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.
Blog Entry © Wednesday, September 3, 2025, by James Pate Williams, Jr. Solution of Exercise 1.11 in Modern Quantum Chemistry an Introduction to Advanced Electronic Structure Theory © 1996 by Attila Szabo and Neil S. Ostlund
// EigenVV2x2.cpp (c) Wednesday, September 3, 2025
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Solution to Exercise 1.11 in "Quantum Chemistry
// an Introduction to Advanced Electronic Structure
// Theory (c) 1996 by Attila Szabo and Neil S. Ostlund
#include "pch.h"
#include "framework.h"
#include "EigenVV2x2.h"
#define MAX_LOADSTRING 100
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
std::wstring text; // output wide string
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_EIGENVV2X2, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_EIGENVV2X2));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex;
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_EIGENVV2X2));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_EIGENVV2X2);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
#define IDC_STATIC1 1000
#define IDC_STATIC2 1010
#define IDC_STATIC3 1020
#define IDC_STATIC4 1030
#define IDC_EDIT_A11 2000
#define IDC_EDIT_A12 2010
#define IDC_EDIT_A21 2020
#define IDC_EDIT_A22 2030
#define IDC_EDIT_MULTILINE 3000
#define IDC_BUTTON_COMPUTE 4000
#define IDC_BUTTON_CANCEL 4010
//
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
static HFONT hFont = { };
static HWND hEditMultiline = { };
static HWND hEditA11 = { };
static HWND hEditA12 = { };
static HWND hEditA21 = { };
static HWND hEditA22 = { };
switch (message)
{
case WM_CREATE:
{
hFont = CreateFont(16, 0, 0, 0, FW_NORMAL, FALSE, FALSE, FALSE,
ANSI_CHARSET, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New Bold");
CreateWindowEx(0, L"STATIC", L"A[1][1]:", WS_CHILD | WS_VISIBLE,
10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC1, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[1][2]:", WS_CHILD | WS_VISIBLE,
10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC2, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[2][1]:", WS_CHILD | WS_VISIBLE,
10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC3, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[2][2]:", WS_CHILD | WS_VISIBLE,
10, 100, 80, 20, hWnd, (HMENU)IDC_STATIC4, hInst, NULL);
hEditA11 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 10, 200, 20, hWnd, (HMENU)IDC_EDIT_A11, hInst, NULL);
hEditA12 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 40, 200, 20, hWnd, (HMENU)IDC_EDIT_A12, hInst, NULL);
hEditA21 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 70, 200, 20, hWnd, (HMENU)IDC_EDIT_A21, hInst, NULL);
hEditA22 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 100, 200, 20, hWnd, (HMENU)IDC_EDIT_A22, hInst, NULL);
hEditMultiline = CreateWindowEx(
WS_EX_CLIENTEDGE, // Extended style for sunken border
TEXT("EDIT"), // Class name
TEXT(""), // Initial text (can be blank)
WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
310, 10, 300, 300, // Position and size
hWnd, // Parent window handle
(HMENU)IDC_EDIT_MULTILINE, // Unique control ID
hInst, // Application instance
NULL // Extra parameter
);
CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_COMPUTE, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
220, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_CANCEL, hInst, NULL);
SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, TRUE);
SetDlgItemText(hWnd, IDC_EDIT_A11, L"3");
SetDlgItemText(hWnd, IDC_EDIT_A12, L"1");
SetDlgItemText(hWnd, IDC_EDIT_A21, L"1");
SetDlgItemText(hWnd, IDC_EDIT_A22, L"3");
}
break;
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDC_BUTTON_COMPUTE:
{
WCHAR line[128] = L"";
text = L"";
// eigenvalues
std::vector<double> omega(3);
// matrix
std::vector<std::vector<double>> A(3,
std::vector<double>(3));
std::vector<std::vector<double>> B(3,
std::vector<double>(3));
// eigenvectors
std::vector<std::vector<double>> c(3,
std::vector<double>(3));
GetWindowText(hEditA11, line, 128);
std::wstring A11Str(line);
A[1][1] = std::stod(A11Str);
GetWindowText(hEditA12, line, 128);
std::wstring A12Str(line);
A[1][2] = std::stod(A12Str);
GetWindowText(hEditA21, line, 128);
std::wstring A21Str(line);
A[2][1] = std::stod(A21Str);
GetWindowText(hEditA22, line, 128);
std::wstring A22Str(line);
A[2][2] = std::stod(A22Str);
double term1 = A[1][1] + A[2][2];
double term2 = pow(A[2][2] - A[1][1], 2.0);
double term3 = 4.0 * A[1][2] * A[2][1];
// compute eigenvalues
omega[1] = 0.5 * (term1 - sqrt(term2 + term3));
omega[2] = 0.5 * (term1 + sqrt(term2 + term3));
swprintf_s(line, L"Eigenvalues:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
text += std::wstring(line);
swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
text += std::wstring(line);
// compute eigenvalues using a unitary transformation
// matrix A must be symmetric
double theta0 = 0.0;
if (A[1][1] == A[2][2])
{
theta0 = 0.5 * acos(0.0);
}
else
{
theta0 = 0.5 * atan(2.0 * A[1][2] /
(A[1][1] - A[2][2]));
}
// compute the eigenvalues
omega[1] = A[1][1] * pow(cos(theta0), 2.0) +
A[2][2] * pow(sin(theta0), 2.0) +
A[1][2] * sin(2.0 * theta0);
omega[2] = A[1][1] * pow(cos(theta0), 2.0) +
A[2][2] * pow(sin(theta0), 2.0) -
A[1][2] * sin(2.0 * theta0);
swprintf_s(line, L"Eigenvalues:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
text += std::wstring(line);
swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
text += std::wstring(line);
// compute eigenvectors
c[1][1] = cos(theta0);
c[1][2] = sin(theta0);
c[2][1] = sin(theta0);
c[2][2] = -cos(theta0);
swprintf_s(line, L"Eigenvectors:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"c 11 = %13.10lf\r\n", c[1][1]);
text += std::wstring(line);
swprintf_s(line, L"c 12 = %13.10lf\r\n", c[1][2]);
text += std::wstring(line);
swprintf_s(line, L"c 21 = %13.10lf\r\n", c[2][1]);
text += std::wstring(line);
swprintf_s(line, L"c 22 = %13.10lf\r\n", c[2][2]);
text += std::wstring(line);
SetWindowText(hEditMultiline, text.c_str());
break;
}
case IDC_BUTTON_CANCEL:
{
PostQuitMessage(0);
break;
}
break;
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC hdc = BeginPaint(hWnd, &ps);
// TODO: Add any drawing code that uses hdc here...
EndPaint(hWnd, &ps);
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
Numerical Explorations 