Matlab(tm) Quick Reference

http://web.usna.navy.mil/~mecheng/DESIGN/CAD/MATLAB/matlab/matlab.html


                    A BRIEF LIST OF MATLAB COMMANDS

Some Basic Commands (Note command syntax is case-sensitive!)

     matlab    loads the program matlab into your workspace.
     quit      quits matlab, returning you to the operating system.
     exit      same as quit.
     who       lists all of the variables in your matlab workspace.
     whos      list the variables and describes their matrix size.
     clear     deletes all matrices from active workspace.
     clear x   deletes the matrix  x  from active workspace.
     ...       the ellipsis defining a line continuation is three
               successive periods.
     save      saves all the matrices defined in the current     
               session into the file, matlab.mat.
     load      loads contents of matlab.mat into current workspace.
     save filename  saves the contents of workspace into 
                    filename.mat
     save filename x y z
               saves the matrices x, y and z into the file titled
               filename.mat.
     load filename  loads the contents of filename into current
                    workspace; the file can be a binary (.mat) file
                    or an ASCII file.
     !         the ! preceding any unix command causes the unix
               command to be executed from matlab.

Commands involving functions

     inline    define a function, e.g.  f = inline('x^2')
     fplot     generate the graph of a function, e.g. fplot(f,[a,b])
               plots f (a string defn) over the interval [a,b]
     fzero     find the zero of a function, e.g.  fzero(f,x0), 
               computes zero of f near x0 or if x0 a vector then
               in the interval [x0_1, x0_2].

Commands Useful in Plotting.

     plot(x,y) creates an Cartesian plot of the vectors x & y.
     plot(y)   creates a plot of y vs. the numerical values of the
               elements in the y-vector.
     semilogx(x,y) plots log(x) vs y.
     semilogy(x,y)  plots x vs log(y)
     loglog(x,y)    plots log(x) vs log(y).
     grid      creates a grid on the graphics plot.
     title('text')  places a title at top of graphics plot.
     xlabel('text') writes 'text' beneath the x-axis of a plot.
     ylabel('text') writes 'text' beside the y-axis of a plot.
     text(x,y,'text')    writes 'text' at the location (x,y) .
     text(x,y,'text','sc') writes 'text' at point x,y assuming
                         lower left corner is (0,0) and upper
                         right corner is (1,1).
     gtext('text') writes text according to placement of mouse
     hold on   maintains the current plot in the graphics window
               while executing subsequent plotting     commands.
     hold off  turns OFF the 'hold on' option.
     polar(theta,r) creates a polar plot of the vectors r & theta
                    where theta is in radians.
     bar(x)    creates a bar graph of the vector x. (Note also
               the command stairs(y).)

     bar(x,y)  creates a bar-graph of the elements of the vector y,
               locating the bars according to the vector elements
               of 'x'. (Note also the command stairs(x,y).)
     hist(x)   creates a histogram. This differs from the bargraph
               in that frequency is plotted on the vertical axis.
     mesh(z)   creates a surface in xyz space where z is a matrix
               of the values of the function z(x,y). z can be
               interpreted to be the height of the surface above
               some xy reference plane.
     surf(z)   similar to mesh(z), only surface elements depict
               the surface rather than a mesh grid.
     contour(z)     draws a contour map in xy space of the function
                    or surface z.
     meshc(z)  draws the surface z with a contour plot beneath it.
     meshgrid  [X,Y]=meshgrid(x,y) transforms the domain specified
               by vectors x and y into arrays X and Y that can be
               used in evaluating functions for 3D mesh/surf plots.
     print     sends the contents of graphics window to printer.
     print filename -dps      writes the contents of current
               graphics to 'filename' in postscript format.


Equation Fitting

     polyfit(x,y,n) returns the coefficients of the n-degree
          polynomial for the vectors x and y. n must be at least 1
          larger than the length of the vectors x and y. If n+1 =
          length(x) the result is an interpolating polynomial. If
          n+1 > length(x) the result is a least-squares polynomial
          fit. The coefficients are stored in order with that of
          the highest order term first and the lowest order last.
     polyval(c,x)   calculates the values of the polynomial whose
          coefficients are stored in  c, calculating for every
          value of the vector x.

Data Analysis Commands

     max(x)    returns the maximum value of the elements in a
               vector or if x is a matrix, returns a row vector
               whose elements are the maximum values from each
               respective column of the matrix.
     min (x)   returns the minimum of x (see max(x) for details).
     mean(x)   returns the mean value of the elements of a vector
               or if x is a matrix, returns a row vector whose
               elements are the mean value of the elements from
               each column of the matrix.
     median(x) same as mean(x), only returns the median value.
     sum(x)    returns the sum of the elements of a vector or if x
               is a matrix, returns the sum of the elements from
               each respective column of the matrix.
     prod(x)   same as sum(x), only returns the product of
               elements.
     std(x)    returns the standard deviation of the elements of a
               vector or if x is a matrix, a row vector whose
               elements are the standard deviations of each
               column of the matrix.
     sort(x)   sorts the values in the vector x or the columns of
               a matrix and places them in ascending order. Note
               that this command will destroy any association that
               may exist between the elements in a row of matrix x.
     hist(x)   plots a histogram of the elements of vector, x. Ten
               bins are scaled based on the max and min values.
     hist(x,n) plots a histogram with 'n' bins scaled between the
               max and min values of the elements.
     hist((x(:,2))  plots a histogram of the elements of the 2nd
                    column from the matrix x.
     fliplr(x) reverses the order of a vector. If x is a matrix,
               this reverse the order of the columns in the matrix.
     flipud(x) reverses the order of a matrix in the sense of
               exchanging or reversing the order of the matrix
               rows. This will not reverse a row vector!
     reshape(A,m,n)      reshapes the matrix A into an mxn matrix
               from element (1,1) working column-wise.

SPECIAL MATRICES

     zeros(n)  creates an nxn matrix whose elements are zero.
     zeros(m,n)   creates a  m-row, n-column matrix of zeros.
     ones(n)   creates a n x n square matrix whose elements are 1's
     ones(m,n)' creates a mxn matrix whose elements are 1's.
     ones(A)   creates an m x n matrix of 1's, where m and n are 
               based on the size of an existing matrix, A. 
     zeros(A)  creates an mxn matrix of 0's, where m and n are
               based on the size of the existing matrix, A.
     eye(n)    creates the nxn identity matrix with 1's on the
               diagonal.

Miscellaneous Commands

     length(x) returns the number elements in a vector.
     size(x)   returns the size m(rows) and n(columns) of matrix x.
     rand      returns a random number between 0 and 1.
     randn     returns a random number selected from a normal
               distribution with a mean of 0 and variance of 1.
     rand(A)   returns a matrix of size A of random numbers.








ALGEBRAIC OPERATIONS IN MATLAB

Scalar Calculations. 
                         +         addition       
                         -         subtraction
                         *         multiplication
                         /         right division (a/b means a  b)
                         \         left division  (a\b means b  a)
                         ^         exponentiation



The precedence or order of the calculations included in a single
line of code follows the below order:
          Precedence                Operation
               1         parentheses
               2         exponentiation, left to right
               3         multiplication and division, left  right
               4         addition and subtraction, left  right

MATRIX ALGEBRA
     In matrix multiplication, the elements of the product, C, of
two matrices A*B is calculated from

          Cij =  (Aik * Bkj)   {summation over the double index k}

To form this sum, the number of columns of the first or left matrix
(A) must be equal to the number of rows in the second or right
matrix (B). The resulting product, matrix C, has an order for which
the number of rows equals the number of rows of the first (left)
matrix (A) and the product (C) has a number of columns equal to the
number of columns in the second (right) matrix (B). It is clear
that A*B IS NOT NECESSARILY EQUAL TO B*A! 

     The PRODUCT OF A SCALAR AND A MATRIX is a matrix in which
every element of the matrix has been multiplied by the scalar. 

ARRAY PRODUCTS

     Sometimes it is desired to simply multiply or divide each
element of an matrix by the corresponding element of another
matrix. These are called 'array operations" in 'matlab'. Array or
element-by-element operations are executed when the operator is
preceded by a '.' (period). Thus

     a .* b    multiplies each element of a by the respective
               element of b
     a ./ b    divides each element of a by the respective element
               of b
     a .\ b    divides each element of b by the respective element
               of a
     a .^ b    raise each element of a by the respective b element
     
TRANSPOSE OF A MATRIX

     x'        The transpose of a matrix is obtained by
               interchanging the rows and columns. The 'matlab'
               operator that creates the transpose is the single
               quotation mark, '.

INNER PRODUCT OF TWO VECTORS

     The inner product of two row vectors G1 and G2 is G1*G2'.
     The inner product of two column vectors H and J is H'*J.


OUTER PRODUCT OF TWO VECTORS

     If two row vectors exist, G1 and G2, the outer product is
simply

     G1' * G2       {Note G1' is nx1 and G2 is 1xn}

and the result is a square matrix in contrast to the scalar result
for the inner product. DON'T CONFUSE THE OUTER PRODUCT WITH THE
VECTOR PRODUCT IN MECHANICS! If the two vectors are column vectors,
the outer product must be formed by the product of one vector times
the transpose of the second!



SOLUTION TO SIMULTANEOUS EQUATIONS

     Using the Matrix Inverse

     inv(a)    returns the inverse of the matrix  a.
               If ax=b is a matrix equation and  a  is the
               coefficient matrix, the solution  x  is  x=inv(a)*b.

     Using Back Substitution

     a\b       returns a column vector solution for the matrix
               equation  ax=b where a is a coefficient matrix.
     b/a       returns a row vector solution for the matrix
               equation  xa=b where a is a coefficient matrix.