Collection of Education/collectionofeducationcarat1997.iso/SCIENCE/MATLAB.ZIP/HELP

Text File | 1986-02-06 | 34KB | 757 lines

HELP is available

NEWS  MATLAB NEWS dated 9/15/83.
      HELP is now a lot faster.

INTRO Welcome to MATLAB.

      Here are a few sample statements:

      A = <1 2; 3 4>
      b = <5 6>'
      x = A\b
      <V,D> = eig(A),  norm(A-V*D/V)
      help \ , help eig
      exec('demo',7)

      For more information, see the MATLAB Users' Guide which  is
      contained in file ...  or may be obtained from ... .

<     < > Brackets used in forming vectors and matrices.
      <6.9  9.64  SQRT(-1)>  is  a  vector  with  three  elements
      separated  by  blanks.   <6.9,  9.64, sqrt(-1)> is the same
      thing.  <1+I 2-I 3>  and  <1 +I 2 -I 3>  are not the  same.
      The first has three elements, the second has five.
      <11 12 13; 21 22 23>  is a 2 by 3 matrix .   The  semicolon
      ends the first row.

      Vectors and matrices can be used inside < > brackets.
      <A B; C>  is allowed if the number of rows  of   A   equals
      the  number  of rows of  B  and the number of columns of  A
      plus the number of columns of   B   equals  the  number  of
      columns  of   C  .   This  rule  generalizes in a hopefully
      obvious way to allow fairly complicated constructions.

      A = < >  stores an empty matrix in  A , thereby removing it
      from the list of current variables.

      For the use of < and > on the left of  the  =  in  multiple
      assignment statements, see LU, EIG, SVD and so on.

      In WHILE and IF clauses, <>  means  less  than  or  greater
      than,  i.e.  not  equal, < means less than, > means greater
      than, <= means less than or equal, >= means greater than or
      equal.

      For the use of > and < to delineate macros, see MACRO.

>     See < .  Also see MACRO.

(     ( ) Used to indicate precedence in  arithmetic  expressions
      in  the  usual way.  Used to enclose arguments of functions
      in the usual way.  Used to enclose  subscripts  of  vectors
      and  matrices  in  a  manner somewhat more general than the
      usual way.  If  X   and   V  are  vectors,  then   X(V)  is
      <X(V(1)),  X(V(2)),  ...,  X(V(N))> .  The components of  V
      are rounded to nearest integers and used as subscripts.  An
      error  occurs  if  any  such  subscript  is  less than 1 or
      greater than the dimension of  X .  Some examples:
      X(3)  is the third element of  X .
      X(<1 2 3>)  is the first three elements of  X .  So is
      X(<SQRT(2), SQRT(3), 4*ATAN(1)>)  .
      If  X  has  N  components,  X(N:-1:1) reverses them.
      The same indirect subscripting is used in matrices.  If   V
      has   M  components and  W  has  N  components, then A(V,W)
      is the  M by N  matrix formed from the elements of A  whose
      subscripts are the elements of  V  and  W .  For example...
      A(<1,5>,:) = A(<5,1>,:)  interchanges rows 1 and 5 of  A .

)     See  ( .

=     Used in assignment statements and to mean equality in WHILE
      and IF clauses.

.     Decimal point.  314/100, 3.14  and   .314E1   are  all  the
      same.

      Element-by-element multiplicative operations  are  obtained
      using  .*  ,  ./  , or .\ .  For example, C = A ./ B is the
      matrix with elements  c(i,j) = a(i,j)/b(i,j) .

      Kronecker tensor products and quotients are  obtained  with
      .*. , ./.  and .\. .  See KRON.

      Two or  more  points  at  the  end  of  the  line  indicate
      continuation.    The   total  line  length  limit  is  1024
      characters.

,     Used to separate matrix subscripts and function  arguments.
      Used  at  the  end  of  FOR, WHILE and IF clauses.  Used to
      separate statements  in  multi-statement  lines.   In  this
      situation,  it  may  be  replaced  by semicolon to suppress
      printing.

;     Used inside brackets to end rows.
      Used after an expression or statement to suppress printing.
      See SEMI.

\     Backslash or matrix left division.   A\B   is  roughly  the
      same  as   INV(A)*B  , except it is computed in a different
      way.  If  A  is an N by N matrix and  B  is a column vector
      with  N  components, or a matrix with several such columns,
      then X = A\B  is the solution to  the  equation   A*X  =  B
      computed  by  Gaussian  elimination.   A warning message is
      printed if  A is badly scaled or nearly singular.
      A\EYE produces the inverse of  A .

      If  A  is an  M by N  matrix with  M < or > N  and  B  is a
      column vector with  M  components, or a matrix with several
      such columns, then  X = A\B  is the solution in  the  least
      squares  sense  to  the under- or overdetermined system  of
      equations A*X = B .  The  effective  rank,  K,  of   A   is
      determined  from  the  QR  decomposition  with pivoting.  A
      solution  X  is  computed  which  has  at  most  K  nonzero
      components  per column.  If  K < N this will usually not be
      the same solution as PINV(A)*B .
      A\EYE produces a generalized inverse of  A .

      If A and B have the  same  dimensions,  then  A  .\  B  has
      elements a(i,j)\b(i,j) .

      Also, see EDIT.

/     Slash or matrix right division.  B/A  is roughly  the  same
      as  B*INV(A) .  More precisely,  B/A = (A'\B')' .  See \ .

      IF A and B have the  same  dimensions,  then  A  ./  B  has
      elements a(i,j)/b(i,j) .

      Two or more slashes together on a line indicate  a  logical
      end of line.  Any following text is ignored.

'     Transpose.  X'  is the complex conjugate transpose of  X  .
      Quote.   'ANY  TEXT'   is a vector whose components are the
      MATLAB internal codes for the characters.  A  quote  within
      the text is indicated by two quotes.  See DISP and FILE .

+     Addition.  X + Y .  X and Y must have the same dimensions.

-     Subtraction.  X  -  Y  .   X  and  Y  must  have  the  same
      dimensions.

*     Matrix multiplication, X*Y .  Any scalar (1  by  1  matrix)
      may multiply anything.  Otherwise, the number of columns of
      X must equal the number of rows of Y .

      Element-by-element multiplication is obtained with X .* Y .

      The Kronecker tensor product is denoted by X .*. Y .

      Powers.  X**p  is  X  to the   p   power.   p   must  be  a
      scalar.  If  X  is a matrix, see  FUN .

:     Colon.  Used in subscripts,  FOR  iterations  and  possibly
      elsewhere.
      J:K  is the same as  <J, J+1, ..., K>
      J:K  is empty if  J > K .
      J:I:K  is the same as  <J, J+I, J+2I, ..., K>
      J:I:K  is empty if  I > 0 and J > K or if I < 0 and J < K .
      The colon notation can be used to pick out  selected  rows,
      columns and elements of vectors and matrices.
      A(:)  is all the  elements  of  A,  regarded  as  a  single
      column.
      A(:,J)  is the  J-th  column of A
      A(J:K)  is  A(J),A(J+1),...,A(K)
      A(:,J:K)  is  A(:,J),A(:,J+1),...,A(:,K) and so on.
      For the use of the colon in the FOR statement, See FOR .

ABS   ABS(X)  is the absolute value, or complex modulus,  of  the
      elements of X .

ANS   Variable created automatically  when  expressions  are  not
      assigned to anything else.

ATAN  ATAN(X)  is the arctangent of  X .  See FUN .

BASE  BASE(X,B) is a vector containing the base B  representation
      of   X  .   This is often used in conjunction with DISPLAY.
      DISPLAY(X,B)  is  the  same  as  DISPLAY(BASE(X,B)).    For
      example,    DISP(4*ATAN(1),16)   prints   the   hexadecimal
      representation of pi.

CHAR  CHAR(K)  requests  an  input  line  containing   a   single
      character  to  replace  MATLAB  character  number  K in the
      following table.  For example, CHAR(45) replaces backslash.
      CHAR(-K) replaces the alternate character number K.

                K  character alternate name
              0 - 9   0 - 9    0 - 9   digits
             10 - 35  A - Z    a - z   letters
               36                      blank
               37       (        (     lparen