-->dir
 ans  =
 
Thumbs.db                oracle.pdf plotquad.in   trans.fun   
Windows Media Player.lnk plot.in    problems.sce  trans.sci   
arrowdemo.in             plot1.png  sep16.txt     vat.in      
iterate2d.in             plot2.eps  sphereplot.in vati.in     
iterate3d.in             plot2.png  su09.sci      zz.sce      
 
-->A=[1 1;1 -1]
 A  =
 
    1.    1.  
    1.  - 1.  
 
-->inv(A)
 ans  =
 
    0.5    0.5  
    0.5  - 0.5  
 
-->eye(3,3)
 ans  =
 
    1.    0.    0.  
    0.    1.    0.  
    0.    0.    1.  
 
-->B=[A eye(2,2)]
 B  =
 
    1.    1.    1.    0.  
    1.  - 1.    0.    1.  
 
-->rref(B)
 ans  =
 
    1.    0.    0.5    0.5  
    0.    1.    0.5  - 0.5  
 
-->B
 B  =
 
    1.    1.    1.    0.  
    1.  - 1.    0.    1.  
 
-->B(2,:)=B(2,:)-B(1,:)
 B  =
 
    1.    1.    1.    0.  
    0.  - 2.  - 1.    1.  
 
-->B(2,:)=B(2,:)/(-2)
 B  =
 
    1.    1.    1.     0.   
    0.    1.    0.5  - 0.5  
 
-->B(1,:)=B(1,:) - B(2,:)
 B  =
 
    1.    0.    0.5    0.5  
    0.    1.    0.5  - 0.5  
 
-->Ainverse = B(:,3:4)
 Ainverse  =
 
    0.5    0.5  
    0.5  - 0.5  
 
-->A^(-1)
 ans  =
 
    0.5    0.5  
    0.5  - 0.5  
 
-->1/A
 ans  =
 
    0.5    0.5  
    0.5  - 0.5  
 
-->A=[2 1; 4 2]
 A  =
 
    2.    1.  
    4.    2.  
 
-->A^(-1)
       !--error 19 
Problem is singular.

 
 
-->rref([A eye(2,2)])
 ans  =
 
    1.    0.5    0.    0.25  
    0.    0.     1.  - 0.5   
 
-->A=[1 2 0 1 3; 3 4 2 3 3; 1 3 -1 0 1]
 A  =
 
    1.    2.    0.    1.    3.  
    3.    4.    2.    3.    3.  
    1.    3.  - 1.    0.    1.  
 
-->A(2,:)=A(2,:)-3*A(1,:)
 A  =
 
    1.    2.    0.    1.    3.  
    0.  - 2.    2.    0.  - 6.  
    1.    3.  - 1.    0.    1.  
 
-->A(3,:) = A(3,:)-A(1,:)
 A  =
 
    1.    2.    0.    1.    3.  
    0.  - 2.    2.    0.  - 6.  
    0.    1.  - 1.  - 1.  - 2.  
 
-->A(2,:) = A(2,:)/(-2)
 A  =
 
    1.    2.    0.    1.    3.  
    0.    1.  - 1.    0.    3.  
    0.    1.  - 1.  - 1.  - 2.  
 
-->A(1,:) = A(1,:) -2*A(2,:)
 A  =
 
    1.    0.    2.    1.  - 3.  
    0.    1.  - 1.    0.    3.  
    0.    1.  - 1.  - 1.  - 2.  
 
-->A(3,:) = A(3,:) -1*A(2,:)
 A  =
 
    1.    0.    2.    1.  - 3.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.  - 1.  - 5.  
 
-->A(3,:)=A(3,:)/(-1)
 A  =
 
    1.    0.    2.    1.  - 3.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 
-->A(1,:)=A(1,:)-A(3,:)
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 
-->for i=1:5, 2^i, end
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 
-->for i=1:5, 2^i, end
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 
-->lines(0)
 
-->for i=1:5, 2^i, end
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 
-->for i=1:5
-->2^i
-->end
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 
-->for i=1:5
-->2^i
-->for i=1:5, 2^i, end
-->for i=1:5, 2^i, end
-->for i=1:5, 2^i, end
-->A
-->end
 ans  =
 
    2.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 ans  =
 
    4.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 ans  =
 
    8.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 ans  =
 
    16.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 ans  =
 
    2.  
 ans  =
 
    4.  
 ans  =
 
    8.  
 ans  =
 
    16.  
 ans  =
 
    32.  
 A  =
 
    1.    0.    2.    0.  - 8.  
    0.    1.  - 1.    0.    3.  
    0.    0.    0.    1.    5.  
 
-->A=[2 1; 1 3]
 A  =
 
    2.    1.  
    1.    3.  
 
-->X=[1;0]
 X  =
 
    1.  
    0.  
 
-->exec('interate2d.in')
                      !--error 241 
File "interate2d.in" does not exist or read access denied.

 
 
-->exec('iterate2d.in')
 
-->for i = 1:10,
-->    X = A*X;
-->    N = norm(X);
-->    X = X/N;
-->    printf("N = %f, X = [%f; %f], i = %d\n", N, X(1,1), X(2,1), i);
-->end;
N = 2.236068, X = [0.894427; 0.447214], i = 1
N = 3.162278, X = [0.707107; 0.707107], i = 2
N = 3.535534, X = [0.600000; 0.800000], i = 3
N = 3.605551, X = [0.554700; 0.832050], i = 4
N = 3.616203, X = [0.536875; 0.843661], i = 5
N = 3.617767, X = [0.529999; 0.847998], i = 6
N = 3.617995, X = [0.527363; 0.849640], i = 7
N = 3.618028, X = [0.526355; 0.850265], i = 8
N = 3.618033, X = [0.525969; 0.850504], i = 9
N = 3.618034, X = [0.525822; 0.850595], i = 10
 
 
 
-->exec('iterate2d.in');
N = 3.618034, X = [0.525766; 0.850629], i = 1
N = 3.618034, X = [0.525744; 0.850643], i = 2
N = 3.618034, X = [0.525736; 0.850648], i = 3
N = 3.618034, X = [0.525733; 0.850650], i = 4
N = 3.618034, X = [0.525732; 0.850650], i = 5
N = 3.618034, X = [0.525731; 0.850651], i = 6
N = 3.618034, X = [0.525731; 0.850651], i = 7
N = 3.618034, X = [0.525731; 0.850651], i = 8
N = 3.618034, X = [0.525731; 0.850651], i = 9
N = 3.618034, X = [0.525731; 0.850651], i = 10
 
-->A*X ./ X
 ans  =
 
    3.618034  
    3.618034  
 
-->exec('plotquad.in')
 
-->// Plot Quad plots the conic section for a given 2x2 symmetric matrix
 
-->// It assumes that the matrix is A and it is already defined.
 
-->// It plots black curves
 
-->theta = 0:%pi/50:2*%pi; // %pi is scilab for the constant pi
 
-->n = size(theta,2); // theta is a 1 x n row vector
 
-->x = zeros(theta); // x and y start as zero vectors
 
-->y = zeros(theta);
 
-->for i = 1:n,
-->    angle = theta(i); // this angle
-->    c = cos(angle);
-->    s = sin(angle);
-->    X = [ c, s ];
-->    r = sqrt(1/abs(X*A*X')); // formula from section 4
-->    x(i) = r*c; // r cos(theta)
-->    y(i) = r*s;
-->end;
 
-->plot(x,y,'k-');
 
-->a = gca(); a.isoview="on";
 
-->title="Conic for A = ["+string(A(1,1))+" "+string(A(1,2)) +"; "+string(A(2,1))+" "+string(A(2,2))+"]";
Warning : redefining function: title                   . Use funcprot(0) to avoid this message

 
-->xtitle(title,"x","y");
 
 
 
-->diary(0)