#include <complex>
#include <vector>
class CmpLinearAlgebra
{
public:
static void CmpPrintMatrix(
int m, int n,
std::vector<std::vector<std::complex<double>>>& Ac);
static void CmpAddition(
size_t m, size_t n,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::vector<std::complex<double>>>& B,
std::vector<std::vector<std::complex<double>>>& C);
static void CmpSubtraction(
size_t m, size_t n,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::vector<std::complex<double>>>& B,
std::vector<std::vector<std::complex<double>>>& C);
static void CmpMultiply(
size_t m, size_t n, size_t p,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::vector<std::complex<double>>>& B,
std::vector<std::vector<std::complex<double>>>& C);
static void CmpAnticommutator(
size_t n,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::vector<std::complex<double>>>& B,
std::vector<std::vector<std::complex<double>>>& C);
static void CmpCommutator(
size_t n,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::vector<std::complex<double>>>& B,
std::vector<std::vector<std::complex<double>>>& C);
static void CmpAdjoint(
size_t m, size_t n,
std::vector<std::vector<std::complex<double>>>& Ac,
std::vector<std::vector<std::complex<double>>>& Ad);
static std::complex<double> CmpDeterminant(
bool& failure, int n,
std::vector<std::vector<std::complex<double>>>& A);
static bool CmpGaussianElimination(
int m, int n,
std::vector<std::vector<std::complex<double>>>& A,
std::vector<std::complex<double>>& b,
std::vector<std::complex<double>>& x,
std::vector<size_t>& pivot);
static bool CmpGaussianFactor(
int n, std::vector<std::vector<std::complex<double>>>& M,
std::vector<size_t>& pivot);
static bool CmpGaussianSolution(
int n, std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::complex<double>>& b,
std::vector<std::complex<double>>& x,
std::vector<size_t>& pivot);
static bool CmpSubstitution(
int m, int n, std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::complex<double>>& b,
std::vector<std::complex<double>>& x,
std::vector<size_t>& pivot);
static bool CmpInverse(
int n, std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::vector<std::complex<double>>>& Mi);
static void CmpCharPolyAndAdjoint(
int n,
std::vector<std::vector<std::complex<double>>>& C,
std::vector<std::vector<std::complex<double>>>& I,
std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::vector<std::complex<double>>>& adjoint,
std::vector<std::complex<double>>& a);
static void CmpMatrixKernel(
int m, int n,
std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::vector<std::complex<double>>>& X,
size_t& r);
static void CmpMatrixImage(
int m, int n,
std::vector<std::vector<std::complex<double>>>& M,
std::vector<std::vector<std::complex<double>>>& N,
std::vector<std::vector<std::complex<double>>>& X,
int rank);
};
#include <vector>
class DblLinearAlgebra
{
public:
static void DblPrintMatrix(
int m, int n, std::vector<std::vector<double>>& A);
static void DblAddition(
size_t m, size_t n,
std::vector<std::vector<double>>& A,
std::vector<std::vector<double>>& B,
std::vector<std::vector<double>>& C);
static void DblSubtraction(
size_t m, size_t n,
std::vector<std::vector<double>>& A,
std::vector<std::vector<double>>& B,
std::vector<std::vector<double>>& C);
static void DblMultiply(
size_t m, size_t n, size_t p,
std::vector<std::vector<double>>& A,
std::vector<std::vector<double>>& B,
std::vector<std::vector<double>>& C);
static void DblAnticommutator(
size_t n,
std::vector<std::vector<double>>& A,
std::vector<std::vector<double>>& B,
std::vector<std::vector<double>>& C);
static void DblCommutator(
size_t n,
std::vector<std::vector<double>>& A,
std::vector<std::vector<double>>& B,
std::vector<std::vector<double>>& C);
static double DblDeterminant(
bool& failure, int n,
std::vector<std::vector<double>>& A);
static bool DblGaussianElimination(
int m, int n, std::vector<std::vector<double>>& A,
std::vector<double>& b, std::vector<double>& x,
std::vector<size_t>& pivot);
static bool DblGaussianFactor(
int n, std::vector<std::vector<double>>& M,
std::vector<size_t>& pivot);
static bool DblGaussianSolution(
int n, std::vector<std::vector<double>>& M,
std::vector<double>& b, std::vector<double>& x,
std::vector<size_t>& pivot);
static bool DblSubstitution(
int n, std::vector<std::vector<double>>& M,
std::vector<double>& b, std::vector<double>& x,
std::vector<size_t>& pivot);
static bool DblInverse(
int n, std::vector<std::vector<double>>& M,
std::vector<std::vector<double>>& A);
static void DblCharPolyAndAdjoint(
int n,
std::vector<std::vector<double>>& C,
std::vector<std::vector<double>>& I,
std::vector<std::vector<double>>& M,
std::vector<std::vector<double>>& adjoint,
std::vector<double>& a);
static void DblMatrixKernel(
int m, int n,
std::vector<std::vector<double>>& M,
std::vector<std::vector<double>>& X,
size_t& r);
static void DblMatrixImage(
int m, int n,
std::vector<std::vector<double>>& M,
std::vector<std::vector<double>>& N,
std::vector<std::vector<double>>& X,
int rank);
};
// Exercises from "Modern Quantum Chemistry An Introduction to Advanced
// Electronic Structure Theory" by Attila Szabo and Neil S. Ostlund
// https://chemistlibrary.wordpress.com/wp-content/uploads/2015/02/modern-quantum-chemistry.pdf
// Program (c) Tuesday, August 12, 2025 by James Pate Williams, Jr.
#include <complex>
#include <iomanip>
#include <iostream>
#include <vector>
#include "DblLinearAlgebra.h"
#include "CmpLinearAlgebra.h"
int main()
{
double AArcb[3][3] = { { 2, 3, -1 }, { 4, 4, -3 }, { -2, 3, -1 } };
double AArso[3][3] = { { 1, 1, 0 }, { 1, 2, 2 }, { 0, 2, -1 } };
double BBrso[3][3] = { { 1, -1, 1 }, { -1, 0, 0 }, { 1, 0, 1} };
double BBr[3][3] = { { 1, -1, 1 }, { -1 , 0, 0 }, { 1, 0, 1 } };
double AAcr[3][3] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
double AAci[3][3] = { { 1, 1, 2 }, { 3, 0, 1 }, { 0, 2, 4 } };
double BBcr[3][3] = { { 1, 0, 1 }, { 1 , 1, 0 }, { 0, 1, 1 } };
double BBci[3][3] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
int m = 3, n = 3, p = 3;
std::vector<double> br(3);
std::vector<size_t> pivot(3);
std::vector<std::vector<double>> Arcb(3, std::vector<double>(3));
std::vector<std::vector<double>> Arso(3, std::vector<double>(3));
std::vector<std::vector<double>> Brso(3, std::vector<double>(3));
std::vector<std::vector<double>> Br(3, std::vector<double>(3));
std::vector<std::vector<double>> Cr(3, std::vector<double>(3));
std::vector<std::vector<double>> Ai(3, std::vector<double>(3));
std::vector<std::vector<double>> Ari(3, std::vector<double>(3));
std::vector<std::vector<std::complex<double>>> Ac(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Bc(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Cc(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Dc(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Ec(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Fc(3,
std::vector<std::complex<double>>(3));
std::vector<std::vector<std::complex<double>>> Gc(3,
std::vector<std::complex<double>>(3));
for (int i = 0; i < m; i++)
{
for (int j = 0; j < p; j++)
{
Arcb[i][j] = AArcb[i][j];
Arso[i][j] = AArso[i][j];
Brso[i][j] = BBrso[i][j];
Ac[i][j]._Val[0] = AAcr[i][j];
Ac[i][j]._Val[1] = AAci[i][j];
}
}
for (int i = 0; i < p; i++)
{
for (int j = 0; j < n; j++)
{
Br[i][j] = BBr[i][j];
Bc[i][j]._Val[0] = BBcr[i][j];
Bc[i][j]._Val[1] = BBci[i][j];
}
}
DblLinearAlgebra::DblMultiply(3, 3, 3, Arcb, Br, Cr);
std::cout << "Ar * Br = Cr Conte & de Boor" << std::endl;
DblLinearAlgebra::DblPrintMatrix(3, 3, Cr);
std::cout << std::endl;
CmpLinearAlgebra::CmpMultiply(3, 3, 3, Ac, Bc, Cc);
std::cout << "Ac * Bc = Cc" << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Cc);
std::cout << std::endl;
// Exercise 1.2
std::cout << "Exercise 1.2 page 5 Commutator" << std::endl;
DblLinearAlgebra::DblCommutator(3, Arso, Brso, Cr);
DblLinearAlgebra::DblPrintMatrix(3, 3, Cr);
std::cout << std::endl;
std::cout << "Exercise 1.2 page 5 Anticommutator" << std::endl;
DblLinearAlgebra::DblAnticommutator(3, Arso, Brso, Cr);
DblLinearAlgebra::DblPrintMatrix(3, 3, Cr);
std::cout << std::endl;
CmpLinearAlgebra::CmpAdjoint(3, 3, Cc, Dc);
std::cout << "Exercise 1.3 page 6 Cc adjoint" << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Dc);
std::cout << std::endl;
CmpLinearAlgebra::CmpAdjoint(3, 3, Ac, Ec);
CmpLinearAlgebra::CmpAdjoint(3, 3, Bc, Fc);
CmpLinearAlgebra::CmpMultiply(3, 3, 3, Fc, Ec, Gc);
std::cout << "Exercise 1.3 page 6 Bc adjoint * Ac adjoint" << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Gc);
std::cout << std::endl;
std::cout << "Ar matrix" << std::endl;
DblLinearAlgebra::DblPrintMatrix(3, 3, Arcb);
bool inv = DblLinearAlgebra::DblInverse(n, Arcb, Ai);
std::cout << std::endl;
std::cout << "Ar Conte & de Boor inverse = " << inv << std::endl;
DblLinearAlgebra::DblPrintMatrix(3, 3, Ai);
std::cout << std::endl;
std::cout << "Ar * Ar inverse" << std::endl;
DblLinearAlgebra::DblMultiply(3, 3, 3, Arcb, Ai, Ari);
DblLinearAlgebra::DblPrintMatrix(3, 3, Ari);
std::cout << std::endl;
std::cout << "Ac" << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Ac);
std::cout << std::endl;
inv = CmpLinearAlgebra::CmpInverse(3, Ac, Bc);
std::cout << "Ac inverse = " << inv << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Bc);
CmpLinearAlgebra::CmpMultiply(3, 3, 3, Ac, Bc, Cc);
std::cout << std::endl;
std::cout << "Ac * AC inverse" << std::endl;
CmpLinearAlgebra::CmpPrintMatrix(3, 3, Cc);
}
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
View all posts by jamespatewilliamsjr
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