Memory organisation

TArray$<$T$>$ can handle numerical arrays with various memory organisation, as long as the spacing (steps) along each axis is regular. The five axis are labeled X,Y,Z,T,U. The examples below illustrates the memory location for a 2-dimensional, $N_x=4 \times N_y=3$. The first index is along the X axis and the second index along the Y axis.

    | (0,0)  (0,1)  (0,2)  (0,3) |
    | (1,0)  (1,1)  (1,2)  (1,3) |
    | (2,0)  (2,1)  (2,2)  (2,3) |

In the first case, the array is completely packed ( $Step_X=1, Step_Y=N_X=4$), with zero offset, while in the second case, $Step_X=2, Step_Y=10, Offset=10$:

    | 0  1  2  3  |         | 10 12 14 16 |
Ex1 | 4  5  6  7  |     Ex2 | 20 22 24 26 |
    | 8  9  10 11 |         | 30 32 34 36 |

For matrices and vectors, an optional argument ( MemoryMapping) can be used to select the memory mapping, where two basic schemes are available:
CMemoryMapping and FortranMemoryMapping.
In the case where CMemoryMapping is used, a given matrix line is packed in memory, while the columns are packed when FortranMemoryMapping is used. The first index when addressing the matrix elements (line number index) runs along the Y-axis if CMemoryMapping is used, and along the X-axis in the case of FortranMemoryMapping. Arithmetic operations between matrices with different memory organisation is allowed as long as the two matrices have the same sizes (Number of rows and columns). The following code example and the corresponding output illustrates these two memory mappings. The TMatrix$<$T$>$::TransposeSelf() method changes effectively the matrix memory mapping, which is also the case of TMatrix$<$T$>$::Transpose() method without argument.

TArray<r_4> X(4,2); 
X = RegularSequence(1,1);
cout << "Array X= " << X << endl;
TMatrix<r_4> X_C(X, true, BaseArray::CMemoryMapping);
cout << "Matrix X_C (CMemoryMapping) = " << X_C << endl;
TMatrix<r_4> X_F(X, true, BaseArray::FortranMemoryMapping);
cout << "Matrix X_F (FortranMemoryMapping) = " << X_F << endl;

This code would produce the following output (X_F = Transpose(X_C)) :

Array X= 
--- TArray<f>  ND=2 SizeX*Y*...= 4x2 ---
1, 2, 3, 4
5, 6, 7, 8

Matrix X_C (CMemoryMapping) = 
--- TMatrix<f>(NRows=2, NCols=4) ND=2 SizeX*Y*...= 4x2 ---
1, 2, 3, 4
5, 6, 7, 8

Matrix X_F (FortranMemoryMapping) = 
--- TMatrix<f>(NRows=4, NCols=2) ND=2 SizeX*Y*...= 4x2 ---
1, 5
2, 6
3, 7
4, 8