طريقة التنصيف هذا البرنامج جاهز للتنفيذ مباشرة بعد نقله الى برنامج turbo c
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/*
* BISECTION ALGORITHM 2.1
*
* To find a solution to f(x) = 0 given the continuous function
* f on the interval [a,b], where f(a) and f(b) have
* opposite signs:
*
* INPUT: endpoints a,b; tolerance TOL;
* maximum number of iterations N0.
*
* OUTPUT: approximate solution p or
* a message that the algorithm fails.
*/
#include
#include
#define ZERO 1.0E-20
#define true 1
#define false 0
main()
{
double A,FA,B,FB,C,P,FP,TOL;
int I,NO,OK,FLAG;
FILE *OUP[1];
double absval(double);
double F(double);
void INPUT(int *, double *, double *, double *, double *, double *, int *);
void OUTPUT(FILE **, int *);
INPUT(&OK, &A, &B, &FA, &FB, &TOL, &NO);
if (OK) {
OUTPUT(OUP, &FLAG);
/* STEP 1 */
I = 1;
/* STEP 2 */
OK = true;
while ((I<=NO) && OK) {
/* STEP 3 */
/* compute P(I) */
C = (B - A) / 2.0;
P = A + C;
/* STEP 4 */
FP = F(P);
if (FLAG == 2) fprintf(*OUP,"%3d %15.8e %15.7e \n",I,P,FP);
if ((absval(FP) /* procedure completed successfully */
fprintf(*OUP,"\nApproximate solution P = %11.8f \n",P);
fprintf(*OUP,"with F(P) = %12.8f\n",FP);
fprintf(*OUP,"Number of iterations = %3d",I);
fprintf(*OUP," Tolerance = %15.8e\n",TOL);
OK = false;
}
else {
/* STEP 5 */
I++;
/* STEP 6 */
/* compute A(I) and B(I) */
if ((FA*FP) > 0.0) {
A = P; FA = FP;
}
else {
B = P; FB = FP;
}
}
}
if (OK) {
/* STEP 7 */
/* procedure completed unsuccessfully */
fprintf(*OUP,"\nIteration number %3d",NO);
fprintf(*OUP," gave approximation %12.8f\n",P);
fprintf(*OUP,"F(P) = %12.8f not within tolerance : %15.8e\n",FP,TOL);
}
fclose(*OUP);
}
return 0;
}
/* Change function F for a new problem */
double F(double X)
{
double f;
f = ( X + 4.0 ) * X * X - 10.0;
return f;
}
void INPUT(int *OK, double *A, double *B, double *FA, double *FB, double *TOL, int *NO)
{
double X;
char AA;
printf("This is the Bisection Method.\n");
printf("Has the function F been created in the program immediately preceding\n");
printf("the INPUT function?\n");
printf("Enter Y or N\n");
scanf("%c",&AA);
if ((AA == 'Y') || (AA == 'y')) {
*OK = false;
while (!(*OK)) {
printf("Input endpoints A < B separated by blank\n");
scanf("%lf %lf", A, B);
if (*A > *B) {
X = *A; *A = *B; *B = X;
}
if (*A == *B) printf("A cannot equal B\n");
else {
*FA = F(*A);
*FB = F(*B);
if (*FA*(*FB) > 0.0) printf("F(A) and F(B) have same sign\n");
else *OK = true;
}
}
*OK = false;
while(!(*OK)) {
printf("Input tolerance\n");
scanf("%lf", TOL);
if (*TOL <= 0.0) printf("Tolerance must be positive\n");
else *OK = true;
}
*OK = false;
while (!(*OK)) {
printf("Input maximum number of iterations - no decimal point\n");
scanf("%d", NO);
if (*NO <= 0) printf("Must be positive integer\n");
else *OK = true;
}
}
else {
printf("The program will end so that the function F can be created\n");
*OK = false;
}
}
void OUTPUT(FILE **OUP, int *FLAG)
{
char NAME[30];
printf("Select output destination\n");
printf("1. Screen\n");
printf("2. Text file\n");
printf("Enter 1 or 2\n");
scanf("%d", FLAG);
if (*FLAG == 2) {
printf("Input the file name in the form - drive:name.ext\n");
printf("A:OUTPUT.DTA\n");
scanf("%s", NAME);
*OUP = fopen(NAME, "w");
}
else *OUP = stdout;
fprintf(*OUP,"Bisection Method\n");
printf("Select amount of output\n");
printf("1. Answer only\n");
printf("2. All intermeditate approximations\n");
printf("Enter 1 or 2\n");
scanf("%d", FLAG);
if (*FLAG == 2) fprintf(*OUP, " I P F(P)\n");
}
/* Absolute Value Function */
double absval(double val)
{
if (val >= 0) return val;
else return -val;
}
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