R编程中向量的点积

在数学中，点积或也称为标量积是一种代数运算，它采用两个等长的数字序列并返回一个数字。让我们给出两个向量 A和B，我们必须找到两个向量的点积。

鉴于，

$A = a_1i + a_2j + a_3k$

和，

$B = b_1i + b_2j + b_3k$

where,

i: the unit vector along the x directions

j: the unit vector along the y directions

k: the unit vector along the z directions

然后点积计算为：

$DotProduct = a_1 * b_1 + a_2 * b_2 + a_3 * b_3$

例子：

给定两个向量 A 和 B，

A = 3i + 5j + 4k,

and

B = 2i + 7j + 5k

Dot Product = 3 * 2 + 5 * 7 + 4 * 5 = 6 + 35 + 20 + 61 

在 R 中计算点积

R 语言提供了一种非常有效的方法来计算两个向量的点积。通过使用几何库中可用的dot()方法，可以做到这一点。

Syntax: dot(x, y, d = NULL)

Parameters:

x: Matrix of vectors

y: Matrix of vectors

d: Dimension along which to calculate the dot product

Return: Vector with length of dth dimension

示例 1：

R

# R Program illustrating
# dot product of two vectors
  
# Import the required library
library(geometry)
  
# Taking two scalar values
a = 5
b = 7
  
# Calculating dot product using dot()
print(dot(a, b, d = TRUE))

输出：

[1] 35

示例 2：

R

# R Program illustrating
# dot product of two vectors
  
# Import the required library
library(geometry)
  
# Taking two complex values
a = 3 + 1i
b = 7 + 6i
  
# Calculating dot product using dot()
print(dot(a, b, d = TRUE))

输出：

[1] 15+25i

示例 3：

R

# R Program illustrating
# dot product of two vectors
  
# Import the required library
library(geometry)
  
# Taking two simple vectors
a = c(1, 4)
b = c(7, 4)
  
# Calculating dot product using dot()
print(dot(a, b, d = TRUE))

输出：

[1] 23

示例 4：

在以下示例中，让我们采用两个二维数组并计算这两个数组的点积。要在 R 中创建二维数组，请参阅 R 中的多维数组。

R

# R Program illustrating
# dot product of two vectors
  
# Import the required library
library(geometry)
  
# Taking two 2D array
vector1 = c(2, 1)
vector2 = c(0, 3)
a = array(c(vector1, vector2), dim = c(2, 2))
vector1 = c(4, 2)
vector2 = c(9, 3)
b = array(c(vector1, vector2), dim = c(2, 2))
  
# Calculating dot product using dot()
print(dot(a, b, d = TRUE))

输出：

[1] 10  9