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"Math Operators on Vectors"
Vector Operator Method
Results =

vector v1 = ( , , , , )
vector v2 = ( , , , , )

[ Initial vector-v1: ( 1.0, 2.0, 3.0, 4.0, 5.0 ) ]
[ Initial vector-v2: ( 6.0, 7.0, 8.0, 9.0, 10.0 ) ]

Operations on Vectors

Standard vector addition, subtraction, multiplication and division are performed basically by one method with variations to accomodate the various operations. We have shown the same implementation under Smalltalk (please see menu)  "Vectors and Matrices in Smalltalk".

Algorithm Creation

As an example we show the model function for the dot product of two vectors:

A.B = ∑ni=1 Ai Bi

where the dot product of two vectors produces a scalar quantity.

Testing the Vector Operator Method

In order to test the Vector Operator Method, a new TestMathOperators() static method has been added and executed. Supporting code and methods are not shown.

           static void TestMathOperators();
                 VectorR v1 = new VectorR(new double[] { t1, t2, t3, t4, t5 });
                 VectorR v2 = new VectorR(new double[] { t7, t8, t9, t10, t11 };
                 double d = 20;
                 ListBox1.Items.Add(" v1 = " + v1);
                 ListBox1.Items.Add(" v2 = " + v2);
                 ListBox1.Items.Add(" d = " + d);
                 ListBox1.Items.Add(" v2 + v1 = " + (v2 + v1));
                 ListBox1.Items.Add(" v2 - v1 = " + (v2 - v1));
                 ListBox1.Items.Add(" v1 * d = " + (v1 * d));
                 ListBox1.Items.Add(" v1 / d = " + (v1 / d));

As a sample we provide the input data points using two double arrays vector v1 and vector v2. Results are seen on the screen above.

The user can manipulate all values and try variations on the vectors themselves by specifying new vector values.

Other Implementations...

Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation

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