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Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Hermite/fns.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Hermite/fns.maple | 451 |
1 files changed, 0 insertions, 451 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Hermite/fns.maple b/src/GeneralizedPolynomial-Uniform/Hermite/fns.maple deleted file mode 100644 index 806ab4f..0000000 --- a/src/GeneralizedPolynomial-Uniform/Hermite/fns.maple +++ /dev/null @@ -1,451 +0,0 @@ -# Maple code to define Hermite interpolating functions/coords/coeffs/mols -# $Header$ - -# -# Note: -# interpolation order 2 <==> fn order 3, 3-point (2nd order) derivative mols -# interpolation order 3 <==> fn order 3, 5-point (4th order) derivative mols -# interpolation order 4 <==> fn order 5, 5-point (4th order) derivative mols -# - -################################################################################ -################################################################################ -################################################################################ - -# -# derivative primitives -# (argument is a procedure which should map m into the DATA() reference) -# - -dx_3point := -proc(f::procedure(integer)) -(1/2) * (-f(-1) + f(+1)) -end proc; - -dx_5point := -proc(f::procedure(integer)) -(1/12) * (f(-2) - 8*f(-1) + 8*f(+1) - f(+2)) -end proc; - -################################################################################ -################################################################################ -################################################################################ - -# -# 1-D interpolating functions -# - -fn_1d_order3 := -proc(x) -+ c0 + c1*x + c2*x^2 + c3*x^3 -end proc; - -fn_1d_order5 := -proc(x) -+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 -end proc; - -################################################################################ - -# coordinates for 1-D interpolating functions -coord_list_1d := [x]; - -################################################################################ - -# -# coefficients in 1-D interpolating functions -# - -coeffs_set_1d_order3 := {c0, c1, c2, c3}; -coeffs_set_1d_order5 := {c0, c1, c2, c3, c4, c5}; - -################################################################################ - -# -# 1-D derivative molecules (argument = molecule center) -# - -deriv_1d_dx_3point := proc(i::integer) - dx_3point(proc(mi::integer) DATA(i+mi) end proc) - end proc; -deriv_1d_dx_5point := proc(i::integer) - dx_5point(proc(mi::integer) DATA(i+mi) end proc) - end proc; - -################################################################################ -################################################################################ -################################################################################ - -# -# 2-D interpolating functions -# - -fn_2d_order3 := -proc(x,y) -+ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 -+ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y -+ c00 + c10*x + c20*x^2 + c30*x^3 -end proc; - -fn_2d_order5 := -proc(x,y) -+ c05*y^5 + c15*x*y^5 + c25*x^2*y^5 + c35*x^3*y^5 + c45*x^4*y^5 + c55*x^5*y^5 -+ c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 + c54*x^5*y^4 -+ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 + c53*x^5*y^3 -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 + c52*x^5*y^2 -+ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y + c51*x^5*y -+ c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 + c50*x^5 -end proc; - -################################################################################ - -# coordinates for 2-D interpolating functions -coord_list_2d := [x,y]; - -################################################################################ - -# -# coefficients in 2-D interpolating functions -# - -coeffs_set_2d_order3 := { - c03, c13, c23, c33, - c02, c12, c22, c32, - c01, c11, c21, c31, - c00, c10, c20, c30 - }; - -coeffs_set_2d_order5 := { - c05, c15, c25, c35, c45, c55, - c04, c14, c24, c34, c44, c54, - c03, c13, c23, c33, c43, c53, - c02, c12, c22, c32, c42, c52, - c01, c11, c21, c31, c41, c51, - c00, c10, c20, c30, c40, c50 - }; - -################################################################################ - -# -# 2-D derivative molecules (arguments = molecule center) -# - -deriv_2d_dx_3point := proc(i::integer, j::integer) - dx_3point( - proc(mi::integer) DATA(i+mi,j) end proc - ) - end proc; -deriv_2d_dy_3point := proc(i::integer, j::integer) - dx_3point( - proc(mj::integer) DATA(i,j+mj) end proc - ) - end proc; -deriv_2d_dxy_3point := proc(i::integer, j::integer) - dx_3point( - proc(mi::integer) - dx_3point(proc(mj::integer) DATA(i+mi,j+mj) end proc) - end proc - ) - end proc; - -deriv_2d_dx_5point := proc(i::integer, j::integer) - dx_5point( - proc(mi::integer) DATA(i+mi,j) end proc - ) - end proc; -deriv_2d_dy_5point := proc(i::integer, j::integer) - dx_5point( - proc(mj::integer) DATA(i,j+mj) end proc - ) - end proc; -deriv_2d_dxy_5point := proc(i::integer, j::integer) - dx_5point( - proc(mi::integer) - dx_5point(proc(mj::integer) DATA(i+mi,j+mj) end proc) - end proc - ) - end proc; - -################################################################################ -################################################################################ -################################################################################ - -# -# 3-D interpolating functions -# - -fn_3d_order3 := -proc(x,y,z) -# z^3 --------------------------------------------------------------- -+ c033*y^3*z^3 + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 -+ c023*y^2*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 -+ c013*y *z^3 + c113*x*y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 -+ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 -# z^2 --------------------------------------------------------------- -+ c032*y^3*z^2 + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 -+ c022*y^2*z^2 + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 -+ c012*y *z^2 + c112*x*y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 -+ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 -# z^1 --------------------------------------------------------------- -+ c031*y^3*z + c131*x*y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z -+ c021*y^2*z + c121*x*y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z -+ c011*y *z + c111*x*y *z + c211*x^2*y *z + c311*x^3*y *z -+ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z -# z^0 --------------------------------------------------------------- -+ c030*y^3 + c130*x*y^3 + c230*x^2*y^3 + c330*x^3*y^3 -+ c020*y^2 + c120*x*y^2 + c220*x^2*y^2 + c320*x^3*y^2 -+ c010*y + c110*x*y + c210*x^2*y + c310*x^3*y -+ c000 + c100*x + c200*x^2 + c300*x^3 -end proc; - -fn_3d_order5 := -proc(x,y,z) -# z^5 -+ c055*y^5*z^5 + c155*x*y^5*z^5 + c255*x^2*y^5*z^5 + c355*x^3*y^5*z^5 + c455*x^4*y^5*z^5 + c555*x^5*y^5*z^5 -+ c045*y^4*z^5 + c145*x*y^4*z^5 + c245*x^2*y^4*z^5 + c345*x^3*y^4*z^5 + c445*x^4*y^4*z^5 + c545*x^5*y^4*z^5 -+ c035*y^3*z^5 + c135*x*y^3*z^5 + c235*x^2*y^3*z^5 + c335*x^3*y^3*z^5 + c435*x^4*y^3*z^5 + c535*x^5*y^3*z^5 -+ c025*y^2*z^5 + c125*x*y^2*z^5 + c225*x^2*y^2*z^5 + c325*x^3*y^2*z^5 + c425*x^4*y^2*z^5 + c525*x^5*y^2*z^5 -+ c015*y *z^5 + c115*x*y *z^5 + c215*x^2*y *z^5 + c315*x^3*y *z^5 + c415*x^4*y *z^5 + c515*x^5*y *z^5 -+ c005 *z^5 + c105*x *z^5 + c205*x^2 *z^5 + c305*x^3 *z^5 + c405*x^4 *z^5 + c505*x^5 *z^5 -# z^4 -+ c054*y^5*z^4 + c154*x*y^5*z^4 + c254*x^2*y^5*z^4 + c354*x^3*y^5*z^4 + c454*x^4*y^5*z^4 + c554*x^5*y^5*z^4 -+ c044*y^4*z^4 + c144*x*y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 + c544*x^5*y^4*z^4 -+ c034*y^3*z^4 + c134*x*y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 + c534*x^5*y^3*z^4 -+ c024*y^2*z^4 + c124*x*y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 + c524*x^5*y^2*z^4 -+ c014*y *z^4 + c114*x*y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 + c514*x^5*y *z^4 -+ c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 + c504*x^5 *z^4 -# z^3 -+ c053*y^5*z^3 + c153*x*y^5*z^3 + c253*x^2*y^5*z^3 + c353*x^3*y^5*z^3 + c453*x^4*y^5*z^3 + c553*x^5*y^5*z^3 -+ c043*y^4*z^3 + c143*x*y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 + c543*x^5*y^4*z^3 -+ c033*y^3*z^3 + c133*x*y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 + c533*x^5*y^3*z^3 -+ c023*y^2*z^3 + c123*x*y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 + c523*x^5*y^2*z^3 -+ c013*y *z^3 + c113*x*y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 + c513*x^5*y *z^3 -+ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 + c503*x^5 *z^3 -# z^2 -+ c052*y^5*z^2 + c152*x*y^5*z^2 + c252*x^2*y^5*z^2 + c352*x^3*y^5*z^2 + c452*x^4*y^5*z^2 + c552*x^5*y^5*z^2 -+ c042*y^4*z^2 + c142*x*y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 + c542*x^5*y^4*z^2 -+ c032*y^3*z^2 + c132*x*y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 + c532*x^5*y^3*z^2 -+ c022*y^2*z^2 + c122*x*y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 + c522*x^5*y^2*z^2 -+ c012*y *z^2 + c112*x*y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 + c512*x^5*y *z^2 -+ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 + c502*x^5 *z^2 -# z^1 -+ c051*y^5*z + c151*x*y^5*z + c251*x^2*y^5*z + c351*x^3*y^5*z + c451*x^4*y^5*z + c551*x^5*y^5*z -+ c041*y^4*z + c141*x*y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z + c541*x^5*y^4*z -+ c031*y^3*z + c131*x*y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z + c531*x^5*y^3*z -+ c021*y^2*z + c121*x*y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z + c521*x^5*y^2*z -+ c011*y *z + c111*x*y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z + c511*x^5*y *z -+ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z + c501*x^5 *z -# z^0 -+ c050*y^5 + c150*x*y^5 + c250*x^2*y^5 + c350*x^3*y^5 + c450*x^4*y^5 + c550*x^5*y^5 -+ c040*y^4 + c140*x*y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 + c540*x^5*y^4 -+ c030*y^3 + c130*x*y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 + c530*x^5*y^3 -+ c020*y^2 + c120*x*y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 + c520*x^5*y^2 -+ c010*y + c110*x*y + c210*x^2*y + c310*x^3*y + c410*x^4*y + c510*x^5*y -+ c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 + c500*x^5 -end proc; - -################################################################################ - -# coordinates for 3-D interpolating functions -coord_list_3d := [x,y,z]; - -################################################################################ - -# -# coefficients in 3-D interpolating functions -# - -coeffs_set_3d_order3 := { - # z^3 - c033, c133, c233, c333, - c023, c123, c223, c323, - c013, c113, c213, c313, - c003, c103, c203, c303, - # z^2 - c032, c132, c232, c332, - c022, c122, c222, c322, - c012, c112, c212, c312, - c002, c102, c202, c302, - # z^1 - c031, c131, c231, c331, - c021, c121, c221, c321, - c011, c111, c211, c311, - c001, c101, c201, c301, - # z^0 - c030, c130, c230, c330, - c020, c120, c220, c320, - c010, c110, c210, c310, - c000, c100, c200, c300 - }; - -coeffs_set_3d_order5 := { - # z^5 - c055, c155, c255, c355, c455, c555, - c045, c145, c245, c345, c445, c545, - c035, c135, c235, c335, c435, c535, - c025, c125, c225, c325, c425, c525, - c015, c115, c215, c315, c415, c515, - c005, c105, c205, c305, c405, c505, - # z^4 - c054, c154, c254, c354, c454, c554, - c044, c144, c244, c344, c444, c544, - c034, c134, c234, c334, c434, c534, - c024, c124, c224, c324, c424, c524, - c014, c114, c214, c314, c414, c514, - c004, c104, c204, c304, c404, c504, - # z^3 - c053, c153, c253, c353, c453, c553, - c043, c143, c243, c343, c443, c543, - c033, c133, c233, c333, c433, c533, - c023, c123, c223, c323, c423, c523, - c013, c113, c213, c313, c413, c513, - c003, c103, c203, c303, c403, c503, - # z^2 - c052, c152, c252, c352, c452, c552, - c042, c142, c242, c342, c442, c542, - c032, c132, c232, c332, c432, c532, - c022, c122, c222, c322, c422, c522, - c012, c112, c212, c312, c412, c512, - c002, c102, c202, c302, c402, c502, - # z^1 - c051, c151, c251, c351, c451, c551, - c041, c141, c241, c341, c441, c541, - c031, c131, c231, c331, c431, c531, - c021, c121, c221, c321, c421, c521, - c011, c111, c211, c311, c411, c511, - c001, c101, c201, c301, c401, c501, - # z^0 - c050, c150, c250, c350, c450, c550, - c040, c140, c240, c340, c440, c540, - c030, c130, c230, c330, c430, c530, - c020, c120, c220, c320, c420, c520, - c010, c110, c210, c310, c410, c510, - c000, c100, c200, c300, c400, c500 - }; - -################################################################################ - -# -# 3-D derivative molecules (arguments = molecule center) -# - -deriv_3d_dx_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mi::integer) DATA(i+mi,j,k) end proc - ) - end proc; -deriv_3d_dy_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mj::integer) DATA(i,j+mj,k) end proc - ) - end proc; -deriv_3d_dz_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mk::integer) DATA(i,j,k+mk) end proc - ) - end proc; -deriv_3d_dxy_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mi::integer) - dx_3point( - proc(mj::integer) DATA(i+mi,j+mj,k) end proc - ) - end proc - ) - end proc; -deriv_3d_dxz_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mi::integer) - dx_3point( - proc(mk::integer) DATA(i+mi,j,k+mk) end proc - ) - end proc - ) - end proc; -deriv_3d_dyz_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mj::integer) - dx_3point( - proc(mk::integer) DATA(i,j+mj,k+mk) end proc - ) - end proc - ) - end proc; -deriv_3d_dxyz_3point := proc(i::integer, j::integer, k::integer) - dx_3point( - proc(mi::integer) - dx_3point( - proc(mj::integer) - dx_3point( - proc(mk::integer) - DATA(i+mi,j+mj,k+mk) - end proc - ) - end proc - ) - end proc - ) - end proc; - -deriv_3d_dx_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mi::integer) DATA(i+mi,j,k) end proc - ) - end proc; -deriv_3d_dy_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mj::integer) DATA(i,j+mj,k) end proc - ) - end proc; -deriv_3d_dz_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mk::integer) DATA(i,j,k+mk) end proc - ) - end proc; -deriv_3d_dxy_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mi::integer) - dx_5point( - proc(mj::integer) DATA(i+mi,j+mj,k) end proc - ) - end proc - ) - end proc; -deriv_3d_dxz_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mi::integer) - dx_5point( - proc(mk::integer) DATA(i+mi,j,k+mk) end proc - ) - end proc - ) - end proc; -deriv_3d_dyz_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mj::integer) - dx_5point( - proc(mk::integer) DATA(i,j+mj,k+mk) end proc - ) - end proc - ) - end proc; -deriv_3d_dxyz_5point := proc(i::integer, j::integer, k::integer) - dx_5point( - proc(mi::integer) - dx_5point( - proc(mj::integer) - dx_5point( - proc(mk::integer) - DATA(i+mi,j+mj,k+mk) - end proc - ) - end proc - ) - end proc - ) - end proc; - -################################################################################ -################################################################################ -################################################################################ |