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Extreme Optimization Mathematics Library for .NET

Vector Basics

The Vector class is an abstract base class that exposes the mathematical methods and properties of vectors. It also contains a default implementation for these methods and properties. A series of derived classes implement specific types of vectors. These are listed in the table below.

Class	Description
GeneralVector	A standard vector. The components can take on any value. This is the most common type.
BandVector	A vector that has one or more zero components at the beginning and/or at the end.
ConstantVector	A vector whose elements are all equal to the same real number.
VectorView	A vector that represents a range or slice of another vector.
RowVector	A vector that represents (part of) a row in a matrix.
ColumnVector	A vector that represents (part of) a column in a matrix.
DiagonalVector	A vector that represents (part of) a diagonal in a matrix.

The Vector class does not specify how vector components should be stored. This is left entirely up to the derived classes. The derived vector types provide their own optimized implementations for many of the base methods and properties. Wherever possible, use is made of optimized implementations of the Basic Linear Algebra Subroutines (BLAS).

Some vector types put restrictions on the components that can be changed. For example, you can only modify the non-zero elements of a BandVector. If you try to assign a value to a read-only component, an exception of type ComponentReadonlyException is thrown.

GeneralVector, as the name suggests, can be used to represent any vector. It is the only vector type whose components are all guaranteed to be writable. For this reason, it is used by methods that overwrite their vector argument

Stand-alone and derived vectors

Vectors come in two guises: stand-alone vectors and derived vectors.

Stand-alone vectors 'own' their components. Changing the value of a component does not have any side-effects. If there are no vectors derived from it, no operation unrelated to the stand-alone vector can change any of its components.

Derived vectors take their components from another vector or a matrix. Changing the value of a component also changes the value of the corresponding component in the vector or matrix from which it is derived. Changes to this underlying vector or matrix are reflected in the derived vector.

Many methods return vectors, so how are we to know whether the return value is a stand-alone vector or a derived vector? The rule is simple:

If a method returns a new vector whose components consists of the unmodified components of another vector or matrix, then this return value is a derived vector.

If a method returns a new vector whose components are the result of a calculation involving the components of one or more vectors or matrices, then the return value is a stand-alone vector.

Some methods return a reference to the instance the method was called on. In this case, the return value is not a new vector and the above rule does not apply. A method call on a vector has no effect on whether the instance is a stand-alone or a derived vector. There is just one exception: the CloneData method. This method converts a derived vector to a stand-alone vector.

Copying vectors

There are three ways to make a copy of a vector.

The ShallowCopy method creates a derived vector that is a memberwise clone of the original. The new vector has the same type and length as the original vector. When you change the value of a component of this vector, the value of the corresponding component in the original vector changes as well, and vice versa.

The Clone method creates a stand-alone vector that is a complete copy of the original. This method creates a vector of the same type as the original, and makes its own copy of the component storage. When you change the value of a component of this vector, the value of the corresponding component in the original vector does not change. Likewise, if you change the value of a component of the original vector, the value of the corresponding component in the copied vector does not change.

The Clone method takes an optional parameter of type CloningMethod. This parameter specifies if you want to preserve the read-only components of the vector. The possible values for this parameter are listed in the following table:

You can convert a shallow copy to a full copy by calling the CloneData method. This method ensures that an instance has its own copy of the data. After a call to this method, any changes to the elements of this vector will only affect this instance.

// Create a vector, a shallow copy, and a clone:
Vector v = new GeneralVector(1, 2, 3, 4, 5);
Vector vShallowCopy = v.ShallowCopy();
Vector vClone = v.Clone();
// This prints '2':
Console.WriteLine("v[1] = {0}", v[1]);
// Now change the value of the 2nd component.
v[1] = -1;
// Component changed. This prints '-1':
Console.WriteLine("v[1] = {0}", v[1]);
// Shallow copy changed, also. This prints '-1':
Console.WriteLine("vShallowCopy[1] = {0}", v[1]);
// Clone is left unchanged. This prints '2':
Console.WriteLine("vClone[1] = {0}", v[1]);

' Create a vector, a shallow copy, and a clone:
Vector v = new GeneralVector(1, 2, 3, 4, 5)
Vector vShallowCopy = v.ShallowCopy()
Vector vClone = v.Clone()
' This prints '2':
Console.WriteLine("v(1) = {0}", v(1))
' Now change the value of the 2nd component.
v(1) = -1
' Component changed. This prints '-1':
Console.WriteLine("v(1) = {0}", v(1))
' Shallow copy changed, also. This prints '-1':
Console.WriteLine("vShallowCopy(1) = {0}", v(1))
' Clone is left unchanged. This prints '2':
Console.WriteLine("vClone(1) = {0}", v(1))

The third way to copy a vector is by calling the vector's ToGeneralVector method. This method returns a stand-alone GeneralVector whose components are copied from the original vector. If this method is called on a GeneralVector, a new vector is still created. In all cases, the components of the new vector are guaranteed to be stored in a contiguous block of memory.

You can copy the components of a vector to another, previously created vector using the CopyTo method. The first variant of this method takes the second (destination) vector as its first and only argument. There is another variant that takes a second parameter, indicating the index in the destination where copying should begin. Care should be taken that you don't try to modify elements that are read-only. Any such attempt will result in a ComponentReadOnlyException.

Finally, the Swap method swaps the components between two vectors.

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