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slimay

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发表于 2021-5-12 17:35 | 只看该作者

[其他] 复变函数表达式计算器zi

本帖最后由 slimay 于 2021-5-12 20:35 编辑
复变函数表达式计算器，支持多重复变函数混合嵌套计算。是实数表达式计算器的升级版, 打通了冥数的计算,所有函数均推广至复域.
第三方进化路线,后者均是前者在多维空间, 多维数域,多维度矩阵 上 的升级.后者在输入降维数据后运行的结果与前者一致.保证了多维度向下兼容性.
REVPOLISH -> ZI  //多维表达式计算
FPLOT -> FP3       //多维绘图
I -> MAT               //多维综合工具
示例:
> zi sin(5+7i)*cos(6-3i)+sin(5+7i)*i
/***
  = -28817/6 + 4899/2(i)   //渐进分数表示
  = -4802.848508148568 + 2449.503431876684(i)   //浮点表示
  =  5391.421042267110 * exp[(i)2.669968709666] //极坐标表示
***/
支持实数同名的复变函数:
  +, -, *, /, , ^, pi=3.1415926536, e=2.71828182846
  rand, round, int, ceil, floor, sqrt, lg, ln, exp, abs, arg
  torad, sin, cos, tan, arcsin, arccos, arctan
  sinh, cosh, tanh, arcsinh, arccosh, arctanh


存为a.txt,  解码base92格式  : bse -d92 a.txt a.zip
  1. 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slimay

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发表于 2021-5-12 17:52 | 只看该作者
本帖最后由 slimay 于 2021-5-12 18:04 编辑

实现的复变函数库, 可推广至四元数域
  1. /*

  2. 	COMPLEX MATHLIB &COPYRIGHT@2021~2023 BY SLIMAY

  3. 	复变函数库

  4. */

  5. 

  6. #include <math.h>

  7. 

  8. //定义复数类型 

  9. typedef double Complex;

  10. 

  11. #define _REZ 0

  12. #define _IMZ 1

  13. 

  14. #define MATH_PI 3.1415926535897932

  15. #define MATH_E  2.7182818284590452

  16. 

  17. ////////////////////////////////// 定义复恒量

  18. static const Complex Z_0 [2] = {0,       0};

  19. static const Complex Z_1 [2] = {1,       0};

  20. static const Complex Z_i [2] = {0,       1};

  21. static const Complex Z__i[2] = {0,      -1};

  22. static const Complex Z_pi[2] = {0, MATH_PI};

  23. static const Complex Z_e [2] = {0, MATH_E };

  24. 

  25. ////////////////////////////////// 定义复数 模 加、减、乘、除

  26. //实例化一个复数 

  27. Complex* Z_init(double x, double y)

  28. {

  29. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  30. 	*(Z_RET + _REZ) = x;

  31. 	*(Z_RET + _IMZ) = y;

  32. 	return Z_RET;

  33. }

  34. //复数的模长, (一维函数) 

  35. Complex* Z_abs(Complex* x) 

  36. {

  37. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  38. 	Complex* Z_RET = Z_init(r, 0);

  39. 	return Z_RET;

  40. }

  41. //角度转弧度, (一维函数,只对实部运算, 虚部归零) 

  42. Complex* Z_torad(Complex* x) 

  43. {

  44. 	Complex* Z_RET = Z_init((*(x+_REZ)) / 180.0 * MATH_PI, 0);

  45. 	return Z_RET;

  46. }

  47. //复数的辐角 (一维函数, 只返回0到2*PI范围内的辐角弧度, 虚部归零)

  48. Complex* Z_arg(Complex* x) 

  49. {

  50. 	double arg = 0; 

  51. 	

  52. 	if((*(x+_REZ)) == 0)

  53. 	{		

  54. 		if((*(x+_IMZ)) != 0)

  55. 		{

  56. 			arg = ((*(x+_IMZ)) > 0) ?(MATH_PI/2.0) :(-MATH_PI/2.0);

  57. 		}

  58. 	}

  59. 	else

  60. 	{

  61. 		arg = atan( (*(x+_IMZ)) / (*(x+_REZ)) );	

  62. 		if((*(x+_REZ)) < 0)

  63. 		{

  64. 			arg += ((*(x+_IMZ)) > 0) ?(MATH_PI) :(-MATH_PI);

  65. 		}

  66. 	}

  67. 	Complex* Z_RET = Z_init(arg, 0);

  68. 	return Z_RET;

  69. }

  70. //随机一个复数, 辐角不超过 x的辐角,模长为x的模长. 

  71. Complex* Z_rand(Complex* x) 

  72. {

  73. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  74. 	double s = (r < 2) ?(rand() % 8192/8192.0) :(rand() % ((int)r));

  75. 	Complex* Z_RET = Z_init(s, 0);

  76. 	return Z_RET;

  77. }

  78. //复数加

  79. Complex* Z_add(Complex* x, Complex* y)

  80. {

  81. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  82. 	*(Z_RET + _REZ) = (*(x+_REZ)) + (*(y+_REZ));

  83. 	*(Z_RET + _IMZ) = (*(x+_IMZ)) + (*(y+_IMZ));

  84. 	return Z_RET;

  85. }

  86. //复数减

  87. Complex* Z_sub(Complex* x, Complex* y)

  88. {

  89. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  90. 	*(Z_RET + _REZ) = (*(x+_REZ)) - (*(y+_REZ));

  91. 	*(Z_RET + _IMZ) = (*(x+_IMZ)) - (*(y+_IMZ)); 

  92. 	return Z_RET;

  93. }

  94. //复数乘

  95. Complex* Z_mul(Complex* x, Complex* y)

  96. {

  97. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  98. 	*(Z_RET + _REZ) = (*(x+_REZ))*(*(y+_REZ)) - (*(x+_IMZ))*(*(y+_IMZ));

  99. 	*(Z_RET + _IMZ) = (*(x+_REZ))*(*(y+_IMZ)) + (*(x+_IMZ))*(*(y+_REZ)); 

  100. 	return Z_RET;

  101. }

  102. //复数除

  103. Complex* Z_div(Complex* x, Complex* y)

  104. {

  105. 	double r2 = (*(y+_REZ))*(*(y+_REZ)) + (*(y+_IMZ))*(*(y+_IMZ));

  106. 	if(r2 == 0)

  107. 	{

  108. 		printf("Cannot div 0.\n");

  109. 		exit(1);

  110. 	}

  111. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  112. 	*(Z_RET + _REZ) = ((*(x+_REZ))*(*(y+_REZ)) + (*(x+_IMZ))*(*(y+_IMZ))) / r2;

  113. 	*(Z_RET + _IMZ) = ((*(x+_IMZ))*(*(y+_REZ)) - (*(x+_REZ))*(*(y+_IMZ))) / r2; 

  114. 	return Z_RET;

  115. }

  116. //复取余 

  117. Complex* Z_rest(Complex* x, Complex* y)

  118. {

  119. 	if((*(y+_REZ)) == 0)

  120. 	{

  121. 		printf("Can't % 0.\n");

  122. 		exit(1);

  123. 	}

  124. 	Complex* Z_RET  = Z_init((double)(((int)(*(x+_REZ))) % ((int)(*(y+_REZ)))), 0);

  125. 	return Z_RET;

  126. }

  127. 

  128. ////////////////////////////////// 定义复变函数 (即实变函数在复域上的推广) 

  129. //EXP函数

  130. Complex* Z_exp(Complex* x) 

  131. {

  132. 	Complex* Z_RET  = (Complex*) malloc (2 * sizeof(double));

  133. 	*(Z_RET + _REZ) = exp(*(x+_REZ)) * cos(*(x+_IMZ));

  134. 	*(Z_RET + _IMZ) = exp(*(x+_REZ)) * sin(*(x+_IMZ)); 

  135. 	return Z_RET;

  136. }

  137. 

  138. //自然对数 (旧版),0无辐角 

  139. Complex* Z_log2(Complex* x)

  140. {                    

  141. 	if( (*(x+_REZ)) == 0 )

  142. 	{

  143. 		printf("Can't ln(0+bi).\n");

  144. 		exit(1);

  145. 	}

  146. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));                   

  147. 	Complex* Z_RET = Z_init(log(r), atan((*(x+_IMZ))/(*(x+_REZ))));

  148. 	return Z_RET;

  149. }

  150. //自然对数

  151. Complex* Z_ln(Complex* x) 

  152. {

  153. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  154. 	if(r ==0)

  155. 	{

  156. 		printf("Can't ln(0).\n");

  157. 		exit(1);

  158. 	}

  159. 	double arg = (*(Z_arg(x)+_REZ));                 

  160. 	Complex* Z_RET = Z_init(log(r), arg);

  161. 	return Z_RET;

  162. }

  163. 

  164. //常用对数

  165. Complex* Z_log10(Complex* x) 

  166. {

  167. 	Complex* lnx = Z_ln(x);                   

  168. 	Complex* Z_RET = Z_init((*(lnx+_REZ))/log(10), (*(lnx+_IMZ))/log(10));

  169. 	return Z_RET;

  170. }

  171. 

  172. //次方函数

  173. Complex* Z_pow(Complex* x, Complex* y)

  174. {

  175. 	Complex* lnx = Z_ln(x);

  176. 	Complex* Z_RET = Z_exp(Z_mul(y, lnx));

  177. 	return Z_RET;

  178. }

  179. 

  180. //开方函数

  181. Complex* Z_sqrt(Complex* x) 

  182. {                     

  183. 	Complex* Z_RET = Z_pow(x, Z_init(0.5, 0));

  184. 	return Z_RET;

  185. }

  186. 

  187. //四舍五入

  188. Complex* Z_round(Complex* x)

  189. {

  190. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  191. 	Complex* Z_RET = Z_init((*(x+_REZ))/r * (double)((int)r),  (*(x+_IMZ))/r * (double)((int)r));

  192. 	return Z_RET;

  193. }

  194. 

  195. //向下取整

  196. Complex* Z_floor(Complex* x)

  197. {

  198. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  199. 	Complex* Z_RET = Z_init((*(x+_REZ))/r * (double)(floor(r)),  (*(x+_IMZ))/r * (double)((int)r));

  200. 	return Z_RET;

  201. }

  202. 

  203. //向上取整

  204. Complex* Z_ceil(Complex* x)

  205. {

  206. 	double r = sqrt((*(x+_REZ))*(*(x+_REZ))+(*(x+_IMZ))*(*(x+_IMZ)));

  207. 	Complex* Z_RET = Z_init((*(x+_REZ))/r * (double)(ceil(r)),  (*(x+_IMZ))/r * (double)((int)r));

  208. 	return Z_RET;

  209. }

  210. 

  211. ////////////////////////////////// 定义复变三角函数

  212. //正弦函数

  213. Complex* Z_sin(Complex* x)

  214. {

  215. 	Complex*  ix = Z_mul( Z_i, x);

  216. 	Complex* _ix = Z_mul(Z__i, x);

  217. 	

  218. 	Complex* Z_RET = Z_mul(Z_init(0, -0.5), Z_sub(Z_exp(ix),Z_exp(_ix))); 

  219. 	return Z_RET;

  220. }

  221. //余弦函数

  222. Complex* Z_cos(Complex* x) 

  223. {    

  224. 	Complex*  ix = Z_mul( Z_i, x);

  225. 	Complex* _ix = Z_mul(Z__i, x);

  226. 	

  227. 	Complex* Z_RET = Z_mul(Z_init(0.5, 0), Z_add(Z_exp(ix),Z_exp(_ix)));

  228. 	return Z_RET;

  229. }

  230. //正切函数

  231. Complex* Z_tan(Complex* x) 

  232. {                      

  233. 	Complex* Z_RET = Z_div(Z_sin(x), Z_cos(x));

  234. 	return Z_RET;

  235. }

  236. 

  237. //反正弦函数

  238. Complex* Z_asin(Complex* x)

  239. {

  240. 	Complex*  sqrt1subz2 = Z_sqrt(Z_sub(Z_1, Z_mul(x, x)));

  241. 	Complex* Z_RET = Z_mul(Z_i, Z_ln(Z_sub(Z_mul(Z_i, x), sqrt1subz2))); 

  242. 	return Z_RET;

  243. }

  244. //反余弦函数

  245. Complex* Z_acos(Complex* x) 

  246. {                    

  247. 	Complex*  sqrt1subz2 = Z_sqrt(Z_sub(Z_1, Z_mul(x, x)));

  248. 	Complex* Z_RET = Z_mul(Z__i, Z_ln(Z_sub(x, Z_mul(Z_i, sqrt1subz2)))); 

  249. }

  250. //反正切函数

  251. Complex* Z_atan(Complex* x) 

  252. {      

  253. 	Complex*  s = Z_init(0,-0.5);                               

  254. 	Complex* Z_RET = Z_mul(s, Z_ln(Z_div(Z_sub(Z_i, x), Z_add(Z_i, x))));

  255. 	return Z_RET;

  256. }

  257. 

  258. ////////////////////////////////// 定义复变双曲函数

  259. //双曲正弦函数

  260. Complex* Z_sinh(Complex* x)

  261. {

  262. 	Complex* _x = Z_init(-(*(x+_REZ)), -(*(x+_IMZ)));

  263. 	Complex* Z_RET = Z_mul(Z_init(0.5, 0), Z_sub(Z_exp(x), Z_exp(_x)));

  264. 	return Z_RET;

  265. }

  266. //双曲余弦函数

  267. Complex* Z_cosh(Complex* x) 

  268. {                    

  269. 	Complex* _x = Z_init(-(*(x+_REZ)), -(*(x+_IMZ)));

  270. 	Complex* Z_RET = Z_mul(Z_init(0.5, 0), Z_add(Z_exp(x), Z_exp(_x)));

  271. 	return Z_RET;

  272. }

  273. //双曲正切函数

  274. Complex* Z_tanh(Complex* x) 

  275. {                     

  276. 	Complex* Z_RET = Z_div(Z_sinh(x), Z_cosh(x));

  277. 	return Z_RET;

  278. }

  279. 

  280. //反双曲正弦函数

  281. Complex* Z_asinh(Complex* x)

  282. {

  283. 	Complex*  sqrtz2add1 = Z_sqrt(Z_add(Z_init(1,0), Z_mul(x, x)));

  284. 	Complex* Z_RET = Z_ln(Z_sub(x, sqrtz2add1)); 

  285. 	return Z_RET;

  286. }

  287. //反双曲余弦函数

  288. Complex* Z_acosh(Complex* x)

  289. {

  290. 	Complex*  sqrtz2sub1 = Z_sqrt(Z_sub(Z_init(1,0), Z_mul(x, x)));

  291. 	Complex* Z_RET = Z_ln(Z_sub(x, sqrtz2sub1)); 

  292. 	return Z_RET;

  293. }

  294. //反双曲正切函数

  295. Complex* Z_atanh(Complex* x) 

  296. {

  297. 	Complex*  s1 = Z_init(1, 0);

  298. 	Complex*  halfs1 = Z_init(0.5, 0);              

  299. 	Complex* Z_RET = Z_mul(halfs1, Z_ln(Z_div(Z_add(s1, x), Z_sub(s1, x))));	

  300. 	return Z_RET;

  301. }
复制代码
新第三方预告,升级版的mat加入了矩阵表达式计算器,类似matlab
mat
格式：
mat "[expression1] [expression2] [expression3] [.] ..."

示例:
mat "[A=1,0;1,1]  [B=A^(2)]  [C=A^(-1)+B]  [(A^(-1))-C]  [det(A)]  [tr(A)]  [A^(50)]"

输入格式：
    {E = en(2)}      <==>   [1   0]
                            [0   1]
    {A = 1,,2;3,8,7} <==>   [1   0   2]
                            [3   8   7]

矩阵函数:
    +, -, *, ^, A^(-1), A^(n), cp(A), rot(A), en(A)
    gs(A), diag(A), lad(A), tri(A)
    tr(A), r(A), det(A)
    lf(n): 控制精度

example:
    mat "[A=1,0;1,1] [B=A^(2)] [C=A^(-1)+B] [(A^(-1))-C] [det(A
    You can use the letters A to O to name the matrix
    {E = en(2)}      <==>   [1   0]
                            [0   1]
    {A = 1,,2;3,8,7} <==>   [1   0   2]
                            [3   8   7]
matrix functions:
    +, -, *, ^, A^(-1), A^(n), cp(A), rot(A), en(A)
    gs(A), diag(A), lad(A), tri(A)
    tr(A), r(A), det(A)
    lf(n): control print precision
2

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Byaidu

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2013-7-14 
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发表于 2021-5-24 00:32 | 只看该作者
大佬太厉害了

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