My matlab script is throwing an error for array dimensionality. "Arrays have incompatible sizes for this operation."

The error I'm getting is, "Arrays have incompatible sizes for this operation.

Error in deflection_calculation>@(x)sum(F.*max(x-sort([x_f;x_r]),0),1) (line 16)

bm = cell2mat(arrayfun(@(x) sum(F.*max(x-sort([x_f;x_r]),0),1),xcp,'UniformOutput',false)); % (lbf*inch)"

Here's the code I was working with. You can play with the numbers and let me know which dimension is actually causing the problem and what change can solve the problem. Thanks.

function Shaft_deflection_calculation(E,F,x_f,x_r,x_s,d)
E = 30*10^6;
F = [20; 45];
x_f = [5.25; 5.25];
x_r = [0.5; 10];
x_s = [1;2;3;4;5;6];
d = [1;1;1;1;1;1;1];
% calculations %%%%%%%%%%%%%%%%%%%
xcp = sort([x_f; x_r; x_s]);
xp_l = sort(cell2mat(arrayfun(@(x) (find(xcp==x)),[x_f;x_r],'UniformOutput',false)));
for i = 1:length(xp_l)
    if xp_l(i) >1 && xp_l(i) < length(xcp), d = [d(1:xp_l(i)-1); d(xp_l(i)-1); d(xp_l(i):end)]; end
end
I = repmat(pi*d.^4/64,1,size(F,2)); % calculate the second moment of area (inch^4)
% calculation of the bending moment distribution using singularity functions
bm = cell2mat(arrayfun(@(x) sum(F.*max(x-sort([x_f;x_r]),0),1),xcp,'UniformOutput',false)); % (lbf*inch)
if x_f(end) == xcp(end) || x_r(end) == xcp(end), F = F(1:end-1,:); xp_l = xp_l(1:end-1); end
if(~isempty(x_s))
    xs_l = sort(cell2mat(arrayfun(@(x) (find(xcp==x)),x_s,'UniformOutput',false)));
    step = bm(xs_l,:)./I(xs_l,:) - bm(xs_l,:)./I(xs_l-1,:); % (lbf/inch^3) 
    slope2 = ((bm(xs_l+1,:)-bm(xs_l,:))./I(xs_l,:))./(xcp(xs_l+1)-xcp(xs_l)); slope1 = ((bm(xs_l,:)-bm(xs_l-1,:))./I(xs_l-1,:))./(xcp(xs_l)-xcp(xs_l-1)); 
    delta_slope = slope2-slope1; % (lbf/inch^4)
    % apply boundary conditions
    c1 = -((1/6)*sum((F./I(xp_l,:)).*max(x_r(end)-xcp(xp_l,:),0).^3,1) + (1/2)*sum(step.*max(x_r(end)-x_s,0).^2,1) + (1/6)*sum(delta_slope.*max(x_r(end)-x_s,0).^3,1))/x_r(end); % (lbf/inch^2) 
    % define functions to calculate the deflection and the slope
    theta = @(x) (1/E)*((1/2)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^2,1) + sum(step.*max(x-x_s,0),1) + (1/2)*sum(delta_slope.*max(x-x_s,0).^2,1)+c1); % (radians)
    delta = @(x) (1/E)*((1/6)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^3,1) + (1/2)*sum(step.*max(x-x_s,0).^2,1) + (1/6)*sum(delta_slope.*max(x-x_s,0).^3,1)+c1*x); % (inches)
else
    c1 = -((1/6)*sum((F./I(xp_l,:)).*max(x_r(end)-xcp(xp_l,:),0).^3,1))/x_r(end); % (lbf/inch^2) 
    theta = @(x) (1/E)*((1/2)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^2,1)+c1); % (radians)
    delta = @(x) (1/E)*((1/6)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^3,1)+c1*x); % (inches)
end
delta_r = cell2mat(arrayfun(delta,sort([x_f;x_r]),'UniformOutput',false)); 
theta_r = cell2mat(arrayfun(theta,sort([x_f;x_r]),'UniformOutput',false)); 
str = 'deflection in the xy plane (inches):'; fprintf('%s \n\n',str); fprintf('%+5.3e \n',delta_r(:,1)');
str = 'slope about the z axis (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',theta_r(:,1)');
str = 'deflection in the xz plane (inches):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',delta_r(:,2)');
str = 'slope about the y axis (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',theta_r(:,2)');
str = 'resultant deflection (inches):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',(sqrt(sum(delta_r.^2,2)))');
str = 'resultant slope (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',(sqrt(sum(theta_r.^2,2)))');
end

Answer 1

[Stephen23]

In lieu of actual information, assuming that all input arguments are scalar:

Shaft_deflection_calculation(1,2,3,4,5,6)

Arrays have incompatible sizes for this operation.

Error in solution>@(x)sum(F.*max(x-sort([x_f;x_r]),0),1) (line 17)
bm = cell2mat(arrayfun(@(x) sum(F.*max(x-sort([x_f;x_r]),0),1),xcp,'UniformOutput',false)); % (lbf*inch)

Error in solution>Shaft_deflection_calculation (line 17)
bm = cell2mat(arrayfun(@(x) sum(F.*max(x-sort([x_f;x_r]),0),1),xcp,'UniformOutput',false)); % (lbf*inch)

The cause is the anonymous function on that line, in particular this part:

F.*max(x-sort([x_f;x_r]),0)

^ has size 2x1

^^^^^^^^^^^^^^^^^^^^^^^^ has size 4x1

"what change can solve the problem"

• Do not multiply a 2x1 array with a 4x1 array.
• Check your code as you write it.

function Shaft_deflection_calculation(E,F,x_f,x_r,x_s,d)
E = 30*10^6;
F = [20; 45];
x_f = [5.25; 5.25];
x_r = [0.5; 10];
x_s = [1;2;3;4;5;6];
d = [1;1;1;1;1;1;1];
% calculations %%%%%%%%%%%%%%%%%%%
xcp = sort([x_f; x_r; x_s]);
xp_l = sort(cell2mat(arrayfun(@(x) (find(xcp==x)),[x_f;x_r],'UniformOutput',false)));
for i = 1:length(xp_l)
    if xp_l(i) >1 && xp_l(i) < length(xcp), d = [d(1:xp_l(i)-1); d(xp_l(i)-1); d(xp_l(i):end)]; end
end
I = repmat(pi*d.^4/64,1,size(F,2)); % calculate the second moment of area (inch^4)
% calculation of the bending moment distribution using singularity functions
bm = cell2mat(arrayfun(@(x) sum(F.*max(x-sort([x_f;x_r]),0),1),xcp,'UniformOutput',false)); % (lbf*inch)
if x_f(end) == xcp(end) || x_r(end) == xcp(end), F = F(1:end-1,:); xp_l = xp_l(1:end-1); end
if(~isempty(x_s))
    xs_l = sort(cell2mat(arrayfun(@(x) (find(xcp==x)),x_s,'UniformOutput',false)));
    step = bm(xs_l,:)./I(xs_l,:) - bm(xs_l,:)./I(xs_l-1,:); % (lbf/inch^3) 
    slope2 = ((bm(xs_l+1,:)-bm(xs_l,:))./I(xs_l,:))./(xcp(xs_l+1)-xcp(xs_l)); slope1 = ((bm(xs_l,:)-bm(xs_l-1,:))./I(xs_l-1,:))./(xcp(xs_l)-xcp(xs_l-1)); 
    delta_slope = slope2-slope1; % (lbf/inch^4)
    % apply boundary conditions
    c1 = -((1/6)*sum((F./I(xp_l,:)).*max(x_r(end)-xcp(xp_l,:),0).^3,1) + (1/2)*sum(step.*max(x_r(end)-x_s,0).^2,1) + (1/6)*sum(delta_slope.*max(x_r(end)-x_s,0).^3,1))/x_r(end); % (lbf/inch^2) 
    % define functions to calculate the deflection and the slope
    theta = @(x) (1/E)*((1/2)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^2,1) + sum(step.*max(x-x_s,0),1) + (1/2)*sum(delta_slope.*max(x-x_s,0).^2,1)+c1); % (radians)
    delta = @(x) (1/E)*((1/6)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^3,1) + (1/2)*sum(step.*max(x-x_s,0).^2,1) + (1/6)*sum(delta_slope.*max(x-x_s,0).^3,1)+c1*x); % (inches)
else
    c1 = -((1/6)*sum((F./I(xp_l,:)).*max(x_r(end)-xcp(xp_l,:),0).^3,1))/x_r(end); % (lbf/inch^2) 
    theta = @(x) (1/E)*((1/2)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^2,1)+c1); % (radians)
    delta = @(x) (1/E)*((1/6)*sum((F./I(xp_l,:)).*max(x-xcp(xp_l,:),0).^3,1)+c1*x); % (inches)
end
delta_r = cell2mat(arrayfun(delta,sort([x_f;x_r]),'UniformOutput',false)); 
theta_r = cell2mat(arrayfun(theta,sort([x_f;x_r]),'UniformOutput',false)); 
str = 'deflection in the xy plane (inches):'; fprintf('%s \n\n',str); fprintf('%+5.3e \n',delta_r(:,1)');
str = 'slope about the z axis (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',theta_r(:,1)');
str = 'deflection in the xz plane (inches):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',delta_r(:,2)');
str = 'slope about the y axis (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',theta_r(:,2)');
str = 'resultant deflection (inches):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',(sqrt(sum(delta_r.^2,2)))');
str = 'resultant slope (radians):'; fprintf('\n %s \n\n',str); fprintf('%+5.3e \n',(sqrt(sum(theta_r.^2,2)))');
end