User Commands  - la (1)

NAME
la(1f) - interpret matrix expressions using a shell-like interface

CONTENTS

Synopsis
Description
Options
Author
Examples

SYNOPSIS
la [expression(s)] | [ --help| --version]

DESCRIPTION
la(1) is an interactive computer program that serves as a convenient "laboratory" for computations involving matrices. It provides easy access to matrix software developed by the LINPACK and EISPACK projects. The capabilities range from standard tasks such as solving simultaneous linear equations and inverting matrices, through symmetric and nonsymmetric eigenvalue problems, to fairly sophisticated matrix tools such as the singular value decomposition.

la(1) can stand for Linear Algebra or Los Alamos, but not Los Angelos.

OPTIONS
--help display this help and exit
--version
  output version information and exit
expression(s)
  if expressions are supplied they are evaluated and the program terminates.

AUTHOR
This is heavily based on a program from the Department of Computer Science, University of New Mexico, by Cleve Moler.

EXAMPLES
Sample commands 

    # Example 1: introductory usage:
    la
    a=<1 2 3;5 4 6;7 8 9>
    b=<5;6;7>
    a*b
    b*a
    det(a)
    quit
An explanation of Example 1: 

    > // For this session the <> character is the LA prompt.
    >  <> A=<1 2 3;5 4 6;7 8 9>            <---  you enter this
    >  A     =                             <---  LA response
    >      1.    2.    3.
    >      5.    4.    6.
    >      7.    8.    9.
    >  <> b=<5;6;7>
    >  b     =
    >      5.
    >      6.
    >      7.


    >  <> A*b             <--- you enter "multiply A and b"


    >  ANS   =            <--- LA response
    >     38.
    >     91.
    >    146.


    >  <> b*A             <---you enter "multiply b and A"
    >     /--ERROR                         <--- LA response
    >  INCOMPATIBLE FOR MULTIPLICATION


    >  <> det(A)         <--- Take the determinant of A


    >  ANS   =           <---LA response


    >     18.


    >  <> quit           <--- you quit LA


    >  total flops        34
    >  ADIOS
    > // --------------------------------------
Example 2: Simple looping and conditionals are also available 

    la
    //Eigenvalue sensitivity example. See section 8 of the Users’ Guide.
    B = <3 0 7; 0 2 0; 0 0 1>
    L = <1 0 0; 2 1 0; -3 4 1>,  M = L\L’
    A = M*B/M
    A = round(A)
    <X,D> = eig(A)
    long,  diag(D),  short
    cond(X)
    X = X/diag(X(3,:)),  cond(X)
    Y = inv(X’),  Y’*A*X
    for j = 1:3, c(j) = norm(Y(:,j))*norm(X(:,j));
    E = -1.e-6*Y(:,1)*X(:,1)’
    eig(A + .4*E),  eig(A + .5*E)
    r = .4;  s = .5;
    while s-r > 1.e-14, t = (r+s)/2; d = eig(A+t*E); ...
      if imag(d(1))=0, r = t; else, s = t;
    long,  t = r
    A+t*e,  eig(A+t*E)
    <X,D> = eig(A+t*E);  X = X/diag(X(3,:))
    short,  cond(X)
    // --------------------------------------
Use the HELP command for further information. For example, to enter HELP on the entire manual, display directions for using HELP and place a User manual in the file "la.userguide.txt", enter 

    la
    <>help manual
    continue ...
    h // show directions for using "help"
    w la.userguide.txt
    continue ...
    q
    quit

Nemo Release 3.1 la (1) February 23, 2025
Generated by manServer 1.08 from b35c6845-1240-4b6a-b7e3-4870a1504675 using man macros.