第1章 MATLAB 概述
1.1 创建变量
>> a=2 % 创建变量
a =
2
>> whos % 查看变量属性
Name Size Bytes Class Attributes
a 1x1 8 double
>> b=8
b =
8
>> c=a+b
c =
10
>> d=tan(a)
d =
-2.1850
>> e=sin(b)
e =
0.9894
>> whos
Name Size Bytes Class Attributes
a 1x1 8 double
b 1x1 8 double
c 1x1 8 double
d 1x1 8 double
e 1x1 8 double
1.2 数值显示格式
| 格式 |
显示格式 |
格式效果说明 |
| short |
3.1416 |
默认格式，保留 4 位小数，整数部分超过 3 位的小数用 shortE 格式 |
| shortE |
3.1416e+00 |
用 1 位整数和 4 位小数表示，倍数关系用科学记数法表示成十进制指数形式 |
| shortG |
3.1416 |
保证 5 位有效数字，当为\(10 ^ {-5} \sim 10 ^ 5\) 时，自动调整数位，超出时用 shortE 格式 |
| shortEng |
3.1416e+000 |
短工程记数法，小数点后包含 4 位数，指数为 3 的倍数 |
| long |
3.141592653589793 |
15 位小数，最多 2 位整数，共 16 位十进制数，否则用 longE 格式表示 |
| longE |
3.141592653589793e+00 |
15 位小数的科学记数法 |
| longG |
3.14159265358979 |
保证 15 位有效数字，当为\(10 ^ {-15} \sim 10 ^ {15}\) 时，自动调整数位，超出时用 longE 格式 |
| longEng |
3.14159265358979e+000 |
长工程记数法，包含 15 位有效位数，指数为 3 的倍数 |
| rat |
355/113 |
rational，用分数有理数近似表示 |
| hex |
400921fb54442d18 |
十六进制格式表示 |
| + |
+ |
正 / 负数和零分别用 +、-、空格表示 |
| bank |
3.14 |
限两位小数，用于表示元、角、分 |
| compact |
不留空行显示 |
在显示结果之间没有空行的紧凑格式 |
| loose |
留空行显示 |
在显示结果之间有空行的稀疏格式 |
>> pi
ans =
3.1416
>> format long
>> pi
ans =
3.141592653589793
>> format longE
>> pi
ans =
3.141592653589793e+00
>> format shortE
>> pi
ans =
3.1416e+00
>> format % 重置为默认值
>> pi
ans =
3.1416
>> format compact % 重置为紧凑格式
>> pi
ans =
3.1416
1.3 函数
新建“函数 funa.m 文件”
function f=funa(var)
f=sin(var);
end
>> type funa.m % 显示函数内容
function f=funa(var)
f=sin(var);
end
>> x=[0 pi/2 pi 3*pi/2 2*pi]
x =
0 1.5708 3.1416 4.7124 6.2832
>> sinx=funa(x) % 调用函数
sinx =
0 1.0000 0.0000 -1.0000 -0.0000
1.4 脚本
新建 “脚本 sroot.m 文件”
% sroot 用于求 A*X=b
A=[1 2 1; 2 -1 3; 3 1 2];
b=[7; 7; 18];
X=A\b
>> sroot
错误使用 /
矩阵维度必须一致。
出错 sroot ( 第 4 行 )
X=A/b
^
>> sroot
X =
7
1
-2
1.5 函数列表
1.5.1 初等函数列表
>> help elfun
Elementary math functions.
Trigonometric.
sin - Sine.
sind - Sine of argument in degrees.
sinh - Hyperbolic sine.
asin - Inverse sine.
asind - Inverse sine, result in degrees.
asinh - Inverse hyperbolic sine.
cos - Cosine.
cosd - Cosine of argument in degrees.
cosh - Hyperbolic cosine.
acos - Inverse cosine.
acosd - Inverse cosine, result in degrees.
acosh - Inverse hyperbolic cosine.
tan - Tangent.
tand - Tangent of argument in degrees.
tanh - Hyperbolic tangent.
atan - Inverse tangent.
atand - Inverse tangent, result in degrees.
atan2 - Four quadrant inverse tangent.
atan2d - Four quadrant inverse tangent, result in degrees.
atanh - Inverse hyperbolic tangent.
sec - Secant.
secd - Secant of argument in degrees.
sech - Hyperbolic secant.
asec - Inverse secant.
asecd - Inverse secant, result in degrees.
asech - Inverse hyperbolic secant.
csc - Cosecant.
cscd - Cosecant of argument in degrees.
csch - Hyperbolic cosecant.
acsc - Inverse cosecant.
acscd - Inverse cosecant, result in degrees.
acsch - Inverse hyperbolic cosecant.
cot - Cotangent.
cotd - Cotangent of argument in degrees.
coth - Hyperbolic cotangent.
acot - Inverse cotangent.
acotd - Inverse cotangent, result in degrees.
acoth - Inverse hyperbolic cotangent.
hypot - Square root of sum of squares.
deg2rad - Convert angles from degrees to radians.
rad2deg - Convert angles from radians to degrees.
Exponential.
exp - Exponential.
expm1 - Compute exp(x)-1 accurately.
log - Natural logarithm.
log1p - Compute log(1+x) accurately.
log10 - Common (base 10) logarithm.
log2 - Base 2 logarithm and dissect floating point number.
pow2 - Base 2 power and scale floating point number.
realpow - Power that will error out on complex result.
reallog - Natural logarithm of real number.
realsqrt - Square root of number greater than or equal to zero.
sqrt - Square root.
nthroot - Real n-th root of real numbers.
nextpow2 - Next higher power of 2.
Complex.
abs - Absolute value.
angle - Phase angle.
complex - Construct complex data from real and imaginary parts.
conj - Complex conjugate.
imag - Complex imaginary part.
real - Complex real part.
unwrap - Unwrap phase angle.
isreal - True for real array.
cplxpair - Sort numbers into complex conjugate pairs.
Rounding and remainder.
fix - Round towards zero.
floor - Round towards minus infinity.
ceil - Round towards plus infinity.
round - Round towards nearest integer.
mod - Modulus (signed remainder after division).
rem - Remainder after division.
sign - Signum.
1.5.2 高等函数列表
>> help specfun
Specialized math functions.
Specialized math functions.
airy - Airy functions.
besselj - Bessel function of the first kind.
bessely - Bessel function of the second kind.
besselh - Bessel functions of the third kind (Hankel function).
besseli - Modified Bessel function of the first kind.
besselk - Modified Bessel function of the second kind.
beta - Beta function.
betainc - Incomplete beta function.
betaincinv - Inverse incomplete beta function.
betaln - Logarithm of beta function.
ellipj - Jacobi elliptic functions.
ellipke - Complete elliptic integral.
erf - Error function.
erfc - Complementary error function.
erfcx - Scaled complementary error function.
erfinv - Inverse error function.
erfcinv - Inverse complementary error function.
expint - Exponential integral function.
gamma - Gamma function.
gammainc - Incomplete gamma function.
gammaincinv - Inverse incomplete gamma function.
gammaln - Logarithm of gamma function.
psi - Psi (polygamma) function.
legendre - Associated Legendre function.
cross - Vector cross product.
dot - Vector dot product.
Number theoretic functions.
factor - Prime factors.
isprime - True for prime numbers.
primes - Generate list of prime numbers.
gcd - Greatest common divisor.
lcm - Least common multiple.
rat - Rational approximation.
rats - Rational output.
perms - All possible permutations.
nchoosek - All combinations of N elements taken K at a time.
factorial - Factorial function.
Coordinate transforms.
cart2sph - Transform Cartesian to spherical coordinates.
cart2pol - Transform Cartesian to polar coordinates.
pol2cart - Transform polar to Cartesian coordinates.
sph2cart - Transform spherical to Cartesian coordinates.
hsv2rgb - Convert hue-saturation-value colors to red-green-blue.
rgb2hsv - Convert red-green-blue colors to hue-saturation-value.
1.5.3 矩阵函数列表
>> help elmat
Elementary matrices and matrix manipulation.
Elementary matrices.
zeros - Zeros array.
ones - Ones array.
eye - Identity matrix.
repmat - Replicate and tile array.
repelem - Replicate elements of an array.
combinations- Generate all element combinations of arrays.
linspace - Linearly spaced vector.
logspace - Logarithmically spaced vector.
freqspace - Frequency spacing for frequency response.
meshgrid - X and Y arrays for 3-D plots.
accumarray - Construct an array with accumulation.
: - Regularly spaced vector and index into matrix.
Basic array information.
size - Size of array.
length - Length of vector.
ndims - Number of dimensions.
numel - Number of elements.
disp - Display matrix or text.
isempty - True for empty array.
isequal - True if arrays are numerically equal.
isequaln - True if arrays are numerically equal, treating NaNs as equal.
height - Number of rows.
width - Number of columns.
Matrix manipulation.
cat - Concatenate arrays.
reshape - Reshape array by rearranging existing elements.
resize - Resize data by adding or removing elements.
paddata - Pad data.
trimdata - Trim data.
diag - Diagonal matrices and diagonals of matrix.
blkdiag - Block diagonal concatenation.
tril - Extract lower triangular part.
triu - Extract upper triangular part.
fliplr - Flip matrix in left/right direction.
flipud - Flip matrix in up/down direction.
flip - Flip the order of elements.
rot90 - Rotate matrix 90 degrees.
: - Regularly spaced vector and index into matrix.
find - Find indices of nonzero elements.
end - Last index.
sub2ind - Linear index from multiple subscripts.
ind2sub - Multiple subscripts from linear index.
bsxfun - Binary singleton expansion function.
Multi-dimensional array functions.
ndgrid - Generate arrays for N-D functions and interpolation.
permute - Permute array dimensions.
ipermute - Inverse permute array dimensions.
shiftdim - Shift dimensions.
circshift - Shift array circularly.
squeeze - Remove singleton dimensions.
Array utility functions.
isscalar - True for scalar.
isvector - True for vector.
isrow - True for row vector.
iscolumn - True for column vector.
ismatrix - True for matrix.
Special variables and constants.
eps - Floating point relative accuracy.
realmax - Largest positive floating point number.
realmin - Smallest positive floating point number.
intmax - Largest positive integer value.
intmin - Smallest integer value.
flintmax - Largest consecutive integer in floating point format.
pi - 3.1415926535897....
i - Imaginary unit.
inf - Infinity.
nan - Not-a-Number.
isnan - True for Not-a-Number.
isinf - True for infinite elements.
isfinite - True for finite elements.
j - Imaginary unit.
true - True array.
false - False array.
Specialized matrices.
compan - Companion matrix.
gallery - Test matrices.
hadamard - Hadamard matrix.
hankel - Hankel matrix.
hilb - Hilbert matrix.
invhilb - Inverse Hilbert matrix.
magic - Magic square.
pascal - Pascal matrix.
rosser - Classic symmetric eigenvalue test problem.
toeplitz - Toeplitz matrix.
vander - Vandermonde matrix.
wilkinson - Wilkinson's eigenvalue test matrix.
Controlling multithreading setting.
maxNumCompThreads - Controls the maximum number of computational threads.
1.6 语句
>> a=11
a =
11
>> rho=(1+sqrt(a))/2 % 函数 sqrt 求平方根
rho =
2.1583
>> b=abs(3+8i) % 函数 abs 用于求绝对值或复数的模
b =
8.5440
>> x=sqrt(besselk(5/3,rho-1)) % besselk 为第二类修正的 Bessel 函数
x =
0.8931
>> x=sqrt(besselk(5/3,rho-i))
x =
0.2916 + 0.2398i
1.7 常用命令
| 命令 |
命令说明 |
命令 |
命令说明 |
| clc |
清除命令行窗口中的所有显示内容 |
cd |
显示或改变当前工作目录 |
| clf |
清除图形窗口 |
dir |
显示当前目录或指定目录下的文件 |
| clear |
清理内存变量 |
load |
加载指定文件的变量 |
| disp |
显示变量或文字内容 |
diary |
日志文件命令 |
| exit |
退出 MATLAB |
! |
调用 DOS 命令 |
| quit |
退出 MATLAB，等同于 exit |
pack |
收集内存碎片 |
| home |
将光标移至命令行窗口的左上角 |
hold |
图形保持开关 |
| echo |
命令行窗口信息显示开关 |
path |
显示搜索目录 |
| type |
显示指定 M 文件的内容 |
save |
保存内存变量到指定文件 |
| more |
控制命令行窗口的分页输出 |
close |
关闭指定图形窗口 |
1.8 标点符号
| 名称 |
符号 |
功能 |
| 空格 |
|
变量分隔符：数组行元素分隔符：矩阵一行中各元素间的分隔符：程序语句关键词分隔符 |
| 逗号 |
, |
分隔要显示计算结果的各语句：变量分隔符：矩阵一行中各元素间的分隔符：函数参数分隔符 |
| 点号 |
. |
数值中的小数点：结构数组的域访问符 |
| 分号 |
; |
分隔不显示计算结果的各语句；矩阵行与行的分隔符 |
| 冒号 |
: |
用于生成一维数值数组；表示一维数组的全部元素或多维数组中某一维的全部元素 |
| 百分号 |
% |
注释语句说明符，凡在其后的字符均被视为注释性内容而不被执行 |
| 单引号 |
' |
字符串标识符 |
| 叹号 |
! |
调用操作系统运算 |
| 续行符 |
… |
长命令行需要分行时用于连接下行 |
| 赋值号 |
= |
将表达式赋值给一个变量 |
| 圆括号 |
() |
用于矩阵元素引用：用于函数输入变量列表；确定运算的优先级 |
| 方括号 |
[] |
向量和矩阵的标识符；用于函数输出列表 |
| 花括号 |
{} |
标识构造元胞数组 |
| 下画线 |
_ |
用于变量、函数或文件名中的连字符 |
| at 符 |
@ |
用在函数名前形成函数句柄：用在目录名前形成用户对象类目录 |
1.9 帮助命令
| 命令 |
功能 |
命令 |
功能 |
| demo |
运行 MATLAB 演示程序 |
lookfor |
按照指定的关键字查找所有相关的 M 文件 |
| help |
获取在线帮助 |
helpwin |
运行帮助窗口，列出函数组的主题 |
| who |
列出当前工作区窗口中的所有变量 |
which |
显示指定函数或文件的路径 |
| doc |
在网络浏览器中显示指定内容的 HTML 格式帮助文件或启动 helpdesk |
what |
列出当前目录或指定目录下的 M 文件、 MAT 文件和 MEX 文件 |
| exist |
检查变量、脚本、函数、文件夹或类的存在性 |
whos |
列出当前工作空间中变量的更多信息 |
1.9.1 help 命令
help name % 显示 name（可以是函数、方法、类、工具箱或变量等）指定的帮助信息
| 类型名 |
功能 |
类型名 |
功能 |
| general |
通用命令 |
graphics |
通用图形函数 |
| elfun |
基本数学函数 |
control |
控制系统工具箱函数 |
| elmat |
基本矩阵及矩阵操作 |
ops |
操作符及特殊字符 |
| mathfun |
矩阵函数、数值线性代数 |
polyfyn |
多项式和内插函数 |
| datafun |
数据分析及傅里叶变换 |
lang |
语言结构及调试 |
| strfun |
字符串函数 |
funfun |
非线性数值功能函数 |
| iofun |
低级文件输入 / 输出函数 |
... |
... |
1.9.2 lookfor 命令
lookfor keyword % 在搜索路径中所有 MATLAB 程序文件的第一个注释行（ H1 行）中，搜索指定的关键字，搜索结果显示所有匹配文件的 H1 行
lookfor keyword -all % 搜索 MATLAB 程序文件的第一个完整注释块
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