在 Python 中解決線性矩陣方程或線性標量方程組

要解決線性矩陣方程，請在 Python 中使用 numpy.linalg.solve() 方法。該方法計算完全確定的（即滿秩）線性矩陣方程 ax = b 的“精確”解 x。返回系統 a x = b 的解。返回的形狀與 b 相同。第一個引數 a 是係數矩陣。第二個引數 b 是縱座標或“因變數”值。

步驟

首先，匯入所需的庫 -

import numpy as np

使用 array() 方法建立兩個二維 numpy 陣列。考慮方程組 x0 + 2 * x1 = 1 和 3 * x0 + 5 * x1 = 2 -

arr1 = np.array([[1, 2], [3, 5]])
arr2 = np.array([1, 2])

顯示陣列 -

print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

檢查兩個陣列的維度 -

print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

檢查兩個陣列的形狀 -

Print(“\nShape of Array1…\n”,arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

要解決線性矩陣方程，請使用 numpy.linalg.solve() 方法 -

print("\nResult...\n",np.linalg.solve(arr1, arr2))

示例

import numpy as np

# Creating two 2D numpy arrays using the array() method

# Consider the system of equations x0 + 2 * x1 = 1 and 3 * x0 + 5 * x1 = 2
arr1 = np.array([[1, 2], [3, 5]])
arr2 = np.array([1, 2])

# Display the arrays
print("Array1...\n",arr1)
print("\nArray2...\n",arr2)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n",arr1.ndim)
print("\nDimensions of Array2...\n",arr2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n",arr1.shape)
print("\nShape of Array2...\n",arr2.shape)

# To solve a linear matrix equation, use the numpy.linalg.solve() method in Python.
print("\nResult...\n",np.linalg.solve(arr1, arr2))

輸出

Array1...
[[1 2]
[3 5]]

Array2...
[1 2]

Dimensions of Array1...
2

Dimensions of Array2...
1

Shape of Array1...
(2, 2)

Shape of Array2...
(2,)

Result...
[-1. 1.]

AmitDiwan

更新於: 2022年2月25日

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