Problem finding the local maximum of a function in C - c

Question

I'm designing an algorithm to define a simple method able to find the local maximum of a function f (x) given in an interval [a, b]
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define PI 3.141592653
float funtion_(float a, float x){
float result=0;
result = a * (sin (PI*x));
return result;
}
int main (){
double A = 4.875; //average of the digits of the identification card
double a = 0.0, b =1.0; //maximum and minimum values of the interval [a, b]
double h=0;
double N;
double Max, x;
double sin_;
double inf;
printf ("input the minux value: ");
scanf ("%lf", &inf);
printf ("input the N value: ");
scanf ("%lf", &N);
h= (b-a)/N;
printf("h = %lf\n", h);
x=a-h;
Max = -inf;
do {
x = x+h;
sin_ = funtion_(A, x);
if (sin_>=Max){
Max = sin_;
}
}while (x==b);
printf ("Maximum value: %lf.5", Max);
return 0;
}
The algorithm implements the function f (x) = A * sin (pi * x), where A is the average of the digits of my ID, and inf variable is assigned a number sufficiently greater than the values ​​reached by the function in the interval [a, b] = [0.1].
The algorithm must find the local maximum of the function but it is the maximum returns always zero. do not understand why. What problem may be the logic of my solution?, this problem can be solved by this simple algorithm or some optimization by backtracking is necessary ? Thanks for your responses.

Answer 1

Several problems with this code; probably the most glaring is:
int a = 0, b = 1;
float Max, x;
/* ... */
do {
/* ... */
} while (x == b);
You cannot compare an int and a float for equality. It might work once in a great while due to dumb luck :) but you cannot expect this code to function reliably.
I strongly recommend changing all your int variables to double, all your float variables to double, and all the scanf(3) and printf(3) calls to match. While you can combine different primitive number types in one program, and even in one expression or statement, subtle differences in execution will take you hours to discover.
Furthermore, comparing floating point formats for equality is almost never a good idea. Instead, compare the difference between two numbers to a epsilon value:
if (fabs(a-b) < 0.001)
/* consider them equal */
You might want to scale your epsilon so that it matches the scale of your problem; since float really only supports about seven digits of precision, this comparison wouldn't work well:
if (fabsf(123456789 - 123456789.1) < 0.5)
/* oops! fabsf(3) used to force float */
/* and float can't tell the difference */
You might want to find a good introduction to numerical analysis. (Incidentally, one of my favorite classes back in school. :)
update
The core of the problem is your while(x == b). I fixed that and a few smaller problems, and this code seems to work:
#include
#include
#include
#define PI 3.141592653
float funtion_(float a, float x)
{
float result = 0;
result = a * (sin(PI * x));
return result;
}
int main()
{
float A = 4.875; //average of the digits of the identification card
float a = 0.0, b = 1.0; //maximum and minimum values of the interval [a, b]
float h = 0;
float N;
float Max, x;
float sin_;
float inf;
printf("\ninput the inf value: ");
scanf("%f", &inf);
printf("\ninput the N value: ");
scanf("%f", &N);
h = (b - a) / N;
x = a - h;
Max = -inf;
do {
x = x + h;
sin_ = funtion_(A, x);
if (sin_ >= Max) {
Max = sin_;
printf("\n new Max: %f found at A: %f x: %f\n", Max, A, x);
}
} while (x < b);
printf("Maximum value: %.5f\n", Max);
return 0;
}
Running this program with some small inputs:
$ ./localmax
input the inf value: 1
input the N value: 10
new Max: 0.000000 found at A: 4.875000 x: 0.000000
new Max: 1.506458 found at A: 4.875000 x: 0.100000
new Max: 2.865453 found at A: 4.875000 x: 0.200000
new Max: 3.943958 found at A: 4.875000 x: 0.300000
new Max: 4.636401 found at A: 4.875000 x: 0.400000
new Max: 4.875000 found at A: 4.875000 x: 0.500000
Maximum value: 4.87500
$

Answer 2

You are doing your calculations, in particular the initialisation of h, with integer arithmetic. So in the statement:
h = (b-a) / N;
a, b, and N are all integers so the expression is evaluated as an integer expression, and then converted to a float for assignment to h. You will probably find that the value of h is zero. Try adding the following line after the calculation of h:
printf("h = %f\n", h);
After you've fixed that by doing the calculations with floating point, you need to fix your while loop. The condition x = b is definitely not what you want (I noticed it was originally x == b before your formatting edit, but that's not right either).

Answer 3

Should the while condition be: while(x <= b)

Answer 4

while (x = b);
There is no way to exit the loop. b is always 1.