(* File: Phi-matrix-pc   Author: Hongyou Wu   Date: 2000 Sep 01 *)
(*                                                              *)
(* Input: npieces, \[Lambda]                                    *)
(*                                                              *)
(* Optional input: a[i], f[i], q[i], w[i]                       *)
(*                                                              *)
(* Output: \[Phi].                                              *)


Clear[iZZ,jZZ,kZZ,lZZ,cZZ,dZZ,eZZ,fZZ,tfZZ,gZZ,phZZ,tZZ];

cZZ=\[Lambda];

Do[{fZZ[iZZ,cZZ]=Sqrt[(q[iZZ]-cZZ*w[iZZ])/f[iZZ]];
    gZZ[iZZ,1,1,tZZ_,cZZ]=Cosh[fZZ[iZZ,cZZ](tZZ-a[iZZ-1])];
    gZZ[iZZ,1,2,tZZ_,cZZ]=If[cZZ==q[iZZ]/w[iZZ], (tZZ-a[iZZ-1])/f[iZZ],
                             Sinh[fZZ[iZZ,cZZ](tZZ-a[iZZ-1])]/f[iZZ]/fZZ[iZZ,cZZ]];
    gZZ[iZZ,2,1,tZZ_,cZZ]=f[iZZ]*fZZ[iZZ,cZZ]*Sinh[fZZ[iZZ,cZZ](tZZ-a[iZZ-1])];
    gZZ[iZZ,2,2,tZZ_,cZZ]=Cosh[fZZ[iZZ,cZZ](tZZ-a[iZZ-1])];
   },{iZZ,1,npieces}];

tfZZ[dZZ_,eZZ_,tZZ_]=If[dZZ<=tZZ&&tZZ<=eZZ,1,0];

Do[phZZ[1,jZZ,kZZ,tZZ_,cZZ]=tfZZ[a[0],a[1],tZZ]gZZ[1,jZZ,kZZ,tZZ,cZZ],
   {jZZ,1,2},{kZZ,1,2}];

tfZZ[dZZ_,eZZ_,tZZ_]=If[dZZ<tZZ&&tZZ<=eZZ,1,0];

Do[phZZ[iZZ,jZZ,kZZ,tZZ_,cZZ]=tfZZ[a[iZZ-1],a[iZZ],tZZ]*
    Sum[gZZ[iZZ,jZZ,lZZ,tZZ,cZZ]phZZ[iZZ-1,lZZ,kZZ,a[iZZ-1],cZZ],{lZZ,1,2}],
   {iZZ,2,npieces},{jZZ,1,2},{kZZ,1,2}];

Do[\[Phi][iZZ,jZZ,tZZ_,cZZ]=Sum[phZZ[kZZ,iZZ,jZZ,tZZ,cZZ],{kZZ,1,npieces}],
   {iZZ,1,2},{jZZ,1,2}];

Clear[cZZ,fZZ,gZZ,tfZZ,phZZ];