function Aufgabe40(fall)
% Approximationstheorie, WS 2007/08
% Programmierbeispiel zu Aufgabe 40, Blatt 14
% (benötigt newtonpoly.m, greville.m, bspval.m, divdiff.m)
%
% Aufruf: Aufgabe40(fall)
% fall = 1: r=3, Knoten {0,0,0,1,1,1}
% fall = 2: r=4, Knoten {0,0,0,0,1,1,1,1}
% fall = 3: r=3, äquidistante Verteilung
% fall = 4: r=4, äquidistante Verteilung
% fall = 5: r=3, zufällige Verteilung
% fall = 6: r=4, zufällige Verteilung
% fall = 7: durchläuft alle Fälle

if fall < 1 | fall > 7
    error('Inputvariable muss aus {1,...,7} sein')
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 1 | fall == 7
    clc
    fprintf('Fall 1: r=3, Knoten {0,0,0,1,1,1} \n \n');
    fprintf('Greville-Abszissen \n ');
    g1 = greville([0 0 0 1 1 1],3)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A1=bspval([0 0 0 1 1 1],[eye(3)],g1)
    inv_A1= inv(A1)
    
    if fall == 1
        xx = 0:.01:1;
        for k = 1:3
            p(k,:) = newtonpoly(g1,A1(k,:),xx);
        end
        plot(xx,p)
    end
    
    Norm_invA1 = norm(inv_A1,inf)
    pause
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 2 | fall == 7
    clc
    fprintf('Fall 2: r=4, Knoten {0,0,0,0,1,1,1,1} \n \n');
    fprintf('Greville-Abszissen \n ');
    g2 = greville([0 0 0 0 1 1 1 1],4)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A2=bspval([0 0 0 0 1 1 1 1],[eye(4)],g2)
    inv_A2= inv(A2)
    
    if fall == 2
        xx = 0:.01:1;
        for k = 1:4
            p(k,:) = newtonpoly(g2,A2(k,:),xx);
        end
        figure
        plot(xx,p)
    end
    
    Norm_invA2 = norm(inv_A2,inf)
    pause
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 3 | fall == 7
    clc
    fprintf('Fall 3: r=3, äquidistante Verteilung \n \n');
    fprintf('Stützstellenvektor \n');
    a3 = [0:.1:1]
    fprintf('Greville-Abszissen \n ');
    g3 = greville(a3,3)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A3=bspval(a3,[eye(8)],g3)
    inv_A3= inv(A3)

    Norm_invA3 = norm(inv_A3,inf)
    pause
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 4 | fall == 7
    clc
    fprintf('Fall 4: r=4, äquidistante Verteilung \n \n');
    fprintf('Stützstellenvektor \n');
    a4 = [0:.1:1]
    fprintf('Greville-Abszissen \n ');
    g4 = greville(a4,4)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A4=bspval(a4,[eye(7)],g4)
    inv_A4= inv(A4)

    Norm_invA4 = norm(inv_A4,inf)
    pause
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 5 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 5 | fall == 7
    clc
    fprintf('Fall 5: r=3, Knoten zufällig verteilt \n \n');
    fprintf('Stützstellenvektor \n');
    a5 = sort(rand(1,10))
    fprintf('Greville-Abszissen \n ');
    g5 = greville(a5,3)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A5=bspval(a5,[eye(7)],g5)
    inv_A5= inv(A5)

    Norm_invA5 = norm(inv_A5,inf)
    pause
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Fall 6 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if fall == 6 | fall == 7
    clc
    fprintf('Fall 6: r=4, Knoten zufällig verteilt \n \n');
    fprintf('Stützstellenvektor \n');
    a6 = sort(rand(1,12))
    fprintf('Greville-Abszissen \n ');
    g6 = greville(a6,4)

    fprintf('Kollokationsmatrix und Inverse: \n');
    A6=bspval(a6,[eye(8)],g6)
    inv_A6= inv(A6)

    Norm_invA1 = norm(inv_A6,inf)
end