From 02b31342e0dba3703c1a3a91352f7ae19764d7ce Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 29 Nov 2021 13:18:22 +0100
Subject: gauss quadratur zeugs

---
 buch/chapters/060-integral/gq/kreis.cpp | 66 +++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)
 create mode 100644 buch/chapters/060-integral/gq/kreis.cpp

(limited to 'buch/chapters/060-integral/gq/kreis.cpp')

diff --git a/buch/chapters/060-integral/gq/kreis.cpp b/buch/chapters/060-integral/gq/kreis.cpp
new file mode 100644
index 0000000..c9723cc
--- /dev/null
+++ b/buch/chapters/060-integral/gq/kreis.cpp
@@ -0,0 +1,66 @@
+/*
+ * kreis.cpp -- Gauss Quadrature Example
+ *
+ * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+ */
+#include <iostream>
+#include <iomanip>
+#include <cstdlib>
+#include <cstdio>
+#include <cmath>
+#include <gsl/gsl_integration.h>
+
+double	xmax = 0.990;
+
+double	f(double x, void *) {
+	return sqrt(1-x*x);
+}
+
+double	do_integration(size_t n) {
+	// set up integration gauss quadrature
+	gsl_function	func;
+	func.function = f;
+	func.params = NULL;
+
+	gsl_integration_fixed_workspace	*ws
+		= gsl_integration_fixed_alloc(
+			gsl_integration_fixed_legendre,
+			n, -xmax, xmax, 0, 0);
+	double	result = 0;
+	gsl_integration_fixed(&func, &result, ws);
+	gsl_integration_fixed_free(ws);
+	return result;
+}
+
+double	do_trapez(size_t n) {
+	double	h = 2 * xmax / n;	
+	double	s = 0;
+	for (int i = 0; i <= n; i++) {
+		double	x = -xmax + i * h;
+		double	a = f(x, NULL);
+		if ((i == 0) || (i == n)) {
+			a = a * 0.5;
+		}
+		s += a;
+	}
+	return h * s;
+}
+
+void	do_table(double limit) {
+	xmax = limit;
+	for (int n = 2; n <= 20; n += 2) {
+		printf("%d & %.16f & %.16f \\\\\n", n, do_integration(n),
+			do_trapez(10 * n));
+	}
+	double	amax = acos(xmax);
+	double	expected = (M_PI / 2 - amax) + sin(amax) * cos(amax);
+	printf("\\infty & %.16f & %.16f \\\\\n", expected, expected);
+}
+
+int	main(int argc, char *argv[]) {
+	do_table(0.5);
+	do_table(0.9);
+	do_table(0.99);
+	do_table(0.999);
+	return EXIT_SUCCESS;
+}
-- 
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