/* phi_tri.c    Phi and derivatives for order 1 through 4 for Galerkin FEM
 *              and dimension 1 (x) through 4 (x,y,z,t)   on triangles
 *  phi11(c,x) is linear(order 1) FEM phi function in 1 dimension(x)
 *             =c[0]+c[1]*x  c is a vector of polynomial coefficients
 *  phi11x(c,x) is first derivative of phi11(c,x)
 *   
 *  phi21(c,x) is second order FEM phi function in 1 dimension
 *  phi21x(c,x) is first derivative of phi21(c,x)
 *  phi21xx(c,x) is second derivative of phi21(c,x)
 *
 *  phi22(c,x,y) is second order FEM phi function in 2 dimensions
 *               = c[0]+c[1]*x+c[2]*y+c[3]*x*x+c[4]*x*y+c[5]*y*y
 *  phi22x(c,x,y) is partial derivative of phi22(c,x,y) with respect to x
 *  phi22y(c,x,y) is partial derivative of phi22(c,x,y) with respect to y
 *  phi22xx(c,x,y) is second partial of phi22(c,x,y) with respect to x
 *  phi22xy(c,x,y) is second partial of phi22(c,x,y) wrt x and wrt y
 *  phi22yy(c,x,y) is second partial of phi22(c,x,y) with respect to y
 *
 *  ...  up to fourth derivative of fourth order phi in four dimensions
 *  phi44(c,x,y,z,t) is fourth order four dimensional FEM phi function
 *  ...
 *  phi44tttt(c,x,y,z,t) is fourth partial of phi44(c,x,y,z,t) wrt t
 */

double phi11(double c[], double x)
{
  return c[0]+c[1]*x;
}
double phi11x(double c[], double x)
{
  return c[1];
}



double phi21(double c[], double x)
{
  return c[0]+c[1]*x+c[2]*x*x;
}
double phi21x(double c[], double x)
{
  return c[1]+c[2]*2.0*x;
}
double phi21xx(double c[], double x)
{
  return c[2]*2.0;
}



double phi31(double c[], double x)
{
  return c[0]+c[1]*x+c[2]*x*x+c[3]*x*x*x;
}
double phi31x(double c[], double x)
{
  return c[1]+c[2]*2.0*x+c[3]*3.0*x*x;
}
double phi31xx(double c[], double x)
{
  return c[2]*2.0+c[3]*6.0*x;
}
double phi31xxx(double c[], double x)
{
  return c[3]*6.0;
}



double phi41(double c[], double x)
{
  return c[0]+c[1]*x+c[2]*x*x+c[3]*x*x*x+c[4]*x*x*x*x;
}
double phi41x(double c[], double x)
{
  return c[1]+c[2]*2.0*x+c[3]*3.0*x*x+c[4]*4.0*x*x*x;
}
double phi41xx(double c[], double x)
{
  return c[2]*2.0+c[3]*6.0*x+c[4]*12.0*x*x;
}
double phi41xxx(double c[], double x)
{
  return c[3]*6.0+c[4]*24.0*x;
}
double phi41xxxx(double c[], double x)
{
  return c[4]*24.0;
}



double phi12(double c[], double x, double y)
{
  return c[0]+c[1]*x+c[2]*y;
}
double phi12x(double c[], double x, double y)
{
  return c[1];
}
double phi12y(double c[], double x, double y)
{
  return c[2];
}



double phi22(double c[], double x, double y)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*x*x+c[4]*x*y+c[5]*y*y;
}
double phi22x(double c[], double x, double y)
{
  return c[1]+c[3]*2.0*x+c[4]*y;
}
double phi22y(double c[], double x, double y)
{
  return c[2]+c[4]*x+c[5]*2.0*y;
}
double phi22xx(double c[], double x, double y)
{
  return c[3]*2.0;
}
double phi22xy(double c[], double x, double y)
{
  return c[4];
}
double phi22yy(double c[], double x, double y)
{
  return c[5]*2.0;
}



double phi32(double c[], double x, double y)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*x*x+c[4]*x*y+c[5]*y*y+
         c[6]*x*x*x+c[7]*x*x*y+c[8]*x*y*y+c[9]*y*y*y;
}
double phi32x(double c[], double x, double y)
{
  return c[1]+c[3]*2.0*x+c[4]*y+
         c[6]*3.0*x*x+c[7]*2.0*x*y+c[8]*y*y;
}
double phi32y(double c[], double x, double y)
{
  return c[2]+c[4]*x+c[5]*2.0*y+
         c[7]*x*x+c[8]*2.0*x*y+c[9]*3.0*y*y ;
}
double phi32xx(double c[], double x, double y)
{
  return c[3]*2.0+c[6]*6.0*x+c[7]*2.0*y;
}
double phi32xy(double c[], double x, double y)
{
  return c[4]+c[7]*2.0*x+c[8]*2.0*y;
}
double phi32yy(double c[], double x, double y)
{
  return c[5]*2.0+c[8]*2.0*x+c[9]*6.0*y;
}
double phi32xxx(double c[], double x, double y)
{
  return c[6]*6.0;
}
double phi32xxy(double c[], double x, double y)
{
  return c[7]*2.0;
}
double phi32xyy(double c[], double x, double y)
{
  return c[8]*2.0;
}
double phi32yyy(double c[], double x, double y)
{
  return c[9]*6.0;
}



double phi42(double c[], double x, double y)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*x*x+c[4]*x*y+c[5]*y*y+
         c[6]*x*x*x+c[7]*x*x*y+c[8]*x*y*y+c[9]*y*y*y+
         c[10]*x*x*x*x+c[11]*x*x*x*y+c[12]*x*x*y*y+
	 c[13]*x*y*y*y+c[14]*y*y*y*y;
}
double phi42x(double c[], double x, double y)
{
  return c[1]+c[3]*2.0*x+c[3]*y+
         c[6]*3.0*x*x+c[7]*2.0*x*y+c[8]*y*y+
         c[13]*y*y*y;
}
double phi42y(double c[], double x, double y)
{
  return c[0]; /* TBD */
}
double phi42xx(double c[], double x, double y)
{
  return c[0];
}
double phi42xy(double c[], double x, double y)
{
  return c[0];
}
double phi42yy(double c[], double x, double y)
{
  return c[0];
}
double phi42xxx(double c[], double x, double y)
{
  return c[0];
}
double phi42xxy(double c[], double x, double y)
{
  return c[0];
}
double phi42xyy(double c[], double x, double y)
{
  return c[0];
}
double phi42yyy(double c[], double x, double y)
{
  return c[0];
}
double phi42xxxx(double c[], double x, double y)
{
  return c[10]*24.0;
}
double phi42xxxy(double c[], double x, double y)
{
  return c[11]*6.0;
}
double phi42xxyy(double c[], double x, double y)
{
  return c[12]*4.0;
}
double phi42xyyy(double c[], double x, double y)
{
  return c[13]*6.0;
}
double phi42yyyy(double c[], double x, double y)
{
  return c[14]*24.0;
}



double phi13(double c[], double x, double y, double z)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*z;
}
double phi13x(double c[], double x, double y, double z)
{
  return c[1];
}
double phi13y(double c[], double x, double y, double z)
{
  return c[2];
}
double phi13z(double c[], double x, double y, double z)
{
  return c[3];
}



double phi23(double c[], double x, double y, double z)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*z+
         c[4]*x*x+c[5]*x*y+c[6]*x*z+
         c[7]*y*y+c[8]*y*z+c[9]*z*z;
}
double phi23x(double c[], double x, double y, double z)
{
  return c[1]+c[4]*2.0*x+c[5]*y+c[6]*z;
}
double phi23y(double c[], double x, double y, double z)
{
  return c[2]+c[5]*x+c[7]*2.0*y+c[8]*z;
}
double phi23z(double c[], double x, double y, double z)
{
  return c[3]+c[6]*x+c[8]*y+c[9]*2.0*z;
}
double phi23xx(double c[], double x, double y, double z)
{
  return c[4]*2.0;
}
double phi23xy(double c[], double x, double y, double z)
{
  return c[5];
}
double phi23xz(double c[], double x, double y, double z)
{
  return c[6];
}
double phi23yy(double c[], double x, double y, double z)
{
  return c[7]*2.0;
}
double phi23yz(double c[], double x, double y, double z)
{
  return c[8];
}
double phi23zz(double c[], double x, double y, double z)
{
  return c[9]*2.0;
}



double phi33(double c[], double x, double y, double z)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*z+
         c[4]*x*x+c[5]*x*y+c[6]*x*z+
         c[7]*y*y+c[8]*y*z+c[9]*z*z+
         c[10]*x*x*x+c[11]*x*x*y+c[12]*x*x*z+
         c[13]*x*y*y+c[14]*x*y*z+c[15]*x*z*z+
         c[16]*y*y*y+c[17]*y*y*z+c[18]*y*z*z+c[19]*z*z*z;
}
double phi33x(double c[], double x, double y, double z)
{
  return c[0]; /* TBD */
}
double phi33y(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33z(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33xx(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33xy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33xz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33yy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33yz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33zz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi33xxx(double c[], double x, double y, double z)
{
  return c[10]*6.0;
}
double phi33xxy(double c[], double x, double y, double z)
{
  return c[11]*2.0;
}
double phi33xxz(double c[], double x, double y, double z)
{
  return c[12]*2.0;
}
double phi33xyy(double c[], double x, double y, double z)
{
  return c[13]*2.0;
}
double phi33xyz(double c[], double x, double y, double z)
{
  return c[14];
}
double phi33xzz(double c[], double x, double y, double z)
{
  return c[15]*2.0;
}
double phi33yyy(double c[], double x, double y, double z)
{
  return c[16]*6.0;
}
double phi33yyz(double c[], double x, double y, double z)
{
  return c[17]*2.0;
}
double phi33yzz(double c[], double x, double y, double z)
{
  return c[18]*2.0;
}
double phi33zzz(double c[], double x, double y, double z)
{
  return c[19]*6.0;
}

double phi43(double c[], double x, double y, double z)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*z+
         c[4]*x*x+c[5]*x*y+c[6]*x*z+
         c[7]*y*y+c[8]*y*z+c[9]*z*z+
         c[10]*x*x*x+c[11]*x*x*y+c[12]*x*x*z+
         c[13]*x*y*y+c[14]*x*y*z+c[15]*x*z*z+
         c[16]*y*y*y+c[17]*y*y*z+c[18]*y*z*z+c[19]*z*z*z+
         c[20]*x*x*x*x+c[21]*x*x*x*y+c[22]*x*x*x*z+
         c[23]*x*x*y*y+c[24]*x*x*y*z+c[25]*x*x*z*z+
         c[26]*x*y*y*y+c[27]*x*y*y*z+c[28]*x*y*z*z+
         c[29]*x*z*z*z+c[30]*y*y*y*y+c[30]*y*y*y*z+
         c[31]*y*y*z*z+c[32]*y*z*z*z+c[33]*z*z*z*z;
}
double phi43x(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43y(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43z(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xx(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43zz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxx(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xyy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xyz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yyy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yyz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43zzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxxx(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxxy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxxz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxyy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxyz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xxzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xyyy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xyyz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xyzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43xzzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yyyy(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yyyz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yyzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43yzzz(double c[], double x, double y, double z)
{
  return c[0];
}
double phi43zzzz(double c[], double x, double y, double z)
{
  return c[0];
}



double phi14(double c[], double x, double y, double z, double t)
{
  return c[0]+c[1]*x+c[2]*y+c[3]*z+c[4]*t;
}
double phi14x(double c[], double x, double y, double z, double t)
{
  return c[1];
}
double phi14y(double c[], double x, double y, double z, double t)
{
  return c[2];
}
double phi14z(double c[], double x, double y, double z, double t)
{
  return c[3];
}
double phi14t(double c[], double x, double y, double z, double t)
{
  return c[4];
}

/* ... */

double phi44zzzz(double c[], double x, double y, double z, double t)
{
  return c[0]; /* TBD */
}

/* end phi_tri.c */