Caculating the sum of elements and building a vector and a matrix with letters

Question

Lee Cohen 2018-4-7

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评论： John BG 2018-4-8

采纳的回答： John BG

I created the following matrix:

Here's the code:

n = input('enter n\n');

A=[sym('m%d', [n 1]) sym('x%d', [n 1]) sym('y%d', [n 1]) sym('z%d', [n 1])];

I need to build the following vector and matrix:

Once with using loops and once without using loops. I don't succeed to create a sum of elements, that are letters. How Can I build those arrays?

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Answer 1

John BG 2018-4-7

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https://ww2.mathworks.cn/matlabcentral/answers/393328-caculating-the-sum-of-elements-and-building-a-vector-and-a-matrix-with-letters#answer_313928

在 MATLAB Online 中打开

Hi Lee

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

1.-

Simulating data

n=12
m=randi([1 10],n,1);
x=randi([-13 13],n,1);
y=randi([-13 13],n,1);
z=randi([-13 13],n,1);

2.-

Your matrix

A=[m x y z]

3.-

the v vector

v=[sum(m.*x) sum(m.*y) sum(m.*z)]

it's the same as

v=[sum(A(:,1).*A(:,2)) sum(A(:,1).*A(:,3)) sum(A(:,1).*A(:,4))]

4.-

Regarding the Inertia matrix I, once you have keyed in the matrix A with the couple lines shown in your question

n = input('enter n\n');
A=[sym('m%d', [n 1]) sym('x%d', [n 1]) sym('y%d', [n 1]) sym('z%d', [n 1])];

the generatrion of I is more compact using vectors m x y and z

To get these vectors one can easily extract m x y z with

m=A(:,1);
x=A(:,2);
y=A(:,3);
z=A(:,3);

then, note that it may be the case that you need I to be 3D so you can address the Inertia moment for any given i-th layer

I0=zeros(3,3,n)
% 1st row of I
I0(1,1,:)=m.*(x).^2
I0(2,1,:)=m.*x.*y
I0(3,1,:)=m.*x.*z
% 2nd row of I
I0(1,2,:)=m.*x.*y
I0(2,2,:)=m.*(y).^2
I0(3,2,:)=m.*z.*y
% 3rd row of I
I0(1,3,:)=m.*x.*z
I0(2,3,:)=m.*y.*z
I0(3,3,:)=m.*(z).^2

5.-

then one can obtain the sum matrix I just adding along 3rd dimension of I0

I=sum(I0,3)

f you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

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John BG 2018-4-8

在 MATLAB Online 中打开

no problem, here we go:

1.-

 generating data
n=12
m=randi([1 10],n,1);
x=randi([-13 13],n,1);
y=randi([-13 13],n,1);
z=randi([-13 13],n,1);
A=[m x y z]   % A, the matrix you start the question with
m=A(:,1);
x=A(:,2);
y=A(:,3);
z=A(:,3);

2.-

the equivalent to

% v=[sum(m.*x) sum(m.*y) sum(m.*z)]

.

is

.

mx=0;
for k=1:1:numel(m)
    mx=mx+m(k)*x(k);
end
my=0;
for k=1:1:numel(m)
    my=my+m(k)*y(k);
end
mz=0;
for k=1:1:numel(m)
    mz=mz+m(k)*z(k);
end
v_sum=[mx my mz]

.

or

.

p=[x y z];
v_sum=[0 0 0]
for k=1:1:numel(m)
    v_sum=v_sum+m(k)*p(k,:);
end

3.-

the equivalent to

v=[sum(A(:,1).*A(:,2)) sum(A(:,1).*A(:,3)) sum(A(:,1).*A(:,4))]

is

I_sum=zeros(3);
for k=1:1:numel(m)
    I_sum=I_sum+m(k)*[(x(k))^2 x(k)*y(k) x(k)*z(k);x(k)*y(k) (y(k))^2 y(k)*z(k); x(k)*y(k) z(k)*y(k) (z(k))^2];
end

.

or

.

I_sum=zeros(3);
for k=1:1:numel(m)
    D=zeros(3);
    p1=p(k,:);
    for s1=1:1:3
        for s2=1:1:3
            D(s1,s2)=p1(s1)*p1(s2);
        end
    end
    I_sum=I_sum+m(k)*D;
end