大衍之數揲卦法的後半段

gistfile1.txt

#!/usr/bin/python
# -*- coding: utf-8 -*-

import random
# import numpy as np

# fmt: off

# from 易經

# 六十四卦中的第幾卦, 0 到 63

yi = [
    "乾", "坤", "屯", "蒙", "需", "訟", "師",
    "比", "小畜", "履", "泰", "否",
    "同人", "大有", "謙", "豫", "隨",
    "蠱", "臨", "觀", "噬嗑", "賁",
    "剝", "復", "無妄", "大畜", "頤",
    "大過", "坎", "離",
    "咸", "恆", "遯", "大壯",
    "晉", "明夷", "家人", "睽",
    "蹇", "解", "損", "益", "夬", "姤", "萃",
    "升", "困", "井", "革", "鼎", "震",
    "艮", "漸", "歸妹", "豐", "旅", "巽",
    "兌", "渙", "節", "中孚",
    "小過", "既濟", "未濟",
]

# from wiki 易經條目

# 乾卦：六個 1，數字是 63
# 屯卦：[1, 0, 0, 0, 1, 0] => 17

yi_order = [63, 0, 17, 34, 23, 58, 2, 16, 55, 59, 7, 56, 61, 47, 4, 8, 25, 38, 3, 48, 41, \
            37, 32, 1, 57, 39, 33, 30, 18, 45, 28, 14, 60, 15, 40, 5, 53, 43, 20, 10, 35, 49, \
            31, 62, 24, 6, 26, 22, 29, 46, 9, 36, 52, 11, 13, 44, 54, 27, 50, 19, 51, 12, 21, 42]
# fmt: on

# 將卦的六爻，以 0 代表陰爻，1 代表陽爻，轉換為 0 to 63 的數字,
# 第一爻在最底下，第六爻在最上面，與揲卦順序一致
# 例如：[0, 0, 0, 0, 0, 0] => 0，[0, 0, 0, 1, 0, 1] => 40


def binary_to_int(l):
    assert type(l) is list and len(l) in [6, 7]
    x = 0
    for n in range(len(l)):
        if l[n] == 1:
            x = x + (2**n)
    return x


# 找出 list 裡符合某個內容的元素的 index + 1
# 是用來找 本卦 vs 之卦 改變的是哪幾爻
# find_index([0, 1, 0, 1, 0, 0], 1) => [2, 4]
# find_index([0, 1, 0, 1, 0, 0], 0) => [1, 3, 5, 6]


def find_index(l, v):
    return [(n + 1) for n in range(len(l)) if (l[n] == v)]


# 一個卦有卦辭，加上六個爻辭，可以用 kua * 7 + yo 來找到卦辭與爻辭。
# 用九與用六，放在最後，位址在 64*7+0=448 與 64*7+1=449
# yo = 0，傳回卦辭
# yo = 1..6，傳回爻辭


def lookup_yi(kua, yo):
    assert type(kua) is list and type(yo) is int
    assert (len(kua) == 6 and yo in [0, 1, 2, 3, 4, 5, 6]) or (
        len(kua) == 7 and yo in [0, 1]
    )
    n = binary_to_int(kua)
    assert n * 7 + yo < 450
    if False:
        return yi[n * 7 + yo]
    else:
        # 測試用，忽略卦辭爻辭的內容
        nn = ["", "一", "二", "三", "四", "五", "六"]
        final_result = n * 7 + yo
        if final_result == 448:
            return "用九"
        elif final_result == 449:
            return "用六"
        else:
            if yo == 0:
                return yi[yi_order.index(n)] + "卦"
            else:
                return yi[yi_order.index(n)] + "卦第" + nn[yo] + "爻"


# 輸入揲蓍法所得的六個數，得到對應的卦辭或爻辭


def post_pu_kua(kua):
    assert type(kua) == list and len(kua) == 6

    # 將老陰 (6) 少陽 (7) 少陰 (8) 老陽 (9) 對應到陰爻與陽爻，得到本卦
    aa = [0 if x in (6, 8) else 1 for x in kua]  # 本卦

    # 因為變卦的邏輯是 遇六 變 陽，遇九 變 陰，所以在之卦中 數字 6, 7 是陽爻，8, 9 是陰爻
    bb = [1 if x in (6, 7) else 0 for x in kua]  # 變卦

    # 找出本卦之卦兩者不同的爻，1 代表爻陰陽不同，0 代表相同，
    # sum(cc) 算出有幾個變爻
    # find_index(cc, 1) 找出變爻的位置
    # find_index(cc, 0) 找出不變爻的位置

    cc = [1 if aa[n] != bb[n] else 0 for n in range(6)]

    if sum(cc) == 0:  # 零個變爻
        return (lookup_yi(aa, 0),)  # 本卦的卦辭
    elif sum(cc) == 1:  # 一個變爻
        pos = find_index(cc, 1)
        return (lookup_yi(aa, pos[0]),)  # 本卦變爻的爻辭
    elif sum(cc) == 2:  # 兩個變爻
        pos = find_index(cc, 1)
        return (lookup_yi(aa, pos[1]), lookup_yi(aa, pos[0]))  # 以本卦的兩個變爻解卦，上爻為主
    elif sum(cc) == 3:  # 三個變爻
        return (lookup_yi(bb, 0), lookup_yi(aa, 0))  # 以兩卦卦義解卦，變卦為主
    elif sum(cc) == 4:  # 四個變爻
        pos = find_index(cc, 0)
        return (lookup_yi(bb, pos[0]), lookup_yi(bb, pos[1]))  # 以變卦未變的兩爻解卦，下爻為主
    elif sum(cc) == 5:  # 五個變爻
        pos = find_index(cc, 0)
        return (lookup_yi(bb, pos[0]),)  # 變卦未變的爻辭
    elif sum(cc) == 6:  # 六個變爻
        if aa == [1, 1, 1, 1, 1, 1]:
            return (lookup_yi([0, 0, 0, 0, 0, 0, 1], 0),)  # 用九
        elif aa == [0, 0, 0, 0, 0, 0]:
            return (lookup_yi([0, 0, 0, 0, 0, 0, 1], 1),)  # 用六
        else:
            return (lookup_yi(bb, 0),)  # 變卦卦辭
    else:
        raise

# ｢四營｣（「分二、掛一、揲四、歸奇」）
# 跑出來的結果，6 非常少，不確定是否正常
def yin(n):
    # 分而為二以象兩：隨機將這 n 個分為兩堆，亂數從 2 開始，是為了接著掛一以象三的步驟，不至於把左邊或右邊一堆拿光
    s = random.randint(2, n - 2)    
    # s = np.random.binomial(n - 2, 0.5) + 1
    left = n - s
    right = s
    # 掛一以象三：再從其中任何一堆隨機取出一個
    l_r = random.randint(0, 1)
    if l_r == 0:
        left = left - 1
    else:
        right = right - 1
    # 揲之以四以象四時：現在兩堆分別以四個四個計算，從右手邊開始，剩下的竹籤（餘數＝1至4）夾於無名指和中指間，以象徵閏；再算左手邊的竹籤，剩餘的夾在中指和食指間。
    if right % 4:
        right = right - right % 4
    else:
        right = right - 4
    if left % 4:
        left = left - left % 4
    else:
        left = left - 4
    return left + right

# 三變成一爻
def make_yo():
    n = yin(yin(yin(49)))
    return n // 4


if __name__ == "__main__":
    kua = [random.randint(6, 9) for n in range(6)]
    # kua = [make_yo() for n in range(6)]
    print(kua)
    print(post_pu_kua(kua))

還好吧，二進位數與十進位數互相轉換是程式入門題目。

術業有專攻，您會的我也不會啊。