restart; clamped_spline := proc(xx::list,y::list,fp0::numeric,fpn::numeric,S::name) local N, I, X, A, AA, FP0, FPN, M, H, XA, XL, XU, XZ, C, J, B, D, SS, L, P; if nops(xx)<>nops(y) then ERROR("Both lists must be the same size"); fi; N:=nops(xx)-1; for I from 0 to N do X[I]:= xx[I+1]; A[I]:=y[I+1]; od; FP0 := fp0; FPN := fpn; STEP 1 M := N - 1; for I from 0 to M do H[I] := X[I+1] - X[I]; od; STEP 2 XA[0] := 3.0 * (A[1] - A[0]) / H[0] - 3.0 * FP0; XA[N] := 3.0 * FPN - 3.0 * (A[N] - A[N-1]) / H[N-1]; STEP 3 for I from 1 to M do XA[I] := 3.0*(A[I+1]*H[I-1]-A[I]*(X[I+1]-X[I-1])+A[I-1]*H[I])/(H[I]*H[I-1]); od; STEP 4 XL[0] := 2.0 * H[0]; XU[0] := 0.5; XZ[0] := XA[0] / XL[0]; STEP 5 for I from 1 to M do XL[I] := 2.0 * (X[I+1] - X[I-1]) - H[I-1] * XU[I-1]; XU[I] := H[I] / XL[I]; XZ[I] := (XA[I] - H[I-1] * XZ[I-1]) / XL[I]; od; STEP 6 XL[N] := H[N-1] * (2.0 - XU[N-1]); XZ[N] := (XA[N] - H[N-1] * XZ[N-1]) / XL[N]; C[N] := XZ[N]; STEP 7 for I from 1 to N do J := N - I; C[J] := XZ[J] - XU[J] * C[J+1]; B[J] := (A[J+1] - A[J]) / H[J] - H[J] * (C[J+1] + 2.0 * C[J]) / 3.0; D[J] := (C[J+1] - C[J]) / (3.0 * H[J]); od; STEP 8 printf(`\n\nThe coefficients of the clamped cubic spline S[i]\non the subintervals are:\n`); printf(` a(i) b(i) c(i) d(i)\n`); for I from 0 to M do printf(` %13.8f %13.8f %13.8f %13.8f \n`, A[I], B[I], C[I], D[I]); od; printf(`\n\n`); for I from 0 to M do SS[I]:=A[I]+B[I]*(x-X[I])+C[I]*(x-X[I])^2+D[I]*(x-X[I])^3; od; L:=[seq([x<X[I+1],SS[I]],I=0..M)]; P:=[seq(op(L[I]),I=1..M+1)]; P := subsop(2*M+1=NULL,P); S:=simplify(piecewise(op(P))); end;

Warning, imaginary unit `I` used as a local variable in procedure clamped_spline

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n,&F^inF^[oF^[oF_[o?(F_inFa[oF^[oFeinFb[o>&FfinFf[o,&&F`inFh[oF^[oFe[oF_[o>&Fgin6#Fa[o,&*($"#IF_[oF^[o,&&Fain6#F^[oF^[o&FainFh\oF_[oF^[o&FfinFh\oF_[oF^[o*&F[]oF^[oFcinF^[oF_[o>&Fgin6#F^in,&*&F[]oF^[oFdinF^[oF^[o*(F[]oF^[o,&&FainFe]oF^[o&Fain6#F`\oF_[oF^[o&FfinF\^oF_[oF_[o?(F_inF^[oF^[oFeinFb[o>&FginFf[o*(F[]oF^[o,(*&&FainFh[oF^[o&Ffin6#,&F_inF^[oF^[oF_[oF^[oF^[o*&F[\oF^[o,&Fe\oF^[o&F`inFf^oF_[oF^[oF_[o*&&FainFf^oF^[oFc\oF^[oF^[oF^[o*&Fc\oF^[oFe^oF^[oF_[o>&FhinFh\o*&$"#?F_[oF^[oFa]oF^[o>&FiinFh\o$""&F_[o>&FjinFh\o*&Fg\oF^[oF__oF_[o?(F_inF^[oF^[oFeinFb[oC%>&FhinFf[o,&*&Fa_oF^[oFi^oF^[oF^[o*&Fe^oF^[o&FiinFf^oF^[oF_[o>&FiinFf[o*&Fc\oF^[oF]`oF_[o>&FjinFf[o*&,&F`^oF^[o*&Fe^oF^[o&FjinFf^oF^[oF_[oF^[oF]`oF_[o>&FhinFe]o*&F]^oF^[o,&Fa_oF^[o&FiinF\^oF_[oF^[o>&FjinFe]o*&,&Fd]oF^[o*&F]^oF^[o&FjinF\^oF^[oF_[oF^[oF\aoF_[o>&F[jnFe]oFaao?(F_inF^[oF^[oF^inFb[oC&>F\jn,&F^inF^[oF_inF_[o>&F[jn6#F\jn,&&FjinF^boF^[o*&&FiinF^boF^[o&F[jn6#,&F\jnF^[oF^[oF^[oF^[oF_[o>&F]jnF^bo,&*&,&&FainFdboF^[o&FainF^boF_[oF^[o&FfinF^boF_[oF^[o*(F]coF^[o,&FcboF^[o*&Fa_oF^[oF]boF^[oF^[oF^[oF[]oF_[oF_[o>&F^jnF^bo*(,&FcboF^[oF]boF_[oF^[oF[]oF_[oF]coF_[o-I'printfGF(6#Iho|+|+The~coefficients~of~the~clamped~cubic~spline~S[i]|+on~the~subintervals~are:|+GF(-Ffco6#IZ~~~~~~~~~~a(i)~~~~~~~~~~b(i)~~~~~~~~~~c(i)~~~~~~~~~~d(i)|+GF(?(F_inFa[oF^[oFeinFb[o-Ffco6'I?~%13.8f~%13.8f~%13.8f~%13.8f~|+GF(F[\o&F]jnFf[o&F[jnFf[o&F^jnFf[o-Ffco6#I#|+|+GF(?(F_inFa[oF^[oFeinFb[o>&F_jnFf[o,*F[\oF^[o*&F`doF^[o,&I"xGF(F^[oFe[oF_[oF^[oF^[o*&FadoF^[o)F[eo""#F^[oF^[o*&FbdoF^[o)F[eo""$F^[oF^[o>F`jn7#-I$seqGFbhn6$7$2F\eoFe\oFhdo/F_in;Fa[oFein>Fajn7#-Ffeo6$-I#opGFbhn6#&F`jnFf[o/F_in;F^[o,&FeinF^[oF^[oF^[o>Fajn-I'subsopGFbhn6$/,&*&F_eoF^[oFeinF^[oF^[oF^[oF^[oI%NULLGFbhnFajn>F[in-I)simplifyGF(6#-I*piecewiseGFbhn6#-Fafo6#FajnF(F(F(7#F]hn

clamped_spline_dir:=proc() printf(`clamped_spline returns the piecewise cubic spline.\n\n`); printf(`The output also includes a table of values\n`); printf(`for the cubic polynomials\n\n`); printf(`S[i](x)=a[i]+b[i](x-x[i])+c[i](x-x[i])^2+d[i](x-x[i])^3\n\n`); printf(`for i=0..n-1 making up the spline.\n\n`); printf(`The arguments for clamped_spline are:\n`); printf(`(1)the list of x-values\n`); printf(`(2)the list of f(x) or y-values\n`); printf(`(3)f'(x[0])\n`); printf(`(4)f'(x[n])\n`); printf(`(5)the variable for returning the piecewise cubic spline\n\n`); printf(`If assigning the result to a variable, have the\n`); printf(`variable and the 5th argument the same.\n\n`); printf(`If S is the variable for returning the spline\n`); printf(`and has already been given a value,\n`); printf(`the procedure should be preceded by the statement:\n`); printf(`S:='S'`); end;

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