MATLAB: Create a vector form a polynomial evaluation

vector . polynomial .

Hi, I have a polynomials coefficients matrix of W rows in the form f(x)= ax^2 + bx + c

M= [a1 b1 c1 ; a2 b2 c2 ; … … …];

and a column-vector of x

X=[

I solve in this way:

y1M1 = polyval(M ( 1 , : ), X(1,:) );

y2M2 = polyval(M ( 2 , : ), X(2,:) );

y3M3 = polyval(M ( 3 , : ), X(3,:) );

…

example: M1 -> M(1,:) -> (a1 * (x1)^2) + (b1 * x1) + c1

Is possible a combination of commands to obtain a single vector with all the y ?

If I'm not clear, please ask me… thanks

Best Answer

y = cellfun(@(x,y)polyval(x,y),num2cell(M,2),num2cell(X));

y = arrayfun(@(n)polyval(M(n,:),X(n)),(1:numel(X))');

Related Solutions

MATLAB: Alternates of polyval and polyfit

https://en.wikipedia.org/wiki/Vandermonde_matrix

Suppose you had a polynomial of degree 2, y = a2*x^2 + a1*x^1 + a0*x^0, a2, a1, a0 unknown then you can write that as

[x^2, x^1, x^0] * [a2; a1; a0] = y

Now fill in those values as columns for all known x, y

A = [x1^2, x1, 1
     x2^2, x2, 1
     x3^2, x3, 1
     ...]
b = [y1;
     y2
     y3
     ...]

and then it follows that

  A * [a2; a1; a0] = b

which is a (possibly overdetermined) system of simultaneous linear equations you can solve by your favorite method

MATLAB: Max and Min Slopes

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

Related Solutions

MATLAB: Alternates of polyval and polyfit

MATLAB: Max and Min Slopes

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