/[escript]/trunk/finley/src/ShapeFunctions.c
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Diff of /trunk/finley/src/ShapeFunctions.c

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revision 1197 by elspeth, Wed Mar 22 02:46:56 2006 UTC revision 1198 by btully, Tue Jun 19 00:24:29 2007 UTC
# Line 322  void Finley_Shape_Rec9(int NumV,double* Line 322  void Finley_Shape_Rec9(int NumV,double*
322    for (i=0;i<NumV;i++) {    for (i=0;i<NumV;i++) {
323      x=V(1,i);      x=V(1,i);
324      y=V(2,i);      y=V(2,i);
325      S(1,i)=(10.)+(-3.)*x+(9.)*x*y+(-3.)*y+(2.)*x*x+(-0.6e1)*x*y*y+(-0.6e1)*x*x*y+(2.)*y*y+(4.)*x*x*y*y;      S(1,i)= + 1.0 - 3.0*x + 2.0*x*x - 3.0*y + 9.0*x*y - 6.0*x*x*y + 2.0*y*y - 6.0*x*y*y + 4.0*x*x*y*y;
326      S(2,i)=(-10.)*x+(3.)*x*y+(2.)*x*x+(-2.)*x*y*y+(-0.6e1)*x*x*y+(4.)*x*x*y*y;      S(2,i)= - 1.0*x + 2.0*x*x + 3.0*x*y - 6.0*x*x*y - 2.0*x*y*y + 4.0*x*x*y*y;
327      S(3,i)=(10.)*x*y+(-2.)*x*y*y+(-2.)*x*x*y+(4.)*x*x*y*y;      S(3,i)= + 1.0*x*y - 2.0*x*x*y - 2.0*x*y*y + 4.0*x*x*y*y;
328      S(4,i)=(3.)*x*y+(-10.)*y+(-0.6e1)*x*y*y+(-2.)*x*x*y+(2.)*y*y+(4.)*x*x*y*y;      S(4,i)= - 1.0*y + 3.0*x*y - 2.0*x*x*y + 2.0*y*y - 6.0*x*y*y + 4.0*x*x*y*y;
329      S(5,i)=(4.)*x+(-0.12e2)*x*y+(-4.)*x*x+(8.)*x*y*y+(0.12e2)*x*x*y+(-8.)*x*x*y*y;      S(5,i)= + 4.0*x - 4.0*x*x - 12.0*x*y + 12.0*x*x*y + 8.0*x*y*y - 8.0*x*x*y*y;
330      S(6,i)=(-4.)*x*y+(4.)*x*y*y+(8.)*x*x*y+(-8.)*x*x*y*y;      S(6,i)= - 4.0*x*y + 8.0*x*x*y + 4.0*x*y*y - 8.0*x*x*y*y;
331      S(7,i)=(-4.)*x*y+(8.)*x*y*y+(4.)*x*x*y+(-8.)*x*x*y*y;      S(7,i)= - 4.0*x*y + 4.0*x*x*y + 8.0*x*y*y - 8.0*x*x*y*y;
332      S(8,i)=(-0.12e2)*x*y+(4.)*y+(0.12e2)*x*y*y+(8.)*x*x*y+(-4.) *y*y+(-8.)*x*x*y*y;      S(8,i)= + 4.0*y - 12.0*x*y + 8.0*x*x*y - 4.0*y*y + 12.0*x*y*y - 8.0*x*x*y*y;
333      S(9,i)=(0.16e2)*x*y+(-0.16e2)*x*y*y+(-0.16e2)*x*x*y+(0.16e2)*x*x*y*y;      S(9,i)= + 16.0*x*y - 16.0*x*x*y - 16.0*x*y*y + 16.0*x*x*y*y;
334      DSDV(1, 1,i)=(-3.)+(9.)*y+(4.)*x+(-0.6e1)*y*y+(-0.12e2)*x*y+(8.)*x*y*y;      DSDV(1,1,i)= - 3.0 + 4.0*x + 9.0*y - 12.0*x*y - 6.0*y*y + 8.0*x*y*y;
335      DSDV(2, 1,i)=(-10.)+(3.)*y+(4.)*x+(-2.)*y*y+(-0.12e2)*x*y+(8.)*x*y*y;      DSDV(1,2,i)= - 3.0 + 9.0*x - 6.0*x*x + 4.0*y - 12.0*x*y + 8.0*x*x*y;
336      DSDV(3, 1,i)=(10.)*y+(-2.)*y*y+(-4.)*x*y+(8.)*x*y*y;      DSDV(2,1,i)= - 1.0 + 4.0*x + 3.0*y - 12.0*x*y - 2.0*y*y + 8.0*x*y*y;
337      DSDV(4, 1,i)=(3.)*y+(-0.6e1)*y*y+(-4.)*x*y+(8.)*x*y*y;      DSDV(2,2,i)= + 3.0*x - 6.0*x*x - 4.0*x*y + 8.0*x*x*y;
338      DSDV(5, 1,i)=(4.)+(-0.12e2)*y+(-8.)*x+(8.)*y*y+(0.24e2)*x*y+(-0.16e2)*x*y*y;      DSDV(3,1,i)= + 1.0*y - 4.0*x*y - 2.0*y*y + 8.0*x*y*y;
339      DSDV(6, 1,i)=(-4.)*y+(4.)*y*y+(0.16e2)*x*y+(-0.16e2)*x*y*y;      DSDV(3,2,i)= + 1.0*x - 2.0*x*x - 4.0*x*y + 8.0*x*x*y;
340      DSDV(7, 1,i)=(-4.)*y+(8.)*y*y+(8.)*x*y+(-0.16e2)*x*y*y;      DSDV(4,1,i)= + 3.0*y - 4.0*x*y - 6.0*y*y + 8.0*x*y*y;
341      DSDV(8, 1,i)=(-0.12e2)*y+(0.12e2)*y*y+(0.16e2)*x*y+(-0.16e2)*x*y*y;      DSDV(4,2,i)= - 1.0 + 3.0*x - 2.0*x*x + 4.0*y - 12.0*x*y + 8.0*x*x*y;
342      DSDV(9, 1,i)=(0.16e2)*y+(-0.16e2)*y*y+(-0.32e2)*x*y+(0.32e2)*x*y*y;      DSDV(5,1,i)= + 4.0 - 8.0*x - 12.0*y + 24.0*x*y + 8.0*y*y - 16.0*x*y*y;
343      DSDV(1, 2,i)=(9.)*x+(-3.)+(-0.12e2)*x*y+(-0.6e1)*x*x+(4.)*y+(8.)*x*x*y;      DSDV(5,2,i)= - 12.0*x + 12.0*x*x + 16.0*x*y - 16.0*x*x*y;
344      DSDV(2, 2,i)=(3.)*x+(-4.)*x*y+(-0.6e1)*x*x+(8.)*x*x*y;      DSDV(6,1,i)= - 4.0*y + 16.0*x*y + 4.0*y*y - 16.0*x*y*y;
345      DSDV(3, 2,i)=(10.)*x+(-4.)*x*y+(-2.)*x*x+(8.)*x*x*y;      DSDV(6,2,i)= - 4.0*x + 8.0*x*x + 8.0*x*y - 16.0*x*x*y;
346      DSDV(4, 2,i)=(3.)*x+(-10.)+(-0.12e2)*x*y+(-2.)*x*x+(4.)*y+(8.)*x*x*y;      DSDV(7,1,i)= - 4.0*y + 8.0*x*y + 8.0*y*y - 16.0*x*y*y;
347      DSDV(5, 2,i)=(-0.12e2)*x+(0.16e2)*x*y+(0.12e2)*x*x+(-0.16e2)*x*x*y;      DSDV(7,2,i)= - 4.0*x + 4.0*x*x + 16.0*x*y - 16.0*x*x*y;
348      DSDV(6, 2,i)=(-4.)*x+(8.)*x*y+(8.)*x*x+(-0.16e2)*x*x*y;      DSDV(8,1,i)= - 12.0*y + 16.0*x*y + 12.0*y*y - 16.0*x*y*y;
349      DSDV(7, 2,i)=(-4.)*x+(0.16e2)*x*y+(4.)*x*x+(-0.16e2)*x*x*y;      DSDV(8,2,i)= + 4.0 - 12.0*x + 8.0*x*x - 8.0*y + 24.0*x*y - 16.0*x*x*y;
350      DSDV(8, 2,i)=(-0.12e2)*x+(4.)+(0.24e2)*x*y+(8.)*x*x+(-8.)*y+(-0.16e2)*x*x*y;      DSDV(9,1,i)= + 16.0*y - 32.0*x*y - 16.0*y*y + 32.0*x*y*y;
351      DSDV(9, 2,i)=(0.16e2)*x+(-0.32e2)*x*y+(-0.16e2)*x*x+(0.32e2)*x*x*y;      DSDV(9,2,i)= + 16.0*x - 16.0*x*x - 32.0*x*y + 32.0*x*x*y;
352    }    }
353    #undef NUMSHAPES    #undef NUMSHAPES
354    #undef DIM    #undef DIM
# Line 778  void Finley_Shape_Hex20(int NumV,double* Line 778  void Finley_Shape_Hex20(int NumV,double*
778    }    }
779    #undef NUMSHAPES    #undef NUMSHAPES
780    #undef DIM    #undef DIM
781    }
782    
783    /**************************************************************/
784    
785    void Finley_Shape_Hex27(int NumV,double* v,double* s,double* dsdv) {
786      #define NUMSHAPES 27
787      #define DIM 3
788      double x,y,z;
789      int i;
790      for (i=0;i<NumV;i++) {
791        x=V(1,i);
792        y=V(2,i);
793        z=V(3,i);
794        S(1,i)= + 1.0 - 3.0*x + 2.0*x*x - 3.0*y + 9.0*x*y - 6.0*x*x*y + 2.0*y*y - 6.0*x*y*y + 4.0*x*x*y*y - 3.0*z + 9.0*x*z - 6.0*x*x*z + 9.0*y*z - 27.0*x*y*z + 18.0*x*x*y*z - 6.0*y*y*z + 18.0*x*y*y*z - 12.0*x*x*y*y*z + 2.0*z*z - 6.0*x*z*z + 4.0*x*x*z*z - 6.0*y*z*z + 18.0*x*y*z*z - 12.0*x*x*y*z*z + 4.0*y*y*z*z - 12.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
795        S(2,i)= - 1.0*x + 2.0*x*x + 3.0*x*y - 6.0*x*x*y - 2.0*x*y*y + 4.0*x*x*y*y + 3.0*x*z - 6.0*x*x*z - 9.0*x*y*z + 18.0*x*x*y*z + 6.0*x*y*y*z - 12.0*x*x*y*y*z - 2.0*x*z*z + 4.0*x*x*z*z + 6.0*x*y*z*z - 12.0*x*x*y*z*z - 4.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
796        S(3,i)= + 1.0*x*y - 2.0*x*x*y - 2.0*x*y*y + 4.0*x*x*y*y - 3.0*x*y*z + 6.0*x*x*y*z + 6.0*x*y*y*z - 12.0*x*x*y*y*z + 2.0*x*y*z*z - 4.0*x*x*y*z*z - 4.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
797        S(4,i)= - 1.0*y + 3.0*x*y - 2.0*x*x*y + 2.0*y*y - 6.0*x*y*y + 4.0*x*x*y*y + 3.0*y*z - 9.0*x*y*z + 6.0*x*x*y*z - 6.0*y*y*z + 18.0*x*y*y*z - 12.0*x*x*y*y*z - 2.0*y*z*z + 6.0*x*y*z*z - 4.0*x*x*y*z*z + 4.0*y*y*z*z - 12.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
798        S(5,i)= - 1.0*z + 3.0*x*z - 2.0*x*x*z + 3.0*y*z - 9.0*x*y*z + 6.0*x*x*y*z - 2.0*y*y*z + 6.0*x*y*y*z - 4.0*x*x*y*y*z + 2.0*z*z - 6.0*x*z*z + 4.0*x*x*z*z - 6.0*y*z*z + 18.0*x*y*z*z - 12.0*x*x*y*z*z + 4.0*y*y*z*z - 12.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
799        S(6,i)= + 1.0*x*z - 2.0*x*x*z - 3.0*x*y*z + 6.0*x*x*y*z + 2.0*x*y*y*z - 4.0*x*x*y*y*z - 2.0*x*z*z + 4.0*x*x*z*z + 6.0*x*y*z*z - 12.0*x*x*y*z*z - 4.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
800        S(7,i)= - 1.0*x*y*z + 2.0*x*x*y*z + 2.0*x*y*y*z - 4.0*x*x*y*y*z + 2.0*x*y*z*z - 4.0*x*x*y*z*z - 4.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
801        S(8,i)= + 1.0*y*z - 3.0*x*y*z + 2.0*x*x*y*z - 2.0*y*y*z + 6.0*x*y*y*z - 4.0*x*x*y*y*z - 2.0*y*z*z + 6.0*x*y*z*z - 4.0*x*x*y*z*z + 4.0*y*y*z*z - 12.0*x*y*y*z*z + 8.0*x*x*y*y*z*z;
802        S(9,i)= + 4.0*x - 4.0*x*x - 12.0*x*y + 12.0*x*x*y + 8.0*x*y*y - 8.0*x*x*y*y - 12.0*x*z + 12.0*x*x*z + 36.0*x*y*z - 36.0*x*x*y*z - 24.0*x*y*y*z + 24.0*x*x*y*y*z + 8.0*x*z*z - 8.0*x*x*z*z - 24.0*x*y*z*z + 24.0*x*x*y*z*z + 16.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
803        S(10,i)= - 4.0*x*y + 8.0*x*x*y + 4.0*x*y*y - 8.0*x*x*y*y + 12.0*x*y*z - 24.0*x*x*y*z - 12.0*x*y*y*z + 24.0*x*x*y*y*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z + 8.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
804        S(11,i)= - 4.0*x*y + 4.0*x*x*y + 8.0*x*y*y - 8.0*x*x*y*y + 12.0*x*y*z - 12.0*x*x*y*z - 24.0*x*y*y*z + 24.0*x*x*y*y*z - 8.0*x*y*z*z + 8.0*x*x*y*z*z + 16.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
805        S(12,i)= + 4.0*y - 12.0*x*y + 8.0*x*x*y - 4.0*y*y + 12.0*x*y*y - 8.0*x*x*y*y - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z + 12.0*y*y*z - 36.0*x*y*y*z + 24.0*x*x*y*y*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z - 8.0*y*y*z*z + 24.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
806        S(13,i)= + 4.0*z - 12.0*x*z + 8.0*x*x*z - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z - 4.0*z*z + 12.0*x*z*z - 8.0*x*x*z*z + 12.0*y*z*z - 36.0*x*y*z*z + 24.0*x*x*y*z*z - 8.0*y*y*z*z + 24.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
807        S(14,i)= - 4.0*x*z + 8.0*x*x*z + 12.0*x*y*z - 24.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z + 4.0*x*z*z - 8.0*x*x*z*z - 12.0*x*y*z*z + 24.0*x*x*y*z*z + 8.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
808        S(15,i)= + 4.0*x*y*z - 8.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z - 4.0*x*y*z*z + 8.0*x*x*y*z*z + 8.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
809        S(16,i)= - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z + 4.0*y*z*z - 12.0*x*y*z*z + 8.0*x*x*y*z*z - 8.0*y*y*z*z + 24.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
810        S(17,i)= - 4.0*x*z + 4.0*x*x*z + 12.0*x*y*z - 12.0*x*x*y*z - 8.0*x*y*y*z + 8.0*x*x*y*y*z + 8.0*x*z*z - 8.0*x*x*z*z - 24.0*x*y*z*z + 24.0*x*x*y*z*z + 16.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
811        S(18,i)= + 4.0*x*y*z - 8.0*x*x*y*z - 4.0*x*y*y*z + 8.0*x*x*y*y*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z + 8.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
812        S(19,i)= + 4.0*x*y*z - 4.0*x*x*y*z - 8.0*x*y*y*z + 8.0*x*x*y*y*z - 8.0*x*y*z*z + 8.0*x*x*y*z*z + 16.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
813        S(20,i)= - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z + 4.0*y*y*z - 12.0*x*y*y*z + 8.0*x*x*y*y*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z - 8.0*y*y*z*z + 24.0*x*y*y*z*z - 16.0*x*x*y*y*z*z;
814        S(21,i)= + 16.0*x*y - 16.0*x*x*y - 16.0*x*y*y + 16.0*x*x*y*y - 48.0*x*y*z + 48.0*x*x*y*z + 48.0*x*y*y*z - 48.0*x*x*y*y*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z - 32.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
815        S(22,i)= + 16.0*x*z - 16.0*x*x*z - 48.0*x*y*z + 48.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z - 16.0*x*z*z + 16.0*x*x*z*z + 48.0*x*y*z*z - 48.0*x*x*y*z*z - 32.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
816        S(23,i)= - 16.0*x*y*z + 32.0*x*x*y*z + 16.0*x*y*y*z - 32.0*x*x*y*y*z + 16.0*x*y*z*z - 32.0*x*x*y*z*z - 16.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
817        S(24,i)= - 16.0*x*y*z + 16.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z + 16.0*x*y*z*z - 16.0*x*x*y*z*z - 32.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
818        S(25,i)= + 16.0*y*z - 48.0*x*y*z + 32.0*x*x*y*z - 16.0*y*y*z + 48.0*x*y*y*z - 32.0*x*x*y*y*z - 16.0*y*z*z + 48.0*x*y*z*z - 32.0*x*x*y*z*z + 16.0*y*y*z*z - 48.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
819        S(26,i)= - 16.0*x*y*z + 16.0*x*x*y*z + 16.0*x*y*y*z - 16.0*x*x*y*y*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z - 32.0*x*y*y*z*z + 32.0*x*x*y*y*z*z;
820        S(27,i)= + 64.0*x*y*z - 64.0*x*x*y*z - 64.0*x*y*y*z + 64.0*x*x*y*y*z - 64.0*x*y*z*z + 64.0*x*x*y*z*z + 64.0*x*y*y*z*z - 64.0*x*x*y*y*z*z;
821        DSDV(1,1,i)= - 3.0 + 4.0*x + 9.0*y - 12.0*x*y - 6.0*y*y + 8.0*x*y*y + 9.0*z - 12.0*x*z - 27.0*y*z + 36.0*x*y*z + 18.0*y*y*z - 24.0*x*y*y*z - 6.0*z*z + 8.0*x*z*z + 18.0*y*z*z - 24.0*x*y*z*z - 12.0*y*y*z*z + 16.0*x*y*y*z*z;
822        DSDV(1,2,i)= - 3.0 + 9.0*x - 6.0*x*x + 4.0*y - 12.0*x*y + 8.0*x*x*y + 9.0*z - 27.0*x*z + 18.0*x*x*z - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z - 6.0*z*z + 18.0*x*z*z - 12.0*x*x*z*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z;
823        DSDV(1,3,i)= - 3.0 + 9.0*x - 6.0*x*x + 9.0*y - 27.0*x*y + 18.0*x*x*y - 6.0*y*y + 18.0*x*y*y - 12.0*x*x*y*y + 4.0*z - 12.0*x*z + 8.0*x*x*z - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z;
824        DSDV(2,1,i)= - 1.0 + 4.0*x + 3.0*y - 12.0*x*y - 2.0*y*y + 8.0*x*y*y + 3.0*z - 12.0*x*z - 9.0*y*z + 36.0*x*y*z + 6.0*y*y*z - 24.0*x*y*y*z - 2.0*z*z + 8.0*x*z*z + 6.0*y*z*z - 24.0*x*y*z*z - 4.0*y*y*z*z + 16.0*x*y*y*z*z;
825        DSDV(2,2,i)= + 3.0*x - 6.0*x*x - 4.0*x*y + 8.0*x*x*y - 9.0*x*z + 18.0*x*x*z + 12.0*x*y*z - 24.0*x*x*y*z + 6.0*x*z*z - 12.0*x*x*z*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z;
826        DSDV(2,3,i)= + 3.0*x - 6.0*x*x - 9.0*x*y + 18.0*x*x*y + 6.0*x*y*y - 12.0*x*x*y*y - 4.0*x*z + 8.0*x*x*z + 12.0*x*y*z - 24.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z;
827        DSDV(3,1,i)= + 1.0*y - 4.0*x*y - 2.0*y*y + 8.0*x*y*y - 3.0*y*z + 12.0*x*y*z + 6.0*y*y*z - 24.0*x*y*y*z + 2.0*y*z*z - 8.0*x*y*z*z - 4.0*y*y*z*z + 16.0*x*y*y*z*z;
828        DSDV(3,2,i)= + 1.0*x - 2.0*x*x - 4.0*x*y + 8.0*x*x*y - 3.0*x*z + 6.0*x*x*z + 12.0*x*y*z - 24.0*x*x*y*z + 2.0*x*z*z - 4.0*x*x*z*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z;
829        DSDV(3,3,i)= - 3.0*x*y + 6.0*x*x*y + 6.0*x*y*y - 12.0*x*x*y*y + 4.0*x*y*z - 8.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z;
830        DSDV(4,1,i)= + 3.0*y - 4.0*x*y - 6.0*y*y + 8.0*x*y*y - 9.0*y*z + 12.0*x*y*z + 18.0*y*y*z - 24.0*x*y*y*z + 6.0*y*z*z - 8.0*x*y*z*z - 12.0*y*y*z*z + 16.0*x*y*y*z*z;
831        DSDV(4,2,i)= - 1.0 + 3.0*x - 2.0*x*x + 4.0*y - 12.0*x*y + 8.0*x*x*y + 3.0*z - 9.0*x*z + 6.0*x*x*z - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z - 2.0*z*z + 6.0*x*z*z - 4.0*x*x*z*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z;
832        DSDV(4,3,i)= + 3.0*y - 9.0*x*y + 6.0*x*x*y - 6.0*y*y + 18.0*x*y*y - 12.0*x*x*y*y - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z;
833        DSDV(5,1,i)= + 3.0*z - 4.0*x*z - 9.0*y*z + 12.0*x*y*z + 6.0*y*y*z - 8.0*x*y*y*z - 6.0*z*z + 8.0*x*z*z + 18.0*y*z*z - 24.0*x*y*z*z - 12.0*y*y*z*z + 16.0*x*y*y*z*z;
834        DSDV(5,2,i)= + 3.0*z - 9.0*x*z + 6.0*x*x*z - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z - 6.0*z*z + 18.0*x*z*z - 12.0*x*x*z*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z;
835        DSDV(5,3,i)= - 1.0 + 3.0*x - 2.0*x*x + 3.0*y - 9.0*x*y + 6.0*x*x*y - 2.0*y*y + 6.0*x*y*y - 4.0*x*x*y*y + 4.0*z - 12.0*x*z + 8.0*x*x*z - 12.0*y*z + 36.0*x*y*z - 24.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z;
836        DSDV(6,1,i)= + 1.0*z - 4.0*x*z - 3.0*y*z + 12.0*x*y*z + 2.0*y*y*z - 8.0*x*y*y*z - 2.0*z*z + 8.0*x*z*z + 6.0*y*z*z - 24.0*x*y*z*z - 4.0*y*y*z*z + 16.0*x*y*y*z*z;
837        DSDV(6,2,i)= - 3.0*x*z + 6.0*x*x*z + 4.0*x*y*z - 8.0*x*x*y*z + 6.0*x*z*z - 12.0*x*x*z*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z;
838        DSDV(6,3,i)= + 1.0*x - 2.0*x*x - 3.0*x*y + 6.0*x*x*y + 2.0*x*y*y - 4.0*x*x*y*y - 4.0*x*z + 8.0*x*x*z + 12.0*x*y*z - 24.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z;
839        DSDV(7,1,i)= - 1.0*y*z + 4.0*x*y*z + 2.0*y*y*z - 8.0*x*y*y*z + 2.0*y*z*z - 8.0*x*y*z*z - 4.0*y*y*z*z + 16.0*x*y*y*z*z;
840        DSDV(7,2,i)= - 1.0*x*z + 2.0*x*x*z + 4.0*x*y*z - 8.0*x*x*y*z + 2.0*x*z*z - 4.0*x*x*z*z - 8.0*x*y*z*z + 16.0*x*x*y*z*z;
841        DSDV(7,3,i)= - 1.0*x*y + 2.0*x*x*y + 2.0*x*y*y - 4.0*x*x*y*y + 4.0*x*y*z - 8.0*x*x*y*z - 8.0*x*y*y*z + 16.0*x*x*y*y*z;
842        DSDV(8,1,i)= - 3.0*y*z + 4.0*x*y*z + 6.0*y*y*z - 8.0*x*y*y*z + 6.0*y*z*z - 8.0*x*y*z*z - 12.0*y*y*z*z + 16.0*x*y*y*z*z;
843        DSDV(8,2,i)= + 1.0*z - 3.0*x*z + 2.0*x*x*z - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z - 2.0*z*z + 6.0*x*z*z - 4.0*x*x*z*z + 8.0*y*z*z - 24.0*x*y*z*z + 16.0*x*x*y*z*z;
844        DSDV(8,3,i)= + 1.0*y - 3.0*x*y + 2.0*x*x*y - 2.0*y*y + 6.0*x*y*y - 4.0*x*x*y*y - 4.0*y*z + 12.0*x*y*z - 8.0*x*x*y*z + 8.0*y*y*z - 24.0*x*y*y*z + 16.0*x*x*y*y*z;
845        DSDV(9,1,i)= + 4.0 - 8.0*x - 12.0*y + 24.0*x*y + 8.0*y*y - 16.0*x*y*y - 12.0*z + 24.0*x*z + 36.0*y*z - 72.0*x*y*z - 24.0*y*y*z + 48.0*x*y*y*z + 8.0*z*z - 16.0*x*z*z - 24.0*y*z*z + 48.0*x*y*z*z + 16.0*y*y*z*z - 32.0*x*y*y*z*z;
846        DSDV(9,2,i)= - 12.0*x + 12.0*x*x + 16.0*x*y - 16.0*x*x*y + 36.0*x*z - 36.0*x*x*z - 48.0*x*y*z + 48.0*x*x*y*z - 24.0*x*z*z + 24.0*x*x*z*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z;
847        DSDV(9,3,i)= - 12.0*x + 12.0*x*x + 36.0*x*y - 36.0*x*x*y - 24.0*x*y*y + 24.0*x*x*y*y + 16.0*x*z - 16.0*x*x*z - 48.0*x*y*z + 48.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z;
848        DSDV(10,1,i)= - 4.0*y + 16.0*x*y + 4.0*y*y - 16.0*x*y*y + 12.0*y*z - 48.0*x*y*z - 12.0*y*y*z + 48.0*x*y*y*z - 8.0*y*z*z + 32.0*x*y*z*z + 8.0*y*y*z*z - 32.0*x*y*y*z*z;
849        DSDV(10,2,i)= - 4.0*x + 8.0*x*x + 8.0*x*y - 16.0*x*x*y + 12.0*x*z - 24.0*x*x*z - 24.0*x*y*z + 48.0*x*x*y*z - 8.0*x*z*z + 16.0*x*x*z*z + 16.0*x*y*z*z - 32.0*x*x*y*z*z;
850        DSDV(10,3,i)= + 12.0*x*y - 24.0*x*x*y - 12.0*x*y*y + 24.0*x*x*y*y - 16.0*x*y*z + 32.0*x*x*y*z + 16.0*x*y*y*z - 32.0*x*x*y*y*z;
851        DSDV(11,1,i)= - 4.0*y + 8.0*x*y + 8.0*y*y - 16.0*x*y*y + 12.0*y*z - 24.0*x*y*z - 24.0*y*y*z + 48.0*x*y*y*z - 8.0*y*z*z + 16.0*x*y*z*z + 16.0*y*y*z*z - 32.0*x*y*y*z*z;
852        DSDV(11,2,i)= - 4.0*x + 4.0*x*x + 16.0*x*y - 16.0*x*x*y + 12.0*x*z - 12.0*x*x*z - 48.0*x*y*z + 48.0*x*x*y*z - 8.0*x*z*z + 8.0*x*x*z*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z;
853        DSDV(11,3,i)= + 12.0*x*y - 12.0*x*x*y - 24.0*x*y*y + 24.0*x*x*y*y - 16.0*x*y*z + 16.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z;
854        DSDV(12,1,i)= - 12.0*y + 16.0*x*y + 12.0*y*y - 16.0*x*y*y + 36.0*y*z - 48.0*x*y*z - 36.0*y*y*z + 48.0*x*y*y*z - 24.0*y*z*z + 32.0*x*y*z*z + 24.0*y*y*z*z - 32.0*x*y*y*z*z;
855        DSDV(12,2,i)= + 4.0 - 12.0*x + 8.0*x*x - 8.0*y + 24.0*x*y - 16.0*x*x*y - 12.0*z + 36.0*x*z - 24.0*x*x*z + 24.0*y*z - 72.0*x*y*z + 48.0*x*x*y*z + 8.0*z*z - 24.0*x*z*z + 16.0*x*x*z*z - 16.0*y*z*z + 48.0*x*y*z*z - 32.0*x*x*y*z*z;
856        DSDV(12,3,i)= - 12.0*y + 36.0*x*y - 24.0*x*x*y + 12.0*y*y - 36.0*x*y*y + 24.0*x*x*y*y + 16.0*y*z - 48.0*x*y*z + 32.0*x*x*y*z - 16.0*y*y*z + 48.0*x*y*y*z - 32.0*x*x*y*y*z;
857        DSDV(13,1,i)= - 12.0*z + 16.0*x*z + 36.0*y*z - 48.0*x*y*z - 24.0*y*y*z + 32.0*x*y*y*z + 12.0*z*z - 16.0*x*z*z - 36.0*y*z*z + 48.0*x*y*z*z + 24.0*y*y*z*z - 32.0*x*y*y*z*z;
858        DSDV(13,2,i)= - 12.0*z + 36.0*x*z - 24.0*x*x*z + 16.0*y*z - 48.0*x*y*z + 32.0*x*x*y*z + 12.0*z*z - 36.0*x*z*z + 24.0*x*x*z*z - 16.0*y*z*z + 48.0*x*y*z*z - 32.0*x*x*y*z*z;
859        DSDV(13,3,i)= + 4.0 - 12.0*x + 8.0*x*x - 12.0*y + 36.0*x*y - 24.0*x*x*y + 8.0*y*y - 24.0*x*y*y + 16.0*x*x*y*y - 8.0*z + 24.0*x*z - 16.0*x*x*z + 24.0*y*z - 72.0*x*y*z + 48.0*x*x*y*z - 16.0*y*y*z + 48.0*x*y*y*z - 32.0*x*x*y*y*z;
860        DSDV(14,1,i)= - 4.0*z + 16.0*x*z + 12.0*y*z - 48.0*x*y*z - 8.0*y*y*z + 32.0*x*y*y*z + 4.0*z*z - 16.0*x*z*z - 12.0*y*z*z + 48.0*x*y*z*z + 8.0*y*y*z*z - 32.0*x*y*y*z*z;
861        DSDV(14,2,i)= + 12.0*x*z - 24.0*x*x*z - 16.0*x*y*z + 32.0*x*x*y*z - 12.0*x*z*z + 24.0*x*x*z*z + 16.0*x*y*z*z - 32.0*x*x*y*z*z;
862        DSDV(14,3,i)= - 4.0*x + 8.0*x*x + 12.0*x*y - 24.0*x*x*y - 8.0*x*y*y + 16.0*x*x*y*y + 8.0*x*z - 16.0*x*x*z - 24.0*x*y*z + 48.0*x*x*y*z + 16.0*x*y*y*z - 32.0*x*x*y*y*z;
863        DSDV(15,1,i)= + 4.0*y*z - 16.0*x*y*z - 8.0*y*y*z + 32.0*x*y*y*z - 4.0*y*z*z + 16.0*x*y*z*z + 8.0*y*y*z*z - 32.0*x*y*y*z*z;
864        DSDV(15,2,i)= + 4.0*x*z - 8.0*x*x*z - 16.0*x*y*z + 32.0*x*x*y*z - 4.0*x*z*z + 8.0*x*x*z*z + 16.0*x*y*z*z - 32.0*x*x*y*z*z;
865        DSDV(15,3,i)= + 4.0*x*y - 8.0*x*x*y - 8.0*x*y*y + 16.0*x*x*y*y - 8.0*x*y*z + 16.0*x*x*y*z + 16.0*x*y*y*z - 32.0*x*x*y*y*z;
866        DSDV(16,1,i)= + 12.0*y*z - 16.0*x*y*z - 24.0*y*y*z + 32.0*x*y*y*z - 12.0*y*z*z + 16.0*x*y*z*z + 24.0*y*y*z*z - 32.0*x*y*y*z*z;
867        DSDV(16,2,i)= - 4.0*z + 12.0*x*z - 8.0*x*x*z + 16.0*y*z - 48.0*x*y*z + 32.0*x*x*y*z + 4.0*z*z - 12.0*x*z*z + 8.0*x*x*z*z - 16.0*y*z*z + 48.0*x*y*z*z - 32.0*x*x*y*z*z;
868        DSDV(16,3,i)= - 4.0*y + 12.0*x*y - 8.0*x*x*y + 8.0*y*y - 24.0*x*y*y + 16.0*x*x*y*y + 8.0*y*z - 24.0*x*y*z + 16.0*x*x*y*z - 16.0*y*y*z + 48.0*x*y*y*z - 32.0*x*x*y*y*z;
869        DSDV(17,1,i)= - 4.0*z + 8.0*x*z + 12.0*y*z - 24.0*x*y*z - 8.0*y*y*z + 16.0*x*y*y*z + 8.0*z*z - 16.0*x*z*z - 24.0*y*z*z + 48.0*x*y*z*z + 16.0*y*y*z*z - 32.0*x*y*y*z*z;
870        DSDV(17,2,i)= + 12.0*x*z - 12.0*x*x*z - 16.0*x*y*z + 16.0*x*x*y*z - 24.0*x*z*z + 24.0*x*x*z*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z;
871        DSDV(17,3,i)= - 4.0*x + 4.0*x*x + 12.0*x*y - 12.0*x*x*y - 8.0*x*y*y + 8.0*x*x*y*y + 16.0*x*z - 16.0*x*x*z - 48.0*x*y*z + 48.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z;
872        DSDV(18,1,i)= + 4.0*y*z - 16.0*x*y*z - 4.0*y*y*z + 16.0*x*y*y*z - 8.0*y*z*z + 32.0*x*y*z*z + 8.0*y*y*z*z - 32.0*x*y*y*z*z;
873        DSDV(18,2,i)= + 4.0*x*z - 8.0*x*x*z - 8.0*x*y*z + 16.0*x*x*y*z - 8.0*x*z*z + 16.0*x*x*z*z + 16.0*x*y*z*z - 32.0*x*x*y*z*z;
874        DSDV(18,3,i)= + 4.0*x*y - 8.0*x*x*y - 4.0*x*y*y + 8.0*x*x*y*y - 16.0*x*y*z + 32.0*x*x*y*z + 16.0*x*y*y*z - 32.0*x*x*y*y*z;
875        DSDV(19,1,i)= + 4.0*y*z - 8.0*x*y*z - 8.0*y*y*z + 16.0*x*y*y*z - 8.0*y*z*z + 16.0*x*y*z*z + 16.0*y*y*z*z - 32.0*x*y*y*z*z;
876        DSDV(19,2,i)= + 4.0*x*z - 4.0*x*x*z - 16.0*x*y*z + 16.0*x*x*y*z - 8.0*x*z*z + 8.0*x*x*z*z + 32.0*x*y*z*z - 32.0*x*x*y*z*z;
877        DSDV(19,3,i)= + 4.0*x*y - 4.0*x*x*y - 8.0*x*y*y + 8.0*x*x*y*y - 16.0*x*y*z + 16.0*x*x*y*z + 32.0*x*y*y*z - 32.0*x*x*y*y*z;
878        DSDV(20,1,i)= + 12.0*y*z - 16.0*x*y*z - 12.0*y*y*z + 16.0*x*y*y*z - 24.0*y*z*z + 32.0*x*y*z*z + 24.0*y*y*z*z - 32.0*x*y*y*z*z;
879        DSDV(20,2,i)= - 4.0*z + 12.0*x*z - 8.0*x*x*z + 8.0*y*z - 24.0*x*y*z + 16.0*x*x*y*z + 8.0*z*z - 24.0*x*z*z + 16.0*x*x*z*z - 16.0*y*z*z + 48.0*x*y*z*z - 32.0*x*x*y*z*z;
880        DSDV(20,3,i)= - 4.0*y + 12.0*x*y - 8.0*x*x*y + 4.0*y*y - 12.0*x*y*y + 8.0*x*x*y*y + 16.0*y*z - 48.0*x*y*z + 32.0*x*x*y*z - 16.0*y*y*z + 48.0*x*y*y*z - 32.0*x*x*y*y*z;
881        DSDV(21,1,i)= + 16.0*y - 32.0*x*y - 16.0*y*y + 32.0*x*y*y - 48.0*y*z + 96.0*x*y*z + 48.0*y*y*z - 96.0*x*y*y*z + 32.0*y*z*z - 64.0*x*y*z*z - 32.0*y*y*z*z + 64.0*x*y*y*z*z;
882        DSDV(21,2,i)= + 16.0*x - 16.0*x*x - 32.0*x*y + 32.0*x*x*y - 48.0*x*z + 48.0*x*x*z + 96.0*x*y*z - 96.0*x*x*y*z + 32.0*x*z*z - 32.0*x*x*z*z - 64.0*x*y*z*z + 64.0*x*x*y*z*z;
883        DSDV(21,3,i)= - 48.0*x*y + 48.0*x*x*y + 48.0*x*y*y - 48.0*x*x*y*y + 64.0*x*y*z - 64.0*x*x*y*z - 64.0*x*y*y*z + 64.0*x*x*y*y*z;
884        DSDV(22,1,i)= + 16.0*z - 32.0*x*z - 48.0*y*z + 96.0*x*y*z + 32.0*y*y*z - 64.0*x*y*y*z - 16.0*z*z + 32.0*x*z*z + 48.0*y*z*z - 96.0*x*y*z*z - 32.0*y*y*z*z + 64.0*x*y*y*z*z;
885        DSDV(22,2,i)= - 48.0*x*z + 48.0*x*x*z + 64.0*x*y*z - 64.0*x*x*y*z + 48.0*x*z*z - 48.0*x*x*z*z - 64.0*x*y*z*z + 64.0*x*x*y*z*z;
886        DSDV(22,3,i)= + 16.0*x - 16.0*x*x - 48.0*x*y + 48.0*x*x*y + 32.0*x*y*y - 32.0*x*x*y*y - 32.0*x*z + 32.0*x*x*z + 96.0*x*y*z - 96.0*x*x*y*z - 64.0*x*y*y*z + 64.0*x*x*y*y*z;
887        DSDV(23,1,i)= - 16.0*y*z + 64.0*x*y*z + 16.0*y*y*z - 64.0*x*y*y*z + 16.0*y*z*z - 64.0*x*y*z*z - 16.0*y*y*z*z + 64.0*x*y*y*z*z;
888        DSDV(23,2,i)= - 16.0*x*z + 32.0*x*x*z + 32.0*x*y*z - 64.0*x*x*y*z + 16.0*x*z*z - 32.0*x*x*z*z - 32.0*x*y*z*z + 64.0*x*x*y*z*z;
889        DSDV(23,3,i)= - 16.0*x*y + 32.0*x*x*y + 16.0*x*y*y - 32.0*x*x*y*y + 32.0*x*y*z - 64.0*x*x*y*z - 32.0*x*y*y*z + 64.0*x*x*y*y*z;
890        DSDV(24,1,i)= - 16.0*y*z + 32.0*x*y*z + 32.0*y*y*z - 64.0*x*y*y*z + 16.0*y*z*z - 32.0*x*y*z*z - 32.0*y*y*z*z + 64.0*x*y*y*z*z;
891        DSDV(24,2,i)= - 16.0*x*z + 16.0*x*x*z + 64.0*x*y*z - 64.0*x*x*y*z + 16.0*x*z*z - 16.0*x*x*z*z - 64.0*x*y*z*z + 64.0*x*x*y*z*z;
892        DSDV(24,3,i)= - 16.0*x*y + 16.0*x*x*y + 32.0*x*y*y - 32.0*x*x*y*y + 32.0*x*y*z - 32.0*x*x*y*z - 64.0*x*y*y*z + 64.0*x*x*y*y*z;
893        DSDV(25,1,i)= - 48.0*y*z + 64.0*x*y*z + 48.0*y*y*z - 64.0*x*y*y*z + 48.0*y*z*z - 64.0*x*y*z*z - 48.0*y*y*z*z + 64.0*x*y*y*z*z;
894        DSDV(25,2,i)= + 16.0*z - 48.0*x*z + 32.0*x*x*z - 32.0*y*z + 96.0*x*y*z - 64.0*x*x*y*z - 16.0*z*z + 48.0*x*z*z - 32.0*x*x*z*z + 32.0*y*z*z - 96.0*x*y*z*z + 64.0*x*x*y*z*z;
895        DSDV(25,3,i)= + 16.0*y - 48.0*x*y + 32.0*x*x*y - 16.0*y*y + 48.0*x*y*y - 32.0*x*x*y*y - 32.0*y*z + 96.0*x*y*z - 64.0*x*x*y*z + 32.0*y*y*z - 96.0*x*y*y*z + 64.0*x*x*y*y*z;
896        DSDV(26,1,i)= - 16.0*y*z + 32.0*x*y*z + 16.0*y*y*z - 32.0*x*y*y*z + 32.0*y*z*z - 64.0*x*y*z*z - 32.0*y*y*z*z + 64.0*x*y*y*z*z;
897        DSDV(26,2,i)= - 16.0*x*z + 16.0*x*x*z + 32.0*x*y*z - 32.0*x*x*y*z + 32.0*x*z*z - 32.0*x*x*z*z - 64.0*x*y*z*z + 64.0*x*x*y*z*z;
898        DSDV(26,3,i)= - 16.0*x*y + 16.0*x*x*y + 16.0*x*y*y - 16.0*x*x*y*y + 64.0*x*y*z - 64.0*x*x*y*z - 64.0*x*y*y*z + 64.0*x*x*y*y*z;
899        DSDV(27,1,i)= + 64.0*y*z - 128.0*x*y*z - 64.0*y*y*z + 128.0*x*y*y*z - 64.0*y*z*z + 128.0*x*y*z*z + 64.0*y*y*z*z - 128.0*x*y*y*z*z;
900        DSDV(27,2,i)= + 64.0*x*z - 64.0*x*x*z - 128.0*x*y*z + 128.0*x*x*y*z - 64.0*x*z*z + 64.0*x*x*z*z + 128.0*x*y*z*z - 128.0*x*x*y*z*z;
901        DSDV(27,3,i)= + 64.0*x*y - 64.0*x*x*y - 64.0*x*y*y + 64.0*x*x*y*y - 128.0*x*y*z + 128.0*x*x*y*z + 128.0*x*y*y*z - 128.0*x*x*y*y*z;
902      }
903      #undef NUMSHAPES
904      #undef DIM
905  }  }
906    
907  /**************************************************************/  /**************************************************************/

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