Basic matlab commands need to learn

MATRICES COMMANDS

1. 1.      Sum(a)
2. 2.      A’
3. 3.      Sum(a’)’
4. 4.      Diag(A)
5. 5.      Fliplr(a)
6. 6.      Diag(fliplr(a))
7. 7.      A(4,2)=a(8)
8. 8.      To add an element,
9. 9.      A(4,5)=17; than 17= a(20)

10.  1:10 = 1 2 3 4 5 6 7 8 9 10

11.  A(1:3,4) refers to first 3 elements of 4th column of matrix (a)

12.  A(:,end) refers to sum of all the elements of last column of a

13.  0 : pi/4 : 2*pi

ans =  0    0.7854    1.5708    2.3562    3.1416    3.9270    4.7124    5.4978    6.2832

14.  Magic function creates a square matrix automatically that has magic numbers, i.e all its rows and columns add upto same no., eg

B = magic(4)

B =

    16     2     3    13

     5    11    10     8

     9     7     6    12

     4    14    15     1

15.  Swapping of 2 columns of a matrix b, a = b(:,[1 3 2 4])

A =

    16     3     2    13

     5    10    11     8

     9     6     7    12

     4    15    14     1

This is Durer’s engraving matrix

16.  Elementary matrices

    zeros       - Zeros array.

    ones        - Ones array.

    eye         - Identity matrix.

    repmat      - Replicate and tile array.

    rand        - Uniformly distributed random numbers.

    randn       - Normally distributed random numbers.

    linspace    - Linearly spaced vector.

    logspace   - Logarithmically spaced vector.

    freqspace  - Frequency spacing for frequency response.

    meshgrid    - X and Y arrays for 3-D plots.

    accumarray  - Construct an array with accumulation.

    :           - Regularly spaced vector and index into matrix.

17.   Basic array information

    size        - Size of array.

    length      - Length of vector.

    ndims       - Number of dimensions.

    numel       - Number of elements.

    disp        - Display matrix or text.

    isempty     - True for empty array.

    isequal     - True if arrays are numerically equal.

    isequalwithequalnans - True if arrays are numerically equal.

1. 18.    Matrix manipulation

    cat         - Concatenate arrays.

    reshape     - Change size.

    diag        - Diagonal matrices and diagonals of matrix.

    blkdiag     - Block diagonal concatenation.

    tril        - Extract lower triangular part.

    triu        - Extract upper triangular part.

    fliplr      - Flip matrix in left/right direction.

    flipud      - Flip matrix in up/down direction.

    flipdim     - Flip matrix along specified dimension.

    rot90       - Rotate matrix 90 degrees.

    :           - Regularly spaced vector and index into matrix.

    find        - Find indices of nonzero elements.

    end         - Last index.

    sub2ind     - Linear index from multiple subscripts.

    ind2sub     - Multiple subscripts from linear index.

19.   Multi-dimensional array functions

    ndgrid      - Generate arrays for N-D functions and interpolation.

    permute     - Permute array dimensions.

    ipermute    - Inverse permute array dimensions.

    shiftdim    - Shift dimensions.

    circshift   - Shift array circularly.

    squeeze     - Remove singleton dimensions.

20.  Array utility functions

    isscalar    - True for scalar.

    isvector    - True for vector.

21.  Specialized matrices

    compan      - Companion matrix.

    gallery     - Higham test matrices.

    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.

EXPRESSIONS

Like most other programming languages, MATLAB provides mathematical expressions, but unlike most programming languages, these expressions involve entire matrices. The building blocks of expressions are

Variables, Numbers, Operators, Functions

MATLAB is case sensitive

1. Variable: num_students = 25 creates a 1-by-1 matrix named num_students and stores the value 25 in its single element
2. Numbers: MATLAB uses conventional decimal notation, with an optional decimal point and leading plus or minus sign, for numbers. Scientific notation uses the letter e to specify a power-of-ten scale factor. Imaginary numbers use either i or j as a suffix. Some examples of legal numbers are

3                            -99                 0.0001

9.6397238      1.60210e-20         6.02252e23

1i                       -3.14159j           3e5i

1. Operators: Expressions use familiar arithmetic operators and precedence rules.

+   Addition

-    Subtraction

*   Multiplication

/    Division

\    Left division (described in "Matrices and Linear Algebra" in the MATLAB    documentation)

^   Power

'    Complex conjugate transpose

( )  Specify evaluation order

OPERATORS

Converting a character value to hexadecimal value, we use double:

Eg. S = ‘ A B C D’

X = double(S)

Returns:

X = 65    32    66    32 ( ASCII characters of A B C and D)

And to convert numbers to strings, use keyword: char

Eg.  X = 65

S = char(x)

Returns S = ‘A’

Arithmetic Operations:

+Plus

-Minus

.Decimal point

=Assignment

*Matrix multiplication

 /Matrix right division

 \Matrix left division

 ^Matrix power

 'Matrix transpose

 .*Array multiplication (element-wise)

 ./Array right division (element-wise)

 .\Array left division (element-wise)

 .^Array power (element-wise)

 .'Array transpose

Bitwise Operations

Bitand Bit-wise AND

 Bitcmp Bit-wise complement

 Bitor Bit-wise OR

 bitmax Maximum floating-point integer

 bitset Set bit at specified position

 bitshift Bit-wise shift

 bitget Get bit at specified position bit

 xor Bit-wise XOR

Relational Operators

< Less than

 > Greater than

 >= Greater than or equal to

 == Equal to

 ~= Not equal to

LOGICAL OPERATORS

&& Logical AND

|| Logical OR

 & Logical AND for arrays

 | Logical OR for arrays

 ~ Logical NOT

all Test to determine if all elements are nonzero

 any Test for any nonzero elements

 false False array

find Find indices and values of nonzero elements

 is* Detect state

 isa Determine if item is object of given class

 iskeyword Determine if string is MATLAB keyword

 isvarname Determine if string is valid variable name

 logical Convert numeric values to logical

true True array

xor Logical EXCLUSIVE OR

Elementary math functions

1. 1.        Trigonometric.

    sin         - Sine

    sind        - Sine of argument in degrees.

    sinh        - Hyperbolic sine.

    asin        - Inverse sine.

    asind       - Inverse sine, result in degrees.

    asinh       - Inverse hyperbolic sine.

    cos         - Cosine.

    cosd        - Cosine of argument in degrees.

    cosh        - Hyperbolic cosine.

    acos        - Inverse cosine.

    acosd       - Inverse cosine, result in degrees.

    acosh       - Inverse hyperbolic cosine.

    tan         - Tangent.

    tand        - Tangent of argument in degrees.

    tanh        - Hyperbolic tangent.

    atan        - Inverse tangent.

    atand       - Inverse tangent, result in degrees.

    atan2       - Four quadrant inverse tangent.

    atanh       - Inverse hyperbolic tangent.

    sec         - Secant.

    secd        - Secant of argument in degrees.

    sech        - Hyperbolic secant.

    asec        - Inverse secant.

    asecd       - Inverse secant, result in degrees.

    asech       - Inverse hyperbolic secant.

    csc         - Cosecant.

    cscd        - Cosecant of argument in degrees.

    csch        - Hyperbolic cosecant.

    acsc        - Inverse cosecant.

    acscd       - Inverse cosecant, result in degrees.

    acsch       - Inverse hyperbolic cosecant.

    cot         - Cotangent.

    cotd        - Cotangent of argument in degrees.

    coth        - Hyperbolic cotangent.

    acot        - Inverse cotangent.

    acotd       - Inverse cotangent, result in degrees.

    acoth       - Inverse hyperbolic cotangent.

1. 2.        Exponential.

    exp         - Exponential.

    expm1       - Compute exp(x)-1 accurately.

    log         - Natural logarithm.

    log1p       - Compute log(1+x) accurately.

    log10       - Common (base 10) logarithm.

    log2        - Base 2 logarithm and dissect floating point number.

    pow2        - Base 2 power and scale floating point number.

    realpow     - Power that will error out on complex result.

    reallog     - Natural logarithm of real number.

    realsqrt    - Square root of number greater than or equal to zero.

    sqrt        - Square root.

    nthroot     - Real n-th root of real numbers.

    nextpow2    - Next higher power of 2.

1. 3.       Complex

    abs         - Absolute value.

    angle       - Phase angle.

    complex     - Construct complex data from real and imaginary parts.

    conj        - Complex conjugate.

    imag        - Complex imaginary part.

    real        - Complex real part.

    unwrap      - Unwrap phase angle.

    isreal      - True for real array.

    cplxpair    - Sort numbers into complex conjugate pairs.

1. 4.        Rounding and remainder

    fix         - Round towards zero.

    floor       - Round towards minus infinity.

    ceil        - Round towards plus infinity.

    round       - Round towards nearest integer.

    mod         - Modulus (signed remainder after division).

    rem         - Remainder after division.

    sign        - Signum.

1. 5.      Specialized math functions

    airy        - Airy functions.

    besselj     - Bessel function of the first kind.

    bessely     - Bessel function of the second kind.

    besselh     - Bessel functions of the third kind (Hankel function).

    besseli     - Modified Bessel function of the first kind.

    besselk     - Modified Bessel function 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 function.

    gamma       - Gamma function.

    gammainc    - Incomplete gamma function.

    gammaln     - Logarithm of gamma function.

    psi         - Psi (polygamma) function.

    legendre    - Associated Legendre function.

    cross       - Vector cross product.

    dot         - Vector dot product.

1. 6.       Number theoretic functions

    factor      - Prime factors.

    isprime     - True for prime numbers.

    primes      - Generate list of prime numbers.

    gcd         - Greatest common divisor.

    lcm         - Least common multiple.

    rat         - Rational approximation.

    rats        - Rational output.

    perms       - All possible permutations.

    nchoosek    - All combinations of N elements taken K at a time.

    factorial   - Factorial function.

1. 7.      Coordinate transforms.

    cart2sph    - Transform Cartesian to spherical coordinates.

    cart2pol    - Transform Cartesian to polar coordinates.

    pol2cart    - Transform polar to Cartesian coordinates.

    sph2cart    - Transform spherical to Cartesian coordinates.

    hsv2rgb     - Convert hue-saturation-value colors to red-green-blue.

    rgb2hsv     - Convert red-green-blue colors to hue-saturation-value.

1. 8.        Special variables and constants

    ans         - Most recent answer.

    eps         - Floating point relative accuracy.

    realmax     - Largest positive floating point number.

   realmin     - Smallest positive floating point number.

    pi          -  3.1415926535897....

    i, j        -   Imaginary unit.

    inf         -  Infinity.

    NaN      - Not-a-Number.

    isnan     - True for Not-a-Number.

    isinf       - True for infinite elements.

    isfinite    - True for finite elements.

    why        - Succinct answer.