> For the complete documentation index, see [llms.txt](https://coding-courses.gitbook.io/matlab/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://coding-courses.gitbook.io/matlab/crashcourse/essential-commands/matrix-input-access.md). # Matrix Input and Access ## Basic syntax {% hint style="info" %} To try out the commands on this page just type them directly into the MATLAB Command Window and hit \ to execute them. {% endhint %} Most MATLAB commands follow one of the following syntaxes ``` variable = expression; variable = command(arguments); variable = command(arguments) command(arguments) ``` The semicolon at the end of a command `;` suppresses the display of the result or the output of the command. Lines can be commented out by starting the line with a percentage sign `%`. ``` % this is a comment which will not be executed command(arguments) ``` ## Variables In MATLAB, we store any kind of data (numbers, strings etc.) in `variables`. Here are a few examples of how to assign variables. ``` x = 1 % store scalar value y = 3 + 2 * exp(x); % evaluate expression and store value z = 3 + 2 * exp(x) % evaluate expression, store and print value y % print value to console display(y) % equivalent u = 'I am not a number' % store strings ``` ## Vectors and matrices Vectors and matrices are a special type of variables which can be created, accessed and modified using special commands. **Creating vectors and matrices** We can create row and column vectors either by entering them directly or by transposing vectors. ``` a = [1, 2, 3, 4, 5] % row vector b = [6; 7; 8; 9; 10] % column vector z = a' % column vector by transposing row vector u = b' % row vector by transposing column vector ``` We can create matrices in a similar fashion by entering them row by row or by concatenating previously entered vectors or matrices. ``` A = [1, 2; 3, 4] % declare matrix directly by rows b = [5; 6]; B = [A, b] % join columns of 2x2 matrix A and 2x1 vector b C = [A; b'] % join rows of 2x2 matrix A and 1x2 vector b' ``` **Accessing matrix and vector elements** We can access elements of a vector by supplying the indices of the values that we want to select in parentheses. ``` a = [5, 6, 7, 8, 9]; % row vector b = a'; % column vector a(4) % returns the 4-th element a(2:4) % returns elements 2-4 of row-vector a([1, 3, 4]) % returns elements 1, 3, 4 of row-vector a([1; 3; 4]) % equivalent b([1, 3, 4]) % returns elements 1, 3, 4 of column vector ``` We can access elements of a matrix in a similar fashion by supplying either the indices with respect to the column-wise index or by supplying row and column indices separately. ``` A = [1, 2, 3; 4, 5, 6; 7, 8, 9] A(4:6) % returns elements 4-6 counting columnwise A(2,3) % returns element in row 2, column 3 A(1:2, 2:3) % return submatrix with rows 1-2, columns 2-3 A([1, 3], [1, 2]) % return submatrix with rows 1, 3 and columns 1, 2 ``` We can also use the colon-operator `:` to select all elements of a specific dimension. ``` A(2, :) % return second row of the matrix A(:, 3) % return third row of the matrix A(1:2, :) % return submatrix with first two rows ``` The concepts discussed in this section extend easily to arrays of higher dimensions that 2. **Replacing elements in matrices** We can use the tools from the last section to easily replace individual elements of a matrix or even sub-matrices. ``` A = [1, 2, 3; 4, 5, 6; 7, 8, 9] A(2,3) = 10 % replace element in row 2, column 3 A(1:2, 1:2) = zeros(2,2) % replace upper left 2x2 submatrix A(:, 1) = [0, 1, 2]' % replace first column ``` ## Special vectors and matrices MATLAB supplies you with a set of functions that allow to create vectors or matrices that have a special form. These functions are often useful to avoid unnecessary repetition of inputs. **linspace and : operator** The `linspace` command and the `:` operator allow to create row vectors of sequences that are linearly spaced. Consider first the `:` operator. ``` a = 2:5 % sequence from 2 to 5 in increments of 1 b = 2:3:11 % sequence from 2 to 11 in increments of 3 c = 0:0.2:1 % sequence from 0 to 1 in increments of 0.2 ``` The `linspace(x1, x2, N)` command generates a row vector containing a sequence of N linearly spaced points between x1 and x2. If N is omitted, it generates 100 points. ``` c = linspace(0, 1, 6) % same as c above d = linspace(2, 9, 3) % sequence from 2 to 8 with 3 values ``` **logspace** The logspace operators works the same way as the linspace operator, but it produces a sequence of uniformly spaced values in the log-10 space, i.e. logspace(x1, x2, N) generates N points between 10^x1 and 10^x2. ``` e = logspace(0, 2, 4) % logarithmically spaced values between 1 and 100 ``` **zeros, ones, nan** These commands create matrices of the supplied dimensions which are filled with 0, 1 or missing values (nan = not a number). ``` A = zeros(2, 3) B = ones(1, 4) C = nan(2,2) ``` **eye** eye(n) creates an identity matrix (i.e. a square matrix with ones on the main diagonal and zeros everywhere else) of dimension . ``` eye(3) ``` **diag** If X is a matrix, diag(X), returns the column vector which extracts the main diagonal of the matrix X. If x is a vectors, diag(X) returns a square diagonal matrix which has the vector x on its main diagonal ``` X = [1, 2; 3, 4] x = [2, 5]; diag(X) diag(x) ``` **repmat** repmat(A, M, N) replicates the vector/matrix A copy its rows M times and its columns N times. ``` A = repmat([1, 2, 3], 4, 1) % copy row vector a 4 times along rows B = repmat([1 ,2; 3, 4], 2, 2) % copy matrix 2 times along each dimension ``` **reshape** reshape transforms a matrix into an matrix and can be used if the number of elements does not change i.e. if . It can e.g. be used to convert a matrix into a vector or vice versa. ``` X = [1, 2, 3; 4, 5, 6] reshape(X, 1, 6) % reshape into 1x6 vector reshape(X, 3, 2) % reshape into 3x2 matrix ``` Note that for the reshape command, the elements retain their index in the matrix which is counted column-wise.