why is the answer 0.8058 ?

Hi, i am new to matlab and i am trying to understand this code below. I know it is a matrix but i still don't understand why the answer is 0.8058. How does it work?

DD = 1:1:6

D= 1:1:6

X(DD)=D(DD)/ (D+1)

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x = 0.8058 0.8058 0.8058 0.8058 0.8058 0.8058

[William Rose]

@Ronald Eboue Teto, This was a good question. The answer was not obvious to me. See my answer below for why x=.8058. I learned something by answering this.

Answer 1

[Image Analyst]

You're doing a matrix division not an element by element division. Is that what you expected? What did you expect? Did you want this instead?

DD = 1:1:6
D= 1:1:6
X(DD) = D(DD) ./ (D+1)

X =

0.5 0.66667 0.75 0.8 0.83333 0.85714

Answer 2

[William Rose]

You get the same answer by doing

mrdivide(D,D+1)

See the man page for matrix right divide.

Matlab finds the value of x that gives the least-squares solution to

x(D+1)=D, where D and D+1 are vectors. You can show by calculus that the least squares solution to the above

is

x=dot(D,D+1)/dot(D+1,D+1).

And if you try it in Matlab, you get the same answer, x=0.8058.

[William Rose]

x=B/A finds the least squares solution to xA=B.

where A, B are column vectors and x is a scalar. It also works for row vectors, just flip which (xA-B) is transposed.

and this derivative=0 when SumSqErr is minimized. Therefore the minimum is at

, i.e. , i.e.

x=dot(A,B)/dot(A,A)

In this case, we have

x=D/(D+1);

which means A corresponds to D+1 and B corresponds to D, i.e.

x=dot(D+1,D)/dot(D+1,D+1)

Answer 3

[DGM]

It's a vector because you specified that it must be. Let's start off by simplifying things:

D(DD) is D(1:6). Since D has six elements, D(DD) is the same as D.

Similarly, X is defined as a vector having six elements, and the value of each element is the result of the RHS of the expression. It's the same as doing

X=zeros([1 6]);
X(:)=D/(D+1)

If you expect X to be a scalar, just use the result directly

D= 1:6
X=D/(D+1)