MATLAB: Indexing n-th element with increasing offset.

indexing

Good day

I'm trying to find a whey how it would be possible to index a n-th element with increasing offset in a arrey of zeros (expectation – 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1…). I found a whey, but its something like from first grade. Maybe someone would share some ideas, or give a hint of how it would be possible to reduce repeating typing…

x=1:1:100;
g=cumsum(x)<100;
g_idx=find(g);
X=zeros(size(x));
X(g_idx(1))=1;
X(cumsum(g_idx(1:2)))=1;
X(cumsum(g_idx(1:3)))=1;
X(cumsum(g_idx(1:4)))=1;
X(cumsum(g_idx(1:5)))=1;
X(cumsum(g_idx(1:6)))=1;
X(cumsum(g_idx(1:7)))=1;
X(cumsum(g_idx(1:8)))=1;
X(cumsum(g_idx(1:9)))=1;
X(cumsum(g_idx(1:10)))=1;
X(cumsum(g_idx(1:11)))=1;
X(cumsum(g_idx(1:12)))=1;
X(cumsum(g_idx(1:13)))=1

Best Answer

%%
a=1:13;
b=cumsum(a);
X=zeros(1,100);
X(b)=1

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One approach:

x0=0; x1=5;  g0=0; g1=0;
y0= 0; y1= 150;
A1 = [x0^3,x0^2,x0,1;
     3*x0^2,2*x0,1,0;
     x1^3,x1^2,x1,1;
     3*x1^2,2*x1,1,0];
 
 C1 = A1\[y0,g0,y1,g1]'; % Solve for the four cubic Hermite coefficients
n = 1000;
X1 = linspace(x0,x1,n);
Y1 = C1'*[X1.^3;X1.^2;X1;ones(1,n)];
% second segment  
x2=10; y2= 0;  g1= 0; g2=0;
A2 = [x1^3,x1^2,x1,1;
     3*x1^2,2*x1,1,0;
     x2^3,x2^2,x2,1;
     3*x2^2,2*x2,1,0];
 
C2 = A2\[y1,g1,y2,g2]';
X2 = linspace(x1,x2,n);
Y2 = C2'*[X2.^3;X2.^2;X2;ones(1,n)];
dY1 = gradient(Y1, X1(2)-X1(1));                    % Calculate Gradient

[Y1max,idxY1(1)] = max(dY1);
[Y1min,idxY1(2)] = min(dY1);
dY2 = gradient(Y2, X2(2)-X2(1));                    % Calculate Gradient
[Y2max,idxY2(1)] = max(dY2);
[Y2min,idxY2(2)] = min(dY2);
plot(X1,Y1)
hold on
plot(X2,Y2)
plot(X1(idxY1(1)), Y1(idxY1(1)), '^')
plot(X1(idxY1(2)), Y1(idxY1(2)), 'v')
plot(X2(idxY2(1)), Y2(idxY2(1)), '^')
plot(X2(idxY2(2)), Y2(idxY2(2)), 'v')
hold off
title('cubic hermite')
xlabel('x')
ylabel('y');

This uses the gradient (link) function to calculate the numerical derivative of the vectors, then finds the maxima and minima.

Experiment to get the result you want.

Best Answer

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