MatrixVector Namespace Reference

Two dimensional array represents matrix, column and row vector. More...

Classes
class	mat
class	row
class	vec

Functions
template<typename T >
T **	allocateTemp (int ncol, int nrow)
	Allocate ncol, nrow two dimension array for any type, return a pointer.
template<typename T >
T **	allocate (int ncol, int nrow)
	Allocate a matrix: height = ncol, width = nrow.
template<typename T >
T **	vecVecToArrArr (vector< vector< T > > vv)
	Convert Vector< Vector<T> > to dynamic T**.
template<typename T >
vector< vector< T > >	arrArrToVecVec (T **arr, int ncol, int nrow)
	Convert T** arr to vector<vector<T>> v2.
mat	concat (mat m1, mat m2)
mat	identity (int n)
vec	backwardSubstitute (mat a, vec b)
	Backward Substitute.
mat	ltri (mat m, int index)
	Get the L triangle from a matrix.
std::pair< mat, mat >	utri (mat m)
	Assume the diagonal entries are not zero, compute the U triangle matrix Lk..(L2 (L1 A))= U TODO: fix the code if a_{ii} = 0.
mat	geneMat (int ncol, int nrow, int init)
mat	geneMatRandom (int ncol, int nrow, int fst, int snd)
	Generate random matrix in interval from fst to snd.

Detailed Description

Two dimensional array represents matrix, column and row vector.

1. Good: column vector can be represented as arr[n][0] row vector can be represented as arr[0][n] matrix can be represented as arr[n][m]

Function Documentation

allocate()

template<typename T >

T ** MatrixVector::allocate	(	int	ncol,
		int	nrow
	)

Allocate a matrix: height = ncol, width = nrow.

Parameters

ncol	is the height of matrix
nrow	is the width of matrix

Returns

T**

allocateTemp()

template<typename T >

T ** MatrixVector::allocateTemp	(	int	ncol,
		int	nrow
	)

Allocate ncol, nrow two dimension array for any type, return a pointer.

Parameters

ncol	is number of column
nrow	is number of row

Returns

T**

TODO: Change ncol => width nrow => heigh

Parameters

ncol	is number of column
nrow	is number of row

Returns

T**

arrArrToVecVec()

template<typename T >

vector< vector< T > > MatrixVector::arrArrToVecVec	(	T **	arr,
		int	ncol,
		int	nrow
	)

Convert T** arr to vector<vector<T>> v2.

int ncol = 2;
int nrow = 3;
int arr[2][3] = {
{1, 2, 3},
{4, 5, 6}
};
 
 
vector<vector<int>> v3 = {
{1, 2, 3},
{4, 5, 6}
};
 
int* pt = &arr[0][0];
vector<vector<int>> vv = arrArrToVecVec<int>(&pt, ncol, nrow);
assert(arr[0][0] == v3[0][0]);
assert(arr[0][1] == v3[0][1]);
assert(arr[0][2] == v3[0][2]);
assert(arr[1][0] == v3[1][0]);
assert(arr[1][1] == v3[1][1]);
assert(arr[1][2] == v3[1][2]);

Use std::move() ?

int ncol = 2;
int nrow = 3;
int arr[2][3] = {
{1, 2, 3},
{4, 5, 6}
};
 
 
vector<vector<int>> v3 = {
{1, 2, 3},
{4, 5, 6}
};
 
int* pt = &arr[0][0];
vector<vector<int>> vv = arrArrToVecVec<int>(&pt, ncol, nrow);
assert(arr[0][0] == v3[0][0]);
assert(arr[0][1] == v3[0][1]);
assert(arr[0][2] == v3[0][2]);
assert(arr[1][0] == v3[1][0]);
assert(arr[1][1] == v3[1][1]);
assert(arr[1][2] == v3[1][2]);

Use std::move() ?

backwardSubstitute()

vec MatrixVector::backwardSubstitute	(	mat	a,
		vec	b
	)

Backward Substitute.

Parameters

[int]	a - upper triangle
[int]	b - column vector

Returns

column vector x

\[ Ax = b \]

a11 a12 a13 x[0] = b[0]
    a22 a23 x[1] = b[1]
        a33 x[2] = b[2]

Parameters

[int]	a - upper triangle
[int]	b - column vector

Returns

column vector x

\[ Ax = b \]

a11 a12 a13 x[0] = b[0]
    a22 a23 x[1] = b[1]
        a33 x[2] = b[2]

geneMatRandom()

mat MatrixVector::geneMatRandom	(	int	ncol,
		int	nrow,
		int	fst,
		int	snd
	)

Generate random matrix in interval from fst to snd.

ltri()

mat MatrixVector::ltri	(	mat	m,
		int	index
	)

Get the L triangle from a matrix.

\[ \begin{equation} \begin{aligned} &v_k = \begin{bmatrix} 0 \\ \vdots \\ 0 \\ l_{k+1,k} \\ l_{k+2,k} \\ \vdots \\ l_{m,k} \\ \end{bmatrix} \\ &v_k e_{k}^{*} = \begin{bmatrix} 0 & & & & \\ & \ddots & & & \\ & & 0 & & \\ & & l_{k+1,k} & & \\ & & \vdots & \ddots & \\ & & l_{m,k} & & 0 \\ \end{bmatrix} \\ \end{aligned} \end{equation} \]

Ref

\[ \begin{equation} \begin{aligned} &v_k = \begin{bmatrix} 0 \\ \vdots \\ 0 \\ l_{k+1,k} \\ l_{k+2,k} \\ \vdots \\ l_{m,k} \\ \end{bmatrix} \\ &v_k e_{k}^{*} = \begin{bmatrix} 0 & & & & \\ & \ddots & & & \\ & & 0 & & \\ & & l_{k+1,k} & & \\ & & \vdots & \ddots & \\ & & l_{m,k} & & 0 \\ \end{bmatrix} \\ \end{aligned} \end{equation} \]

Ref

vecVecToArrArr()

template<typename T >

T ** MatrixVector::vecVecToArrArr

(

vector< vector< T > >

vv

)

Convert Vector< Vector<T> > to dynamic T**.

Parameters

vv	is vector of vector type.

Returns

T type of two dimensions array