数据库中的复数运算与临时表使用

### 数据库中的复数运算与临时表使用 #### 1. 复数除法的用户自定义函数实现 我们可以创建一个名为 `dbo.cxDivide` 的用户自定义函数来实现复数除法。该函数依据公式计算结果复数的实部和虚部，具体代码如下： ```sql CREATE FUNCTION dbo.cxDivide( @cx1 as complex, @cx2 as complex) RETURNS complex AS BEGIN IF dbo.cxValid(@cx1) = 0 OR dbo.cxValid(@cx2) = 0 RETURN NULL DECLARE @a1 AS decimal(19,9), @b1 AS decimal(19,9), @a2 AS decimal(19,9), @b2 AS decimal(19,9) DECLARE @real AS decimal(19,9), @imaginary AS decimal(19,9) SET @a1 = dbo.cxGetReal(@cx1) SET @a2 = dbo.cxGetReal(@cx2) SET @b1 = dbo.cxGetImaginary(@cx1) SET @b2 = dbo.cxGetImaginary(@cx2) -- ((a1*a2 + b1*b2)/(a2*a2 + b2*b2)) + ((a2*b1 - a1*b2)/(a2*a2 + b2*b2))i SET @real = (@a1*@a2 + @b1*@b2)/(@a2*@a2 + @b2*@b2) SET @imaginary = (@a2*@b1 - @a1*@b2)/(@a2*@a2 + @b2*@b2) RETURN dbo.cxStrForm(@real, @imaginary) END GO ``` #### 2. 复数的极坐标形式与向量大小计算 复数还可以用极坐标形式 `(r, θ)` 表示。其中，`r` 是向量的大小，即复平面上原点到点 `(a, b)` 的距离；`θ` 是实轴与表示复数的向量之间的夹角。 可以使用勾股定理计算复数向量的大小，公式为 `r = SQRT(a^2 + b^2)`。以下是实现该计算的用户自定义函数 `dbo.cxVectorSize`： ```sql CREATE FUNCTION dbo.cxVectorSize( @cx as complex) RETURNS decimal(19,9) AS BEGIN IF dbo.cxValid(@cx) = 0 RETURN NULL DECLARE @real AS decimal(19,9), @imaginary AS decimal(19,9) SET @real = dbo.cxGetReal(@cx) SET @imaginary = dbo.cxGetImaginary(@cx) -- r = SQRT(a^2 + b^2) RETURN SQRT(@real*@real + @imaginary*@imaginary) END GO ``` #### 3. 复数函数的使用 为了测试复数函数，我们可以创建一个简单的表 `T1` 来存储复数，并对该表执行一些查询。 ```sql CREATE TABLE T1 ( key_col int NOT NULL PRIMARY KEY, cx1 complex NOT NULL, cx2 complex NOT NULL ) INSERT INTO T1 VALUES(1, '5 + 2i', '2 + 4i') INSERT INTO T1 VALUES(2, '2 + 9i', '4 + 5i') INSERT INTO T1 VALUES(3, '7 + 4i', '3 + 2i') INSERT INTO T1 VALUES(4, '3 + 2i', '6 + 3i') INSERT INTO T1 VALUES(5, '4 + 3i', '7 + 2i') INSERT INTO T1 VALUES(6, '1 + 4i', '4 + 3i') INSERT INTO T1 VALUES(7, '7 + 2i', '8 + 1i') INSERT INTO T1 VALUES(8, '2 + 3i', '3 + 6i') INSERT INTO T1 VALUES(9, '3 + 6i', '2 + 8i') INSERT INTO T1 VALUES(10, '2 + 1i', '3 + 2i') ``` 以下查询展示了如何在查询中嵌入复数函数进行加法、减法、乘法和除法运算： ```sql SELECT key_col, cx1, cx2, dbo.cxAdd(cx1, cx2) AS cxAdd, dbo.cxSubtract(cx1, cx2) AS cxSubtract, dbo.cxMult(cx1, cx2) AS cxMult, dbo.cxDivide(cx1, cx2) AS cxDivide FROM T1 ``` 运算结果如下表所示： | key_col | cx1 | cx2 | cxAdd | cxSubtract | cxMultiply | cxDivide | | ---- | ---- | ---- | ---- | ---- | ---- | ---- | | 1 | 5 + 2i | 2 + 4i | 7 + 6i | 3 - 2i | 2 + 24i | 0.9 - 0.8i | | 2 | 2 + 9i | 4 + 5i | 6 + 14i | 2 + 4i | 37 + 46i | 1.29268292 + 0.63414634i | | 3 | 7 + 4i | 3 + 2i | 10 + 6i | 4 + 2i | 13 + 26i | 2.2307