Commit 534bcb59 authored by Taddeus Kroes's avatar Taddeus Kroes

Merge branch 'master' of ssh://vo20.nl/git/uva

parents da036965 ad6e4432
CFLAGS := -Wextra -Wall -Werror -g -std=c99 -D_GNU_SOURCE
LDFLAGS := -lm
progs := bisection numdiff sqrt newton_raphson
all: $(progs)
bisection: bisection.c
numdiff: numdiff.c
sqrt: sqrt.c
newton_raphson: newton_raphson.c
$(progs): CFLAGS += -DMAIN_$@
clean: ; $(RM) $(progs)
#include <stdio.h>
#include <math.h>
static double bisect(double (*f)(double), double a, double b, double tolerance,
unsigned int *steps, unsigned int max_steps, double approximation,
int error_per_step)
{
double c = INFINITY;
for ( *steps = 1; *steps < max_steps; *steps += 1) {
c = (a + b) / 2;
if ( error_per_step )
printf("step %2d error: %.3E (%3f%%)\n", *steps,
fabs(approximation - c),
100 * fabs(c - approximation) / approximation);
if (f(c) == 0 || (b - a) / 2 < tolerance)
return c;
if (signbit(f(c)) == signbit(f(a)))
a = c;
else
b = c;
}
return c;
}
#ifdef MAIN_bisection
static inline double f(double x) { return x * sin(x) - 1.0; }
int main(void)
{
double approximation = 1.11415714087193008730052518;
unsigned int steps;
bisect(&f, 0.0, 2.0, 10e-12, &steps, 100, approximation, 0);
printf("bisection of x * sin(x) - 1 for x in [%.1f, %.1f] in %d steps.\n",
0.0, 2.0, steps);
return 0;
}
#endif
#include <stdio.h>
#include <math.h>
static double newton_raphson(double (*f)(double), double (*df)(double),
double start_x, double tolerance, unsigned int *steps,
unsigned int max_steps, double approximation, int error_per_step)
{
double x = start_x, last_x = x - 1;
for( *steps = 1; fabs(x - last_x) >= tolerance; (*steps)++ ) {
if ( *steps == max_steps )
return NAN;
last_x = x;
x -= f(x) / df(x);
if ( error_per_step )
printf("step %2d error: %.3E (%3f%%)\n", *steps,
fabs(approximation - last_x),
100 * fabs(last_x - approximation) / approximation);
}
return x;
}
#ifdef MAIN_newton_raphson
static inline double f1(double x) { return x * x - x + 2; }
static inline double df1(double x) { return 2 * x - 1; }
static inline double f2(double x) { return x * x * x - 3 * x - 2; }
static inline double df2(double x) { return 3 * x * x - 3; }
static inline double f3(double x) { return (x * x + 1) * (x - 4); }
static inline double df3(double x) { return 3 * x * x - 8 * x + 1; }
int main(void)
{
unsigned int steps;
double result;
result = newton_raphson(&f1, &df1, 0, 10e-12, &steps, 100, 0, 0);
printf("f1 using newton-raphson = %.20f (%d steps)\n", result, steps);
result = newton_raphson(&f2, &df2, -10, 10e-12, &steps, 100, 0, 0);
printf("f2 using newton-raphson = %.20f (%d steps)\n", result, steps);
result = newton_raphson(&f2, &df2, 10, 10e-12, &steps, 100, 0, 0);
printf("f2 using newton-raphson = %.20f (%d steps)\n", result, steps);
result = newton_raphson(&f3, &df3, 0, 10e-12, &steps, 100, 0, 0);
printf("f3 using newton-raphson = %.20f (%d steps)\n", result, steps);
return 0;
}
#endif
#include <stdio.h>
#include <math.h>
#include <float.h>
static double numdiff_central(double (*f)(double), double x, double h) {
return (f(x + h) - f(x - h)) / (2 * h);
}
static double numdiff_right(double (*f)(double), double x, double h) {
return (f(x + h) - f(x)) / h;
}
#define NUMDIFF(f, x) { \
volatile double h = sqrt(DBL_EPSILON) * (x); \
\
printf("right-hand diff. of " #f "(x) for x = " #x ": %lf\n", \
numdiff_right(f, x, h)); \
\
printf("central diff. of " #f "(x) for x = " #x ": %lf\n", \
numdiff_central(f, x, h)); \
\
printf("calculated h = √e * (" #x "): %lf\n\n", h); \
}
int main(void)
{
NUMDIFF(sin, M_PI / 3.0);
NUMDIFF(sin, 100 * M_PI + M_PI / 3.0);
NUMDIFF(sin, 10e12 * M_PI + M_PI / 3.0);
return 0;
}
#include <stdio.h>
#include <math.h>
#include "bisection.c"
#include "newton_raphson.c"
static double regula_falsi(double (*f)(double), double a, double b,
double tolerance, unsigned int *steps, unsigned int max_steps,
double approximation, int error_per_step)
{
int side = 0;
double c, fc, fa = f(a), fb = f(b);
for( *steps = 1; *steps < max_steps; (*steps)++ ) {
c = (fa * b - fb * a) / (fa - fb);
if ( error_per_step )
printf("step %2d error: %.3E (%3f%%)\n", *steps,
fabs(approximation - c),
100 * fabs(c - approximation) / approximation);
if ( fabs(b - a) < tolerance * fabs(b + a) )
break;
fc = f(c);
if ( fc * fb > 0 ) {
b = c;
fb = fc;
if( side == -1 )
fa /= 2;
side = -1;
} else if (fa * fc > 0) {
a = c;
fa = fc;
if( side == 1 )
fb /= 2;
side = 1;
} else
break;
}
return c;
}
#ifdef MAIN_sqrt
static inline double f(double x) { return x * x - 2; }
static inline double df(double x) { return 2 * x; }
int main(void)
{
unsigned int steps;
double approx = 1.41421356237309504880168872420, result;
printf("√2 is approximate = %.20f\n", approx);
result = bisect(&f, 1, 2, 10e-12, &steps, 100, approx, 0);
printf("√2 using bisection = %.20f (%d steps)\n", result, steps);
result = regula_falsi(&f, 1, 2, 10e-12, &steps, 100, approx, 0);
printf("√2 using regula falsi = %.20f (%d steps)\n", result, steps);
result = newton_raphson(&f, &df, 1.4, 10e-12, &steps, 100, approx, 0);
printf("√2 using newton-raphson = %.20f (%d steps)\n", result, steps);
return 0;
}
#endif
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