input-matrix-operations3

有限元计算程序

/* ======================================================== */
/* MATRIX OEPRATION III                                     */
/*                                                          */
/* Test basic matrix arithmetic and linear equation solvers */
/* ======================================================== */

print "\n =========== COPY A MATRIX ===========\n";

X = [1.0 kN, 2.0 Pa, 3 m];
Y = Copy(X);
Z = X;
PrintMatrix(X,Y,Z);

print "\n =========== TRANSPOSE A MATRIX ===========\n";

Y = Trans(X);
PrintMatrix(X, Y);

print "\n =========== MATRIX ADDITION ===========\n";

/* Initialize */
X = Diag([4, 1]);
Y = One([4]);
X = ColumnUnits(X, [ksi, ft, N, m]);
Y = ColumnUnits(Y, [psi, in, kN,km]);
X = RowUnits(X, [psi, in, kN, mm]);
Y = RowUnits(Y, [ksi, ft, N, mm]);

Z = X + Y;
U = Y + X;
PrintMatrix(X, Y, Z, U);
print "\n =========== MATRIX SUBSTRACTION ===========\n";
Z = X - Y;
U = Y - X;
PrintMatrix(X, Y, Z, U);


print "\n =========== MATRIX MULTIPLICATION ===========\n";
X = [2, 3, 5; 4, 6, 7; 10, 2, 3];
Z = One([3, 4]);
Y = One([3, 1]);

print "\n ===== Non-Dimensional Matrix Mulitiplication \n";
U = X*Z;
V = X*Y;
PrintMatrix(X, Y, Z, U, V);

X = ColumnUnits(X, [psi*in, psi*in, lbf]);
X = RowUnits(X, [in], [3]);

Y = RowUnits(Y, [ft, ft, rad]);

print "\n ===== Dimensional Matrix Mulitiplication \n";
U = X*Y;
PrintMatrix(X, Y, U);

print "\n =========== MATRIX INVERSE ===========\n";

print "\n ===== Non-Dimensional Matrix Inverse\n";

X = [3,  4, 5, 7,  9,  10;
     1,  6, 7, 9, 20, 100;
     11,26,47, 9,  2,  13;
     12, 6,87, 1,  3,  33;
     11, 0, 1, 6,  31,  5;
     81, 71,2, 2,   1,  54];
Y = Inverse(X);

IL = X*Y;    /* left Identity Matrix  */
IR = Y*X;    /* Right Identity Matrix */
PrintMatrix(X, Y, IL, IR);

X = ColumnUnits(X, [N/m, N/m, N, N/m, N/m, N]);
X = RowUnits(X, [m], [3]);
X = RowUnits(X, [m], [6]);

Y = Inverse(X);
IL = X*Y;    /* left Identity Matrix  */
IR = Y*X;    /* Right Identity Matrix */
PrintMatrix(X, Y, IL, IR);

print "\n====== DECOMPOSE MATRIX INTO [L][U] TRIANGLES =======\n";

Y = Decompose(X);
PrintMatrix(X, Y);

print "\n====== LINEAR MATRIX EQUATION SOLVER [A]{x} = {b} =======\n";

A = [3,  4, 5, 7,  9,  10;
     1,  6, 7, 9, 20, 100;
     11,26,47, 9,  2,  13;
     12, 6,87, 1,  3,  33;
     11, 0, 1, 6,  31,  5;
     81, 71,2, 2,   1,  54];
A = ColumnUnits(A, [N/m, N/m, N, N/m, N/m, N]);
A = RowUnits(A, [m], [3]);
A = RowUnits(A, [m], [6]);

b = [20 N; 100 N;  10 N*m;
      3 N;   2 N; 200 N*m];
PrintMatrix(A, b);

print "\n ---  Solve By Matrix Inverse \n";
Y = Inverse(A);
x = Y*b;
print "\n ---  Check Results \n";
R = A*x -b;
PrintMatrix(x, R);

print "\n";
print "\n ---  Solve By Matrix Solver \n";
x = Solve(A, b);
print "\n ---  Check Results \n";
R = A*x -b;
PrintMatrix(x, R);

print "\n";
print "\n ---  Solve By Matrix LU Decomposition and Backsubstitution \n";
LU = Decompose(A);
x  = Substitution(LU, b);
print "\n ---  Check Results \n";
R = A*x -b;
PrintMatrix(x, R);