python计算行列式

2017-12-20 18:27:00 by wst

数学知识

---

回过头来再看数学，课本上讲的每一个解题步骤不都是一个算法吗？

突然发现自己学了那么多算法，可是仔细想来，自己又能实现几个呢？

正好在复习行列式，顺便实现下：

# -*- coding:utf-8 -*-

import math


__author__ = "alan.wan"
__email__ = "movingheart000@gmail.com"


def get_son_matrix(df, i, j):
    """ Generate matrix that remove line i and column j

    :param df: original matrix
    :param i: line number
    :param j: column number
    :return: new matrix
    """
    l = len(df)
    new_list = [[0 for x in range(l-1)] for y in range(l-1)]
    for index in range(l):
        for column in range(l):
            if index < i and column < j:
                new_list[index][column] = df[index][column]
            elif index > i and column < j:
                new_list[index-1][column] = df[index][column]
            elif index > i and column > j:
                new_list[index-1][column-1] = df[index][column]
            elif index < i and column > j:
                new_list[index][column-1] = df[index][column]
    return new_list


def calculate_det(df, n=0):
    """Calculate determinant of df

    :param df: input matrix
    :param n: calculate by line n
    :return: results
    """
    cl = len(df)
    if cl == 2:
        return df[0][0] * df[1][1] - df[1][0] * df[0][1]
    s = 0
    for tl in range(cl):
        temp_df = get_son_matrix(df, n, tl)
        s += df[n][tl] * math.pow(-1, n+tl+2) * calculate_det(temp_df)
    return s

if __name__ == "__main__":
    df = [
        [5, 3, -1, 2, 0],
        [1, 7, 2, 5, 2],
        [0, -2, 3, 1, 0],
        [0, -4, -1, 4, 0],
        [0, 2, 3, 5, 0]
    ]

    print calculate_det(df)

 

---