C#二元一次方程參數(shù)求解
Jul 06, 2016 pm 01:30 PM
本文記錄了關(guān)于求直線斜率及縱截距值的簡單方法，只是簡單的記錄下求解思路，最終還需根據(jù)具體項(xiàng)目進(jìn)行優(yōu)化。 設(shè)直線方程式為：y=kx+b 編程思想： 1、代入y1與x1的值，得到：y1=kx1+b 2、代入y2與x2的值，得到：y2=kx2+b 3、首先算出一個(gè)系數(shù)m=kx1 / kx2 或
本文記錄了關(guān)于求直線斜率及縱截距值的簡單方法，只是簡單的記錄下求解思路，最終還需根據(jù)具體項(xiàng)目進(jìn)行優(yōu)化。
設(shè)直線方程式為：y=kx+b
編程思想：
1、代入y1與x1的值，得到：y1=kx1+b
2、代入y2與x2的值，得到：y2=kx2+b???????
3、首先算出一個(gè)系數(shù)m=kx1 / kx2 或 m=kx2 / kx1
4、根據(jù)第三步，將 y1=kx1+b 或 y2=kx2+b 乘以系數(shù)m，使 kx1==kx2 ,注意 kx1與kx2不能為0???????
4、將2個(gè)函數(shù)相減，例如：my2-my1=mb-b 即 m(y2-y1)=(m-1)b??????
5、算出縱截距b=(m(y2-y1))/(m-1) 注意：m不能為1 同時(shí)注意浮點(diǎn)數(shù)四舍五入問題???????
6、將b值y1=kx1+b中，求出斜率k值
?
示例代碼：
<span style="color: #0000ff;">using</span><span style="color: #000000;"> System;
</span><span style="color: #0000ff;">namespace</span><span style="color: #000000;"> Demo
{
</span><span style="color: #0000ff;">class</span><span style="color: #000000;"> PRogram
{
</span><span style="color: #0000ff;">private</span> <span style="color: #0000ff;">static</span> <span style="color: #0000ff;">readonly</span> <span style="color: #0000ff;">int</span> _decimaldigits = <span style="color: #800080;">2</span>;<span style="color: #008000;">//</span><span style="color: #008000;">小數(shù)位數(shù)保留2位</span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><summary></summary></span>
<span style="color: #808080;">///</span><span style="color: #008000;"> 計(jì)算斜率k及縱截距b值
</span><span style="color: #808080;">///</span> <span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="x1"></span><span style="color: #008000;">坐標(biāo)點(diǎn)x1</span><span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="x2"></span><span style="color: #008000;">坐標(biāo)點(diǎn)x2</span><span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="y1"></span><span style="color: #008000;">坐標(biāo)點(diǎn)y1</span><span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="y2"></span><span style="color: #008000;">坐標(biāo)點(diǎn)y2</span><span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="kvalue"></span><span style="color: #008000;">斜率k值</span><span style="color: #808080;"></span>
<span style="color: #808080;">///</span> <span style="color: #808080;"><param name="bvalue"></span><span style="color: #008000;">縱截距b值</span><span style="color: #808080;"></span>
<span style="color: #0000ff;">private</span> <span style="color: #0000ff;">static</span> <span style="color: #0000ff;">void</span> Calculate(<span style="color: #0000ff;">float</span> x1, <span style="color: #0000ff;">float</span> x2, <span style="color: #0000ff;">float</span> y1, <span style="color: #0000ff;">float</span> y2, <span style="color: #0000ff;">ref</span> <span style="color: #0000ff;">float</span> kvalue, <span style="color: #0000ff;">ref</span> <span style="color: #0000ff;">float</span> bvalue)<span style="color: #008000;">//</span><span style="color: #008000;">求方程y=kx+b 系數(shù) k ,b</span>
<span style="color: #000000;"> {
</span><span style="color: #0000ff;">float</span> coefficient = <span style="color: #800080;">1</span>;<span style="color: #008000;">//</span><span style="color: #008000;">系數(shù)值</span>
<span style="color: #0000ff;">try</span><span style="color: #000000;">
{
</span><span style="color: #0000ff;">if</span> ((x1 == <span style="color: #800080;">0</span>) || (x2 == <span style="color: #800080;">0</span>) || (x1 == x2)) <span style="color: #0000ff;">return</span>; <span style="color: #008000;">//</span><span style="color: #008000;">排除為零的情況以及x1，x2相等時(shí)無法運(yùn)算的情況
</span><span style="color: #008000;">//</span><span style="color: #008000;">if (y1 == y2) return; </span><span style="color: #008000;">//</span><span style="color: #008000;">根據(jù)具體情況而定，如何這兩個(gè)值相等，得到的就是一條直線</span>
<span style="color: #0000ff;">float</span> temp = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">if</span> (x1 >=<span style="color: #000000;"> x2)
{
coefficient </span>= (<span style="color: #0000ff;">float</span>)Math.Round((x1 /<span style="color: #000000;"> x2), _decimaldigits);
temp </span>= y2 * coefficient; <span style="color: #008000;">//</span><span style="color: #008000;">將對(duì)應(yīng)的函數(shù)乘以系數(shù)</span>
bvalue = (<span style="color: #0000ff;">float</span>)Math.Round(((temp - y1) / (coefficient - <span style="color: #800080;">1</span><span style="color: #000000;">)), _decimaldigits);
kvalue </span>= (<span style="color: #0000ff;">float</span>)Math.Round(((y1 - bvalue) / x1), _decimaldigits); <span style="color: #008000;">//</span><span style="color: #008000;">求出k值</span>
<span style="color: #000000;"> }
</span><span style="color: #0000ff;">else</span><span style="color: #000000;">
{
coefficient </span>= x2 /<span style="color: #000000;"> x1;
temp </span>= y1 *<span style="color: #000000;"> coefficient;
bvalue </span>= (<span style="color: #0000ff;">float</span>)Math.Round(((temp - y2) / (coefficient - <span style="color: #800080;">1</span>)), _decimaldigits);<span style="color: #008000;">//</span><span style="color: #008000;">求出b值</span>
kvalue = (<span style="color: #0000ff;">float</span>)Math.Round(((y2 - bvalue) / x2), _decimaldigits); <span style="color: #008000;">//</span><span style="color: #008000;">求出k值</span>
<span style="color: #000000;"> }
}
</span><span style="color: #0000ff;">catch</span><span style="color: #000000;">
{
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">x系數(shù)不能為0或相等</span><span style="color: #800000;">"</span><span style="color: #000000;">);
}
}
</span><span style="color: #0000ff;">static</span> <span style="color: #0000ff;">void</span> Main(<span style="color: #0000ff;">string</span><span style="color: #000000;">[] args)
{
</span><span style="color: #0000ff;">float</span> x1 = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">float</span> y1 = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">float</span> x2 = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">float</span> y2 = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">float</span> kvalue = <span style="color: #800080;">0</span><span style="color: #000000;">;
</span><span style="color: #0000ff;">float</span> bvalue = <span style="color: #800080;">0</span><span style="color: #000000;">;
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">計(jì)算直線斜率k及縱截距b</span><span style="color: #800000;">"</span><span style="color: #000000;">);
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">請(qǐng)輸入x1值</span><span style="color: #800000;">"</span><span style="color: #000000;">);
x1 </span>=<span style="color: #000000;"> Convert.ToSingle(Console.ReadLine());
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">請(qǐng)輸入y1值</span><span style="color: #800000;">"</span><span style="color: #000000;">);
y1 </span>=<span style="color: #000000;"> Convert.ToSingle(Console.ReadLine());
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">請(qǐng)輸入x2值</span><span style="color: #800000;">"</span><span style="color: #000000;">);
x2 </span>=<span style="color: #000000;"> Convert.ToSingle(Console.ReadLine());
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">請(qǐng)輸入y2值</span><span style="color: #800000;">"</span><span style="color: #000000;">);
y2 </span>=<span style="color: #000000;"> Convert.ToSingle(Console.ReadLine());
Calculate(x1, x2, y1, y2, </span><span style="color: #0000ff;">ref</span> kvalue, <span style="color: #0000ff;">ref</span><span style="color: #000000;"> bvalue);
Console.WriteLine(</span><span style="color: #800000;">"</span><span style="color: #800000;">直線方程為：y={0}x+{1}</span><span style="color: #800000;">"</span><span style="color: #000000;">, kvalue, bvalue);
Console.ReadKey();
}
}
}</span>
運(yùn)行結(jié)果：
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