input-matrix2

有限元程序

/* ========================================== */
/* MATRIX OEPRATION II                        */
/*                                            */
/* Test basic matrix operations with units    */
/* ========================================== */

print "=====================================\n";
print "*** Operations on matrices with units\n";
print "=====================================\n\n";

print "\n";
print "====================================\n";
print "*** Build a matrix/vector with units\n";
print "====================================\n\n";

X = [1.0 kN, 2.0 Pa, 3 m];
Y = [1 kN; 2 Pa; 3 m];
Z = [1 lbf*ft; 1 m^2; 1 psi*in^2];
U = [1 m/sec, 1 kg*m/sec^2, 1 in^4];
PrintMatrix(X, Y, Z, U);

print "\n";
print "======================================================\n";
print "*** Build a general matrix with units                 \n";
print "***                                                   \n";
print "*** Demonstrate RowUnits() and ColumnUnits() functions\n";
print "======================================================\n\n";

X  = [1 kN, 2 kg; 3, 4];     /* This is OK     */
X1 = [1 kN, 2 ; 3 kg, 4];    /* This is NOT OK */
PrintMatrix(X);

X = Diag([4, 1]);
Y = One( [4, 2]);
Y = RowUnits(Y, [kN]);
PrintMatrix(Y);

print "\n"; 
print "*** Assign a set of units to column buffer \n"; 

X = ColumnUnits(X, [ksi, ft, N, m]);
Y = ColumnUnits(Y, [ksi]);
PrintMatrix(X, Y);

print "\n"; 
print "*** Assign a set of units to row buffer \n"; 

X = RowUnits(X, [psi, ft, kN, mm]);
PrintMatrix(X, Y);

X = One([4, 3]);

print "\n"; 
print "*** Assign an units to column [1] of column buffer \n"; 

X = ColumnUnits(X, [psi], [1]);
PrintMatrix(X);

print "\n"; 
print "*** Assign an units to row [2] of row buffer \n"; 

X = RowUnits(X, [ksi], [2]);
PrintMatrix(X);

print "\n"; 
print "*** Replace units in column buffer with given matched units  \n"; 

X = One([6]);
X = ColumnUnits(X, [ton],  [1]);
X = ColumnUnits(X, [mile],[3]);
X = ColumnUnits(X, [klb],  [4]);

X = ColumnUnits(X, [ft],   [6]);

Y = ColumnUnits(X, [in, lb]);
PrintMatrix(X, Y);

print "\n"; 
print "*** Replace units in row buffer with given matched units  \n";

X = RowUnits(X, [yard, mil, kips, deg_F, psi,rad]);
Y = RowUnits(X, [ksi, in, lbf, deg_C]);
PrintMatrix(X, Y);

print "\n"; 
print "*** Print Matrix\n";

X = One([3, 4]);
X = ColumnUnits(X, [psi], [1]);
X = ColumnUnits(X, [kN],  [2]);
X = ColumnUnits(X, [km],  [4]);
X = RowUnits(X, [psi, N, mm]);
PrintMatrix(X);

print "\n"; 
print "============================================\n";
print "*** Extract a matrix element from a matrix  \n";
print "============================================\n\n";

K = [ 3, 4, 5; 6, 79, 100; 3, 4, 5];
K = RowUnits(K, [km], [1]);
K = RowUnits(K, [sec], [3]);
K = ColumnUnits(K, [MPa], [1]);
K = ColumnUnits(K, [N*m], [3]);

PrintMatrix(K);

print "\n";
print "   K[1][1] = ", K[1][1], "\n";
print "   K[1][2] = ", K[1][2], "\n";
print "   K[1][3] = ", K[1][3], "\n";
print "   K[2][1] = ", K[2][1], "\n";
print "   K[2][2] = ", K[2][2], "\n";
print "   K[2][3] = ", K[2][3], "\n";
print "   K[3][1] = ", K[3][1], "\n";
print "   K[3][2] = ", K[3][2], "\n";
print "   K[3][3] = ", K[3][3], "\n";

print "\n";
print "*** Assign matrix element with a quantity of same units \n";

K[1][1] = 2*K[1][1];
K[1][2] = 2*K[1][2];
K[1][3] = 2*K[1][3];
K[2][1] = 2*K[2][1];
K[2][2] = 2*K[2][2];
K[2][3] = 2*K[2][3];
K[3][1] = 2*K[3][1];
K[3][2] = 2*K[3][2];
K[3][3] = 2*K[3][3];

PrintMatrix(K);

print "\n==== Assign matrix element with a quantity of different units \n";
K[1][1] = 2 m;

print "\n";
print "*** K[1][1] = ", K[1][1], "\n";

print "\n";
print "*** Assign a non-dimensional matrix element with a quantity with units \n";

K[2][2] = 2 m;

print "\n";
print "*** K[2][2] = ", K[2][2], "\n";

PrintMatrix(X);

print "\n";
print "*** Cast a 1x1 matrix into a quantity \n";

K = [100 kPa];

PrintMatrix(K);

print "\n";
print " K = ", QuanCast(K), "\n";

print "\n"; 
print "============================================\n";
print "*** Extract Submatrices from larger matrices\n";
print "============================================\n\n";

print "\n";
print "*** Extract a 2x2 matrix A from 3x4 matrix X starting at corner (1,1) \n";

A = Matrix([2,2]);
A = Extract(A,X,[1,1]);
PrintMatrix(A);

print "\n";
print "*** Extract 2nd column of matrix X and store in matrix B \n";

B = Matrix([3,1]);
B = Extract(B,X,[1,2]);
PrintMatrix(B);

print "\n";
print "*** Extract 3rd row of matrix X and store in matrix C\n";

C = Matrix([1,4]);
C = Extract(C,X,[3,1]);

PrintMatrix(C);

print "\n"; 
print "============================\n";
print "*** Replace mattrix contents\n";
print "============================\n\n";

A = [2 , 3 ; 6, 3];
Y = Put(X, A, [1,1]);
PrintMatrix(X, Y, A);

print "\n";
print "===================================\n";
print "*** Remove dimensions from a matrix\n";
print "===================================\n\n";

X = One([3, 4]);
X = ColumnUnits(X, [psi], [1]);
X = ColumnUnits(X, [kN],  [2]);
X = ColumnUnits(X, [km],  [4]);
Y = MDimenLess(X);
PrintMatrix(X, Y);

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