input-matrix3

有限元程序

/* ======================================================== */
/* MATRIX OEPRATION III                                     */
/*                                                          */
/* Test basic matrix arithmetic                             */
/* ======================================================== */

print "============================\n";
print "Test basic matrix arithmetic\n";
print "============================\n\n";

print "\n";
print "=================\n";
print "*** Copy a matrix\n";
print "=================\n\n";

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

print "\n";
print "=========================================\n";
print "*** Scale matrices by a physical quantity\n";
print "=========================================\n\n";

print "\n";
print "*** Amplify matrix content by a factor of 2 (Example 1)\n";

X = One([4]);
X = ColumnUnits(X, [ksi, lbf, ksi, ft]);
X = RowUnits(X, [psi, in, kips, lb]);
Y = X*2;
Z = 2*X;
PrintMatrix(X, Y, Z);

print "\n";
print "*** Amplify matrix content by a factor of 2 in (Example 2)\n";

Y = X*2 in;
Z = (2 in)*X;
PrintMatrix(X, Y, Z);

print "\n";
print "*** Reduce Matrix Content by a factor of 2 in (Example 3)\n";

print "X [1][4] = ", X[1][4],"\n";
Y = X/2 in;
print "Y [1][4] = ", Y[1][4],"\n";
PrintMatrix(X, Y);

print "\n";
print "====================\n";
print "*** Matrix transpose\n";
print "====================\n\n";

print "*** Matrix transpose (Example 1)\n";

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

print "\n";
print "*** Matrix transpose (Example 2)\n";

response = [ 0 sec, 0 cm/sec, 0 cm/sec^2 ;
             1 sec, 2 cm/sec, 3 cm/sec^2 ];
PrintMatrix( response );

transpose1 = Trans(response);
PrintMatrix( transpose1 );

print "\n";
print "============================================================\n";
print "*** Maximum and minimum matrix elements                     \n";
print "                                                            \n";
print "    Min ( A )  Return a (1x1) matrix containing the minimum \n";
print "               matrix element in matrix A.                  \n";
print "                                                            \n";
print "    Max ( A )  Return a (1x1) matrix containing the maximum \n";
print "               matrix element in matrix A.                  \n";
print "============================================================\n\n";

A = [ 3.78,  9.7, -4.7,  10.50  ;
      0.00, -5.8,  0.2,  -9.34] ;

MaxValue = Max( A );
MinValue = Min( A );

PrintMatrix(A);

print "\n";
print "Max(A) =", MaxValue ,"\n";
print "Min(A) =", MinValue ,"\n";

print "\n";
print "============================================================\n";
print "*** Euclidean Norm                                          \n";
print "                                                            \n";
print "    L2Norm( A )  Compute L2 norm of either a (1xn) matrix   \n";
print "                 or a (nx1) matrix.                         \n";
print "============================================================\n\n";

testVector = [ 1, 2, 3, 4 ];
norm = L2Norm( testVector );

PrintMatrix( testVector );
print "\n";
print "L2 norm of testVector is :", norm, "\n";

print "\n";
print "===================================\n";
print "*** Matrix addition and subtraction\n";
print "===================================\n\n";

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]);

print "\n";
print "*** Matrix addition\n\n";

Z = X + Y;
U = Y + X;
PrintMatrix(X, Y, Z, U);

print "\n";
print "*** Matrix subtraction\n\n";

Z = X - Y;
U = Y - X;
PrintMatrix(X, Y, Z, U);

print "\n";
print "==============================================\n";
print "*** Matrix multiplication (without dimensions)\n";
print "==============================================\n\n";

X = [2, 3, 5; 4, 6, 7; 10, 2, 3];
Z = One([3, 4]);
Y = One([3, 1]);

U = X*Z;
V = X*Y;
PrintMatrix(X, Y, Z, U, V);

print "\n";
print "===========================================\n";
print "*** Matrix multiplication (with dimensions)\n";
print "===========================================\n\n";

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

U = X*Y;
PrintMatrix(X, Y, U);

print "\n";
print "===============================================\n";
print "*** Compute inverse of a non-dimensional matrix\n";
print "===============================================\n\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);

print "\n";
print "============================================\n";
print "*** Compute inverse of a matrix having units\n";
print "============================================\n\n";

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";
print "===============\n";
print "*** End of Test\n";
print "===============\n";

quit;