MATLAB program design and application 2.4 Common internal functions of MATLAB

MATLAB程序设计与应用

2. 第2章 MATLABData and its arithmetic

2.4 MATLAB常用内部函数

Internal function is by MATLAB System according to the needs of general users provide users with a set of program,Also known as the system function or library function.

2.4.1 常用数学函数

MATLAB提供了许多数学函数,函数的自变量规定为矩阵变量,运算法则是将函数逐项作用于矩阵的元素上,Thus the result of the operation was a and the independent variables with the same dimension and size of matrix,With independent variable matrix is the matrix type.

>> A = [4,2;3,6]

A =

     4     2
     3     6

>> B = sqrt(A)

B =

    2.0000    1.4142
    1.7321    2.4495

常用的数学函数

函数名	功能	函数名	功能
sin/sind	正弦函数,The input values for arc/角度	abs	绝对值函数
cos/cosd	余弦函数,The input values for arc/角度	rem	求余
tan/tand	正切函数,The input values for arc/角度	mod	求模
asin/asind	反正弦函数,The return value for arc/角度	fix	向零方向取整
acos/acosd	反余弦函数,The return value for arc/角度	floor	不大于自变量的最大整数
atan/atand	反正切函数,The return value for arc/角度	ceil	不小于自变量的最小整数
sinh/asinh	双曲正弦函数/反双曲正弦函数	round	四舍五入到最邻近的整数
cosh/acosh	双曲余弦函数/反双曲余弦函数	sign	符号函数
tanh/atanh	双曲正切函数/反双曲正切函数	gcd	最大公约数
sqrt	平方根函数	lcm	最小公倍数
log	自然对数函数	factorial	阶乘
log10	常用对数函数	isprime	判断是否为素数
log2	以2为底的对数函数	primes	Generate prime number list
exp	自然指数函数	perms	生成所有排列
pow2	2的幂	randperm	To generate arbitrary arrangement

使用说明：

1. 三角函数有以弧度为单位的函数和以角度为单位的函数,In the Angle of function in the function name followed“d”,以示区别.

2. abs函数可以求实数的绝对值、复数的模、字符串的ASCII码值.例如, abs(-4). abs(3+4i)、abs(‘a’)的值分别为4、5、97.

3. Seek more operation and operator have the same place, but not quite the same,The main difference is that for negative integer division when the operation of different.对于整数a、 b来说,Seek more operations or modular arithmetic method is first integer quotientc=a/b,
   Strives for the remainder or dier=a-c*b.Residual operation in takec的值时,向0方向取整(fix函数),For modular arithmetic in the calculationc的值时,向负无穷方向取整（floor函数）.

   rem与 mod 函数的区别是,当b≠0时,rem(a,b)=a-b.*fix(a./b),而mod(a,b)=a-b.*floor(a/b);当b=0时,rem(a,0)=NaN 而mod(a,0)=a.

   显然,如果a、b符号相同,那么rem(a,b)=mod(a,b).如果a、b符号相反,那么
   mod(a,b)=rem(a,b)+b.rem(a,b)的符号与a相同,而 mod(a,b)的符号与b相同.例如,rem(7,4)=mod(7,4)=3;rem(-7,-4)=mod(-7,-4)=-3;rem(7,-4)=3,而 mod(7,-4)=-1:rem(-7,4)-3,而mod(-7,4)=1 .

4. 用于取整的函数有fix、floor、ceil、round,要注意它们的区别.round The round () function.设a为最靠近x的正整数(|x|≥a),则其余3The difference between a function：

   

设x=2.45,则fix(x)、floor(x)、ceil(x)、round(x)的结果分别是2、2、3、2.又设x=-2.65,则fix(x)、floor(x)、 ceil(x)、 round(x)的结果分别是-2、-3、-2、-3.

5. About function.当x<0时,sign(x)=-1:当x=0时,sign(x)=0:当x>0时,sign(x)=1.

2.4.2 Matrix of transcendental function

MATLABAlso provides some direct effects on the matrix of transcendental function,The function names in the internal function name suffix tom,And the input parametersA必须是方阵.

1. 矩阵平方根

   sqrtm(A)计算矩阵A的平方根√A.

   >> A = [4,2;3,6];
   >> B = sqrtm(A)
   
   B =
   
       1.9171    0.4652
       0.6978    2.3823
   
   >> B * B
   
   ans =
   
       4.0000    2.0000
       3.0000    6.0000
   

   若AFor real symmetric positive definite matrices or complex Hermitian（Hermitian)正定阵,Also must be able to calculate the square root of it.But some matrix,如 A=[0,1;0,0]Won't get the square root.若矩阵AWith negative eigenvalues of,则sqrtm(A)Will be a complex matrix.

   >> A = [4,9;16,25];
   >> eig(A)
   
   ans =
   
      -1.4452
      30.4452
   
   >> B = sqrtm(A)
   
   B =
   
      0.9421 + 0.9969i   1.5572 - 0.3393i
      2.7683 - 0.6032i   4.5756 + 0.2053i
   

2. 矩阵对数

   logm(A)计算矩阵4 的自然对数.The function of input parameters and the conditions of the relationship between the output and the functionsqrtm(A)完全一样.

   >> A = [4,9;1,5];
   >> L = logm(A);
   >> L
   
   L =
   
       1.0639    2.4308
       0.2701    1.3340
   

3. 矩阵指数

   expm(A)The function of the matrix exponential is oe的A次幂.

   L =
   
       1.0639    2.4308
       0.2701    1.3340
   
   >> B = expm(L)
   
   B =
   
       4.0000    9.0000
       1.0000    5.0000
   

4. Common matrix function

   funm(A,@fun)对方阵A计算由 funDefine the function of matrix function value.例如,当fun取exp时,funm(A,@exp)Matrix can be calculatedA的指数,与 expm(A)The calculation results of.

   >> A = [2,-1;1,0];
   >> funm(A,@exp)
   
   ans =
   
       5.4366   -2.7183
       2.7183         0
   
   >> expm(A)
   
   ans =
   
       5.4366   -2.7183
       2.7183         0
   

   funm函数可以用于 exp、log . sin、cos, sinh和 cosh等函数,But for the square root of matrix can only usesqrtm函数.