Routine Name: randSymPosDefMat
Author: Brandon Furman
Language: C++
Description/Purpose: The purpose of this function is generate a square, positive definite matrix. It generates the matrix by multiplying a random matrix by its transpose and adding m to each of the diagonal entries.
Input: This routine accepts a single integer, m, that defines the number of rows and columns in the matrix.
Output: The functions returns an array2D object with m rows and m columns.
Usage/Example: Usage is straightforward. To generate a 4x4 matrix the function can be called like in the following code:
array2D mat;
mat = randSymPosDefMat(4);
for (int i = 0; i < 4; i++) {
for (int j = 0; j < 4; j++) {
std::cout << mat(i, j) << " ";
}
std::cout << std::endl;
}
Executing this code outputs the following to console:
5.00906 1.0635 1.15012 0.361192
1.0635 5.49797 1.67021 0.781994
1.15012 1.67021 6.00258 1.03384
0.361192 0.781994 1.03384 4.86117
If a 20x20 matrix is desired, then we can call
randSymPosDefMat(20);
and doing so yields
25.5612 3.72904 5.50075 3.98441 4.53272 5.44157 4.13524 4.78415 4.14961 3.38296 4.85773 4.19826 4.62052 4.45429 4.57553 4.4834 4.56055 4.55898 4.97196 4.13268
3.72904 25.4588 5.04753 4.69621 4.5128 4.53037 4.77446 5.08259 4.96795 3.09428 4.54811 5.32652 4.39218 4.57116 4.61463 4.34823 5.09619 4.11683 4.4667 4.80072
5.50075 5.04753 29.1397 5.70031 6.53303 6.34842 5.99064 6.82419 6.0324 4.58241 5.78911 6.80117 6.46275 6.29489 6.97015 6.14338 6.32256 6.02631 5.51659 6.24748
3.98441 4.69621 5.70031 26.3857 4.92052 4.25707 5.1233 5.62027 5.03991 3.63948 4.46727 6.23411 4.45951 4.5714 5.17467 4.67939 5.55565 4.7854 5.06466 5.30582
4.53272 4.5128 6.53303 4.92052 26.1584 5.36655 4.68383 5.38357 5.82465 3.63259 4.86619 5.67009 5.24956 5.48552 5.92689 5.00543 5.06607 4.9948 4.50318 5.21884
5.44157 4.53037 6.34842 4.25707 5.36655 26.9697 5.00394 5.2561 5.39696 3.94759 4.84704 4.95256 5.57147 4.82143 5.17914 5.30176 5.312 5.01816 4.99961 4.8492
4.13524 4.77446 5.99064 5.1233 4.68383 5.00394 26.8055 5.05112 5.44708 4.03133 4.76949 5.8173 5.44134 4.87463 4.70835 5.56251 5.65518 5.03639 5.14701 5.12807
4.78415 5.08259 6.82419 5.62027 5.38357 5.2561 5.05112 27.2305 5.94041 3.68883 5.75954 6.33164 5.20995 5.21331 5.6338 4.85625 5.08408 4.71661 5.37146 6.18144
4.14961 4.96795 6.0324 5.03991 5.82465 5.39696 5.44708 5.94041 27.0366 3.34593 5.31533 5.97516 5.40777 5.09995 5.20261 4.95466 5.03782 4.88274 5.03109 5.75628
3.38296 3.09428 4.58241 3.63948 3.63259 3.94759 4.03133 3.68883 3.34593 24.1869 3.11167 4.16201 3.59533 4.39895 4.1912 3.42855 3.70083 2.77389 3.25658 3.11108
4.85773 4.54811 5.78911 4.46727 4.86619 4.84704 4.76949 5.75954 5.31533 3.11167 26.7814 5.68096 5.38849 4.71861 5.09558 4.38057 5.24362 4.67564 5.32189 5.32808
4.19826 5.32652 6.80117 6.23411 5.67009 4.95256 5.8173 6.33164 5.97516 4.16201 5.68096 27.3367 5.59265 5.60074 5.86391 4.98279 6.23149 4.98854 5.0906 5.88916
4.62052 4.39218 6.46275 4.45951 5.24956 5.57147 5.44134 5.20995 5.40777 3.59533 5.38849 5.59265 26.9103 4.92699 5.43072 5.29207 5.5732 5.05206 4.78726 4.87043
4.45429 4.57116 6.29489 4.5714 5.48552 4.82143 4.87463 5.21331 5.09995 4.39895 4.71861 5.60074 4.92699 26.9586 5.90533 4.59418 5.01136 4.40864 4.74629 4.63461
4.57553 4.61463 6.97015 5.17467 5.92689 5.17914 4.70835 5.6338 5.20261 4.1912 5.09558 5.86391 5.43072 5.90533 26.778 5.12819 5.34192 4.72948 4.88981 5.4709
4.4834 4.34823 6.14338 4.67939 5.00543 5.30176 5.56251 4.85625 4.95466 3.42855 4.38057 4.98279 5.29207 4.59418 5.12819 26.2617 5.13328 4.85725 4.88268 4.89677
4.56055 5.09619 6.32256 5.55565 5.06607 5.312 5.65518 5.08408 5.03782 3.70083 5.24362 6.23149 5.5732 5.01136 5.34192 5.13328 26.6492 5.54225 5.33857 5.08487
4.55898 4.11683 6.02631 4.7854 4.9948 5.01816 5.03639 4.71661 4.88274 2.77389 4.67564 4.98854 5.05206 4.40864 4.72948 4.85725 5.54225 26.4095 4.95707 5.02316
4.97196 4.4667 5.51659 5.06466 4.50318 4.99961 5.14701 5.37146 5.03109 3.25658 5.32189 5.0906 4.78726 4.74629 4.88981 4.88268 5.33857 4.95707 26.1839 5.29577
4.13268 4.80072 6.24748 5.30582 5.21884 4.8492 5.12807 6.18144 5.75628 3.11108 5.32808 5.88916 4.87043 4.63461 5.4709 4.89677 5.08487 5.02316 5.29577 26.3874
Implementation/Code: The following is the code for randSymDiagDomMat(int m):
array2D randSymPosDefMat(int m) {
array2D A, B;
A = randMat(m,m);
B.allocateMem(m, m);
double sum = 0.0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < m; j++) {
for (int k = 0; k < m; k++) {
sum = sum + A(i, k) * A(j, k);
}
if (i == j) sum = sum + m;
B(i, j) = sum;
sum = 0.0;
}
}
return B;
}
Last Modified: April/2019