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Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log')
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diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log b/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log deleted file mode 100644 index 84b0264..0000000 --- a/src/GeneralizedPolynomial-Uniform/Lagrange-maximum-degree/2d.log +++ /dev/null @@ -1,4728 +0,0 @@ - |\^/| Maple 7 (IBM INTEL LINUX) -._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc. - \ MAPLE / All rights reserved. Maple is a registered trademark of - <____ ____> Waterloo Maple Inc. - | Type ? for help. -# util.maple -- misc utility routines -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/util.maple,v 1.4 2002/08/20 16:46:06 jthorn Exp $ -> -# -# fix_rationals - convert numbers to RATIONAL() calls -# nonmatching_names - find names in a list which *don't* have a specified prefix -# sprint_numeric_list - convert a numeric list to a valid C identifier suffix -# print_name_list_dcl - print C declarations for a list of names -# -# hypercube_points - compute all (integer) points in an N-dimensional hypercube -# -# ftruncate - truncate a file to zero length -# -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function converts all {integer, rational} subexpressions of its -# input except integer exponents and -1 factors in products, into function -# calls -# RATIONAL(num,den) -# This is useful in conjunction with the C() library function, since -# -# C( (1/3) * foo * bar ) -# t0 = foo*bar/3; -# -# generates a (slow) division (and runs the risk of mixed-mode-arithmetic -# problems), while -# -# C((1.0/3.0) * foo * bar); -# t0 = 0.3333333333*foo*bar; -# -# suffers from roundoff error. With this function, -# -# fix_rationals((1/3) * foo * bar); -# RATIONAL(1,3) foo bar -# C(%); -# t0 = RATIONAL(1.0,3.0)*foo*bar; -# -# which a C preprocessor macro can easily convert to the desired -# -# t0 = (1.0/3.0)*foo*bar; -# -# Additionally, this function can be told to leave certain types of -# subexpressions unconverged. For example, -# fix_rationals(expr, type, specfunc(integer, DATA)); -# will leave all subexpressions of the form DATA(integer arguments) -# unconverted. -# -# Arguments: -# expr = (in) The expression to be converted. -# inert_fn = (optional in) -# If specified, this argument should be a Boolean procedure -# or the name of a Boolean procedure. This procedure should -# take one or more argument, and return true if and only if -# the first argument should *not* be converted, i.e. if we -# should leave this expression unchanged. See the last -# example above. -# ... = (optional in) -# Any further arguments are passed as additional arguments to -# the inert_fn procedure. -# -> fix_rationals := -> proc( -> expr::{ -> algebraic, name = algebraic, -> list({algebraic, name = algebraic}), -> set ({algebraic, name = algebraic}) -> }, -> inert_fn::{name, procedure} -> ) -> local nn, k, -> base, power, fbase, fpower, -> fn, fn_args_list, -> num, den, mult; -> -# do we want to convert this expression? -> if ((nargs >= 2) and inert_fn(expr, args[3..nargs])) -> then return expr; -> end if; -> -# recurse over lists and sets -> if (type(expr, {list,set})) -> then return map(fix_rationals, expr, args[2..nargs]); -> end if; -> -# recurse over equation right hand sides -> if (type(expr, name = algebraic)) -> then return ( lhs(expr) = fix_rationals(rhs(expr), args[2..nargs]) ); -> end if; -> -# recurse over functions other than RATIONAL() -> if (type(expr, function)) -> then -> fn := op(0, expr); -> if (fn <> 'RATIONAL') -> then -> fn_args_list := [op(expr)]; -> fn_args_list := map(fix_rationals, fn_args_list, args[2..nargs]); -> fn; return '%'( op(fn_args_list) ); -> end if; -> end if; -> -> nn := nops(expr); -> -# recurse over sums -> if (type(expr, `+`)) -> then return sum('fix_rationals(op(k,expr), args[2..nargs])', 'k'=1..nn); -> end if; -> -# recurse over products -# ... leaving leading -1 factors intact, i.e. not converted to RATIONAL(-1,1) -> if (type(expr, `*`)) -> then -> if (op(1, expr) = -1) -> then return -1*fix_rationals(remove(type, expr, 'identical(-1)'), -> args[2..nargs]); -> else return product('fix_rationals(op(k,expr), args[2..nargs])', -> 'k'=1..nn); -> end if; -> end if; -> -# recurse over powers -# ... leaving integer exponents intact -> if (type(expr, `^`)) -> then -> base := op(1, expr); -> power := op(2, expr); -> -> fbase := fix_rationals(base, args[2..nargs]); -> if (type(power, integer)) -> then fpower := power; -> else fpower := fix_rationals(power, args[2..nargs]); -> end if; -> return fbase ^ fpower; -> end if; -> -# fix integers and fractions -> if (type(expr, integer)) -> then return 'RATIONAL'(expr, 1); -> end if; -> if (type(expr, fraction)) -> then -> num := op(1, expr); -> den := op(2, expr); -> -> return 'RATIONAL'(num, den); -> end if; -> -# turn Maple floating-point into integer fraction, then recursively fix that -> if (type(expr, float)) -> then -> mult := op(1, expr); -> power := op(2, expr); -> return fix_rationals(mult * 10^power, args[2..nargs]); -> end if; -> -# identity op on names -> if (type(expr, name)) -> then return expr; -> end if; -> -# unknown type -> error "%0", -> "unknown type for expr!", -> " whattype(expr) = ", whattype(expr), -> " expr = ", expr; -> end proc; -fix_rationals := proc(expr::{algebraic, name = algebraic, -list({algebraic, name = algebraic}), set({algebraic, name = algebraic})}, -inert_fn::{procedure, name}) -local nn, k, base, power, fbase, fpower, fn, fn_args_list, num, den, mult; - if 2 <= nargs and inert_fn(expr, args[3 .. nargs]) then return expr - end if; - if type(expr, {set, list}) then - return map(fix_rationals, expr, args[2 .. nargs]) - end if; - if type(expr, name = algebraic) then - return lhs(expr) = fix_rationals(rhs(expr), args[2 .. nargs]) - end if; - if type(expr, function) then - fn := op(0, expr); - if fn <> 'RATIONAL' then - fn_args_list := [op(expr)]; - fn_args_list := - map(fix_rationals, fn_args_list, args[2 .. nargs]); - fn; - return '%'(op(fn_args_list)) - end if - end if; - nn := nops(expr); - if type(expr, `+`) then return - sum('fix_rationals(op(k, expr), args[2 .. nargs])', 'k' = 1 .. nn) - end if; - if type(expr, `*`) then - if op(1, expr) = -1 then return -fix_rationals( - remove(type, expr, 'identical(-1)'), args[2 .. nargs]) - else return product('fix_rationals(op(k, expr), args[2 .. nargs])', - 'k' = 1 .. nn) - end if - end if; - if type(expr, `^`) then - base := op(1, expr); - power := op(2, expr); - fbase := fix_rationals(base, args[2 .. nargs]); - if type(power, integer) then fpower := power - else fpower := fix_rationals(power, args[2 .. nargs]) - end if; - return fbase^fpower - end if; - if type(expr, integer) then return 'RATIONAL'(expr, 1) end if; - if type(expr, fraction) then - num := op(1, expr); den := op(2, expr); return 'RATIONAL'(num, den) - end if; - if type(expr, float) then - mult := op(1, expr); - power := op(2, expr); - return fix_rationals(mult*10^power, args[2 .. nargs]) - end if; - if type(expr, name) then return expr end if; - error "%0", "unknown type for expr!", " whattype(expr) = ", - whattype(expr), " expr = ", expr -end proc - -> -################################################################################ -> -# -# This function finds names in a list which *don't* have a specified prefix. -# -# Arguments: -# name_list = A list of the names. -# prefix = The prefix we want to filter out. -# -# Results: -# This function returns the subset list of names which don't have the -# specified prefix. -# -> nonmatching_names := -> proc( name_list::list({name,string}), prefix::{name,string} ) -> -> select( proc(n) -> evalb(not StringTools[IsPrefix](prefix,n)); -> end proc -> , -> name_list -> ); -> end proc; -nonmatching_names := proc( -name_list::list({name, string}), prefix::{name, string}) - select(proc(n) evalb(not StringTools[IsPrefix](prefix, n)) end proc, - name_list) -end proc - -> -################################################################################ -> -# -# This function converts a numeric list to a string which is a valid -# C identifier suffix: elements are separated by "_", decimal points are -# replaced by "x", and all nonzero values have explicit +/- signs, which -# are replaced by "p"/"m". -# -# For example, [0,-3.5,+4] --> "0_m3x5_p4". -# -> sprint_numeric_list := -> proc(nlist::list(numeric)) -> -# generate preliminary string, eg "+0_-3.5_+4" -> map2(sprintf, "%+a", nlist); -> ListTools[Join](%, "_"); -> cat(op(%)); -> -# fixup bad characters -> StringTools[SubstituteAll](%, "+0", "0"); -> StringTools[CharacterMap](".+-", "xpm", %); -> -> return %; -> end proc; -sprint_numeric_list := proc(nlist::list(numeric)) - map2(sprintf, "%+a", nlist); - ListTools[Join](%, "_"); - cat(op(%)); - StringTools[SubstituteAll](%, "+0", "0"); - StringTools[CharacterMap](".+-", "xpm", %); - return % -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C declarations for a list of names. -# -# Argument: -# name_list = A list of the names. -# type_name = The C type of the names, eg. "double". -# file_name = The file name to write the declaration to. This is -# truncated before writing. -# -> print_name_list_dcl := -> proc( name_list::list({name,string}), -> type_name::string, -> file_name::string ) -> local blanks, separator_string; -> -> ftruncate(file_name); -> -> map( -> proc(var::{name,string}) -> fprintf(file_name, -> "%s %s;\n", -> type_name, var); -> end proc -> , -> name_list -> ); -> -> fclose(file_name); -> NULL; -> end proc; -print_name_list_dcl := proc( -name_list::list({name, string}), type_name::string, file_name::string) -local blanks, separator_string; - ftruncate(file_name); - map(proc(var::{name, string}) - fprintf(file_name, "%s %s;\n", type_name, var) - end proc, name_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes a list of all the (integer) points in an -# N-dimensional hypercube, in lexicographic order. The present -# implementation requires N <= 4. -# -# Arguments: -# cmin,cmax = N-element lists of cube minimum/maximum coordinates. -# -# Results: -# The function returns a set of d-element lists giving the coordinates. -# For example, -# hypercube([0,0], [2,1] -# returns -# { [0,0], [0,1], [1,0], [1,1], [2,0], [2,1] } -> hypercube_points := -> proc(cmin::list(integer), cmax::list(integer)) -> local N, i,j,k,l; -> -> N := nops(cmin); -> if (nops(cmax) <> N) -> then error -> "must have same number of dimensions for min and max coordinates!"; -> fi; -> -> if (N = 1) -> then return [seq([i], i=cmin[1]..cmax[1])]; -> elif (N = 2) -> then return [ -> seq( -> seq([i,j], j=cmin[2]..cmax[2]), -> i=cmin[1]..cmax[1]) -> ]; -> elif (N = 3) -> then return [ -> seq( -> seq( -> seq([i,j,k], k=cmin[3]..cmax[3]), -> j=cmin[2]..cmax[2] ), -> i=cmin[1]..cmax[1]) -> ]; -> elif (N = 4) -> then return [ -> seq( -> seq( -> seq( -> seq([i,j,k,l], l=cmin[4]..cmax[4]), -> k=cmin[3]..cmax[3] ), -> j=cmin[2]..cmax[2]), -> i=cmin[1]..cmax[1]) -> ]; -> else -> error "implementation restriction: must have N <= 4, got %1!", N; -> fi; -> end proc; -hypercube_points := proc(cmin::list(integer), cmax::list(integer)) -local N, i, j, k, l; - N := nops(cmin); - if nops(cmax) <> N then error - "must have same number of dimensions for min and max coordinates!" - end if; - if N = 1 then return [seq([i], i = cmin[1] .. cmax[1])] - elif N = 2 then return - [seq(seq([i, j], j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] - elif N = 3 then return [seq( - seq(seq([i, j, k], k = cmin[3] .. cmax[3]), j = cmin[2] .. cmax[2]) - , i = cmin[1] .. cmax[1])] - elif N = 4 then return [seq(seq(seq( - seq([i, j, k, l], l = cmin[4] .. cmax[4]), k = cmin[3] .. cmax[3]), - j = cmin[2] .. cmax[2]), i = cmin[1] .. cmax[1])] - else error "implementation restriction: must have N <= 4, got %1!", N - end if -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function truncates a file to 0 length if it exists, or creates -# it at that length if it doesn't exist. -# -# Arguments: -# file_name = (in) The name of the file. -# -> ftruncate := -> proc(file_name::string) -> fopen(file_name, 'WRITE'); -> fclose(%); -> NULL; -> end proc; -ftruncate := - - proc(file_name::string) fopen(file_name, 'WRITE'); fclose(%); NULL end proc - -# interpolate.maple -- compute interpolation formulas/coefficients -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/interpolate.maple,v 1.10 2002/08/28 11:31:09 jthorn Exp $ -> -# -# <<<representation of numbers, data values, etc>>> -# Lagrange_polynomial_interpolant - compute Lagrange polynomial interpolant -# Hermite_polynomial_interpolant - compute Hermite polynomial interpolant -# coeffs_as_lc_of_data - coefficients of ... (linear combination of data) -# -# print_coeffs__lc_of_data - print C code to compute coefficients -# print_fetch_data - print C code to fetch input array chunk into struct data -# print_store_coeffs - print C code to store struct coeffs "somewhere" -# print_interp_cmpt__lc_of_data - print C code for computation of interpolant -# -# coeff_name - name of coefficient of data at a given [m] coordinate -# data_var_name - name of variable storing data value at a given [m] coordinate -# -> -################################################################################ -> -# -# ***** representation of numbers, data values, etc ***** -# -# We use RATIONAL(p.0,q.0) to denote the rational number p/q. -# -# We use DATA(...) to represent the data values being interpolated at a -# specified [m] coordinate, where the arguments are the [m] coordinates. -# -# We use COEFF(...) to represent the molecule coefficient at a specified -# [m] coordinate, where the arguments are the [m] coordinates. -# -# For example, the usual 1-D centered 2nd order 1st derivative molecule -# would be written -# RATIONAL(-1.0,2.0)*DATA(-1) + RATIONA(1.0,2.0)*DATA(1) -# and its coefficients as -# COEFF(-1) = RATIONAL(-1.0,2.0) -# COEFF(1) = RATIONAL(1.0,2.0) -# -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes a Lagrange polynomial interpolant in any -# number of dimensions. -# -# Arguments: -# fn = The interpolation function. This should be a procedure in the -# coordinates, having the coefficients as global variables. For -# example, -# proc(x,y) c00 + c10*x + c01*y end proc -# coeff_list = A set of the interpolation coefficients (coefficients in -# the interpolation function), for example [c00, c10, c01]. -# coord_list = A list of the coordinates (independent variables in the -# interpolation function), for example [x,y]. -# posn_list = A list of positions (each a list of numeric values) where the -# interpolant is to use data, for example hypercube([0,0], [1,1]). -# Any positions may be used; if they're redundant (as in the -# example) the least-squares interpolant is computed. -# -# Results: -# This function returns the interpolating polynomial, in the form of -# an algebraic expression in the coordinates and the data values. -# -> Lagrange_polynomial_interpolant := -> proc( -> fn::procedure, coeff_list::list(name), -> coord_list::list(name), posn_list::list(list(numeric)) -> ) -> local posn, data_eqns, coeff_eqns; -> -# coefficients of interpolating polynomial -> data_eqns := { seq( fn(op(posn))='DATA'(op(posn)) , posn=posn_list ) }; -> coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); -> if (has(coeff_eqns, '_t')) -> then error "interpolation coefficients aren't uniquely determined!"; -> end if; -> -# interpolant as a polynomial in the coordinates -> return subs(coeff_eqns, eval(fn))(op(coord_list)); -> end proc; -Lagrange_polynomial_interpolant := proc(fn::procedure, coeff_list::list(name), -coord_list::list(name), posn_list::list(list(numeric))) -local posn, data_eqns, coeff_eqns; - data_eqns := {seq(fn(op(posn)) = 'DATA'(op(posn)), posn = posn_list)}; - coeff_eqns := linalg[leastsqrs](data_eqns, {op(coeff_list)}); - if has(coeff_eqns, '_t') then - error "interpolation coefficients aren't uniquely determined!" - end if; - return subs(coeff_eqns, eval(fn))(op(coord_list)) -end proc - -> -################################################################################ -> -# -# This function computes a Hermite polynomial interpolant in any -# number of dimensions. This is a polynomial which -# * has values which match the given data DATA() at a specified set of -# points, and -# * has derivatives which match the specified finite-difference derivatives -# of the given data DATA() at a specified set of points -# -# For the derivative matching, we actually match all possible products -# of 1st derivatives, i.e. in 2-D we match dx, dy, and dxy, in 3-D we -# match dx, dy, dz, dxy, dxz, dyz, and dxyz, etc etc. -# -# Arguments: -# fn = The interpolation function. This should be a procedure in the -# coordinates, having the coefficients as global variables. For -# example, -# proc(x,y) -# + c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 -# + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 -# + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y -# + c00 + c10*x + c20*x^2 + c30*x^3 -# end proc; -# coeff_set = A set of the interpolation coefficients (coefficients in -# the interpolation function), for example -# { -# c03, c13, c23, c33, -# c02, c12, c22, c32, -# c01, c11, c21, c31, -# c00, c10, c20, c30 -# } -# coord_list = A list of the coordinates (independent variables in the -# interpolation function), for example [x,y]. -# deriv_set = A set of equations of the form -# {coords} = proc -# giving the derivatives which are to be matched, and the -# procedures to compute their finite-difference approximations. -# Each procedure should take N_dims integer arguments specifying -# an evaluation point, and return a suitable linear combination -# of the DATA() for the derivative at that point. For example -# { -# {x} = proc(i::integer, j::integer) -# - 1/2*DATA(i-1,j) + 1/2*DATA(i+1,j) -# end proc -# , -# {y} = proc(i::integer, j::integer) -# - 1/2*DATA(i,j-1) + 1/2*DATA(i,j+1) -# end proc -# , -# {x,y} = proc(i::integer, j::integer) -# - 1/4*DATA(i-1,j+1) + 1/4*DATA(i+1,j+1) -# + 1/4*DATA(i-1,j-1) - 1/4*DATA(i+1,j-1) -# end proc -# } -# fn_posn_set = A set of positions (each a list of numeric values) -# where the interpolant is to match the given data DATA(), -# for example -# {[0,0], [0,1], [1,0], [1,1]} -# deriv_posn_set = A list of positions (each a list of numeric values) -# where the interpolant is to match the derivatives -# specified by deriv_set , for example -# {[0,0], [0,1], [1,0], [1,1]} -# -# Results: -# This function returns the interpolating polynomial, in the form of -# an algebraic expression in the coordinates and the data values. -# -> Hermite_polynomial_interpolant := -> proc( -> fn::procedure, -> coeff_set::set(name), -> coord_list::list(name), -> deriv_set::set(set(name) = procedure), -> fn_posn_set::set(list(numeric)), -> deriv_posn_set::set(list(numeric)) -> ) -> local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; -> -> -# -# compute a set of equations -# {fn(posn) = DATA(posn)} -# giving the function values to be matched -# -> fn_eqnset := map( -> # return equation that fn(posn) = DATA(posn) -> proc(posn::list(integer)) -> fn(op(posn)) = 'DATA'(op(posn)); -> end proc -> , -> fn_posn_set -> ); -> -> -# -# compute a set of equations -# { diff(fn,coords)(posn) = DERIV(coords)(posn) } -# giving the derivative values to be matched, where DERIV(coords) -# is a placeholder for the appropriate derivative -# -> map( -> # return set of equations for this particular derivative -> proc(deriv_coords::set(name)) -> local deriv_fn; -> fn(op(coord_list)); -> diff(%, op(deriv_coords)); -> deriv_fn := unapply(%, op(coord_list)); -> map( -> proc(posn::list(integer)) -> deriv_fn(op(posn)) = 'DERIV'(op(deriv_coords))(op(posn)); -> end proc -> , -> deriv_posn_set -> ); -> end proc -> , -> map(lhs, deriv_set) -> ); -> deriv_eqnset := `union`(op(%)); -> -> -# -# solve overall set of equations for coefficients -# in terms of DATA() and DERIV() values -# -> coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); -> if (indets(map(rhs,%)) <> {}) -> then error "no unique solution for coefficients -- %1 eqns for %2 coeffs", -> nops(fn_eqnset union deriv_eqnset), -> nops(coeff_set); -> fi; -> -> -# -# compute a set of substitution equations -# {'DERIV'(coords) = procedure} -# -> subs_eqnset := map( -> proc(eqn::set(name) = procedure) -> 'DERIV'(op(lhs(eqn))) = rhs(eqn); -> end proc -> , -> deriv_set -> ); -> -> -# -# compute the coefficients in terms of the DATA() values -# -> subs(subs_eqnset, coeff_eqns); -> eval(%); -> -# -# compute the interpolant as a polynomial in the coordinates -# -> subs(%, fn(op(coord_list))); -> end proc; -Hermite_polynomial_interpolant := proc(fn::procedure, coeff_set::set(name), -coord_list::list(name), deriv_set::set(set(name) = procedure), -fn_posn_set::set(list(numeric)), deriv_posn_set::set(list(numeric))) -local fn_eqnset, deriv_eqnset, coeff_eqns, subs_eqnset; - fn_eqnset := map( - proc(posn::list(integer)) fn(op(posn)) = 'DATA'(op(posn)) end proc, - fn_posn_set); - map(proc(deriv_coords::set(name)) - local deriv_fn; - fn(op(coord_list)); - diff(%, op(deriv_coords)); - deriv_fn := unapply(%, op(coord_list)); - map(proc(posn::list(integer)) - deriv_fn(op(posn)) = - 'DERIV'(op(deriv_coords))(op(posn)) - end proc, deriv_posn_set) - end proc, map(lhs, deriv_set)); - deriv_eqnset := `union`(op(%)); - coeff_eqns := solve[linear](fn_eqnset union deriv_eqnset, coeff_set); - if indets(map(rhs, %)) <> {} then error - "no unique solution for coefficients -- %1 eqns for %2 coeffs", - nops(fn_eqnset union deriv_eqnset), nops(coeff_set) - end if; - subs_eqnset := map(proc(eqn::(set(name) = procedure)) - 'DERIV'(op(lhs(eqn))) = rhs(eqn) - end proc, deriv_set); - subs(subs_eqnset, coeff_eqns); - eval(%); - subs(%, fn(op(coord_list))) -end proc - -> -################################################################################ -> -# -# This function takes as input an interpolating polynomial, expresses -# it as a linear combination of the data values, and returns the coefficeints -# of that form. -# -# Arguments: -# interpolant = The interpolating polynomial (an algebraic expression -# in the coordinates and the data values). -# posn_list = The same list of data positions used in the interpolant. -# -# Results: -# This function returns the coefficients, as a list of equations of the -# form COEFF(...) = value , where each value is a polynomial in the -# coordinates. The order of the list matches that of posn_list. -# -> coeffs_as_lc_of_data := -> proc( -> interpolant::algebraic, -> posn_list::list(list(numeric)) -> ) -> local data_list, interpolant_as_lc_of_data; -> -# interpolant as a linear combination of the data values -> data_list := [ seq( 'DATA'(op(posn)) , posn=posn_list ) ]; -> interpolant_as_lc_of_data := collect(interpolant, data_list); -> -# coefficients of the data values in the linear combination -> return map( -> proc(posn::list(numeric)) -> coeff(interpolant_as_lc_of_data, DATA(op(posn))); -> 'COEFF'(op(posn)) = %; -> end proc -> , -> posn_list -> ); -> end proc; -coeffs_as_lc_of_data := proc( -interpolant::algebraic, posn_list::list(list(numeric))) -local data_list, interpolant_as_lc_of_data; - data_list := [seq('DATA'(op(posn)), posn = posn_list)]; - interpolant_as_lc_of_data := collect(interpolant, data_list); - return map(proc(posn::list(numeric)) - coeff(interpolant_as_lc_of_data, DATA(op(posn))); - 'COEFF'(op(posn)) = % - end proc, posn_list) -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function prints C expressions for the coefficients of an -# interpolating polynomial. (The polynomial is expressed as linear -# combinations of the data values with coefficients which are -# RATIONAL(p,q) calls.) -# -# Arguments: -# coeff_list = A list of the coefficients, as returned from -# coeffs_as_lc_of_data() . -# coeff_name_prefix = A prefix string for the coefficient names. -# temp_name_type = The C type to be used for Maple-introduced temporary -# names, eg. "double". -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_coeffs__lc_of_data := -> proc( coeff_list::list(specfunc(numeric,COEFF) = algebraic), -> coeff_name_prefix::string, -> temp_name_type::string, -> file_name::string ) -> global `codegen/C/function/informed`; -> local coeff_list2, cmpt_list, temp_name_list; -> -# convert LHS of each equation from a COEFF() call (eg COEFF(-1,+1)) -# to a Maple/C variable name (eg coeff_I_m1_p1) -> coeff_list2 := map( -> proc(coeff_eqn::specfunc(numeric,COEFF) = algebraic) -> local posn; -> posn := [op(lhs(coeff_eqn))]; -> coeff_name(posn,coeff_name_prefix); -> convert(%, name); # codegen[C] wants LHS -> # to be an actual Maple *name* -> % = fix_rationals(rhs(coeff_eqn)); -> end proc -> , -> coeff_list -> ); -> -# -# generate the C code -# -> -# tell codegen[C] not to warn about unknown RATIONAL() and DATA() "fn calls" -# via undocumented :( global table -> `codegen/C/function/informed`['RATIONAL'] := true; -> `codegen/C/function/informed`['DATA'] := true; -> -> ftruncate(file_name); -> -# optimized computation sequence for all the coefficients -# (may use local variables t0,t1,t2,...) -> cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; -> -# list of the t0,t1,t2,... local variables -> temp_name_list := nonmatching_names(map(lhs,cmpt_list), coeff_name_prefix); -> -# declare the t0,t1,t2,... local variables (if there are any) -> if (nops(temp_name_list) > 0) -> then print_name_list_dcl(%, temp_name_type, file_name); -> fi; -> -# now print the optimized computation sequence -> codegen[C](cmpt_list, filename=file_name); -> -> fclose(file_name); -> -> NULL; -> end proc; -print_coeffs__lc_of_data := proc( -coeff_list::list(specfunc(numeric, COEFF) = algebraic), -coeff_name_prefix::string, temp_name_type::string, file_name::string) -local coeff_list2, cmpt_list, temp_name_list; -global `codegen/C/function/informed`; - coeff_list2 := map(proc( - coeff_eqn::(specfunc(numeric, COEFF) = algebraic)) - local posn; - posn := [op(lhs(coeff_eqn))]; - coeff_name(posn, coeff_name_prefix); - convert(%, name); - % = fix_rationals(rhs(coeff_eqn)) - end proc, coeff_list); - `codegen/C/function/informed`['RATIONAL'] := true; - `codegen/C/function/informed`['DATA'] := true; - ftruncate(file_name); - cmpt_list := [codegen[optimize](coeff_list2, tryhard)]; - temp_name_list := - nonmatching_names(map(lhs, cmpt_list), coeff_name_prefix); - if 0 < nops(temp_name_list) then - print_name_list_dcl(%, temp_name_type, file_name) - end if; - codegen[C](cmpt_list, filename = file_name); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C expression to assign the data-value -# variables, eg -# data->data_m1_p1 = DATA(-1,1); -# -# Arguments: -# posn_list = The same list of positions as was used to compute the -# interpolating polynomial. -# data_var_name_prefix = A prefix string for the data variable names. -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_fetch_data := -> proc( -> posn_list::list(list(numeric)), -> data_var_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> map( -> proc(posn::list(numeric)) -> fprintf(file_name, -> "%s = %a;\n", -> data_var_name(posn,data_var_name_prefix), -> DATA(op(posn))); -> end proc -> , -> posn_list -> ); -> fclose(file_name); -> -> NULL; -> end proc; -print_fetch_data := proc(posn_list::list(list(numeric)), -data_var_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - fprintf(file_name, "%s = %a;\n", - data_var_name(posn, data_var_name_prefix), DATA(op(posn))) - end proc, posn_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a sequence of C expression to store the interpolation -# coefficients in COEFF(...) expressions, eg -# COEFF(1,-1) = factor * coeffs->coeff_p1_m1; -# -# Arguments: -# posn_list = The list of positions in the molecule. -# coeff_name_prefix = A prefix string for the coefficient names, -# eg "factor * coeffs->coeff_" -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_store_coeffs := -> proc( -> posn_list::list(list(numeric)), -> coeff_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> map( -> proc(posn::list(numeric)) -> fprintf(file_name, -> "%a = %s;\n", -> 'COEFF'(op(posn)), -> coeff_name(posn,coeff_name_prefix)); -> end proc -> , -> posn_list -> ); -> fclose(file_name); -> -> NULL; -> end proc; -print_store_coeffs := proc(posn_list::list(list(numeric)), -coeff_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - fprintf(file_name, "%a = %s;\n", 'COEFF'(op(posn)), - coeff_name(posn, coeff_name_prefix)) - end proc, posn_list); - fclose(file_name); - NULL -end proc - -> -################################################################################ -> -# -# This function prints a C expression to evaluate a molecule, i.e. -# to compute the molecule as a linear combination of the data values. -# -# Arguments: -# posn_list = The list of positions in the molecule. -# coeff_name_prefix = A prefix string for the coefficient names. -# data_var_name_prefix = A prefix string for the data variable names. -# file_name = The file name to write the coefficients to. This is -# truncated before writing. -# -> print_evaluate_molecule := -> proc( -> posn_list::list(list(numeric)), -> coeff_name_prefix::string, -> data_var_name_prefix::string, -> file_name::string -> ) -> -> ftruncate(file_name); -> -# list of "coeff*data_var" terms -> map( -> proc(posn::list(numeric)) -> sprintf("%s*%s", -> coeff_name(posn,coeff_name_prefix), -> data_var_name(posn,data_var_name_prefix)); -> end proc -> , -> posn_list -> ); -> -> ListTools[Join](%, "\n + "); -> cat(op(%)); -> fprintf(file_name, " %s;\n", %); -> -> fclose(file_name); -> -> NULL; -> end proc; -print_evaluate_molecule := proc(posn_list::list(list(numeric)), -coeff_name_prefix::string, data_var_name_prefix::string, file_name::string) - ftruncate(file_name); - map(proc(posn::list(numeric)) - sprintf("%s*%s", coeff_name(posn, coeff_name_prefix), - data_var_name(posn, data_var_name_prefix)) - end proc, posn_list); - ListTools[Join](%, "\n + "); - cat(op(%)); - fprintf(file_name, " %s;\n", %); - fclose(file_name); - NULL -end proc - -> -################################################################################ -################################################################################ -################################################################################ -> -# -# This function computes the name of the coefficient of the data at a -# given [m] position, i.e. it encapsulates our naming convention for this. -# -# Arguments: -# posn = (in) The [m] coordinates. -# name_prefix = A prefix string for the coefficient name. -# -# Results: -# The function returns the coefficient, as a Maple string. -# -> coeff_name := -> proc(posn::list(numeric), name_prefix::string) -> cat(name_prefix, sprint_numeric_list(posn)); -> end proc; -coeff_name := proc(posn::list(numeric), name_prefix::string) - cat(name_prefix, sprint_numeric_list(posn)) -end proc - -> -################################################################################ -> -# -# This function computes the name of the variable in which the C code -# will store the input data at a given [m] position, i.e. it encapsulates -# our naming convention for this. -# -# Arguments: -# posn = (in) The [m] coordinates. -# name_prefix = A prefix string for the variable name. -# -# Results: -# The function returns the variable name, as a Maple string. -# -> data_var_name := -> proc(posn::list(numeric), name_prefix::string) -> cat(name_prefix, sprint_numeric_list(posn)); -> end proc; -data_var_name := proc(posn::list(numeric), name_prefix::string) - cat(name_prefix, sprint_numeric_list(posn)) -end proc - -# Maple code to compute lists of point positions in hypercube-shaped molecules -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/common/cube_posns.maple,v 1.3 2002/08/20 16:56:41 jthorn Exp $ -> -################################################################################ -> -# -# 1D interpolation points -# -> posn_list_1d_size2 := hypercube_points([ 0], [+1]); - posn_list_1d_size2 := [[0], [1]] - -> posn_list_1d_size3 := hypercube_points([-1], [+1]); - posn_list_1d_size3 := [[-1], [0], [1]] - -> posn_list_1d_size4 := hypercube_points([-1], [+2]); - posn_list_1d_size4 := [[-1], [0], [1], [2]] - -> posn_list_1d_size5 := hypercube_points([-2], [+2]); - posn_list_1d_size5 := [[-2], [-1], [0], [1], [2]] - -> posn_list_1d_size6 := hypercube_points([-2], [+3]); - posn_list_1d_size6 := [[-2], [-1], [0], [1], [2], [3]] - -> posn_list_1d_size7 := hypercube_points([-3], [+3]); - posn_list_1d_size7 := [[-3], [-2], [-1], [0], [1], [2], [3]] - -> -################################################################################ -> -# -# 2D interpolation points (Fortran ordering) -# -> posn_list_2d_size2 := map(ListTools[Reverse], -> hypercube_points([ 0, 0], [+1,+1])); - posn_list_2d_size2 := [[0, 0], [1, 0], [0, 1], [1, 1]] - -> posn_list_2d_size3 := map(ListTools[Reverse], -> hypercube_points([-1,-1], [+1,+1])); -posn_list_2d_size3 := [[-1, -1], [0, -1], [1, -1], [-1, 0], [0, 0], [1, 0], - - [-1, 1], [0, 1], [1, 1]] - -> posn_list_2d_size4 := map(ListTools[Reverse], -> hypercube_points([-1,-1], [+2,+2])); -posn_list_2d_size4 := [[-1, -1], [0, -1], [1, -1], [2, -1], [-1, 0], [0, 0], - - [1, 0], [2, 0], [-1, 1], [0, 1], [1, 1], [2, 1], [-1, 2], [0, 2], [1, 2], - - [2, 2]] - -> posn_list_2d_size5 := map(ListTools[Reverse], -> hypercube_points([-2,-2], [+2,+2])); -posn_list_2d_size5 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [-2, -1], - - [-1, -1], [0, -1], [1, -1], [2, -1], [-2, 0], [-1, 0], [0, 0], [1, 0], - - [2, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], [-2, 2], [-1, 2], [0, 2], - - [1, 2], [2, 2]] - -> posn_list_2d_size6 := map(ListTools[Reverse], -> hypercube_points([-2,-2], [+3,+3])); -posn_list_2d_size6 := [[-2, -2], [-1, -2], [0, -2], [1, -2], [2, -2], [3, -2], - - [-2, -1], [-1, -1], [0, -1], [1, -1], [2, -1], [3, -1], [-2, 0], [-1, 0], - - [0, 0], [1, 0], [2, 0], [3, 0], [-2, 1], [-1, 1], [0, 1], [1, 1], [2, 1], - - [3, 1], [-2, 2], [-1, 2], [0, 2], [1, 2], [2, 2], [3, 2], [-2, 3], [-1, 3], - - [0, 3], [1, 3], [2, 3], [3, 3]] - -> -################################################################################ -> -# -# 3D interpolation points (Fortran ordering) -# -> posn_list_3d_size2 := map(ListTools[Reverse], -> hypercube_points([ 0, 0, 0], [+1,+1,+1])); -posn_list_3d_size2 := [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], - - [1, 0, 1], [0, 1, 1], [1, 1, 1]] - -> posn_list_3d_size3 := map(ListTools[Reverse], -> hypercube_points([-1,-1,-1], [+1,+1,+1])); -posn_list_3d_size3 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [-1, 0, -1], - - [0, 0, -1], [1, 0, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], [-1, -1, 0], - - [0, -1, 0], [1, -1, 0], [-1, 0, 0], [0, 0, 0], [1, 0, 0], [-1, 1, 0], - - [0, 1, 0], [1, 1, 0], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [-1, 0, 1], - - [0, 0, 1], [1, 0, 1], [-1, 1, 1], [0, 1, 1], [1, 1, 1]] - -> posn_list_3d_size4 := map(ListTools[Reverse], -> hypercube_points([-1,-1,-1], [+2,+2,+2])); -posn_list_3d_size4 := [[-1, -1, -1], [0, -1, -1], [1, -1, -1], [2, -1, -1], - - [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [-1, 1, -1], [0, 1, -1], - - [1, 1, -1], [2, 1, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], - - [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-1, 0, 0], [0, 0, 0], - - [1, 0, 0], [2, 0, 0], [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], - - [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [-1, -1, 1], [0, -1, 1], - - [1, -1, 1], [2, -1, 1], [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], - - [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [-1, 2, 1], [0, 2, 1], - - [1, 2, 1], [2, 2, 1], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], - - [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-1, 1, 2], [0, 1, 2], - - [1, 1, 2], [2, 1, 2], [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2]] - -> posn_list_3d_size5 := map(ListTools[Reverse], -> hypercube_points([-2,-2,-2], [+2,+2,+2])); -posn_list_3d_size5 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], - - [2, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], [1, -1, -2], - - [2, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], [1, 0, -2], [2, 0, -2], - - [-2, 1, -2], [-1, 1, -2], [0, 1, -2], [1, 1, -2], [2, 1, -2], [-2, 2, -2], - - [-1, 2, -2], [0, 2, -2], [1, 2, -2], [2, 2, -2], [-2, -2, -1], [-1, -2, -1], - - [0, -2, -1], [1, -2, -1], [2, -2, -1], [-2, -1, -1], [-1, -1, -1], - - [0, -1, -1], [1, -1, -1], [2, -1, -1], [-2, 0, -1], [-1, 0, -1], [0, 0, -1], - - [1, 0, -1], [2, 0, -1], [-2, 1, -1], [-1, 1, -1], [0, 1, -1], [1, 1, -1], - - [2, 1, -1], [-2, 2, -1], [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], - - [-2, -2, 0], [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [-2, -1, 0], - - [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [-2, 0, 0], [-1, 0, 0], - - [0, 0, 0], [1, 0, 0], [2, 0, 0], [-2, 1, 0], [-1, 1, 0], [0, 1, 0], - - [1, 1, 0], [2, 1, 0], [-2, 2, 0], [-1, 2, 0], [0, 2, 0], [1, 2, 0], - - [2, 2, 0], [-2, -2, 1], [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], - - [-2, -1, 1], [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [-2, 0, 1], - - [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [-2, 1, 1], [-1, 1, 1], - - [0, 1, 1], [1, 1, 1], [2, 1, 1], [-2, 2, 1], [-1, 2, 1], [0, 2, 1], - - [1, 2, 1], [2, 2, 1], [-2, -2, 2], [-1, -2, 2], [0, -2, 2], [1, -2, 2], - - [2, -2, 2], [-2, -1, 2], [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], - - [-2, 0, 2], [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [-2, 1, 2], - - [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [-2, 2, 2], [-1, 2, 2], - - [0, 2, 2], [1, 2, 2], [2, 2, 2]] - -> posn_list_3d_size6 := map(ListTools[Reverse], -> hypercube_points([-2,-2,-2], [+3,+3,+3])); -posn_list_3d_size6 := [[-2, -2, -2], [-1, -2, -2], [0, -2, -2], [1, -2, -2], - - [2, -2, -2], [3, -2, -2], [-2, -1, -2], [-1, -1, -2], [0, -1, -2], - - [1, -1, -2], [2, -1, -2], [3, -1, -2], [-2, 0, -2], [-1, 0, -2], [0, 0, -2], - - [1, 0, -2], [2, 0, -2], [3, 0, -2], [-2, 1, -2], [-1, 1, -2], [0, 1, -2], - - [1, 1, -2], [2, 1, -2], [3, 1, -2], [-2, 2, -2], [-1, 2, -2], [0, 2, -2], - - [1, 2, -2], [2, 2, -2], [3, 2, -2], [-2, 3, -2], [-1, 3, -2], [0, 3, -2], - - [1, 3, -2], [2, 3, -2], [3, 3, -2], [-2, -2, -1], [-1, -2, -1], [0, -2, -1], - - [1, -2, -1], [2, -2, -1], [3, -2, -1], [-2, -1, -1], [-1, -1, -1], - - [0, -1, -1], [1, -1, -1], [2, -1, -1], [3, -1, -1], [-2, 0, -1], - - [-1, 0, -1], [0, 0, -1], [1, 0, -1], [2, 0, -1], [3, 0, -1], [-2, 1, -1], - - [-1, 1, -1], [0, 1, -1], [1, 1, -1], [2, 1, -1], [3, 1, -1], [-2, 2, -1], - - [-1, 2, -1], [0, 2, -1], [1, 2, -1], [2, 2, -1], [3, 2, -1], [-2, 3, -1], - - [-1, 3, -1], [0, 3, -1], [1, 3, -1], [2, 3, -1], [3, 3, -1], [-2, -2, 0], - - [-1, -2, 0], [0, -2, 0], [1, -2, 0], [2, -2, 0], [3, -2, 0], [-2, -1, 0], - - [-1, -1, 0], [0, -1, 0], [1, -1, 0], [2, -1, 0], [3, -1, 0], [-2, 0, 0], - - [-1, 0, 0], [0, 0, 0], [1, 0, 0], [2, 0, 0], [3, 0, 0], [-2, 1, 0], - - [-1, 1, 0], [0, 1, 0], [1, 1, 0], [2, 1, 0], [3, 1, 0], [-2, 2, 0], - - [-1, 2, 0], [0, 2, 0], [1, 2, 0], [2, 2, 0], [3, 2, 0], [-2, 3, 0], - - [-1, 3, 0], [0, 3, 0], [1, 3, 0], [2, 3, 0], [3, 3, 0], [-2, -2, 1], - - [-1, -2, 1], [0, -2, 1], [1, -2, 1], [2, -2, 1], [3, -2, 1], [-2, -1, 1], - - [-1, -1, 1], [0, -1, 1], [1, -1, 1], [2, -1, 1], [3, -1, 1], [-2, 0, 1], - - [-1, 0, 1], [0, 0, 1], [1, 0, 1], [2, 0, 1], [3, 0, 1], [-2, 1, 1], - - [-1, 1, 1], [0, 1, 1], [1, 1, 1], [2, 1, 1], [3, 1, 1], [-2, 2, 1], - - [-1, 2, 1], [0, 2, 1], [1, 2, 1], [2, 2, 1], [3, 2, 1], [-2, 3, 1], - - [-1, 3, 1], [0, 3, 1], [1, 3, 1], [2, 3, 1], [3, 3, 1], [-2, -2, 2], - - [-1, -2, 2], [0, -2, 2], [1, -2, 2], [2, -2, 2], [3, -2, 2], [-2, -1, 2], - - [-1, -1, 2], [0, -1, 2], [1, -1, 2], [2, -1, 2], [3, -1, 2], [-2, 0, 2], - - [-1, 0, 2], [0, 0, 2], [1, 0, 2], [2, 0, 2], [3, 0, 2], [-2, 1, 2], - - [-1, 1, 2], [0, 1, 2], [1, 1, 2], [2, 1, 2], [3, 1, 2], [-2, 2, 2], - - [-1, 2, 2], [0, 2, 2], [1, 2, 2], [2, 2, 2], [3, 2, 2], [-2, 3, 2], - - [-1, 3, 2], [0, 3, 2], [1, 3, 2], [2, 3, 2], [3, 3, 2], [-2, -2, 3], - - [-1, -2, 3], [0, -2, 3], [1, -2, 3], [2, -2, 3], [3, -2, 3], [-2, -1, 3], - - [-1, -1, 3], [0, -1, 3], [1, -1, 3], [2, -1, 3], [3, -1, 3], [-2, 0, 3], - - [-1, 0, 3], [0, 0, 3], [1, 0, 3], [2, 0, 3], [3, 0, 3], [-2, 1, 3], - - [-1, 1, 3], [0, 1, 3], [1, 1, 3], [2, 1, 3], [3, 1, 3], [-2, 2, 3], - - [-1, 2, 3], [0, 2, 3], [1, 2, 3], [2, 2, 3], [3, 2, 3], [-2, 3, 3], - - [-1, 3, 3], [0, 3, 3], [1, 3, 3], [2, 3, 3], [3, 3, 3]] - -# Maple code to define Lagrange interpolating functions/coords/coeffs -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple,v 1.2 2002/08/20 16:31:24 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 -# -> -> fn_2d_order1 := -> proc(x,y) -> + c01*y -> + c00 + c10*x -> end proc; - fn_2d_order1 := proc(x, y) c01*y + c00 + c10*x end proc - -> -> fn_2d_order2 := -> proc(x,y) -> + c02*y^2 -> + c01*y + c11*x*y -> + c00 + c10*x + c20*x^2 -> end proc; -fn_2d_order2 := - - proc(x, y) c02*y^2 + c01*y + c11*x*y + c00 + c10*x + c20*x^2 end proc - -> -> fn_2d_order3 := -> proc(x,y) -> + c03*y^3 -> + c02*y^2 + c12*x*y^2 -> + c01*y + c11*x*y + c21*x^2*y -> + c00 + c10*x + c20*x^2 + c30*x^3 -> end proc; -fn_2d_order3 := proc(x, y) - c03*y^3 + c02*y^2 + c12*x*y^2 + c01*y + c11*x*y + c21*x^2*y + c00 - + c10*x + c20*x^2 + c30*x^3 -end proc - -> -> fn_2d_order4 := -> proc(x,y) -> + c04*y^4 -> + c03*y^3 + c13*x*y^3 -> + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 -> + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y -> + c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 -> end; -fn_2d_order4 := proc(x, y) - c04*y^4 + c03*y^3 + c13*x*y^3 + c02*y^2 + c12*x*y^2 + c22*x^2*y^2 - + c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c00 + c10*x + c20*x^2 - + c30*x^3 + c40*x^4 -end proc - -> -######################################## -> -# coordinates for 2-D interpolating functions -> coords_list_2d := [x,y]; - coords_list_2d := [x, y] - -> -######################################## -> -# -# coefficients in 2-D interpolating functions -# -> -> coeffs_list_2d_order1 := [ -> c01, -> c00, c10 -> ]; - coeffs_list_2d_order1 := [c01, c00, c10] - -> coeffs_list_2d_order2 := [ -> c02, -> c01, c11, -> c00, c10, c20 -> ]; - coeffs_list_2d_order2 := [c02, c01, c11, c00, c10, c20] - -> coeffs_list_2d_order3 := [ -> c03, -> c02, c12, -> c01, c11, c21, -> c00, c10, c20, c30 -> ]; - coeffs_list_2d_order3 := [c03, c02, c12, c01, c11, c21, c00, c10, c20, c30] - -> coeffs_list_2d_order4 := [ -> c04, -> c03, c13, -> c02, c12, c22, -> c01, c11, c21, c31, -> c00, c10, c20, c30, c40 -> ]; -coeffs_list_2d_order4 := - - [c04, c03, c13, c02, c12, c22, c01, c11, c21, c31, c00, c10, c20, c30, c40] - -> -################################################################################ -> -# -# 3-D interpolating functions -# -> -> fn_3d_order1 := -> proc(x,y,z) -# z^0 ----------- -> + c010*y -> + c000 + c100*x -# z^1 ----------- -> + c001*z -> end proc; - fn_3d_order1 := proc(x, y, z) c010*y + c000 + c100*x + c001*z end proc - -> -> fn_3d_order2 := -> proc(x,y,z) -# z^0 -------------------------- -> + c020*y^2 -> + c010*y + c110*x*y -> + c000 + c100*x + c200*x^2 -# z^1 -------------------------- -> + c011*y*z -> + c001*z + c101*x*z -# z^2 -------------------------- -> + c002*z^2 -> end proc; -fn_3d_order2 := proc(x, y, z) - c020*y^2 + c010*y + c110*x*y + c000 + c100*x + c200*x^2 + c011*y*z - + c001*z + c101*x*z + c002*z^2 -end proc - -> -> fn_3d_order3 := -> proc(x,y,z) -# z^0 ------------------------------------------- -> + c030*y^3 -> + c020*y^2 + c120*x*y^2 -> + c010*y + c110*x*y + c210*x^2*y -> + c000 + c100*x + c200*x^2 + c300*x^3 -# z^1 ------------------------------------------- -> + c021*y^2*z -> + c011*y *z + c111*x*y*z -> + c001 *z + c101*x *z + c201*x^2*z -# z^2 ------------------------------------------- -> + c012*y*z^2 -> + c002 *z^2 + c102*x*z^2 -# z^3 ------------------------------------------- -> + c003 *z^3 -> end proc; -fn_3d_order3 := proc(x, y, z) - c030*y^3 + c020*y^2 + c120*x*y^2 + c010*y + c110*x*y + c210*x^2*y - + c000 + c100*x + c200*x^2 + c300*x^3 + c021*y^2*z + c011*y*z - + c111*x*y*z + c001*z + c101*x*z + c201*x^2*z + c012*y*z^2 + c002*z^2 - + c102*x*z^2 + c003*z^3 -end proc - -> -> fn_3d_order4 := -> proc(x,y,z) -# z^0 -------------------------------------------------------- -> + c040*y^4 -> + c030*y^3 + c130*x*y^3 -> + c020*y^2 + c120*x*y^2 + c220*x^2*y^2 -> + c010*y + c110*x*y + c210*x^2*y + c310*x^3*y -> + c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 -# z^1 ------------------------------------------- -> + c031*y^3*z -> + c021*y^2*z + c121*x*y^2*z -> + c011*y *z + c111*x*y *z + c211*x^2*y*z -> + c001 *z + c101*x *z + c201*x^2 *z + c301*x^3*z -# z^2 ------------------------------------------- -> + c022*y^2*z^2 -> + c012*y *z^2 + c112*x*y*z^2 -> + c002 *z^2 + c102*x *z^2 + c202*x^2*z^2 -# z^3 ------------------------------------------- -> + c013*y *z^3 -> + c003 *z^3 + c103*x *z^3 -# z^4 ------------------------------------------- -> + c004 *z^4 -> end; -fn_3d_order4 := proc(x, y, z) - c102*x*z^2 + c012*y*z^2 + c111*x*y*z + c121*x*y^2*z + c211*x^2*y*z - + c112*x*y*z^2 + c010*y + c110*x*y + c011*y*z + c101*x*z + c120*x*y^2 - + c210*x^2*y + c021*y^2*z + c201*x^2*z + c130*x*y^3 + c220*x^2*y^2 - + c310*x^3*y + c031*y^3*z + c301*x^3*z + c022*y^2*z^2 + c202*x^2*z^2 - + c013*y*z^3 + c103*x*z^3 + c000 + c100*x + c001*z + c020*y^2 - + c200*x^2 + c002*z^2 + c030*y^3 + c300*x^3 + c003*z^3 + c040*y^4 - + c400*x^4 + c004*z^4 -end proc - -> -######################################## -> -# 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^0 ----- -> c010, -> c000, c100, -> # z^1 ----- -> c001 -> ]; - coeffs_list_3d_order1 := [c010, c000, c100, c001] - -> coeffs_list_3d_order2 := [ -> # z^0 ----------- -> c020, -> c010, c110, -> c000, c100, c200, -> # z^1 ----------- -> c011, -> c001, c101, -> # z^2 ----------- -> c002 -> ]; -coeffs_list_3d_order2 := - - [c020, c010, c110, c000, c100, c200, c011, c001, c101, c002] - -> coeffs_list_3d_order3 := [ -> # z^0 ---------------- -> c030, -> c020, c120, -> c010, c110, c210, -> c000, c100, c200, c300, -> # z^1 ---------------- -> c021, -> c011, c111, -> c001, c101, c201, -> # z^2 ---------------- -> c012, -> c002, c102, -> # z^3 ---------------- -> c003 -> ]; -coeffs_list_3d_order3 := [c030, c020, c120, c010, c110, c210, c000, c100, c200, - - c300, c021, c011, c111, c001, c101, c201, c012, c002, c102, c003] - -> coeffs_list_3d_order4 := [ -> # z^0 ----------------------- -> c040, -> c030, c130, -> c020, c120, c220, -> c010, c110, c210, c310, -> c000, c100, c200, c300, c400, -> # z^1 ----------------------- -> c031, -> c021, c121, -> c011, c111, c211, -> c001, c101, c201, c301, -> # z^2 ----------------------- -> c022, -> c012, c112, -> c002, c102, c202, -> # z^3 ----------------------- -> c013, -> c003, c103, -> # z^4 ----------------------- -> c004 -> ]; -coeffs_list_3d_order4 := [c040, c030, c130, c020, c120, c220, c010, c110, c210, - - c310, c000, c100, c200, c300, c400, c031, c021, c121, c011, c111, c211, - - c001, c101, c201, c301, c022, c012, c112, c002, c102, c202, c013, c003, - - c103, c004] - -> -################################################################################ -# 2d.maple -- compute Lagrange interpolation coefficients in 2-D -# $Header: /cactusdevcvs/CactusBase/LocalInterp/src/GeneralizedPolynomial-Uniform/Lagrange/2d.maple,v 1.2 2002/08/20 16:31:24 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 := - - (1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1)) y - - - 1/4 DATA(1, 1) + 3/4 DATA(0, 0) + 1/4 DATA(1, 0) + 1/4 DATA(0, 1) - - + (1/2 DATA(1, 1) - 1/2 DATA(0, 0) + 1/2 DATA(1, 0) - 1/2 DATA(0, 1)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size2); -[COEFF(0, 0) = 3/4 - 1/2 y - 1/2 x, COEFF(1, 0) = 1/4 - 1/2 y + 1/2 x, - - COEFF(0, 1) = - 1/2 x + 1/4 + 1/2 y, COEFF(1, 1) = 1/2 y - 1/4 + 1/2 x] - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order1.smooth0/coeffs-I.compute.c"); -bytes used=1000980, alloc=917336, time=0.08 -> -# d/dx -> simplify( diff(interp_2d_cube_order1_smooth0,x) ); - 1/2 DATA(1, 1) - 1/2 DATA(0, 0) + 1/2 DATA(1, 0) - 1/2 DATA(0, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size2); - [COEFF(0, 0) = -1/2, COEFF(1, 0) = 1/2, COEFF(0, 1) = -1/2, COEFF(1, 1) = 1/2] - -> 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) ); - 1/2 DATA(1, 1) - 1/2 DATA(0, 0) - 1/2 DATA(1, 0) + 1/2 DATA(0, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size2); -bytes used=2001372, alloc=1376004, time=0.15 - [COEFF(0, 0) = -1/2, COEFF(1, 0) = -1/2, COEFF(0, 1) = 1/2, COEFF(1, 1) = 1/2] - -> 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); -interp_2d_cube_order2_smooth0 := (1/6 DATA(0, 1) + 1/6 DATA(1, -1) - - + 1/6 DATA(0, -1) - 1/3 DATA(0, 0) + 1/6 DATA(-1, -1) + 1/6 DATA(1, 1) - - 2 - - 1/3 DATA(-1, 0) - 1/3 DATA(1, 0) + 1/6 DATA(-1, 1)) y + ( - - 1/6 DATA(-1, 1) - 1/6 DATA(-1, -1) - 1/6 DATA(0, -1) - 1/6 DATA(1, -1) - - + 1/6 DATA(1, 1) + 1/6 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 - - + 2/9 DATA(0, 1) - 1/9 DATA(1, -1) + 2/9 DATA(0, -1) + 5/9 DATA(0, 0) - - - 1/9 DATA(-1, -1) - 1/9 DATA(1, 1) + 2/9 DATA(-1, 0) + 2/9 DATA(1, 0) - - - 1/9 DATA(-1, 1) + (1/6 DATA(1, 0) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) - - - 1/6 DATA(-1, 0) - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1)) x + ( - - - 1/3 DATA(0, 1) + 1/6 DATA(1, -1) - 1/3 DATA(0, -1) - 1/3 DATA(0, 0) - - + 1/6 DATA(-1, -1) + 1/6 DATA(1, 1) + 1/6 DATA(-1, 0) + 1/6 DATA(1, 0) - - 2 - + 1/6 DATA(-1, 1)) x - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size3); - 2 2 -[COEFF(-1, -1) = - 1/9 + 1/6 y - 1/6 y - 1/6 x + 1/4 x y + 1/6 x , - - 2 2 - COEFF(0, -1) = 2/9 - 1/6 y + 1/6 y - 1/3 x , - - 2 2 - COEFF(1, -1) = - 1/6 y - 1/4 x y - 1/9 + 1/6 x + 1/6 y + 1/6 x , - - 2 2 - COEFF(-1, 0) = - 1/3 y - 1/6 x + 1/6 x + 2/9, - - 2 2 - COEFF(0, 0) = - 1/3 y - 1/3 x + 5/9, - - 2 2 - COEFF(1, 0) = - 1/3 y + 1/6 x + 2/9 + 1/6 x , - - 2 2 - COEFF(-1, 1) = 1/6 y + 1/6 y + 1/6 x - 1/6 x - 1/4 x y - 1/9, - - 2 2 - COEFF(0, 1) = 1/6 y + 1/6 y - 1/3 x + 2/9, - - 2 2 - COEFF(1, 1) = 1/6 y + 1/6 x - 1/9 + 1/6 y + 1/6 x + 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=3001624, alloc=1769148, time=0.22 -bytes used=4001856, alloc=1834672, time=0.29 -> -# d/dx -> simplify( diff(interp_2d_cube_order2_smooth0,x) ); -1/4 y DATA(1, 1) + 1/4 y DATA(-1, -1) - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, 1) - - + 1/6 DATA(1, 0) - 1/6 DATA(-1, -1) + 1/6 DATA(1, -1) - 1/6 DATA(-1, 0) - - - 1/6 DATA(-1, 1) + 1/6 DATA(1, 1) - 2/3 x DATA(0, 1) + 1/3 x DATA(1, -1) - - - 2/3 x DATA(0, -1) - 2/3 x DATA(0, 0) + 1/3 x DATA(-1, -1) - - + 1/3 x DATA(1, 1) + 1/3 x DATA(-1, 0) + 1/3 x DATA(1, 0) - - + 1/3 x DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/3 x + 1/4 y - 1/6, COEFF(0, -1) = - 2/3 x, - - COEFF(1, -1) = - 1/4 y + 1/3 x + 1/6, COEFF(-1, 0) = 1/3 x - 1/6, - - COEFF(0, 0) = - 2/3 x, COEFF(1, 0) = 1/3 x + 1/6, - - COEFF(-1, 1) = - 1/4 y - 1/6 + 1/3 x, COEFF(0, 1) = - 2/3 x, - - COEFF(1, 1) = 1/4 y + 1/6 + 1/3 x] - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dx.compute.c"); -bytes used=5002008, alloc=1834672, time=0.37 -> -# d/dy -> simplify( diff(interp_2d_cube_order2_smooth0,y) ); -1/3 y DATA(0, 1) + 1/3 y DATA(1, -1) + 1/3 y DATA(0, -1) - 2/3 y DATA(0, 0) - - + 1/3 y DATA(-1, -1) + 1/3 y DATA(1, 1) - 2/3 y DATA(-1, 0) - - - 2/3 y DATA(1, 0) + 1/3 y DATA(-1, 1) + 1/6 DATA(-1, 1) - - - 1/6 DATA(-1, -1) - 1/6 DATA(0, -1) - 1/6 DATA(1, -1) + 1/6 DATA(1, 1) - - + 1/6 DATA(0, 1) + 1/4 x DATA(1, 1) + 1/4 x DATA(-1, -1) - - - 1/4 x DATA(1, -1) - 1/4 x DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/4 x + 1/3 y - 1/6, COEFF(0, -1) = - 1/6 + 1/3 y, - - COEFF(1, -1) = - 1/6 - 1/4 x + 1/3 y, COEFF(-1, 0) = - 2/3 y, - - COEFF(0, 0) = - 2/3 y, COEFF(1, 0) = - 2/3 y, - - COEFF(-1, 1) = 1/3 y + 1/6 - 1/4 x, COEFF(0, 1) = 1/3 y + 1/6, - - COEFF(1, 1) = 1/3 y + 1/4 x + 1/6] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dy.compute.c"); -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order2_smooth0,x,x) ); -bytes used=6002212, alloc=1834672, time=0.42 -- 2/3 DATA(0, 1) + 1/3 DATA(1, -1) - 2/3 DATA(0, -1) - 2/3 DATA(0, 0) - - + 1/3 DATA(-1, -1) + 1/3 DATA(1, 1) + 1/3 DATA(-1, 0) + 1/3 DATA(1, 0) - - + 1/3 DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/3, COEFF(0, -1) = -2/3, COEFF(1, -1) = 1/3, - - COEFF(-1, 0) = 1/3, COEFF(0, 0) = -2/3, COEFF(1, 0) = 1/3, - - COEFF(-1, 1) = 1/3, COEFF(0, 1) = -2/3, COEFF(1, 1) = 1/3] - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxx.compute.c"); -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order2_smooth0,x,y) ); - 1/4 DATA(1, 1) + 1/4 DATA(-1, -1) - 1/4 DATA(1, -1) - 1/4 DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/4, COEFF(0, -1) = 0, COEFF(1, -1) = -1/4, COEFF(-1, 0) = 0, - - COEFF(0, 0) = 0, COEFF(1, 0) = 0, COEFF(-1, 1) = -1/4, COEFF(0, 1) = 0, - - COEFF(1, 1) = 1/4] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dxy.compute.c"); -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order2_smooth0,y,y) ); -1/3 DATA(0, 1) + 1/3 DATA(1, -1) + 1/3 DATA(0, -1) - 2/3 DATA(0, 0) - - + 1/3 DATA(-1, -1) + 1/3 DATA(1, 1) - 2/3 DATA(-1, 0) - 2/3 DATA(1, 0) - - + 1/3 DATA(-1, 1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size3); -[COEFF(-1, -1) = 1/3, COEFF(0, -1) = 1/3, COEFF(1, -1) = 1/3, - - COEFF(-1, 0) = -2/3, COEFF(0, 0) = -2/3, COEFF(1, 0) = -2/3, - - COEFF(-1, 1) = 1/3, COEFF(0, 1) = 1/3, COEFF(1, 1) = 1/3] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order2.smooth0/coeffs-dyy.compute.c"); -bytes used=7002528, alloc=1834672, time=0.52 -> -################################################################################ -> -# -# 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=8002908, alloc=1900196, time=0.59 -bytes used=9003224, alloc=1900196, time=0.65 -bytes used=10004308, alloc=1965720, time=0.71 -bytes used=11004468, alloc=1965720, time=0.77 -interp_2d_cube_order3_smooth0 := (- 3/40 DATA(2, 0) + 1/40 DATA(0, 0) - - - 1/40 DATA(1, 0) + 1/40 DATA(0, 1) - 1/40 DATA(1, 1) - 1/40 DATA(0, -1) - - - 3/40 DATA(-1, -1) + 1/40 DATA(1, -1) + 3/40 DATA(-1, 0) - - + 3/40 DATA(-1, 1) + 3/40 DATA(2, -1) - 1/40 DATA(0, 2) - 3/40 DATA(-1, 2) - - 2 / - - 3/40 DATA(2, 1) + 1/40 DATA(1, 2) + 3/40 DATA(2, 2)) x y + | - \ - - 7/100 DATA(2, 0) - 1/25 DATA(0, 0) - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) - - 13 - + 3/50 DATA(1, 1) - 1/50 DATA(0, -1) + 6/25 DATA(-1, -1) - --- DATA(1, -1) - 100 - - 13 - - 1/50 DATA(-1, 0) - --- DATA(-1, 1) - 9/100 DATA(2, -1) - 100 - - + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) + 2/25 DATA(2, 1) + 2/25 DATA(1, 2) - - \ - - 3/50 DATA(2, 2)| x y + (- 1/40 DATA(2, 0) + 1/40 DATA(0, 0) - / - - + 1/40 DATA(1, 0) - 1/40 DATA(0, 1) - 1/40 DATA(1, 1) + 3/40 DATA(0, -1) - - - 3/40 DATA(-1, -1) + 3/40 DATA(1, -1) - 1/40 DATA(-1, 0) - - + 1/40 DATA(-1, 1) - 3/40 DATA(2, -1) - 3/40 DATA(0, 2) + 3/40 DATA(-1, 2) - - 2 - + 1/40 DATA(2, 1) - 3/40 DATA(1, 2) + 3/40 DATA(2, 2)) x y - - 13 93 37 37 - + --- DATA(2, 0) + --- DATA(0, 0) + --- DATA(1, 0) + --- DATA(0, 1) - 100 200 200 200 - - 17 11 23 - - --- DATA(1, 1) + -- DATA(0, -1) - --- DATA(-1, -1) - 1/50 DATA(1, -1) - 200 50 200 - - 11 17 13 - + -- DATA(-1, 0) - 1/50 DATA(-1, 1) - --- DATA(2, -1) + --- DATA(0, 2) - 50 200 100 - - 17 - - --- DATA(-1, 2) - 2/25 DATA(2, 1) - 2/25 DATA(1, 2) + 7/200 DATA(2, 2) - 200 - - + (1/8 DATA(2, 0) + 1/8 DATA(0, 0) + 1/8 DATA(1, 0) - 1/8 DATA(0, 1) - - - 1/8 DATA(1, 1) - 1/24 DATA(0, -1) - 1/24 DATA(-1, -1) - 1/24 DATA(1, -1) - - + 1/8 DATA(-1, 0) - 1/8 DATA(-1, 1) - 1/24 DATA(2, -1) + 1/24 DATA(0, 2) - - + 1/24 DATA(-1, 2) - 1/8 DATA(2, 1) + 1/24 DATA(1, 2) + 1/24 DATA(2, 2)) - - 3 / 49 57 63 117 - y + |- --- DATA(2, 0) - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) - \ 400 400 400 400 - - 103 223 109 157 - + --- DATA(1, 1) - ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(1, -1) - 400 1200 1200 1200 - - 31 111 89 43 - - --- DATA(-1, 0) + --- DATA(-1, 1) + ---- DATA(2, -1) + ---- DATA(0, 2) - 400 400 1200 1200 - - 131 69 37 149 \ - - ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(1, 2) - ---- DATA(2, 2)| y - 1200 400 1200 1200 / - - / 43 57 117 63 - + |---- DATA(2, 0) - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) - \1200 400 400 400 - - 103 31 109 111 - + --- DATA(1, 1) - --- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(1, -1) - 400 400 1200 400 - - 223 157 131 49 - - ---- DATA(-1, 0) - ---- DATA(-1, 1) - ---- DATA(2, -1) - --- DATA(0, 2) - 1200 1200 1200 400 - - 89 37 69 149 \ - + ---- DATA(-1, 2) + ---- DATA(2, 1) + --- DATA(1, 2) - ---- DATA(2, 2)| x - 1200 1200 400 1200 / - - / 21 19 - + |1/80 DATA(2, 0) - -- DATA(0, 0) + 9/80 DATA(1, 0) - -- DATA(0, 1) - \ 80 80 - - 11 23 13 - + -- DATA(1, 1) - -- DATA(0, -1) + -- DATA(-1, -1) + 7/80 DATA(1, -1) - 80 80 80 - - 11 17 - + -- DATA(-1, 0) + 9/80 DATA(-1, 1) + 3/80 DATA(2, -1) - -- DATA(0, 2) - 80 80 - - 13 \ 2 - + 7/80 DATA(-1, 2) - 1/80 DATA(2, 1) + -- DATA(1, 2) - 3/80 DATA(2, 2)| x - 80 / - - + (1/24 DATA(2, 0) + 1/8 DATA(0, 0) - 1/8 DATA(1, 0) + 1/8 DATA(0, 1) - - - 1/8 DATA(1, 1) + 1/8 DATA(0, -1) - 1/24 DATA(-1, -1) - 1/8 DATA(1, -1) - - - 1/24 DATA(-1, 0) - 1/24 DATA(-1, 1) + 1/24 DATA(2, -1) + 1/8 DATA(0, 2) - - - 1/24 DATA(-1, 2) + 1/24 DATA(2, 1) - 1/8 DATA(1, 2) + 1/24 DATA(2, 2)) - - 3 / 17 21 19 - x + |- -- DATA(2, 0) - -- DATA(0, 0) - -- DATA(1, 0) + 9/80 DATA(0, 1) - \ 80 80 80 - - 11 11 13 - + -- DATA(1, 1) + -- DATA(0, -1) + -- DATA(-1, -1) + 9/80 DATA(1, -1) - 80 80 80 - - 23 - - -- DATA(-1, 0) + 7/80 DATA(-1, 1) + 7/80 DATA(2, -1) + 1/80 DATA(0, 2) - 80 - - 13 \ 2 - + 3/80 DATA(-1, 2) + -- DATA(2, 1) - 1/80 DATA(1, 2) - 3/80 DATA(2, 2)| y - 80 / - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=12010172, alloc=1965720, time=0.82 - 2 13 2 13 2 2 109 -[COEFF(-1, -1) = - 3/40 x y + -- y + -- x - 3/40 x y - ---- x + 6/25 x y - 80 80 1200 - - 109 23 3 3 2 2 - - ---- y - --- - 1/24 y - 1/24 x , COEFF(0, -1) = 3/40 x y - 1/40 x y - 1200 200 - - 223 11 11 2 3 31 3 23 2 - - ---- y + -- + -- y + 1/8 x - --- x - 1/50 x y - 1/24 y - -- x , - 1200 50 80 400 80 - - 2 3 2 2 2 - COEFF(1, -1) = 9/80 y - 1/50 - 1/24 y + 7/80 x + 1/40 x y + 3/40 x y - - 111 157 13 3 89 131 - + --- x - ---- y - --- x y - 1/8 x , COEFF(2, -1) = ---- y - ---- x - 400 1200 100 1200 1200 - - 17 2 3 2 2 2 - - 9/100 x y - --- + 7/80 y - 1/24 y - 3/40 x y + 3/40 x y + 3/80 x - 200 - - 3 2 23 2 11 2 11 2 - + 1/24 x , COEFF(-1, 0) = - 1/40 x y - -- y + -- x + -- + 3/40 x y - 80 80 50 - - 3 3 223 31 3 93 - - 1/50 x y - 1/24 x + 1/8 y - ---- x - --- y, COEFF(0, 0) = 1/8 y + --- - 1200 400 200 - - 2 2 57 21 2 57 21 2 - + 1/40 x y + 1/40 x y - 1/25 x y - --- y - -- x - --- x - -- y - 400 80 400 80 - - 3 37 19 2 3 3 63 2 - + 1/8 x , COEFF(1, 0) = --- - -- y - 1/8 x + 1/8 y - --- y - 1/40 x y - 200 80 400 - - 2 117 2 2 13 - + 9/80 x - 1/100 x y + --- x + 1/40 x y, COEFF(2, 0) = - 1/40 x y + --- - 400 100 - - 17 2 3 2 3 49 2 - - -- y + 1/24 x + 7/100 x y + 1/80 x + 1/8 y - --- y - 3/40 x y - 80 400 - - 43 2 3 13 111 - + ---- x, COEFF(-1, 1) = - 1/50 + 1/40 x y - 1/24 x - --- x y + --- y - 1200 100 400 - - 157 3 2 2 2 3 - - ---- x - 1/8 y + 7/80 y + 9/80 x + 3/40 x y , COEFF(0, 1) = - 1/8 y - 1200 - - 63 2 2 3 37 2 - - 1/100 x y - --- x - 1/40 x y + 1/40 x y + 1/8 x + --- + 9/80 y - 400 200 - - 117 19 2 3 3 11 2 - + --- y - -- x , COEFF(1, 1) = 3/50 x y - 1/8 x - 1/8 y + -- y - 400 80 80 - - 2 103 103 11 2 17 2 - - 1/40 x y + --- y + --- x + -- x - --- - 1/40 x y , COEFF(2, 1) = - 400 400 80 200 - - 2 2 69 3 3 13 2 - 1/40 x y - 2/25 - 1/80 x + --- y + 2/25 x y - 1/8 y + 1/24 x + -- y - 400 80 - - 2 37 2 17 2 - - 3/40 x y + ---- x, COEFF(-1, 2) = 3/40 x y - --- - 9/100 x y + 7/80 x - 1200 200 - - 89 131 3 2 2 3 - + ---- x - ---- y - 1/24 x - 3/40 x y + 3/80 y + 1/24 y , COEFF(0, 2) - 1200 1200 - - 43 3 2 13 2 17 2 - = ---- y + 1/8 x - 3/40 x y + 7/100 x y + --- + 1/80 y - -- x - 1200 100 80 - - 3 49 2 13 2 69 - + 1/24 y - --- x - 1/40 x y , COEFF(1, 2) = 2/25 x y + -- x + --- x - 400 80 400 - - 2 3 37 3 2 2 - - 3/40 x y - 1/8 x - 2/25 + ---- y + 1/24 y + 1/40 x y - 1/80 y , - 1200 - - 2 2 149 3 2 - COEFF(2, 2) = 3/40 x y - 3/80 y - ---- y + 1/24 y + 3/40 x y - 3/50 x y - 1200 - - 2 149 3 - - 3/80 x - ---- x + 7/200 + 1/24 x ] - 1200 - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-I.compute.c"); -bytes used=13010356, alloc=2031244, time=0.89 -bytes used=14014296, alloc=2031244, time=0.96 -bytes used=15017972, alloc=2031244, time=1.06 -bytes used=16018212, alloc=2031244, time=1.13 -bytes used=17018832, alloc=2031244, time=1.22 -bytes used=18019192, alloc=2031244, time=1.30 -bytes used=19019652, alloc=2031244, time=1.40 -bytes used=20019840, alloc=2031244, time=1.46 -> -# d/dx -> simplify( diff(interp_2d_cube_order3_smooth0,x) ); -bytes used=21020004, alloc=2031244, time=1.52 -3/20 x y DATA(1, -1) - 1/20 x y DATA(-1, 0) + 1/20 x y DATA(-1, 1) - - - 3/20 x y DATA(2, -1) - 3/20 x y DATA(0, 2) + 3/20 x y DATA(-1, 2) - - + 1/20 x y DATA(2, 1) - 3/20 x y DATA(1, 2) + 3/20 x y DATA(2, 2) - - - 1/20 x y DATA(1, 1) - 1/20 x y DATA(2, 0) + 1/20 x y DATA(0, 0) - - 43 - + 1/20 x y DATA(1, 0) - 1/20 x y DATA(0, 1) + ---- DATA(2, 0) - 1200 - - 21 11 11 - - -- x DATA(0, 0) + -- x DATA(1, 1) + -- x DATA(-1, 0) - 40 40 40 - - 13 23 - + 7/40 x DATA(1, -1) + -- x DATA(-1, -1) - -- x DATA(0, -1) - 40 40 - - 19 - + 9/40 x DATA(1, 0) - -- x DATA(0, 1) - 3/50 y DATA(2, 2) - 40 - - + 1/40 x DATA(2, 0) - 1/25 y DATA(0, 0) + 7/100 y DATA(2, 0) - - + 7/100 y DATA(0, 2) - 9/100 y DATA(2, -1) - 9/100 y DATA(-1, 2) - - + 2/25 y DATA(1, 2) + 2/25 y DATA(2, 1) - 1/50 y DATA(0, -1) - - 13 13 - - --- y DATA(1, -1) + 6/25 y DATA(-1, -1) - --- y DATA(-1, 1) - 100 100 - - - 1/50 y DATA(-1, 0) - 1/100 y DATA(0, 1) - 1/100 y DATA(1, 0) - - 2 - + 3/40 y DATA(2, 2) + 3/50 y DATA(1, 1) + 3/40 x DATA(2, -1) - - 2 2 2 - + 1/40 y DATA(1, 2) - 3/40 y DATA(2, 1) - 3/40 y DATA(-1, 2) - - 17 2 - + 9/40 x DATA(-1, 1) - -- x DATA(0, 2) - 3/8 x DATA(1, 0) - 40 - - 2 - + 3/8 x DATA(0, 1) - 3/40 x DATA(2, 2) + 7/40 x DATA(-1, 2) - - 13 2 - + -- x DATA(1, 2) - 1/40 x DATA(2, 1) + 1/8 x DATA(2, 0) - 40 - - 2 2 2 - + 3/8 x DATA(0, 0) + 1/8 x DATA(2, -1) - 3/8 x DATA(1, -1) - - 2 2 2 - - 1/8 x DATA(-1, 0) - 3/8 x DATA(1, 1) - 1/8 x DATA(-1, 2) - - 2 2 2 - - 1/8 x DATA(-1, 1) - 3/8 x DATA(1, 2) + 3/8 x DATA(0, 2) - - 2 2 2 - + 1/8 x DATA(2, 2) + 1/8 x DATA(2, 1) + 3/8 x DATA(0, -1) - - 2 2 2 - - 1/8 x DATA(-1, -1) - 3/40 y DATA(-1, -1) + 1/40 y DATA(1, -1) - - 2 2 2 - - 1/40 y DATA(0, -1) + 1/40 y DATA(0, 1) - 1/40 y DATA(1, 1) - - 2 2 2 - + 3/40 y DATA(-1, 0) + 3/40 y DATA(-1, 1) + 3/40 y DATA(2, -1) - - 2 2 2 - - 1/40 y DATA(0, 2) - 3/40 y DATA(2, 0) - 1/40 y DATA(1, 0) - - 2 - + 1/40 y DATA(0, 0) + 3/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) - - 57 117 63 103 - - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + --- DATA(1, 1) - 400 400 400 400 - - 31 109 111 223 - - --- DATA(0, -1) - ---- DATA(-1, -1) + --- DATA(1, -1) - ---- DATA(-1, 0) - 400 1200 400 1200 - - 157 131 49 89 - - ---- DATA(-1, 1) - ---- DATA(2, -1) - --- DATA(0, 2) + ---- DATA(-1, 2) - 1200 1200 400 1200 - - 37 69 149 - + ---- DATA(2, 1) + --- DATA(1, 2) - ---- DATA(2, 2) - 1200 400 1200 - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=22023600, alloc=2096768, time=1.59 - 2 13 109 2 -[COEFF(-1, -1) = - 3/20 x y - 3/40 y + -- x + 6/25 y - ---- - 1/8 x , - 40 1200 - - 2 31 23 2 - COEFF(0, -1) = 3/8 x + 3/20 x y - 1/50 y - --- - -- x - 1/40 y , - 400 40 - - 111 2 13 2 - COEFF(1, -1) = --- + 1/40 y - --- y + 3/20 x y - 3/8 x + 7/40 x, - 400 100 - - 2 131 2 - COEFF(2, -1) = 1/8 x + 3/40 x - ---- - 9/100 y + 3/40 y - 3/20 x y, - 1200 - - 2 223 2 11 - COEFF(-1, 0) = 3/40 y - 1/20 x y - ---- - 1/8 x - 1/50 y + -- x, - 1200 40 - - 2 21 57 2 - COEFF(0, 0) = - 1/25 y + 1/20 x y + 1/40 y - -- x - --- + 3/8 x , - 40 400 - - 2 2 117 - COEFF(1, 0) = - 1/40 y + 1/20 x y - 1/100 y - 3/8 x + 9/40 x + ---, - 400 - - 2 2 43 - COEFF(2, 0) = - 1/20 x y + 1/8 x - 3/40 y + 1/40 x + ---- + 7/100 y, - 1200 - - 157 2 13 2 - COEFF(-1, 1) = - ---- + 3/40 y - --- y + 9/40 x - 1/8 x + 1/20 x y, - 1200 100 - - 2 63 2 19 - COEFF(0, 1) = 1/40 y - --- + 3/8 x - 1/100 y - 1/20 x y - -- x, - 400 40 - - 103 2 2 11 - COEFF(1, 1) = - 1/20 x y + --- - 3/8 x + 3/50 y - 1/40 y + -- x, - 400 40 - - 2 2 37 - COEFF(2, 1) = 1/20 x y - 3/40 y + 1/8 x + 2/25 y + ---- - 1/40 x, - 1200 - - 2 89 2 - COEFF(-1, 2) = - 1/8 x + ---- + 7/40 x - 3/40 y + 3/20 x y - 9/100 y, - 1200 - - 2 2 17 49 - COEFF(0, 2) = - 1/40 y - 3/20 x y + 7/100 y + 3/8 x - -- x - ---, - 40 400 - - 69 13 2 2 - COEFF(1, 2) = --- + -- x + 1/40 y - 3/8 x + 2/25 y - 3/20 x y, - 400 40 - - 2 149 2 - COEFF(2, 2) = 3/40 y - ---- + 3/20 x y - 3/50 y + 1/8 x - 3/40 x] - 1200 - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dx.compute.c"); -bytes used=23023764, alloc=2096768, time=1.67 -bytes used=24024212, alloc=2096768, time=1.75 -bytes used=25024544, alloc=2096768, time=1.84 -> -# d/dy -> simplify( diff(interp_2d_cube_order3_smooth0,y) ); -bytes used=26024784, alloc=2096768, time=1.94 -bytes used=27025040, alloc=2096768, time=2.00 -1/20 x y DATA(1, -1) + 3/20 x y DATA(-1, 0) + 3/20 x y DATA(-1, 1) - - + 3/20 x y DATA(2, -1) - 1/20 x y DATA(0, 2) - 3/20 x y DATA(-1, 2) - - - 3/20 x y DATA(2, 1) + 1/20 x y DATA(1, 2) + 3/20 x y DATA(2, 2) - - - 1/20 x y DATA(1, 1) - 3/20 x y DATA(2, 0) + 1/20 x y DATA(0, 0) - - 49 - - 1/20 x y DATA(1, 0) + 1/20 x y DATA(0, 1) - --- DATA(2, 0) - 400 - - - 1/25 x DATA(0, 0) + 3/50 x DATA(1, 1) - 1/50 x DATA(-1, 0) - - 13 - - --- x DATA(1, -1) + 6/25 x DATA(-1, -1) - 1/50 x DATA(0, -1) - 100 - - - 1/100 x DATA(1, 0) - 1/100 x DATA(0, 1) - 3/40 y DATA(2, 2) - - 21 17 - + 7/100 x DATA(2, 0) - -- y DATA(0, 0) - -- y DATA(2, 0) - 40 40 - - + 1/40 y DATA(0, 2) + 7/40 y DATA(2, -1) + 3/40 y DATA(-1, 2) - - 13 11 - - 1/40 y DATA(1, 2) + -- y DATA(2, 1) + -- y DATA(0, -1) - 40 40 - - 13 - + 9/40 y DATA(1, -1) + -- y DATA(-1, -1) + 7/40 y DATA(-1, 1) - 40 - - 23 19 - - -- y DATA(-1, 0) + 9/40 y DATA(0, 1) - -- y DATA(1, 0) - 40 40 - - 2 11 - + 1/8 y DATA(2, 2) + -- y DATA(1, 1) - 9/100 x DATA(2, -1) - 40 - - 2 2 2 - + 1/8 y DATA(1, 2) - 3/8 y DATA(2, 1) + 1/8 y DATA(-1, 2) - - 13 2 - - --- x DATA(-1, 1) + 7/100 x DATA(0, 2) + 1/40 x DATA(1, 0) - 100 - - 2 - - 1/40 x DATA(0, 1) - 3/50 x DATA(2, 2) - 9/100 x DATA(-1, 2) - - 2 - + 2/25 x DATA(1, 2) + 2/25 x DATA(2, 1) - 1/40 x DATA(2, 0) - - 2 2 2 - + 1/40 x DATA(0, 0) - 3/40 x DATA(2, -1) + 3/40 x DATA(1, -1) - - 2 2 2 - - 1/40 x DATA(-1, 0) - 1/40 x DATA(1, 1) + 3/40 x DATA(-1, 2) - - 2 2 2 - + 1/40 x DATA(-1, 1) - 3/40 x DATA(1, 2) - 3/40 x DATA(0, 2) - - 2 2 2 - + 3/40 x DATA(2, 2) + 1/40 x DATA(2, 1) + 3/40 x DATA(0, -1) - - 2 2 2 - - 3/40 x DATA(-1, -1) - 1/8 y DATA(-1, -1) - 1/8 y DATA(1, -1) - - 2 2 2 - - 1/8 y DATA(0, -1) - 3/8 y DATA(0, 1) - 3/8 y DATA(1, 1) - - 2 2 2 - + 3/8 y DATA(-1, 0) - 3/8 y DATA(-1, 1) - 1/8 y DATA(2, -1) - - 2 2 2 - + 1/8 y DATA(0, 2) + 3/8 y DATA(2, 0) + 3/8 y DATA(1, 0) - - 2 - + 3/8 y DATA(0, 0) - 1/20 x y DATA(0, -1) - 3/20 x y DATA(-1, -1) - - 57 63 117 103 - - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + --- DATA(1, 1) - 400 400 400 400 - - 223 109 157 - - ---- DATA(0, -1) - ---- DATA(-1, -1) - ---- DATA(1, -1) - 1200 1200 1200 - - 31 111 89 43 - - --- DATA(-1, 0) + --- DATA(-1, 1) + ---- DATA(2, -1) + ---- DATA(0, 2) - 400 400 1200 1200 - - 131 69 37 149 - - ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(1, 2) - ---- DATA(2, 2) - 1200 400 1200 1200 - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 2 2 109 13 -[COEFF(-1, -1) = - 1/8 y - 3/40 x + 6/25 x - 3/20 x y - ---- + -- y, - 1200 40 - - 2 2 223 11 - COEFF(0, -1) = - 1/20 x y - 1/50 x + 3/40 x - 1/8 y - ---- + -- y, - 1200 40 - - 2 157 2 13 - COEFF(1, -1) = 1/20 x y - 1/8 y - ---- + 9/40 y + 3/40 x - --- x, - 1200 100 - - 2 89 2 - COEFF(2, -1) = - 9/100 x - 3/40 x + 7/40 y + 3/20 x y + ---- - 1/8 y , - 1200 - - 23 2 31 2 - COEFF(-1, 0) = - -- y - 1/40 x - --- + 3/20 x y + 3/8 y - 1/50 x, - 40 400 - - 21 57 2 2 - COEFF(0, 0) = - -- y - --- - 1/25 x + 1/20 x y + 3/8 y + 1/40 x , - 40 400 - - 2 19 63 2 - COEFF(1, 0) = 1/40 x - 1/20 x y - -- y - --- - 1/100 x + 3/8 y , - 40 400 - - 49 2 2 17 - COEFF(2, 0) = - 3/20 x y - --- + 3/8 y - 1/40 x - -- y + 7/100 x, - 400 40 - - 13 111 2 2 - COEFF(-1, 1) = - --- x + 7/40 y + --- + 1/40 x - 3/8 y + 3/20 x y, - 100 400 - - 2 2 117 - COEFF(0, 1) = - 1/40 x + 1/20 x y + 9/40 y - 3/8 y - 1/100 x + ---, - 400 - - 11 2 2 103 - COEFF(1, 1) = -- y + 3/50 x - 1/40 x - 3/8 y - 1/20 x y + ---, - 40 400 - - 2 13 2 69 - COEFF(2, 1) = 2/25 x + 1/40 x + -- y - 3/20 x y - 3/8 y + ---, - 40 400 - - 2 2 131 - COEFF(-1, 2) = 1/8 y + 3/40 x - 9/100 x - 3/20 x y - ---- + 3/40 y, - 1200 - - 2 2 43 - COEFF(0, 2) = 7/100 x - 1/20 x y - 3/40 x + 1/8 y + 1/40 y + ----, - 1200 - - 2 37 2 - COEFF(1, 2) = 1/20 x y - 3/40 x + ---- + 1/8 y - 1/40 y + 2/25 x, - 1200 - - 2 149 2 - COEFF(2, 2) = 1/8 y - 3/40 y + 3/20 x y - 3/50 x - ---- + 3/40 x ] - 1200 - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dy.compute.c"); -bytes used=28025200, alloc=2162292, time=2.08 -bytes used=29025372, alloc=2162292, time=2.17 -bytes used=30025660, alloc=2162292, time=2.26 -bytes used=31025832, alloc=2162292, time=2.37 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order3_smooth0,x,x) ); -1/40 DATA(2, 0) + 3/4 x DATA(0, 0) - 3/4 x DATA(1, 1) - 1/4 x DATA(-1, 0) - - - 3/4 x DATA(1, -1) - 1/4 x DATA(-1, -1) + 3/4 x DATA(0, -1) - - - 3/4 x DATA(1, 0) + 3/4 x DATA(0, 1) + 3/20 y DATA(2, 2) - - + 1/4 x DATA(2, 0) + 1/20 y DATA(0, 0) - 1/20 y DATA(2, 0) - - - 3/20 y DATA(0, 2) - 3/20 y DATA(2, -1) + 3/20 y DATA(-1, 2) - - - 3/20 y DATA(1, 2) + 1/20 y DATA(2, 1) + 3/20 y DATA(0, -1) - - + 3/20 y DATA(1, -1) - 3/20 y DATA(-1, -1) + 1/20 y DATA(-1, 1) - - - 1/20 y DATA(-1, 0) - 1/20 y DATA(0, 1) + 1/20 y DATA(1, 0) - - - 1/20 y DATA(1, 1) + 1/4 x DATA(2, -1) - 1/4 x DATA(-1, 1) - - + 3/4 x DATA(0, 2) + 1/4 x DATA(2, 2) - 1/4 x DATA(-1, 2) - - 21 - - 3/4 x DATA(1, 2) + 1/4 x DATA(2, 1) - -- DATA(0, 0) + 9/40 DATA(1, 0) - 40 - - 19 11 23 13 - - -- DATA(0, 1) + -- DATA(1, 1) - -- DATA(0, -1) + -- DATA(-1, -1) - 40 40 40 40 - - 11 - + 7/40 DATA(1, -1) + -- DATA(-1, 0) + 9/40 DATA(-1, 1) + 3/40 DATA(2, -1) - 40 - - 17 13 - - -- DATA(0, 2) + 7/40 DATA(-1, 2) - 1/40 DATA(2, 1) + -- DATA(1, 2) - 40 40 - - - 3/40 DATA(2, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 13 23 -[COEFF(-1, -1) = - 1/4 x - 3/20 y + --, COEFF(0, -1) = 3/4 x + 3/20 y - --, - 40 40 - - COEFF(1, -1) = 7/40 + 3/20 y - 3/4 x, - - 11 - COEFF(2, -1) = - 3/20 y + 3/40 + 1/4 x, COEFF(-1, 0) = -- - 1/20 y - 1/4 x, - 40 - - 21 - COEFF(0, 0) = - -- + 1/20 y + 3/4 x, COEFF(1, 0) = - 3/4 x + 1/20 y + 9/40, - 40 - - COEFF(2, 0) = 1/4 x - 1/20 y + 1/40, COEFF(-1, 1) = 9/40 - 1/4 x + 1/20 y, - - 19 11 - COEFF(0, 1) = - -- - 1/20 y + 3/4 x, COEFF(1, 1) = - 1/20 y + -- - 3/4 x, - 40 40 - - COEFF(2, 1) = - 1/40 + 1/20 y + 1/4 x, - - 17 - COEFF(-1, 2) = - 1/4 x + 7/40 + 3/20 y, COEFF(0, 2) = - 3/20 y + 3/4 x - --, - 40 - - 13 - COEFF(1, 2) = - 3/20 y - 3/4 x + --, COEFF(2, 2) = - 3/40 + 1/4 x + 3/20 y] - 40 - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxx.compute.c"); -bytes used=32026056, alloc=2162292, time=2.48 -bytes used=33027468, alloc=2162292, time=2.58 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order3_smooth0,x,y) ); -7/100 DATA(2, 0) + 1/20 x DATA(0, 0) - 1/20 x DATA(1, 1) - 1/20 x DATA(-1, 0) - - + 3/20 x DATA(1, -1) - 3/20 x DATA(-1, -1) + 3/20 x DATA(0, -1) - - + 1/20 x DATA(1, 0) - 1/20 x DATA(0, 1) + 3/20 y DATA(2, 2) - - - 1/20 x DATA(2, 0) + 1/20 y DATA(0, 0) - 3/20 y DATA(2, 0) - - - 1/20 y DATA(0, 2) + 3/20 y DATA(2, -1) - 3/20 y DATA(-1, 2) - - + 1/20 y DATA(1, 2) - 3/20 y DATA(2, 1) - 1/20 y DATA(0, -1) - - + 1/20 y DATA(1, -1) - 3/20 y DATA(-1, -1) + 3/20 y DATA(-1, 1) - - + 3/20 y DATA(-1, 0) + 1/20 y DATA(0, 1) - 1/20 y DATA(1, 0) - - - 1/20 y DATA(1, 1) - 3/20 x DATA(2, -1) + 1/20 x DATA(-1, 1) - - - 3/20 x DATA(0, 2) + 3/20 x DATA(2, 2) + 3/20 x DATA(-1, 2) - - - 3/20 x DATA(1, 2) + 1/20 x DATA(2, 1) - 1/25 DATA(0, 0) - - - 1/100 DATA(1, 0) - 1/100 DATA(0, 1) + 3/50 DATA(1, 1) - 1/50 DATA(0, -1) - - 13 13 - + 6/25 DATA(-1, -1) - --- DATA(1, -1) - 1/50 DATA(-1, 0) - --- DATA(-1, 1) - 100 100 - - - 9/100 DATA(2, -1) + 7/100 DATA(0, 2) - 9/100 DATA(-1, 2) - - + 2/25 DATA(2, 1) + 2/25 DATA(1, 2) - 3/50 DATA(2, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); -bytes used=34028660, alloc=2162292, time=2.68 -[COEFF(-1, -1) = - 3/20 x + 6/25 - 3/20 y, - - 13 - COEFF(0, -1) = 3/20 x - 1/50 - 1/20 y, COEFF(1, -1) = 1/20 y - --- + 3/20 x, - 100 - - COEFF(2, -1) = 3/20 y - 3/20 x - 9/100, - - COEFF(-1, 0) = 3/20 y - 1/20 x - 1/50, COEFF(0, 0) = 1/20 x - 1/25 + 1/20 y, - - COEFF(1, 0) = - 1/20 y - 1/100 + 1/20 x, - - COEFF(2, 0) = - 3/20 y - 1/20 x + 7/100, - - 13 - COEFF(-1, 1) = 3/20 y - --- + 1/20 x, - 100 - - COEFF(0, 1) = - 1/20 x + 1/20 y - 1/100, - - COEFF(1, 1) = - 1/20 x + 3/50 - 1/20 y, - - COEFF(2, 1) = - 3/20 y + 1/20 x + 2/25, - - COEFF(-1, 2) = - 9/100 - 3/20 y + 3/20 x, - - COEFF(0, 2) = 7/100 - 1/20 y - 3/20 x, - - COEFF(1, 2) = - 3/20 x + 1/20 y + 2/25, - - COEFF(2, 2) = 3/20 x + 3/20 y - 3/50] - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dxy.compute.c"); -bytes used=35028816, alloc=2162292, time=2.75 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order3_smooth0,y,y) ); - 17 -- -- DATA(2, 0) + 1/20 x DATA(0, 0) - 1/20 x DATA(1, 1) + 3/20 x DATA(-1, 0) - 40 - - + 1/20 x DATA(1, -1) - 3/20 x DATA(-1, -1) - 1/20 x DATA(0, -1) - - - 1/20 x DATA(1, 0) + 1/20 x DATA(0, 1) + 1/4 y DATA(2, 2) - - - 3/20 x DATA(2, 0) + 3/4 y DATA(0, 0) + 3/4 y DATA(2, 0) - - + 1/4 y DATA(0, 2) - 1/4 y DATA(2, -1) + 1/4 y DATA(-1, 2) - - + 1/4 y DATA(1, 2) - 3/4 y DATA(2, 1) - 1/4 y DATA(0, -1) - - - 1/4 y DATA(1, -1) - 1/4 y DATA(-1, -1) - 3/4 y DATA(-1, 1) - - + 3/4 y DATA(-1, 0) - 3/4 y DATA(0, 1) + 3/4 y DATA(1, 0) - - - 3/4 y DATA(1, 1) + 3/20 x DATA(2, -1) + 3/20 x DATA(-1, 1) - - - 1/20 x DATA(0, 2) + 3/20 x DATA(2, 2) - 3/20 x DATA(-1, 2) - - 21 19 - + 1/20 x DATA(1, 2) - 3/20 x DATA(2, 1) - -- DATA(0, 0) - -- DATA(1, 0) - 40 40 - - 11 11 13 - + 9/40 DATA(0, 1) + -- DATA(1, 1) + -- DATA(0, -1) + -- DATA(-1, -1) - 40 40 40 - - 23 - + 9/40 DATA(1, -1) - -- DATA(-1, 0) + 7/40 DATA(-1, 1) + 7/40 DATA(2, -1) - 40 - - 13 - + 1/40 DATA(0, 2) + 3/40 DATA(-1, 2) + -- DATA(2, 1) - 1/40 DATA(1, 2) - 40 - - - 3/40 DATA(2, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size4); - 13 11 -[COEFF(-1, -1) = - 1/4 y - 3/20 x + --, COEFF(0, -1) = -- - 1/4 y - 1/20 x, - 40 40 - - COEFF(1, -1) = - 1/4 y + 9/40 + 1/20 x, - - 23 - COEFF(2, -1) = 7/40 + 3/20 x - 1/4 y, COEFF(-1, 0) = 3/20 x + 3/4 y - --, - 40 - - 21 19 - COEFF(0, 0) = 3/4 y + 1/20 x - --, COEFF(1, 0) = 3/4 y - -- - 1/20 x, - 40 40 - - 17 - COEFF(2, 0) = - -- + 3/4 y - 3/20 x, COEFF(-1, 1) = - 3/4 y + 3/20 x + 7/40, - 40 - - 11 - COEFF(0, 1) = - 3/4 y + 1/20 x + 9/40, COEFF(1, 1) = - 3/4 y - 1/20 x + --, - 40 - - 13 - COEFF(2, 1) = - 3/20 x + -- - 3/4 y, COEFF(-1, 2) = - 3/20 x + 1/4 y + 3/40, - 40 - - COEFF(0, 2) = 1/4 y + 1/40 - 1/20 x, COEFF(1, 2) = 1/20 x + 1/4 y - 1/40, - - COEFF(2, 2) = 3/20 x - 3/40 + 1/4 y] - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order3.smooth0/coeffs-dyy.compute.c"); -bytes used=36029536, alloc=2162292, time=2.85 -bytes used=37029756, alloc=2162292, time=2.94 -> -################################################################################ -> -# -# 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=38029976, alloc=2162292, time=3.04 -bytes used=39030204, alloc=2162292, time=3.10 -bytes used=40030440, alloc=2162292, time=3.16 -bytes used=41032164, alloc=2162292, time=3.22 -bytes used=42032408, alloc=2162292, time=3.28 -bytes used=43032708, alloc=2162292, time=3.34 -interp_2d_cube_order4_smooth0 := (- 1/60 DATA(1, 1) - 1/60 DATA(-1, -1) - - + 1/60 DATA(1, -1) + 1/60 DATA(-1, 1) + 1/30 DATA(2, -1) - - - 1/120 DATA(-1, 2) - 1/30 DATA(2, 1) + 1/120 DATA(-1, -2) - - + 1/60 DATA(-2, -2) + 1/120 DATA(1, 2) + 1/60 DATA(2, 2) - - - 1/60 DATA(-2, 2) + 1/30 DATA(-2, 1) - 1/120 DATA(1, -2) - - 3 - - 1/60 DATA(2, -2) - 1/30 DATA(-2, -1)) x y + (- 1/35 DATA(2, 0) - - - 1/70 DATA(1, 0) - 1/140 DATA(1, 1) + 1/140 DATA(-1, -1) - - - 1/140 DATA(1, -1) + 1/70 DATA(-1, 0) + 1/140 DATA(-1, 1) - - - 1/70 DATA(2, -1) - 1/70 DATA(-1, 2) - 1/70 DATA(2, 1) - - - 1/70 DATA(-1, -2) - 1/35 DATA(-2, -2) + 1/70 DATA(1, 2) - - + 1/35 DATA(2, 2) - 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + 1/35 DATA(-2, 0) - - 2 - + 1/70 DATA(1, -2) + 1/35 DATA(2, -2) + 1/70 DATA(-2, -1)) x y + ( - - - 1/49 DATA(2, 0) + 1/49 DATA(0, 0) + 1/98 DATA(1, 0) + 1/98 DATA(0, 1) - - + 1/196 DATA(1, 1) + 1/98 DATA(0, -1) + 1/196 DATA(-1, -1) - - + 1/196 DATA(1, -1) + 1/98 DATA(-1, 0) + 1/196 DATA(-1, 1) - - - 1/98 DATA(2, -1) - 1/49 DATA(0, 2) - 1/98 DATA(-1, 2) - 1/98 DATA(2, 1) - - - 1/98 DATA(-1, -2) - 1/49 DATA(0, -2) + 1/49 DATA(-2, -2) - - - 1/98 DATA(1, 2) + 1/49 DATA(2, 2) + 1/49 DATA(-2, 2) - 1/98 DATA(-2, 1) - - - 1/49 DATA(-2, 0) - 1/98 DATA(1, -2) + 1/49 DATA(2, -2) - - 2 2 /37 37 - - 1/98 DATA(-2, -1)) x y + |--- DATA(1, 1) + --- DATA(-1, -1) - \300 300 - - 37 37 21 21 - - --- DATA(1, -1) - --- DATA(-1, 1) - --- DATA(2, -1) - --- DATA(-1, 2) - 300 300 200 200 - - 21 21 11 21 - + --- DATA(2, 1) + --- DATA(-1, -2) - --- DATA(-2, -2) + --- DATA(1, 2) - 200 200 150 200 - - 11 11 21 21 - - --- DATA(2, 2) + --- DATA(-2, 2) - --- DATA(-2, 1) - --- DATA(1, -2) - 150 150 200 200 - - 11 21 \ - + --- DATA(2, -2) + --- DATA(-2, -1)| x y + (- 1/70 DATA(0, 1) - 150 200 / - - - 1/140 DATA(1, 1) + 1/70 DATA(0, -1) + 1/140 DATA(-1, -1) - - + 1/140 DATA(1, -1) - 1/140 DATA(-1, 1) - 1/70 DATA(2, -1) - - - 1/35 DATA(0, 2) - 1/70 DATA(-1, 2) + 1/70 DATA(2, 1) + 1/70 DATA(-1, -2) - - + 1/35 DATA(0, -2) - 1/35 DATA(-2, -2) - 1/70 DATA(1, 2) + 1/35 DATA(2, 2) - - + 1/35 DATA(-2, 2) + 1/70 DATA(-2, 1) + 1/70 DATA(1, -2) - - 2 - - 1/35 DATA(2, -2) - 1/70 DATA(-2, -1)) x y + (- 1/60 DATA(1, 1) - - - 1/60 DATA(-1, -1) + 1/60 DATA(1, -1) + 1/60 DATA(-1, 1) - - - 1/120 DATA(2, -1) + 1/30 DATA(-1, 2) + 1/120 DATA(2, 1) - - - 1/30 DATA(-1, -2) + 1/60 DATA(-2, -2) - 1/30 DATA(1, 2) - - + 1/60 DATA(2, 2) - 1/60 DATA(-2, 2) - 1/120 DATA(-2, 1) - - 3 - + 1/30 DATA(1, -2) - 1/60 DATA(2, -2) + 1/120 DATA(-2, -1)) x y - - 96 541 246 246 - + ---- DATA(2, 0) + ---- DATA(0, 0) + ---- DATA(1, 0) + ---- DATA(0, 1) - 1225 1225 1225 1225 - - 24 - - ---- DATA(1, 1) + (1/60 DATA(2, 0) - 1/30 DATA(1, 0) - 1/30 DATA(1, 1) - 1225 - - + 1/30 DATA(-1, -1) - 1/30 DATA(1, -1) + 1/30 DATA(-1, 0) - - + 1/30 DATA(-1, 1) + 1/60 DATA(2, -1) + 1/30 DATA(-1, 2) + 1/60 DATA(2, 1) - - + 1/30 DATA(-1, -2) - 1/60 DATA(-2, -2) - 1/30 DATA(1, 2) - - + 1/60 DATA(2, 2) - 1/60 DATA(-2, 2) - 1/60 DATA(-2, 1) - 1/60 DATA(-2, 0) - - 3 - - 1/30 DATA(1, -2) + 1/60 DATA(2, -2) - 1/60 DATA(-2, -1)) x + ( - - 1/120 DATA(2, 0) + 1/20 DATA(0, 0) - 1/30 DATA(1, 0) + 1/20 DATA(0, 1) - - - 1/30 DATA(1, 1) + 1/20 DATA(0, -1) - 1/30 DATA(-1, -1) - - - 1/30 DATA(1, -1) - 1/30 DATA(-1, 0) - 1/30 DATA(-1, 1) - - + 1/120 DATA(2, -1) + 1/20 DATA(0, 2) - 1/30 DATA(-1, 2) - - + 1/120 DATA(2, 1) - 1/30 DATA(-1, -2) + 1/20 DATA(0, -2) - - + 1/120 DATA(-2, -2) - 1/30 DATA(1, 2) + 1/120 DATA(2, 2) - - + 1/120 DATA(-2, 2) + 1/120 DATA(-2, 1) + 1/120 DATA(-2, 0) - - 4 - - 1/30 DATA(1, -2) + 1/120 DATA(2, -2) + 1/120 DATA(-2, -1)) x + ( - - 1/20 DATA(2, 0) + 1/20 DATA(0, 0) + 1/20 DATA(1, 0) - 1/30 DATA(0, 1) - - - 1/30 DATA(1, 1) - 1/30 DATA(0, -1) - 1/30 DATA(-1, -1) - - - 1/30 DATA(1, -1) + 1/20 DATA(-1, 0) - 1/30 DATA(-1, 1) - - - 1/30 DATA(2, -1) + 1/120 DATA(0, 2) + 1/120 DATA(-1, 2) - - - 1/30 DATA(2, 1) + 1/120 DATA(-1, -2) + 1/120 DATA(0, -2) - - + 1/120 DATA(-2, -2) + 1/120 DATA(1, 2) + 1/120 DATA(2, 2) - - + 1/120 DATA(-2, 2) - 1/30 DATA(-2, 1) + 1/20 DATA(-2, 0) - - 4 - + 1/120 DATA(1, -2) + 1/120 DATA(2, -2) - 1/30 DATA(-2, -1)) y + ( - - - 1/30 DATA(0, 1) - 1/30 DATA(1, 1) + 1/30 DATA(0, -1) + 1/30 DATA(-1, -1) - - + 1/30 DATA(1, -1) - 1/30 DATA(-1, 1) + 1/30 DATA(2, -1) + 1/60 DATA(0, 2) - - + 1/60 DATA(-1, 2) - 1/30 DATA(2, 1) - 1/60 DATA(-1, -2) - - - 1/60 DATA(0, -2) - 1/60 DATA(-2, -2) + 1/60 DATA(1, 2) + 1/60 DATA(2, 2) - - + 1/60 DATA(-2, 2) - 1/30 DATA(-2, 1) - 1/60 DATA(1, -2) - - 3 / 41 - - 1/60 DATA(2, -2) + 1/30 DATA(-2, -1)) y + |- --- DATA(2, 0) - \ 196 - - 57 53 83 181 - - --- DATA(0, 0) - --- DATA(1, 0) + --- DATA(0, 1) + ---- DATA(1, 1) - 196 196 735 1470 - - 83 181 181 53 - + --- DATA(0, -1) + ---- DATA(-1, -1) + ---- DATA(1, -1) - --- DATA(-1, 0) - 735 1470 1470 196 - - 181 113 191 71 - + ---- DATA(-1, 1) + --- DATA(2, -1) + ---- DATA(0, 2) + ---- DATA(-1, 2) - 1470 735 5880 5880 - - 113 71 191 - + --- DATA(2, 1) + ---- DATA(-1, -2) + ---- DATA(0, -2) - 735 5880 5880 - - 289 71 289 289 - - ---- DATA(-2, -2) + ---- DATA(1, 2) - ---- DATA(2, 2) - ---- DATA(-2, 2) - 5880 5880 5880 5880 - - 113 41 71 289 - + --- DATA(-2, 1) - --- DATA(-2, 0) + ---- DATA(1, -2) - ---- DATA(2, -2) - 735 196 5880 5880 - - 113 \ 2 /17 31 - + --- DATA(-2, -1)| y + |--- DATA(0, 1) + --- DATA(1, 1) - 735 / \105 210 - - 17 31 31 31 - - --- DATA(0, -1) - --- DATA(-1, -1) - --- DATA(1, -1) + --- DATA(-1, 1) - 105 210 210 210 - - 11 17 11 - - --- DATA(2, -1) + --- DATA(0, 2) + 1/84 DATA(-1, 2) + --- DATA(2, 1) - 105 420 105 - - 17 31 - - 1/84 DATA(-1, -2) - --- DATA(0, -2) + --- DATA(-2, -2) + 1/84 DATA(1, 2) - 420 420 - - 31 31 11 - - --- DATA(2, 2) - --- DATA(-2, 2) + --- DATA(-2, 1) - 1/84 DATA(1, -2) - 420 420 105 - - 31 11 \ /17 17 - + --- DATA(2, -2) - --- DATA(-2, -1)| y + |--- DATA(2, 0) + --- DATA(1, 0) - 420 105 / \420 105 - - 31 31 31 17 - + --- DATA(1, 1) - --- DATA(-1, -1) + --- DATA(1, -1) - --- DATA(-1, 0) - 210 210 210 105 - - 31 11 - - --- DATA(-1, 1) + 1/84 DATA(2, -1) - --- DATA(-1, 2) + 1/84 DATA(2, 1) - 210 105 - - 11 31 11 31 - - --- DATA(-1, -2) + --- DATA(-2, -2) + --- DATA(1, 2) - --- DATA(2, 2) - 105 420 105 420 - - 31 17 11 - + --- DATA(-2, 2) - 1/84 DATA(-2, 1) - --- DATA(-2, 0) + --- DATA(1, -2) - 420 420 105 - - 31 \ /191 - - --- DATA(2, -2) - 1/84 DATA(-2, -1)| x + |---- DATA(2, 0) - 420 / \5880 - - 57 83 53 181 - - --- DATA(0, 0) + --- DATA(1, 0) - --- DATA(0, 1) + ---- DATA(1, 1) - 196 735 196 1470 - - 53 181 181 83 - - --- DATA(0, -1) + ---- DATA(-1, -1) + ---- DATA(1, -1) + --- DATA(-1, 0) - 196 1470 1470 735 - - 181 71 41 113 - + ---- DATA(-1, 1) + ---- DATA(2, -1) - --- DATA(0, 2) + --- DATA(-1, 2) - 1470 5880 196 735 - - 71 113 41 289 - + ---- DATA(2, 1) + --- DATA(-1, -2) - --- DATA(0, -2) - ---- DATA(-2, -2) - 5880 735 196 5880 - - 113 289 289 71 - + --- DATA(1, 2) - ---- DATA(2, 2) - ---- DATA(-2, 2) + ---- DATA(-2, 1) - 735 5880 5880 5880 - - 191 113 289 - + ---- DATA(-2, 0) + --- DATA(1, -2) - ---- DATA(2, -2) - 5880 735 5880 - - 71 \ 2 246 24 - + ---- DATA(-2, -1)| x + ---- DATA(0, -1) - ---- DATA(-1, -1) - 5880 / 1225 1225 - - 24 246 24 - - ---- DATA(1, -1) + ---- DATA(-1, 0) - ---- DATA(-1, 1) - 1225 1225 1225 - - 99 96 99 99 - - ---- DATA(2, -1) + ---- DATA(0, 2) - ---- DATA(-1, 2) - ---- DATA(2, 1) - 1225 1225 1225 1225 - - 99 96 51 - - ---- DATA(-1, -2) + ---- DATA(0, -2) + ---- DATA(-2, -2) - 1225 1225 1225 - - 99 51 51 99 - - ---- DATA(1, 2) + ---- DATA(2, 2) + ---- DATA(-2, 2) - ---- DATA(-2, 1) - 1225 1225 1225 1225 - - 96 99 51 - + ---- DATA(-2, 0) - ---- DATA(1, -2) + ---- DATA(2, -2) - 1225 1225 1225 - - 99 - - ---- DATA(-2, -1) - 1225 - -> -# I -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=44034460, alloc=2162292, time=3.41 - 2 2 3 3 4 2 -[COEFF(-2, -2) = 1/49 x y + 1/60 x y + 1/60 x y + 1/120 x - 1/35 x y - - 2 3 11 289 2 3 289 2 51 - - 1/35 x y - 1/60 y - --- x y - ---- y - 1/60 x - ---- x + ---- - 150 5880 5880 1225 - - 31 4 31 2 2 3 - + --- x + 1/120 y + --- y, COEFF(-1, -2) = - 1/98 x y - 1/30 x y - 420 420 - - 21 2 3 4 113 2 3 3 - + --- x y - 1/70 x y + 1/120 x y + 1/120 y + --- x - 1/60 y + 1/30 x - 200 735 - - 71 2 4 2 11 99 - + ---- y - 1/30 x - 1/84 y + 1/70 x y - --- x - ----, COEFF(0, -2) = - 5880 105 1225 - - 2 191 2 17 4 4 2 2 3 - 1/35 x y + ---- y - --- y + 1/20 x + 1/120 y - 1/49 x y - 1/60 y - 5880 420 - - 96 41 2 21 2 3 - + ---- - --- x , COEFF(1, -2) = - --- x y + 1/70 x y - 1/120 x y - 1225 196 200 - - 3 3 11 4 2 2 2 - - 1/30 x - 1/60 y + --- x + 1/120 y - 1/98 x y - 1/84 y + 1/70 x y - 105 - - 71 2 99 113 2 3 4 31 - + ---- y - ---- + --- x + 1/30 x y - 1/30 x , COEFF(2, -2) = - --- x - 5880 1225 735 420 - - 3 2 51 3 4 2 2 289 2 - + 1/60 x + 1/35 x y + ---- - 1/60 x y + 1/120 x + 1/49 x y - ---- x - 1225 5880 - - 31 11 4 2 289 2 3 3 - + --- y + --- x y + 1/120 y - 1/35 x y - ---- y - 1/60 x y - 1/60 y , - 420 150 5880 - - 3 4 99 11 3 3 - COEFF(-2, -1) = - 1/60 x - 1/30 y - ---- - --- y - 1/30 x y + 1/30 y - 1225 105 - - 4 113 2 2 71 2 2 2 21 - + 1/120 x + --- y + 1/70 x y + ---- x - 1/98 x y + --- x y - 735 5880 200 - - 3 2 2 4 - + 1/120 x y - 1/84 x - 1/70 x y, COEFF(-1, -1) = 1/140 x y - 1/30 x - - 2 2 3 181 2 3 4 181 2 - + 1/196 x y + 1/30 y + ---- x - 1/60 x y - 1/30 y + ---- y - 1470 1470 - - 3 31 2 3 37 31 24 - - 1/60 x y - --- x + 1/140 x y + 1/30 x + --- x y - --- y - ----, - 210 300 210 1225 - - 83 2 17 3 246 53 2 2 2 - COEFF(0, -1) = --- y - --- y + 1/30 y + ---- - --- x + 1/98 x y - 735 105 1225 196 - - 4 2 4 24 2 - + 1/20 x + 1/70 x y - 1/30 y , COEFF(1, -1) = - ---- - 1/140 x y - 1225 - - 181 2 2 31 3 3 3 181 2 - + ---- y + 1/140 x y - --- y + 1/60 x y + 1/30 y + 1/60 x y + ---- x - 1470 210 1470 - - 37 4 31 4 3 2 2 - - --- x y - 1/30 x + --- x - 1/30 y - 1/30 x + 1/196 x y , - 300 210 - - 2 3 3 11 2 - COEFF(2, -1) = - 1/70 x y - 1/120 x y + 1/30 y - --- y - 1/70 x y - 105 - - 99 3 3 4 113 2 4 71 2 - - ---- + 1/30 x y + 1/60 x - 1/30 y + --- y + 1/120 x + ---- x - 1225 735 5880 - - 2 2 21 191 2 96 41 2 - - 1/98 x y + 1/84 x - --- x y, COEFF(-2, 0) = ---- x + ---- - --- y - 200 5880 1225 196 - - 3 2 2 2 4 17 4 - - 1/60 x + 1/35 x y - 1/49 x y + 1/120 x - --- x + 1/20 y , - 420 - - 246 3 17 83 2 4 2 - COEFF(-1, 0) = ---- + 1/30 x - --- x + --- x + 1/20 y + 1/70 x y - 1225 105 735 - - 4 2 2 53 2 - - 1/30 x + 1/98 x y - --- y , - 196 - - 57 2 4 2 2 4 541 57 2 - COEFF(0, 0) = - --- x + 1/20 y + 1/49 x y + 1/20 x + ---- - --- y , - 196 1225 196 - - 4 2 2 53 2 83 2 4 246 - COEFF(1, 0) = 1/20 y + 1/98 x y - --- y + --- x - 1/30 x + ---- - 196 735 1225 - - 2 3 17 96 2 191 2 - - 1/70 x y - 1/30 x + --- x, COEFF(2, 0) = ---- - 1/35 x y + ---- x - 105 1225 5880 - - 41 2 3 17 2 2 4 4 - - --- y + 1/60 x + --- x - 1/49 x y + 1/120 x + 1/20 y , COEFF(-2, 1) - 196 420 - - 21 3 2 3 71 2 11 3 - = - --- x y - 1/60 x + 1/70 x y - 1/30 y + ---- x + --- y - 1/120 x y - 200 5880 105 - - 2 2 3 4 2 113 2 4 99 - - 1/98 x y + 1/30 x y + 1/120 x + 1/70 x y + --- y - 1/30 y - ---- - 735 1225 - - 3 37 3 2 - - 1/84 x, COEFF(-1, 1) = 1/60 x y - --- x y + 1/60 x y - 1/140 x y - 300 - - 4 3 181 2 2 24 31 181 2 - - 1/30 x + 1/30 x + ---- x + 1/140 x y - ---- - --- x + ---- y - 1470 1225 210 1470 - - 3 4 2 2 31 83 2 53 2 - - 1/30 y - 1/30 y + 1/196 x y + --- y, COEFF(0, 1) = --- y - --- x - 210 735 196 - - 2 2 17 3 4 4 246 2 - + 1/98 x y + --- y - 1/30 y + 1/20 x - 1/30 y + ---- - 1/70 x y, - 105 1225 - - 3 2 3 181 2 3 - COEFF(1, 1) = - 1/60 x y - 1/140 x y - 1/60 x y + ---- x - 1/30 x - 1470 - - 24 181 2 37 3 2 2 2 31 - - ---- + ---- y + --- x y - 1/30 y + 1/196 x y - 1/140 x y + --- x - 1225 1470 300 210 - - 4 31 4 3 3 - - 1/30 y + --- y - 1/30 x , COEFF(2, 1) = - 1/30 x y - 1/30 y + 1/84 x - 210 - - 2 21 71 2 4 113 2 2 2 - + 1/70 x y + --- x y + ---- x - 1/30 y + --- y - 1/98 x y - 200 5880 735 - - 3 4 99 3 2 11 - + 1/120 x y + 1/120 x - ---- + 1/60 x - 1/70 x y + --- y, COEFF(-2, 2) - 1225 105 - - 2 31 3 51 3 11 289 2 - = - 1/35 x y + --- x - 1/60 x y + ---- - 1/60 x y + --- x y - ---- y - 420 1225 150 5880 - - 3 2 31 289 2 4 4 2 2 - + 1/60 y + 1/35 x y - --- y - ---- x + 1/120 x + 1/120 y + 1/49 x y - 420 5880 - - 3 3 2 71 2 3 - - 1/60 x , COEFF(-1, 2) = - 1/120 x y - 1/70 x y + ---- y + 1/60 y - 5880 - - 4 21 3 11 2 2 113 2 3 - + 1/120 y - --- x y + 1/30 x - --- x - 1/98 x y + --- x + 1/30 x y - 200 105 735 - - 99 2 4 41 2 191 2 - - ---- - 1/70 x y + 1/84 y - 1/30 x , COEFF(0, 2) = - --- x + ---- y - 1225 196 5880 - - 4 4 96 2 3 2 2 17 - + 1/120 y + 1/20 x + ---- - 1/35 x y + 1/60 y - 1/49 x y + --- y, - 1225 420 - - 99 71 2 3 3 4 21 - COEFF(1, 2) = - ---- + ---- y + 1/120 x y - 1/30 x + 1/120 y + --- x y - 1225 5880 200 - - 11 2 2 113 2 3 3 2 - + --- x - 1/98 x y + --- x + 1/60 y - 1/30 x y + 1/70 x y - 105 735 - - 2 4 3 289 2 - - 1/70 x y + 1/84 y - 1/30 x , COEFF(2, 2) = 1/60 x y - ---- x - 5880 - - 289 2 11 31 3 4 3 2 - - ---- y - --- x y - --- x + 1/60 x + 1/120 y + 1/60 y + 1/35 x y - 5880 150 420 - - 2 2 2 31 3 51 4 - + 1/49 x y + 1/35 x y - --- y + 1/60 x y + ---- + 1/120 x ] - 420 1225 - -> print_coeffs__lc_of_data(%, "coeffs_I->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-I.compute.c"); -bytes used=45034944, alloc=2162292, time=3.47 -bytes used=46035108, alloc=2162292, time=3.54 -bytes used=47035352, alloc=2162292, time=3.60 -bytes used=48052304, alloc=2162292, time=3.67 -bytes used=49052696, alloc=2227816, time=3.74 -bytes used=50052952, alloc=2227816, time=3.86 -bytes used=51053208, alloc=2227816, time=3.97 -bytes used=52055716, alloc=2227816, time=4.04 -bytes used=53062388, alloc=2227816, time=4.13 -bytes used=54063168, alloc=2227816, time=4.27 -bytes used=55063348, alloc=2227816, time=4.36 -bytes used=56070108, alloc=2227816, time=4.45 -bytes used=57070308, alloc=2227816, time=4.57 -bytes used=58070564, alloc=2227816, time=4.72 -bytes used=59070836, alloc=2227816, time=4.78 -bytes used=60071040, alloc=2227816, time=4.91 -bytes used=61071296, alloc=2227816, time=5.05 -bytes used=62071508, alloc=2227816, time=5.13 -bytes used=63071660, alloc=2227816, time=5.27 -bytes used=64071832, alloc=2227816, time=5.34 -bytes used=65072432, alloc=2227816, time=5.51 -bytes used=66072588, alloc=2227816, time=5.61 -> -# d/dx -> simplify( diff(interp_2d_cube_order4_smooth0,x) ); -bytes used=67072804, alloc=2358864, time=5.68 -bytes used=68073096, alloc=2358864, time=5.74 -bytes used=69073300, alloc=2424388, time=5.81 -17 17 31 31 ---- DATA(2, 0) + --- DATA(1, 0) + --- DATA(1, 1) - --- DATA(-1, -1) -420 105 210 210 - - 31 17 31 - + --- DATA(1, -1) - --- DATA(-1, 0) - --- DATA(-1, 1) + 1/84 DATA(2, -1) - 210 105 210 - - 2 2 2 - - 1/10 x DATA(1, 2) + 1/20 x DATA(2, 2) - 1/20 x DATA(-2, 2) - - 2 2 - - 1/20 x DATA(-2, 1) + 1/40 x y DATA(2, 1) + 1/35 x y DATA(2, 1) - - 11 11 31 - - --- DATA(-1, 2) + 1/84 DATA(2, 1) - --- DATA(-1, -2) + --- DATA(-2, -2) - 105 105 420 - - 2 2 2 - + 1/20 x y DATA(-1, 1) - 1/40 x y DATA(-2, 1) + 1/10 x y DATA(-1, 2) - - 2 - + 1/35 x y DATA(0, -1) + 1/20 x y DATA(-2, -2) - 1/70 x y DATA(-1, 1) - - 2 2 - - 1/35 x y DATA(2, -1) + 1/20 x y DATA(2, 2) + 1/10 x y DATA(1, -2) - - 2 3 - + 1/40 x y DATA(-2, -1) - 2/35 x y DATA(0, 2) + 1/120 y DATA(1, 2) - - 3 3 3 - - 1/60 y DATA(1, 1) - 1/60 y DATA(-1, -1) + 1/30 x DATA(-2, -1) - - 3 3 3 - + 1/5 x DATA(0, -1) + 1/5 x DATA(0, 1) + 1/60 y DATA(-1, 1) - - 2 2 2 - - 1/35 y DATA(2, 0) - 1/70 y DATA(1, 0) - 1/140 y DATA(1, 1) - - 3 3 3 - - 1/30 y DATA(-2, -1) + 1/60 y DATA(-2, -2) + 1/60 y DATA(2, 2) - - 3 3 3 - - 1/60 y DATA(-2, 2) + 1/30 y DATA(-2, 1) - 1/120 y DATA(1, -2) - - 3 2 2 - - 1/60 y DATA(2, -2) + 1/140 y DATA(-1, -1) - 1/140 y DATA(1, -1) - - 2 2 2 - + 1/70 y DATA(-1, 0) + 1/140 y DATA(-1, 1) - 1/70 y DATA(2, -1) - - 2 2 3 - - 1/70 y DATA(-1, 2) - 1/70 y DATA(2, 1) + 1/60 y DATA(1, -1) - - 3 3 3 - + 1/30 y DATA(2, -1) - 1/120 y DATA(-1, 2) - 1/30 y DATA(2, 1) - - 3 2 37 - + 1/120 y DATA(-1, -2) + 1/70 y DATA(-2, -1) + --- y DATA(1, 1) - 300 - - 37 2 2 - + --- y DATA(-1, -1) - 1/70 y DATA(-1, -2) + 1/70 y DATA(1, 2) - 300 - - 2 2 2 - + 1/35 y DATA(2, 2) - 1/35 y DATA(-2, 2) + 1/70 y DATA(-2, 1) - - 2 2 21 - - 1/35 y DATA(-2, -2) - 1/20 x y DATA(1, 1) + --- y DATA(1, 2) - 200 - - 11 11 21 - - --- y DATA(2, 2) + --- y DATA(-2, 2) - --- y DATA(-2, 1) - 150 150 200 - - 21 11 21 - - --- y DATA(1, -2) + --- y DATA(2, -2) + --- y DATA(-2, -1) - 200 150 200 - - 37 2 2 - - --- y DATA(-1, 1) + 1/35 y DATA(-2, 0) + 1/70 y DATA(1, -2) - 300 - - 2 2 - + 1/35 y DATA(2, -2) - 1/10 x y DATA(1, 2) - 1/35 x y DATA(0, 1) - - 2 - - 1/10 x y DATA(-1, -2) + 1/70 x y DATA(1, -1) - 1/35 x y DATA(-1, 2) - - 11 2 2 - + --- DATA(1, 2) - 2/49 x y DATA(0, -2) + 1/49 x y DATA(1, 0) - 105 - - 2 - + 1/49 x y DATA(-1, 0) + 1/35 x y DATA(-2, 1) - 2/35 x y DATA(2, -2) - - - 1/35 x y DATA(-2, -1) + 1/35 x y DATA(1, -2) + 1/35 x y DATA(-1, -2) - - + 2/35 x y DATA(0, -2) - 2/35 x y DATA(-2, -2) - 1/35 x y DATA(1, 2) - - 2 - + 2/35 x y DATA(2, 2) + 2/35 x y DATA(-2, 2) - 1/49 x y DATA(1, -2) - - 2 2 2 - + 2/49 x y DATA(2, -2) - 1/49 x y DATA(-2, -1) + 1/49 x y DATA(0, 1) - - 2 2 31 - + 1/49 x y DATA(0, -1) - 2/49 x y DATA(0, 2) - --- DATA(2, 2) - 420 - - 2 2 2 - + 2/49 x y DATA(2, 2) + 2/49 x y DATA(-2, 2) + 1/98 x y DATA(-1, -1) - - 2 2 2 - + 1/98 x y DATA(1, -1) + 1/98 x y DATA(1, 1) - 2/49 x y DATA(2, 0) - - 2 3 3 - + 2/49 x y DATA(0, 0) - 2/15 x DATA(1, 1) + 1/30 x DATA(-2, 1) - - 3 3 3 - - 2/15 x DATA(-1, -2) + 1/30 x DATA(-2, -2) - 2/15 x DATA(1, 2) - - 3 3 3 - + 1/30 x DATA(2, 2) + 1/30 x DATA(-2, 2) - 2/15 x DATA(-1, -1) - - 3 3 3 - - 2/15 x DATA(1, -1) - 2/15 x DATA(-1, 1) + 1/30 x DATA(2, -1) - - 3 3 3 - - 2/15 x DATA(-1, 2) + 1/30 x DATA(2, 0) + 1/5 x DATA(0, 0) - - 3 3 37 - - 2/15 x DATA(1, -2) + 1/30 x DATA(2, -2) - --- y DATA(1, -1) - 300 - - 21 21 21 - - --- y DATA(2, -1) - --- y DATA(-1, 2) + --- y DATA(2, 1) - 200 200 200 - - 21 11 2 - + --- y DATA(-1, -2) - --- y DATA(-2, -2) + 1/98 x y DATA(-1, 1) - 200 150 - - 53 3 181 - - -- x DATA(0, 1) + 1/30 x DATA(2, 1) + --- x DATA(1, 1) - 98 735 - - 191 57 226 - + ---- x DATA(2, 0) - -- x DATA(0, 0) + --- x DATA(1, -2) - 2940 98 735 - - 3 3 3 - + 1/5 x DATA(0, 2) + 1/5 x DATA(0, -2) - 2/15 x DATA(1, 0) - - 3 3 71 - - 2/15 x DATA(-1, 0) + 1/30 x DATA(-2, 0) + ---- x DATA(-2, -1) - 2940 - - 191 71 226 - + ---- x DATA(-2, 0) + ---- x DATA(-2, 1) + --- x DATA(-1, -2) - 2940 2940 735 - - 289 226 289 - - ---- x DATA(-2, -2) + --- x DATA(1, 2) - ---- x DATA(2, 2) - 2940 735 2940 - - 289 2 2 - - ---- x DATA(2, -2) - 1/49 x y DATA(2, -1) - 1/10 x DATA(1, 1) - 2940 - - 2 2 2 - + 1/10 x DATA(-1, -1) - 1/10 x DATA(1, -1) + 1/10 x DATA(-1, 0) - - 2 2 2 - + 1/10 x DATA(-1, 1) + 1/20 x DATA(2, -1) + 1/10 x DATA(-1, 2) - - 2 289 181 - + 1/20 x DATA(2, 1) - ---- x DATA(-2, 2) + --- x DATA(1, -1) - 2940 735 - - 181 71 226 - + --- x DATA(-1, 1) + ---- x DATA(2, -1) + --- x DATA(-1, 2) - 735 2940 735 - - 71 181 53 - + ---- x DATA(2, 1) + --- x DATA(-1, -1) - -- x DATA(0, -1) - 2940 735 98 - - 41 41 166 - - -- x DATA(0, 2) - -- x DATA(0, -2) + --- x DATA(1, 0) - 98 98 735 - - 166 2 2 - + --- x DATA(-1, 0) - 1/20 x DATA(-2, 0) - 1/10 x DATA(1, -2) - 735 - - 2 2 2 - + 1/20 x DATA(2, -2) - 1/20 x DATA(-2, -1) + 1/20 x DATA(2, 0) - - 2 2 2 - - 1/10 x DATA(1, 0) - 1/49 x y DATA(-1, 2) - 1/40 x y DATA(2, -1) - - 2 2 2 - - 1/20 x y DATA(-1, -1) + 1/20 x y DATA(1, -1) - 1/49 x y DATA(2, 1) - - 2 2 2 - - 2/49 x y DATA(-2, 0) - 1/49 x y DATA(-2, 1) - 1/49 x y DATA(-1, -2) - - 2 2 - + 2/49 x y DATA(-2, -2) - 1/49 x y DATA(1, 2) + 1/70 x y DATA(-1, -1) - - 2 2 - - 1/20 x y DATA(2, -2) - 1/20 x y DATA(-2, 2) - 1/70 x y DATA(1, 1) - - 2 2 31 - + 1/10 x DATA(-1, -2) - 1/20 x DATA(-2, -2) + --- DATA(-2, 2) - 420 - - 17 11 31 - - 1/84 DATA(-2, 1) - --- DATA(-2, 0) + --- DATA(1, -2) - --- DATA(2, -2) - 420 105 420 - - - 1/84 DATA(-2, -1) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=70074076, alloc=2489912, time=5.88 - 11 289 3 2 2 -[COEFF(-2, -2) = - --- y - ---- x - 2/35 x y + 1/60 y - 1/20 x + 1/20 x y - 150 2940 - - 2 31 3 2 3 11 - - 1/35 y + --- + 1/30 x + 2/49 x y , COEFF(-1, -2) = - 2/15 x - --- - 420 105 - - 21 2 2 2 2 226 - + --- y - 1/70 y + 1/35 x y - 1/49 x y + 1/10 x - 1/10 x y + --- x - 200 735 - - 3 2 3 41 - + 1/120 y , COEFF(0, -2) = - 2/49 x y + 2/35 x y + 1/5 x - -- x, - 98 - - 11 2 226 2 3 - COEFF(1, -2) = 1/35 x y + --- - 1/49 x y + --- x + 1/10 x y - 1/120 y - 105 735 - - 2 21 3 2 2 - - 1/10 x - --- y - 2/15 x + 1/70 y , COEFF(2, -2) = - 1/20 x y - 200 - - 2 31 3 2 2 11 - - 2/35 x y + 1/35 y - --- - 1/60 y + 2/49 x y + 1/20 x + --- y - 420 150 - - 289 3 21 2 - - ---- x + 1/30 x , COEFF(-2, -1) = --- y + 1/40 x y - 1/84 - 1/35 x y - 2940 200 - - 2 71 2 3 3 2 - - 1/49 x y + ---- x - 1/20 x + 1/30 x - 1/30 y + 1/70 y , - 2940 - - 3 2 2 3 - COEFF(-1, -1) = - 2/15 x + 1/10 x - 1/20 x y + 1/70 x y - 1/60 y - - 2 37 181 31 2 - + 1/140 y + --- y + --- x - --- + 1/98 x y , - 300 735 210 - - 2 53 3 - COEFF(0, -1) = 1/49 x y - -- x + 1/5 x + 1/35 x y, COEFF(1, -1) = - 98 - - 2 2 3 181 37 31 2 - - 1/10 x + 1/98 x y + 1/60 y + --- x + 1/70 x y - --- y + --- - 1/140 y - 735 300 210 - - 2 3 3 71 2 - + 1/20 x y - 2/15 x , COEFF(2, -1) = 1/30 y + 1/84 + ---- x - 1/40 x y - 2940 - - 2 21 2 2 3 - - 1/49 x y - --- y - 1/35 x y + 1/20 x - 1/70 y + 1/30 x , - 200 - - 191 2 2 2 3 17 - COEFF(-2, 0) = ---- x + 1/35 y - 2/49 x y - 1/20 x + 1/30 x - ---, - 2940 420 - - 3 2 17 2 166 2 - COEFF(-1, 0) = - 2/15 x + 1/70 y - --- + 1/49 x y + --- x + 1/10 x , - 105 735 - - 3 57 2 - COEFF(0, 0) = 1/5 x - -- x + 2/49 x y , - 98 - - 2 2 17 2 3 166 - COEFF(1, 0) = 1/49 x y - 1/70 y + --- - 1/10 x - 2/15 x + --- x, - 105 735 - - 2 17 3 191 2 2 - COEFF(2, 0) = - 2/49 x y + --- + 1/30 x + ---- x - 1/35 y + 1/20 x , - 420 2940 - - 3 2 71 21 2 - COEFF(-2, 1) = 1/30 x - 1/40 x y + ---- x - --- y - 1/20 x + 1/35 x y - 2940 200 - - 2 2 3 3 2 - + 1/70 y - 1/84 - 1/49 x y + 1/30 y , COEFF(-1, 1) = 1/60 y + 1/98 x y - - 2 31 2 181 3 37 - + 1/140 y - --- + 1/20 x y + --- x - 2/15 x - 1/70 x y - --- y - 210 735 300 - - 2 3 2 53 - + 1/10 x , COEFF(0, 1) = 1/5 x - 1/35 x y + 1/49 x y - -- x, COEFF(1, 1) - 98 - - 3 181 2 2 2 - = - 1/60 y - 1/70 x y + --- x + 1/98 x y - 1/20 x y - 1/140 y - 735 - - 3 37 31 2 2 2 - - 2/15 x + --- y + --- - 1/10 x , COEFF(2, 1) = - 1/49 x y + 1/40 x y - 300 210 - - 21 71 3 3 2 2 - + 1/35 x y + --- y + 1/84 + ---- x + 1/30 x - 1/30 y + 1/20 x - 1/70 y - 200 2940 - - 31 2 3 11 2 - , COEFF(-2, 2) = --- - 1/20 x y + 1/30 x + 2/35 x y + --- y + 2/49 x y - 420 150 - - 3 2 289 2 - - 1/60 y - 1/35 y - ---- x - 1/20 x , COEFF(-1, 2) = - 1/35 x y - 2940 - - 2 3 11 3 2 2 21 - - 1/70 y - 2/15 x - --- - 1/120 y - 1/49 x y + 1/10 x y - --- y - 105 200 - - 226 2 2 3 41 - + --- x + 1/10 x , COEFF(0, 2) = - 2/49 x y + 1/5 x - 2/35 x y - -- x, - 735 98 - - 2 21 3 3 2 - COEFF(1, 2) = - 1/35 x y - 1/10 x + --- y + 1/120 y - 2/15 x - 1/49 x y - 200 - - 2 11 2 226 2 31 3 - + 1/70 y + --- - 1/10 x y + --- x, COEFF(2, 2) = 1/20 x - --- + 1/60 y - 105 735 420 - - 2 2 11 289 2 3 - + 1/20 x y + 2/49 x y - --- y + 2/35 x y - ---- x + 1/35 y + 1/30 x ] - 150 2940 - -> print_coeffs__lc_of_data(%, "coeffs_dx->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dx.compute.c"); -bytes used=71074548, alloc=2489912, time=5.96 -bytes used=72074804, alloc=2489912, time=6.03 -bytes used=73076960, alloc=2489912, time=6.10 -bytes used=74077744, alloc=2489912, time=6.24 -bytes used=75078056, alloc=2489912, time=6.32 -bytes used=76078252, alloc=2489912, time=6.46 -bytes used=77078548, alloc=2489912, time=6.53 -bytes used=78078716, alloc=2489912, time=6.69 -bytes used=79078944, alloc=2489912, time=6.78 -bytes used=80079564, alloc=2489912, time=6.91 -> -# d/dy -> simplify( diff(interp_2d_cube_order4_smooth0,y) ); -bytes used=81080236, alloc=2489912, time=7.01 -bytes used=82080460, alloc=2489912, time=7.07 -bytes used=83081684, alloc=2489912, time=7.13 -17 31 17 31 ---- DATA(0, 1) + --- DATA(1, 1) - --- DATA(0, -1) - --- DATA(-1, -1) -105 210 105 210 - - 31 2 2 - - --- DATA(1, -1) + 1/35 x DATA(0, -2) - 1/35 x DATA(0, 2) - 210 - - 2 2 2 - + 1/70 x DATA(0, -1) + 1/10 y DATA(0, -1) - 1/20 y DATA(0, -2) - - 2 2 53 - - 1/10 y DATA(0, 1) + 1/20 y DATA(0, 2) - -- y DATA(-1, 0) - 98 - - 166 41 2 - + --- y DATA(0, -1) - -- y DATA(-2, 0) - 2/49 x y DATA(0, 2) - 735 98 - - 2 2 2 - + 1/49 x y DATA(0, -1) - 2/49 x y DATA(0, -2) - 2/49 x y DATA(2, 0) - - 2 2 2 - + 2/49 x y DATA(0, 0) + 1/49 x y DATA(1, 0) + 1/49 x y DATA(-1, 0) - - 2 - - 2/49 x y DATA(-2, 0) - 2/35 x y DATA(2, 0) - 1/35 x y DATA(1, 0) - - 2 - + 1/49 x y DATA(0, 1) + 2/35 x y DATA(-2, 0) + 1/35 x y DATA(-1, 0) - - 2 53 41 57 - - 1/70 x DATA(0, 1) - -- y DATA(1, 0) - -- y DATA(2, 0) - -- y DATA(0, 0) - 98 98 98 - - 191 191 3 - + ---- y DATA(0, -2) + ---- y DATA(0, 2) + 1/5 y DATA(1, 0) - 2940 2940 - - 3 3 3 - + 1/5 y DATA(-1, 0) + 1/5 y DATA(-2, 0) - 2/15 y DATA(0, -1) - - 3 166 3 - + 1/30 y DATA(0, 2) + --- y DATA(0, 1) + 1/30 y DATA(0, -2) - 735 - - 3 3 3 - + 1/5 y DATA(2, 0) + 1/5 y DATA(0, 0) - 2/15 y DATA(0, 1) - - 31 11 2 - + --- DATA(-1, 1) - --- DATA(2, -1) - 1/70 x DATA(1, 2) - 210 105 - - 2 2 2 - + 1/35 x DATA(2, 2) + 1/35 x DATA(-2, 2) + 1/70 x DATA(-2, 1) - - 2 17 - - 1/49 x y DATA(2, 1) - 1/35 x y DATA(2, 1) + --- DATA(0, 2) - 420 - - 11 17 - + 1/84 DATA(-1, 2) + --- DATA(2, 1) - 1/84 DATA(-1, -2) - --- DATA(0, -2) - 105 420 - - 31 2 2 - + --- DATA(-2, -2) + 1/98 x y DATA(-1, 1) - 1/49 x y DATA(-2, 1) - 420 - - 2 2 - - 1/49 x y DATA(-1, 2) + 2/49 x y DATA(-2, -2) + 1/70 x y DATA(-1, 1) - - 2 2 - - 1/35 x y DATA(2, -1) + 2/49 x y DATA(2, 2) - 1/49 x y DATA(1, -2) - - 2 3 3 - - 1/49 x y DATA(-2, -1) + 1/30 y DATA(1, 2) - 2/15 y DATA(1, 1) - - 3 3 3 - - 2/15 y DATA(-1, -1) + 1/120 x DATA(-2, -1) - 2/15 y DATA(-1, 1) - - 2 3 3 - - 1/10 y DATA(1, 1) - 2/15 y DATA(-2, -1) + 1/30 y DATA(-2, -2) - - 3 3 3 - + 1/30 y DATA(2, 2) + 1/30 y DATA(-2, 2) - 2/15 y DATA(-2, 1) - - 3 3 2 - + 1/30 y DATA(1, -2) + 1/30 y DATA(2, -2) + 1/10 y DATA(-1, -1) - - 2 2 2 - + 1/10 y DATA(1, -1) - 1/10 y DATA(-1, 1) + 1/10 y DATA(2, -1) - - 2 2 3 - + 1/20 y DATA(-1, 2) - 1/10 y DATA(2, 1) - 2/15 y DATA(1, -1) - - 3 3 3 - - 2/15 y DATA(2, -1) + 1/30 y DATA(-1, 2) - 2/15 y DATA(2, 1) - - 3 2 181 - + 1/30 y DATA(-1, -2) + 1/10 y DATA(-2, -1) + --- y DATA(1, 1) - 735 - - 181 2 2 - + --- y DATA(-1, -1) - 1/20 y DATA(-1, -2) + 1/20 y DATA(1, 2) - 735 - - 2 2 2 - + 1/20 y DATA(2, 2) + 1/20 y DATA(-2, 2) - 1/10 y DATA(-2, 1) - - 2 2 71 - - 1/20 y DATA(-2, -2) + 1/98 x y DATA(1, 1) + ---- y DATA(1, 2) - 2940 - - 289 289 226 - - ---- y DATA(2, 2) - ---- y DATA(-2, 2) + --- y DATA(-2, 1) - 2940 2940 735 - - 71 289 226 - + ---- y DATA(1, -2) - ---- y DATA(2, -2) + --- y DATA(-2, -1) - 2940 2940 735 - - 181 2 2 - + --- y DATA(-1, 1) - 1/20 y DATA(1, -2) - 1/20 y DATA(2, -2) - 735 - - 2 2 - - 1/49 x y DATA(1, 2) - 1/49 x y DATA(-1, -2) - 1/70 x y DATA(1, -1) - - - 1/35 x y DATA(-1, 2) + 1/84 DATA(1, 2) + 1/35 x y DATA(-2, 1) - - + 2/35 x y DATA(2, -2) + 1/35 x y DATA(-2, -1) + 1/35 x y DATA(1, -2) - - - 1/35 x y DATA(-1, -2) - 2/35 x y DATA(-2, -2) + 1/35 x y DATA(1, 2) - - 2 - + 2/35 x y DATA(2, 2) - 2/35 x y DATA(-2, 2) - 1/40 x y DATA(1, -2) - - 2 2 31 - - 1/20 x y DATA(2, -2) - 1/10 x y DATA(-2, -1) - --- DATA(2, 2) - 420 - - 2 2 2 - + 1/20 x y DATA(2, 2) - 1/20 x y DATA(-2, 2) - 1/20 x y DATA(-1, -1) - - 2 2 3 - + 1/20 x y DATA(1, -1) - 1/20 x y DATA(1, 1) - 1/60 x DATA(1, 1) - - 3 3 3 - - 1/120 x DATA(-2, 1) - 1/30 x DATA(-1, -2) + 1/60 x DATA(-2, -2) - - 3 3 3 - - 1/30 x DATA(1, 2) + 1/60 x DATA(2, 2) - 1/60 x DATA(-2, 2) - - 3 3 3 - - 1/60 x DATA(-1, -1) + 1/60 x DATA(1, -1) + 1/60 x DATA(-1, 1) - - 3 3 3 - - 1/120 x DATA(2, -1) + 1/30 x DATA(-1, 2) + 1/30 x DATA(1, -2) - - 3 181 226 - - 1/60 x DATA(2, -2) + --- y DATA(1, -1) + --- y DATA(2, -1) - 735 735 - - 71 226 71 - + ---- y DATA(-1, 2) + --- y DATA(2, 1) + ---- y DATA(-1, -2) - 2940 735 2940 - - 289 2 3 - - ---- y DATA(-2, -2) + 1/20 x y DATA(-1, 1) + 1/120 x DATA(2, 1) - 2940 - - 37 21 21 - + --- x DATA(1, 1) - --- x DATA(1, -2) + --- x DATA(-2, -1) - 300 200 200 - - 21 21 11 - - --- x DATA(-2, 1) + --- x DATA(-1, -2) - --- x DATA(-2, -2) - 200 200 150 - - 21 11 11 - + --- x DATA(1, 2) - --- x DATA(2, 2) + --- x DATA(2, -2) - 200 150 150 - - 2 2 2 - + 1/10 x y DATA(2, -1) - 1/140 x DATA(1, 1) + 1/140 x DATA(-1, -1) - - 2 2 2 - + 1/140 x DATA(1, -1) - 1/140 x DATA(-1, 1) - 1/70 x DATA(2, -1) - - 2 2 11 - - 1/70 x DATA(-1, 2) + 1/70 x DATA(2, 1) + --- x DATA(-2, 2) - 150 - - 37 37 21 - - --- x DATA(1, -1) - --- x DATA(-1, 1) - --- x DATA(2, -1) - 300 300 200 - - 21 21 37 - - --- x DATA(-1, 2) + --- x DATA(2, 1) + --- x DATA(-1, -1) - 200 200 300 - - 2 2 2 - + 1/70 x DATA(1, -2) - 1/35 x DATA(2, -2) - 1/70 x DATA(-2, -1) - - 2 2 2 - - 1/40 x y DATA(-1, 2) - 1/49 x y DATA(2, -1) + 1/98 x y DATA(-1, -1) - - 2 2 2 - + 1/98 x y DATA(1, -1) - 1/10 x y DATA(2, 1) + 1/10 x y DATA(-2, 1) - - 2 2 2 - + 1/40 x y DATA(-1, -2) + 1/20 x y DATA(-2, -2) + 1/40 x y DATA(1, 2) - - 2 2 - + 1/70 x y DATA(-1, -1) + 2/49 x y DATA(2, -2) + 2/49 x y DATA(-2, 2) - - 2 2 - - 1/70 x y DATA(1, 1) + 1/70 x DATA(-1, -2) - 1/35 x DATA(-2, -2) - - 31 11 31 - - --- DATA(-2, 2) + --- DATA(-2, 1) - 1/84 DATA(1, -2) + --- DATA(2, -2) - 420 105 420 - - 11 - - --- DATA(-2, -1) - 105 - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=84082964, alloc=2555436, time=7.20 - 289 2 31 11 2 -[COEFF(-2, -2) = - ---- y - 1/35 x + --- - --- x - 2/35 x y + 1/20 x y - 2940 420 150 - - 2 2 3 3 3 - + 2/49 x y - 1/20 y + 1/30 y + 1/60 x , COEFF(-1, -2) = - 1/30 x - - 2 2 2 3 21 2 - - 1/49 x y + 1/40 x y - 1/20 y + 1/30 y + --- x + 1/70 x - 1/84 - 200 - - 71 - + ---- y - 1/35 x y, - 2940 - - 3 191 2 2 17 2 - COEFF(0, -2) = 1/30 y + ---- y + 1/35 x - 1/20 y - --- - 2/49 x y, - 2940 420 - - 2 2 21 71 3 - COEFF(1, -2) = - 1/20 y - 1/40 x y - --- x + ---- y + 1/30 y + 1/35 x y - 200 2940 - - 2 3 2 2 - - 1/49 x y - 1/84 + 1/30 x + 1/70 x , COEFF(2, -2) = - 1/20 y - - 2 11 289 3 2 3 - - 1/20 x y + --- x - ---- y - 1/60 x - 1/35 x + 2/35 x y + 1/30 y - 150 2940 - - 31 2 2 2 11 21 - + --- + 2/49 x y, COEFF(-2, -1) = 1/10 y - 1/49 x y - --- + --- x - 420 105 200 - - 3 226 3 2 2 - + 1/35 x y - 2/15 y + --- y + 1/120 x - 1/10 x y - 1/70 x , - 735 - - 3 3 2 2 2 - COEFF(-1, -1) = - 1/60 x - 2/15 y + 1/140 x + 1/10 y + 1/98 x y - - 2 37 31 181 - - 1/20 x y + --- x - --- + --- y + 1/70 x y, - 300 210 735 - - 17 2 2 3 2 166 - COEFF(0, -1) = - --- + 1/10 y + 1/70 x - 2/15 y + 1/49 x y + --- y, - 105 735 - - 181 2 2 2 31 37 - COEFF(1, -1) = --- y + 1/10 y + 1/20 x y + 1/140 x - --- - --- x - 735 210 300 - - 2 3 3 2 - + 1/98 x y - 1/70 x y - 2/15 y + 1/60 x , COEFF(2, -1) = 1/10 x y - - 3 3 2 2 226 2 - - 1/120 x - 2/15 y - 1/70 x - 1/49 x y + --- y - 1/35 x y + 1/10 y - 735 - - 11 21 3 41 2 - - --- - --- x, COEFF(-2, 0) = 1/5 y - -- y + 2/35 x y - 2/49 x y, - 105 200 98 - - 53 2 3 - COEFF(-1, 0) = - -- y + 1/49 x y + 1/5 y + 1/35 x y, - 98 - - 57 3 2 - COEFF(0, 0) = - -- y + 1/5 y + 2/49 x y, - 98 - - 3 2 53 - COEFF(1, 0) = - 1/35 x y + 1/5 y + 1/49 x y - -- y, - 98 - - 41 3 2 226 - COEFF(2, 0) = - -- y + 1/5 y - 2/35 x y - 2/49 x y, COEFF(-2, 1) = --- y - 98 735 - - 2 3 2 2 2 3 11 - - 1/10 y - 2/15 y + 1/70 x + 1/10 x y - 1/49 x y - 1/120 x + --- - 105 - - 21 2 3 3 - - --- x + 1/35 x y, COEFF(-1, 1) = - 1/10 y + 1/60 x - 2/15 y - 200 - - 37 2 31 2 2 181 - + 1/70 x y - --- x + 1/98 x y + --- + 1/20 x y - 1/140 x + --- y, - 300 210 735 - - 17 2 3 2 166 2 - COEFF(0, 1) = --- - 1/70 x - 2/15 y + 1/49 x y + --- y - 1/10 y , - 105 735 - - 2 37 3 3 2 2 - COEFF(1, 1) = - 1/20 x y + --- x - 1/60 x - 2/15 y + 1/98 x y - 1/10 y - 300 - - 31 181 2 2 3 - + --- + --- y - 1/70 x y - 1/140 x , COEFF(2, 1) = - 1/10 y + 1/120 x - 210 735 - - 11 2 2 226 3 21 - + --- - 1/10 x y + 1/70 x + --- y - 1/35 x y - 2/15 y + --- x - 105 735 200 - - 2 2 2 3 3 - - 1/49 x y, COEFF(-2, 2) = 2/49 x y + 1/20 y - 1/60 x + 1/30 y - - 2 11 31 289 2 - + 1/35 x + --- x - --- - ---- y - 2/35 x y - 1/20 x y , COEFF(-1, 2) = - 150 420 2940 - - 2 2 3 71 2 - - 1/40 x y - 1/35 x y + 1/20 y + 1/30 x + 1/84 + ---- y - 1/70 x - 2940 - - 2 3 21 - - 1/49 x y + 1/30 y - --- x, - 200 - - 2 17 3 2 191 2 - COEFF(0, 2) = - 1/35 x + --- + 1/30 y - 2/49 x y + ---- y + 1/20 y , - 420 2940 - - 3 2 2 3 - COEFF(1, 2) = 1/84 + 1/30 y - 1/49 x y - 1/70 x - 1/30 x + 1/35 x y - - 2 2 21 71 3 - + 1/20 y + 1/40 x y + --- x + ---- y, COEFF(2, 2) = 2/35 x y + 1/30 y - 200 2940 - - 11 31 289 2 2 3 2 - - --- x - --- - ---- y + 1/35 x + 2/49 x y + 1/60 x + 1/20 x y - 150 420 2940 - - 2 - + 1/20 y ] - -> print_coeffs__lc_of_data(%, "coeffs_dy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dy.compute.c"); -bytes used=85083136, alloc=2555436, time=7.28 -bytes used=86083376, alloc=2555436, time=7.35 -bytes used=87083652, alloc=2555436, time=7.44 -bytes used=88083808, alloc=2555436, time=7.60 -bytes used=89087088, alloc=2555436, time=7.68 -bytes used=90087256, alloc=2555436, time=7.86 -bytes used=91087488, alloc=2555436, time=7.95 -bytes used=92087708, alloc=2555436, time=8.14 -bytes used=93087872, alloc=2555436, time=8.22 -bytes used=94088076, alloc=2555436, time=8.41 -> -# d^2/dx^2 -> simplify( diff(interp_2d_cube_order4_smooth0,x,x) ); -bytes used=95088296, alloc=2555436, time=8.51 -bytes used=96088500, alloc=2555436, time=8.57 -191 57 166 53 ----- DATA(2, 0) - -- DATA(0, 0) + --- DATA(1, 0) - -- DATA(0, 1) -2940 98 735 98 - - 181 53 181 181 - + --- DATA(1, 1) - -- DATA(0, -1) + --- DATA(-1, -1) + --- DATA(1, -1) - 735 98 735 735 - - 166 2 2 - + --- DATA(-1, 0) + 3/5 x DATA(0, -2) + 3/5 x DATA(0, 2) - 735 - - 2 2 2 - + 3/5 x DATA(0, -1) + 1/49 y DATA(0, -1) - 2/49 y DATA(0, -2) - - 2 2 - + 1/49 y DATA(0, 1) - 2/49 y DATA(0, 2) + 1/35 y DATA(0, -1) - - 2 - + 3/5 x DATA(0, 1) + 2/35 y DATA(0, -2) - 2/35 y DATA(0, 2) - - 181 71 - - 1/35 y DATA(0, 1) + --- DATA(-1, 1) + ---- DATA(2, -1) - 735 2940 - - 2 2 - + 1/5 x DATA(-1, 0) - 2/5 x DATA(1, 2) + 1/10 x DATA(2, 2) - - 2 2 - + 1/10 x DATA(-2, 2) + 1/10 x DATA(-2, 1) + 1/20 x y DATA(2, 1) - - 41 226 71 - - -- DATA(0, 2) + --- DATA(-1, 2) + ---- DATA(2, 1) + 1/10 x DATA(2, 0) - 98 735 2940 - - 226 41 289 - - 1/5 x DATA(1, 0) + --- DATA(-1, -2) - -- DATA(0, -2) - ---- DATA(-2, -2) - 735 98 2940 - - 2 - + 1/10 x y DATA(-1, 1) - 1/20 x y DATA(2, -1) + 1/98 y DATA(1, 1) - - 2 2 2 - + 1/98 y DATA(-1, -1) + 1/98 y DATA(1, -1) + 1/98 y DATA(-1, 1) - - 2 2 2 - - 1/49 y DATA(2, -1) - 1/49 y DATA(-1, 2) - 1/49 y DATA(2, 1) - - 2 - - 1/49 y DATA(-2, -1) - 1/70 y DATA(1, 1) + 1/70 y DATA(-1, -1) - - 2 2 2 - - 1/49 y DATA(-1, -2) - 1/49 y DATA(1, 2) + 2/49 y DATA(2, 2) - - 2 2 2 - + 2/49 y DATA(-2, 2) - 1/49 y DATA(-2, 1) + 2/49 y DATA(-2, -2) - - - 1/35 y DATA(1, 2) + 2/35 y DATA(2, 2) + 2/35 y DATA(-2, 2) - - + 1/35 y DATA(-2, 1) + 1/35 y DATA(1, -2) - 2/35 y DATA(2, -2) - - 2 - - 1/35 y DATA(-2, -1) - 1/70 y DATA(-1, 1) - 1/49 y DATA(1, -2) - - 2 - + 2/49 y DATA(2, -2) + 1/10 x y DATA(1, -1) + 1/5 x y DATA(-1, 2) - - 226 - + --- DATA(1, 2) - 1/20 x y DATA(-2, 1) - 1/10 x y DATA(2, -2) - 735 - - + 1/20 x y DATA(-2, -1) + 1/5 x y DATA(1, -2) - 1/5 x y DATA(-1, -2) - - + 1/10 x y DATA(-2, -2) - 1/5 x y DATA(1, 2) + 1/10 x y DATA(2, 2) - - 289 - - 1/10 x y DATA(-2, 2) - ---- DATA(2, 2) + 1/70 y DATA(1, -1) - 2940 - - - 1/35 y DATA(2, -1) - 1/35 y DATA(-1, 2) + 1/35 y DATA(2, 1) - - + 1/35 y DATA(-1, -2) - 2/35 y DATA(-2, -2) - 1/5 x DATA(1, 1) - - - 1/5 x DATA(1, -2) - 1/10 x DATA(-2, -1) - 1/10 x DATA(-2, 1) - - + 1/5 x DATA(-1, -2) - 1/10 x DATA(-2, -2) - 1/5 x DATA(1, 2) - - 2 - + 1/10 x DATA(2, 2) + 1/10 x DATA(2, -2) - 2/5 x DATA(1, 1) - - 2 2 - - 2/5 x DATA(-1, -1) - 2/5 x DATA(1, -1) - 1/10 x DATA(-2, 0) - - 2 2 2 - - 2/5 x DATA(-1, 1) + 1/10 x DATA(2, -1) - 2/5 x DATA(-1, 2) - - 2 - + 1/10 x DATA(2, 1) - 1/10 x DATA(-2, 2) - 1/5 x DATA(1, -1) - - + 1/5 x DATA(-1, 1) + 1/10 x DATA(2, -1) + 1/5 x DATA(-1, 2) - - 2 - + 1/10 x DATA(2, 1) + 1/5 x DATA(-1, -1) - 2/5 x DATA(1, -2) - - 2 2 - + 1/10 x DATA(2, -2) + 1/10 x DATA(-2, -1) - 1/10 x y DATA(-1, -1) - - 2 2 - - 1/10 x y DATA(1, 1) - 2/5 x DATA(-1, -2) + 1/10 x DATA(-2, -2) - - 2 289 71 - + 2/49 y DATA(0, 0) - ---- DATA(-2, 2) + ---- DATA(-2, 1) - 2940 2940 - - 191 226 289 - + ---- DATA(-2, 0) + --- DATA(1, -2) - ---- DATA(2, -2) - 2940 735 2940 - - 71 2 2 - + ---- DATA(-2, -1) - 2/49 y DATA(2, 0) + 1/49 y DATA(-1, 0) - 2940 - - 2 2 2 - - 2/49 y DATA(-2, 0) + 1/49 y DATA(1, 0) - 2/5 x DATA(1, 0) - - 2 2 2 - - 2/5 x DATA(-1, 0) + 1/10 x DATA(-2, 0) + 3/5 x DATA(0, 0) - - 2 - + 1/10 x DATA(2, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=97091392, alloc=2555436, time=8.63 - 2 289 2 -[COEFF(-2, -2) = 2/49 y - 2/35 y + 1/10 x y - ---- - 1/10 x + 1/10 x , - 2940 - - 2 226 2 - COEFF(-1, -2) = 1/35 y - 2/5 x + --- - 1/5 x y + 1/5 x - 1/49 y , - 735 - - 41 2 2 - COEFF(0, -2) = - -- + 2/35 y + 3/5 x - 2/49 y , - 98 - - 2 226 2 - COEFF(1, -2) = 1/35 y - 2/5 x + --- - 1/49 y + 1/5 x y - 1/5 x, - 735 - - 2 289 2 - COEFF(2, -2) = - 2/35 y + 1/10 x - 1/10 x y + 1/10 x - ---- + 2/49 y , - 2940 - - 2 2 71 - COEFF(-2, -1) = - 1/49 y + 1/10 x + 1/20 x y - 1/10 x - 1/35 y + ----, - 2940 - - 2 181 2 - COEFF(-1, -1) = 1/70 y + 1/5 x - 1/10 x y + 1/98 y + --- - 2/5 x , - 735 - - 2 2 53 - COEFF(0, -1) = 3/5 x + 1/49 y + 1/35 y - --, - 98 - - 181 2 2 - COEFF(1, -1) = --- + 1/98 y - 1/5 x - 2/5 x + 1/10 x y + 1/70 y, - 735 - - 2 2 71 - COEFF(2, -1) = - 1/35 y + 1/10 x - 1/49 y + ---- + 1/10 x - 1/20 x y, - 2940 - - 2 2 191 - COEFF(-2, 0) = 1/10 x - 2/49 y + ---- - 1/10 x, - 2940 - - 166 2 2 - COEFF(-1, 0) = 1/5 x + --- + 1/49 y - 2/5 x , - 735 - - 2 57 2 - COEFF(0, 0) = 3/5 x - -- + 2/49 y , - 98 - - 166 2 2 - COEFF(1, 0) = - 1/5 x + --- + 1/49 y - 2/5 x , - 735 - - 2 2 191 - COEFF(2, 0) = 1/10 x - 2/49 y + 1/10 x + ----, - 2940 - - 2 2 71 - COEFF(-2, 1) = - 1/10 x - 1/49 y + 1/10 x + 1/35 y - 1/20 x y + ----, - 2940 - - 181 2 2 - COEFF(-1, 1) = --- - 1/70 y + 1/98 y + 1/10 x y - 2/5 x + 1/5 x, - 735 - - 53 2 2 - COEFF(0, 1) = - 1/35 y - -- + 3/5 x + 1/49 y , - 98 - - 2 2 181 - COEFF(1, 1) = - 1/5 x + 1/98 y - 1/10 x y - 2/5 x + --- - 1/70 y, - 735 - - 2 71 2 - COEFF(2, 1) = 1/35 y - 1/49 y + ---- + 1/10 x + 1/20 x y + 1/10 x , - 2940 - - 2 289 2 - COEFF(-2, 2) = 1/10 x - ---- + 2/35 y - 1/10 x + 2/49 y - 1/10 x y, - 2940 - - 2 2 226 - COEFF(-1, 2) = - 2/5 x - 1/49 y + 1/5 x - 1/35 y + --- + 1/5 x y, - 735 - - 2 2 41 - COEFF(0, 2) = - 2/49 y - 2/35 y + 3/5 x - --, - 98 - - 2 226 2 - COEFF(1, 2) = - 1/5 x y - 1/5 x - 2/5 x - 1/35 y + --- - 1/49 y , - 735 - - 2 2 289 - COEFF(2, 2) = 2/49 y + 2/35 y + 1/10 x + 1/10 x - ---- + 1/10 x y] - 2940 - -> print_coeffs__lc_of_data(%, "coeffs_dxx->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxx.compute.c"); -bytes used=98091548, alloc=2555436, time=8.70 -bytes used=99091708, alloc=2555436, time=8.83 -bytes used=100092244, alloc=2555436, time=8.91 -bytes used=101092436, alloc=2555436, time=9.07 -bytes used=102092596, alloc=2555436, time=9.25 -bytes used=103092832, alloc=2555436, time=9.38 -> -# d^2/dxdy -> simplify( diff(interp_2d_cube_order4_smooth0,x,y) ); -bytes used=104093572, alloc=2555436, time=9.47 - 37 37 37 -1/35 x DATA(0, -1) + --- DATA(1, 1) + --- DATA(-1, -1) - --- DATA(1, -1) - 300 300 300 - - 37 21 2 - - --- DATA(-1, 1) - --- DATA(2, -1) - 1/10 x DATA(1, 2) - 300 200 - - 2 2 2 - + 1/20 x DATA(2, 2) - 1/20 x DATA(-2, 2) - 1/40 x DATA(-2, 1) - - 21 21 - - 2/49 x y DATA(2, 1) - --- DATA(-1, 2) + --- DATA(2, 1) - 200 200 - - 21 11 - + --- DATA(-1, -2) - --- DATA(-2, -2) + 1/49 x y DATA(-1, 1) - 200 150 - - 2 2 - - 2/49 x y DATA(2, -1) - 1/20 y DATA(1, 1) - 1/20 y DATA(-1, -1) - - 2 2 2 - + 1/20 y DATA(1, -1) + 1/20 y DATA(-1, 1) + 1/10 y DATA(2, -1) - - 2 2 2 - - 1/40 y DATA(-1, 2) - 1/10 y DATA(2, 1) - 1/10 y DATA(-2, -1) - - 2 - - 1/70 y DATA(1, 1) + 1/70 y DATA(-1, -1) + 1/40 y DATA(-1, -2) - - 2 2 2 - + 1/40 y DATA(1, 2) + 1/20 y DATA(2, 2) - 1/20 y DATA(-2, 2) - - 2 2 - + 1/10 y DATA(-2, 1) + 1/20 y DATA(-2, -2) + 1/35 y DATA(1, 2) - - + 2/35 y DATA(2, 2) - 2/35 y DATA(-2, 2) + 1/35 y DATA(-2, 1) - - + 1/35 y DATA(1, -2) + 2/35 y DATA(2, -2) + 1/35 y DATA(-2, -1) - - 2 2 - + 1/70 y DATA(-1, 1) - 1/40 y DATA(1, -2) - 1/20 y DATA(2, -2) - - 21 - + 1/49 x y DATA(1, -1) - 2/49 x y DATA(-1, 2) + --- DATA(1, 2) - 200 - - - 2/49 x y DATA(-2, 1) + 4/49 x y DATA(2, -2) - 2/49 x y DATA(-2, -1) - - - 2/49 x y DATA(1, -2) - 2/49 x y DATA(-1, -2) + 4/49 x y DATA(-2, -2) - - - 2/49 x y DATA(1, 2) + 4/49 x y DATA(2, 2) + 4/49 x y DATA(-2, 2) - - 11 - - --- DATA(2, 2) - 1/70 y DATA(1, -1) - 1/35 y DATA(2, -1) - 150 - - - 1/35 y DATA(-1, 2) - 1/35 y DATA(2, 1) - 1/35 y DATA(-1, -2) - - - 2/35 y DATA(-2, -2) - 1/70 x DATA(1, 1) + 1/35 x DATA(1, -2) - - - 1/35 x DATA(-2, -1) + 1/35 x DATA(-2, 1) + 1/35 x DATA(-1, -2) - - - 2/35 x DATA(-2, -2) - 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2) - - 2 2 - - 2/35 x DATA(2, -2) - 1/20 x DATA(1, 1) - 1/20 x DATA(-1, -1) - - 2 2 2 - + 1/20 x DATA(1, -1) + 1/20 x DATA(-1, 1) - 1/40 x DATA(2, -1) - - 2 2 - + 1/10 x DATA(-1, 2) + 1/40 x DATA(2, 1) + 2/35 x DATA(-2, 2) - - + 1/70 x DATA(1, -1) - 1/70 x DATA(-1, 1) - 1/35 x DATA(2, -1) - - - 1/35 x DATA(-1, 2) + 1/35 x DATA(2, 1) + 1/70 x DATA(-1, -1) - - 2 2 2 - + 1/10 x DATA(1, -2) - 1/20 x DATA(2, -2) + 1/40 x DATA(-2, -1) - - 2 - + 1/49 x y DATA(-1, -1) + 1/49 x y DATA(1, 1) - 1/10 x DATA(-1, -2) - - 2 11 21 - + 1/20 x DATA(-2, -2) + --- DATA(-2, 2) - --- DATA(-2, 1) - 150 200 - - 21 11 21 - - --- DATA(1, -2) + --- DATA(2, -2) + --- DATA(-2, -1) - 200 150 200 - - + 2/49 x y DATA(-1, 0) - 2/35 y DATA(2, 0) - 1/35 y DATA(1, 0) - - + 1/35 y DATA(-1, 0) + 2/49 x y DATA(0, -1) + 2/35 y DATA(-2, 0) - - - 4/49 x y DATA(2, 0) - 1/35 x DATA(0, 1) - 2/35 x DATA(0, 2) - - + 2/35 x DATA(0, -2) - 4/49 x y DATA(0, -2) + 2/49 x y DATA(1, 0) - - + 2/49 x y DATA(0, 1) + 4/49 x y DATA(0, 0) - 4/49 x y DATA(-2, 0) - - - 4/49 x y DATA(0, 2) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=105096984, alloc=2555436, time=9.52 - 2 11 2 -[COEFF(-2, -2) = 4/49 x y + 1/20 y - 2/35 y - 2/35 x - --- + 1/20 x , - 150 - - 2 2 21 - COEFF(-1, -2) = 1/35 x - 1/10 x - 2/49 x y - 1/35 y + 1/40 y + ---, - 200 - - COEFF(0, -2) = - 4/49 x y + 2/35 x, - - 21 2 2 - COEFF(1, -2) = - 2/49 x y + 1/35 x - --- + 1/10 x + 1/35 y - 1/40 y , - 200 - - 2 11 2 - COEFF(2, -2) = - 1/20 y + --- + 2/35 y - 2/35 x + 4/49 x y - 1/20 x , - 150 - - 2 21 2 - COEFF(-2, -1) = 1/40 x + --- - 1/35 x - 1/10 y + 1/35 y - 2/49 x y, - 200 - - 2 37 2 - COEFF(-1, -1) = - 1/20 y + 1/49 x y + --- + 1/70 y + 1/70 x - 1/20 x , - 300 - - COEFF(0, -1) = 2/49 x y + 1/35 x, - - 2 2 37 - COEFF(1, -1) = - 1/70 y + 1/20 x + 1/20 y + 1/49 x y + 1/70 x - ---, - 300 - - 2 21 2 - COEFF(2, -1) = - 1/35 x - 1/35 y + 1/10 y - 2/49 x y - --- - 1/40 x , - 200 - - COEFF(-2, 0) = 2/35 y - 4/49 x y, COEFF(-1, 0) = 2/49 x y + 1/35 y, - - COEFF(0, 0) = 4/49 x y, COEFF(1, 0) = - 1/35 y + 2/49 x y, - - COEFF(2, 0) = - 2/35 y - 4/49 x y, - - 2 21 2 - COEFF(-2, 1) = - 1/40 x + 1/35 x - --- + 1/10 y + 1/35 y - 2/49 x y, - 200 - - 37 2 2 - COEFF(-1, 1) = - --- - 1/70 x + 1/20 x + 1/70 y + 1/20 y + 1/49 x y, - 300 - - COEFF(0, 1) = 2/49 x y - 1/35 x, - - 37 2 2 - COEFF(1, 1) = - 1/70 x + --- - 1/20 x + 1/49 x y - 1/20 y - 1/70 y, - 300 - - 2 21 2 - COEFF(2, 1) = - 1/35 y - 1/10 y + 1/35 x - 2/49 x y + --- + 1/40 x , - 200 - - 2 2 11 - COEFF(-2, 2) = 2/35 x - 1/20 x - 1/20 y + 4/49 x y + --- - 2/35 y, - 150 - - 2 2 21 - COEFF(-1, 2) = - 1/35 x - 1/40 y + 1/10 x - --- - 1/35 y - 2/49 x y, - 200 - - COEFF(0, 2) = - 4/49 x y - 2/35 x, - - 2 2 21 - COEFF(1, 2) = 1/40 y - 2/49 x y - 1/10 x + 1/35 y - 1/35 x + ---, - 200 - - 2 2 11 - COEFF(2, 2) = 1/20 y + 1/20 x - --- + 2/35 x + 2/35 y + 4/49 x y] - 150 - -> print_coeffs__lc_of_data(%, "coeffs_dxy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dxy.compute.c"); -bytes used=106097284, alloc=2555436, time=9.59 -bytes used=107097536, alloc=2555436, time=9.71 -bytes used=108099596, alloc=2555436, time=9.81 -bytes used=109099792, alloc=2555436, time=9.98 -bytes used=110100132, alloc=2555436, time=10.14 -bytes used=111100580, alloc=2555436, time=10.31 -bytes used=112100732, alloc=2555436, time=10.47 -> -# d^2/dy^2 -> simplify( diff(interp_2d_cube_order4_smooth0,y,y) ); -bytes used=113100928, alloc=2555436, time=10.54 - 41 57 53 166 -- -- DATA(2, 0) - -- DATA(0, 0) - -- DATA(1, 0) + --- DATA(0, 1) - 98 98 98 735 - - 181 - + --- DATA(1, 1) + 1/5 y DATA(0, -1) + 2/35 x DATA(-2, 0) - 735 - - 166 - - 2/35 x DATA(2, 0) - 1/5 y DATA(0, 1) + --- DATA(0, -1) - 735 - - 181 181 53 181 - + --- DATA(-1, -1) + --- DATA(1, -1) - -- DATA(-1, 0) + --- DATA(-1, 1) - 735 735 98 735 - - 226 2 2 - + --- DATA(2, -1) - 1/49 x DATA(1, 2) + 2/49 x DATA(2, 2) - 735 - - 2 2 - + 2/49 x DATA(-2, 2) - 1/49 x DATA(-2, 1) - 1/5 x y DATA(2, 1) - - 191 71 226 71 - + ---- DATA(0, 2) + ---- DATA(-1, 2) + --- DATA(2, 1) + ---- DATA(-1, -2) - 2940 2940 735 2940 - - 191 289 - + ---- DATA(0, -2) - ---- DATA(-2, -2) + 1/10 x y DATA(-1, 1) - 2940 2940 - - 2 2 - + 1/5 x y DATA(2, -1) - 2/5 y DATA(1, 1) - 2/5 y DATA(-1, -1) - - 2 2 2 - - 2/5 y DATA(1, -1) - 2/5 y DATA(-1, 1) - 2/5 y DATA(2, -1) - - 2 2 2 - + 1/10 y DATA(-1, 2) - 2/5 y DATA(2, 1) - 2/5 y DATA(-2, -1) - - 2 - - 1/5 y DATA(1, 1) + 1/5 y DATA(-1, -1) + 1/10 y DATA(-1, -2) - - 2 2 2 - + 1/10 y DATA(1, 2) + 1/10 y DATA(2, 2) + 1/10 y DATA(-2, 2) - - 2 2 - - 2/5 y DATA(-2, 1) + 1/10 y DATA(-2, -2) + 1/10 y DATA(1, 2) - - + 1/10 y DATA(2, 2) + 1/10 y DATA(-2, 2) - 1/5 y DATA(-2, 1) - - - 1/10 y DATA(1, -2) - 1/10 y DATA(2, -2) + 1/5 y DATA(-2, -1) - - 2 2 - - 1/5 y DATA(-1, 1) + 1/10 y DATA(1, -2) + 1/10 y DATA(2, -2) - - 71 - + 1/10 x y DATA(1, -1) - 1/20 x y DATA(-1, 2) + ---- DATA(1, 2) - 2940 - - + 1/5 x y DATA(-2, 1) - 1/10 x y DATA(2, -2) - 1/5 x y DATA(-2, -1) - - - 1/20 x y DATA(1, -2) + 1/20 x y DATA(-1, -2) + 1/10 x y DATA(-2, -2) - - + 1/20 x y DATA(1, 2) + 1/10 x y DATA(2, 2) - 1/10 x y DATA(-2, 2) - - 289 - - ---- DATA(2, 2) + 1/5 y DATA(1, -1) + 1/5 y DATA(2, -1) - 2940 - - + 1/10 y DATA(-1, 2) - 1/5 y DATA(2, 1) - 1/10 y DATA(-1, -2) - - - 1/10 y DATA(-2, -2) - 1/70 x DATA(1, 1) + 1/35 x DATA(1, -2) - - + 1/35 x DATA(-2, -1) + 1/35 x DATA(-2, 1) - 1/35 x DATA(-1, -2) - - - 2/35 x DATA(-2, -2) + 1/35 x DATA(1, 2) + 2/35 x DATA(2, 2) - - 2 2 - + 2/35 x DATA(2, -2) + 1/98 x DATA(1, 1) + 1/98 x DATA(-1, -1) - - 2 2 2 - + 1/98 x DATA(1, -1) + 1/98 x DATA(-1, 1) - 1/49 x DATA(2, -1) - - 2 2 - - 1/49 x DATA(-1, 2) - 1/49 x DATA(2, 1) - 2/35 x DATA(-2, 2) - - - 1/70 x DATA(1, -1) + 1/70 x DATA(-1, 1) - 1/35 x DATA(2, -1) - - - 1/35 x DATA(-1, 2) - 1/35 x DATA(2, 1) + 1/70 x DATA(-1, -1) - - 2 2 2 - - 1/49 x DATA(1, -2) + 2/49 x DATA(2, -2) - 1/49 x DATA(-2, -1) - - 2 - - 1/10 x y DATA(-1, -1) - 1/10 x y DATA(1, 1) - 1/49 x DATA(-1, -2) - - 2 289 226 - + 2/49 x DATA(-2, -2) - ---- DATA(-2, 2) + --- DATA(-2, 1) - 2940 735 - - 41 71 - - -- DATA(-2, 0) - 1/10 y DATA(0, -2) + ---- DATA(1, -2) - 98 2940 - - 289 226 - - ---- DATA(2, -2) + --- DATA(-2, -1) + 1/10 y DATA(0, 2) - 2940 735 - - 2 2 2 - + 3/5 y DATA(0, 0) - 2/5 y DATA(0, -1) + 3/5 y DATA(-1, 0) - - 2 2 2 - + 3/5 y DATA(1, 0) + 1/10 y DATA(0, 2) + 1/10 y DATA(0, -2) - - 2 2 2 - - 2/5 y DATA(0, 1) + 1/49 x DATA(1, 0) - 2/49 x DATA(0, 2) - - 2 2 2 - - 2/49 x DATA(0, -2) + 1/49 x DATA(0, 1) + 3/5 y DATA(-2, 0) - - 2 2 2 - + 3/5 y DATA(2, 0) - 2/49 x DATA(-2, 0) + 2/49 x DATA(0, 0) - - 2 2 - + 1/49 x DATA(0, -1) + 1/49 x DATA(-1, 0) + 1/35 x DATA(-1, 0) - - 2 - - 1/35 x DATA(1, 0) - 2/49 x DATA(2, 0) - -> coeffs_as_lc_of_data(%, posn_list_2d_size5); -bytes used=114101228, alloc=2555436, time=10.61 - 2 289 2 -[COEFF(-2, -2) = - 2/35 x + 1/10 y - ---- - 1/10 y + 1/10 x y + 2/49 x , - 2940 - - 2 71 2 - COEFF(-1, -2) = 1/10 y + ---- - 1/35 x + 1/20 x y - 1/49 x - 1/10 y, - 2940 - - 2 191 2 - COEFF(0, -2) = 1/10 y + ---- - 2/49 x - 1/10 y, - 2940 - - 2 71 2 - COEFF(1, -2) = - 1/49 x + ---- + 1/10 y - 1/10 y + 1/35 x - 1/20 x y, - 2940 - - 289 2 2 - COEFF(2, -2) = - 1/10 y - 1/10 x y + 2/35 x - ---- + 2/49 x + 1/10 y , - 2940 - - 226 2 2 - COEFF(-2, -1) = - 1/5 x y + --- + 1/5 y + 1/35 x - 1/49 x - 2/5 y , - 735 - - 181 2 2 - COEFF(-1, -1) = --- - 1/10 x y + 1/98 x + 1/5 y - 2/5 y + 1/70 x, - 735 - - 2 2 166 - COEFF(0, -1) = 1/5 y - 2/5 y + 1/49 x + ---, - 735 - - 181 2 2 - COEFF(1, -1) = - 1/70 x + 1/10 x y + --- + 1/5 y + 1/98 x - 2/5 y , - 735 - - 2 226 2 - COEFF(2, -1) = - 1/35 x - 2/5 y + 1/5 x y + --- - 1/49 x + 1/5 y, - 735 - - 41 2 2 - COEFF(-2, 0) = - -- + 2/35 x - 2/49 x + 3/5 y , - 98 - - 53 2 2 - COEFF(-1, 0) = - -- + 3/5 y + 1/35 x + 1/49 x , - 98 - - 2 2 57 - COEFF(0, 0) = 2/49 x + 3/5 y - --, - 98 - - 2 2 53 - COEFF(1, 0) = 3/5 y + 1/49 x - -- - 1/35 x, - 98 - - 41 2 2 - COEFF(2, 0) = - -- + 3/5 y - 2/35 x - 2/49 x , - 98 - - 2 2 226 - COEFF(-2, 1) = 1/35 x - 1/5 y + 1/5 x y - 1/49 x - 2/5 y + ---, - 735 - - 2 2 181 - COEFF(-1, 1) = 1/10 x y + 1/70 x - 2/5 y - 1/5 y + 1/98 x + ---, - 735 - - 2 166 2 - COEFF(0, 1) = - 1/5 y - 2/5 y + --- + 1/49 x , - 735 - - 181 2 2 - COEFF(1, 1) = - 1/5 y + --- - 1/70 x + 1/98 x - 2/5 y - 1/10 x y, - 735 - - 2 2 226 - COEFF(2, 1) = - 2/5 y - 1/49 x + --- - 1/5 x y - 1/5 y - 1/35 x, - 735 - - 2 2 289 - COEFF(-2, 2) = 2/49 x + 1/10 y - 1/10 x y + 1/10 y - 2/35 x - ----, - 2940 - - 2 71 2 - COEFF(-1, 2) = 1/10 y + ---- - 1/20 x y + 1/10 y - 1/35 x - 1/49 x , - 2940 - - 2 2 191 - COEFF(0, 2) = 1/10 y - 2/49 x + 1/10 y + ----, - 2940 - - 71 2 2 - COEFF(1, 2) = 1/35 x + 1/10 y + ---- + 1/20 x y + 1/10 y - 1/49 x , - 2940 - - 2 2 289 - COEFF(2, 2) = 2/49 x + 1/10 y + 1/10 y + 1/10 x y - ---- + 2/35 x] - 2940 - -> print_coeffs__lc_of_data(%, "coeffs_dyy->coeff_", "fp", -> "2d.coeffs/2d.cube.order4.smooth0/coeffs-dyy.compute.c"); -bytes used=115101596, alloc=2555436, time=10.70 -bytes used=116101756, alloc=2555436, time=10.85 -bytes used=117101948, alloc=2555436, time=10.94 -bytes used=118102268, alloc=2555436, time=11.10 -bytes used=119102436, alloc=2555436, time=11.27 -bytes used=120102772, alloc=2555436, time=11.41 -> -################################################################################ -> quit -bytes used=120843640, alloc=2555436, time=11.51 |