Changeset 8073 for trunk/MagicSoft/Mars/mbase/MMath.cc

Timestamp:

10/16/06 19:43:37 (18 years ago)

Author:

tbretz

Message:

*** empty log message ***

File:

• trunk/MagicSoft/Mars/mbase/MMath.cc (modified) (4 diffs)

trunk/MagicSoft/Mars/mbase/MMath.cc

@@ -554 +554 @@
 // An exact solution of the cubic polynomial equation:
 //
-// x^3 + a*x^2 + b*x + c = 0
+//   x^3 + a*x^2 + b*x + c = 0
 //
 // was first published by Gerolamo Cardano (1501-1576) in his treatise,
@@ -563 +563 @@
 // discovered. Zeno source code
 //
+// http://home.att.net/~srschmitt/cubizen.html
+//
 // % compute real or complex roots of cubic polynomial
 // function cubic( var z1, z2, z3 : real, a, b, c : real ) : real
@@ -598 +600 @@
 // end function
 //
+// see also http://en.wikipedia.org/wiki/Cubic_equation
+//
 Int_t MMath::SolvePol3(Double_t a, Double_t b, Double_t c,
                        Double_t &x1, Double_t &x2, Double_t &x3)
 {
+    //    Double_t coeff[4] = { 1, a, b, c };
+    //    return TMath::RootsCubic(coeff, x1, x2, x3) ? 1 : 3;
+
     const Double_t Q = (a*a - 3*b)/9;
     const Double_t R = (9*b*a - 27*c - 2*a*a*a)/54;
@@ -607 +614 @@
     // ----- The single-real / duplicate-roots solution -----
 
+    // D<0:  three real roots
+    // D>0:  one real root
+    // D==0: maximum two real roots (two identical roots)
+
+    // R==0: only one unique root
+    // R!=0: two roots
+
     if (D==0)
     {
         const Double_t r = MMath::Sqrt3(R);
 
-        x1 = 2*r - a/3.;               // real root
-        x2 =   r - a/3.;               // real root
-
+        x1 = r - a/3.;               // real root
+        if (R==0)
+            return 1;
+
+        x2 = 2*r - a/3.;               // real root
         return 2;
     }