int main (void)
{
float a2, a1, a0;
float r1 = 0, r2 = 0;
printf("Enter coefficients of Quadratic Equation a2*x^2 + a1*x + a0 = 0 \n");
printf("in the order a2, a1, a0, separated by spaces: ");
scanf("%f %f %f", &a2, &a1, &a0);
int num_root = quad_roots(a2, a1, a0, &r1, &r2);
switch (num_root)
{
case 2:
printf("There are 2 distinct real roots with x = %.6g or x = %.6g\n", r1, r2);
break;
case 1:
case -1:
printf("There is 1 distinct real root with x = %g\n", r1);
break;
case 0:
printf("There is not real roots for the equation\n");
break;
case -2:
printf("Any number is a root\n");
default:
break;
}
return 0;
}
int main(void)
{
/* Create "double" type arrays to store coeffients A (3) and the roots (2) */
double A[3], roots[2];
/* Prompt for the coefficients */
printf("Enter coefficients a, b, and c, of the Quadratic Equation in the form:\na*(x)^2 + bx + c\nin the order a, b, then c (separated by spaces):");
// for the sake of clarity, a, b, c will be referred as A[2], A[1], A[0]
scanf("%lf %lf %lf", A+2, A+1, A);
/* Solve equation using function "quad_roots" (on file "quadSol.c")" */
/* depending on the kind of discriminants */
switch (quad_roots(A, roots)) {
/* A[2] == A[1] == 0, where A[0] != 0, therefore not an equation */
case -3:
printf("case -3\na and b are the same... and equal to 0.\nAre you kidding?, that one is not an equation\n");
break;
/* A[0] == A[1] == A[2] == 0, ALL the coefficients are ceros */
case -2:
printf("case -2\nSorry, there is no meaningful solution, you know... like life\n");
break;
/* A[0] == 0 and A[1] != 0, this is a LINEAR equation, with just ONE solution */
case -1:
printf("case -1\nx = %f\nHey Einstein! This is not quadratic, it's a LINEAR equation\n", roots[0]);
break;
/* (A[1])^2 > 4(A[2]*A[0]), discriminant > 0, there are two different real roots */
case 0:
printf("case 0\nx = %f\nx = %f\n", roots[0], roots[1]);
break;
/* (A[1])^2 < 4(A[2]*A[0]), discriminant < 0, solutions are complex conjugate roots */
case 1:
printf("case 1\nx = %f (is a real number)\nx = %f(is an imaginary number)\n", roots[0], roots[1]);
break;
/* (A[1])^2 == 4(A[2]*A[0]), discriminant == 0, roots[0] == roots[1] ? */
case 2:
printf("case 2\nx = %f is equal to:\nx = %f\n", roots[0], roots[1]);
break;
}
return 0;
}
int rcubic_roots(double complex* argv, double complex* roots)
{
/* Chan, Joey, JMCSC, ync12 */
double complex a2 = *(argv+0),
a1 = *(argv+1),
a0 = *(argv+2);
//printf("rcubic a2 = %10.5g + %10.5gi\n", creal(a2), cimag(a2));
//printf("rcubic a1 = %10.5g + %10.5gi\n", creal(a1), cimag(a1));
//printf("rcubic a0 = %10.5g + %10.5gi\n", creal(a0), cimag(a0));
double complex *r1 = roots+1,
*r2 = roots+2,
*r3 = roots+3;
double ALLOWED_ERROR = DBL_EPSILON;
double complex UNITY_1 = 1. + 0.*I; /* Unity Real root */
double complex UNITY_2 = -1./2. - sqrt(3.)/2.*I; /* Real part of the complex unity root */
double complex UNITY_3 = -1./2. + sqrt(3.)/2.*I; /* Imaginary part of the complex unity root */
int result;
double complex a, b, p;
double complex y_n, y_n1;
a = (1./3.)* cpow(9.*a1*a2- 2.*a2*a2*a2 - 27.*a0, (1./3.));
b = -a2/3.;
/* alpha is 0, p cannot be calculated */
if (a == 0)
{
*r1 = b;
double complex z[3] = {(1.+0*I), (0. + 0*I), (a1 - a2*a2/3.)};
quad_roots(z, r1);
*r2 += b;
*r3 += b;
}
/* Normal calculation */
else
{
p = (a1 - a2*a2/3.)/(a*a);
int count = 1; /* Counter for number of iterations */
double complex difference; /* Difference between y_n and y_(n+1) */
y_n = cabs(p) < 2. ? 1.-p/3. : 1./p;
y_n1 = y_n - (y_n*y_n*y_n + p*y_n - 1)/(3*y_n*y_n + p);
difference = cabs(y_n1-y_n);
while ( (cabs(y_n-y_n1) > ALLOWED_ERROR && cabs(difference) < cabs(y_n1-y_n)) ||
count < 3)
{
count++;
difference = cabs(y_n1-y_n);
y_n = y_n1;
y_n1 = y_n - (y_n*y_n*y_n + p*y_n - 1)/(3*y_n*y_n + p);
}
*r1 = a*y_n1+b;
double complex z[3] = {1. + 0*I, a2+(*r1), -a0/(*r1)};
quad_roots(z, r1);
}
qsort(roots+1, 3, sizeof(double complex), ascending);
return 0;
}
int rcubic_roots(double *a,double *root)
/* <Elkrief>_<Alexandre>_exer_1c */
{double p,alpha,beta,i,fx,df,ytemp,y,big,small,middle,delta_quad,p2,y2;
double root_inter1[3],root_inter2[3],quad1[3],quad2[3];
int quad_case;
if (a[1]==0 && a[2]==0){
printf("a[2]=a[1]=%f\n",a[0]);
if (a[0]>0){
root[1]=-pow(fabs(a[0]),1.0/3.0);
//real part of x=-sign(a[0])|a[0]|^(1/3)*cubic root of unity
root[2]=-pow(fabs(a[0]),1.0/3.0)*(-0.5);
//imaginary part of x=-sign(a[0])|a[0]|^(1/3)*cubic root of unity
root[3]=pow(fabs(a[0]),1.0/3.0)*sqrt(3)*0.5;
}
else{root[1]=pow(fabs(a[0]),1.0/3.0);
root[2]=pow(fabs(a[0]),1.0/3.0)*(-0.5);
root[3]=pow(fabs(a[0]),1.0/3.0)*sqrt(3)*0.5;
}
return(0);
}
else if(a[0]==0){
printf("a[0]=%f\n",a[0]);
root[1]=0;
quad1[0]=a[1];
quad1[1]=a[2]
quad1[2]=1;
quad_case=quad_roots(quad1,root_inter1);
printf("root_inter=%lf, %lf\n",root_inter1[1],root_inter1[2]);
root[2]=root_inter1[1];
root[3]=root_inter1[2];
printf("quad_case=%d\n",quad_case);
if (root[2]<0 && root[3]>0){
middle=root[1];
small=root[2];
big=root[3];
}
else if(root[3]<0){
big=root[1];
middle=root[3];
small=root[2];
}
else{
big=root[3];
middle=root[2];
small=root[1];
}
root[1]=small;
root[2]=middle;
root[3]=big;
if (root[1]==root[2] && root[2]==root[3]){
return(1);
}
else if (root[1]==root[2] || root[2]==root[3] || root[1]==root[3]){
return(2);
}
else if (root[1]!=root[2] && root[2]!=root[3] && root[1]!=root[3]){
return(3);
}
else if(quad_case==0){return(0);}
else{printf("test");
return(0);}
}
else if(a[0]==a[1]*a[2]){
printf("a[0]=a[1]*a[2]\n");
printf("a[1]=%f\n",a[1]);
printf("sqrt(a[1])=%f\n",sqrt(a[1]));
if(a[1]<0){
if (fabs(a[2])>sqrt(fabs(a[1]))){
root[1]=-a[2];
root[2]=-sqrt(-a[1]);
root[3]=sqrt(-a[1]);
}
else{
root[1]=-sqrt(-a[1]);
root[2]=-a[2];
root[3]=sqrt(-a[1]);
}
return(3);
}
else{
root[1]=-a[2];
root[2]=0;
root[3]=sqrt(a[1]);
return(0);
}
}
else if(3*a[1]==a[2]*a[2] && 27*a[0]==a[2]*a[2]*a[2]){
printf("3-27 case\n");
root[1]=-a[2]/3.0;
root[2]=-a[2]/3.0;
root[3]=-a[2]/3.0;
return(1);
}
else {
beta= -a[2]/3.0;
printf("a[0] print=%f\n",a[0]);
printf("beta print=%lf \n", beta);
if ((beta*beta*beta+a[2]*beta*beta+a[1]*beta+a[0])>0){
printf("neg\n");
alpha=-pow((beta*beta*beta+a[2]*beta*beta+a[1]*beta+a[0]),1.0/3.0);
//alpha=-pow(fabs(((beta+a[2])*beta+a[1])*1+a[0]/beta),1.0/3.0)*pow(fabs(beta),1.0/3.0);
}
else{
printf("pos\n");
printf("kk=%lf\n",beta*beta*beta+a[2]*beta*beta+a[1]*beta+a[0]);
alpha=pow(fabs(beta*beta*beta+a[2]*beta*beta+a[1]*beta+a[0]),1.0/3.0);
//alpha=pow(fabs(((beta+a[2])*beta+a[1])*1+a[0]/beta),1.0/3.0)*pow(fabs(beta),1.0/3.0);
}
printf("alpha=%lf, beta=%e \n",alpha,beta);
//p=(3*beta*beta+2*a[2]*beta+a[1])/(alpha*alpha);
p=((3*beta*beta+2*a[2]*beta+a[1])/alpha)/alpha;
printf("p=%lf \n",p);
printf("Reduced cubic: y^3+%lf*y-1=0 \n",p);
i=0;
p2=-3/pow(4,1.0/3.0);
y2=-1/pow(2,1.0/3.0);
//printf("p2=%f, y2=%f\n",p2,y2);
//special case Q3-vi
if (fabs(p-p2)<0.01){
printf("p-p2 case\n");
if (alpha*y2+beta<alpha*(1/(y2*y2))+beta){
root[1]=alpha*y2+beta;
root[2]=alpha*y2+beta;
root[3]=alpha*(1/(y2*y2))+beta;
}
else{
root[1]=alpha*(1/(y2*y2))+beta;
root[2]=alpha*y2+beta;
root[3]=alpha*y2+beta;
}
//printf("Roots=%lf %lf %lf\n", root[1],root[2],root[3]);
return(2);
}
//special case Q3-v
else if (p==0){
printf("p=0 case\n");
root[1]=1;
root[2]=-0.5;
root[3]=sqrt(3)/2.0;
return(0);
}
else if (fabs(p)<2) {
y=1-p/3;
printf("|p|<2\n");
}
else {
y=1/p;
printf("|p|>2\n");
}
printf("y=%f \n",y);
while (ytemp!=y && i<4){
fx=y*y*y+p*y-1;
df=3*y*y+p;
ytemp=y;
y=y-fx/df;
//printf("%.25lf \n",y);
i=i+1;
}
root[1]=alpha*y+beta;
quad2[0]=(-a[0]/(root[1]));
quad2[1]=(a[2]+root[1]);
quad2[2]=1;
quad_case=quad_roots(quad2, root_inter2);
printf("root_inter=%lf, %lf\n",root_inter2[1],root_inter2[2]);
root[2]=root_inter2[1];
root[3]=root_inter2[2];
printf("Quadratic coeffs: %f, %f \n",a[2]+(root[1]),-a[0]/(root[1]));
//ordering the roots in ascending order
delta_quad=(a[2]+(root[1]))*(a[2]+(root[1]))-4*(-a[0]/(root[1]));
printf("Delta_quad= %lf\n",delta_quad);
if (delta_quad>=0){
if (root[1]>root[2] && root[1]>root[3]){
big=root[1];
if (root[2]>root[3]){
middle=root[2];
small=root[3];
}
else{
middle=root[3];
small=root[2];
}
}
else if (root[2]>root[3]){
big=root[2];
if (root[1]>root[3]){
middle=root[1];
small=root[3];
}
else{
middle=root[3];
small=root[1];
}
}
else{
big=root[3];
if (root[1]>root[2]){
middle=root[1];
small=root[2];
}
else{
middle=root[2];
small=root[1];
}
}
root[1]=small;
root[2]=middle;
root[3]=big;
if (root[1]==root[2] && root[2]==root[3]){
return(1);
}
else if (root[1]==root[2] || root[2]==root[3] || root[1]==root[3]){
return(2);
}
else {
return(3);
}
}
else{
printf("JJJJ = %lf, %lf , %lf\n\n\n", root[1],root[2],root[3]);
return(0);
}
}
}
