## Table of Contents

MATLAB Reference Guide
Quick Reference Tables
General Purpose Commands
Operators and Special Characters
Language Constructs and Debugging
Matrices and Matrix Manipulation

Elementary Matrices
Specialized Matrices

Math Functions

Elementary Functions
Specialized Math Functions

Matrix Functions - Numerical Linear Algebra
Data Analysis and Fourier Transform Functions
Polynomial and Interpolation Functions
Function Functions
Sparse Matrix Functions

## Quick Reference Tables

MATLAB provides 20 main categories of functions. Some of MATLAB's functions are built into the interpreter, while others take the form of
M-files. The M-file functions, and in the case of the built-in functions, M-files containing only help text, are organized into 20 directories, each containing the files associated with a category. The MATLAB command help displays an online table of these main categories.

    -----------------------------------------------------------------------------------------
    MATLAB's Main Categories of Functions
    -----------------------------------------------------------------------------------------
    color                                  Color control and lighting model functions.
    datafun                                Data analysis and Fourier transform functions.
    demos                                  Demonstrations and samples.
    elfun                                  Elementary math functions.
    elmat                                  Elementary matrices and matrix manipulation.
    funfun                                 Function functions -- nonlinear numerical methods.
    general                                General purpose commands.
    graphics                               General purpose graphics functions.
    iofun                                  Low-level file I/O functions.
    lang                                   Language constructs and debugging.
    matfun                                 Matrix functions -- numerical linear algebra.
    ops                                    Operators and special characters.
    plotxy                                 Two dimensional graphics.
    plotxyz                                Three dimensional graphics.
    polyfun                                Polynomial and interpolation functions.
    sparfun                                Sparse matrix functions.
    specfun                                Specialized math functions.
    specmat                                Specialized matrices.
    sounds                                 Sound processing functions.
    strfun                                 Character string functions.
    -----------------------------------------------------------------------------------------

The following pages contain tables of functions within each of these specific areas. If you execute help on one of the directory names listed on the left side of this table, MATLAB displays an online version of the tables within that area.

## General Purpose Commands

    -------------------------------------------------------------------------------
    Managing Commands and Functions
    -------------------------------------------------------------------------------
    demo                             Run demos.
    expo                             Run MATLAB EXPO demonstration program.
    help                             Online documentation.
    info                             Information about MATLAB and The MathWorks.
    lasterr                          Last error message generated.
    lookfor                          Keyword search through the help entries.
    path                             Control MATLAB's search path.
    subscribe                        Become a subscribing MATLAB user.
    type                             List M-file.
    ver                              Current MATLAB and toolbox versions.
    version                          Current MATLAB version number.
    what                             Directory listing of M-, MAT- and MEX-files.
    whatsnew                         Display README files for MATLAB and toolboxes.
    which                            Locate functions and files.
    -------------------------------------------------------------------------------

    --------------------------------------------------------------------------------
    Managing Variables and the Workspace
    --------------------------------------------------------------------------------
    clear                                 Clear variables and functions from memory.
    disp                                  Display matrix or text.
    length                                Length of vector.
    load                                  Retrieve variables from disk.
    pack                                  Consolidate workspace memory.
    save                                  Save workspace variables to disk.
    size                                  Size of matrix.
    who                                   List current variables.
    whos                                  List current variables, long form.
    --------------------------------------------------------------------------------

    --------------------------------------------------------------------------------------------------
    Working with Files and the Operating Environment
    --------------------------------------------------------------------------------------------------
    cd                                                Change current working directory.
    cedit                                             Set command line editing parameters (UNIX only).
    delete                                            Delete file.
    diary                                             Save text of MATLAB session.
    dir                                               Directory listing.
    getenv                                            Get environment value.
    hostid                                            MATLAB server host identification number.
    ls                                                Directory listing.
    matlabroot                                        Root directory of MATLAB installation.
    pwd                                               Show current working directory.
    tempdir                                           Name of system temporary directory.
    tempname                                          Unique name for temporary file.
    terminal                                          Set graphics terminal type.
    unix                                              Execute operating system command; return result.
    !                                                 Execute operating system command.
    --------------------------------------------------------------------------------------------------

    -----------------------------------------------------------------------
    Controlling the Command Window
    -----------------------------------------------------------------------
    clc                             Clear command window.
    echo                            Echo commands inside script files.
    format                          Set output format.
    home                            Send cursor home.
    more                            Control paged output in command window.
    -----------------------------------------------------------------------

    --------------------------------------------------------------------------
    Starting and Quitting from MATLAB
    --------------------------------------------------------------------------
    matlabrc                           Master startup M-file.
    quit                               Terminate MATLAB.
    startup                            M-file executed when MATLAB is invoked.
    --------------------------------------------------------------------------

## Operators and Special Characters

    -------------------------------------------------------------
    Operators and Special Characters
    -------------------------------------------------------------
    +                                 Plus.
    --                                Minus.
    *                                 Matrix multiplication.
    .*                                Array multiplication.
    ^                                 Matrix power.
    .^                                Array power.
    kron                              Kronecker tensor product.
    \                                 Backslash or left division.
    /                                 Slash or right division.
    ./                                Array division.
    :                                 Colon.
    ()                                Parentheses.
    []                                Brackets.
    .                                 Decimal point.
    ..                                Parent directory.
    ...                               Continuation.
    ,                                 Comma.
    ;                                 Semicolon.
    %                                 Comment.
    !                                 Exclamation point.
    '                                 Transpose and quote.
    .'                                Nonconjugated transpose.
    =                                 Assignment.
    ==                                Equality.
    <>                          Relational operators.
    &                             Logical AND.
    |                                 Logical OR.
    ~                                 Logical NOT.
    xor                               Logical EXCLUSIVE OR.
    -------------------------------------------------------------

    -----------------------------------------------------------
    Logical Functions
    -----------------------------------------------------------
    all                True if all elements of vector are true.
    any                True if any element of vector is true.
    exist              Check if variables or functions exist.
    find               Find indices of nonzero elements.
    finite             True for finite elements.
    isempty            True for empty matrix.
    ishold             True if hold is on.
    isieee             True for IEEE floating-point arithmetic.
    isinf              True for infinite elements.
    isletter           True for alphabetic character.
    isnan              True for Not-A-Number.
    isreal             True if all matrix elements are real.
    issparse           True for sparse matrix.
    isstr              True for text string.
    -----------------------------------------------------------

## Language Constructs and Debugging

    ------------------------------------------------------------------------
    MATLAB as a Programming Language
    ------------------------------------------------------------------------
    eval                              Execute string with MATLAB expression.
    feval                             Execute function specified by string.
    function                          Add new function.
    global                            Define global variable.
    nargchk                           Validate number of input arguments.
    ------------------------------------------------------------------------

    ------------------------------------------------------------------
    Control Flow
    ------------------------------------------------------------------
    break         Terminate execution of loop.
    else          Used with if.
    elseif        Used with if.
    end           Terminate the scope of for, while and if statements.
    error         Display message and abort function.
    for           Repeat statements a specific number of times.
    if            Conditionally execute statements.
    return        Return to invoking function.
    while         Repeat statements an indefinite number of times.
    ------------------------------------------------------------------

    ---------------------------------------------------------------
    Interactive Input
    ---------------------------------------------------------------
    input              Prompt for user input.
    keyboard           Invoke keyboard as if it were a script file.
    menu               Generate menu of choices for user input.
    pause              Wait for user response.
    ---------------------------------------------------------------

    ------------------------------------------
    Debugging
    ------------------------------------------
    dbclear    Remove breakpoint.
    dbcont     Resume execution.
    dbdown     Change local workspace context.
    dbquit     Quit debug mode.
    dbstack    List who called whom.
    dbstatus   List all breakpoints.
    dbstep     Execute one or more lines.
    dbstop     Set breakpoint.
    dbtype     List M-file with line numbers.
    dbup       Change local workspace context.
    mexdebug   Enable MEX-file debugging.
    ------------------------------------------

## Matrices and Matrix Manipulation

### Elementary Matrices

    ----------------------------------------------------------------------
    Elementary Matrices
    ----------------------------------------------------------------------
    eye                  Identity matrix.
    gallery              Test matrices - matrix condition and eigenvalues.
    linspace             Linearly spaced vector.
    logspace             Logarithmically spaced vector.
    meshgrid             X and Y arrays for 3-D plots.
    ones                 Ones matrix.
    rand                 Uniformly distributed random numbers.
    randn                Normally distributed random numbers.
    zeros                Zeros matrix.
    :                    Regularly spaced vector.
    ----------------------------------------------------------------------

    ---------------------------------------------------------------------
    Special Variables and Constants
    ---------------------------------------------------------------------
    ans                              Most recent answer.
    computer                         Computer type.
    eps                              Floating-point relative accuracy.
    flops                            Count of floating-point operations.
    i, j                             Imaginary unit.
    inf                              Infinity.
    NaN                              Not-a-Number.
    nargin                           Number of function input arguments.
    nargout                          Number of function output arguments.
    pi                               3.1415926535897....
    realmax                          Largest floating-point number.
    realmin                          Smallest floating-point number
    ---------------------------------------------------------------------

    ------------------------------------------
    Time and Dates
    ------------------------------------------
    clock           Wall clock.
    cputime         Elapsed CPU time.
    date            Calendar.
    etime           Elapsed time function.
    tic, toc        Stopwatch timer functions.
    ------------------------------------------

    -------------------------------------------------------------------
    Matrix Manipulation
    -------------------------------------------------------------------
    diag                 Create or extract diagonals.
    fliplr               Flip matrix in the left/right direction.
    flipud               Flip matrix in the up/down direction.
    isreal               True for matrix containing real elements only.
    reshape              Change size.
    rot90                Rotate matrix 90 degrees.
    tril                 Extract lower triangular part.
    triu                 Extract upper triangular part.
    :                    Index into matrix, rearrange matrix.
    -------------------------------------------------------------------

### Specialized Matrices

    ----------------------------------------------------------------
    Specialized Matrices
    ----------------------------------------------------------------
    compan                Companion matrix.
    hadamard              Hadamard matrix.
    hankel                Hankel matrix.
    hilb                  Hilbert matrix.
    invhilb               Inverse Hilbert matrix.
    magic                 Magic square.
    pascal                Pascal matrix.
    rosser                Classic symmetric eigenvalue test problem.
    toeplitz              Toeplitz matrix.
    vander                Vandermonde matrix.
    wilkinson             Wilkinson's eigenvalue test matrix.
    ----------------------------------------------------------------

## Math Functions

### Elementary Functions

    ---------------------------------------------------------
    Elementary Math Functions
    ---------------------------------------------------------
    abs                        Absolute value.
    acos                       Inverse cosine.
    acosh                      Inverse hyperbolic cosine.
    acot                       Inverse cotangent.
    acoth                      Inverse hyperbolic cotangent.
    acsc                       Inverse cosecant.
    acsch                      Inverse hyperbolic cosecant.
    angle                      Phase angle.
    asec                       Inverse secant.
    asech                      Inverse hyperbolic secant.
    asin                       Inverse sine.
    asinh                      Inverse hyperbolic sine.
    atan                       Inverse tangent.
    atan2                      Four quadrant inverse tangent.
    atanh                      Inverse hyperbolic tangent.
    ceil                       Round towards plus infinity.
    conj                       Complex conjugate.
    cos                        Cosine.
    cosh                       Hyperbolic cosine.
    cot                        Cotangent.
    coth                       Hyperbolic cotangent.
    csc                        Cosecant.
    csch                       Hyperbolic cosecant.
    exp                        Exponential.
    fix                        Round towards zero.
    floor                      Round towards minus infinity.
    gcd                        Greatest common divisor.
    imag                       Complex imaginary part.
    lcm                        Least common multiple.
    log                        Natural logarithm.
    log10                      Common logarithm.
    real                       Complex real part.
    rem                        Remainder after division.
    round                      Round towards nearest integer.
    sec                        Secant.
    sech                       Hyperbolic secant.
    sign                       Signum function.
    sin                        Sine.
    sinh                       Hyperbolic sine.
    sqrt                       Square root.
    tan                        Tangent.
    tanh                       Hyperbolic tangent.
    ---------------------------------------------------------

### Specialized Math Functions

    -------------------------------------------------------------------------
    Specialized Math Functions
    -------------------------------------------------------------------------
    bessel                      Bessel functions.
    besseli                     Modified Bessel functions of the first kind.
    besselj                     Bessel functions of the first kind.
    besselk                     Modified Bessel functions of the second kind.
    bessely                     Bessel functions of the second kind.
    beta                        Beta function.
    betainc                     Incomplete beta function.
    betaln                      Logarithm of beta function.
    ellipj                      Jacobi elliptic functions.
    ellipke                     Complete elliptic integral.
    erf                         Error function.
    erfc                        Complementary error function.
    erfcx                       Scaled complementary error function.
    erfinv                      Inverse error function.
    expint                      Exponential integral.
    gamma                       Gamma function.
    gammainc                    Incomplete gamma function.
    gammaln                     Logarithm of gamma function.
    legendre                    Associated Legendre functions.
    log2                        Dissect floating point numbers.
    pow2                        Scale floating point numbers.
    rat                         Rational approximation.
    rats                        Rational output.
    -------------------------------------------------------------------------

## Matrix Functions - Numerical Linear Algebra

    ----------------------------------------------------------------
    Matrix Analysis
    ----------------------------------------------------------------
    cond             Matrix condition number.
    det              Determinant.
    etree            Elimination tree of a matrix.
    norm             Matrix or vector norm.
    null             Null space.
    orth             Orthogonalization.
    rcond            LINPACK reciprocal condition estimator.
    rank             Number of linearly independent rows or columns.
    rref             Reduced row echelon form.
    subspace         Angle between two subspaces.
    trace            Sum of diagonal elements.
    ----------------------------------------------------------------

    --------------------------------------------------------------------
    Linear Equations
    --------------------------------------------------------------------
    chol              Cholesky factorization.
    inv               Matrix inverse.
    lscov             Least squares in the presence of known covariance.
    lu                Factors from Gaussian elimination.
    nnls              Non-negative least-squares.
    pinv              Pseudoinverse.
    qr                Orthogonal-triangular decomposition.
    \ and /               Linear equation solution.
    --------------------------------------------------------------------

    -----------------------------------------------------------------------------------
    Eigenvalues and Singular Values
    -----------------------------------------------------------------------------------
    balance                          Diagonal scaling to improve eigenvalue accuracy.
    cdf2rdf                          Complex diagonal form to real block diagonal form.
    eig                              Eigenvalues and eigenvectors.
    hess                             Hessenberg form.
    poly                             Characteristic polynomial.
    qz                               Generalized eigenvalues.
    rsf2csf                          Real block diagonal form to complex diagonal form.
    schur                            Schur decomposition.
    svd                              Singular value decomposition.
    -----------------------------------------------------------------------------------

    ---------------------------------------------------
    Matrix Functions
    ---------------------------------------------------
    expm              Matrix exponential.
    funm              Evaluate general matrix function.
    logm              Matrix logarithm.
    sqrtm             Matrix square root.
    ---------------------------------------------------

    ----------------------------------------------------------
    Low Level Functions
    ----------------------------------------------------------
    qrdelete             Delete columns from QR factorization.
    qrinsert             Insert columns into QR factorization.
    ----------------------------------------------------------

## Data Analysis and Fourier Transform Functions

    -----------------------------------------------------------------
    Basic Operations
    -----------------------------------------------------------------
    cumprod           Cumulative product of elements.
    cumsum            Cumulative sum of elements.
    max               Largest component.
    mean              Average or mean value.
    median            Median value.
    min               Smallest component.
    prod              Product of elements.
    sort              Sort in ascending order.
    std               Standard deviation.
    sum               Sum of elements.
    trapz             Numerical integration using trapezoidal method.
    -----------------------------------------------------------------

    -------------------------------------------------------------------
    Finite Differences
    -------------------------------------------------------------------
    del2                Five-point discrete Laplacian.
    diff                Difference function and approximate derivative.
    gradient            Approximate gradient.
    -------------------------------------------------------------------

    --------------------------------------
    Correlation
    --------------------------------------
    corrcoef     Correlation coefficients.
    cov          Covariance matrix.
    --------------------------------------

    ---------------------------------------------------------------------
    Filtering and Convolution
    ---------------------------------------------------------------------
    conv                       Convolution and polynomial multiplication.
    conv2                      Two-dimensional convolution.
    deconv                     Deconvolution and polynomial division.
    filter                     One-dimensional digital filter.
    filter2                    Two-dimensional digital filter.
    ---------------------------------------------------------------------

    -----------------------------------------------------------------------
    Fourier Transforms
    -----------------------------------------------------------------------
    abs                 Magnitude.
    angle               Phase angle.
    cplxpair            Sort numbers into complex conjugate pairs.
    fft                 Discrete Fourier transform.
    fft2                Two-dimensional discrete Fourier transform.
    fftshift            Move zeroth lag to center of spectrum.
    ifft                Inverse discrete Fourier transform.
    ifft2               Two-dimensional inverse discrete Fourier transform.
    nextpow2            Next higher power of 2.
    unwrap              Remove phase angle jumps across 360\xa1  boundaries.
    -----------------------------------------------------------------------

    ---------------------------------------
    Vector Functions
    ---------------------------------------
    cross             Vector cross product.
    dot               Vector dot product.
    ---------------------------------------

## Polynomial and Interpolation Functions

    -------------------------------------------------------
    Polynomials
    -------------------------------------------------------
    conv         Multiply polynomials.
    deconv       Divide polynomials.
    poly         Construct polynomial with specified roots.
    polyder      Differentiate polynomial.
    polyeig      Solve polynomial eigenvalue problem.
    polyfit      Fit polynomial to data.
    polyval      Evaluate polynomial.
    polyvalm     Evaluate polynomial with matrix argument.
    residue      Partial-fraction expansion (residues).
    roots        Find polynomial roots.
    -------------------------------------------------------

    ---------------------------------------------------------------------
    Data Interpolation
    ---------------------------------------------------------------------
    griddata            Data gridding.
    interp1             One-dimensional interpolation (1-D table lookup).
    interp2             Two-dimensional interpolation (2-D table lookup).
    interpft            One-dimensional interpolation using FFT method.
    ---------------------------------------------------------------------

## Function Functions

    ---------------------------------------------------------------------------------------------------
    Function Functions - Nonlinear Numerical Methods
    ---------------------------------------------------------------------------------------------------
    fmin                                              Minimize function of one variable.
    fmins                                             Minimize function of several variables.
    fplot                                             Plot function.
    fzero                                             Find zero of function of one variable.
    ode23                                             Solve differential equations, low order method.
    ode45                                             Solve differential equations, high order method.
    quad                                              Numerically evaluate integral, low order method.
    quad8                                             Numerically evaluate integral, high order method.
    ---------------------------------------------------------------------------------------------------

## Sparse Matrix Functions

    ----------------------------------------------------------------
    Elementary Sparse Matrices
    ----------------------------------------------------------------
    spdiags                     Sparse matrix formed from diagonals.
    speye                       Sparse identity matrix.
    sprandn                     Sparse random matrix.
    sprandsym                   Sparse symmetric random matrix.
    ----------------------------------------------------------------

    ---------------------------------------------------------------------------
     Full to Sparse Conversion
    ---------------------------------------------------------------------------
    find                        Find indices of nonzero entries.
    full                        Convert sparse matrix to full matrix.
    sparse                      Create sparse matrix from nonzeros and indices.
    spconvert                   Convert from sparse matrix external format.
    ---------------------------------------------------------------------------

    -------------------------------------------------------------------------------------------------
    Working with Nonzero Entries of Sparse Matrices
    -------------------------------------------------------------------------------------------------
    issparse                                         True if matrix is sparse.
    nnz                                              Number of nonzero entries.
    nonzeros                                         Nonzero entries.
    nzmax                                            Amount of storage allocated for nonzero entries.
    spalloc                                          Allocate memory for nonzero entries.
    spfun                                            Apply function to nonzero entries.
    spones                                           Replace nonzero entries with ones.
    -------------------------------------------------------------------------------------------------

    --------------------------------------------------------------
    Visualizing Sparse Matrices
    --------------------------------------------------------------
    gplot                        Plot graph, as in "graph theory."
    spy                          Visualize sparsity structure.
    --------------------------------------------------------------

    ------------------------------------------------------------
    Reordering Algorithms
    ------------------------------------------------------------
    colmmd                 Column minimum degree.
    colperm                Order columns based on nonzero count.
    dmperm                 Dulmage-Mendelsohn decomposition.
    randperm               Random permutation vector.
    symmmd                 Symmetric minimum degree.
    symrcm                 Reverse Cuthill-McKee ordering.
    ------------------------------------------------------------

    ------------------------------------------------------------
    Norm, Condition Number, and Rank
    ------------------------------------------------------------
    condest                           Estimate 1-norm condition.
    normest                           Estimate 2-norm.
    sprank                            Structural rank.
    ------------------------------------------------------------

    ---------------------------------------------------------
    Miscellaneous
    ---------------------------------------------------------
    spaugment      Form least squares augmented system.
    spparms        Set parameters for sparse matrix routines.
    symbfact       Symbolic factorization analysis.
    ---------------------------------------------------------