manjrekarom · June 5, 2017 16:15 · Feb 24, 2014 · Nov 5, 2013
diff --git a/octave.md b/octave.md
@@ -96,6 +96,11 @@ Let `A` be the matrix: `A = [1 2; 3 4; 5 6]`
 
 The semicolon indicates a new row and a space or comma is a new column. Instead of typing a semicolon it is also possible to hit `enter`.
 
+Output last element in Matrix
+
+	>> A(end, end)
+	ans = 6
+
 #### Display Data
 
 	% show number in first row and second column

diff --git a/octave.md b/octave.md
@@ -0,0 +1,305 @@
+Octave CheatSheet
+-----------------
+
+> GNU Octave is a high-level interpreted language, primarily intended for numerical computations.  
+> (via [GNU Octave](http://www.gnu.org/software/octave/))
+
+### Basics
+
+* not equal `~=`
+* logical AND `&&`
+* logical OR `||`
+* logical XOR `xor(1,0)`
+
+A semicolon `;` at the end of a line will suppress the output
+
+`v = 1:5` creates a 1x5 Matrix (linear vector) with the numbers one to five.
+`v = 1:0.1:2` also creates a vector but with the numbers from one to two with a step size of 0.1.
+
+	>> v = 1:5
+	v =
+
+		1   2   3   4   5 
+
+	>> v = 1:0.1:2
+	v =
+
+    1.0000    1.1000    1.2000    1.3000    1.4000    1.5000    1.6000    1.7000    1.8000    1.9000    2.0000
+
+To display the 5th number of this vectors use `v(5)`. _Beware that ocatve is 1 based_.
+Displaying a range of numbers use `v(3:5)` to display the 3rd, 4th, and 5th number.
+
+### Useful functions
+
+`help _function name_` will give you the man page of this function.
+
+`ones(x [, y])` creates a matrix with ones. If only `x` is provided it is a squared matrix of size `x`. If `y` is provides it has the size x cross y.
+
+`zeros(x [, y])` behaves the same as `ones()` but will give a zero-matrix.
+
+`rand(x [, y])` Return a matrix with random elements uniformly distributed on the interval (0, 1).
+
+`randn(x [, y])` Return a matrix with normally distributed random elements having zero mean and variance one.  The arguments are handled the same as the arguments for `rand`.
+
+`hist(x [, y])` Produce histogram counts of plots. `y` is the number of buckets.
+
+`eye(x [, y]])` Produces an identity matrix.
+
+`size(A [, DIM])` Return the number of rows and colums of A.  
+	`DIM = 1` number rows  
+	`DIM = 2` number columns
+
+`length(A)` Return the _length_ of the object A. For Matrix objects, the length is the number of rows or columns, whichever is greater (this odd definition is used for compatibility with MATHLAB).
+
+	log(a)		% natural logarithm
+	abs(a)		% absolute value
+	sign(a)		% signum function
+	exp(a)		% compute e^a
+
+`who` Lists currently defined varibales matchin the given pattern.
+`whos` Provide detailed information on currently defined variables.
+
+`sum(a)`, `sum(A,1)` sums up all columns.
+`sum(A,2)` sums up all rows
+`prod(a)` takes the product of each column
+
+`floor(a)` rounds down
+`ceil(a)` rounds up
+
+`clear` will clear all variables or only the ones who are named.
+
+### Save and Load Data
+
+You can save and load data in octave easily with the two commands `save` and `load`.
+
+To save a specific variable `v` to the file `filename.dat`
+
+	save filename.dat v; % save data of v in binary format
+	save filename.txt v --ascii % save data of v in readable version
+
+Loading data is as simple as saving.
+
+	% both are equivalent
+	load filename.dat
+	load('filename.dat')
+
+The file will be saved in the current directory and will be loaded from the current dir.
+
+### Matrixes
+
+Let `A` be the matrix: `A = [1 2; 3 4; 5 6]`
+
+	A =
+		1	2
+		3	4
+		5	6
+
+The semicolon indicates a new row and a space or comma is a new column. Instead of typing a semicolon it is also possible to hit `enter`.
+
+#### Display Data
+
+	% show number in first row and second column
+	>> A(1,2)
+	ans = 2
+
+	% show second row: colon means 'all'
+	>> A(2,:)
+	ans =
+		3	4
+
+	% show second column
+	>> A(:,2)
+	ans =
+		2
+		4
+		6
+
+#### Assign new Data
+
+	% replace second column by 10, 11, and 12
+	>> A(:,2) = [10,11,12]
+	% in this case it doesn't matter if comma or semicolon is used
+	>> A(:,2) = [10;11;12]
+
+#### Concatinating Matrixes
+
+	>> B = [20 21; 22 23; 24 25]
+	>> C = [A B] % A B
+	ans =
+
+    	1   2
+    	3   4
+    	5  	6
+    	20  21
+		22  23
+		24	25
+
+	>> D = [A; B] % A append B
+	ans =
+		1	2	20	21
+		3	4	22	23
+		5	6	24	25
+
+#### Transpose a matrix or a vector
+
+	>> A'
+	ans =
+		1	3	5
+		2	4	6
+
+#### max values and find()
+
+	>> max(magic(4)) % returns a 1x4 vector with max-values per column
+	ans =
+		16	14	15	13
+
+	>> [val, ind] = max(magic(4)) % retuns 2 vectors: 1. values, 2. indexes
+	val =
+		16	14	15	13
+	ind =
+		1	4	4	1
+
+To find the largest value in a matrix you can either chain to `max()` functions or take the complete matrix.
+
+	>> max(max(A)); % Both are equivalent
+	>> max(A(:))
+	ans =
+		6
+
+You can search thru matrixes and vectors with a condition
+
+	>> find(A < 3) % returns a index-vector where number < 3
+	ans =
+		1
+		4
+
+#### Flipping a matrix
+
+Sometimes it is necessary to flip a matrix upsidedown.
+
+	>> flipud(A)
+	ans =
+		5	6
+		3	4
+		1	2
+
+_Hint: useful in combination with the identity matrix `flipud(eye(4))`_
+
+#### Sum of diagonals in a square matrix
+
+Example: A magic matrix is a square matrix where the sum of rows, columns and diagonals are the same result. Let's check the sum of diagonals
+
+	>> M = magic(4);
+	>> sum(sum(M.*eye(4))) % sum of diagonal top left to bottom right
+	ans = 34
+
+	>> sum(sum(M.* flipud(eye(4) ))) % sum of diagonal bottom left to top right
+	ans = 34
+
+#### Inverse matrix
+
+There exists serveral ways to create a inverse matrix in octave
+
+	>> inv(M)			% warning: yes
+	>> pinv(M)			% warning: no
+	>> M^-1				% warning: no
+	>> M\eye(size(M))	% warning: yes
+
+### Ploting
+
+`plot(x, y)` plot a graph with `x` as x-axis and `y` as y-axis. `x` and `y` has to match in length.
+
+`hold on` will plot updated in the current plot instead of replace the current plot.
+
+`plot(x, y2, 'r')` will plot a graph in red.
+
+`axis([a b c d])` X-axis will start at `a` and goes to `b`, and Y-axis will start from `c` and goes to `d`. Example `axis([0.5 1 -1 1])`
+
+`clf;` clear figure
+
+`imagesc(A)` grid of colors for matrix
+`colorbar` display colorbar, kind of legend
+`colormap gray` display only gray-scale
+
+Example: `imagesc(A), colorbar, colormap gray;`
+
+#### Labels
+
+`xlabel('Zoidberg')`, `ylabel('Bender')`, `legend('fry', 'lila')`, `title('Futurama')`
+
+`print -dpng 'myPlot.png'` export plot as PNG file. For other format see `help plot`
+
+`close` close the plot, as simple as that.
+
+`figure(1); plot(x, y)` plot graph as _figure 1_
+`figure(2); plot(x, y2)` plot graph as _figure 2_
+
+`subplot(x,y,POS);` plot multiple graphs in one windows as a X-by-Y grid at position `POS`
+
+	>> subplot(1,2,1);
+	>> plot(x, y);
+	>> subplot(1,2,2);
+	>> plot(x, y2);
+
+
+
+### Functions & control statements
+
+Functions are saved in files with the file-ending `.m` for MATHLAB. The syntax is quite simple:
+
+	function y = function_name(x)
+		y = x^2;
+
+	% y is the return value
+	% x is a parameter
+	% is also possible to return multiple values
+
+	function [y1, y2] = function_name(x)
+		y1 = x^2
+		y2 = x^3
+
+Call your function in octave like `function_name(5)`. You have to be in the same dir as the file or add it to your search-path (`addpath()`).
+
+`for`- and `while`-loops are easy and useful in octave.
+
+	>> for i=1:10
+	>>		disp(i)
+	>> end;
+
+	>> i = 1;
+	>> while (i ~= 10)
+	>>		disp(i);
+	>>		i = i+1;
+	>> endwhile;
+
+It is also possible to use `if`-conditions
+
+	% i = 10
+	>> if (i == 10)
+	>>		sprintf('yes')
+	>> else
+	>> 		sprintf('no')
+	>> endif
+	ans = yes
+
+
+### Various
+
+The following commands can be used within octave:
+
+* `cd`
+* `pwd`
+* `ls [-la]`
+* `dir`
+
+It is possible to change octave's prompt. Use `PS1('>> ');` to change the promt to `>> `
+
+`disp(a);` will display the variable `a`. Useful in loops or conditions.
+
+`magic(x)` Create an N-by-N magic square.
+
+For more controll in displaying stuff use `sprintf('%i', a);`. It follows the C-standard.
+
+`format long` or `format short` adjusts the length of output in octave.
+
+`addpath('_path_')` will add a path to the search-path for octave. I.e. Octave will also look in this path for functions and files.
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