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复数运算 (complex)

单精度浮点复数运算，用于数字信号处理。

数据结构​

struct complex_t {
    float real;
    float imag;
};

API​

void complex_add(struct complex_t * z, struct complex_t * a, struct complex_t * b);
void complex_sub(struct complex_t * z, struct complex_t * a, struct complex_t * b);
void complex_mul(struct complex_t * z, struct complex_t * a, struct complex_t * b);
void complex_div(struct complex_t * z, struct complex_t * a, struct complex_t * b);
void complex_neg(struct complex_t * z, struct complex_t * a);
void complex_conj(struct complex_t * z, struct complex_t * a);
void complex_expj(struct complex_t * z, float phi);
void complex_proj(struct complex_t * z, struct complex_t * a);
void complex_normalize(struct complex_t * z, struct complex_t * a);
float complex_abs(struct complex_t * z);
float complex_arg(struct complex_t * z);
  • complex_add/sub/mul/div — 四则运算，z = a op b
  • complex_neg — 取负，z = -a
  • complex_conj — 共轭，z = a*
  • complex_expj — 旋转因子，z = exp(j * phi)
  • complex_proj — 投影到黎曼球面
  • complex_normalize — 归一化为单位复数
  • complex_abs — 模，|z|
  • complex_arg — 幅角，arg(z)（弧度）

使用示例​

复数乘法​

struct complex_t a = { 1.0f, 2.0f };
struct complex_t b = { 3.0f, 4.0f };
struct complex_t z;

complex_mul(&z, &a, &b);

旋转因子​

struct complex_t z;
complex_expj(&z, 3.14159265f / 4.0f);

求模与幅角​

struct complex_t a = { 3.0f, 4.0f };
float r = complex_abs(&a);
float theta = complex_arg(&a);