# Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers, use '.^'.

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Raul Flores on 4 Apr 2020
Edited: VBBV on 3 Dec 2022
I don't really get what is wrong with this code:
clear all; close all; clc;
L = 200;
%length of beam in cm
E = 52000;
%modulus of eleasticity in kN/cm^2
I = 32000;
%moment of inertia in cm^4
w = 0.4;
x = linspace(0,200,20);
%discretizing the domain
dx = L/(20-1);
%dx = domain length/(no. of nodes-1) for
i = 1:length(x);
%deflection of the beam
y(i)= (-w*(x(i)^5-(3*L^2*x(i).^3)+(2*L^3*x(i)^2)))/(120*E*I);
%slope analytical
s(i)= (-w*(5*x(i)^4-(9*L^2*x(i)^2)+(4*L^3*x(i))))/(120*E*I);
%bending moment analytical
M(i)= (-w*(20*x(i)^3-(18*L^2*x(i))+(4*L^3)))/120;
%numerical slope
sn(i)= ((-w*((x(i)+dx)^5-(3*L^2*(x(i)+dx)^3)+(2*L^3*(x(i)+dx)^2)))/(120*E*I)- (-w*((x(i)-dx)^5-(3*L^2*(x(i)-dx)^3)+(2*L^3*(x(i)-dx)^2)))/(120*E*I))/(2*dx);
%numerical bending moment
Mn(i) = (E*I/dx^2)*(sn(i)- (2*y(i))+2*(-w*((x(i)-dx)^5-(3*L^2*(x(i)-dx)^3)+(2*L^3*(x(i)-dx)^2)))/(120*E*I));
figure(1)
plot(x,y,x,s,'*',x,sn)
grid on
figure(2)
plot(x,M,x,Mn)
grid on
Errors:
Error using ^ (line 51)
Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar. To perform elementwise matrix powers, use
'.^'.
Error in untitled (line 16)
y(i)= (-w*(x(i)^5-(3*L^2*x(i).^3)+(2*L^3*x(i)^2)))/(120*E*I);

Steven Lord on 4 Apr 2020
x^5 is conceptually equivalent to x*x*x*x*x using matrix multiplication.
x.^5 is conceptually equivalent to x.*x.*x.*x.*x using element-wise multiplication.
If x is a 1-by-n vector, x*x is not defined (the inner matrix dimensions don't match) and so neither is x^5.
If x is a 1-by-n vector, both x.*x and x.^5 are defined.
In one place on that line you're using .^ on the vector x and in two places you're using ^.

VBBV on 3 Dec 2022
Edited: VBBV on 3 Dec 2022
The element wise power for a scalar should not affect much on your calculation unless vectors are multiplied or raised to power
clear all; close all; clc;
L = 200;
%length of beam in cm
E = 52000;
%modulus of eleasticity in kN/cm^2
I = 32000;
%moment of inertia in cm^4
w = 0.4;
x = linspace(0,200,20);
%discretizing the domain
dx = L/(20-1);
%dx = domain length/(no. of nodes-1)
for i = 1:length(x)
%deflection of the beam
y(i)= (-w*(x(i)^5-(3*L^2*x(i)^3)+(2*L^3*x(i)^2)))/(120*E*I); % This should not affect
%slope analytical
s(i)= (-w*(5*x(i)^4-(9*L^2*x(i)^2)+(4*L^3*x(i))))/(120*E*I);
%bending moment analytical
M(i)= (-w*(20*x(i)^3-(18*L^2*x(i))+(4*L^3)))/120;
%numerical slope
sn(i)= ((-w*((x(i)+dx)^5-(3*L^2*(x(i)+dx)^3)+(2*L^3*(x(i)+dx)^2)))/(120*E*I)- (-w*((x(i)-dx)^5-(3*L^2*(x(i)-dx)^3)+(2*L^3*(x(i)-dx)^2)))/(120*E*I))/(2*dx);
%numerical bending moment
Mn(i) = (E*I/dx^2)*(sn(i)- (2*y(i))+2*(-w*((x(i)-dx)^5-(3*L^2*(x(i)-dx)^3)+(2*L^3*(x(i)-dx)^2)))/(120*E*I));
end
figure(1)
plot(x,y,x,s,'*',x,sn)
grid on
figure(2)
plot(x,M,x,Mn)
grid on
y(i)= (-w*(x(i)^5-(3*L^2*x(i).^3)+(2*L^3*x(i)^2)))/(120*E*I); % whether you use .^ or ^ bcoz x(i) is scalar

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