Determinant of a (Square Integer) Matrix

[bplus]

By recursive calls:

Code: QB64: [Select]

1. Option _Explicit ' determinantOfMatrix.bas b+ 2022-03-11 translate from
2. ''''// C++ program to find Determinant of a matrix
3. ''''#include <iostream>
4. ''''using namespace std;
5. ' Hope the above isn't important because WTH?
6.  
7. ''''// Dimension of input square matrix
8. ''''#define N 4
9. ' Again not sure??  oh this is for testing 4 x 4, the 3 x 3 is commented out
10.  
11.  
12.  
13.  
14. ''''// Driver program to test above functions
15. ' that are defined below :)
16.  
17. ''''int main()
18. ''''{
19. ''''    /* int mat[N][N] = {{6, 1, 1},
20. ''''                     {4, -2, 5},
21. ''''                     {2, 8, 7}}; */
22.  
23. ''''    int mat[N][N] = { { 1, 0, 2, -1 },
24. ''''                      { 3, 0, 0, 5 },
25. ''''                      { 2, 1, 4, -3 },
26. ''''                      { 1, 0, 5, 0 } };
27. ' well crap we need a way to read in a Matrix from a string
28.  
29. Dim m$
30. m$ = "1,2;3,4"
31. ReDim As Integer mat(0, 0)
32. readStr2Mat m$, mat()
33. displayMat mat(), 2, 2
34. Print " D ="; determinantOfMatrix%(mat(), 2)
35. Print
36. m$ = "2, -3,1;2,0,-1 ;1, 4, 5"
37. ReDim As Integer mat(0, 0)
38. readStr2Mat m$, mat()
39. displayMat mat(), 3, 3
40. Print " D ="; determinantOfMatrix%(mat(), 3)
41. Print
42. m$ = "1, 0, 2, -1;3, 0, 0, 5;2, 1, 4, -3;1, 0, 5, 0 "
43. ReDim As Integer mat(0, 0)
44. readStr2Mat m$, mat()
45. displayMat mat(), 4, 4
46. Print " D ="; determinantOfMatrix%(mat(), 4)
47.  
48. ''''    // Function call
49. ''''    cout <<"Determinant of the matrix is : " << determinantOfMatrix(mat, N);
50. ''''    return 0;
51. ''''}
52.  
53. ''''// this code is contributed by shivanisinghss2110
54. ''''Output
55.  
56.  
57. ' Move from near start to end
58. ''''// Function to get cofactor of mat[p][q] in temp[][]. n is
59. ''''// current dimension of mat[][]
60. ''''void getCofactor(int mat[N][N], int temp[N][N], int p,
61. ''''                 int q, int n)
62.  
63. Sub getCofactor (mat() As Integer, temp() As Integer, p As Integer, q As Integer, n As Integer)
64.     Dim row, col, i, j
65.     'Print "getCoFactor p, q, n: "; p, q, n
66.  
67.     ''''{
68.     ''''    int i = 0, j = 0;
69.  
70.     ''''    // Looping for each element of the matrix
71.     ''''    for (int row = 0; row < n; row++)
72.     ''''    {
73.     ''''        for (int col = 0; col < n; col++)
74.     ''''        {
75.     For row = 0 To n - 1
76.         For col = 0 To n - 1
77.  
78.             ''''            //  Copying into temporary matrix only those
79.             ''''            //  element which are not in given row and
80.             ''''            //  column
81.             ''''            if (row != p && col != q)
82.             If (row <> p) And (col <> q) Then
83.                 ''''            {
84.                 ''''                temp[i][j++] = mat[row][col];
85.  
86.                 ' is j increased before or after temp(i, j) is assigned???
87.                 temp(i, j) = mat(row, col)
88.                 j = j + 1 ' I think j should be increased after temp copy  so temp(0,0) is filled
89.                 If j = n - 1 Then
90.                     j = 0: i = i + 1
91.                 End If
92.  
93.                 ''''                // Row is filled, so increase row index and
94.                 ''''                // reset col index
95.                 ''''                if (j == n - 1)
96.                 ''''                {
97.                 ''''                    j = 0;
98.                 ''''                    i++;
99.                 ''''                }
100.                 ''''            }
101.                 ''''        }
102.                 ''''    }
103.                 ''''}
104.             End If
105.         Next
106.     Next
107. End Sub
108.  
109.  
110. ' also moved
111. ''''/* Recursive function for finding determinant of matrix.
112. ''''   n is current dimension of mat[][]. */
113. ''''int determinantOfMatrix(int mat[N][N], int n)
114. Function determinantOfMatrix% (mat() As Integer, n As Integer)
115.     ''''{
116.     ''''    int D = 0; // Initialize result
117.     Dim As Integer D, sign, f
118.  
119.     ''''    //  Base case : if matrix contains single element
120.     ''''    if (n == 1)
121.     ''''        return mat[0][0];
122.  
123.     If n = 1 Then
124.         determinantOfMatrix% = mat(0, 0)
125.     Else
126.         ''''    int temp[N][N]; // To store cofactors
127.         Dim temp(n, n) As Integer
128.         ''''    int sign = 1; // To store sign multiplier
129.         sign = 1
130.  
131.         ''''    // Iterate for each element of first row
132.         ''''    for (int f = 0; f < n; f++)
133.         For f = 0 To n - 1
134.  
135.             ''''    {
136.             ''''        // Getting Cofactor of mat[0][f]
137.             ''''        getCofactor(mat, temp, 0, f, n);
138.             getCofactor mat(), temp(), 0, f, n
139.             ''''        D += sign * mat[0][f]
140.             ''''             * determinantOfMatrix(temp, n - 1);
141.             D = D + sign * mat(0, f) * determinantOfMatrix%(temp(), n - 1)
142.             ''''        // terms are to be added with alternate sign
143.             ''''        sign = -sign;
144.             sign = -sign
145.             ''''    }
146.         Next
147.         ''''    return D;
148.         determinantOfMatrix% = D
149.     End If
150.     ''''}
151. End Function
152.  
153. 'also moved
154. ''''/* function for displaying the matrix */
155. ''''void display(int mat[N][N], int row, int col)
156. Sub displayMat (mat() As Integer, row As Integer, col As Integer)
157.     Dim As Integer i, j
158.     ''''{
159.     ''''    for (int i = 0; i < row; i++)
160.     ''''    {
161.     ''''        for (int j = 0; j < col; j++)
162.     ''''            cout <<"  " <<  mat[i][j];
163.     ''''        cout <<"n";
164.     ' the hell
165.     For i = 0 To row - 1
166.         For j = 0 To col - 1
167.             Print Right$("   " + _Trim$(Str$(mat(i, j))), 3); ' hey no more than 2 digit numbers OK?
168.             ''''    }
169.             ''''}
170.         Next
171.         Print
172.     Next
173. End Sub
174.  
175. Sub readStr2Mat (s$, mat() As Integer) ' commas separate columns, semi-colons separate rows
176.     Dim As Integer i, j
177.     ReDim rows$(0)
178.     Split s$, ";", rows$()
179.     ReDim As Integer mat(UBound(rows$), UBound(rows$))
180.     For i = 0 To UBound(rows$)
181.         ReDim nums$(0)
182.         Split rows$(i), ",", nums$()
183.         For j = 0 To UBound(nums$)
184.             mat(i, j) = Val(nums$(j))
185.         Next
186.     Next
187. End Sub
188.  
189. Sub Split (SplitMeString As String, delim As String, loadMeArray() As String)
190.     Dim curpos As Long, arrpos As Long, LD As Long, dpos As Long 'fix use the Lbound the array already has
191.     curpos = 1: arrpos = LBound(loadMeArray): LD = Len(delim)
192.     dpos = InStr(curpos, SplitMeString, delim)
193.     Do Until dpos = 0
194.         loadMeArray(arrpos) = Mid$(SplitMeString, curpos, dpos - curpos)
195.         arrpos = arrpos + 1
196.         If arrpos > UBound(loadMeArray) Then ReDim _Preserve loadMeArray(LBound(loadMeArray) To UBound(loadMeArray) + 1000) As String
197.         curpos = dpos + LD
198.         dpos = InStr(curpos, SplitMeString, delim)
199.     Loop
200.     loadMeArray(arrpos) = Mid$(SplitMeString, curpos)
201.     ReDim _Preserve loadMeArray(LBound(loadMeArray) To arrpos) As String 'get the ubound correct
202. End Sub
203.  
204.  

[jack]

hi bplus
here's a challenge for you, find the inverse of an integer matrix which inverse is an integer matrix

[bplus]

Adj() / D

All Integer, hmm... for what purpose?

[jack]

to show example of an inverse, it looks so much better when the inverse is all integers and it's an interesting task
here's a very simple program that will generate a couple matrix whose inverse is also integer

Code: QB64: [Select]

1. Dim As _Integer64 n, i, j
2. n = 4
3. For j = 1 To n
4.     For i = 1 To n
5.         Print Using "#########"; binomial(n + j - 1, i - 1);
6.     Next
7.     Print
8. Next
9. Print
10. For i = 1 To n
11.     For j = 1 To n
12.         Print Using "#########"; binomial(n + j - 1, i - 1);
13.     Next
14.     Print
15. Next
16.  
17. Function fac&& (n As _Integer64)
18.     Dim As _Integer64 f, i
19.     f = 1&&
20.     For i = 1&& To n
21.         f = f * i
22.     Next
23.     fac = f
24. End Function
25.  
26. Function binomial&& (n As _Integer64, k As _Integer64)
27.     binomial = fac(n) / (fac(k) * fac(n - k))
28. End Function
29.  

you can make variations of the matrix by adding or subtracting rows or columns you can also raise the matrix to some integer power and it's inverse will still be integer

[bplus]

Thankyou @BSpinoza I think I've looked over that guys stuff or similar before, old, old style QB with line numbers and worse foreign language so don't know what he's talking about. Looks like it is wealth of tech code but I think I'd rather translate C++ code.

This translation stuff is not worth effort unless I know for what this may be used and don't say for mass transporter, I already did that joke ;-))