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Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple | 306 |
1 files changed, 0 insertions, 306 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple deleted file mode 100644 index e363b10..0000000 --- a/src/GeneralizedPolynomial-Uniform/Lagrange-tensor-product/fns.maple +++ /dev/null @@ -1,306 +0,0 @@ -# Maple code to define Lagrange interpolating functions/coords/coeffs -# $Header$ - -################################################################################ - -# -# 1-D interpolating functions -# - -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_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_order5 := -proc(x) -+ c0 + c1*x + c2*x^2 + c3*x^3 + c4*x^4 + c5*x^5 -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; - -######################################## - -# coordinates for 1-D interpolating functions -coords_list_1d := [x]; - -######################################## - -# -# coefficients in 1-D interpolating functions -# - -coeffs_list_1d_order1 := [c0, c1]; -coeffs_list_1d_order2 := [c0, c1, c2]; -coeffs_list_1d_order3 := [c0, c1, c2, c3]; -coeffs_list_1d_order4 := [c0, c1, c2, c3, c4]; -coeffs_list_1d_order5 := [c0, c1, c2, c3, c4, c5]; -coeffs_list_1d_order6 := [c0, c1, c2, c3, c4, c5, c6]; - -################################################################################ - -# -# 2-D interpolating functions (tensor-product) -# - -fn_2d_order1 := -proc(x,y) -+ c01*y + c11*x*y -+ c00 + c10*x -end proc; - -fn_2d_order2 := -proc(x,y) -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 -+ c01*y + c11*x*y + c21*x^2*y -+ c00 + c10*x + c20*x^2 -end proc; - -fn_2d_order3 := -proc(x,y) -+ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 -+ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y -+ c00 + c10*x + c20*x^2 + c30*x^3 -end proc; - -fn_2d_order4 := -proc(x,y) -+ c04*y^4 + c14*x*y^4 + c24*x^2*y^4 + c34*x^3*y^4 + c44*x^4*y^4 -+ c03*y^3 + c13*x*y^3 + c23*x^2*y^3 + c33*x^3*y^3 + c43*x^4*y^3 -+ c02*y^2 + c12*x*y^2 + c22*x^2*y^2 + c32*x^3*y^2 + c42*x^4*y^2 -+ c01*y + c11*x*y + c21*x^2*y + c31*x^3*y + c41*x^4*y -+ c00 + c10*x + c20*x^2 + c30*x^3 + c40*x^4 -end; - -######################################## - -# coordinates for 2-D interpolating functions -coords_list_2d := [x,y]; - -######################################## - -# -# coefficients in 2-D interpolating functions (tensor-product) -# - -coeffs_list_2d_order1 := [ - c01, c11, - c00, c10 - ]; -coeffs_list_2d_order2 := [ - c02, c12, c22, - c01, c11, c21, - c00, c10, c20 - ]; -coeffs_list_2d_order3 := [ - c03, c13, c23, c33, - c02, c12, c22, c23, - c01, c11, c21, c13, - c00, c10, c20, c30 - ]; -coeffs_list_2d_order4 := [ - c04, c14, c24, c34, c44, - c03, c13, c23, c33, c43, - c02, c12, c22, c32, c42, - c01, c11, c21, c31, c41, - c00, c10, c20, c30, c40 - ]; - -################################################################################ - -# -# 3-D interpolating functions (tensor-product) -# - -fn_3d_order1 := -proc(x,y,z) -# z^1 ------------------- -+ c011 *y*z + c111*x*y*z -+ c001 *z + c101*x *z -# z^0 ------------------- -+ c010 *y + c110*x*y -+ c000 + c100*x -end proc; - -fn_3d_order2 := -proc(x,y,z) -# z^2 -------------------------------------------------- -+ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 -+ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 -+ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 -# z -------------------------------------------------- -+ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z -+ c011 *y *z + c111*x *y *z + c211*x^2*y *z -+ c001 *z + c101*x *z + c201*x^2 *z -# z^0 ------------------------------------------------ -+ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 -+ c010 *y + c110*x *y + c210*x^2*y -+ c000 + c100*x + c200*x^2 -end proc; - -fn_3d_order3 := -proc(x,y,z) -# z^3 --------------------------------------------------------------------- -+ c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 -+ c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 -+ c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 -+ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 -# z^2 --------------------------------------------------------------------- -+ c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 -+ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 -+ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 -+ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 -# z --------------------------------------------------------------------- -+ c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z -+ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z -+ c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z -+ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z -# z^0 --------------------------------------------------------------------- -+ c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 -+ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 -+ c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y -+ c000 + c100*x + c200*x^2 + c300*x^3 -end proc; - -fn_3d_order4 := -proc(x,y,z) -# z^4 ---------------------------------------------------------------------------------------- -+ c044 *y^4*z^4 + c144*x *y^4*z^4 + c244*x^2*y^4*z^4 + c344*x^3*y^4*z^4 + c444*x^4*y^4*z^4 -+ c034 *y^3*z^4 + c134*x *y^3*z^4 + c234*x^2*y^3*z^4 + c334*x^3*y^3*z^4 + c434*x^4*y^3*z^4 -+ c024 *y^2*z^4 + c124*x *y^2*z^4 + c224*x^2*y^2*z^4 + c324*x^3*y^2*z^4 + c424*x^4*y^2*z^4 -+ c014 *y *z^4 + c114*x *y *z^4 + c214*x^2*y *z^4 + c314*x^3*y *z^4 + c414*x^4*y *z^4 -+ c004 *z^4 + c104*x *z^4 + c204*x^2 *z^4 + c304*x^3 *z^4 + c404*x^4 *z^4 -# z^3 ---------------------------------------------------------------------------------------- -+ c043 *y^4*z^3 + c143*x *y^4*z^3 + c243*x^2*y^4*z^3 + c343*x^3*y^4*z^3 + c443*x^4*y^4*z^3 -+ c033 *y^3*z^3 + c133*x *y^3*z^3 + c233*x^2*y^3*z^3 + c333*x^3*y^3*z^3 + c433*x^4*y^3*z^3 -+ c023 *y^2*z^3 + c123*x *y^2*z^3 + c223*x^2*y^2*z^3 + c323*x^3*y^2*z^3 + c423*x^4*y^2*z^3 -+ c013 *y *z^3 + c113*x *y *z^3 + c213*x^2*y *z^3 + c313*x^3*y *z^3 + c413*x^4*y *z^3 -+ c003 *z^3 + c103*x *z^3 + c203*x^2 *z^3 + c303*x^3 *z^3 + c403*x^4 *z^3 -# z^2 ---------------------------------------------------------------------------------------- -+ c042 *y^4*z^2 + c142*x *y^4*z^2 + c242*x^2*y^4*z^2 + c342*x^3*y^4*z^2 + c442*x^4*y^4*z^2 -+ c032 *y^3*z^2 + c132*x *y^3*z^2 + c232*x^2*y^3*z^2 + c332*x^3*y^3*z^2 + c432*x^4*y^3*z^2 -+ c022 *y^2*z^2 + c122*x *y^2*z^2 + c222*x^2*y^2*z^2 + c322*x^3*y^2*z^2 + c422*x^4*y^2*z^2 -+ c012 *y *z^2 + c112*x *y *z^2 + c212*x^2*y *z^2 + c312*x^3*y *z^2 + c412*x^4*y *z^2 -+ c002 *z^2 + c102*x *z^2 + c202*x^2 *z^2 + c302*x^3 *z^2 + c402*x^4 *z^2 -# z ---------------------------------------------------------------------------------------- -+ c041 *y^4*z + c141*x *y^4*z + c241*x^2*y^4*z + c341*x^3*y^4*z + c441*x^4*y^4*z -+ c031 *y^3*z + c131*x *y^3*z + c231*x^2*y^3*z + c331*x^3*y^3*z + c431*x^4*y^3*z -+ c021 *y^2*z + c121*x *y^2*z + c221*x^2*y^2*z + c321*x^3*y^2*z + c421*x^4*y^2*z -+ c011 *y *z + c111*x *y *z + c211*x^2*y *z + c311*x^3*y *z + c411*x^4*y *z -+ c001 *z + c101*x *z + c201*x^2 *z + c301*x^3 *z + c401*x^4 *z -# z^0 ---------------------------------------------------------------------------------------- -+ c040 *y^4 + c140*x *y^4 + c240*x^2*y^4 + c340*x^3*y^4 + c440*x^4*y^4 -+ c030 *y^3 + c130*x *y^3 + c230*x^2*y^3 + c330*x^3*y^3 + c430*x^4*y^3 -+ c020 *y^2 + c120*x *y^2 + c220*x^2*y^2 + c320*x^3*y^2 + c420*x^4*y^2 -+ c010 *y + c110*x *y + c210*x^2*y + c310*x^3*y + c410*x^4*y -+ c000 + c100*x + c200*x^2 + c300*x^3 + c400*x^4 -end; - -######################################## - -# coordinates for 3-D interpolating functions -coords_list_3d := [x,y,z]; - -######################################## - -# -# coefficients in 3-D interpolating functions -# - -coeffs_list_3d_order1 := [ - # z^1 ----- - c011, c111, - c001, c101, - # z^0 ----- - c010, c110, - c000, c100 - ]; -coeffs_list_3d_order2 := [ - # z^2 ----------- - c022, c122, c222, - c012, c112, c212, - c002, c102, c202, - # z^1 ----------- - c021, c121, c221, - c011, c111, c211, - c001, c101, c201, - # z^0 ----------- - c020, c120, c220, - c010, c110, c210, - c000, c100, c200 - ]; -coeffs_list_3d_order3 := [ - # z^3 ----------------- - c033, c133, c233, c333, - c023, c123, c223, c323, - c013, c113, c213, c313, - c003, c103, c203, c303, - # z^2 ----------------- - c032, c132, c232, c332, - c022, c122, c222, c322, - c012, c112, c212, c312, - c002, c102, c202, c302, - # z^1 ----------------- - c031, c131, c231, c331, - c021, c121, c221, c321, - c011, c111, c211, c311, - c001, c101, c201, c301, - # z^0 ----------------- - c030, c130, c230, c330, - c020, c120, c220, c320, - c010, c110, c210, c310, - c000, c100, c200, c300 - ]; -coeffs_list_3d_order4 := [ - # z^4 ----------------------- - c044, c144, c244, c344, c444, - c034, c134, c234, c334, c434, - c024, c124, c224, c324, c424, - c014, c114, c214, c314, c414, - c004, c104, c204, c304, c404, - # z^3 ----------------------- - c043, c143, c243, c343, c443, - c033, c133, c233, c333, c433, - c023, c123, c223, c323, c423, - c013, c113, c213, c313, c413, - c003, c103, c203, c303, c403, - # z^2 ----------------------- - c042, c142, c242, c342, c442, - c032, c132, c232, c332, c432, - c022, c122, c222, c322, c422, - c012, c112, c212, c312, c412, - c002, c102, c202, c302, c402, - # z^1 ----------------------- - c041, c141, c241, c341, c441, - c031, c131, c231, c331, c431, - c021, c121, c221, c321, c421, - c011, c111, c211, c311, c411, - c001, c101, c201, c301, c401, - # z^0 ----------------------- - c040, c140, c240, c340, c440, - c030, c130, c230, c330, c430, - c020, c120, c220, c320, c420, - c010, c110, c210, c310, c410, - c000, c100, c200, c300, c400 - ]; - -################################################################################ |