function polyinvert

hold off

% Original polynomial interpolation
x = linspace(1,101,11)'
y = 1./x
plot(x,y,'kx')
legend('Original points')
hold on
pause
p1 = polyfit(x,y,10)
x1 = linspace(1,101,100);
y1 = polyval(p1,x1);
y = 1./x1;
plot(x1,y,'k-',x1,y1,'r-')
legend('Original points','Original curve','Polynomial fit')
pause
hold off

% Inverted polynomial interpolation
x = linspace(1,101,11)';
y = 1./x;
plot(y,x,'kx')
legend('Inverted points')
hold on
pause
p2 = polyfit(y,x,10)
y2 = linspace(min(y),max(y),100);
x2 = polyval(p2,y2);
x = 1./y2;
plot(y2,x,'k-',y2,x2,'r-')
legend('Inverted points','Inverted curve','Polynomial fit')
pause
hold off

% Original problem repeated but with cubic spline interpolation added
x = linspace(1,101,11)'
y = 1./x
plot(x,y,'kx')
legend('Original points')
hold on
p1 = polyfit(x,y,10)
x1 = linspace(1,101,100);
y1 = polyval(p1,x1);
y2 = spline(x,y,x1);
y = 1./x1;
plot(x1,y,'k-',x1,y1,'r-',x1,y2,'b-')
legend('Original points','Original curve','Polynomial fit','Cubic spline fit')
pause
hold off

% Inverted problem repeated but with cubic spline interpolation added
x = linspace(1,101,11)';
y = 1./x;
plot(y,x,'kx')
legend('Inverted points')
hold on
y2 = linspace(min(y),max(y),100);
x2 = spline(y,x,y2);
x = 1./y2;
plot(y2,x,'k-',y2,x2,'b-')
legend('Inverted points','Inverted curve','Cubic spline fit')