/var/www2/hermes2d/hermes2d/src/shapeset_common.h File Reference

Go to the source code of this file.

Defines
#define	lambda1(x, y)   (((y) + 1) / 2)
#define	lambda2(x, y)   (-((x) + (y)) / 2)
#define	lambda3(x, y)   (((x) + 1) / 2)
#define	lambda1x(x, y)   (0.0)
#define	lambda2x(x, y)   (-1.0 / 2.0)
#define	lambda3x(x, y)   (1.0 / 2.0)
#define	lambda1y(x, y)   (1.0 / 2.0)
#define	lambda2y(x, y)   (-1.0 / 2.0)
#define	lambda3y(x, y)   (0.0)
#define	phi0(x)   (-2.0 * 1.22474487139158904909864203735)
#define	phi1(x)   (-2.0 * 1.58113883008418966599944677222 * (x))
#define	phi2(x)   (-1.0 / 2.0 * 1.87082869338697069279187436616 * (5 * (x) * (x) - 1))
#define	phi3(x)   (-1.0 / 2.0 * 2.12132034355964257320253308631 * (7 * (x) * (x) - 3) * (x))
#define	phi4(x)   (-1.0 / 4.0 * 2.34520787991171477728281505677 * (21 * (x) * (x) * (x) * (x) - 14 * (x) * (x) + 1))
#define	phi5(x)   (-1.0 / 4.0 * 2.54950975679639241501411205451 * ((33 * (x) * (x) - 30) * (x) * (x) + 5) * (x))
#define	phi6(x)   (-1.0 / 32.0 * 2.73861278752583056728484891400 * (((429 * (x) * (x) - 495) * (x) * (x) + 135) * (x) * (x) - 5))
#define	phi7(x)   (-1.0 / 32.0 * 2.91547594742265023543707643877 * (((715 * (x) * (x) - 1001) * (x) * (x) + 385) * (x) * (x) - 35) * (x))
#define	phi8(x)   (-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((2431 * (x) * (x) - 4004) * (x) * (x) + 2002) * (x) * (x) - 308) * (x) * (x) + 7))
#define	phi9(x)   (-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((4199 * (x) * (x) - 7956) * (x) * (x) + 4914) * (x) * (x) - 1092) * (x) * (x) + 63) * (x))
#define	phi0x(x)   (0)
#define	phi1x(x)   (-2.0 * 1.58113883008418966599944677222)
#define	phi2x(x)   (-1.0 / 2.0 * 1.87082869338697069279187436616 * (10 * (x)))
#define	phi3x(x)   (-1.0 / 2.0 * 2.12132034355964257320253308631 * (21.0*(x)*(x)-3.0))
#define	phi4x(x)   (-1.0 / 4.0 * 2.34520787991171477728281505677 * ((84.0*(x)*(x)-28.0)*(x)))
#define	phi5x(x)   (-1.0 / 4.0 * 2.54950975679639241501411205451 * ((165.0*(x)*(x)-90.0)*(x)*(x)+5.0))
#define	phi6x(x)   (-1.0 / 32.0 * 2.73861278752583056728484891400 * (((2574.0*(x)*(x)-1980.0)*(x)*(x)+270.0)*(x)))
#define	phi7x(x)   (-1.0 / 32.0 * 2.91547594742265023543707643877 * (((5005.0*(x)*(x)-5005.0)*(x)*(x)+1155.0)*(x)*(x)-35.0))
#define	phi8x(x)   (-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((19448.0*(x)*(x)-24024.0)*(x)*(x)+8008.0)*(x)*(x)-616.0)*(x)))
#define	phi9x(x)   (-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((37791.0*(x)*(x)-55692.0)*(x)*(x)+24570.0)*(x)*(x)-3276.0)*(x)*(x)-63.0))
#define	phi0xx(x)   (0)
#define	phi1xx(x)   (0)
#define	phi2xx(x)   (-1.0 / 2.0 * 1.87082869338697069279187436616 * 10)
#define	phi3xx(x)   (-1.0 / 2.0 * 2.12132034355964257320253308631 * (42.0*(x)))
#define	phi4xx(x)   (-1.0 / 4.0 * 2.34520787991171477728281505677 * ((252.0*(x)*(x)-28.0)))
#define	phi5xx(x)   (-1.0 / 4.0 * 2.54950975679639241501411205451 * ((660.0*(x)*(x)*(x)-180.0*(x))))
#define	phi6xx(x)   (-1.0 / 32.0 * 2.73861278752583056728484891400 * (((12870.0*(x)*(x)-5940.0)*(x)*(x)+270.0)))
#define	phi7xx(x)   (-1.0 / 32.0 * 2.91547594742265023543707643877 * (((30030.0*(x)*(x)-20020.0)*(x)*(x)+2310.0)*(x)))
#define	phi8xx(x)   (-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((136136.0*(x)*(x)-120120.0)*(x)*(x)+24024.0)*(x)*(x)-616.0)))
#define	phi9xx(x)   (-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((302328.0*(x)*(x)-334152.0)*(x)*(x)+98280.0)*(x)*(x)-6552.0)*(x)*(x)))
#define	Legendre0(x)   (1.0)
#define	Legendre1(x)   (x)
#define	Legendre2(x)   (1.0 / 2.0 * (3 * (x) * (x) - 1))
#define	Legendre3(x)   (1.0 / 2.0 * (5 * (x) * (x) - 3) * (x))
#define	Legendre4(x)   (1.0 / 8.0 * ((35 * (x) * (x) - 30) * (x) * (x) + 3))
#define	Legendre5(x)   (1.0 / 8.0 * ((63 * (x) * (x) - 70) * (x) * (x) + 15) * (x))
#define	Legendre6(x)   (1.0 / 16.0 * (((231 * (x) * (x) - 315) * (x) * (x) + 105) * (x) * (x) - 5))
#define	Legendre7(x)   (1.0 / 16.0 * (((429 * (x) * (x) - 693) * (x) * (x) + 315) * (x) * (x) - 35) * (x))
#define	Legendre8(x)   (1.0 / 128.0 * ((((6435 * (x) * (x) - 12012) * (x) * (x) + 6930) * (x) * (x) - 1260) * (x) * (x) + 35))
#define	Legendre9(x)   (1.0 / 128.0 * ((((12155 * (x) * (x) - 25740) * (x) * (x) + 18018) * (x) * (x) - 4620) * (x) * (x) + 315) * (x))
#define	Legendre10(x)   (1.0 / 256.0 * (((((46189 * (x) * (x) - 109395) * (x) * (x) + 90090) * (x) * (x) - 30030) * (x) * (x) + 3465) * (x) * (x) - 63))
#define	Legendre0x(x)   (0.0)
#define	Legendre1x(x)   (1.0)
#define	Legendre2x(x)   (3.0 * (x))
#define	Legendre3x(x)   (15.0 / 2.0 * (x) * (x) - 3.0 / 2.0)
#define	Legendre4x(x)   (5.0 / 2.0 * (x) * (7.0 * (x) * (x) - 3.0))
#define	Legendre5x(x)   ((315.0 / 8.0 * (x) * (x) - 105.0 / 4.0) * (x) * (x) + 15.0 / 8.0)
#define	Legendre6x(x)   (21.0 / 8.0 * (x) * ((33.0 * (x) * (x) - 30.0) * (x) * (x) + 5.0))
#define	Legendre7x(x)   (((3003.0 / 16.0 * (x) * (x) - 3465.0 / 16.0) * (x) * (x) + 945.0 / 16.0) * (x) * (x) - 35.0 / 16.0)
#define	Legendre8x(x)   (9.0 / 16.0 * (x) * (((715.0 * (x) * (x) - 1001.0) * (x) * (x) + 385.0) * (x) * (x) - 35.0))
#define	Legendre9x(x)   ((((109395.0 / 128.0 * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 45045.0 / 64.0) * (x) * (x) - 3465.0 / 32.0) * (x) * (x) + 315.0 / 128.0)
#define	Legendre10x(x)   (2.0 / 256.0 * (x) * ((((230945.0 * (x) * (x) - 437580.0) * (x) * (x) + 270270.0) * (x) * (x) - 60060.0) * (x) * (x) + 3465.0))
#define	Legendre0xx(x)   (0.0)
#define	Legendre1xx(x)   (0.0)
#define	Legendre2xx(x)   (3.0)
#define	Legendre3xx(x)   (15.0 * (x))
#define	Legendre4xx(x)   (105.0 / 2.0 * (x) * (x) - 15.0 / 2.0)
#define	Legendre5xx(x)   (105.0 / 2.0 * (x) * (3.0 * (x) * (x) - 1.0))
#define	Legendre6xx(x)   ((3465.0 / 8.0 * (x) * (x) - 1890.0 / 8.0) * (x) * (x) + 105.0 / 8.0)
#define	Legendre7xx(x)   (63.0 / 8.0 * (x) * ((143.0 * (x) * (x) - 110.0) * (x) * (x) + 15.0))
#define	Legendre8xx(x)   (((45045.0 / 16.0 * (x) * (x) - 45045.0 / 16.0) * (x) * (x) + 10395.0 / 16.0) * (x) * (x) - 315.0 / 16.0)
#define	Legendre9xx(x)   (45.0 / 16.0 * (x) * (((2431.0 * (x) * (x) - 3003.0) * (x) * (x) + 1001.0) * (x) * (x) - 77.0))
#define	Legendre10xx(x)   ((((2078505.0 / 128.0 * (x) * (x) - 765765.0 / 32.0) * (x) * (x) + 675675.0 / 64.0) * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 3465.0 / 128.0)
#define	l0(x)   ((1.0 - (x)) * 0.5)
#define	l1(x)   ((1.0 + (x)) * 0.5)
#define	l0l1(x)   ((1.0 - (x)*(x)) * 0.25)
#define	l2(x)   (phi0(x) * l0l1(x))
#define	l3(x)   (phi1(x) * l0l1(x))
#define	l4(x)   (phi2(x) * l0l1(x))
#define	l5(x)   (phi3(x) * l0l1(x))
#define	l6(x)   (phi4(x) * l0l1(x))
#define	l7(x)   (phi5(x) * l0l1(x))
#define	l8(x)   (phi6(x) * l0l1(x))
#define	l9(x)   (phi7(x) * l0l1(x))
#define	l10(x)   (phi8(x) * l0l1(x))
#define	l11(x)   (phi9(x) * l0l1(x))
#define	dl0(x)   (-0.5)
#define	dl1(x)   (0.5)
#define	dl2(x)   (sqrt(3.0/2.0) * Legendre1(x))
#define	dl3(x)   (sqrt(5.0/2.0) * Legendre2(x))
#define	dl4(x)   (sqrt(7.0/2.0) * Legendre3(x))
#define	dl5(x)   (sqrt(9.0/2.0) * Legendre4(x))
#define	dl6(x)   (sqrt(11.0/2.0) * Legendre5(x))
#define	dl7(x)   (sqrt(13.0/2.0) * Legendre6(x))
#define	dl8(x)   (sqrt(15.0/2.0) * Legendre7(x))
#define	dl9(x)   (sqrt(17.0/2.0) * Legendre8(x))
#define	dl10(x)   (sqrt(19.0/2.0) * Legendre9(x))
#define	dl11(x)   (sqrt(21.0/2.0) * Legendre10(x))
#define	d2l0(x)   (0.0)
#define	d2l1(x)   (0.0)
#define	d2l2(x)   (sqrt(3.0/2.0) * Legendre1x(x))
#define	d2l3(x)   (sqrt(5.0/2.0) * Legendre2x(x))
#define	d2l4(x)   (sqrt(7.0/2.0) * Legendre3x(x))
#define	d2l5(x)   (sqrt(9.0/2.0) * Legendre4x(x))
#define	d2l6(x)   (sqrt(11.0/2.0) * Legendre5x(x))
#define	d2l7(x)   (sqrt(13.0/2.0) * Legendre6x(x))
#define	d2l8(x)   (sqrt(15.0/2.0) * Legendre7x(x))
#define	d2l9(x)   (sqrt(17.0/2.0) * Legendre8x(x))
#define	d2l10(x)   (sqrt(19.0/2.0) * Legendre9x(x))
#define	d2l11(x)   (sqrt(21.0/2.0) * Legendre10x(x))
#define	n11   0.0
#define	n12   -1.0
#define	n21   0.707106781186547524400844362105
#define	n22   0.707106781186547524400844362105
#define	n31   -1.0
#define	n32   0.0
#define	n2t1   0.707106781186547524400844362105
#define	n3t1   -1.0
#define	n3t2   0.707106781186547524400844362105
#define	n1t2   -0.707106781186547524400844362105
#define	n1t3   1.0
#define	n2t3   -0.707106781186547524400844362105
#define	psi0e1_1(x, y)   ((lambda3(x,y) * n21 / n2t1 + lambda2(x,y) * n31 / n3t1))
#define	psi0e1_2(x, y)   ((lambda3(x,y) * n22 / n2t1 + lambda2(x,y) * n32 / n3t1))
#define	psi0e2_1(x, y)   ((lambda1(x,y) * n31 / n3t2 + lambda3(x,y) * n11 / n1t2))
#define	psi0e2_2(x, y)   ((lambda1(x,y) * n32 / n3t2 + lambda3(x,y) * n12 / n1t2))
#define	psi0e3_1(x, y)   ((lambda2(x,y) * n11 / n1t3 + lambda1(x,y) * n21 / n2t3))
#define	psi0e3_2(x, y)   ((lambda2(x,y) * n12 / n1t3 + lambda1(x,y) * n22 / n2t3))
#define	psi0e1x_1(x, y)   ((lambda3x(x,y) * n21 / n2t1 + lambda2x(x,y) * n31 / n3t1))
#define	psi0e1x_2(x, y)   ((lambda3x(x,y) * n22 / n2t1 + lambda2x(x,y) * n32 / n3t1))
#define	psi0e2x_1(x, y)   ((lambda1x(x,y) * n31 / n3t2 + lambda3x(x,y) * n11 / n1t2))
#define	psi0e2x_2(x, y)   ((lambda1x(x,y) * n32 / n3t2 + lambda3x(x,y) * n12 / n1t2))
#define	psi0e3x_1(x, y)   ((lambda2x(x,y) * n11 / n1t3 + lambda1x(x,y) * n21 / n2t3))
#define	psi0e3x_2(x, y)   ((lambda2x(x,y) * n12 / n1t3 + lambda1x(x,y) * n22 / n2t3))
#define	psi0e1y_1(x, y)   ((lambda3y(x,y) * n21 / n2t1 + lambda2y(x,y) * n31 / n3t1))
#define	psi0e1y_2(x, y)   ((lambda3y(x,y) * n22 / n2t1 + lambda2y(x,y) * n32 / n3t1))
#define	psi0e2y_1(x, y)   ((lambda1y(x,y) * n31 / n3t2 + lambda3y(x,y) * n11 / n1t2))
#define	psi0e2y_2(x, y)   ((lambda1y(x,y) * n32 / n3t2 + lambda3y(x,y) * n12 / n1t2))
#define	psi0e3y_1(x, y)   ((lambda2y(x,y) * n11 / n1t3 + lambda1y(x,y) * n21 / n2t3))
#define	psi0e3y_2(x, y)   ((lambda2y(x,y) * n12 / n1t3 + lambda1y(x,y) * n22 / n2t3))
#define	psi1e1_1(x, y)   ((lambda3(x,y) * n21 / n2t1 - lambda2(x,y) * n31 / n3t1))
#define	psi1e1_2(x, y)   ((lambda3(x,y) * n22 / n2t1 - lambda2(x,y) * n32 / n3t1))
#define	psi1e2_1(x, y)   ((lambda1(x,y) * n31 / n3t2 - lambda3(x,y) * n11 / n1t2))
#define	psi1e2_2(x, y)   ((lambda1(x,y) * n32 / n3t2 - lambda3(x,y) * n12 / n1t2))
#define	psi1e3_1(x, y)   ((lambda2(x,y) * n11 / n1t3 - lambda1(x,y) * n21 / n2t3))
#define	psi1e3_2(x, y)   ((lambda2(x,y) * n12 / n1t3 - lambda1(x,y) * n22 / n2t3))
#define	psi1e1x_1(x, y)   ((lambda3x(x,y) * n21 / n2t1 - lambda2x(x,y) * n31 / n3t1))
#define	psi1e1x_2(x, y)   ((lambda3x(x,y) * n22 / n2t1 - lambda2x(x,y) * n32 / n3t1))
#define	psi1e2x_1(x, y)   ((lambda1x(x,y) * n31 / n3t2 - lambda3x(x,y) * n11 / n1t2))
#define	psi1e2x_2(x, y)   ((lambda1x(x,y) * n32 / n3t2 - lambda3x(x,y) * n12 / n1t2))
#define	psi1e3x_1(x, y)   ((lambda2x(x,y) * n11 / n1t3 - lambda1x(x,y) * n21 / n2t3))
#define	psi1e3x_2(x, y)   ((lambda2x(x,y) * n12 / n1t3 - lambda1x(x,y) * n22 / n2t3))
#define	psi1e1y_1(x, y)   ((lambda3y(x,y) * n21 / n2t1 - lambda2y(x,y) * n31 / n3t1))
#define	psi1e1y_2(x, y)   ((lambda3y(x,y) * n22 / n2t1 - lambda2y(x,y) * n32 / n3t1))
#define	psi1e2y_1(x, y)   ((lambda1y(x,y) * n31 / n3t2 - lambda3y(x,y) * n11 / n1t2))
#define	psi1e2y_2(x, y)   ((lambda1y(x,y) * n32 / n3t2 - lambda3y(x,y) * n12 / n1t2))
#define	psi1e3y_1(x, y)   ((lambda2y(x,y) * n11 / n1t3 - lambda1y(x,y) * n21 / n2t3))
#define	psi1e3y_2(x, y)   ((lambda2y(x,y) * n12 / n1t3 - lambda1y(x,y) * n22 / n2t3))

---

Define Documentation

#define d2l0

(

x

)

(0.0)

#define d2l1

(

x

)

(0.0)

#define d2l10

(

x

)

(sqrt(19.0/2.0) * Legendre9x(x))

#define d2l11

(

x

)

(sqrt(21.0/2.0) * Legendre10x(x))

#define d2l2

(

x

)

(sqrt(3.0/2.0) * Legendre1x(x))

#define d2l3

(

x

)

(sqrt(5.0/2.0) * Legendre2x(x))

#define d2l4

(

x

)

(sqrt(7.0/2.0) * Legendre3x(x))

#define d2l5

(

x

)

(sqrt(9.0/2.0) * Legendre4x(x))

#define d2l6

(

x

)

(sqrt(11.0/2.0) * Legendre5x(x))

#define d2l7

(

x

)

(sqrt(13.0/2.0) * Legendre6x(x))

#define d2l8

(

x

)

(sqrt(15.0/2.0) * Legendre7x(x))

#define d2l9

(

x

)

(sqrt(17.0/2.0) * Legendre8x(x))

#define dl0

(

x

)

(-0.5)

#define dl1

(

x

)

(0.5)

#define dl10

(

x

)

(sqrt(19.0/2.0) * Legendre9(x))

#define dl11

(

x

)

(sqrt(21.0/2.0) * Legendre10(x))

#define dl2

(

x

)

(sqrt(3.0/2.0) * Legendre1(x))

#define dl3

(

x

)

(sqrt(5.0/2.0) * Legendre2(x))

#define dl4

(

x

)

(sqrt(7.0/2.0) * Legendre3(x))

#define dl5

(

x

)

(sqrt(9.0/2.0) * Legendre4(x))

#define dl6

(

x

)

(sqrt(11.0/2.0) * Legendre5(x))

#define dl7

(

x

)

(sqrt(13.0/2.0) * Legendre6(x))

#define dl8

(

x

)

(sqrt(15.0/2.0) * Legendre7(x))

#define dl9

(

x

)

(sqrt(17.0/2.0) * Legendre8(x))

#define l0

(

x

)

((1.0 - (x)) * 0.5)

#define l0l1

(

x

)

((1.0 - (x)*(x)) * 0.25)

#define l1

(

x

)

((1.0 + (x)) * 0.5)

#define l10

(

x

)

(phi8(x) * l0l1(x))

#define l11

(

x

)

(phi9(x) * l0l1(x))

#define l2

(

x

)

(phi0(x) * l0l1(x))

#define l3

(

x

)

(phi1(x) * l0l1(x))

#define l4

(

x

)

(phi2(x) * l0l1(x))

#define l5

(

x

)

(phi3(x) * l0l1(x))

#define l6

(

x

)

(phi4(x) * l0l1(x))

#define l7

(

x

)

(phi5(x) * l0l1(x))

#define l8

(

x

)

(phi6(x) * l0l1(x))

#define l9

(

x

)

(phi7(x) * l0l1(x))

#define lambda1	(	x,
		y		)	(((y) + 1) / 2)

#define lambda1x	(	x,
		y		)	(0.0)

#define lambda1y	(	x,
		y		)	(1.0 / 2.0)

#define lambda2	(	x,
		y		)	(-((x) + (y)) / 2)

#define lambda2x	(	x,
		y		)	(-1.0 / 2.0)

#define lambda2y	(	x,
		y		)	(-1.0 / 2.0)

#define lambda3	(	x,
		y		)	(((x) + 1) / 2)

#define lambda3x	(	x,
		y		)	(1.0 / 2.0)

#define lambda3y	(	x,
		y		)	(0.0)

#define Legendre0

(

x

)

(1.0)

#define Legendre0x

(

x

)

(0.0)

#define Legendre0xx

(

x

)

(0.0)

#define Legendre1

(

x

)

(x)

#define Legendre10

(

x

)

(1.0 / 256.0 * (((((46189 * (x) * (x) - 109395) * (x) * (x) + 90090) * (x) * (x) - 30030) * (x) * (x) + 3465) * (x) * (x) - 63))

#define Legendre10x

(

x

)

(2.0 / 256.0 * (x) * ((((230945.0 * (x) * (x) - 437580.0) * (x) * (x) + 270270.0) * (x) * (x) - 60060.0) * (x) * (x) + 3465.0))

#define Legendre10xx

(

x

)

((((2078505.0 / 128.0 * (x) * (x) - 765765.0 / 32.0) * (x) * (x) + 675675.0 / 64.0) * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 3465.0 / 128.0)

#define Legendre1x

(

x

)

(1.0)

#define Legendre1xx

(

x

)

(0.0)

#define Legendre2

(

x

)

(1.0 / 2.0 * (3 * (x) * (x) - 1))

#define Legendre2x

(

x

)

(3.0 * (x))

#define Legendre2xx

(

x

)

(3.0)

#define Legendre3

(

x

)

(1.0 / 2.0 * (5 * (x) * (x) - 3) * (x))

#define Legendre3x

(

x

)

(15.0 / 2.0 * (x) * (x) - 3.0 / 2.0)

#define Legendre3xx

(

x

)

(15.0 * (x))

#define Legendre4

(

x

)

(1.0 / 8.0 * ((35 * (x) * (x) - 30) * (x) * (x) + 3))

#define Legendre4x

(

x

)

(5.0 / 2.0 * (x) * (7.0 * (x) * (x) - 3.0))

#define Legendre4xx

(

x

)

(105.0 / 2.0 * (x) * (x) - 15.0 / 2.0)

#define Legendre5

(

x

)

(1.0 / 8.0 * ((63 * (x) * (x) - 70) * (x) * (x) + 15) * (x))

#define Legendre5x

(

x

)

((315.0 / 8.0 * (x) * (x) - 105.0 / 4.0) * (x) * (x) + 15.0 / 8.0)

#define Legendre5xx

(

x

)

(105.0 / 2.0 * (x) * (3.0 * (x) * (x) - 1.0))

#define Legendre6

(

x

)

(1.0 / 16.0 * (((231 * (x) * (x) - 315) * (x) * (x) + 105) * (x) * (x) - 5))

#define Legendre6x

(

x

)

(21.0 / 8.0 * (x) * ((33.0 * (x) * (x) - 30.0) * (x) * (x) + 5.0))

#define Legendre6xx

(

x

)

((3465.0 / 8.0 * (x) * (x) - 1890.0 / 8.0) * (x) * (x) + 105.0 / 8.0)

#define Legendre7

(

x

)

(1.0 / 16.0 * (((429 * (x) * (x) - 693) * (x) * (x) + 315) * (x) * (x) - 35) * (x))

#define Legendre7x

(

x

)

(((3003.0 / 16.0 * (x) * (x) - 3465.0 / 16.0) * (x) * (x) + 945.0 / 16.0) * (x) * (x) - 35.0 / 16.0)

#define Legendre7xx

(

x

)

(63.0 / 8.0 * (x) * ((143.0 * (x) * (x) - 110.0) * (x) * (x) + 15.0))

#define Legendre8

(

x

)

(1.0 / 128.0 * ((((6435 * (x) * (x) - 12012) * (x) * (x) + 6930) * (x) * (x) - 1260) * (x) * (x) + 35))

#define Legendre8x

(

x

)

(9.0 / 16.0 * (x) * (((715.0 * (x) * (x) - 1001.0) * (x) * (x) + 385.0) * (x) * (x) - 35.0))

#define Legendre8xx

(

x

)

(((45045.0 / 16.0 * (x) * (x) - 45045.0 / 16.0) * (x) * (x) + 10395.0 / 16.0) * (x) * (x) - 315.0 / 16.0)

#define Legendre9

(

x

)

(1.0 / 128.0 * ((((12155 * (x) * (x) - 25740) * (x) * (x) + 18018) * (x) * (x) - 4620) * (x) * (x) + 315) * (x))

#define Legendre9x

(

x

)

((((109395.0 / 128.0 * (x) * (x) - 45045.0 / 32.0) * (x) * (x) + 45045.0 / 64.0) * (x) * (x) - 3465.0 / 32.0) * (x) * (x) + 315.0 / 128.0)

#define Legendre9xx

(

x

)

(45.0 / 16.0 * (x) * (((2431.0 * (x) * (x) - 3003.0) * (x) * (x) + 1001.0) * (x) * (x) - 77.0))

#define n11   0.0

#define n12   -1.0

#define n1t2   -0.707106781186547524400844362105

#define n1t3   1.0

#define n21   0.707106781186547524400844362105

#define n22   0.707106781186547524400844362105

#define n2t1   0.707106781186547524400844362105

#define n2t3   -0.707106781186547524400844362105

#define n31   -1.0

#define n32   0.0

#define n3t1   -1.0

#define n3t2   0.707106781186547524400844362105

#define phi0

(

x

)

(-2.0 * 1.22474487139158904909864203735)

#define phi0x

(

x

)

(0)

#define phi0xx

(

x

)

(0)

#define phi1

(

x

)

(-2.0 * 1.58113883008418966599944677222 * (x))

#define phi1x

(

x

)

(-2.0 * 1.58113883008418966599944677222)

#define phi1xx

(

x

)

(0)

#define phi2

(

x

)

(-1.0 / 2.0 * 1.87082869338697069279187436616 * (5 * (x) * (x) - 1))

#define phi2x

(

x

)

(-1.0 / 2.0 * 1.87082869338697069279187436616 * (10 * (x)))

#define phi2xx

(

x

)

(-1.0 / 2.0 * 1.87082869338697069279187436616 * 10)

#define phi3

(

x

)

(-1.0 / 2.0 * 2.12132034355964257320253308631 * (7 * (x) * (x) - 3) * (x))

#define phi3x

(

x

)

(-1.0 / 2.0 * 2.12132034355964257320253308631 * (21.0*(x)*(x)-3.0))

#define phi3xx

(

x

)

(-1.0 / 2.0 * 2.12132034355964257320253308631 * (42.0*(x)))

#define phi4

(

x

)

(-1.0 / 4.0 * 2.34520787991171477728281505677 * (21 * (x) * (x) * (x) * (x) - 14 * (x) * (x) + 1))

#define phi4x

(

x

)

(-1.0 / 4.0 * 2.34520787991171477728281505677 * ((84.0*(x)*(x)-28.0)*(x)))

#define phi4xx

(

x

)

(-1.0 / 4.0 * 2.34520787991171477728281505677 * ((252.0*(x)*(x)-28.0)))

#define phi5

(

x

)

(-1.0 / 4.0 * 2.54950975679639241501411205451 * ((33 * (x) * (x) - 30) * (x) * (x) + 5) * (x))

#define phi5x

(

x

)

(-1.0 / 4.0 * 2.54950975679639241501411205451 * ((165.0*(x)*(x)-90.0)*(x)*(x)+5.0))

#define phi5xx

(

x

)

(-1.0 / 4.0 * 2.54950975679639241501411205451 * ((660.0*(x)*(x)*(x)-180.0*(x))))

#define phi6

(

x

)

(-1.0 / 32.0 * 2.73861278752583056728484891400 * (((429 * (x) * (x) - 495) * (x) * (x) + 135) * (x) * (x) - 5))

#define phi6x

(

x

)

(-1.0 / 32.0 * 2.73861278752583056728484891400 * (((2574.0*(x)*(x)-1980.0)*(x)*(x)+270.0)*(x)))

#define phi6xx

(

x

)

(-1.0 / 32.0 * 2.73861278752583056728484891400 * (((12870.0*(x)*(x)-5940.0)*(x)*(x)+270.0)))

#define phi7

(

x

)

(-1.0 / 32.0 * 2.91547594742265023543707643877 * (((715 * (x) * (x) - 1001) * (x) * (x) + 385) * (x) * (x) - 35) * (x))

#define phi7x

(

x

)

(-1.0 / 32.0 * 2.91547594742265023543707643877 * (((5005.0*(x)*(x)-5005.0)*(x)*(x)+1155.0)*(x)*(x)-35.0))

#define phi7xx

(

x

)

(-1.0 / 32.0 * 2.91547594742265023543707643877 * (((30030.0*(x)*(x)-20020.0)*(x)*(x)+2310.0)*(x)))

#define phi8

(

x

)

(-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((2431 * (x) * (x) - 4004) * (x) * (x) + 2002) * (x) * (x) - 308) * (x) * (x) + 7))

#define phi8x

(

x

)

(-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((19448.0*(x)*(x)-24024.0)*(x)*(x)+8008.0)*(x)*(x)-616.0)*(x)))

#define phi8xx

(

x

)

(-1.0 / 64.0 * 3.08220700148448822512509619073 * ((((136136.0*(x)*(x)-120120.0)*(x)*(x)+24024.0)*(x)*(x)-616.0)))

#define phi9

(

x

)

(-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((4199 * (x) * (x) - 7956) * (x) * (x) + 4914) * (x) * (x) - 1092) * (x) * (x) + 63) * (x))

#define phi9x

(

x

)

(-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((37791.0*(x)*(x)-55692.0)*(x)*(x)+24570.0)*(x)*(x)-3276.0)*(x)*(x)-63.0))

#define phi9xx

(

x

)

(-1.0 / 128.0 * 6.4807406984078603784382721642 * ((((302328.0*(x)*(x)-334152.0)*(x)*(x)+98280.0)*(x)*(x)-6552.0)*(x)*(x)))

#define psi0e1_1	(	x,
		y		)	((lambda3(x,y) * n21 / n2t1 + lambda2(x,y) * n31 / n3t1))

#define psi0e1_2	(	x,
		y		)	((lambda3(x,y) * n22 / n2t1 + lambda2(x,y) * n32 / n3t1))

#define psi0e1x_1	(	x,
		y		)	((lambda3x(x,y) * n21 / n2t1 + lambda2x(x,y) * n31 / n3t1))

#define psi0e1x_2	(	x,
		y		)	((lambda3x(x,y) * n22 / n2t1 + lambda2x(x,y) * n32 / n3t1))

#define psi0e1y_1	(	x,
		y		)	((lambda3y(x,y) * n21 / n2t1 + lambda2y(x,y) * n31 / n3t1))

#define psi0e1y_2	(	x,
		y		)	((lambda3y(x,y) * n22 / n2t1 + lambda2y(x,y) * n32 / n3t1))

#define psi0e2_1	(	x,
		y		)	((lambda1(x,y) * n31 / n3t2 + lambda3(x,y) * n11 / n1t2))

#define psi0e2_2	(	x,
		y		)	((lambda1(x,y) * n32 / n3t2 + lambda3(x,y) * n12 / n1t2))

#define psi0e2x_1	(	x,
		y		)	((lambda1x(x,y) * n31 / n3t2 + lambda3x(x,y) * n11 / n1t2))

#define psi0e2x_2	(	x,
		y		)	((lambda1x(x,y) * n32 / n3t2 + lambda3x(x,y) * n12 / n1t2))

#define psi0e2y_1	(	x,
		y		)	((lambda1y(x,y) * n31 / n3t2 + lambda3y(x,y) * n11 / n1t2))

#define psi0e2y_2	(	x,
		y		)	((lambda1y(x,y) * n32 / n3t2 + lambda3y(x,y) * n12 / n1t2))

#define psi0e3_1	(	x,
		y		)	((lambda2(x,y) * n11 / n1t3 + lambda1(x,y) * n21 / n2t3))

#define psi0e3_2	(	x,
		y		)	((lambda2(x,y) * n12 / n1t3 + lambda1(x,y) * n22 / n2t3))

#define psi0e3x_1	(	x,
		y		)	((lambda2x(x,y) * n11 / n1t3 + lambda1x(x,y) * n21 / n2t3))

#define psi0e3x_2	(	x,
		y		)	((lambda2x(x,y) * n12 / n1t3 + lambda1x(x,y) * n22 / n2t3))

#define psi0e3y_1	(	x,
		y		)	((lambda2y(x,y) * n11 / n1t3 + lambda1y(x,y) * n21 / n2t3))

#define psi0e3y_2	(	x,
		y		)	((lambda2y(x,y) * n12 / n1t3 + lambda1y(x,y) * n22 / n2t3))

#define psi1e1_1	(	x,
		y		)	((lambda3(x,y) * n21 / n2t1 - lambda2(x,y) * n31 / n3t1))

#define psi1e1_2	(	x,
		y		)	((lambda3(x,y) * n22 / n2t1 - lambda2(x,y) * n32 / n3t1))

#define psi1e1x_1	(	x,
		y		)	((lambda3x(x,y) * n21 / n2t1 - lambda2x(x,y) * n31 / n3t1))

#define psi1e1x_2	(	x,
		y		)	((lambda3x(x,y) * n22 / n2t1 - lambda2x(x,y) * n32 / n3t1))

#define psi1e1y_1	(	x,
		y		)	((lambda3y(x,y) * n21 / n2t1 - lambda2y(x,y) * n31 / n3t1))

#define psi1e1y_2	(	x,
		y		)	((lambda3y(x,y) * n22 / n2t1 - lambda2y(x,y) * n32 / n3t1))

#define psi1e2_1	(	x,
		y		)	((lambda1(x,y) * n31 / n3t2 - lambda3(x,y) * n11 / n1t2))

#define psi1e2_2	(	x,
		y		)	((lambda1(x,y) * n32 / n3t2 - lambda3(x,y) * n12 / n1t2))

#define psi1e2x_1	(	x,
		y		)	((lambda1x(x,y) * n31 / n3t2 - lambda3x(x,y) * n11 / n1t2))

#define psi1e2x_2	(	x,
		y		)	((lambda1x(x,y) * n32 / n3t2 - lambda3x(x,y) * n12 / n1t2))

#define psi1e2y_1	(	x,
		y		)	((lambda1y(x,y) * n31 / n3t2 - lambda3y(x,y) * n11 / n1t2))

#define psi1e2y_2	(	x,
		y		)	((lambda1y(x,y) * n32 / n3t2 - lambda3y(x,y) * n12 / n1t2))

#define psi1e3_1	(	x,
		y		)	((lambda2(x,y) * n11 / n1t3 - lambda1(x,y) * n21 / n2t3))

#define psi1e3_2	(	x,
		y		)	((lambda2(x,y) * n12 / n1t3 - lambda1(x,y) * n22 / n2t3))

#define psi1e3x_1	(	x,
		y		)	((lambda2x(x,y) * n11 / n1t3 - lambda1x(x,y) * n21 / n2t3))

#define psi1e3x_2	(	x,
		y		)	((lambda2x(x,y) * n12 / n1t3 - lambda1x(x,y) * n22 / n2t3))

#define psi1e3y_1	(	x,
		y		)	((lambda2y(x,y) * n11 / n1t3 - lambda1y(x,y) * n21 / n2t3))

#define psi1e3y_2	(	x,
		y		)	((lambda2y(x,y) * n12 / n1t3 - lambda1y(x,y) * n22 / n2t3))