diff options
Diffstat (limited to 'src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple')
| -rw-r--r-- | src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple | 266 |
1 files changed, 0 insertions, 266 deletions
diff --git a/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple b/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple deleted file mode 100644 index e211c8a..0000000 --- a/src/GeneralizedPolynomial-Uniform/Lagrange/fns.maple +++ /dev/null @@ -1,266 +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 -# - -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_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; - -######################################## - -# coordinates for 2-D interpolating functions -coords_list_2d := [x,y]; - -######################################## - -# -# coefficients in 2-D interpolating functions -# - -coeffs_list_2d_order1 := [ - c01, - c00, c10 - ]; -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_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_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_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_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; - -######################################## - -# coordinates for 3-D interpolating functions -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_order2 := [ - # z^0 ----------- - c020, - c010, c110, - c000, c100, c200, - # z^1 ----------- - c011, - c001, c101, - # z^2 ----------- - 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_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 - ]; - -################################################################################ |