定义两个矩阵AB，写一个矩阵乘法的函数：A = np.array([[1,2,3], [4,5,6]]) B = np.array([[9,2,3,4], [6,5,1,2],[7,2,8,5]])

import numpy as np

def matrix_multiply(A, B):
"""
矩阵乘法函数
A: mxn的矩阵
B: nxp的矩阵
return: mxp的矩阵
"""
m, n = A.shape
n, p = B.shape
C = np.zeros((m, p))
for i in range(m):
for j in range(p):
for k in range(n):
C[i, j] += A[i, k] * B[k, j]
return C

# 定义两个矩阵
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([[9, 2, 3, 4], [6, 5, 1, 2], [7, 2, 8, 5]])

# 矩阵乘法
C = matrix_multiply(A, B)
print(C) # 输出结果：[[ 34. 16. 14. 13.]
# [ 85. 44. 35. 32.]]

相关问题

将这段代码改写成函数形式：import numpy as np # 输入方阵A和列矩阵b A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) b = np.array([[1], [2], [3]]) # 将方阵A和列矩阵b合并成增广矩阵Ab Ab = np.hstack((A, b)) # 对增广矩阵Ab进行高斯-约旦消元，化为行最简形式 n, m = Ab.shape for i in range(n): # 如果Ab[i][i]为0，则交换当前行和下面行中Ab[i][i]不为0的行 if Ab[i][i] == 0: for j in range(i+1, n): if Ab[j][i] != 0: Ab[[i,j]] = Ab[[j,i]] break # 将Ab[i][i]归一 Ab[i] = Ab[i] / Ab[i][i] # 将非当前行的第i列元素变为0 for j in range(n): if j != i: Ab[j] = Ab[j] - Ab[j][i]*Ab[i] # 提取未知量x的值 x = Ab[:, -1] # 输出未知量x的值 print(x)

def gaussian_jordan_elimination(A, b):
import numpy as np
# 将方阵A和列矩阵b合并成增广矩阵Ab
Ab = np.hstack((A, b))
# 对增广矩阵Ab进行高斯-约旦消元，化为行最简形式
n, m = Ab.shape
for i in range(n):
# 如果Ab[i][i]为0，则交换当前行和下面行中Ab[i][i]不为0的行
if Ab[i][i] == 0:
for j in range(i+1, n):
if Ab[j][i] != 0:
Ab[[i,j]] = Ab[[j,i]]
break
# 将Ab[i][i]归一
Ab[i] = Ab[i] / Ab[i][i]
# 将非当前行的第i列元素变为0
for j in range(n):
if j != i:
Ab[j] = Ab[j] - Ab[j][i]*Ab[i]
# 提取未知量x的值
x = Ab[:, -1]
# 输出未知量x的值
print(x)

将着两段代码整合（定义两个函数：一个时高斯消去法、一个是LU分解，另外将矩阵的表示方法由增广矩阵A变成稀系数矩阵和另外一个矩阵）：#Gauss消去法 import numpy as np # 构造增广矩阵 A = np.array([[1, -1, 1, 0], [4, 1, 0, 8], [0, 1, 4, 16]],dtype=float) # 高斯消元过程 n = len(A) for i in range(n): # 主元归一化 if A[i][i] == 0: print("主元为0，无法进行消元") break A[i] = A[i] / A[i][i] for j in range(i + 1, n): A[j] = A[j] - A[i] * A[j][i] # 回代过程 x = np.zeros(n, dtype=float) for i in range(n - 1, -1, -1): x[i] = A[i][-1] - np.dot(A[i][i + 1:-1], x[i + 1:]) print("线性方程组的解为：", x) #LU分解 import numpy as np # 构造增广矩阵 A = np.array([[1, -1, 1, 0], [4, 1, 0, 8], [0, 1, 4, 16]], dtype=float) # LU分解 n = len(A) L = np.zeros((n, n)) U = np.zeros((n, n)) for i in range(n): # 计算L的第i列和U的第i行 for j in range(i, n): U[i][j] = A[i][j] - sum(L[i][k] * U[k][j] for k in range(i)) for j in range(i+1, n): L[j][i] = (A[j][i] - sum(L[j][k] * U[k][i] for k in range(i))) / U[i][i] L[i][i] = 1 # 解方程 b = A[:, -1] y = np.zeros(n) for i in range(n): y[i] = b[i] - sum(L[i][j] * y[j] for j in range(i)) x = np.zeros(n) for i in range(n-1, -1, -1): x[i] = (y[i] - sum(U[i][j] * x[j] for j in range(i+1, n))) / U[i][i] print(x)

好的，下面是整合后的代码，其中包括高斯消去法和LU分解两个函数，以及对应的矩阵表示方法：

import numpy as np

def gaussian_elimination(A, b):
    """
    高斯消去法求解线性方程组 Ax=b

    Args:
        A: 系数矩阵
        b: 常数矩阵

    Returns:
        x: 解向量
    """
    n = len(A)
    # 构造增广矩阵
    Ab = np.column_stack((A, b))

    # 高斯消元过程
    for i in range(n):
        # 主元归一化
        if Ab[i][i] == 0:
            print("主元为0，无法进行消元")
            break
        Ab[i] = Ab[i] / Ab[i][i]
        for j in range(i + 1, n):
            Ab[j] = Ab[j] - Ab[i] * Ab[j][i]

    # 回代过程
    x = np.zeros(n)
    for i in range(n - 1, -1, -1):
        x[i] = Ab[i][-1] - np.dot(Ab[i][i + 1:-1], x[i + 1:])

    return x


def LU_decomposition(A, b):
    """
    LU分解求解线性方程组 Ax=b

    Args:
        A: 系数矩阵
        b: 常数矩阵

    Returns:
        x: 解向量
    """
    n = len(A)
    # LU分解
    L = np.zeros((n, n))
    U = np.zeros((n, n))
    for i in range(n):
        # 计算L的第i列和U的第i行
        for j in range(i, n):
            U[i][j] = A[i][j] - sum(L[i][k] * U[k][j] for k in range(i))
        for j in range(i+1, n):
            L[j][i] = (A[j][i] - sum(L[j][k] * U[k][i] for k in range(i))) / U[i][i]
        L[i][i] = 1

    # 解方程
    y = np.zeros(n)
    for i in range(n):
        y[i] = b[i] - sum(L[i][j] * y[j] for j in range(i))

    x = np.zeros(n)
    for i in range(n-1, -1, -1):
        x[i] = (y[i] - sum(U[i][j] * x[j] for j in range(i+1, n))) / U[i][i]

    return x
    

# 稀疏矩阵表示方法
from scipy.sparse import csc_matrix

# 构造系数矩阵
data = np.array([1, 4, 1, -1, 1, 1, 4, 0, 8, 16])
row = np.array([0, 1, 1, 2, 2, 0, 1, 2, 0, 1])
col = np.array([0, 1, 3, 1, 2, 2, 3, 2, 3, 3])
A_sparse = csc_matrix((data, (row, col)), shape=(3, 4)).toarray()

# 构造常数矩阵
b = np.array([0, 8, 16])

# 高斯消去法求解
x1 = gaussian_elimination(A_sparse, b)
print("高斯消去法求解线性方程组 Ax=b 的解为：", x1)

# LU分解求解
x2 = LU_decomposition(A_sparse, b)
print("LU分解求解线性方程组 Ax=b 的解为：", x2)

其中，稀疏矩阵的构造使用了scipy库里的csc_matrix()函数，将data、row、col三个数组作为输入，构造出一个csr_matrix对象，然后再将其转换为普通的numpy数组。