Dot Product Doubt, don't get the result I expected.

Question

Wai Han 2020-9-28

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https://ww2.mathworks.cn/matlabcentral/answers/601204-dot-product-doubt-don-t-get-the-result-i-expected

评论： Wai Han 2020-9-28

Hello I am new to Matlab and I am stuck in doing some maths(dot product) problem today. Please help me out.

I can write the correct code and format in python format, but i got some issues in the matlab. The python code is the following --

% This is the python code
RIMatrix_sph1 = RIMatrix_sph + mass_sph * (np.dot(q1.T, q1) * np.eye(3) - np.dot(q1, q1.T))

The error I encounter in matlab is in this specific part of the code --

(np.dot(q1.T, q1) * np.eye(3) - np.dot(q1, q1.T))

Here is the code I wrote in the Matlab

% This is the MATLAB code
mass_sph = 23.4572;
RIMatrix_sph = [0.0938 0 0; 0 0.0938 0; 0 0 0.0938]
RIMatrix_sph1 = RIMatrix_sph + mass_sph * (dot(transpose(q1),q1) * eye(3) - dot(q1,transpose(q1)))

I would be appreciated if you coulde help me with the problem.

PS.

This is the correct answer return by my python code --

RIMatrix_sph1 = [1.0321 0 0; 0 1.0321 0; 0 0 0.0938]

This is the wrong answer return by my MATLAB code --

RIMatrix_sph1 = [0.0938 -0.938 -0.9382; -0.9382 0.0938 -0.9382; -0.9382 -0.9382 0.0938]

Thank you Again!

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Wai Han 2020-9-28

在 MATLAB Online 中打开

Okay, Thanks for the help guys!

Here is the full python code, the variables are the same in the MATLAB too

import math
import numpy as np
import modern_robotics as mr
pi = math.pi
print("\n------ Question 1 ------")
density = 5600
rad_cyl = 0.02
len_cyl = 0.2
rad_sph = 0.1
mass_cyl = density * pi * len_cyl * rad_cyl**2
print("\nMass of Cylinder: ", mass_cyl, sep='')
Ixx_cyl = mass_cyl * (3 * rad_cyl**2 + len_cyl**2) / 12
Iyy_cyl = Ixx_cyl
Izz_cyl = mass_cyl * rad_cyl**2 / 2
RIMatrix_cyl = np.diag([Ixx_cyl, Iyy_cyl, Izz_cyl])
print("\nRIMatrix_cyl:\n", np.array2string(RIMatrix_cyl, separator=','), sep='')
mass_sph = density * 4/3 * pi * rad_sph**3
print("\nMass of Sphere: ", mass_sph, sep='')
Ixx_sph = mass_sph * 2/5 * rad_sph**2
Iyy_sph = Ixx_sph
Izz_sph = Ixx_sph
RIMatrix_sph = np.diag([Ixx_sph, Iyy_sph, Izz_sph])
print("\nRIMatrix_sph:\n", np.array2string(RIMatrix_sph, separator=','), sep='')
'''exploit Steiner's theorem'''
q1 = np.array([[0], [0], [rad_sph + len_cyl/2]])
RIMatrix_sph1 = RIMatrix_sph + mass_sph * (np.dot(q1.T, q1) * np.eye(3) - np.dot(q1, q1.T))
q2 = np.array([[0], [0], [-rad_sph - len_cyl/2]])
RIMatrix_sph2 = RIMatrix_sph + mass_sph * (np.dot(q2.T, q2) * np.eye(3) - np.dot(q2, q2.T))
print("\nRIMatrix_sph1:\n", np.array2string(RIMatrix_sph1, separator=','), sep='')
print("\nRIMatrix_sph2:\n", np.array2string(RIMatrix_sph2, separator=','), sep='')
RIMatrix_q1 = RIMatrix_cyl + RIMatrix_sph1 + RIMatrix_sph2
RIMatrix_q1_off = np.around(RIMatrix_q1, decimals=2)
print("\nQuestion 1:\n", np.array2string(RIMatrix_q1_off, separator=','), sep='')

Wai Han 2020-9-28

在 MATLAB Online 中打开

This is the MATLAB version --

rho = 5600;
cyl_rad = 0.02;
cyl_length = 0.2; 
sph_rad = 0.1;
cyl_mass = rho*pi*cyl_rad^2*cyl_length
sph_mass = (4*rho*pi*sph_rad^3)/3
% MoI of cylinder
cyl_Ixx =(cyl_mass*(3*cyl_rad^2 + cyl_length^2))/12;
cyl_Iyy = cyl_Ixx;
cyl_Izz = (cyl_mass*cyl_rad^2)/2;
cyl_MoI = diag([cyl_Ixx,cyl_Iyy,cyl_Izz])
%MoI of sphere
sph_Ixx = (sph_mass * sph_rad^2 * 2)/5;
sph_MoI = diag([sph_Ixx,sph_Ixx,sph_Ixx])
%Steiner's theorem
%This is the part which I encounter issuses:
%This picture describes the equation that I used!

q1 = [0,0,sph_rad + cyl_length/2]
q2 = [0,0,-sph_rad - cyl_length/2]
I_cm_sph1 = sph_MoI + sph_mass *(dot(transpose(q1),q1) * eye(3) - dot(q1,transpose(q1)))
I_cm_sph2 = sph_MoI + sph_mass *(dot(transpose(q2),q2) * eye(3) - dot(q2,transpose(q2)))
total_MoI = cyl_MoI + I_cm_sph1 + I_cm_sph2

VBBV 2020-9-28

Use .* for product of matrices

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Answer 1

Stephen23 2020-9-28

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/601204-dot-product-doubt-don-t-get-the-result-i-expected#answer_501739

编辑：Stephen23 2020-9-28

在 MATLAB Online 中打开

You are using the wrong operator. You need basic matrix multiplication, not the dot product:

>> q1 = [0;0;0.2];
>> q1.'*q1
ans =  0.040000
>> q1*q1.'
ans =
   0.000000   0.000000   0.000000
   0.000000   0.000000   0.000000
   0.000000   0.000000   0.040000

As the dot product of two vectors by definition returns a scalar, the numpy.dot implementation is a bit strange. Reading the numpy documentation clarifies that "If both a and b are 2-D arrays, it is matrix multiplication..." , which is what your python code is actually doing (not a dot product). Note that the numpy documentation also recommends using an explicit matrix multiplication, rather than this bizarre overloaded "dot" operator: "..using matmul or a @ b is preferred".

Also note that your screenshot shows (implicit) matrix multiplication of those terms, not the dot product.

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Wai Han 2020-9-28

Thanks for the help Mr.Cobeldick! I've thoroughly read through the links you provided " Wikipedia the dot product ". I was mistakenly calculating the vectors. I got them now..

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Answer 2

VBBV 2020-9-28

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/601204-dot-product-doubt-don-t-get-the-result-i-expected#answer_501649

编辑：madhan ravi 2020-9-28

在 MATLAB Online 中打开

% This is the MATLAB code
mass_sph = 23.4572;
RIMatrix_sph = [0.0938 0 0; 0 0.0938 0; 0 0 0.0938]
RIMatrix_sph1 = RIMatrix_sph + mass_sph * (dot(transpose(q1),q1). * eye(3) - dot(q1,transpose(q1)))

Try the above

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Wai Han 2020-9-28

编辑：Wai Han 2020-9-28

在 MATLAB Online 中打开

Hello, I think I have found the difference.

In this matlab code --

q1 = [0;0;sph_rad + cyl_length/2];
x = dot(transpose(q1),q1)
y = dot(q1,transpose(q1))

The result i get is x = 0.4 and y =0.4 , which in my opinion is wrong for the dot product. I am afraid if it is the correct answer since I am not very familer with the MATLAB function. But by mathematical way, the answer should be the result returned by the python code.

Here is the python code--

q1 = np.array([[0], [0], [0.2]])
x = np.dot(q1.T, q1)
y = np.dot(q1 , q1.T)
print(x)
print(y)

The answer returned is x = [0.04] and y =[0 0 0;0 0 0; 0 0 0.04]

Can someone explain me why that happens?

Again, thanks for your help Sirs!

Stephen23 2020-9-28

编辑：Stephen23 2020-9-28

在 MATLAB Online 中打开

"The result i get is x = 0.4 and y =0.4 , which in my opinion is wrong for the dot product."

According to Wikipedia the dot product is "is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number", and gives this definition:

Wolfram Mathworld gives this definition (amongst others):

X.Y = X1*Y1 + .. + Xn*Yn

Both of these agree with MATLAB.

"But by mathematical way, the answer should be the result returned by the python code."

Not according to standard mathematics taught in most schools and universities. What the numpy code returns is actually the matrix multiplication of a column vector and a row vector, it is NOT the dot product!

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Dot Product Doubt, don't get the result I expected.

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