当还有一个常数（不在矩阵中）时，我该如何对矩阵进行加法、乘法？

Question

我正在尝试（除其他事项外）使用矩阵进行计算。这是我快完成了。

deltaX = -419.375
deltaY = -99.352
deltaZ = -591.349

deltaXYZ = np.array([deltaX,deltaY,deltaZ]).reshape(3,1)

omegaX = 0.850458
omegaY = 1.817245
omegaZ= -7.862245

omegaXR=radians(omegaX/3600)
omegaYR=radians(omegaY/3600)
omegaZR=radians(omegaZ/3600)

delta = (0.99496/(10**6))

x = 3240036.3696 
y = 990578.5272  
z = 5385763.1648 

swerefkoordinates = np.array([x,y,z]).reshape(3,1)

rZ=np.array([cos(omegaZR),sin(omegaZR),0,-sin(omegaZR),cos(omegaZR),0,0,0,1]).reshape(3,3)

rY=np.array([cos(omegaYR),0,-sin(omegaYR),0,1,0,sin(omegaYR),0,cos(omegaYR)]).reshape(3,3)

rX=np.array([1,0,0,0,cos(omegaXR),sin(omegaXR),0,-sin(omegaXR),cos(omegaXR)]).reshape(3,3)

R=np.dot(rZ,rY,rX)

到目前为止一切顺利

下一行计算给我带来了一些麻烦，我的意思是答案错误。

RR92 = deltaXYZ+(delta+1)*np.dot(R,swerefkoordinates)

我正在尝试做的是以下公式（RR92）。

[XYZ] = [deltaX,deltaY,deltaZ]+(1+delta)R[x,y,z]

我很难想象公式（而且我还不允许添加图片）。无论如何，[] 中的内容都是矩阵格式：3 行 1 列。

Answer 1

为了快速得到结果，我将 np.array 转换为矩阵并按如下方式进行计算：

import numpy as np
from numpy import radians, cos, sin, matrix

deltaX = -419.375
deltaY = -99.352
deltaZ = -591.349

deltaXYZ = np.array([deltaX,deltaY,deltaZ]).reshape(3,1)
delXYZ = matrix(deltaXYZ)  # matrix

omegaX = 0.850458
omegaY = 1.817245
omegaZ= -7.862245

omegaXR=radians(omegaX/3600)
omegaYR=radians(omegaY/3600)
omegaZR=radians(omegaZ/3600)

delta = (0.99496/(10**6))

x = 3240036.3696 
y = 990578.5272  
z = 5385763.1648 

swerefkoordinates = np.array([x,y,z]).reshape(1,3)  # 3*1
swc = matrix(swerefkoordinates)  # matrix

rZ=np.array([cos(omegaZR),sin(omegaZR),0,-     sin(omegaZR),cos(omegaZR),0,0,0,1]).reshape(3,3)

rY=np.array([cos(omegaYR),0,-sin(omegaYR),0,1,0,sin(omegaYR),0,cos(omegaYR)]).reshape(3,3)

rX=np.array([1,0,0,0,cos(omegaXR),sin(omegaXR),0,-sin(omegaXR),cos(omegaXR)]).reshape(3,3)

R=np.dot(rZ,rY,rX)
mR = matrix(R)  # matrix

# finally,
RR92 = delXYZ + (delta+1) * (mR*swc.T)  # matrix operatoionz
RR92

# Output
# matrix([[ 3239535.00769073],
#        [  990603.65962255],
#        [ 5385205.71977643]])

Answer 2

我设法解决了问题：

from math import *
from numpy import *
import numpy as np

deltaX = -419.375
deltaY = -99.352
deltaZ = -591.349

deltaXYZ = np.matrix([[deltaX],[deltaY],[deltaZ]])

omegaX = 0.850458
omegaY = 1.817245
omegaZ= -7.862245

omegaXR=radians(omegaX/3600)
omegaYR=radians(omegaY/3600)
omegaZR=radians(omegaZ/3600)

delta = (0.99496/(10**6))

x = 3240036.3696
y = 990578.5272
z = 5385763.1648 

swc = np.matrix([[x],[y],[z]])

#Rotationsmatrix for Z
rZ=np.matrix([[cos(omegaZR),sin(omegaZR),0],[-sin(omegaZR),cos(omegaZR),0],[0,0,1]])

#Rotationsmatrix for Y
rY=np.matrix([[cos(omegaYR),0,-sin(omegaYR)],[0,1,0],[sin(omegaYR),0,cos(omegaYR)]])

#Rotationsmatrix for X
rX=np.matrix([[1,0,0],[0,cos(omegaXR),sin(omegaXR)],[0,-sin(omegaXR),cos(omegaXR)]]).reshape(3,3)

R=rZ*rY*rX

#calculation
RR92 = deltaXYZ + (delta+1) * (R*swc)

print RR92

正确：

3239535.0069 990625.8659 5385201.6355

当还有一个常数（不在矩阵中）时，我该如何对矩阵进行加法、乘法？

How do I do addition, multiplication with matrices, when there is a constant (not in a matrix) as well?

python

matrix

matrix-multiplication

正确：