#!/usr/bin/env python3 """ Ziwei Astrology Calculator - Zhongzhou School (中州派) Steps 1-6: Basic Chart Calculation with Formulas Verified Formulas (2026-02-20): - Step 1: 命宮索引 = (月宮索引 - 時辰索引 + 10) % 12 - Step 2: 五虎遁 + Distance Formula for 命宮干 """ # ============================================================================ # LOOKUP TABLES & CONSTANTS # ============================================================================ branchOrder = ["寅", "卯", "辰", "巳", "午", "未", "申", "酉", "戌", "亥", "子", "丑"] stemOrder = ["甲", "乙", "丙", "丁", "戊", "己", "庚", "辛", "壬", "癸"] # 五虎遁 (Five Tiger Escaping): Maps year stem to stem at 寅 wuhuDun = { "甲": "丙", "己": "丙", "乙": "戊", "庚": "戊", "丙": "庚", "辛": "庚", "丁": "壬", "壬": "壬", "戊": "甲", "癸": "甲", } # 納音五行 (Nayin Five Elements): Maps stem-branch to Nayin element # Complete 60 Jiazi Nayin Table (Verified via 百度百科 & multiple sources) nayinMapping = { # Fire (火六局) "丙寅": ("爐中火", "Fire", 6), "丁卯": ("爐中火", "Fire", 6), "戊午": ("天上火", "Fire", 6), "己未": ("天上火", "Fire", 6), "丙申": ("山下火", "Fire", 6), "丁酉": ("山下火", "Fire", 6), "戊子": ("霹靂火", "Fire", 6), "己丑": ("霹靂火", "Fire", 6), "甲辰": ("佛燈火", "Fire", 6), "乙巳": ("佛燈火", "Fire", 6), "甲戌": ("山頭火", "Fire", 6), "乙亥": ("山頭火", "Fire", 6), # Water (水二局) "甲子": ("海中金", "Metal", 4), "乙丑": ("海中金", "Metal", 4), "壬辰": ("長流水", "Water", 2), "癸巳": ("長流水", "Water", 2), "甲申": ("泉中水", "Water", 2), "乙酉": ("泉中水", "Water", 2), "丙午": ("天河水", "Water", 2), "丁未": ("天河水", "Water", 2), "丙子": ("澗下水", "Water", 2), "丁丑": ("澗下水", "Water", 2), "壬戌": ("大海水", "Water", 2), "癸亥": ("大海水", "Water", 2), # Wood (木三局) "戊辰": ("大林木", "Wood", 3), "己巳": ("大林木", "Wood", 3), "壬午": ("楊柳木", "Wood", 3), "癸未": ("楊柳木", "Wood", 3), "庚寅": ("松柏木", "Wood", 3), "辛卯": ("松柏木", "Wood", 3), "庚申": ("石榴木", "Wood", 3), "辛酉": ("石榴木", "Wood", 3), # Earth (土五局) "庚午": ("路旁土", "Earth", 5), "辛未": ("路旁土", "Earth", 5), "己卯": ("城頭土", "Earth", 5), "庚辰": ("白蠟金", "Metal", 4), "丙戌": ("屋上土", "Earth", 5), "丁亥": ("屋上土", "Earth", 5), "戊申": ("大驛土", "Earth", 5), "己酉": ("大驛土", "Earth", 5), "庚子": ("壁上土", "Earth", 5), "辛丑": ("壁上土", "Earth", 5), # Metal (金四局) "庚午": ("路旁土", "Earth", 5), "辛未": ("路旁土", "Earth", 5), "甲午": ("沙中金", "Metal", 4), "乙未": ("沙中金", "Metal", 4), "壬申": ("劍鋒金", "Metal", 4), "癸酉": ("劍鋒金", "Metal", 4), "庚戌": ("鈎釧金", "Metal", 4), "辛亥": ("鈎釧金", "Metal", 4), "壬寅": ("金箔金", "Metal", 4), "癸卯": ("金箔金", "Metal", 4), } # ✅ CORRECTED Ziwei position by bureau and lunar day remainder # Algorithm: remainder → base_position, then count forward by quotient steps # Verified: Day 22, Wood 3 → remainder 1, quotient 7, base=辰, result=亥 ziweiPositionTable = { 2: {1: "巳", 2: "午"}, # Water 2 Bureau 3: {1: "辰", 2: "寅", 3: "子"}, # Wood 3 Bureau 4: {1: "卯", 2: "午", 3: "未", 4: "戌"}, # Metal 4 Bureau 5: {1: "寅", 2: "午", 3: "戊", 4: "寅", 5: "午"}, # Earth 5 Bureau 6: {1: "午", 2: "辰", 3: "寅", 4: "子", 5: "戌", 6: "申"}, # Fire 6 Bureau } # ✅ CORRECT Tianfu mapping - FIXED relationship with Ziwei (NOT just opposite!) # Mnemonic: "天府南斗令，常對紫微宮，丑卯相更迭，未酉互為根。往來午與戌，蹀躞子和辰，已亥交馳騁，同位在寅申" tianfuMapping = { "寅": "寅", # 同位在寅申 (same palace) "卯": "丑", # 丑卯相更迭 (swap) "辰": "子", # 蹀躞子和辰 (swap) "巳": "亥", # 已亥交馳騁 (opposite) "午": "戌", # 往來午與戌 (swap) "未": "酉", # 未酉互為根 (swap) "申": "申", # 同位在寅申 (same palace) "酉": "未", # 未酉互為根 (swap) "戌": "午", # 往來午與戌 (swap) "亥": "巳", # 已亥交馳騁 (opposite) "子": "辰", # 蹀躞子和辰 (swap) "丑": "卯", # 丑卯相更迭 (swap) } # Major star offsets from Ziwei ziweiStarOffsets = { "紫微": 0, "天機": 1, "太陽": 2, "武曲": -1, "天同": -2, "廉貞": 3 } # Major star offsets from Tianfu tianfuStarOffsets = { "天府": 0, "太陰": -1, "貪狼": -2, "巨門": 1, "天相": 2, "天梁": 3, "七殺": -3, "破軍": -4 } # ============================================================================ # HELPER FUNCTIONS # ============================================================================ def branchToIndex(branch): """Convert branch to 0-based index""" return branchOrder.index(branch) def indexToBranch(index): """Convert 0-based index to branch""" return branchOrder[index % 12] def stemToIndex(stem): """Convert stem to 0-based index""" return stemOrder.index(stem) def indexToStem(index): """Convert 0-based index to stem""" return stemOrder[index % 10] # ============================================================================ # STEP 1: Calculate Life Palace (命宮) # ============================================================================ def calculateLifePalace(lunarMonth, hourBranch): """ STEP 1: Calculate 命宮 (Life Palace) Position Formula: 命宮索引 = (月宮索引 - 時辰索引 + 10) % 12 Args: lunarMonth: Lunar month (1-12) hourBranch: Hour branch string (e.g., "亥") Returns: Tuple: (lifeHouseBranch, lifeHouseIndex) """ monthHouseIndex = (lunarMonth - 1) % 12 hourIndex = branchToIndex(hourBranch) # VERIFIED FORMULA lifeHouseIndex = (monthHouseIndex - hourIndex + 10) % 12 lifeHouseBranch = indexToBranch(lifeHouseIndex) return lifeHouseBranch, lifeHouseIndex # ============================================================================ # STEP 2: Calculate Life Palace Stem (命宮干) # ============================================================================ def calculateLifePalaceStem(yearStem, lifeHouseBranch): """ STEP 2: Calculate 命宮干 using 五虎遁 (Five Tiger Escaping) Formula: 1. Get stem at 寅 from 五虎遁 table 2. Calculate distance from 寅 to life palace 3. Add distance to stem (cycling every 10 stems) Args: yearStem: Year stem (甲-癸) lifeHouseBranch: Life palace branch (from Step 1) Returns: Tuple: (lifeHouseStem, lifeHouseStemBranch) """ # Step 2.1: Get stem at 寅 using 五虎遁 stemAtYin = wuhuDun[yearStem] # Step 2.2: Calculate distance from 寅(index 0) to life house yinIndex = 0 lifeHouseIndex = branchToIndex(lifeHouseBranch) distance = (lifeHouseIndex - yinIndex) % 12 # Step 2.3: Calculate life house stem by adding distance stemAtYinIndex = stemToIndex(stemAtYin) lifeHouseStemIndex = (stemAtYinIndex + distance) % 10 lifeHouseStem = indexToStem(lifeHouseStemIndex) # Step 2.4: Create stem-branch pair lifeHouseStemBranch = lifeHouseStem + lifeHouseBranch return lifeHouseStem, lifeHouseStemBranch # ============================================================================ # STEP 3: Combine Stem-Branch (already done in Step 2) # ============================================================================ def getLifePalaceStemBranch(yearStem, lifeHouseBranch): """STEP 3 is already completed in Step 2""" lifeHouseStem, lifeHouseStemBranch = calculateLifePalaceStem(yearStem, lifeHouseBranch) return lifeHouseStemBranch # ============================================================================ # STEP 4: Determine Five Element Bureau (五行局) via Nayin # ============================================================================ def calculateFiveElementBureau(lifeHouseStemBranch): """ STEP 4: Determine 五行局 using Nayin (納音) system Args: lifeHouseStemBranch: Life palace stem-branch (e.g., "丙寅") Returns: Tuple: (nayinName, element, bureauNumber) """ if lifeHouseStemBranch not in nayinMapping: return None, None, None nayinName, element, bureauNumber = nayinMapping[lifeHouseStemBranch] return nayinName, element, bureauNumber # ============================================================================ # STEP 5: Place Ziwei (紫微) & Tianfu (天府) # ============================================================================ def calculateZiweiPosition(lunarDay, fiveElementBureau): """ STEP 5A: Calculate Ziwei (紫微) position using Odd/Even Difference Method ✅ CORRECT Formula (Verified via multiple examples): 1. quotient = ceil(lunarDay / fiveElementBureau) - Find smallest multiplier level 2. multiplier = quotient * fiveElementBureau - Get actual multiple 3. difference = multiplier - lunarDay - Calculate difference 4. if difference is EVEN: finalNumber = quotient + difference if difference is ODD: finalNumber = quotient - difference 5. ziweiIndex = (finalNumber - 1) % 12 6. ziweiPosition = branchOrder[ziweiIndex] Verified examples: - Wood 3, Day 25: quotient=9, diff=2(even), final=11 → 子 ✓ - Fire 6, Day 7: quotient=2, diff=5(odd), final=-3 → 戌 ✓ Args: lunarDay: Lunar day of birth (1-30) fiveElementBureau: Bureau number (2, 3, 4, 5, 6) Returns: Ziwei branch string """ import math # Step 1: Find smallest multiplier > lunarDay quotient = math.ceil(lunarDay / fiveElementBureau) multiplier = quotient * fiveElementBureau # Step 2: Calculate difference difference = multiplier - lunarDay # Step 3: Calculate final number based on odd/even difference if difference % 2 == 0: # EVEN difference finalNumber = quotient + difference else: # ODD difference finalNumber = quotient - difference # Step 4: Find Ziwei position (counting from 寅 at position 1) ziwei_index = (finalNumber - 1) % 12 ziwei_position = indexToBranch(ziwei_index) return ziwei_position def calculateTianfuPosition(ziweiPosition): """ STEP 5B: Calculate Tianfu (天府) position using FIXED mapping ✅ IMPORTANT: Tianfu has a FIXED relationship with Ziwei (NOT just opposite!) Uses mnemonic: "天府南斗令，常對紫微宮，丑卯相更迭，未酉互為根。 往來午與戌，蹀躞子和辰，已亥交馳騁，同位在寅申" Mapping rules: - 寅/申: Same palace (同位) - 丑↔卯: Swap (相更迭) - 子↔辰: Swap (蹀躞) - 巳↔亥: Opposite (交馳騁) - 午↔戌: Swap (往來) - 未↔酉: Swap (互為根) Args: ziweiPosition: Ziwei branch (from Step 5A) Returns: Tianfu branch string """ return tianfuMapping[ziweiPosition] # ============================================================================ # STEP 6: Place Major Stars (十四主星) # ============================================================================ def placeZiweiStars(ziweiPosition, lifeHouseIndex): """ STEP 6A: Place major stars around Ziwei Args: ziweiPosition: Ziwei branch lifeHouseIndex: Life palace index (0-11) Returns: Dict of star -> branch mappings """ ziweiIndex = branchToIndex(ziweiPosition) stars = {} for starName, offset in ziweiStarOffsets.items(): starIndex = (ziweiIndex + offset) % 12 stars[starName] = indexToBranch(starIndex) return stars def placeTianfuStars(tianfuPosition): """ STEP 6B: Place major stars around Tianfu Args: tianfuPosition: Tianfu branch Returns: Dict of star -> branch mappings """ tianfuIndex = branchToIndex(tianfuPosition) stars = {} for starName, offset in tianfuStarOffsets.items(): starIndex = (tianfuIndex + offset) % 12 stars[starName] = indexToBranch(starIndex) return stars # ============================================================================ # MAIN CALCULATION FUNCTION # ============================================================================ def calculateZiweiChart(name, year, yearStem, lunarMonth, lunarDay, hourBranch): """ Calculate complete Ziwei chart up to Step 6 Args: name: Person's name year: Birth year yearStem: Year stem (甲-癸) lunarMonth: Lunar month (1-12) lunarDay: Lunar day (1-30) hourBranch: Hour branch (子-亥) Returns: Dict with all calculation results """ result = { "name": name, "year": year, "yearStem": yearStem, "lunarMonth": lunarMonth, "lunarDay": lunarDay, "hourBranch": hourBranch, } # STEP 1: Calculate Life Palace lifeHouseBranch, lifeHouseIndex = calculateLifePalace(lunarMonth, hourBranch) result["step1_lifeHouseBranch"] = lifeHouseBranch result["step1_lifeHouseIndex"] = lifeHouseIndex # STEP 2: Calculate Life Palace Stem lifeHouseStem, lifeHouseStemBranch = calculateLifePalaceStem(yearStem, lifeHouseBranch) result["step2_lifeHouseStem"] = lifeHouseStem result["step2_stemAtYin"] = wuhuDun[yearStem] result["step2_lifeHouseStemBranch"] = lifeHouseStemBranch # STEP 4: Determine Five Element Bureau nayinName, element, bureauNumber = calculateFiveElementBureau(lifeHouseStemBranch) result["step4_nayin"] = nayinName result["step4_element"] = element result["step4_fiveElementBureau"] = bureauNumber # STEP 5A: Calculate Ziwei Position ziweiPosition = calculateZiweiPosition(lunarDay, bureauNumber) result["step5_ziweiPosition"] = ziweiPosition # STEP 5B: Calculate Tianfu Position tianfuPosition = calculateTianfuPosition(ziweiPosition) result["step5_tianfuPosition"] = tianfuPosition # STEP 6A: Place Ziwei Stars ziweiStars = placeZiweiStars(ziweiPosition, lifeHouseIndex) result["step6_ziweiStars"] = ziweiStars # STEP 6B: Place Tianfu Stars tianfuStars = placeTianfuStars(tianfuPosition) result["step6_tianfuStars"] = tianfuStars return result # ============================================================================ # MAIN EXECUTION # ============================================================================ if __name__ == "__main__": people = [ {"name": "Bennett", "year": 1984, "yearStem": "甲", "month": 12, "day": 3, "hour": "亥"}, {"name": "Brian", "year": 1986, "yearStem": "丙", "month": 12, "day": 17, "hour": "酉"}, {"name": "Christy", "year": 1989, "yearStem": "己", "month": 12, "day": 2, "hour": "午"}, {"name": "Cherry", "year": 1990, "yearStem": "庚", "month": 11, "day": 4, "hour": "酉"}, {"name": "Elice", "year": 1982, "yearStem": "壬", "month": 8, "day": 14, "hour": "戌"}, ] print("=" * 100) print("ZIWEI ASTROLOGY CALCULATOR - STEPS 1-6") print("=" * 100) print() results = [] for person in people: result = calculateZiweiChart( person["name"], person["year"], person["yearStem"], person["month"], person["day"], person["hour"] ) results.append(result) print(f"{result['name']} ({person['year']}{person['yearStem']}, Lunar {person['month']}/{person['day']}, {person['hour']}時)") print(f" STEP 1 - 命宮: {result['step1_lifeHouseBranch']} (Index {result['step1_lifeHouseIndex']})") print(f" STEP 2 - 命宮干: {result['step2_lifeHouseStem']} (Stem@寅={result['step2_stemAtYin']})") print(f" STEP 2 - 命宮干支: {result['step2_lifeHouseStemBranch']}") print(f" STEP 4 - 五行局: {result['step4_fiveElementBureau']} ({result['step4_nayin']}, {result['step4_element']})") print(f" STEP 5 - Ziwei: {result['step5_ziweiPosition']}, Tianfu: {result['step5_tianfuPosition']}") print(f" STEP 6 - Ziwei Stars: {result['step6_ziweiStars']}") print(f" STEP 6 - Tianfu Stars: {result['step6_tianfuStars']}") print() # Summary table print("=" * 100) print("SUMMARY TABLE") print("=" * 100) print() print(f"{'Name':<10} {'Year':<6} {'命宮':<4} {'命宮干':<4} {'命宮干支':<6} {'五行局':<8} {'Ziwei':<4} {'Tianfu':<4}") print("-" * 100) for r in results: print(f"{r['name']:<10} {r['year']:<6} {r['step1_lifeHouseBranch']:<4} {r['step2_lifeHouseStem']:<4} {r['step2_lifeHouseStemBranch']:<6} {r['step4_fiveElementBureau']}({r['step4_nayin']}) {r['step5_ziweiPosition']:<4} {r['step5_tianfuPosition']:<4}")