这site求解三次方程，并有它使用的方程
我写这个函数是为了得到相同的结果，但它不起作用
void cubicFormula(float a, float b, float c, float d, float *results)
{
float a2 = a*a;
float b2 = b*b;
float b3 = b2*b;
float q = (3*c- b2)/9;
float q2 = q*q;
float q3 = q2*q;
float r = -27*d + b*(9*c-2*b2);
float r2 = r*r;
float discriminant = q3 + r2;
float s = r + sqrtf(discriminant);
float t = r - sqrtf(discriminant);
float term1 = powf((-t + s)/2, 1/3.);
float r13= 2 * sqrtf(q);
results[0] = (- term1 + r13 * cosf(q3/3));
results[1] = (- term1 + r13 * cosf(q3 + (2*M_PI)/3));
results[2] = (- term1 + r13 * cosf(q3 + (4*M_PI)/3));
}
可能是什么问题，是不是我遗漏了什么？
更新:
例如，使用这些值
a = -1.000000;
b = 36.719475;
c = -334.239960;
d = 629.877808;
判别式小于零，所以 r13 是 nan
但是上面提到的网站和我测试过的几个在线求解器找到了三个根
23.775687816485593
2.548516232734247
10.395270950780164
都是实数
您链接的站点提供 Cubic Equation Calculator .您可以从寻找您的代码与他们的代码之间的差异开始:
function cubicsolve(dataForm)
{
var a = parseFloat(dataForm.aIn.value);
var b = parseFloat(dataForm.bIn.value);
var c = parseFloat(dataForm.cIn.value);
var d = parseFloat(dataForm.dIn.value);
if (a == 0)
{
alert("The coefficient of the cube of x is 0. Please use the utility for a SECOND degree quadratic. No further action taken.");
return;
} //End if a == 0
if (d == 0)
{
alert("One root is 0. Now divide through by x and use the utility for a SECOND degree quadratic to solve the resulting equation for the other two roots. No further action taken.");
return;
} //End if d == 0
b /= a;
c /= a;
d /= a;
var disc, q, r, dum1, s, t, term1, r13;
q = (3.0*c - (b*b))/9.0;
r = -(27.0*d) + b*(9.0*c - 2.0*(b*b));
r /= 54.0;
disc = q*q*q + r*r;
dataForm.x1Im.value = 0; //The first root is always real.
term1 = (b/3.0);
if (disc > 0) { // one root real, two are complex
s = r + Math.sqrt(disc);
s = ((s < 0) ? -Math.pow(-s, (1.0/3.0)) : Math.pow(s, (1.0/3.0)));
t = r - Math.sqrt(disc);
t = ((t < 0) ? -Math.pow(-t, (1.0/3.0)) : Math.pow(t, (1.0/3.0)));
dataForm.x1Re.value = -term1 + s + t;
term1 += (s + t)/2.0;
dataForm.x3Re.value = dataForm.x2Re.value = -term1;
term1 = Math.sqrt(3.0)*(-t + s)/2;
dataForm.x2Im.value = term1;
dataForm.x3Im.value = -term1;
return;
}
// End if (disc > 0)
// The remaining options are all real
dataForm.x3Im.value = dataForm.x2Im.value = 0;
if (disc == 0){ // All roots real, at least two are equal.
r13 = ((r < 0) ? -Math.pow(-r,(1.0/3.0)) : Math.pow(r,(1.0/3.0)));
dataForm.x1Re.value = -term1 + 2.0*r13;
dataForm.x3Re.value = dataForm.x2Re.value = -(r13 + term1);
return;
} // End if (disc == 0)
// Only option left is that all roots are real and unequal (to get here, q < 0)
q = -q;
dum1 = q*q*q;
dum1 = Math.acos(r/Math.sqrt(dum1));
r13 = 2.0*Math.sqrt(q);
dataForm.x1Re.value = -term1 + r13*Math.cos(dum1/3.0);
dataForm.x2Re.value = -term1 + r13*Math.cos((dum1 + 2.0*Math.PI)/3.0);
dataForm.x3Re.value = -term1 + r13*Math.cos((dum1 + 4.0*Math.PI)/3.0);
return;
} //End of cubicSolve