// Romberg.cpp : Defines the entry point for the application.
// https://learn.microsoft.com/en-us/windows/win32/controls/create-a-simple-combo-box
#include "stdafx.h"
#include <CommCtrl.h>
#include <math.h>
#include <stdio.h>
#include "Romberg.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
// 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_PTR CALLBACK RombergDialog(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_ROMBERG, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_ROMBERG));
MSG msg;
// Main message loop:
while (GetMessage(&msg, NULL, 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_ROMBERG));
wcex.hCursor = LoadCursor(NULL, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_ROMBERG);
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, NULL, NULL, hInstance, NULL);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
//
// 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)
{
switch (message)
{
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 ID_OPTION_ROMBERGINTEGRATION:
DialogBox(hInst, MAKEINTRESOURCE(IDD_DIALOG1), hWnd, RombergDialog);
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;
}
double f0(double x)
{
return exp(-x * x);
}
double f1(double x)
{
return x * x;
}
double f2(double x)
{
double pi = 4.0 * atan(1.0);
return sin(101.0 * pi * x);
}
double f3(double x)
{
double pi = 4.0 * atan(1.0);
return 1.0 + sin(10.0 * pi * x);
}
double f4(double x)
{
return fabs(x - 1.0 / 3.0);
}
double f5(double x)
{
return sqrt(x);
}
double f6(double x)
{
double result = 1.0;
if (x != 0.0)
result = sin(x) / x;
return result;
}
/* https://en.wikipedia.org/wiki/Romberg%27s_method#Implementation */
char table[8192];
double R1[2048], R2[2048];
void print_row(size_t i, double* R)
{
char buffer[128];
sprintf_s(buffer, 128, "R[%2zu] = ", i);
strcat_s(table, 8192, buffer);
for (size_t j = 0; j <= i; ++j)
{
sprintf_s(buffer, 128, "%.*lf ", 16, R[j]);
strcat_s(table, 8192, buffer);
}
strcat_s(table, 8192, "\r\n");
}
double RombergExtrapolation(
double(*f)(double),
double a, double b,
size_t max_steps,
double acc)
{
double *Rp = &R1[0], *Rc = &R2[0];
double h = (b - a);
Rp[0] = (f(a) + f(b))*h*.5;
print_row(0, Rp);
for (size_t i = 1; i < max_steps; ++i)
{
h /= 2.;
double c = 0;
size_t ep = 1 << (i - 1);
for (size_t j = 1; j <= ep; ++j)
{
c += f(a + (2 * j - 1)*h);
}
Rc[0] = h*c + .5*Rp[0];
for (size_t j = 1; j <= i; ++j)
{
double n_k = pow(4, j);
Rc[j] = (n_k*Rc[j - 1] - Rp[j - 1]) / (n_k - 1);
}
print_row(i, Rc);
if (i > 1 && fabs(Rp[i - 1] - Rc[i]) < acc)
{
return Rc[i];
}
double *rt = Rp;
Rp = Rc;
Rc = rt;
}
return Rp[max_steps - 1];
}
INT_PTR CALLBACK RombergDialog(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
WORD word = LOWORD(wParam);
static TCHAR functions[7][128] =
{
TEXT("f(x) = exp(-x * x)"),
TEXT("f(x) = x * x"),
TEXT("f(x) = sin(101 * pi * x)"),
TEXT("f(x) = 1 + sin(10 * pi * x)"),
TEXT("f(x) = abs(x - 1.0 / 3.0)"),
TEXT("f(x) = sqrt(x)"),
TEXT("f(x) = sin(x) / x or 1 if x = 0")
};
static TCHAR A[1024];
static HWND cbWindow;
static int k = 0;
static int itemIndex;
switch (message)
{
case WM_INITDIALOG:
cbWindow = GetDlgItem(hDlg, IDC_COMBO1);
memset(&A, 0, sizeof(A));
for (k = 0; k < 6; k++)
{
// Add string to combobox.
SendMessage(cbWindow, CB_ADDSTRING, (WPARAM)k, (LPARAM)functions[k]);
}
// Send the CB_SETCURSEL message to display an initial item
// in the selection field
SendMessage(cbWindow, CB_SETCURSEL, (WPARAM)0, (LPARAM)0);
return (INT_PTR)TRUE;
case WM_COMMAND:
if (word == IDOK || word == IDCANCEL)
{
EndDialog(hDlg, word);
return (INT_PTR)TRUE;
}
if (HIWORD(wParam) == CBN_SELCHANGE)
// If the user makes a selection from the list:
// Send CB_GETCURSEL message to get the index of the selected list item.
// Send CB_GETLBTEXT message to get the item.
// Display the item in a messagebox.
{
itemIndex = SendMessage((HWND)lParam, (UINT)CB_GETCURSEL,
(WPARAM)0, (LPARAM)0);
TCHAR listItem[256];
(TCHAR)SendMessage((HWND)lParam, (UINT)CB_GETLBTEXT,
(WPARAM)itemIndex, (LPARAM)listItem);
}
else if (word == IDC_BUTTON1)
{
char buffer[128];
GetDlgItemTextA(hDlg, IDC_EDIT1, buffer, 128);
double a = atof(buffer);
GetDlgItemTextA(hDlg, IDC_EDIT2, buffer, 128);
double b = atof(buffer);
double integral = 0.0;
GetDlgItemTextA(hDlg, IDC_EDIT4, buffer, 128);
double acc = atof(buffer);
int max_steps = GetDlgItemInt(hDlg, IDC_EDIT5, FALSE, FALSE);
switch (itemIndex)
{
case 0:
integral = RombergExtrapolation(f0, a, b, max_steps, acc);
break;
case 1:
integral = RombergExtrapolation(f1, a, b, max_steps, acc);
break;
case 2:
integral = RombergExtrapolation(f2, a, b, max_steps, acc);
break;
case 3:
integral = RombergExtrapolation(f3, a, b, max_steps, acc);
break;
case 4:
integral = RombergExtrapolation(f4, a, b, max_steps, acc);
break;
case 5:
integral = RombergExtrapolation(f5, a, b, max_steps, acc);
break;
case 6:
integral = RombergExtrapolation(f6, a, b, max_steps, acc);
break;
}
sprintf_s(buffer, 128, "Integral = %.*lf\r\n", 16, integral);
strcat_s(table, 8192, buffer);
SetDlgItemTextA(hDlg, IDC_EDIT7, table);
}
else if (word == IDC_BUTTON3)
{
table[0] = '\0';
SetDlgItemTextA(hDlg, IDC_EDIT7, table);
}
}
return (INT_PTR)FALSE;
}
Numerical Explorations 