// 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 