C#行列式计算程序
PermutationGen用来枚举{1,...,n}的所有全排列。
D类用来计算行列式，只能对数值进行计算。
代码
using
System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Determinant
{
class Program
{
static void Main( string [] args)
{
// Console.WriteLine(D.SwitchCount(new int[] { 3, 2, 5, 1, 4 }));
// D.PermutationGen pg = new D.PermutationGen(4);
// pg.FastIteration = true;
// foreach (var p in pg)
// {
// Console.WriteLine(pg.PermutationToString(p));
// }
D d1 = new D( 3 );
d1.Data[ 0 , 0 ] = 1 ;
d1.Data[ 0 , 1 ] = 2 ;
d1.Data[ 0 , 2 ] = - 4 ;
d1.Data[ 1 , 0 ] = - 2 ;
d1.Data[ 1 , 1 ] = 2 ;
d1.Data[ 1 , 2 ] = 1 ;
d1.Data[ 2 , 0 ] = - 3 ;
d1.Data[ 2 , 1 ] = 4 ;
d1.Data[ 2 , 2 ] = - 2 ;
Console.WriteLine(d1.Value);
D d2 = new D( 2 );
d2.Data[ 0 , 0 ] = 3 ;
d2.Data[ 0 , 1 ] = 12 ;
d2.Data[ 1 , 0 ] = 2 ;
d2.Data[ 1 , 1 ] = 1 ;
Console.WriteLine(d2.Value);
Console.ReadKey();
}
}
public class D
{
/// <summary>
/// 计算1-n的一个全排列的逆序数
/// </summary>
/// <param name="permutation"> a permutation of 1-permutation.Length </param>
/// <returns></returns>
public static int SwitchCount( int [] permutation)
{
int count = 0 ;
if (permutation == null || permutation.Length == 0 ) throw new ArgumentException( " 输入不能为空 " , " permutation " );
if (permutation.Length == 1 )
{
return 0 ;
}
for ( int i = 0 ; i < permutation.Length; i ++ )
{
if (permutation[i] < 1 || permutation[i] > permutation.Length) throw new ArgumentException( " 只计算1-n的排列的逆序数 " );
}
for ( int i = 0 ; i < permutation.Length; i ++ )
{
for ( int j = i + 1 ; j < permutation.Length; j ++ )
{
if (permutation[i] > permutation[j]) count ++ ;
else if (permutation[i] == permutation[j]) throw new ArgumentException(String.Format( " 数字{0}重复出现在位置{1}和{2} " , permutation[i], i, j), " permutation " );
}
}
return count;
}
double [,] data;
int n;
PermutationGen pg;
public D( int rank)
{
if (rank < 2 ) throw new ArgumentException( " Rank is at least 2. " );
n = rank;
data = new double [rank, rank];
data.Initialize();
}
public double [,] Data
{
get
{
return data;
}
}
public double Value // calculate the value form the data given
{
get
{
double v = 0 ;
if (pg == null )
{
pg = new PermutationGen(n);
}
foreach (var p in pg)
{
double u = 1 ;
for ( int i = 0 ; i < n; i ++ )
{ // 固定行，选列
u *= data[i, p[i] - 1 ];
}
u *= ((SwitchCount(p) & 1 ) == 1 ? - 1 : 1 );
v += u;
}
return v;
}
}
public class PermutationGen : IEnumerable < int [] >
{
int [] p, t, f;
int len;
StringBuilder pString;
public bool ReturnNewPermutation
{
get ;
set ;
}
public bool FastIteration
{
get ;
set ;
}
public PermutationGen( int length)
{
len = length;
p = new int [length];
t = new int [length]; // 尚未被使用的数字
f = new int [length + 1 ];
for ( int i = len; i >= 0 ; i -- ) // 最前面两个元素不用
{
f[i] = Factorial(i);
}
}
public int Count
{
get
{
return f[len];
}
}
/// <summary>
///
/// </summary>
/// <param name="id"> 1至len </param>
/// <returns></returns>
public int [] GetPermutation( int id)
{
if (id >= f[len] || id < 0 ) throw new ArgumentException( " 1<=id<=len! " );
for ( int i = 0 ; i < len; i ++ ) // 所有数字都未被使用
{
t[i] = i + 1 ;
}
int r, n, m = id;
for ( int i = 0 ; i < len; i ++ )
{
n = Math.DivRem(m, f[len - i - 1 ], out r);
p[i] = GetUnusedNumberN(n + 1 );
m = r;
}
return p;
}
public string PermutationToString( int [] p)
{
int len = p.Length;
if (pString == null )
{
pString = new StringBuilder(len * 3 );
}
pString.Length = 0 ;
pString.Append(p[ 0 ]);
for ( int i = 1 ; i < len; i ++ )
{
pString.Append( " , " );
pString.Append(p[i]);
}
return pString.ToString();
}
public string GetPermutationString()
{
return PermutationToString(p);
}
public static int Factorial( int n)
{
int result = 1 ;
for ( int i = n; i > 1 ; i -- )
{
result *= i;
}
return result;
}
/// <summary>
/// 返回第n个未被使用的元素
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
int GetUnusedNumberN( int n)
{
int count = 0 ;
for ( int i = 0 ; i < len; i ++ )
{
if (t[i] != 0 )
{
count ++ ;
if (count == n)
{
int q = t[i];
t[i] = 0 ; // 返回即被使用
return q;
}
}
}
return 0 ; // 没有足够的剩余元素
}
/// <summary>
/// return the smallest positive integer that is not included in the n elements of array starting for start
/// </summary>
int GetNextSmallest( int [] array, int start, int n, int searchStart)
{
int i;
for (i = searchStart; i <= searchStart + n; i ++ )
{
int j;
for (j = start; j < n; j ++ )
{
if (array[j] == i) break ;
}
if (j == n)
{
return i;
}
}
return 0 ; // impossible, but required by grammar
}
#region IEnumerable<int[]> 成员
public IEnumerator < int [] > GetEnumerator()
{
if (FastIteration)
{
for ( int i = 0 ; i < len; i ++ )
{
p[i] = i + 1 ;
}
for ( int i = 0 ; i < f[len] - 1 ; i ++ ) // 返回第0号到倒数第二个排列
{
yield return ReturnNewPermutation ? p.Clone() as int [] : p;
// 每次迭代构造下次应当返回的排列
for ( int j = len - 1 ; j > 0 ; j -- )
{
if (i / f[j] != (i + 1 ) / f[j])
{
// set p at level j
int k = len - j - 1 ; // convert to p index
p[k] = GetNextSmallest(p, 0 , k, p[k] + 1 );
k ++ ;
while (k < len)
{
p[k] = GetNextSmallest(p, 0 , k, 1 );
k ++ ;
}
break ;
}
}
}
yield return ReturnNewPermutation ? p.Clone() as int [] : p;
}
else
{
if (ReturnNewPermutation)
{
for ( int i = 0 ; i < f[len]; i ++ )
{
yield return GetPermutation(i).Clone() as int [];
}
}
else
{
for ( int i = 0 ; i < f[len]; i ++ )
{
yield return GetPermutation(i);
}
}
}
}
#endregion
#region IEnumerable 成员
System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
#endregion
}
}
}
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Determinant
{
class Program
{
static void Main( string [] args)
{
// Console.WriteLine(D.SwitchCount(new int[] { 3, 2, 5, 1, 4 }));
// D.PermutationGen pg = new D.PermutationGen(4);
// pg.FastIteration = true;
// foreach (var p in pg)
// {
// Console.WriteLine(pg.PermutationToString(p));
// }
D d1 = new D( 3 );
d1.Data[ 0 , 0 ] = 1 ;
d1.Data[ 0 , 1 ] = 2 ;
d1.Data[ 0 , 2 ] = - 4 ;
d1.Data[ 1 , 0 ] = - 2 ;
d1.Data[ 1 , 1 ] = 2 ;
d1.Data[ 1 , 2 ] = 1 ;
d1.Data[ 2 , 0 ] = - 3 ;
d1.Data[ 2 , 1 ] = 4 ;
d1.Data[ 2 , 2 ] = - 2 ;
Console.WriteLine(d1.Value);
D d2 = new D( 2 );
d2.Data[ 0 , 0 ] = 3 ;
d2.Data[ 0 , 1 ] = 12 ;
d2.Data[ 1 , 0 ] = 2 ;
d2.Data[ 1 , 1 ] = 1 ;
Console.WriteLine(d2.Value);
Console.ReadKey();
}
}
public class D
{
/// <summary>
/// 计算1-n的一个全排列的逆序数
/// </summary>
/// <param name="permutation"> a permutation of 1-permutation.Length </param>
/// <returns></returns>
public static int SwitchCount( int [] permutation)
{
int count = 0 ;
if (permutation == null || permutation.Length == 0 ) throw new ArgumentException( " 输入不能为空 " , " permutation " );
if (permutation.Length == 1 )
{
return 0 ;
}
for ( int i = 0 ; i < permutation.Length; i ++ )
{
if (permutation[i] < 1 || permutation[i] > permutation.Length) throw new ArgumentException( " 只计算1-n的排列的逆序数 " );
}
for ( int i = 0 ; i < permutation.Length; i ++ )
{
for ( int j = i + 1 ; j < permutation.Length; j ++ )
{
if (permutation[i] > permutation[j]) count ++ ;
else if (permutation[i] == permutation[j]) throw new ArgumentException(String.Format( " 数字{0}重复出现在位置{1}和{2} " , permutation[i], i, j), " permutation " );
}
}
return count;
}
double [,] data;
int n;
PermutationGen pg;
public D( int rank)
{
if (rank < 2 ) throw new ArgumentException( " Rank is at least 2. " );
n = rank;
data = new double [rank, rank];
data.Initialize();
}
public double [,] Data
{
get
{
return data;
}
}
public double Value // calculate the value form the data given
{
get
{
double v = 0 ;
if (pg == null )
{
pg = new PermutationGen(n);
}
foreach (var p in pg)
{
double u = 1 ;
for ( int i = 0 ; i < n; i ++ )
{ // 固定行，选列
u *= data[i, p[i] - 1 ];
}
u *= ((SwitchCount(p) & 1 ) == 1 ? - 1 : 1 );
v += u;
}
return v;
}
}
public class PermutationGen : IEnumerable < int [] >
{
int [] p, t, f;
int len;
StringBuilder pString;
public bool ReturnNewPermutation
{
get ;
set ;
}
public bool FastIteration
{
get ;
set ;
}
public PermutationGen( int length)
{
len = length;
p = new int [length];
t = new int [length]; // 尚未被使用的数字
f = new int [length + 1 ];
for ( int i = len; i >= 0 ; i -- ) // 最前面两个元素不用
{
f[i] = Factorial(i);
}
}
public int Count
{
get
{
return f[len];
}
}
/// <summary>
///
/// </summary>
/// <param name="id"> 1至len </param>
/// <returns></returns>
public int [] GetPermutation( int id)
{
if (id >= f[len] || id < 0 ) throw new ArgumentException( " 1<=id<=len! " );
for ( int i = 0 ; i < len; i ++ ) // 所有数字都未被使用
{
t[i] = i + 1 ;
}
int r, n, m = id;
for ( int i = 0 ; i < len; i ++ )
{
n = Math.DivRem(m, f[len - i - 1 ], out r);
p[i] = GetUnusedNumberN(n + 1 );
m = r;
}
return p;
}
public string PermutationToString( int [] p)
{
int len = p.Length;
if (pString == null )
{
pString = new StringBuilder(len * 3 );
}
pString.Length = 0 ;
pString.Append(p[ 0 ]);
for ( int i = 1 ; i < len; i ++ )
{
pString.Append( " , " );
pString.Append(p[i]);
}
return pString.ToString();
}
public string GetPermutationString()
{
return PermutationToString(p);
}
public static int Factorial( int n)
{
int result = 1 ;
for ( int i = n; i > 1 ; i -- )
{
result *= i;
}
return result;
}
/// <summary>
/// 返回第n个未被使用的元素
/// </summary>
/// <param name="n"></param>
/// <returns></returns>
int GetUnusedNumberN( int n)
{
int count = 0 ;
for ( int i = 0 ; i < len; i ++ )
{
if (t[i] != 0 )
{
count ++ ;
if (count == n)
{
int q = t[i];
t[i] = 0 ; // 返回即被使用
return q;
}
}
}
return 0 ; // 没有足够的剩余元素
}
/// <summary>
/// return the smallest positive integer that is not included in the n elements of array starting for start
/// </summary>
int GetNextSmallest( int [] array, int start, int n, int searchStart)
{
int i;
for (i = searchStart; i <= searchStart + n; i ++ )
{
int j;
for (j = start; j < n; j ++ )
{
if (array[j] == i) break ;
}
if (j == n)
{
return i;
}
}
return 0 ; // impossible, but required by grammar
}
#region IEnumerable<int[]> 成员
public IEnumerator < int [] > GetEnumerator()
{
if (FastIteration)
{
for ( int i = 0 ; i < len; i ++ )
{
p[i] = i + 1 ;
}
for ( int i = 0 ; i < f[len] - 1 ; i ++ ) // 返回第0号到倒数第二个排列
{
yield return ReturnNewPermutation ? p.Clone() as int [] : p;
// 每次迭代构造下次应当返回的排列
for ( int j = len - 1 ; j > 0 ; j -- )
{
if (i / f[j] != (i + 1 ) / f[j])
{
// set p at level j
int k = len - j - 1 ; // convert to p index
p[k] = GetNextSmallest(p, 0 , k, p[k] + 1 );
k ++ ;
while (k < len)
{
p[k] = GetNextSmallest(p, 0 , k, 1 );
k ++ ;
}
break ;
}
}
}
yield return ReturnNewPermutation ? p.Clone() as int [] : p;
}
else
{
if (ReturnNewPermutation)
{
for ( int i = 0 ; i < f[len]; i ++ )
{
yield return GetPermutation(i).Clone() as int [];
}
}
else
{
for ( int i = 0 ; i < f[len]; i ++ )
{
yield return GetPermutation(i);
}
}
}
}
#endregion
#region IEnumerable 成员
System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
{
return GetEnumerator();
}
#endregion
}
}
}