volume_integral_2d_N_LGL_16.sagews

%typeset_mode True

var('xi, eta, x, y')
N_LGL = 16
xi_LGL = [-0.99999999998420,
          -0.96956804630032,
          -0.89920053307202,
          -0.79200829187099,
          -0.65238870288019,
          -0.48605942188742,
          -0.29983046890075,
          -0.10132627352195,
           0.10132627352195,
           0.29983046890076,
           0.48605942188718,
           0.65238870288226,
           0.79200829186255,
           0.89920053309205,
           0.96956804627192,
           0.99999999999918]

eta_LGL = [-0.99999999998420,
           -0.96956804630032,
           -0.89920053307202,
           -0.79200829187099,
           -0.65238870288019,
           -0.48605942188742,
           -0.29983046890075,
           -0.10132627352195,
            0.10132627352195,
            0.29983046890076,
            0.48605942188718,
            0.65238870288226,
            0.79200829186255,
            0.89920053309205,
            0.96956804627192,
            0.99999999999918]

($\displaystyle \xi$, $\displaystyle \eta$, $\displaystyle x$, $\displaystyle y$)

L_xi_0 =  ((xi - (xi_LGL[1 ])) / (xi_LGL[0] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[0] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[0] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[0] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[0] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[0] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[0] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[0] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[0] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[0] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[0] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[0] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[0] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[0] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[0] - xi_LGL[15]))

L_xi_1 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[1] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[1] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[1] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[1] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[1] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[1] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[1] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[1] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[1] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[1] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[1] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[1] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[1] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[1] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[1] - xi_LGL[15]))

        
L_xi_2 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[2] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[2] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[2] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[2] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[2] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[2] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[2] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[2] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[2] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[2] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[2] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[2] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[2] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[2] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[2] - xi_LGL[15]))


L_xi_3 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[3] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[3] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[3] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[3] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[3] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[3] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[3] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[3] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[3] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[3] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[3] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[3] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[3] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[3] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[3] - xi_LGL[15]))


        
L_xi_4 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[4] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[4] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[4] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[4] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[4] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[4] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[4] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[4] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[4] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[4] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[4] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[4] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[4] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[4] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[4] - xi_LGL[15]))



L_xi_5 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[5] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[5] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[5] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[5] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[5] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[5] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[5] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[5] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[5] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[5] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[5] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[5] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[5] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[5] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[5] - xi_LGL[15]))
        
L_xi_6 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[6] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[6] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[6] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[6] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[6] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[6] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[6] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[6] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[6] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[6] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[6] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[6] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[6] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[6] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[6] - xi_LGL[15]))
        

L_xi_7 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[7] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[7] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[7] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[7] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[7] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[7] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[7] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[7] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[7] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[7] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[7] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[7] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[7] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[7] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[7] - xi_LGL[15]))

L_xi_8 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[8] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[8] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[8] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[8] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[8] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[8] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[8] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[8] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[8] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[8] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[8] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[8] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[8] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[8] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[8] - xi_LGL[15]))

L_xi_9 =  ((xi - (xi_LGL[0 ])) / (xi_LGL[9] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[9] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[9] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[9] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[9] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[9] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[9] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[9] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[9] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[9] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[9] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[9] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[9] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[9] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[9] - xi_LGL[15]))

L_xi_10 = ((xi - (xi_LGL[0 ])) / (xi_LGL[10] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[10] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[10] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[10] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[10] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[10] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[10] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[10] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[10] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[10] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[10] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[10] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[10] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[10] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[10] - xi_LGL[15]))

L_xi_11 = ((xi - (xi_LGL[0 ])) / (xi_LGL[11] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[11] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[11] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[11] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[11] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[11] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[11] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[11] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[11] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[11] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[11] - xi_LGL[10]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[11] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[11] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[11] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[11] - xi_LGL[15]))

L_xi_12 = ((xi - (xi_LGL[0 ])) / (xi_LGL[12] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[12] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[12] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[12] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[12] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[12] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[12] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[12] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[12] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[12] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[12] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[12] - xi_LGL[11]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[12] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[12] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[12] - xi_LGL[15]))

L_xi_13 = ((xi - (xi_LGL[0 ])) / (xi_LGL[13] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[13] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[13] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[13] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[13] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[13] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[13] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[13] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[13] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[13] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[13] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[13] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[13] - xi_LGL[12]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[13] - xi_LGL[14]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[13] - xi_LGL[15]))

L_xi_14 = ((xi - (xi_LGL[0 ])) / (xi_LGL[14] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[14] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[14] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[14] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[14] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[14] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[14] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[14] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[14] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[14] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[14] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[14] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[14] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[14] - xi_LGL[13]))\
        * ((xi - (xi_LGL[15])) / (xi_LGL[14] - xi_LGL[15]))

L_xi_15 = ((xi - (xi_LGL[0 ])) / (xi_LGL[15] - xi_LGL[0 ]))\
        * ((xi - (xi_LGL[1 ])) / (xi_LGL[15] - xi_LGL[1 ]))\
        * ((xi - (xi_LGL[2 ])) / (xi_LGL[15] - xi_LGL[2 ]))\
        * ((xi - (xi_LGL[3 ])) / (xi_LGL[15] - xi_LGL[3 ]))\
        * ((xi - (xi_LGL[4 ])) / (xi_LGL[15] - xi_LGL[4 ]))\
        * ((xi - (xi_LGL[5 ])) / (xi_LGL[15] - xi_LGL[5 ]))\
        * ((xi - (xi_LGL[6 ])) / (xi_LGL[15] - xi_LGL[6 ]))\
        * ((xi - (xi_LGL[7 ])) / (xi_LGL[15] - xi_LGL[7 ]))\
        * ((xi - (xi_LGL[8 ])) / (xi_LGL[15] - xi_LGL[8 ]))\
        * ((xi - (xi_LGL[9 ])) / (xi_LGL[15] - xi_LGL[9 ]))\
        * ((xi - (xi_LGL[10])) / (xi_LGL[15] - xi_LGL[10]))\
        * ((xi - (xi_LGL[11])) / (xi_LGL[15] - xi_LGL[11]))\
        * ((xi - (xi_LGL[12])) / (xi_LGL[15] - xi_LGL[12]))\
        * ((xi - (xi_LGL[13])) / (xi_LGL[15] - xi_LGL[13]))\
        * ((xi - (xi_LGL[14])) / (xi_LGL[15] - xi_LGL[14]))


######################################################################
L_eta_0 =  ((eta - (eta_LGL[1 ])) / (eta_LGL[0] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[0] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[0] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[0] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[0] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[0] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[0] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[0] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[0] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[0] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[0] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[0] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[0] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[0] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[0] - eta_LGL[15]))

L_eta_1 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[1] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[1] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[1] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[1] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[1] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[1] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[1] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[1] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[1] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[1] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[1] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[1] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[1] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[1] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[1] - eta_LGL[15]))

        
L_eta_2 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[2] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[2] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[2] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[2] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[2] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[2] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[2] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[2] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[2] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[2] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[2] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[2] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[2] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[2] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[2] - eta_LGL[15]))


L_eta_3 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[3] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[3] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[3] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[3] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[3] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[3] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[3] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[3] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[3] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[3] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[3] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[3] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[3] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[3] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[3] - eta_LGL[15]))


        
L_eta_4 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[4] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[4] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[4] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[4] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[4] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[4] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[4] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[4] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[4] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[4] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[4] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[4] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[4] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[4] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[4] - eta_LGL[15]))



L_eta_5 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[5] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[5] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[5] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[5] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[5] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[5] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[5] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[5] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[5] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[5] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[5] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[5] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[5] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[5] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[5] - eta_LGL[15]))
        
L_eta_6 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[6] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[6] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[6] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[6] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[6] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[6] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[6] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[6] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[6] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[6] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[6] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[6] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[6] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[6] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[6] - eta_LGL[15]))
        

L_eta_7 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[7] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[7] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[7] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[7] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[7] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[7] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[7] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[7] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[7] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[7] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[7] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[7] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[7] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[7] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[7] - eta_LGL[15]))

L_eta_8 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[8] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[8] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[8] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[8] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[8] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[8] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[8] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[8] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[8] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[8] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[8] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[8] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[8] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[8] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[8] - eta_LGL[15]))

L_eta_9 =  ((eta - (eta_LGL[0 ])) / (eta_LGL[9] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[9] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[9] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[9] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[9] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[9] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[9] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[9] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[9] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[9] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[9] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[9] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[9] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[9] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[9] - eta_LGL[15]))

L_eta_10 = ((eta - (eta_LGL[0 ])) / (eta_LGL[10] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[10] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[10] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[10] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[10] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[10] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[10] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[10] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[10] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[10] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[10] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[10] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[10] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[10] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[10] - eta_LGL[15]))

L_eta_11 = ((eta - (eta_LGL[0 ])) / (eta_LGL[11] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[11] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[11] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[11] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[11] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[11] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[11] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[11] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[11] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[11] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[11] - eta_LGL[10]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[11] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[11] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[11] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[11] - eta_LGL[15]))

L_eta_12 = ((eta - (eta_LGL[0 ])) / (eta_LGL[12] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[12] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[12] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[12] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[12] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[12] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[12] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[12] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[12] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[12] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[12] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[12] - eta_LGL[11]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[12] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[12] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[12] - eta_LGL[15]))

L_eta_13 = ((eta - (eta_LGL[0 ])) / (eta_LGL[13] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[13] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[13] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[13] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[13] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[13] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[13] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[13] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[13] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[13] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[13] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[13] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[13] - eta_LGL[12]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[13] - eta_LGL[14]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[13] - eta_LGL[15]))

L_eta_14 = ((eta - (eta_LGL[0 ])) / (eta_LGL[14] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[14] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[14] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[14] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[14] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[14] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[14] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[14] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[14] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[14] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[14] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[14] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[14] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[14] - eta_LGL[13]))\
        * ((eta - (eta_LGL[15])) / (eta_LGL[14] - eta_LGL[15]))

L_eta_15 = ((eta - (eta_LGL[0 ])) / (eta_LGL[15] - eta_LGL[0 ]))\
        * ((eta - (eta_LGL[1 ])) / (eta_LGL[15] - eta_LGL[1 ]))\
        * ((eta - (eta_LGL[2 ])) / (eta_LGL[15] - eta_LGL[2 ]))\
        * ((eta - (eta_LGL[3 ])) / (eta_LGL[15] - eta_LGL[3 ]))\
        * ((eta - (eta_LGL[4 ])) / (eta_LGL[15] - eta_LGL[4 ]))\
        * ((eta - (eta_LGL[5 ])) / (eta_LGL[15] - eta_LGL[5 ]))\
        * ((eta - (eta_LGL[6 ])) / (eta_LGL[15] - eta_LGL[6 ]))\
        * ((eta - (eta_LGL[7 ])) / (eta_LGL[15] - eta_LGL[7 ]))\
        * ((eta - (eta_LGL[8 ])) / (eta_LGL[15] - eta_LGL[8 ]))\
        * ((eta - (eta_LGL[9 ])) / (eta_LGL[15] - eta_LGL[9 ]))\
        * ((eta - (eta_LGL[10])) / (eta_LGL[15] - eta_LGL[10]))\
        * ((eta - (eta_LGL[11])) / (eta_LGL[15] - eta_LGL[11]))\
        * ((eta - (eta_LGL[12])) / (eta_LGL[15] - eta_LGL[12]))\
        * ((eta - (eta_LGL[13])) / (eta_LGL[15] - eta_LGL[13]))\
        * ((eta - (eta_LGL[14])) / (eta_LGL[15] - eta_LGL[14]))

L_xi = [L_xi_0, L_xi_1, L_xi_2, L_xi_3, L_xi_4, L_xi_5, L_xi_6, L_xi_7,
        L_xi_8, L_xi_9, L_xi_10, L_xi_11, L_xi_12, L_xi_13, L_xi_14, L_xi_15]

L_eta = [L_eta_0, L_eta_1, L_eta_2, L_eta_3, L_eta_4, L_eta_5, L_eta_6, L_eta_7,
        L_eta_8, L_eta_9, L_eta_10, L_eta_11, L_eta_12, L_eta_13, L_eta_14, L_eta_15]

u = e^(-xi^2 / 0.6^2)
u
c_x = 1.

$\displaystyle e^{\left(-2.77777777777778 \, \xi^{2}\right)}$

F_x = c_x * u
F_x

$\displaystyle 1.00000000000000 \, e^{\left(-2.77777777777778 \, \xi^{2}\right)}$

import numpy as np

volume_integral_pq = []
for p in np.arange(N_LGL):
    for q in np.arange(N_LGL):
        print(p * N_LGL + q)
        volume_integral_pq.append(integrate(integrate(1. * diff(L_xi[p], xi) * L_eta[q]  * F_x, xi, -1, 1), eta, -1, 1).n())

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

Too many output messages: 257 (at most 256 per cell -- type 'smc?' to learn how to raise this limit): attempting to terminate...

volume_integral_pq = np.array(volume_integral_pq)
np.savetxt('volume_integral_pq_2d_analytical.csv', volume_integral_pq, delimiter = '')

np.savetxt?

/ext/sage/sage-8.0/local/lib/python2.7/site-packages/urllib3/contrib/pyopenssl.py:46: DeprecationWarning: OpenSSL.rand is deprecated - you should use os.urandom instead import OpenSSL.SSL

File: /ext/sage/sage-8.0/local/lib/python2.7/site-packages/numpy/lib/npyio.py
Signature : np.savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='', footer='', comments='# ')
Docstring :
Save an array to a text file.

fname : filename or file handle
   If the filename ends in ".gz", the file is automatically saved
   in compressed gzip format.  loadtxt understands gzipped files
   transparently.

X : array_like
   Data to be saved to a text file.

fmt : str or sequence of strs, optional
   A single format (%10.5f), a sequence of formats, or a multi-
   format string, e.g. 'Iteration %d -- %10.5f', in which case
   delimiter is ignored. For complex X, the legal options for fmt
   are:

      1. a single specifier, fmt='%.4e', resulting in numbers
         formatted

            like ' (%s+%sj)' % (fmt, fmt)

      2. a full string specifying every real and imaginary part,
         e.g.

            ' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej' for 3 columns

      3. a list of specifiers, one per column - in this case,
         the real

            and imaginary part must have separate specifiers, e.g.
            ['%.3e + %.3ej', '(%.15e%+.15ej)'] for 2 columns

delimiter : str, optional
   String or character separating columns.

newline : str, optional
   String or character separating lines.

   New in version 1.5.0.

header : str, optional
   String that will be written at the beginning of the file.

   New in version 1.7.0.

footer : str, optional
   String that will be written at the end of the file.

   New in version 1.7.0.

comments : str, optional
   String that will be prepended to the "header" and "footer"
   strings, to mark them as comments. Default: '# ',  as expected
   by e.g. "numpy.loadtxt".

   New in version 1.7.0.

save : Save an array to a binary file in NumPy ".npy" format savez
: Save several arrays into an uncompressed ".npz" archive
savez_compressed : Save several arrays into a compressed ".npz"
archive

Further explanation of the fmt parameter
("%[flag]width[.precision]specifier"):

flags:
   "-" : left justify

   "+" : Forces to precede result with + or -.

   "0" : Left pad the number with zeros instead of space (see
   width).

width:
   Minimum number of characters to be printed. The value is not
   truncated if it has more characters.

precision:
   * For integer specifiers (eg. "d,i,o,x"), the minimum number
     of digits.

   * For "e, E" and "f" specifiers, the number of digits to print
     after the decimal point.

   * For "g" and "G", the maximum number of significant digits.

   * For "s", the maximum number of characters.

specifiers:
   "c" : character

   "d" or "i" : signed decimal integer

   "e" or "E" : scientific notation with "e" or "E".

   "f" : decimal floating point

   "g,G" : use the shorter of "e,E" or "f"

   "o" : signed octal

   "s" : string of characters

   "u" : unsigned decimal integer

   "x,X" : unsigned hexadecimal integer

This explanation of "fmt" is not complete, for an exhaustive
specification see [1].

[1] Format Specification Mini-Language, Python Documentation.

>>> x = y = z = np.arange(0.0,5.0,1.0)
>>> np.savetxt('test.out', x, delimiter=',')   # X is an array
>>> np.savetxt('test.out', (x,y,z))   # x,y,z equal sized 1D arrays
>>> np.savetxt('test.out', x, fmt='%1.4e')   # use exponential notation