fpm-tools:la

Build la(1) using fpm(1):

git clone https://github.com/urbanjost/la
cd apps/la
fpm install
la --help

It has extensive built-in help.

NAME

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

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