Argy1risMatrix1

`function Argy1risMatrix1%(coordary)
%ARGy1RISMATRIx1 Summary1 of this function goes here
% Detailed ex1planation goes here
%This gives the Matrix that needs to be solved for the Argyris bases
%functions on the reference triangle.
% Row 1 is phi(x1,y1)
% Row 2 is phi_x(x1,y1)
% Row 3 is phi_y(x1,y1)
% Row 4 is phi_xx(x1,y1)
% Row 5 is phi_yy(x1,y1)
% Row 6 is phi_xy(x1,y1)
% Row 7 is phi(x2,y2)
% Row 8 is phi_x(x2,y2)
% Row 9 is phi_y(x2,y2)
% Row 10 is phi_xx(x2,y2)
% Row 11 is phi_yy(x2,y2)
% Row 12 is phi_xy(x2,y2)
% Row 13 is phi(x3,y3)
% Row 14 is phi_x(x3,y3)
% Row 15 is phi_y(x3,y3)
% Row 16 is phi_xx(x3,y3)
% Row 17 is phi_yy(x3,y3)
% Row 18 is phi_xy(x3,y3)
% Row 19 is dphi/dn1
% Row 20 is dphi/dn2
% Row 21 is dphi/dn3
% phi = c1 c2x c3x^2 c4x^3 c5x^4 c6x^5 c7y c8y^2 c9y^3 c10y^4
%c11y^5 c12xy c13xy^2 c14xy^3 c15xy^4 c16x^2y
%c17x^2*y2 c18x^2*y3 c19x^3y c20x^3*y2 c21x^4*y;

%[x1 y1 x2 y2 x3 y3] = [0 0; 1 0; 0 1];

coordary=[0 0; 1 0; 0 1];
x1=coordary(1,1);y1=coordary(1,2);
x2=coordary(2,1);y2=coordary(2,2);
x3=coordary(3,1);y3=coordary(3,2);

x4 = (x2-x3)/2; x5=(x3-x1)/2; x6=(x2-x1)/2;
y4 = (y2-y3)/2; y5=(y3-y1)/2; y6=(y2-y1)/2;

% A = [ 1 x1 x1^2 x1^3 x1^4 x1^5 y1 y1^2 y1^3 y1^4 y1^5 x1y1 x1y1^2 x1y1^3 x1y1^4 x1^2y1 x1^2*y12 x1^2*y13 x1^3y1 x1^3*y12 x1^4y1;
% 0 1 2x1 3x1^2 4x1^3 5x1^4 0 0 0 0 0 y1 y1^2 y1^3 y1^4 2x1y1 2x1y1^2 2x1y1^3 3x1^2y1 3x1^2*y12 4x1^3y1
% 0 0 0 0 0 0 1 2y1 3y1^2 4y1^3 5y1^4 x1 2x1y1 3x1y1^2 4x1y1^3 x1^2 2x1^2y1 3x1^2*y12 x1^3 2x1^3y1 x1^4;
% 0 0 2 6x1 12x1^2 20x1^3 0 0 0 0 0 0 0 0 0 2y1 2y1^2 2y1^3 6x1y1 6x1y1^2 12x1^2y1
% 0 0 0 0 0 0 0 2 6y1 12y1^2 20y1^3 0 2x1 6x1y1 12x1y1^2 0 2x1^2 6x1^2y1 0 2x1^3 0;
% 0 0 0 0 0 0 0 0 0 0 0 1 2y1 3y1^2 4y1^3 2x1 4x1y1 6x1y1^2 3x1^2
% 6x1^2y1 4x1^3;
% 1 x2 x2^2 x2^3 x2^4 x2^5 y2 y2^2 y2^3 y2^4 y2^5 x2y2 x2y2^2 x2y2^3 x2y2^4 x2^2y2 x2^2*y22 x2^2*y23 x2^3y2 x2^3*y22 x2^4y2;
% 0 1 2x2 3x2^2 4x2^3 5x2^4 0 0 0 0 0 y2 y2^2 y2^3 y2^4 2x2y2 2x2y2^2 2x2y2^3 3x2^2y2 3x2^2*y22 4x2^3y2
% 0 0 0 0 0 0 1 2y2 3y2^2 4y2^3 5y2^4 x2 2x2y2 3x2y2^2 4x2y2^3 x2^2 2x2^2y2 3x2^2*y22 x2^3 2x2^3y2 x2^4;
% 0 0 2 6x2 12x2^2 20x2^3 0 0 0 0 0 0 0 0 0 2y2 2y2^2 2y2^3 6x2y2 6x2y2^2 12x2^2y2
% 0 0 0 0 0 0 0 2 6y2 12y2^2 20y2^3 0 2x2 6x2y2 12x2y2^2 0 2x2^2 6x2^2y2 0 2x2^3 0;
% 0 0 0 0 0 0 0 0 0 0 0 1 2y2 3y2^2 4y2^3 2x2 4x2y2 6x2y2^2 3x2^2
% 6x2^2y2 4x2^3;
% 1 x3 x3^2 x3^3 x3^4 x3^5 y3 y3^2 y3^3 y3^4 y3^5 x3y3 x3y3^2 x3y3^3 x3y3^4 x3^2y3 x3^2*y32 x3^2*y33 x3^3y3 x3^3*y32 x3^4y3;
% 0 1 2x3 3x3^2 4x3^3 5x3^4 0 0 0 0 0 y3 y3^2 y3^3 y3^4 2x3y3 2x3y3^2 2x3y3^3 3x3^2y3 3x3^2*y32 4x3^3y3
% 0 0 0 0 0 0 1 2y3 3y3^2 4y3^3 5y3^4 x3 2x3y3 3x3y3^2 4x3y3^3 x3^2 2x3^2y3 3x3^2*y32 x3^3 2x3^3y3 x3^4;
% 0 0 2 6x3 12x3^2 20x3^3 0 0 0 0 0 0 0 0 0 2y3 2y3^2 2y3^3 6x3y3 6x3y3^2 12x3^2y3
% 0 0 0 0 0 0 0 2 6y3 12y3^2 20y3^3 0 2x3 6x3y3 12x3y3^2 0 2x3^2 6x3^2y3 0 2x3^3 0;
% 0 0 0 0 0 0 0 0 0 0 0 1 2y3 3y3^2 4y3^3 2x3 4x3y3 6x3y3^2 3x3^2
% 6x3^2y3 4x3^3;
% 0 -1/2^0.5 -1/2^0.52x4 -1/2^0.5*3*x42 -1/2^0.5*4*x43 -1/2^0.5*5*x44 -1/2^0.5 -1/2^0.52y4 -1/2^0.5*3*y42 -1/2^0.5*4*y43 -1/2^0.5*5*y44 -1/2^0.5(x4+y4) -1/2^0.5*(y42+2x4y4) -1/2^0.5*(y43+3x4y4^2) -1/2^0.5*(y44+4x4y4^3) -1/2^{0.5*(2*x4*y4+x4}2) -2/2^0.5*(x4*y42+x4^2y4) -1/2^0.5*(2*x4*y43+3x4^2*y42) -1/2^0.5*(3*x42y4+x4^3) -1/2^0.5*(3*x42y4^2+2*x43y4) -1/2^0.5*(4*x43y4+x4^4);
% 0 -1 -2x5 -3x5^2 -4x5^3 -5x5^4 0 0 0 0 0 -y5 -y5^2 -y5^3 -y5^4 -2x5y5 -2x5y5^2 -2x5y5^3 -3x5^2y5 -3x5^2*y52 -4x5^3y5;
% 0 0 0 0 0 0 1 2y6 3y6^2 4y6^3 5y6^4 x6 2x6y6 3x6y6^2 4x6y6^3 x6^2
% 2x6^2y6 3x6^2*y62 x6^3 2x6^3y6 x6^4;];

% Row 1 is phi(x1,y1)
A1=[1,x1,x1^2,x13,x1^4,x15,y1,y1^2,y13,y1^4,y15,x1y1,x1y1^2,x1*y13,x1y1^4,x12y1,x1^2*y12,x1^2*y13,x1^3*y1,x13y1^2,x14y1];

% Row 2 is phi_x(x1,y1)
A2=[0,1,2x1,3x1^2,4*x13,5x1^{4,0,0,0,0,0,y1,y1}2,y1^3,y14,2x1y1,2x1y1^2,2*x1*y13,3x1^2*y1,3*x12y1^2,4*x13y1];

% Row 3 is phi_y(x1,y1)
A3=[0,0,0,0,0,0,1,2y1,3y1^2,4*y13,5y1^{4,x1,2*x1*y1,3*x1*y1}2,4x1y1^3,x12,2x1^2*y1,3*x12y1^2,x13,2x1^3*y1,x14];

% Row 4 is phi_xx(x1,y1)
A4=[0,0,2,6x1,12x1^2,20*x13,0,0,0,0,0,0,0,0,0,2y1,2y1^2,2*y13,6x1y1,6x1y1^2,12*x12*y1];

% Row 5 is phi_yy(x1,y1)
A5=[0,0,0,0,0,0,0,2,6y1,12y1^2,20*y13,0,2x1,6x1y1,12x1y1^2,0,2*x12,6x1^2*y1,0,2*x13,0];

% Row 6 is phi_xy(x1,y1)
A6=[0,0,0,0,0,0,0,0,0,0,0,1,2y1,3y1^2,4*y13,2x1,4x1y1,6x1y1^2,3*x12,6x1^2*y1,4*x13];

% Row 7 is phi(x2,y2)
A7=[1,x2,x2^2,x23,x2^4,x25,y2,y2^2,y23,y2^4,y25,x2y2,x2y2^2,x2*y23,x2y2^4,x22y2,x2^2*y22,x2^2*y23,x2^3*y2,x23y2^2,x24y2];

% Row 8 is phi_x(x2,y2)
A8=[0,1,2x2,3x2^2,4*x23,5x2^{4,0,0,0,0,0,y2,y2}2,y2^3,y24,2x2y2,2x2y2^2,2*x2*y23,3x2^2*y2,3*x22y2^2,4*x23y2];

% Row 9 is phi_y(x2,y2)
A9=[0,0,0,0,0,0,1,2y2,3y2^2,4*y23,5y2^{4,x2,2*x2*y2,3*x2*y2}2,4x2y2^3,x22,2x2^2*y2,3*x22y2^2,x23,2x2^3*y2,x24];

% Row 10 is phi_xx(x2,y2)
A10=[0,0,2,6x2,12x2^2,20*x23,0,0,0,0,0,0,0,0,0,2y2,2y2^2,2*y23,6x2y2,6x2y2^2,12*x22*y2];

% Row 11 is phi_yy(x2,y2)
A11=[0,0,0,0,0,0,0,2,6y2,12y2^2,20*y23,0,2x2,6x2y2,12x2y2^2,0,2*x22,6x2^2*y2,0,2*x23,0];

% Row 12 is phi_xy(x2,y2)
A12=[0,0,0,0,0,0,0,0,0,0,0,1,2y2,3y2^2,4*y23,2x2,4x2y2,6x2y2^2,3*x22,6x2^2*y2,4*x23];

% Row 13 is phi(x3,y3)
A13=[1,x3,x3^2,x33,x3^4,x35,y3,y3^2,y33,y3^4,y35,x3y3,x3y3^2,x3*y33,x3y3^4,x32y3,x3^2*y32,x3^2*y33,x3^3*y3,x33y3^2,x34y3];

% Row 14 is phi_x(x3,y3)
A14=[0,1,2x3,3x3^2,4*x33,5x3^{4,0,0,0,0,0,y3,y3}2,y3^3,y34,2x3y3,2x3y3^2,2*x3*y33,3x3^2*y3,3*x32y3^2,4*x33y3];

% Row 15 is phi_y(x3,y3)
A15=[0,0,0,0,0,0,1,2y3,3y3^2,4*y33,5y3^{4,x3,2*x3*y3,3*x3*y3}2,4x3y3^3,x32,2x3^2*y3,3*x32y3^2,x33,2x3^3*y3,x34];

% Row 16 is phi_xx(x3,y3)
A16=[0,0,2,6x3,12x3^2,20*x33,0,0,0,0,0,0,0,0,0,2y3,2y3^2,2*y33,6x3y3,6x3y3^2,12*x32*y3];

% Row 17 is phi_yy(x3,y3)
A17=[0,0,0,0,0,0,0,2,6y3,12y3^2,20*y33,0,2x3,6x3y3,12x3y3^2,0,2*x32,6x3^2*y3,0,2*x33,0];

% Row 18 is phi_xy(x3,y3)
A18=[0,0,0,0,0,0,0,0,0,0,0,1,2y3,3y3^2,4*y33,2x3,4x3y3,6x3y3^2,3*x32,6x3^2*y3,4*x33];

% Row 19 is dphi/dn1
A19=[0,-1/2^0.5,-1/20.52x4,-1/2^0.5*3*x42,-1/2^0.5*4*x43,-1/2^0.5*5*x44,-1/2^0.5,-1/20.52y4,-1/2^0.5*3*y42,-1/2^0.5*4*y43,-1/2^0.5*5*y44,-1/2^{0.5*(x4+y4),-1/2}0.5(y4^{2+2*x4*y4),-1/2}0.5(y4^3+3*x4*y42),-1/2^0.5*(y44+4x4y4^3),-1/20.5(2x4y4+x4^2),-2/20.5(x4y4^2+x42y4),-1/2^0.5*(2*x4*y43+3x4^2*y42),-1/2^0.5*(3*x42y4+x4^3),-1/20.5(3x4^2*y42+2x4^3*y4),-1/20.5(4*x4^3*y4+x44)];

% Row 20 is dphi/dn2
A20=[0,-1,-2x5,-3x5^2,-4*x53,-5x5^{4,0,0,0,0,0,-y5,-y5}2,-y5^3,-y54,-2x5y5,-2x5y5^2,-2*x5*y53,-3x5^2*y5,-3*x52y5^2,-4*x53y5];

% Row 21 is dphi/dn3
A21=[0,0,0,0,0,0,1,2y6,3y6^2,4*y63,5y6^{4,x6,2*x6*y6,3*x6*y6}2,4x6y6^3,x62,2x6^2*y6,3*x62y6^2,x63,2x6^3*y6,x64];

clc;
disp([A1;A2;A3;A4;A5;A6;A7;A8;A9;A10;A11;A12;A13;A14;A15;A16;A17;A18;A19;A20;A21]);
clear all;
end
输出结果:1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 2.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2.0000 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1.0000 2.0000 3.0000 4.0000 5.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1.0000 0 0 0 0 1.0000 0 0 0 1.0000 0 0 1.0000 0 1.0000
0 0 2.0000 6.0000 12.0000 20.0000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 2.0000 0 0 0 0 2.0000 0 0 0 2.0000 0 0 2.0000 0
0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 2.0000 0 0 3.0000 0 4.0000
1.0000 0 0 0 0 0 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 0 0 0 0 0
0 1.0000 0 0 0 0 0 0 0 0 0 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 0
0 0 0 0 0 0 1.0000 2.0000 3.0000 4.0000 5.0000 0 0 0 0 0 0 0 0 0 0
0 0 2.0000 0 0 0 0 0 0 0 0 0 0 0 0 2.0000 2.0000 2.0000 0 0 0
0 0 0 0 0 0 0 2.0000 6.0000 12.0000 20.0000 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1.0000 2.0000 3.0000 4.0000 0 0 0 0 0 0
0 -0.7071 -0.7071 -0.5303 -0.3536 -0.2210 -0.7071 0.7071 -0.5303 0.3536 -0.2210 0 0.1768 -0.1768 0.1326 0.1768 0 -0.0442 0.1768 -0.0442 0.1326
0 -1.0000 0 0 0 0 0 0 0 0 0 -0.5000 -0.2500 -0.1250 -0.0625 0 0 0 0 0 0
0 0 0 0 0 0 1.0000 0 0 0 0 0.5000 0 0 0 0.2500 0 0 0.1250 0 0.0625
`