 1/6 x y DATA(-1, -2) + 1/96 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, -1) + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) + + 2 2 2 + - 1/18 y x DATA(1, 2) - 1/18 y x DATA(-1, 2) - 1/18 y x DATA(2, 1) + + 2 2 2 2 + - 1/48 x y DATA(-2, -1) - 1/18 y x DATA(1, -2) - 1/18 y x DATA(-1, -2) + + 2 2 2 + + 1/288 y x DATA(-2, -2) + 1/288 y x DATA(2, 2) + 8/9 y x DATA(1, 1) + + 2 2 2 + + 1/288 y x DATA(-2, 2) - 1/18 y x DATA(-2, 1) - 1/18 y x DATA(-2, -1) + + 2 2 2 + + 1/288 y x DATA(2, -2) + 8/9 y x DATA(-1, -1) + 8/9 y x DATA(1, -1) + + 2 2 2 + + 8/9 y x DATA(-1, 1) - 1/18 y x DATA(2, -1) + 1/3 x y DATA(1, -1) + + 2 2 2 + + 1/3 x y DATA(-1, 1) + 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) + + 2 2 2 + - 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) + 1/6 x y DATA(1, 2) + + 2 2 2 + - 1/6 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) - 1/48 x y DATA(-2, -2) + + - 1/18 x y DATA(1, 2) + 1/18 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) + + - 1/9 x y DATA(2, -1) + 8/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) + + + 1/9 x y DATA(-2, 1) + 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) + + 2 2 2 + - 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) + + 2 2 + - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) - 8/9 x y DATA(-1, 1) + + 3 3 3 3 3 3 + + 1/72 x y DATA(2, 2) - 1/36 x y DATA(1, 2) + 1/36 x y DATA(-1, 2) + + 3 3 3 3 3 3 + - 1/18 x y DATA(2, 1) - 1/18 x y DATA(2, -1) + 1/9 x y DATA(1, -1) + + 3 3 + + 1/144 x y DATA(2, 2) + 1/72 x y DATA(2, -2) - 1/18 x y DATA(1, -2) + + + 1/18 x y DATA(-1, -2) - 1/144 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) + + 3 3 3 3 + + 8/9 x y DATA(1, -1) + 1/36 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) + + 3 3 3 3 3 + - 1/9 x y DATA(-1, -1) - 1/9 x y DATA(-1, 1) - 1/72 x y DATA(2, 2) + + 3 3 3 3 3 3 + + 1/9 x y DATA(1, 1) - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) + + 3 3 3 3 + + 1/18 x y DATA(-2, -1) + 1/18 x y DATA(2, -1) - 4/9 x y DATA(1, 1) + + 3 3 3 3 + + 1/72 x y DATA(-2, 2) - 1/18 x y DATA(-2, 1) - 1/36 x y DATA(1, -2) + + 3 3 3 + + 4/9 x y DATA(-1, 1) + 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + + 3 3 2 3 + + 1/18 x y DATA(2, 1) - 1/12 x y DATA(1, -1) - 1/18 x y DATA(-2, -1) + + 3 3 3 + - 1/72 x y DATA(2, -2) + 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) + + 3 3 3 + + 1/72 x y DATA(-2, -2) + 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) + + 3 2 3 3 2 + + 1/48 x y DATA(2, 2) - 1/144 y x DATA(2, 2) - 1/12 x y DATA(-1, 1) + + 3 2 3 2 + - 1/24 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) + + 3 2 3 2 + + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) + + 3 2 3 2 + + 1/48 x y DATA(-2, -2) + 1/12 x y DATA(-1, -1) + + 3 2 3 2 3 + - 1/24 x y DATA(2, 1) + 1/24 x y DATA(2, -1) + 1/9 y x DATA(2, 1) + + 3 3 2 3 2 + + 1/9 y x DATA(2, -1) + 1/12 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) + + 3 2 3 2 3 2 + - 1/48 x y DATA(-2, 2) - 1/24 x y DATA(1, 2) + 1/24 x y DATA(-1, 2) + + 3 3 3 + + 2/9 y x DATA(-1, 1) - 2/9 y x DATA(1, 1) + 1/144 y x DATA(-2, 2) + + 3 3 3 + - 1/9 y x DATA(-2, 1) - 1/9 y x DATA(-2, -1) - 1/144 y x DATA(2, -2) + + 3 3 3 + + 1/72 y x DATA(1, 2) - 1/72 y x DATA(-1, 2) - 2/9 y x DATA(1, -1) + + 3 3 3 + + 1/72 y x DATA(1, -2) - 1/72 y x DATA(-1, -2) + 1/144 y x DATA(-2, -2) + + 3 2 3 + + 2/9 y x DATA(-1, -1) + 1/36 x y DATA(-2, 1) + + 2 3 2 3 + - 1/144 x y DATA(-2, -2) - 1/144 x y DATA(2, -2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(1, -2) + 1/36 x y DATA(2, -1) + 1/36 x y DATA(-2, -1) + + 2 3 2 3 2 3 + - 4/9 x y DATA(1, 1) - 1/144 x y DATA(-2, 2) - 1/144 x y DATA(2, 2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(1, 2) + 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 1) + + 2 2 2 2 2 2 + + 1/48 x y DATA(-2, 1) + 1/6 x y DATA(1, 2) + 1/6 x y DATA(-1, 2) + + 2 2 2 2 2 2 + + 1/48 x y DATA(2, 1) - 1/48 x y DATA(2, -1) - 1/96 x y DATA(2, 2) + + 2 3 2 3 2 3 + + 1/9 x y DATA(-1, -2) - 4/9 x y DATA(-1, -1) - 4/9 x y DATA(1, -1) + + 2 3 + - 4/9 x y DATA(-1, 1) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=225340376, alloc=2752008, time=21.13 +bytes used=226340564, alloc=2752008, time=21.19 + 2 3 3 4 3 3 +[COEFF(-2, -2) = - 1/288 x - 1/72 x y + 1/144 x + 1/144 x y - 1/144 x + + 2 3 3 2 2 3 2 4 2 + - 1/144 x y + 1/72 x y + 1/96 x y + 1/48 x y - 1/96 x y + + 2 4 3 4 2 + + 1/288 y x - 1/288 x y + 1/144 y x + 1/288 x - 1/144 x y - 1/48 x y , + + 2 4 3 3 2 2 + COEFF(-1, -2) = 1/18 x - 1/36 x y - 1/72 y x - 1/18 y x + 1/6 x y + + 2 3 3 3 2 4 2 + + 1/9 x y + 1/72 x - 1/24 x y + 1/24 x y - 1/18 x + 1/18 x y + + 4 3 3 3 4 2 2 + - 1/72 x - 1/9 x y + 1/36 x y + 1/72 x y - 1/6 x y , COEFF(0, -2) = + + 4 2 2 4 2 3 + - 1/48 x y - 5/48 x + 5/48 y x + 1/48 x + 1/12 - 1/12 y - 5/24 x y + + 3 2 2 2 4 3 4 2 + + 1/6 y + 5/16 x y - 1/4 y + 1/24 x y - 1/16 x y , COEFF(1, -2) = + + 3 2 2 2 3 2 4 3 + - 1/18 x y + 1/24 x y - 1/6 x y - 1/72 x - 1/6 x y - 1/36 x y + + 4 3 3 2 4 2 3 3 + - 1/72 x + 1/9 x y + 1/72 y x + 1/18 x + 1/24 x y - 1/36 x y + + 2 3 2 4 3 + + 1/9 x y - 1/18 y x + 1/18 x + 1/72 x y, COEFF(2, -2) = - 1/144 y x + + 2 4 3 2 2 2 + + 1/288 y x + 1/144 x y + 1/96 x y + 1/144 x y - 1/144 x - 1/288 x + + 4 3 3 2 3 3 2 3 + - 1/288 x y + 1/144 x - 1/48 x y + 1/72 x y + 1/48 x y - 1/72 x y + + 4 2 3 4 2 2 + + 1/288 x - 1/144 x y - 1/96 x y , COEFF(-2, -1) = 1/24 x y + + 3 2 2 2 2 4 2 3 + - 1/24 x y + 1/9 x y - 1/48 x y - 1/18 y x + 1/48 x y - 1/18 x y + + 4 2 3 4 3 3 3 2 + + 1/18 x y + 1/36 x y - 1/36 x + 1/18 x y + 1/18 x + 1/36 x + + 3 4 3 3 2 + - 1/18 x - 1/9 y x - 1/36 x y , COEFF(-1, -1) = 1/12 x y - 8/9 x y + + 3 3 3 2 4 4 3 2 2 + + 4/9 x y - 1/9 x y - 4/9 x - 2/9 x y + 1/9 x y + 1/3 x y + + 4 2 3 2 3 2 4 2 + + 1/9 x - 4/9 x y + 8/9 y x + 2/9 y x + 4/9 x - 1/3 x y - 1/12 x y + + 3 4 2 2 2 2 + - 1/9 x , COEFF(0, -1) = 1/3 x y - 5/3 y x + 5/6 x - 2/3 - 5/8 x y + + 3 4 4 3 2 3 2 4 2 + + 4/3 y - 2/3 y - 1/6 x - 1/6 x y + 5/6 x y + 1/2 y + 1/8 x y , + + 3 2 2 3 4 3 + COEFF(1, -1) = 1/9 x + 8/9 x y + 1/3 x y - 4/9 x y + 1/9 x y + + 4 3 2 4 2 2 3 3 + - 2/9 x y - 1/12 x y - 1/12 x y + 8/9 y x - 4/9 x + 1/9 x y + + 2 2 3 4 2 3 + + 1/3 x y - 4/9 x - 2/9 y x + 1/9 x - 4/9 x y , COEFF(2, -1) = + + 4 3 2 3 3 2 2 4 2 + - 1/36 x + 1/9 y x + 1/36 x - 1/18 x y - 1/48 x y + 1/48 x y + + 2 4 3 2 3 2 3 + - 1/18 y x + 1/18 x - 1/36 x y - 1/24 x y + 1/24 x y + 1/18 x y + + 2 3 4 3 3 3 + + 1/36 x y + 1/18 x y - 1/18 x - 1/9 x y, COEFF(-2, 0) = - 1/12 x y + + 4 2 2 3 3 3 + - 5/48 x y + 5/48 y x - 1/24 x y + 5/24 y x + 1/12 x y - 5/24 x y + + 4 3 2 3 4 3 3 3 + + 1/24 x y , COEFF(-1, 0) = 2/3 x y - 1/6 x y + 1/6 x y + 5/3 x y + + 3 2 4 3 + - 5/12 y x - 5/3 y x + 5/12 x y - 2/3 x y , + + 2 3 4 2 3 4 3 + COEFF(0, 0) = 25/8 y x + y - 5/8 x y - 5/4 x y + 1/4 x y - 5/2 y, + + 2 3 4 4 3 3 3 + COEFF(1, 0) = 2/3 x y + 5/12 x y - 5/3 x y - 1/6 x y - 1/6 x y + + 2 3 3 3 3 + - 5/3 y x + 5/12 y x + 2/3 x y , COEFF(2, 0) = 5/24 x y + 1/12 x y + + 4 3 2 2 3 3 3 4 + + 1/24 x y + 5/48 y x - 1/24 x y - 1/12 x y - 5/24 y x - 5/48 x y, + + 3 3 2 4 3 4 2 + COEFF(-2, 1) = - 1/18 x + 1/24 x y + 1/18 x y - 1/9 y x - 1/48 x y + + 3 3 2 4 3 2 2 + + 1/9 x y + 1/18 x y - 1/24 x y + 1/36 x - 1/18 x y + 1/48 x y + + 2 3 4 3 2 2 + + 1/36 x y + 1/18 x - 1/36 x y - 1/36 x - 1/18 y x , COEFF(-1, 1) = + + 3 3 4 3 2 2 2 3 4 3 + - 1/9 x y - 1/9 x + 4/9 x y + 1/3 x y - 1/3 x y + 1/9 x + 1/9 x y + + 2 3 2 2 2 3 4 + + 8/9 y x - 1/12 x y + 4/9 x - 4/9 x y - 4/9 x - 2/9 x y - 8/9 x y + + 4 2 3 4 4 2 2 + + 1/12 x y + 2/9 y x , COEFF(0, 1) = 1/6 x - 1/8 x y - 1/2 y + 2/3 + + 2 3 4 3 2 2 2 2 4 + + 5/6 x y + 4/3 y - 1/6 x y - 5/6 x + 5/8 x y - 5/3 y x + 1/3 x y + + 3 2 3 4 2 4 + - 2/3 y , COEFF(1, 1) = - 1/3 x y - 4/9 x y + 1/12 x y - 1/9 x + + 3 2 3 3 2 2 2 3 4 + + 1/12 x y + 1/9 x y + 4/9 x - 1/3 x y - 2/9 y x - 2/9 x y + + 2 3 4 3 3 2 + + 4/9 x + 8/9 x y - 4/9 x y + 1/9 x y - 1/9 x + 8/9 y x , COEFF(2, 1) + + 3 2 2 2 2 2 2 3 + = 1/18 x y - 1/18 y x - 1/36 x + 1/48 x y + 1/24 x y + 1/36 x y + + 3 2 3 3 4 2 3 + - 1/24 x y - 1/18 x y - 1/9 x y - 1/48 x y - 1/18 x + 1/9 y x + + 3 4 3 4 4 + + 1/18 x - 1/36 x y + 1/36 x + 1/18 x y, COEFF(-2, 2) = - 1/144 x + + 2 2 4 2 4 2 2 3 + + 1/288 y x + 1/288 x + 1/96 x y - 1/288 x - 1/96 x y + 1/72 x y + + 2 3 3 4 3 2 2 + - 1/144 x y - 1/144 x y + 1/144 x - 1/288 x y - 1/48 x y + 1/48 x y + + 3 3 3 4 3 4 + - 1/72 x y + 1/144 y x + 1/144 x y , COEFF(-1, 2) = 1/72 x + + 3 3 3 4 2 3 2 + + 1/36 x y - 1/72 x - 1/24 x y + 1/18 x y - 1/72 y x - 1/18 x + + 3 2 2 3 2 2 2 2 3 + + 1/24 x y + 1/9 x y + 1/6 x y - 1/6 x y - 1/18 y x - 1/9 x y + + 4 3 4 2 + - 1/36 x y + 1/18 x + 1/72 x y, COEFF(0, 2) = - 1/12 - 1/12 y + 5/48 x + + 4 2 4 2 4 2 2 2 3 + + 1/16 x y - 1/48 x + 5/48 y x - 1/48 x y - 5/16 x y - 5/24 x y + + 3 4 3 2 + + 1/6 y + 1/24 x y + 1/4 y , COEFF(1, 2) = - 1/18 x - 1/18 x y + + 3 3 3 4 2 2 4 + - 1/36 x y + 1/72 x + 1/72 x y + 1/6 x y - 1/18 y x + 1/72 x + + 2 3 2 3 4 2 2 3 2 2 + - 1/18 x - 1/24 x y + 1/9 x y - 1/24 x y + 1/9 x y + 1/6 x y + + 3 4 3 3 4 2 + + 1/72 y x - 1/36 x y , COEFF(2, 2) = 1/144 x y - 1/144 x + 1/96 x y + + 4 4 2 2 2 3 + - 1/288 x + 1/144 x - 1/288 x y + 1/288 x - 1/96 x y - 1/72 x y + + 2 3 3 3 2 3 2 + - 1/48 x y + 1/72 x y - 1/144 y x - 1/144 x y + 1/288 y x + + 4 3 3 2 + + 1/144 x y + 1/48 x y ] + +> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); +bytes used=227340944, alloc=2817532, time=21.27 +bytes used=228341108, alloc=2817532, time=21.34 +bytes used=229341284, alloc=2817532, time=21.43 +bytes used=230364276, alloc=2817532, time=21.51 +bytes used=231366896, alloc=2817532, time=21.59 +bytes used=232387828, alloc=2817532, time=21.65 +bytes used=233410164, alloc=2817532, time=21.73 +bytes used=234411164, alloc=2817532, time=21.82 +bytes used=235411816, alloc=2817532, time=21.89 +bytes used=236412028, alloc=2817532, time=22.25 +bytes used=237412372, alloc=2817532, time=22.32 +bytes used=238412628, alloc=2817532, time=22.39 +bytes used=239412864, alloc=2817532, time=22.45 +bytes used=240413072, alloc=2817532, time=22.53 +bytes used=241413260, alloc=2817532, time=22.64 +bytes used=242415104, alloc=2817532, time=22.74 +bytes used=243422528, alloc=2817532, time=22.84 +bytes used=244422796, alloc=2817532, time=22.92 +bytes used=245434308, alloc=2817532, time=23.25 +bytes used=246434640, alloc=2817532, time=23.47 +bytes used=247434804, alloc=2817532, time=23.55 +bytes used=248445404, alloc=2817532, time=23.66 +bytes used=249445736, alloc=2817532, time=23.79 +bytes used=250454324, alloc=2817532, time=24.11 +bytes used=251454648, alloc=2817532, time=24.31 +bytes used=252454820, alloc=2817532, time=24.38 +bytes used=253455412, alloc=2817532, time=24.47 +bytes used=254455864, alloc=2817532, time=24.59 +bytes used=255456212, alloc=2817532, time=24.96 +bytes used=256456488, alloc=2817532, time=25.03 +bytes used=257456656, alloc=2817532, time=25.12 +bytes used=258456848, alloc=2817532, time=25.35 +bytes used=259457064, alloc=2817532, time=25.61 +bytes used=260457280, alloc=2817532, time=25.69 +bytes used=261457952, alloc=2817532, time=25.80 +bytes used=262458396, alloc=2817532, time=26.10 +bytes used=263458644, alloc=2817532, time=26.17 +> +# d^2/dx^2 +> simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); +bytes used=264458908, alloc=2817532, time=26.30 +bytes used=265459400, alloc=2817532, time=26.38 +bytes used=266459604, alloc=2817532, time=26.45 + 3 3 +- 1/12 DATA(2, 0) - 5/24 y DATA(0, 2) + 5/12 y DATA(0, 1) + + 3 3 2 2 + + 5/24 y DATA(0, -2) - 5/12 y DATA(0, -1) - 1/8 x y DATA(0, 2) + + 2 2 2 2 2 2 + - 1/8 x y DATA(0, -2) + 2 x y DATA(0, 1) + 2 x y DATA(0, -1) + + 2 3 2 3 2 3 + + 1/2 x y DATA(0, -1) + 1/4 x y DATA(0, 2) - 1/2 x y DATA(0, 1) + + 2 3 + - 1/4 x y DATA(0, -2) + 5/24 y DATA(0, 2) - 5/3 y DATA(0, 1) + + 2 + - 5/24 y DATA(0, -2) + 5/3 y DATA(0, -1) + 5/48 y DATA(0, -2) + + 2 2 2 + - 5/3 y DATA(0, -1) - 5/3 y DATA(0, 1) + 5/48 y DATA(0, 2) + + 2 2 2 + + 2 y x DATA(0, 1) + 1/4 y x DATA(0, -2) - 2 y x DATA(0, -1) + + 2 + - 1/4 y x DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(1, 0) - 1/12 DATA(-2, 0) + + 2 2 2 + + 4/3 DATA(-1, 0) + 2/3 x y DATA(-1, -1) - 4/3 x y DATA(1, 1) + + 2 2 2 2 2 2 + - 1/48 x y DATA(-2, 2) - 1/48 x y DATA(2, -2) + 1/12 x y DATA(1, -2) + + 2 2 2 2 + + 1/12 x y DATA(-1, -2) - 1/48 x y DATA(-2, -2) + + 2 2 2 2 2 2 + - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) - 4/3 x y DATA(-1, 1) + + 2 2 2 + + 1/6 y x DATA(1, 2) + 1/6 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) + + 2 2 2 2 + + 1/3 x y DATA(-2, -1) - 1/6 y x DATA(1, -2) - 1/6 y x DATA(-1, -2) + + 2 2 2 + + 1/24 y x DATA(-2, -2) - 1/24 y x DATA(2, 2) - 4/3 y x DATA(1, 1) + + 2 2 2 + - 1/24 y x DATA(-2, 2) + 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) + + 2 2 2 + + 1/24 y x DATA(2, -2) + 4/3 y x DATA(-1, -1) + 4/3 y x DATA(1, -1) + + 2 2 2 + - 4/3 y x DATA(-1, 1) - 1/3 y x DATA(2, -1) - 2/3 x y DATA(1, -1) + + 2 2 2 + + 2/3 x y DATA(-1, 1) - 1/3 x y DATA(-2, -1) - 1/48 x y DATA(2, -2) + + 2 2 2 + + 1/24 x y DATA(1, -2) - 1/24 x y DATA(-1, -2) + 1/24 x y DATA(1, 2) + + 2 2 2 + - 1/24 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) + + + 1/12 x y DATA(1, 2) - 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + + - 1/3 x y DATA(2, -1) - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + - 1/3 x y DATA(-2, 1) + 1/3 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) + + 2 2 2 + - 2/3 x y DATA(1, 1) - 1/3 x y DATA(-2, 1) + 1/48 x y DATA(-2, 2) + + 2 2 + + 1/3 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 2/3 x y DATA(-1, 1) + + - 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) + + - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) + 2/3 x y DATA(1, -1) + + 3 3 3 + + 1/24 x y DATA(2, 2) + 1/12 x y DATA(2, -1) + 1/6 x y DATA(1, 1) + + 3 3 3 + - 1/24 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) - 1/6 x y DATA(-1, 1) + + 3 3 3 + - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) + + 3 3 3 + - 1/12 x y DATA(-2, -1) - 1/24 x y DATA(2, -2) + 1/12 x y DATA(1, -2) + + 3 3 3 + - 1/12 x y DATA(-1, -2) + 1/24 x y DATA(-2, -2) + 1/6 x y DATA(-1, -1) + + 3 2 3 2 3 + - 1/6 x y DATA(1, -1) - 1/12 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) + + 2 3 2 3 2 3 + - 1/24 x y DATA(2, -2) + 1/6 x y DATA(1, -2) + 1/12 x y DATA(2, -1) + + 2 3 2 3 2 3 + + 1/12 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, 2) - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) + + 2 3 2 2 2 2 + - 1/12 x y DATA(2, 1) + 1/3 x y DATA(-2, 1) + 1/12 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/12 x y DATA(-1, 2) + 1/3 x y DATA(2, 1) + 1/3 x y DATA(2, -1) + + 2 2 2 3 2 3 + - 1/48 x y DATA(2, 2) + 1/6 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) + + 2 3 2 3 4 + - 1/3 x y DATA(1, -1) + 1/3 x y DATA(-1, 1) - 1/8 x y DATA(-2, 0) + + 4 4 4 + + 1/48 x y DATA(2, -2) - 1/24 x y DATA(1, -2) + 1/24 x y DATA(-1, -2) + + 4 4 4 + - 1/48 x y DATA(-2, -2) - 1/6 x y DATA(-1, -1) + 1/6 x y DATA(1, -1) + + 3 3 2 + - 1/9 y DATA(-1, -2) + 1/9 y DATA(-1, 2) + 1/2 x DATA(2, 0) + + 2 2 2 + + 3 x DATA(0, 0) - 2 x DATA(1, 0) + 1/2 x DATA(-2, 0) + + 2 3 + - 2 x DATA(-1, 0) - 1/144 y DATA(2, 2) - 1/18 y DATA(-2, 1) + + 2 2 + + 1/18 y DATA(-2, -1) - 1/144 y DATA(2, -2) + 5/2 x y DATA(1, 0) + + 2 2 2 2 2 2 + + 5/2 x y DATA(-1, 0) - 5/8 x y DATA(2, 0) - 15/4 x y DATA(0, 0) + + 2 2 2 3 + - 5/8 x y DATA(-2, 0) - 5/8 x y DATA(2, 0) + 2/9 y DATA(1, -1) + + 3 + - 2/9 y DATA(-1, 1) + 1/2 x DATA(2, 0) - x DATA(1, 0) - 1/2 x DATA(-2, 0) + + 3 3 3 + + 2/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) + 1/72 y DATA(2, 1) + + 3 3 3 + - 1/72 y DATA(2, -1) - 2/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) + + 3 3 3 + + 1/72 y DATA(-2, 1) - 1/72 y DATA(-2, -1) + 1/144 y DATA(2, -2) + + 3 2 4 4 + - 1/9 y DATA(1, -2) - 1/2 x y DATA(1, 0) + 1/18 y DATA(-1, 2) + + 4 4 4 + - 1/288 y DATA(-2, -2) + 5/12 y DATA(0, -1) - 2/9 y DATA(1, -1) + + 4 4 4 + + 1/3 y DATA(-1, 0) - 2/9 y DATA(-1, 1) - 2/9 y DATA(-1, -1) + + 4 4 4 + + 5/12 y DATA(0, 1) - 1/288 y DATA(-2, 2) + 1/72 y DATA(-2, 1) + + 4 4 4 + - 2/9 y DATA(1, 1) + 1/72 y DATA(-2, -1) - 1/288 y DATA(2, -2) + + 4 2 4 4 + + 1/18 y DATA(1, -2) - 1/12 x y DATA(1, 2) - 5/48 y DATA(0, -2) + + 4 4 4 + + 1/18 y DATA(-1, -2) - 1/48 y DATA(-2, 0) - 5/48 y DATA(0, 2) + + 4 4 4 + + 1/72 y DATA(2, 1) - 1/48 y DATA(2, 0) + 1/72 y DATA(2, -1) + + 4 4 4 + - 5/8 y DATA(0, 0) + 1/3 y DATA(1, 0) - 1/288 y DATA(2, 2) + + 4 2 4 2 4 + + 1/18 y DATA(1, 2) - 1/12 x y DATA(-1, 2) - 1/2 x y DATA(0, -1) + + 2 4 2 4 2 4 + + 1/3 x y DATA(1, -1) - 1/2 x y DATA(-1, 0) + 1/48 x y DATA(-2, -2) + + 2 4 2 4 2 4 + + 1/48 x y DATA(2, 2) + 1/8 x y DATA(0, 2) - 1/12 x y DATA(2, 1) + + 2 4 2 4 2 4 + + 1/8 x y DATA(2, 0) - 1/12 x y DATA(2, -1) - 1/12 x y DATA(-2, -1) + + 2 4 2 4 2 4 + + 1/48 x y DATA(2, -2) - 1/12 x y DATA(1, -2) + 1/8 x y DATA(0, -2) + + 2 4 2 4 4 + - 1/12 x y DATA(-1, -2) + 1/8 x y DATA(-2, 0) - 1/12 x y DATA(2, -1) + + 4 4 4 + + 1/4 x y DATA(-1, 0) - 1/4 x y DATA(1, 0) + 1/6 x y DATA(1, 1) + + 4 4 2 4 + - 1/48 x y DATA(-2, 2) + 1/12 x y DATA(-2, 1) + 3/4 x y DATA(0, 0) + + 2 4 2 4 4 + + 1/3 x y DATA(-1, 1) + 1/3 x y DATA(-1, -1) - 1/6 x y DATA(-1, 1) + + 4 4 4 + + 1/12 x y DATA(-2, -1) - 1/24 x y DATA(1, 2) + 1/48 x y DATA(2, 2) + + 4 4 4 + + 1/24 x y DATA(-1, 2) - 1/12 x y DATA(2, 1) + 1/8 x y DATA(2, 0) + + 2 2 2 + - 1/18 y DATA(1, 2) - 1/18 y DATA(-1, 2) + 1/288 y DATA(-2, -2) + + 2 2 2 + + 8/9 y DATA(1, -1) - 5/3 y DATA(-1, 0) + 8/9 y DATA(-1, 1) + + 2 2 2 + + 8/9 y DATA(-1, -1) + 1/288 y DATA(-2, 2) - 1/18 y DATA(-2, 1) + + 2 2 2 + + 8/9 y DATA(1, 1) - 1/18 y DATA(-2, -1) + 1/288 y DATA(2, -2) + + 2 2 + + 1/288 y DATA(2, 2) + 1/144 y DATA(2, 2) - 1/18 y DATA(2, 1) + + 2 2 2 + + 5/48 y DATA(2, 0) - 1/18 y DATA(2, -1) + 25/8 y DATA(0, 0) + + 2 + - 5/3 y DATA(1, 0) - 1/9 y DATA(1, 2) - 1/9 y DATA(-1, 2) + + - 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) + 8/9 y DATA(1, 1) + + 2 2 + + 1/144 y DATA(-2, 2) - 1/18 y DATA(1, -2) - 1/18 y DATA(-1, -2) + + 2 + + 5/48 y DATA(-2, 0) + 1/9 y DATA(1, -2) + 1/9 y DATA(-1, -2) + + - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) - 8/9 y DATA(1, -1) + + 2 4 2 4 + + 8/9 y DATA(-1, 1) - 1/2 x y DATA(0, 1) + 1/48 x y DATA(-2, 2) + + 2 4 2 4 2 + - 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 1) - 5/4 x y DATA(-1, 0) + + 2 2 3 + + 5/4 x y DATA(1, 0) + 5/8 x y DATA(-2, 0) + 1/144 y DATA(-2, -2) + + + x DATA(-1, 0) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=267463800, alloc=2817532, time=26.51 + 2 4 2 2 4 2 2 +[COEFF(-2, -2) = 1/48 x y + 1/48 x y + 1/288 y - 1/288 y - 1/48 x y + + 2 3 4 3 2 3 + + 1/24 y x + 1/24 x y - 1/48 x y + 1/144 y - 1/144 y - 1/24 x y + + 4 2 2 2 + - 1/24 x y, COEFF(-1, -2) = 1/24 x y + 1/12 x y - 1/24 x y + 1/12 x y + + 3 2 4 3 2 4 2 + - 1/9 y + 1/9 y - 1/12 x y - 1/12 x y - 1/18 y + 1/18 y - 1/6 y x + + 2 3 2 2 3 + + 1/6 x y , COEFF(0, -2) = - 5/24 y + 5/48 y + 1/4 y x + 5/24 y + + 2 2 2 3 4 2 4 2 + - 1/8 x y - 1/4 x y - 5/48 y + 1/8 x y , COEFF(1, -2) = 1/24 x y + + 2 3 2 2 4 2 + - 1/12 x y - 1/6 y x - 1/9 y + 1/12 x y + 1/18 y - 1/18 y + + 3 2 3 4 2 4 + + 1/12 x y + 1/6 x y + 1/9 y - 1/24 x y - 1/12 x y , COEFF(2, -2) = + + 2 4 4 2 2 4 + - 1/48 x y - 1/288 y + 1/48 x y + 1/24 y x + 1/24 x y + 1/48 x y + + 3 2 2 2 2 3 3 + - 1/144 y + 1/144 y - 1/48 x y + 1/288 y - 1/24 x y - 1/24 x y , + + 2 2 3 2 2 3 + COEFF(-2, -1) = 1/3 x y + 1/3 x y - 1/72 y - 1/18 y + 1/12 x y + + 4 3 2 4 2 2 + + 1/18 y + 1/12 x y - 1/12 x y - 1/12 x y - 1/3 y x - 1/3 x y + + 4 4 2 2 4 + + 1/72 y , COEFF(-1, -1) = - 1/6 x y + 2/3 x y - 8/9 y + 1/3 x y + + 2 2 2 2 3 3 4 2 3 + + 8/9 y - 4/3 x y + 4/3 y x + 2/9 y + 1/6 x y - 2/9 y - 1/3 x y + + 2 3 2 2 4 2 + - 2/3 x y, COEFF(0, -1) = 1/2 x y + 2 x y + 5/12 y - 5/3 y + + 2 4 2 3 2 4 + - 1/2 x y - 2 y x - 5/12 y + 5/3 y, COEFF(1, -1) = 1/3 x y + 2/3 x y + + 4 3 2 2 2 4 2 3 + + 1/6 x y + 2/9 y - 4/3 x y - 8/9 y - 2/3 x y - 2/9 y - 1/3 x y + + 3 2 2 2 2 4 + - 1/6 x y + 8/9 y + 4/3 y x , COEFF(2, -1) = - 1/18 y - 1/12 x y + + 4 2 2 2 2 3 + - 1/12 x y + 1/3 x y + 1/3 x y + 1/18 y - 1/3 x y + 1/12 x y + + 3 3 4 2 2 + - 1/72 y + 1/12 x y + 1/72 y - 1/3 y x , COEFF(-2, 0) = 1/2 x + + 2 4 2 4 2 2 2 + + 1/8 x y + 5/8 x y - 1/48 y - 1/12 + 5/48 y - 5/8 x y - 1/2 x + + 4 2 2 2 4 4 + - 1/8 x y , COEFF(-1, 0) = 4/3 + 5/2 x y - 2 x + 1/4 x y + 1/3 y + x + + 2 4 2 2 + - 1/2 x y - 5/4 x y - 5/3 y , + + 2 4 2 4 2 2 2 + COEFF(0, 0) = 3 x - 5/8 y + 3/4 x y - 5/2 - 15/4 x y + 25/8 y , + + 4 2 2 2 2 2 4 + COEFF(1, 0) = - 1/4 x y + 5/2 x y + 5/4 x y - 5/3 y - 2 x + 1/3 y + + 2 4 2 2 2 4 + - 1/2 x y + 4/3 - x, COEFF(2, 0) = - 5/8 x y + 1/2 x + 1/8 x y + + 2 4 2 2 4 + + 1/8 x y - 5/8 x y + 1/2 x - 1/12 + 5/48 y - 1/48 y , COEFF(-2, 1) = + + 4 2 2 2 2 2 4 + - 1/18 y + 1/12 x y + 1/3 y x - 1/3 x y + 1/3 x y - 1/12 x y + + 3 3 2 4 2 3 + + 1/12 x y + 1/72 y - 1/18 y + 1/72 y - 1/3 x y - 1/12 x y , + + 3 2 4 2 4 + COEFF(-1, 1) = - 2/9 y - 4/3 y x - 1/6 x y + 2/3 x y + 1/3 x y + + 2 2 3 2 3 2 2 4 + + 2/3 x y + 1/3 x y + 8/9 y - 1/6 x y - 4/3 x y + 8/9 y - 2/9 y , + + 3 2 2 2 2 4 4 + COEFF(0, 1) = 5/12 y + 2 x y - 5/3 y - 1/2 x y - 5/3 y + 5/12 y + + 2 3 2 4 2 4 3 + - 1/2 x y + 2 y x , COEFF(1, 1) = - 2/9 y + 1/3 x y + 1/6 x y + + 3 4 2 2 2 2 3 2 + - 2/9 y + 8/9 y + 1/6 x y - 2/3 x y - 4/3 x y + 1/3 x y + 8/9 y + + 2 3 2 + - 4/3 y x - 2/3 x y, COEFF(2, 1) = 1/3 x y - 1/18 y + 1/72 y + 1/3 x y + + 2 3 2 4 2 2 2 2 4 + - 1/12 x y + 1/3 y x + 1/72 y + 1/3 x y - 1/18 y - 1/12 x y + + 4 3 2 2 3 + - 1/12 x y - 1/12 x y , COEFF(-2, 2) = 1/48 x y - 1/24 y x - 1/24 x y + + 2 2 2 2 3 2 4 3 + - 1/48 x y + 1/288 y + 1/144 y + 1/24 x y + 1/48 x y - 1/144 y + + 4 4 3 + + 1/24 x y - 1/288 y - 1/48 x y , COEFF(-1, 2) = - 1/12 x y + 1/9 y + + 4 2 4 2 2 2 4 2 + + 1/24 x y - 1/12 x y - 1/18 y + 1/12 x y + 1/18 y - 1/24 x y + + 2 2 3 3 2 + + 1/6 y x - 1/6 x y - 1/9 y + 1/12 x y , COEFF(0, 2) = 5/48 y + + 2 2 3 4 2 4 2 3 + - 1/8 x y - 5/24 y + 5/24 y - 5/48 y + 1/8 x y + 1/4 x y + + 2 4 2 + - 1/4 y x , COEFF(1, 2) = 1/12 x y + 1/18 y + 1/24 x y - 1/9 y + + 2 2 3 2 2 2 4 2 4 + + 1/6 y x - 1/6 x y + 1/12 x y - 1/18 y - 1/24 x y - 1/12 x y + + 3 3 4 4 2 2 + - 1/12 x y + 1/9 y , COEFF(2, 2) = - 1/288 y + 1/48 x y - 1/48 x y + + 2 2 3 2 4 + + 1/144 y + 1/288 y - 1/48 x y - 1/24 x y - 1/144 y + 1/48 x y + + 2 3 3 2 + + 1/24 x y + 1/24 x y - 1/24 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); +bytes used=268463952, alloc=2817532, time=26.58 +bytes used=269464108, alloc=2817532, time=26.64 +bytes used=270464264, alloc=2817532, time=26.72 +bytes used=271468824, alloc=2817532, time=26.79 +bytes used=272470884, alloc=2817532, time=26.86 +bytes used=273471272, alloc=2817532, time=26.94 +bytes used=274471420, alloc=2817532, time=27.14 +bytes used=275471752, alloc=2817532, time=27.42 +bytes used=276472040, alloc=2817532, time=27.49 +bytes used=277475512, alloc=2817532, time=27.55 +bytes used=278475700, alloc=2817532, time=27.65 +bytes used=279484180, alloc=2817532, time=27.75 +bytes used=280484464, alloc=2817532, time=27.86 +bytes used=281491584, alloc=2817532, time=28.19 +bytes used=282491764, alloc=2817532, time=28.39 +bytes used=283493688, alloc=2817532, time=28.47 +bytes used=284493880, alloc=2817532, time=28.62 +bytes used=285503016, alloc=2817532, time=28.93 +bytes used=286503156, alloc=2817532, time=29.13 +bytes used=287503572, alloc=2817532, time=29.21 +bytes used=288504456, alloc=2817532, time=29.36 +bytes used=289504572, alloc=2817532, time=29.68 +bytes used=290504728, alloc=2817532, time=29.75 +bytes used=291504932, alloc=2817532, time=30.12 +bytes used=292505132, alloc=2817532, time=30.26 +bytes used=293505260, alloc=2817532, time=30.36 +bytes used=294505412, alloc=2817532, time=30.69 +bytes used=295505644, alloc=2817532, time=30.79 +> +# d^2/dxdy +> simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); +bytes used=296505980, alloc=2817532, time=30.89 +bytes used=297506132, alloc=2817532, time=30.96 +bytes used=298506352, alloc=2817532, time=31.03 +1/144 DATA(2, 2) - 1/18 DATA(1, 2) + 1/18 DATA(-1, 2) - 1/18 DATA(2, 1) + + + 1/18 DATA(2, -1) + 4/9 DATA(1, 1) - 1/144 DATA(-2, 2) + 1/18 DATA(-2, 1) + + - 1/18 DATA(-2, -1) - 1/144 DATA(2, -2) + 1/18 DATA(1, -2) + + - 1/18 DATA(-1, -2) + 1/144 DATA(-2, -2) + 4/9 DATA(-1, -1) + + 3 3 + - 4/9 DATA(1, -1) - 4/9 DATA(-1, 1) - 2/3 x y DATA(1, 0) + + 3 3 3 3 3 3 + + 1/6 x y DATA(-2, 0) - 2/3 x y DATA(-1, 0) + 4/9 x y DATA(-1, 1) + + 3 3 3 3 3 3 + + x y DATA(0, 0) - 1/9 x y DATA(2, 1) - 1/9 x y DATA(2, -1) + + + 8/9 x DATA(-1, 1) + 5/24 y DATA(2, 0) - 5/3 y DATA(1, 0) + + - 8/9 x DATA(-1, -1) + 5/3 x DATA(0, -1) - 8/9 x DATA(1, -1) + + 3 3 + + 5/3 y DATA(-1, 0) - 1/72 x DATA(2, 2) + 1/18 x DATA(1, 2) + + 3 3 3 + + 1/18 x DATA(-1, 2) - 1/12 x DATA(0, 2) + 1/72 x DATA(2, -2) + + 3 3 3 + - 1/18 x DATA(1, -2) + 1/12 x DATA(0, -2) - 1/18 x DATA(-1, -2) + + 3 3 3 + + 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) + 2/3 x DATA(0, 1) + + 3 3 + - 4/9 x DATA(1, 1) - 1/72 x DATA(-2, 2) - 5/24 y DATA(-2, 0) + + 3 3 3 3 3 3 + - 2/3 x y DATA(0, 1) + 1/36 x y DATA(-2, 2) - 1/9 x y DATA(-2, 1) + + 3 3 3 3 3 3 + + 4/9 x y DATA(1, 1) + 1/36 x y DATA(2, -2) - 1/9 x y DATA(1, -2) + + 3 3 3 3 3 3 + + 1/6 x y DATA(0, -2) - 1/9 x y DATA(-1, -2) + 1/36 x y DATA(-2, -2) + + 2 2 2 2 2 + + 2/3 x y DATA(-1, -1) + 1/4 x y DATA(1, 1) - 1/16 x y DATA(-2, 2) + + 3 3 3 3 3 3 + - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) + 1/36 x y DATA(2, 2) + + 3 3 3 + + 4/3 x y DATA(1, 0) - 1/12 x y DATA(-2, 0) + 4/3 x y DATA(-1, 0) + + 3 3 3 3 3 + - 5/2 x y DATA(0, 0) + 1/6 x y DATA(2, 0) - 1/9 x y DATA(-2, -1) + + 3 3 3 + + 1/72 x DATA(-2, -2) + 5/3 x y DATA(0, -1) - 5/12 x y DATA(0, 2) + + 3 3 3 3 + + 5/3 x y DATA(0, 1) - 1/12 x y DATA(2, 0) + 4/9 x y DATA(-1, -1) + + 3 3 3 3 + - 2/3 x y DATA(0, -1) - 5/12 x y DATA(0, -2) + 4/9 x DATA(-1, -1) + + 2 2 2 + + 5/4 y x DATA(1, 0) + 5/8 y x DATA(-2, 0) - 5/8 y x DATA(2, 0) + + 2 3 3 + - 5/4 y x DATA(-1, 0) - 5/2 y x DATA(0, 0) - 5/12 y x DATA(2, 0) + + 3 3 3 + + 2/9 y x DATA(-2, 1) + 2/9 y x DATA(-2, -1) - 1/72 y x DATA(2, -2) + + 3 3 3 + - 8/9 y x DATA(1, -1) + 5/3 y x DATA(1, 0) - 5/12 y x DATA(-2, 0) + + 3 3 3 + + 5/3 y x DATA(-1, 0) - 8/9 y x DATA(-1, 1) + 2/9 y x DATA(2, -1) + + 3 3 3 + - 1/12 y x DATA(0, 2) + 4/3 y x DATA(0, 1) - 8/9 y x DATA(1, 1) + + 3 3 3 + - 1/72 y x DATA(-2, 2) - 1/72 y x DATA(-2, -2) - 8/9 y x DATA(-1, -1) + + 3 3 3 + + 4/3 y x DATA(0, -1) + 1/18 y x DATA(1, 2) + 1/18 y x DATA(-1, 2) + + 3 3 2 + - 1/72 y x DATA(2, 2) + 2/9 y x DATA(2, 1) - 1/6 x DATA(2, -1) + + 2 2 2 + - 1/3 x DATA(1, 1) + 1/48 x DATA(-2, 2) - 1/6 x DATA(-2, 1) + + 2 2 2 + + 1/6 x DATA(-2, -1) + 1/48 x DATA(2, -2) - 1/24 x DATA(1, -2) + + 2 2 2 + + 1/24 x DATA(-1, -2) - 1/48 x DATA(-2, -2) - 1/3 x DATA(-1, -1) + + 2 2 2 + + 1/3 x DATA(1, -1) + 1/24 x DATA(1, 2) - 1/24 x DATA(-1, 2) + + 2 2 3 + + 1/6 x DATA(2, 1) - 1/48 x DATA(2, 2) - 2/3 x DATA(0, -1) + + 3 3 3 + + 4/9 x DATA(1, -1) - 4/9 x DATA(-1, 1) + 1/9 x DATA(-2, 1) + + 3 + - 1/9 x DATA(-2, -1) + 5/24 x DATA(0, 2) - 1/18 x DATA(2, 1) + + + 1/18 x DATA(2, -1) - 5/3 x DATA(0, 1) + 8/9 x DATA(1, 1) + + + 1/144 x DATA(-2, 2) - 1/18 x DATA(-2, 1) + 1/18 x DATA(-2, -1) + + - 1/144 x DATA(2, -2) + 1/9 x DATA(1, -2) - 5/24 x DATA(0, -2) + + 2 3 3 + + 5/4 x y DATA(0, 1) + 1/18 y x DATA(1, -2) - 1/12 y x DATA(0, -2) + + 3 2 + + 1/18 y x DATA(-1, -2) - 5/8 x y DATA(0, 2) + 1/9 x DATA(-1, -2) + + 3 2 3 2 3 2 + - 1/2 x y DATA(0, 1) + 1/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 2) + + 3 2 3 2 + - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) + + 3 2 2 2 + - 1/24 x y DATA(2, -2) + 5/8 x y DATA(0, -2) - 5/4 x y DATA(0, -1) + + 3 2 3 2 + - 1/144 x DATA(-2, -2) - 1/4 x y DATA(0, -2) + 1/24 x y DATA(2, 2) + + 3 2 3 2 3 2 + - 1/6 x y DATA(1, 2) - 1/6 x y DATA(-1, 2) + 1/4 x y DATA(0, 2) + + 3 2 3 2 3 2 + - 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) - 1/3 x y DATA(1, -1) + + 2 + + 1/3 x DATA(-1, 1) + 5/24 x y DATA(-2, 0) - 10/3 x y DATA(-1, 0) + + 3 2 3 2 3 2 + + 1/6 x y DATA(1, -2) + 1/6 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) + + 3 2 3 2 3 2 + - 1/3 x y DATA(-1, -1) + 1/2 x y DATA(0, -1) + 1/3 x y DATA(-1, 1) + + + 5/24 x y DATA(2, 0) - 10/3 x y DATA(1, 0) + 1/144 x DATA(2, 2) + + + 25/4 x y DATA(0, 0) + 5/24 x y DATA(0, 2) - 10/3 x y DATA(0, 1) + + 2 3 + + 5/24 x y DATA(0, -2) + 1/4 x y DATA(2, 0) - 10/3 x y DATA(0, -1) + + 2 3 2 3 3 + + 1/2 x y DATA(-1, 0) - 1/2 x y DATA(1, 0) - 2/3 y DATA(-1, 0) + + 3 3 + - 1/9 x DATA(1, 2) - 1/9 x DATA(-1, 2) + 1/6 x y DATA(0, 2) + + 2 3 3 3 + - 1/4 x y DATA(-2, 0) - 1/12 y DATA(2, 0) + 2/3 y DATA(1, 0) + + 3 3 3 2 2 + + 1/12 y DATA(-2, 0) + 4/9 x y DATA(1, -1) - 1/16 x y DATA(2, -2) + + 2 2 2 2 2 2 + + 1/8 x y DATA(1, -2) - 1/8 x y DATA(-1, -2) + 1/16 x y DATA(-2, -2) + + 2 2 2 2 2 2 + + 1/4 x y DATA(-1, -1) - 1/4 x y DATA(1, -1) - 1/4 x y DATA(-1, 1) + + 2 2 2 + + 1/24 y x DATA(1, 2) - 1/24 y x DATA(-1, 2) + 1/3 y x DATA(2, 1) + + 2 2 2 2 + - 1/8 x y DATA(-2, -1) + 1/24 y x DATA(1, -2) - 1/24 y x DATA(-1, -2) + + 2 2 2 + + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) - 2/3 y x DATA(1, 1) + + 2 2 2 + + 1/48 y x DATA(-2, 2) - 1/3 y x DATA(-2, 1) - 1/3 y x DATA(-2, -1) + + 2 2 2 + - 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) - 2/3 y x DATA(1, -1) + + 2 2 2 + + 2/3 y x DATA(-1, 1) + 1/3 y x DATA(2, -1) + 2/3 x y DATA(1, -1) + + 2 2 2 + - 2/3 x y DATA(-1, 1) - 1/24 x y DATA(-2, -1) + 1/48 x y DATA(2, -2) + + 2 2 2 + - 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) + 1/3 x y DATA(1, 2) + + 2 2 2 + + 1/3 x y DATA(-1, 2) + 1/24 x y DATA(2, 1) + 1/48 x y DATA(-2, -2) + + - 1/9 x y DATA(1, 2) - 1/9 x y DATA(-1, 2) - 1/9 x y DATA(2, 1) + + - 1/9 x y DATA(2, -1) + 16/9 x y DATA(1, 1) + 1/144 x y DATA(-2, 2) + + - 1/9 x y DATA(-2, 1) - 1/9 x y DATA(-2, -1) + 1/144 x y DATA(2, -2) + + 2 2 2 + - 2/3 x y DATA(1, 1) + 1/24 x y DATA(-2, 1) - 1/48 x y DATA(-2, 2) + + 2 2 + - 1/24 x y DATA(2, -1) - 1/48 x y DATA(2, 2) + 16/9 x y DATA(-1, 1) + + + 1/144 x y DATA(2, 2) - 1/9 x y DATA(1, -2) - 1/9 x y DATA(-1, -2) + + + 1/144 x y DATA(-2, -2) + 16/9 x y DATA(-1, -1) + 16/9 x y DATA(1, -1) + + 3 3 3 + - 1/72 x y DATA(2, 2) + 1/18 x y DATA(2, -1) - 8/9 x y DATA(1, 1) + + 3 3 3 + - 1/72 x y DATA(-2, 2) + 1/18 x y DATA(-2, 1) - 8/9 x y DATA(-1, 1) + + 3 3 3 + + 2/9 x y DATA(1, 2) + 2/9 x y DATA(-1, 2) + 1/18 x y DATA(2, 1) + + 3 3 3 + + 1/18 x y DATA(-2, -1) - 1/72 x y DATA(2, -2) + 2/9 x y DATA(1, -2) + + 3 3 3 + + 2/9 x y DATA(-1, -2) - 1/72 x y DATA(-2, -2) - 8/9 x y DATA(-1, -1) + + 3 2 3 2 3 + - 8/9 x y DATA(1, -1) + 1/6 x y DATA(-2, 1) - 1/24 x y DATA(-2, -2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, -2) - 1/12 x y DATA(1, -2) - 1/6 x y DATA(2, -1) + + 2 3 2 3 2 3 + + 1/6 x y DATA(-2, -1) + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) + + 2 3 2 3 2 3 + + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) + + 2 3 2 2 2 2 + - 1/6 x y DATA(2, 1) + 1/8 x y DATA(-2, 1) - 1/8 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/8 x y DATA(-1, 2) - 1/8 x y DATA(2, 1) + 1/8 x y DATA(2, -1) + + 2 2 2 3 2 3 + + 1/16 x y DATA(2, 2) + 1/12 x y DATA(-1, -2) - 1/3 x y DATA(-1, -1) + + 2 3 2 3 3 + + 1/3 x y DATA(1, -1) - 1/3 x y DATA(-1, 1) - 1/9 y DATA(-1, -2) + + 3 3 + - 1/9 y DATA(-1, 2) - 1/72 y DATA(2, 2) + 1/9 y DATA(-2, 1) + + 3 + + 1/9 y DATA(-2, -1) + 1/144 y DATA(2, -2) - 4/9 y DATA(1, -1) + + 3 3 3 + + 4/9 y DATA(-1, 1) + 4/9 y DATA(-1, -1) + 1/9 y DATA(1, 2) + + 3 3 3 + + 1/18 y DATA(2, 1) + 1/18 y DATA(2, -1) - 4/9 y DATA(1, 1) + + 3 3 3 + + 1/72 y DATA(-2, 2) - 1/18 y DATA(-2, 1) - 1/18 y DATA(-2, -1) + + 3 3 2 + - 1/72 y DATA(2, -2) + 1/9 y DATA(1, -2) + 1/6 y DATA(1, 2) + + 2 2 2 + - 1/6 y DATA(-1, 2) - 1/48 y DATA(-2, -2) + 1/3 y DATA(1, -1) + + 2 2 2 + + 1/3 y DATA(-1, 1) - 1/3 y DATA(-1, -1) + 1/48 y DATA(-2, 2) + + 2 2 2 + - 1/24 y DATA(-2, 1) - 1/3 y DATA(1, 1) + 1/24 y DATA(-2, -1) + + 2 2 + + 1/48 y DATA(2, -2) - 1/48 y DATA(2, 2) + 1/144 y DATA(2, 2) + + 2 2 + + 1/24 y DATA(2, 1) - 1/24 y DATA(2, -1) - 1/18 y DATA(1, 2) + + + 1/18 y DATA(-1, 2) - 1/9 y DATA(2, 1) - 1/9 y DATA(2, -1) + + 2 + + 8/9 y DATA(1, 1) - 1/144 y DATA(-2, 2) - 1/6 y DATA(1, -2) + + 2 + + 1/6 y DATA(-1, -2) - 1/18 y DATA(1, -2) + 1/18 y DATA(-1, -2) + + - 1/144 y DATA(-2, -2) - 8/9 y DATA(-1, -1) + 8/9 y DATA(1, -1) + + 3 + - 8/9 y DATA(-1, 1) + 1/72 y DATA(-2, -2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=299534960, alloc=2817532, time=31.10 +bytes used=300538760, alloc=2817532, time=31.17 + 3 3 2 2 2 3 +[COEFF(-2, -2) = 1/36 x y - 1/144 y + 1/16 x y + 1/144 x y - 1/24 x y + + 2 2 3 2 3 3 + + 1/48 x y + 1/48 y x - 1/24 x y + 1/72 y + 1/72 x - 1/144 x + + 2 3 3 2 + - 1/48 y - 1/72 x y + 1/144 - 1/72 y x - 1/48 x , COEFF(-1, -2) = + + 2 3 2 2 3 3 + 1/24 x + 1/9 x + 1/6 x y + 1/18 y + 1/12 x y - 1/18 + 2/9 x y + + 2 2 2 2 3 3 3 + - 1/24 y x - 1/9 x y - 1/8 x y - 1/3 x y - 1/9 y - 1/9 x y + + 3 2 3 2 3 + - 1/18 x + 1/6 y + 1/18 y x , COEFF(0, -2) = 5/8 x y - 1/12 y x + + 3 3 3 3 2 3 + - 5/12 x y + 5/24 x y + 1/6 x y - 5/24 x - 1/4 x y + 1/12 x , + + 2 3 2 2 + COEFF(1, -2) = - 1/3 x y + 1/6 x y - 1/6 y - 1/18 y + 1/9 x + + 2 3 2 3 3 3 2 2 + - 1/12 x y + 1/24 y x + 1/18 + 1/18 y x + 1/9 y - 1/18 x + 1/8 x y + + 3 3 2 3 2 2 + - 1/9 x y - 1/24 x - 1/9 x y + 2/9 x y , COEFF(2, -2) = - 1/16 x y + + 3 2 3 2 2 + - 1/72 x y + 1/48 x y + 1/144 x y - 1/24 x y - 1/48 y x - 1/144 x + + 3 2 3 2 3 3 3 + - 1/72 y x + 1/24 x y + 1/48 y - 1/144 - 1/72 y + 1/36 x y + + 3 2 3 3 3 + + 1/72 x + 1/144 y + 1/48 x , COEFF(-2, -1) = - 1/18 - 1/9 x y - 1/9 x + + 3 2 3 2 3 2 3 + - 1/18 y + 1/6 x y + 1/6 x + 1/12 x y - 1/9 x y + 2/9 y x + 1/9 y + + 2 2 3 2 2 2 + - 1/8 x y + 1/18 x y + 1/24 y - 1/24 x y + 1/18 x - 1/3 y x , + + 3 3 3 2 3 + COEFF(-1, -1) = 4/9 x y - 8/9 y x + 16/9 x y + 4/9 - 1/3 x - 8/9 x y + + 3 2 2 3 2 2 + - 1/3 x y - 8/9 x + 2/3 x y + 4/9 x - 8/9 y + 2/3 y x - 1/3 y + + 2 3 3 2 2 3 3 3 + - 1/3 x y + 4/9 y + 1/4 x y , COEFF(0, -1) = - 2/3 x y + 4/3 y x + + 3 3 2 2 3 + + 5/3 x y + 1/2 x y + 5/3 x - 5/4 x y - 10/3 x y - 2/3 x , + + 3 3 3 3 3 3 + COEFF(1, -1) = - 4/9 y - 8/9 x y + 4/9 x - 8/9 x + 4/9 x y - 8/9 y x + + 2 3 2 2 3 2 2 2 + + 1/3 x y + 16/9 x y - 1/4 x y - 1/3 x y + 1/3 y + 1/3 x + 8/9 y + + 2 2 2 3 2 + - 2/3 y x - 4/9 + 2/3 x y , COEFF(2, -1) = 1/3 y x + 1/12 x y + + 3 3 2 2 3 3 + + 2/9 y x + 1/18 y - 1/6 x - 1/9 x y + 1/18 x - 1/24 y - 1/9 x y + + 2 2 2 3 2 3 3 + + 1/18 + 1/8 x y - 1/9 y - 1/6 x y - 1/24 x y + 1/18 x y - 1/9 x , + + 3 3 3 3 2 3 + COEFF(-2, 0) = 1/6 x y - 5/24 y - 5/12 y x - 1/12 x y - 1/4 x y + + 2 3 2 2 3 + + 5/24 x y + 5/8 y x + 1/12 y , COEFF(-1, 0) = - 5/4 y x + 1/2 x y + + 3 3 3 3 3 + + 4/3 x y + 5/3 y x - 10/3 x y - 2/3 y - 2/3 x y + 5/3 y, + + 3 3 3 3 + COEFF(0, 0) = 25/4 x y - 5/2 y x - 5/2 x y + x y , COEFF(1, 0) = + + 2 3 2 3 3 3 3 + - 1/2 x y + 5/4 y x - 5/3 y - 2/3 x y + 5/3 y x + 2/3 y - 10/3 x y + + 3 3 3 2 3 + + 4/3 x y , COEFF(2, 0) = 5/24 y + 1/6 x y + 5/24 x y + 1/4 x y + + 2 3 3 3 2 + - 5/8 y x - 5/12 y x - 1/12 y - 1/12 x y , COEFF(-2, 1) = 1/24 x y + + 2 3 2 2 3 2 3 3 + - 1/3 y x + 2/9 y x + 1/8 x y - 1/12 x y + 1/18 x y - 1/18 y + + 2 2 3 2 3 3 + - 1/9 x y - 1/6 x + 1/18 + 1/6 x y - 1/24 y - 1/9 x y + 1/9 y + + 3 2 2 + + 1/9 x - 1/18 x, COEFF(-1, 1) = 2/3 y x - 4/9 - 8/9 y - 2/3 x y + + 3 2 3 3 3 3 3 2 + - 8/9 x y + 1/3 x + 4/9 y + 16/9 x y - 4/9 x + 4/9 x y + 1/3 x y + + 3 2 2 3 2 2 + - 8/9 y x + 8/9 x + 1/3 y - 1/3 x y - 1/4 x y , COEFF(0, 1) = + + 3 3 2 3 3 3 3 + 4/3 y x - 1/2 x y + 5/3 x y - 2/3 x y - 10/3 x y - 5/3 x + 2/3 x + + 2 3 2 3 2 2 3 + + 5/4 x y , COEFF(1, 1) = - 4/9 x + 1/3 x y + 1/4 x y - 4/9 y + + 2 2 3 2 3 + - 1/3 y + 8/9 y - 1/3 x - 8/9 x y - 2/3 x y - 8/9 y x + 8/9 x + + 2 3 2 3 3 + - 2/3 y x + 1/3 x y + 4/9 x y + 16/9 x y + 4/9, COEFF(2, 1) = - 1/18 + + 3 2 3 2 3 2 2 + + 1/9 x - 1/18 x + 1/24 y - 1/12 x y + 2/9 y x + 1/6 x + 1/24 x y + + 2 3 3 2 2 3 3 3 + - 1/6 x y + 1/18 x y - 1/9 y - 1/8 x y - 1/9 x y + 1/18 y + + 2 2 2 2 + - 1/9 x y + 1/3 y x , COEFF(-2, 2) = - 1/48 x y + 1/48 x + 1/48 y x + + 2 2 2 2 3 + - 1/144 + 1/144 x y + 1/48 y - 1/16 x y - 1/24 x y + 1/144 x + + 3 3 3 3 3 3 2 + - 1/72 x y - 1/144 y - 1/72 x - 1/72 y x + 1/36 x y + 1/24 x y + + 3 2 3 3 2 + + 1/72 y , COEFF(-1, 2) = 1/3 x y - 1/9 y + 1/18 x - 1/24 y x + 1/18 + + 2 2 3 2 2 3 2 3 3 + - 1/24 x + 1/12 x y + 1/8 x y + 2/9 x y - 1/6 y - 1/9 x y + + 3 2 3 + - 1/6 x y - 1/9 x y + 1/18 y - 1/9 x + 1/18 y x , COEFF(0, 2) = 5/24 x + + 2 3 2 3 3 3 3 + - 5/8 x y + 5/24 x y + 1/4 x y + 1/6 x y - 5/12 x y - 1/12 y x + + 3 2 3 2 3 3 + - 1/12 x , COEFF(1, 2) = - 1/12 x y - 1/18 + 1/24 x + 1/18 x + 1/9 y + + 2 3 2 3 2 2 + + 1/6 y + 2/9 x y + 1/24 y x - 1/18 y + 1/18 y x - 1/8 x y - 1/9 x y + + 3 2 3 3 2 3 + - 1/6 x y - 1/9 x y + 1/3 x y - 1/9 x, COEFF(2, 2) = - 1/72 y x + + 3 2 2 2 3 + - 1/72 x - 1/48 x + 1/144 x y + 1/144 - 1/48 y + 1/144 x + 1/24 x y + + 2 3 2 2 2 3 2 3 + - 1/48 y x - 1/72 x y + 1/16 x y - 1/48 x y + 1/24 x y - 1/72 y + + 3 3 + + 1/36 x y + 1/144 y] + +> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); +bytes used=301539208, alloc=2817532, time=31.25 +bytes used=302539400, alloc=2817532, time=31.32 +bytes used=303539592, alloc=2817532, time=31.40 +bytes used=304557648, alloc=2817532, time=31.44 +bytes used=305571464, alloc=2817532, time=31.54 +bytes used=306581776, alloc=2817532, time=31.63 +bytes used=307582028, alloc=2817532, time=31.71 +bytes used=308582248, alloc=2817532, time=31.78 +bytes used=309582476, alloc=2817532, time=32.18 +bytes used=310582696, alloc=2817532, time=32.25 +bytes used=311582884, alloc=2817532, time=32.32 +bytes used=312583056, alloc=2817532, time=32.42 +bytes used=313583260, alloc=2817532, time=32.51 +bytes used=314583428, alloc=2817532, time=32.60 +bytes used=315583596, alloc=2817532, time=32.70 +bytes used=316593332, alloc=2817532, time=33.09 +bytes used=317593536, alloc=2817532, time=33.32 +bytes used=318593748, alloc=2817532, time=33.39 +bytes used=319593964, alloc=2817532, time=33.51 +bytes used=320594120, alloc=2817532, time=33.69 +bytes used=321594408, alloc=2817532, time=34.06 +bytes used=322594856, alloc=2817532, time=34.26 +bytes used=323595080, alloc=2817532, time=34.33 +bytes used=324595308, alloc=2817532, time=34.46 +bytes used=325595460, alloc=2817532, time=34.65 +bytes used=326595828, alloc=2817532, time=35.02 +bytes used=327596080, alloc=2817532, time=35.09 +bytes used=328596388, alloc=2817532, time=35.22 +bytes used=329596548, alloc=2817532, time=35.63 +bytes used=330596860, alloc=2817532, time=35.76 +bytes used=331597036, alloc=2817532, time=35.86 +bytes used=332597196, alloc=2817532, time=36.29 +bytes used=333597480, alloc=2817532, time=36.41 +> +# d^2/dy^2 +> simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); +bytes used=334597656, alloc=2817532, time=36.56 +bytes used=335597820, alloc=2817532, time=36.64 +bytes used=336597976, alloc=2817532, time=36.70 +- 1/12 DATA(0, 2) - 5/2 DATA(0, 0) + 4/3 DATA(0, 1) - 1/12 DATA(0, -2) + + 3 4 4 + + 5/12 x DATA(1, 0) - 5/8 x DATA(0, 0) + 5/12 x DATA(-1, 0) + + 4 4 4 + - 5/48 x DATA(2, 0) + 5/12 x DATA(1, 0) + 1/72 x DATA(1, 2) + + 4 4 4 + + 1/72 x DATA(-1, 2) + 1/18 x DATA(2, 1) - 1/48 x DATA(0, 2) + + 3 3 + - 5/12 x DATA(-1, 0) + 5/24 x DATA(-2, 0) + 1/2 y DATA(0, 2) + + 4 4 4 + + 1/3 x DATA(0, -1) - 1/48 x DATA(0, -2) + 1/3 x DATA(0, 1) + + 4 4 4 + + 1/72 x DATA(1, -2) - 1/288 x DATA(2, -2) + 1/18 x DATA(-2, -1) + + 4 3 2 4 + - 5/48 x DATA(-2, 0) - 5/24 x DATA(2, 0) - 1/2 y x DATA(0, -1) + + 2 4 2 4 2 4 + - 1/2 y x DATA(0, 1) + 1/8 y x DATA(0, -2) + 1/48 y x DATA(2, -2) + + 2 4 2 4 2 4 + - 1/12 y x DATA(-2, -1) + 1/8 y x DATA(-2, 0) - 1/12 y x DATA(1, -2) + + 3 2 3 2 + + 1/4 x y DATA(2, 0) + 5/24 x DATA(2, 0) - 1/2 x y DATA(1, 0) + + 3 2 2 2 2 2 + + 1/2 x y DATA(-1, 0) - 5/8 x y DATA(0, 2) - 5/8 x y DATA(0, -2) + + 2 2 2 2 2 2 + - 15/4 x y DATA(0, 0) + 5/2 x y DATA(0, 1) - 1/8 x y DATA(-2, 0) + + 2 2 2 4 2 4 + + 5/2 x y DATA(0, -1) + 1/3 y x DATA(-1, -1) - 1/12 y x DATA(-1, -2) + + 2 4 2 4 2 4 + + 1/3 y x DATA(-1, 1) + 1/48 y x DATA(-2, -2) - 1/2 y x DATA(-1, 0) + + 2 4 2 4 2 4 + + 1/3 y x DATA(1, -1) + 1/3 y x DATA(1, 1) - 1/2 y x DATA(1, 0) + + 2 4 2 4 2 4 + + 1/8 y x DATA(2, 0) - 1/12 y x DATA(-2, 1) + 1/48 y x DATA(-2, 2) + + 2 2 4 2 4 + - 2 x y DATA(-1, 0) + 1/48 y x DATA(2, 2) - 1/12 y x DATA(2, -1) + + 2 2 2 2 2 2 + + 2 x y DATA(-1, 0) + 2 x y DATA(1, 0) - 1/8 x y DATA(2, 0) + + 2 + - 5/3 x DATA(1, 0) + 4/3 DATA(0, -1) + 2 x y DATA(1, 0) + + 2 2 4 + + 1/4 x y DATA(-2, 0) - 1/4 x y DATA(2, 0) - 2/9 x DATA(-1, -1) + + 2 4 4 + - 5/4 y x DATA(0, -1) - 1/288 x DATA(2, 2) + 1/72 x DATA(-1, -2) + + 4 4 4 + - 2/9 x DATA(1, -1) - 2/9 x DATA(-1, 1) - 2/9 x DATA(1, 1) + + 4 4 2 + - 1/288 x DATA(-2, 2) - 1/288 x DATA(-2, -2) + 5/8 y x DATA(0, -2) + + 2 + + 5/4 y x DATA(0, 1) - 1/2 y DATA(0, -2) - y DATA(0, 1) + + 2 2 + - 5/8 y x DATA(0, 2) + y DATA(0, -1) + 1/2 y DATA(0, 2) + + 2 2 2 + + 1/2 y DATA(0, -2) - 2 y DATA(0, 1) - 2 y DATA(0, -1) + + 4 4 4 + + 1/6 y x DATA(-1, 1) + 1/12 y x DATA(-1, -2) - 1/8 y x DATA(0, -2) + + 2 2 2 + + 3 y DATA(0, 0) - 5/3 x DATA(1, 0) + 5/48 x DATA(0, 2) + + 2 2 2 + - 5/3 x DATA(0, -1) + 5/48 x DATA(0, -2) - 5/3 x DATA(0, 1) + + 2 4 4 + + 25/8 x DATA(0, 0) - 1/6 y x DATA(-1, -1) - 1/48 y x DATA(-2, -2) + + 2 4 4 + + 5/48 x DATA(-2, 0) + 1/48 y x DATA(-2, 2) + 1/6 y x DATA(1, 1) + + 4 4 4 + + 1/4 y x DATA(0, -1) + 1/24 y x DATA(-2, -1) + 1/12 y x DATA(1, -2) + + 2 2 4 + - 5/3 x DATA(-1, 0) + 5/48 x DATA(2, 0) - 1/48 y x DATA(2, -2) + + 4 3 2 + - 1/24 y x DATA(-2, 1) - 1/4 x y DATA(-2, 0) - 5/24 x DATA(-2, 0) + + 4 4 4 + + 1/48 y x DATA(2, 2) + 1/18 x DATA(-2, 1) + 1/18 x DATA(2, -1) + + 4 4 4 + - 1/24 y x DATA(2, 1) + 1/8 y x DATA(0, 2) - 1/4 y x DATA(0, 1) + + 4 4 2 4 + + 1/24 y x DATA(2, -1) - 1/6 y x DATA(1, -1) - 1/12 y x DATA(-1, 2) + + 2 4 2 4 + - 1/12 y x DATA(1, 2) + 5/3 x DATA(-1, 0) + 3/4 y x DATA(0, 0) + + 2 4 2 4 4 + + 1/8 y x DATA(0, 2) - 1/12 y x DATA(2, 1) - 1/12 y x DATA(-1, 2) + + 4 + - 1/12 y x DATA(1, 2) - 8/9 x DATA(-1, 1) - 8/9 x DATA(-1, -1) + + 3 3 + + 8/9 x DATA(1, -1) - 1/144 x DATA(2, 2) + 1/72 x DATA(1, 2) + + 3 3 3 + - 1/72 x DATA(-1, 2) - 1/144 x DATA(2, -2) + 1/72 x DATA(1, -2) + + 3 3 3 + - 1/72 x DATA(-1, -2) + 1/9 x DATA(2, 1) + 1/9 x DATA(2, -1) + + 3 3 2 + - 2/9 x DATA(1, 1) + 1/144 x DATA(-2, 2) + 4/3 x y DATA(-1, -1) + + 2 2 2 2 3 + - 4/3 x y DATA(1, 1) - 1/48 x y DATA(-2, 2) + 1/144 x DATA(-2, -2) + + 3 3 3 + + 2/9 x DATA(-1, -1) + 1/12 y x DATA(-2, 1) - 1/12 y x DATA(-2, -1) + + 3 3 3 + - 1/24 y x DATA(2, -2) - 1/6 y x DATA(1, -1) - 1/6 y x DATA(-1, 1) + + 3 3 3 + + 1/12 y x DATA(2, -1) + 1/6 y x DATA(1, 1) - 1/24 y x DATA(-2, 2) + + 3 3 3 + + 1/24 y x DATA(-2, -2) + 1/6 y x DATA(-1, -1) - 1/12 y x DATA(1, 2) + + 3 3 3 + + 1/12 y x DATA(-1, 2) + 1/24 y x DATA(2, 2) - 1/12 y x DATA(2, 1) + + 2 2 2 + - 1/18 x DATA(2, -1) + 8/9 x DATA(1, 1) + 1/288 x DATA(-2, 2) + + 2 2 2 + - 1/18 x DATA(-2, 1) - 1/18 x DATA(-2, -1) + 1/288 x DATA(2, -2) + + 2 2 2 + - 1/18 x DATA(1, -2) - 1/18 x DATA(-1, -2) + 1/288 x DATA(-2, -2) + + 2 2 2 + + 8/9 x DATA(-1, -1) + 8/9 x DATA(1, -1) - 1/18 x DATA(1, 2) + + 2 2 2 + - 1/18 x DATA(-1, 2) - 1/18 x DATA(2, 1) + 1/288 x DATA(2, 2) + + 3 3 3 + - 2/9 x DATA(1, -1) + 2/9 x DATA(-1, 1) - 1/9 x DATA(-2, 1) + + 3 + - 1/9 x DATA(-2, -1) - 1/9 x DATA(2, 1) - 1/9 x DATA(2, -1) + + + 8/9 x DATA(1, 1) - 1/144 x DATA(-2, 2) + 1/9 x DATA(-2, 1) + + + 1/9 x DATA(-2, -1) + 1/144 x DATA(2, -2) - 1/18 x DATA(1, -2) + + 3 3 + + 1/12 y x DATA(1, -2) - 1/12 y x DATA(-1, -2) + 1/18 x DATA(-1, -2) + + 3 2 3 2 3 2 + + 1/3 x y DATA(1, 1) - 1/24 x y DATA(-2, 2) + 1/6 x y DATA(-2, 1) + + 3 2 3 2 + + 1/6 x y DATA(-2, -1) + 1/24 x y DATA(2, -2) - 1/144 x DATA(-2, -2) + + 3 2 3 2 3 2 + + 1/24 x y DATA(2, 2) - 1/12 x y DATA(1, 2) + 1/12 x y DATA(-1, 2) + + 3 2 3 2 3 2 + - 1/6 x y DATA(2, 1) - 1/6 x y DATA(2, -1) + 1/3 x y DATA(1, -1) + + 2 3 2 3 2 + + 8/9 x DATA(-1, 1) - 1/12 x y DATA(1, -2) + 1/12 x y DATA(-1, -2) + + 3 2 3 2 3 2 + - 1/24 x y DATA(-2, -2) - 1/3 x y DATA(-1, -1) - 1/3 x y DATA(-1, 1) + + + 1/144 x DATA(2, 2) - 1/18 x DATA(1, 2) + 1/18 x DATA(-1, 2) + + 2 2 2 2 2 2 + - 1/48 x y DATA(2, -2) + 1/3 x y DATA(1, -2) + 1/3 x y DATA(-1, -2) + + 2 2 2 2 2 2 + - 1/48 x y DATA(-2, -2) - 4/3 x y DATA(-1, -1) - 4/3 x y DATA(1, -1) + + 2 2 2 2 + - 4/3 x y DATA(-1, 1) + 1/3 y x DATA(1, 2) + 1/3 y x DATA(-1, 2) + + 2 2 2 2 + + 1/24 y x DATA(2, 1) + 1/12 x y DATA(-2, -1) - 1/3 y x DATA(1, -2) + + 2 2 2 + - 1/3 y x DATA(-1, -2) + 1/48 y x DATA(-2, -2) - 1/48 y x DATA(2, 2) + + 2 2 2 + - 2/3 y x DATA(1, 1) - 1/48 y x DATA(-2, 2) + 1/24 y x DATA(-2, 1) + + 2 2 2 + - 1/24 y x DATA(-2, -1) + 1/48 y x DATA(2, -2) + 2/3 y x DATA(-1, -1) + + 2 2 2 + + 2/3 y x DATA(1, -1) - 2/3 y x DATA(-1, 1) - 1/24 y x DATA(2, -1) + + 2 2 2 + - 4/3 x y DATA(1, -1) + 4/3 x y DATA(-1, 1) - 1/6 x y DATA(-2, -1) + + 2 2 2 + - 1/24 x y DATA(2, -2) + 1/3 x y DATA(1, -2) - 1/3 x y DATA(-1, -2) + + 2 2 2 + + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) + 1/6 x y DATA(2, 1) + + 2 + + 1/24 x y DATA(-2, -2) + 1/3 x y DATA(1, 2) - 1/3 x y DATA(-1, 2) + + + 1/12 x y DATA(2, 1) - 1/12 x y DATA(2, -1) - 2/3 x y DATA(1, 1) + + + 1/24 x y DATA(-2, 2) - 1/12 x y DATA(-2, 1) + 1/12 x y DATA(-2, -1) + + 2 2 + + 1/24 x y DATA(2, -2) - 4/3 x y DATA(1, 1) - 1/6 x y DATA(-2, 1) + + 2 2 2 + + 1/24 x y DATA(-2, 2) + 1/6 x y DATA(2, -1) - 1/24 x y DATA(2, 2) + + + 2/3 x y DATA(-1, 1) - 1/24 x y DATA(2, 2) - 1/3 x y DATA(1, -2) + + + 1/3 x y DATA(-1, -2) - 1/24 x y DATA(-2, -2) - 2/3 x y DATA(-1, -1) + + 2 2 2 2 + + 2/3 x y DATA(1, -1) + 1/12 x y DATA(-2, 1) + 1/3 x y DATA(1, 2) + + 2 2 2 2 2 2 + + 1/3 x y DATA(-1, 2) + 1/12 x y DATA(2, 1) + 1/12 x y DATA(2, -1) + + 2 2 + - 1/48 x y DATA(2, 2) + +> coeffs_as_lc_of_data(%, posn_list_2d_size5); +bytes used=337598236, alloc=2817532, time=36.76 +bytes used=338598536, alloc=2817532, time=36.83 + 3 2 2 4 +[COEFF(-2, -2) = 1/144 x - 1/48 x y - 1/24 x y - 1/144 x - 1/48 y x + + 2 2 3 2 2 2 4 3 + + 1/48 y x + 1/288 x - 1/24 x y + 1/24 x y + 1/48 y x + 1/24 y x + + 4 3 2 4 2 2 + - 1/288 x , COEFF(-1, -2) = - 1/72 x - 1/3 y x + 1/72 x + 1/3 x y + + 3 2 2 3 2 2 4 + - 1/12 y x - 1/18 x + 1/3 x y - 1/3 x y + 1/12 x y - 1/12 y x + + 4 2 2 4 4 + + 1/18 x + 1/12 y x , COEFF(0, -2) = 5/8 y x + 1/8 y x - 1/8 y x + + 4 2 2 2 2 + - 1/48 x + 5/48 x + 1/2 y - 5/8 x y - 1/12 - 1/2 y, COEFF(1, -2) = + + 2 4 2 2 3 3 + - 1/18 x + 1/72 x + 1/3 x y - 1/3 x y + 1/12 y x - 1/18 x + 1/72 x + + 2 4 2 3 2 2 4 + - 1/12 y x - 1/3 y x - 1/12 x y + 1/3 x y + 1/12 y x , COEFF(2, -2) + + 2 4 2 2 2 + = - 1/24 x y - 1/48 y x + 1/288 x + 1/144 x - 1/48 x y + 1/24 x y + + 3 3 2 3 2 2 4 4 + - 1/144 x - 1/24 y x + 1/48 y x + 1/24 x y + 1/48 y x - 1/288 x , + + 4 3 2 2 2 + COEFF(-2, -1) = 1/12 x y + 1/18 x - 1/9 x + 1/12 x y - 1/24 y x + + 4 2 4 2 3 3 2 + + 1/24 y x - 1/12 y x - 1/18 x - 1/12 y x + 1/6 x y + 1/9 x + + 2 4 3 2 2 2 + - 1/6 x y , COEFF(-1, -1) = - 2/9 x - 1/3 x y + 8/9 x + 2/3 y x + + 4 2 4 3 3 2 2 2 + - 1/6 y x + 1/3 y x + 1/6 y x + 2/9 x - 4/3 x y - 8/9 x + 4/3 x y + + 2 4 2 2 2 + - 2/3 x y, COEFF(0, -1) = 4/3 - 1/2 y x + y - 5/3 x - 5/4 y x - 2 y + + 4 4 2 2 4 4 + + 1/4 y x + 1/3 x + 5/2 x y , COEFF(1, -1) = 8/9 x - 1/6 y x - 2/9 x + + 2 4 2 2 3 2 3 + + 1/3 y x - 4/3 x y + 2/3 y x + 1/3 x y - 2/9 x + 2/3 x y + + 2 2 2 3 3 2 + - 4/3 x y + 8/9 x - 1/6 y x , COEFF(2, -1) = 1/9 x + 1/6 x y - 1/9 x + + 2 3 4 2 2 3 2 + - 1/18 x + 1/12 y x + 1/24 y x + 1/12 x y - 1/6 x y - 1/12 x y + + 4 2 4 2 2 2 3 2 + + 1/18 x - 1/12 y x - 1/24 y x , COEFF(-2, 0) = - 1/8 x y - 1/4 x y + + 3 2 4 2 4 2 + + 5/24 x + 1/8 y x + 1/4 x y - 5/48 x - 5/24 x + 5/48 x , + + 3 2 2 2 2 4 2 4 + COEFF(-1, 0) = 1/2 x y + 2 x y + 5/3 x - 5/3 x + 5/12 x - 1/2 y x + + 3 2 + - 5/12 x - 2 x y , + + 2 2 4 2 4 2 2 + COEFF(0, 0) = 25/8 x - 5/2 + 3 y - 5/8 x + 3/4 y x - 15/4 x y , + + 2 4 2 2 2 2 3 2 3 + COEFF(1, 0) = - 1/2 y x + 2 x y + 2 x y - 5/3 x - 1/2 x y + 5/12 x + + 4 4 3 2 2 4 + + 5/12 x - 5/3 x, COEFF(2, 0) = - 5/48 x + 1/4 x y + 1/8 y x + + 2 2 2 2 3 + - 1/8 x y - 1/4 x y + 5/48 x - 5/24 x + 5/24 x, COEFF(-2, 1) = + + 3 2 2 4 3 + - 1/9 x + 1/12 x y - 1/12 x y + 1/9 x - 1/24 y x + 1/12 y x + + 2 2 2 4 2 4 3 2 + + 1/24 y x - 1/18 x - 1/12 y x - 1/6 x y + 1/18 x + 1/6 x y , + + 4 2 3 4 + COEFF(-1, 1) = 2/3 x y + 1/6 y x - 2/3 y x - 1/6 y x - 2/9 x + + 2 4 3 2 2 3 2 2 2 + + 1/3 y x + 2/9 x + 8/9 x - 8/9 x + 4/3 x y - 1/3 x y - 4/3 x y , + + 2 2 4 2 4 4 + COEFF(0, 1) = -2 y + 4/3 - 1/2 y x + 5/4 y x + 1/3 x - 1/4 y x - y + + 2 2 2 2 3 4 + + 5/2 x y - 5/3 x , COEFF(1, 1) = - 2/3 y x - 2/3 x y - 2/9 x - 2/9 x + + 4 2 2 2 3 2 4 + + 8/9 x + 1/6 y x - 4/3 x y - 4/3 x y + 1/6 y x + 1/3 y x + + 3 2 2 2 2 4 2 + + 1/3 x y + 8/9 x , COEFF(2, 1) = 1/12 x y + 1/18 x - 1/18 x + + 2 4 2 4 3 3 2 + - 1/12 y x + 1/6 x y - 1/24 y x + 1/12 x y + 1/9 x - 1/6 x y + + 3 2 2 2 + - 1/9 x - 1/12 y x + 1/24 y x , COEFF(-2, 2) = 1/24 x y + 1/288 x + + 3 2 4 4 3 + + 1/24 x y + 1/144 x + 1/48 y x - 1/144 x + 1/48 y x - 1/24 y x + + 4 2 2 2 3 2 + - 1/288 x - 1/48 y x - 1/48 x y - 1/24 x y , COEFF(-1, 2) = - 1/3 x y + + 2 2 2 3 2 2 2 4 3 + - 1/3 x y + 1/3 x y + 1/12 x y + 1/3 y x - 1/12 y x - 1/72 x + + 2 4 3 4 + + 1/18 x - 1/18 x + 1/72 x + 1/12 y x - 1/12 y x , COEFF(0, 2) = + + 4 2 4 2 2 4 2 2 + - 1/48 x - 5/8 y x + 1/2 y + 1/8 y x + 1/2 y + 1/8 y x - 5/8 x y + + 2 3 2 2 2 + + 5/48 x - 1/12, COEFF(1, 2) = - 1/12 x y + 1/3 x y + 1/3 x y + + 2 4 4 3 3 2 + + 1/3 x y + 1/72 x - 1/12 y x - 1/12 y x + 1/72 x - 1/18 x + + 2 2 4 3 + + 1/3 y x - 1/18 x - 1/12 y x , COEFF(2, 2) = - 1/24 x y - 1/144 x + + 2 2 3 2 4 2 3 2 + - 1/48 x y + 1/24 x y - 1/288 x - 1/48 y x + 1/24 y x + 1/288 x + + 4 2 2 4 + + 1/48 y x + 1/144 x - 1/24 x y + 1/48 y x ] + +> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", +> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); +bytes used=339598688, alloc=2817532, time=36.92 +bytes used=340598856, alloc=2817532, time=36.99 +bytes used=341599544, alloc=2817532, time=37.04 +bytes used=342609588, alloc=2817532, time=37.12 +bytes used=343617792, alloc=2817532, time=37.21 +bytes used=344618020, alloc=2817532, time=37.30 +bytes used=345618228, alloc=2817532, time=37.79 +bytes used=346618720, alloc=2817532, time=37.87 +bytes used=347618880, alloc=2817532, time=37.94 +bytes used=348623292, alloc=2817532, time=38.03 +bytes used=349623484, alloc=2817532, time=38.12 +bytes used=350623648, alloc=2817532, time=38.22 +bytes used=351625036, alloc=2817532, time=38.32 +bytes used=352625232, alloc=2817532, time=38.73 +bytes used=353625668, alloc=2817532, time=38.91 +bytes used=354625832, alloc=2817532, time=38.99 +bytes used=355626060, alloc=2817532, time=39.14 +bytes used=356630912, alloc=2817532, time=39.56 +bytes used=357631128, alloc=2817532, time=39.78 +bytes used=358631348, alloc=2817532, time=39.86 +bytes used=359632096, alloc=2817532, time=40.02 +bytes used=360632268, alloc=2817532, time=40.42 +bytes used=361632468, alloc=2817532, time=40.49 +bytes used=362632652, alloc=2817532, time=40.71 +bytes used=363633064, alloc=2817532, time=41.09 +bytes used=364633244, alloc=2817532, time=41.18 +bytes used=365633400, alloc=2817532, time=41.60 +bytes used=366633640, alloc=2817532, time=41.81 +> +################################################################################ +> quit +bytes used=367598444, alloc=2817532, time=41.95 |