MATLAB: How can shape a matrix with predefined vectors

vectors are rows of a matrix

I want to make a 3*12 matrix which its first, second and third row is N1, N2 and N3.

N1, N2 and N3 are 1*12 vectors.

I can use [N1(1) N1(2) ….N1(12); N2(1) N2(2) ….N2(12); N3(1) N3(2) … N3(12)]

but it's ugly and slow, I want to use Matlab special features in matrix handling.

Best Answer

N = [N1; N2; N3];

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MATLAB: Increase compute speed compute angle between 2 vectors

The indirection of anonymous functions costs time. So either use the built-in functions with the same names cross, norm and dot, or hard code the functions directly.

Instead of the expensive trick to determine the positions of instabilities in the ASIN and ACOS methods, use a stable method directly:

atan2(norm(cross(N1 x N2)), dot(N1, N2))

Where N1 and N2 are the normalized input vectors.

N1      = bsxfun(@rdivide, a, sqrt(sum(a .* a ,1)))
N2      = bsxfun(@rdivide, b, sqrt(sum(b .* b ,1)))
N1dotN2 = N1(:, 1) .* N2(:, 1) + N1(:, 2) .* N2(:, 2) + N1(:, 3) .* N2(:, 3);
N1xN2   = [(N1(:, 2) .* N2(:, 3) - N1(:, 3) .* N2(:, 2)), ...
         (N1(:, 3) .* N2(:, 1) - N1(:, 1) .* N2(:, 3)), ...
         (N1(:, 1) .* N2(:, 2) - N1(:, 2) .* N2(:, 1))];
Angle   = atan2(sqrt(sum(N1xN2 .* N1xN2, 1)), N1dotN2);

MATLAB: Trouble using dsolve function

z = a*x+b*x^2+c+........; 
eqn = subs(sym('D2y +5*z+ 2*x + 10*z^2'), z, z);
S = dsolve(eqn, x);

Myself, I would probably toss in a simplify() around the subs() .

Best Answer

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MATLAB: Increase compute speed compute angle between 2 vectors

MATLAB: Trouble using dsolve function

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