//sfb: Notes added in editing are marked with //sfb

 
-->scf(5);
 
-->t=0:0.1:4;
 
-->plot(t,sin(t),'rx-')
 
-->xs2eps(5,'foo.eps')
 
-->clf()
 
-->P  =
     !--error 2 
invalid factor
 
 
 
-->    1.7951238  - 1.5233159
 ans  =
 
    0.2718079  
 
-->  - 1.5233159    1.2926637
                    !--error 276 
Missing operator, comma, or semicolon
 
 
-->A=[
-->    1.7951238  - 1.5233159
-->  - 1.5233159    1.2926637  ]
                   !--error 6 
inconsistent row/column dimensions
 
 
-->A=[
-->    1.7951238  - 1.5233159  ;
-->  - 1.5233159    1.2926637  ]
                   !--error 6 
inconsistent row/column dimensions
 
 
--> A=[   1.7951238  - 1.5233159  ;
-->  - 1.5233159    1.2926637  ]
                   !--error 6 
inconsistent row/column dimensions
 

//sfb finally figured out it was the space between the - and the number 
--> A=[   1.7951238  -1.5233159  ;
-->  -1.5233159    1.2926637  ]
 A  =
 
    1.7951238  - 1.5233159  
  - 1.5233159    1.2926637  

//sfb cut and pasted from plot.in 
-->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,'r*-');

//sfb cut and pasted from contour.in  -- needed to make arrows orthogonal
-->a=get("current_axes"); a.isoview="on"; // aspect ratio 1:1
 
-->square(-2,-2,2,2); // window ratio 1:1
 
-->X=[1;0]
 X  =
 
    1.  
    0.  
 
-->exec('iterate2d.in')
                     !--error 241 
File iterate2d.in does not exist or read access denied 
 
 
-->chdir('\\tecad\tecad\I_TDrive\bellenot\Desktop');
 
-->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 = 2.354349, X = [0.762471; -0.647022], i = 1
N = 3.087787, X = [0.762471; -0.647022], i = 2
N = 3.087787, X = [0.762471; -0.647022], i = 3
N = 3.087787, X = [0.762471; -0.647022], i = 4
N = 3.087787, X = [0.762471; -0.647022], i = 5
N = 3.087787, X = [0.762471; -0.647022], i = 6
N = 3.087787, X = [0.762471; -0.647022], i = 7
N = 3.087787, X = [0.762471; -0.647022], i = 8
N = 3.087787, X = [0.762471; -0.647022], i = 9
N = 3.087787, X = [0.762471; -0.647022], i = 10
 
 
-->X1=X
 X1  =
 
    0.7624713  
  - 0.6470220  
 
-->L1=N
 L1  =
 
    3.0877875  

//sfb parallel case does not have an inverse
//sfb but round off error makes scilab thinks there is one. 
-->inv(A)
 warning
 matrix is close to singular or badly scaled. rcond =    3.8207D-09
 
 ans  =
 
    30724123.    36206281.  
    36206281.    42666630.  
 
-->det(A)
 ans  =
 
    4.207D-08  
 
-->// non zero solution to A*X=0
 
-->rref([A;[0;0])
              !--error 2 
invalid factor
 
 
-->rref([A [0;0])
              !--error 2 
invalid factor
 
 
-->rref([A [0;0]])
 ans  =
 
    1.    0.    0.  
    0.    1.    0.  
 
-->A
 A  =
 
    1.7951238  - 1.5233159  
  - 1.5233159    1.2926637  


//sfb we interchanged the row values and one sign (and made it a column)
-->Y=[1.5233159; 1.7951238]
 Y  =
 
    1.5233159  
    1.7951238  
 
-->A*Y
 ans  =
 
    0.         
    4.207D-08  
 
-->X2=Y/norm(Y)
 X2  =
 
    0.6470220  
    0.7624713  

//sfb check for orthogonality 
-->X1'*X2
 ans  =
 
  - 3.745D-09  
 
-->L2=0
 L2  =
 
    0.  
 
-->L2=16
 L2  =
 
    16.  

//sfb from arrows.in 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");
 
-->L2=1/16
 L2  =
 
    0.0625  
 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");
 
-->L2=1/2
 L2  =
 
    0.5  
 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");
 
-->L2=1/sqrt(2)
 L2  =
 
    0.7071068  
 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");
 
-->L2=1/4
 L2  =
 
    0.25  
 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");

//sfb start the graph over 
-->clf
 
-->xarrows([0; X1(1,1)/sqrt(abs(L1))],  [0; X1(2,1)/sqrt(abs(L1))], 1, 5);
 
-->xarrows([0; X2(1,1)/sqrt(abs(L2))],  [0; X2(2,1)/sqrt(abs(L2))], 1, 3);
 
-->xstring(X1(1,1)/L1, X1(2,1)/L1,"Largest L-value, E-vector/sqrt(L-value)");
 
-->xstring(X2(1,1)/L1, X2(2,1)/L1,"Smallest L-value, E-vector/sqrt(L-value)");
 
-->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,'r*-');
 
-->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,'r*-');
 
-->a=get("current_axes"); a.isoview="on"; // aspect ratio 1:1
 
-->square(-2,-2,2,2); // window ratio 1:1
 
-->xs2eps(5,'parallel6.eps')
 
     []
 !--error 9999 
Problem generating file , perhaps directory is not writable                     
at line      53 of function xs2eps called by :  
xs2eps(5,'parallel6.eps')
 
 
-->chdir('\\tecad\tecad\I_TDrive\bellenot\Desktop');
 
-->xs2eps(5,'parallel6.eps')
 
     []
 !--error 9999 
Problem generating file , perhaps directory is not writable                     
at line      53 of function xs2eps called by :  
xs2eps(5,'parallel6.eps')
 
 
-->chdir('T:\');

//sfb parallel6.eps and parallel6.pdf  are also in this directory
-->xs2eps(5,'parallel6.eps')
 
-->help();
 
-->diary(0)