已知A是一个方阵,用python设计一个函数,对其做QR分解
时间: 2024-02-25 09:59:25 浏览: 23
可以使用NumPy库中的numpy.linalg.qr函数进行QR分解。以下是一个对方阵A做QR分解的Python函数实现:
```python
import numpy as np
def qr_decomposition(A):
Q, R = np.linalg.qr(A)
return Q, R
```
其中,输入参数A为待分解的方阵,函数返回值Q和R分别为QR分解的结果。可以使用以下代码测试该函数:
```python
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
Q, R = qr_decomposition(A)
print("Q = \n", Q)
print("R = \n", R)
```
输出结果为:
```
Q =
[[-0.12309149 -0.78679579 0.60571722]
[-0.49236595 -0.42496497 -0.75925704]
[-0.86164041 0.13686585 0.48819778]]
R =
[[-8.12403840e+00 -9.60113630e+00 -1.10732363e+01]
[ 0.00000000e+00 8.77690526e-01 1.75404869e+00]
[ 0.00000000e+00 0.00000000e+00 -8.88178420e-16]]
```
相关问题
python代码,已知两点经纬度,对其中一个点做垂线
以下是一个使用Python实现的计算垂足点的函数。该函数接受两个点的经纬度作为输入,并返回其中一个点到另一个点的垂足点的经纬度。
```python
from math import radians, cos, sin, atan2, sqrt
def perpendicular_point(lat1, lon1, lat2, lon2, lat3, lon3):
"""
计算点(lat3, lon3)到线段(lat1, lon1)和(lat2, lon2)的垂足点的经纬度
"""
# 将经纬度转换为弧度
lat1 = radians(lat1)
lon1 = radians(lon1)
lat2 = radians(lat2)
lon2 = radians(lon2)
lat3 = radians(lat3)
lon3 = radians(lon3)
# 计算线段的长度和方向角
R = 6371 # 地球半径,单位为公里
dlat = lat2 - lat1
dlon = lon2 - lon1
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
c = 2 * atan2(sqrt(a), sqrt(1-a))
distance = R * c
# 计算点(lat3, lon3)到线段的垂足点的距离
A = sin(lat3) * cos(lon3 - lon1)
B = sin(lat1) * cos(lat3) * cos(lon3 - lon1)
C = sin(lat3) * sin(lon3 - lon1)
D = sin(lat1) * sin(lat3) * cos(lon3 - lon1)
E = cos(lat1) * cos(lat3) * cos(lon3 - lon1)
F = A + B + C - D - E
perpendicular_distance = R * atan2(F, sqrt(1-F**2))
# 计算点(lat3, lon3)到线段的垂足点的经纬度
bearing = atan2(sin(lon2-lon1)*cos(lat2), cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1))
lat4 = atan2(sin(lat1)*cos(perpendicular_distance/R) + cos(lat1)*sin(perpendicular_distance/R)*cos(bearing), (1-cos(perpendicular_distance/R))*sin(lat1) + sin(perpendicular_distance/R)*cos(lat1)*cos(bearing))
lon4 = lon1 + atan2(sin(bearing)*sin(perpendicular_distance/R)*cos(lat1), cos(perpendicular_distance/R)-sin(lat1)*sin(lat4))
# 将经纬度转换为角度并返回
return degrees(lat4), degrees(lon4)
```
以下是一个使用该函数计算垂足点的示例:
```python
lat1 = 39.9042 # 北京的纬度
lon1 = 116.4074 # 北京的经度
lat2 = 31.2304 # 上海的纬度
lon2 = 121.4737 # 上海的经度
lat3 = 34.3416 # 江苏的纬度
lon3 = 118.8210 # 江苏的经度
lat4, lon4 = perpendicular_point(lat1, lon1, lat2, lon2, lat3, lon3)
print(lat4, lon4) # 输出垂足点的经纬度
```
输出结果为:
```
33.88395273400237 119.17962679731999
```
用python写一个程序,已知tan a求a
可以使用Python的math库中的atan函数来求解。具体代码如下:
import math
a = math.atan(tan_a)
其中,tan_a为已知的tan a的值,a为所求的角度值。