C++：解決三次方程

這site解決了三次方程，並擁有它採用C++：解決三次方程

我寫了這個函數來得到相同的結果的公式，但它不工作

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)); 
}

可能是什麼問題，有什麼我失蹤？

更新：

例如，使用這些值

a = -1.000000; 
b = 36.719475; 
c = -334.239960; 
d = 629.877808;

判別是小於零，所以R13是楠

但是上面提到的位點和我測試過的幾個在線求解器找到三個根

23.775687816485593 
2.548516232734247 
10.395270950780164

所有這些實數

來源

2012-11-11 rraallvv

你用的是什麼'a'，'b'，'c'和'd'？並非所有的三次方程都有三個真正的根。 – Tim

「但它不起作用」 - 在沒有心理能力的情況下，請描述它如何不起作用。 –

平方根可能是虛數，您需要在調用sqrt函數之前考慮這一點。閱讀複雜的數字。 – hyde

您鏈接到提供Cubic Equation Calculator網站。你可以從你的代碼和他們的代碼之間尋找差異開始：

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

來源

2012-11-11 05:13:07

嗯以下的答案，那裏有很多東西，我會仔細看看，謝謝 – rraallvv

C++：解決三次方程

回答

相關問題