About Matrix class
In this page we explain a square matrix of 3 rd order for example.
The abbreviation of type name defines as follows:
f ：float， d：double
For example,
float data type : Matrx33f
double data type: Matrix33d
The abbreviation type:
kvs::Matrix33<float> A;
is same as follows:
kvs::Matrix33<float> A;
Member functions
Constructor
There are four types of constructor.
Following example explains the constructor case of "kvs::Matrix33f"
( Notie that the initial value sets to zero in case of the default constructor )
// Default constructor
kvs::Matrix33f A;
// assign all component
kvs::Matrix33f B( 1.0, 2.0, 0.0,
2.0, 2.0, 1.0,
0.0, 1.0, 3.0 );
// Three vector
kvs::Vector3f v0( 1.0, 1.0, 1.0 );
kvs::Vector3f v1( 2.0, 2.0, 1.0 );
kvs::Vector3f v2( 1.0, 2.0, 4.0 );
kvs::Matrix33f C( v0, v1, v2 );
// Array
float elem[9] = { 1.0, 2.0, 3.0,
4.0, 5.0, 6.0,
7.0, 8.0, 9.0 };
kvs::Matrix33f D( elem );
Value substitution: Operator[ ], zero( ), identity( ), set( )
Operator [] : same as arrays
zero(): all element of matrix sets to ZERO
identity(): set as identity matrix
set( T a00, T a01, T a02, T a10, T a11, T a12, T a20, T a21, T a22),
set( T a0[3], T a1[3], T a2[3]),
set(T elem[9] ):
// Operator []
A[0][0] = 1.0; A[0][1] = 1.0; A[0][2] = 3.0;
A[1][0] = 4.0; A[1][1] = 1.0; A[1][2] = 0.0;
A[2][0] = 2.0; A[2][1] = 0.0; A[2][2] = 2.0;
// Zero Matrix
A.zero();
// dentity matrix
A.identity();
// method set(): all components
A.set( 1.0, 2.0, 2.0,
2.0, 2.0, 1.0,
0.0, 1.0, 3.0 );
// method set(): Three vector
A.set( v0, v1, v2 );
// method set(): Array
A.set( elem );
Getting value: Operator [ ]
For example:
float a11 = a[1][1];
std::cout << a[0][0] << " " << a[0][1] << " " << a[0][2] << std::endl;
Standard output: print( ), output operator<<
A.print( );
std::cout << A ;
Above example is same output:
1 2 3
4 5 6
7 8 9
Transposed matrix: transpose( ), transposed( )
transpose( ): superscription (normalize own)
transposed( ): transposed matrix returns (the own value does not change)
// Superscription
A.transpose( );
// Return the transposed matrix
kvs::Matrix33f E = B.transposed( );
Inverse matrix: invert( ), inverted( )
invert( )( ): superscription (normalize own)
inverted( ): inverse matrix returns (the own value does not change)
// Superscription
C.invert( );
// Return the inverse matrix
const kvs::Matrix33f F = B.inverted( );
Trace: trace( ), determinant: determinant( )
For example:
// Trace
float tr = A.trace();
// Determinamt
float det = A.determinant();
The type of return value is the same of vector (Here is float).
Four arithmetic operations： +, -, *, /
Vector Addition and Subtraction are defined as
Operator + (+=) and Operator - ( -= ), respectively.
C = A + B;
A+=C;
A -= B;
std::cout << -A << std::endl;
Operator * ( *= ) multiply matrix by scalar value or vector or matrix.
// Matrix by matrix multiplication
C = A*B
A*=B;
// Scalar by matrix multiplication
int i = 10;
C = i*B;
C = B*i;
C *= i;
// Vector by matrix multiplication
A.set( 1, 1, 1, 1, 1, 1, 2, 2, 2);
v0.set( 1, 1, 1);
kvs::Vector3f x = v0*A; // raw vector by matryx
kvs::Vector3f y = A*v0; // column vector by matrix
Operator / (/= ) divides the each element by scalar value.
D = C/i;
C /= i;
Relational operator: ==, !=
Relational operator compares each component.
For exampe:
// Relational operator
if( A == B ) {
std::cout << "A == B" << std::endl;
}
else if( A != B ) {
std::cout << "A != B" << std::endl; }
Sample program: MatrixTest.tgz
Compile and execute
Let's try to compile and execute above program.
When compiling a KVS program, it is easy to use the automatic Makefile-generation tool kvsmake supplied by KVS.
Here, the option “-G” defines the name of executable file same as the name of current directory.
# kvsmake -G <-- Generate Makefile
# kvsmake <-- Compile
And then,
# ./MatrixTest
Last Updated at Nov. 1, 2015