MATLAB by rudra pratap

66 Interactive Computation
Continuation across several input lines achieved through an ellipsis is not limited
to matrix input. This construct may be used for other commands and for a long
list of command arguments (see Section 4.3.2, page 112), as long as the command
does not exceed 4,096 characters.
3.1.2 Indexing (or subscripting)
Once a matrix exists, its elements are accessed by specifying their row and column
indices. Thus, A ( i , j) in MATLAB refers to the element aij of matrix A, i.e.,
the clement in the ith row and jth column. This notation is fairly common in
computational software packages and programming languages. MATLAB, however,
provides a much higher level of index specification-it allows a range of rows and
columns to be specified at the same time. For example, the statement A(m:n,k:l)
specifies rows rn to n and columns k to l of matrix A. When the rows (or columns)
to be specified range over all rows (or columns) of the matrix, a colon can be used
as the row (or column) index. Thus, A(: ,5:20) refers to the elements in columns
5 through 20 of all the rows of matrix A. This feature makes matrix manipulation
much easier and provides a way to take advantage of the "vectorized" nature of
calculations in MATLAB. (See Fig. 3.1 for examples.)
Dimension
Matrix dimensions are determined automatically by MATLAB, i.e., no explicit dimension
declarations are required. The dimensions of an existing matrix A may be
obtained with the command size (A) or more explicitly with [m , n] =size (A) , which
assigns the number of rows and columns of A to the variables m and n, respectively.
When a matrix is entered by specifying a single element or a few elements of the
matrix, MATLAB creates a matrix just big enough to accommodate the elements.
Thus, if the matrices B and C do not exist already, then
B(2,3) = 5;
produces
0
0
C(3,1:3) [1 2 3] ; produces
0
0
2
3.1.3 Matrix manipulation
As you can see from examples in Fig. 3.1, it is fairly easy to correct wrong Pntries
of a matrix, extract any part or submatrix of a matrix, or delete or add rows and
columns. These manipulations are done with MATLAB's smart indexing feature.
By specifying vectors as the row and column indices of a matrix, one can reference
and modify any submatrix of a matrix. Thus, if A is a 10 x 10 matrix, B is a 5 X 10
matrix, and y is a 20 elements long row vector, then
A([1 3 6 9] ,:) = [B ( 1:3,:); y(1: 10)]