This document contains C++ code that performs Cholesky decomposition on symmetric positive definite matrices. It initializes two sample matrices, performs Cholesky decomposition to calculate the upper triangular Cholesky factor matrices, and then uses forward and backward substitution on the triangular systems to solve for values in column 0, representing the solution to the linear systems.

1. NONAME00.CPP May 8, 2020 Page 1
1 void Venka(){//cholesky sqrt S.P. Venkateshan, Prasanna Swaminathan,
2 //in Computational Methods in Engineering, 2014
3 //Cholesky Decomposition - an overview | ScienceDirect Topics page 7
4 //*****************************************************************************************
5 cout << "See Molanos Method STATIC CONDENSATION SQRT BANDED SYMMETRIC MATRIX-> " << endl;
6 cout << " linkedin copyright 2020 or SCRIBD" << endl;
7 cout << endl;
8 long xmax, i, j, k, i1, ma, mr, l;
9 //*****************************************************************************************
10 /*
11 xmax = 7L;
12 float **a = new float*[xmax+1L];
13 for(i = 1L; i <= xmax; a[i++] = new float[xmax +1L]);
14 for(i=1L; i<= xmax; i++)
15 for(j= i; j <= xmax; a[i][j++]=0.0);
16 a[1][1] = 9 , a[1][2] = 6, a[1][3] = 0, a[1][4] = 3;
17 a[2][2] = 8 , a[2][3] = 0, a[2][4] = 0, a[2][5] = 4;
18 a[3][3] = 16, a[3][4] = 4, a[3][5] = -4, a[3][6] = -20;
19 a[4][4] = 28, a[4][5] = 2, a[4][6] = 0, a[4][7] = 0;
20 a[5][5] = 15, a[5][6] = 9, a[5][7] = 3;
21 a[6][6] = 63, a[6][7] = 13;
22 a[7][7] = 14;
23 a[1][0]= 33 , a[2][0] = 42, a[3][0] = -76, a[4][0] = 137, a[5][0] = 154,
24 a[6][0] = 454, a[7][0] = 191;
25 */
26 xmax = 4L;
27 float **a = new float *[xmax+1L];
28 for(i = 1L; i <= xmax; a[i++] = new float [xmax +1L]);
29 //*****************************************************************************************
30 for(i=1L; i<= xmax; i++)
31 for(j= i; j <= xmax; a[i][j++]=0.0);
32 //*****************************************************************************************
33 a[1][1] = 4 , a[1][2] = 1, a[1][3] = 1, a[1][4] = 1;
34 a[2][2] = 4 , a[2][3] = 1, a[2][4] = 1;
35 a[3][3] = 4 , a[3][4] = 1;
36 a[4][4] = 4 ;
37 a[1][0]= 15.9 , a[2][0] = 17.7, a[3][0] = 13.2, a[4][0] = 9.9;
38 //*****************************************************************************************
39 for(i=1L; i<= xmax; i++){ //cholesky decmposition upper triangular matrix
40 for(j=i, i1=i-(k=1L); k <= i1; a[i][j]-=a[k][i]*a[k++][j]);
41 for(a[i][j++]=sqrt(a[i][j]); j<= xmax; a[i][j++]/=a[i][i])
42 for(k=1L; k<= i1; a[i][j]-=a[k][i]*a[k++][j]);
43 }
44 //*****************************************************************************************
45 for(i=1L; i<= xmax; i++){
46 for(j=i; j<= xmax; j++)
47 cout << "c[" << i << "][" << j << "]= " << a[i][j] << " ";
48 cout << endl;
49 }
50 cout << endl;
51 //*****************************************************************************************
52 for(i=1L; i<= xmax; a[i++][0L]/=a[i][i])//forward substitution
53 for(i1=i-(k=1L); k <= i1; a[i][0L]-=a[k][i]*a[k++][0L]);
54 //*****************************************************************************************
55 for(i=1L; i<= xmax; i++)
56 cout << "y[" << i << "]= " << a[i][0L] << " ";
57 cout << endl << endl;
58 //*****************************************************************************************
59 for(i=xmax; i >= 1L; a[i--][0L]/=a[i][i])//backward substitution
60 for(ma = (mr = xmax - (j = i + 1L) + (l = 2L)) > xmax ? xmax : mr; l <= ma; a[i][0L] -= a[i]
[i-1L+l++] * a[j++][0L]);
61 //*****************************************************************************************
62 for(i=1L; i<= xmax; i++)
63 cout << "y[" << i << "]= " << a[i][0L] << " ";
64 cout << endl;
65 getch();
66 }
67