[Matlab] Description of system constants - commonly used constants and commonly used special matrix functions

Past review

[Summary] ⧫ [Matlab Six Degrees of Freedom Robot] Series Article Summary \blacklozenge \fcolorbox{black}{aqua}{[Matlab Six Degrees of Freedom Robot] Series Article Summary}
$⧫\boxed{[Matlabsixdegrees\; of\; freedomrobot]series\; ofarticles}$

foreword

This article introduces some pre-defined special variables in Matlab, usually calledconstant, two tables are listed below, includingcommon constantandCommonly used special matrix functions。

---

The following is the text of this article, including the tables and codes of commonly used constants and commonly used special matrix functions and a step-by-step analysis of the code.

text

1. Commonly used constants

Definition: Knowing the motion parameters of each joint, find the pose of the end effector relative to the reference coordinate system.

1. Table of common constants

constant	illustrate	constant	illustrate
i,j	Imaginary unit, defined as $\sqrt{-1}$	eps	Relative Accuracy of Floating-Point Arithmetic
pi	PI	realmax	largest positive real number
Inf	Unprecedented	realmin	smallest positive real number
NaN	Indeterminate $(0/0)$	ans	default variable name

2. Code example

In MATLAB programming, when defining a variable, avoid having the same name as the constant, so as not to change the value of the constant and cause inconvenience to the calculation.
MATLAB code input constant output is as follows:

>> i
ans = 0 + 1i

>> pi
ans = 3.14159265358979

>> inf
ans = Inf

>> nan
ans = NaN

>> eps
ans = 2.22044604925031e-16

>> realmax
ans = 1.79769313486232e+308

>> realmin
ans = 2.2250738585072e-308

>> ans
>> 

first inputanswill appear after inputrealminThe value of $ans=2.2250738585072e-308$ , when using the commandclearAfter that, a null value will appear.

2. Commonly used special matrix functions

1. Table of commonly used special matrix functions

Function name	illustrate	Function name	illustrate
zeros	All $0$ matrix	eye	identity matrix
ones	All $1$ matrix	compan	Adjoint matrix
rand	uniformly distributed random matrix	hilb	$Hilbert$ matrix
randn	Normally distributed random matrix	invhilb	$Hilbert$ inverse matrix
magic	Rubik's cube matrix	vander	$Vander$ matrix
diag	diagonal matrix	pascal	$Pascal$ matrix
trio	upper triangular matrix	hadamard	$Hadamard$ matrix
trill	lower triangular matrix	tender()	$Hankel$ matrix

2. Code example

After the MATLAB code is typed into a special matrix generation function, the output is as follows:

zeros

>> zeros
ans = 0
>> zeros(3)
ans =  0     0     0
	   0     0     0
	   0     0     0

ones

>> ones
ans = 1
>> ones(3)
ans = 1     1     1
      1     1     1
      1     1     1

rand

>> rand
ans =  0.400758135480105
>> rand(3)
ans =    0.764893793995034         0.464428454367176         0.927653178179463
         0.582893514061483         0.513381433938698          0.23087376700534
         0.217163157933335         0.862468459521113         0.344401924372255

randn

>> randn
ans = 0.375644208035345
>> randn(3)
ans =   -0.112892984467453        -0.313987577226449        -0.731194789130593
         0.479258573665327         0.159292754138156         -2.60703227023313
         0.605389358206988        -0.600365174356452        0.0765585801546292

magic

>> magic(3)
ans = 8     1     6
      3     5     7
      4     9     2
>> magic(5)
ans = 17    24     1     8    15
      23     5     7    14    16
       4     6    13    20    22
      10    12    19    21     3
      11    18    25     2     9

设$A=\left[\begin{array}{ccc}2& 5& 7\\ 4& 7& 3\\ 8& 9& 2\end{array}\right]$
diag(A)、triu(A)、tril(A)

>> diag(A)
ans =
     2
     7
     2
     
>> triu(A)
ans =
     2     5     7
     0     7     3
     0     0     2
     
>> tril(A)
ans =
     2     0     0
     4     7     0
     8     9     2

---

Summarize

The above is the description of the system constants. This article introduces the constant names and function names of constants and special matrices in detail, as well as the implementation of their codes. MATLAB provides functions for common constants and special matrices, which makes our calculation process more convenient.

references

MATLAB/Simulink System Simulation——Tsinghua University Press