Math: "dot product" of Complex is real number.

Brain failure #2. Also I don't know if such thing as dot product exists here :-)
mosra · Feb 27, 2013 · c847e15 · c847e15
1 parent 1eea843
commit c847e15
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Showing 2 changed files with 8 additions and 8 deletions.
diff --git a/src/Math/Complex.h b/src/Math/Complex.h
@@ -43,12 +43,12 @@ template<class T> class Complex {
          * @brief Dot product
          *
          * @f[
-         *      c_0 \cdot c_1 = c_0 \overline{c_1} = (a_0 a_1 + b_0 b_1) + i(a_1 b_0 - a_0 b_1)
+         *      c_0 \cdot c_1 = a_0 a_1 + b_0 b_1
          * @f]
          * @see dot() const
          */
-        inline static Complex<T> dot(const Complex<T>& a, const Complex<T>& b) {
-            return a*b.conjugated();
+        inline static T dot(const Complex<T>& a, const Complex<T>& b) {
+            return a._real*b._real + a._imaginary*b._imaginary;
         }
 
         /**
@@ -277,20 +277,20 @@ template<class T> class Complex {
          *
          * Should be used instead of length() for comparing complex number length
          * with other values, because it doesn't compute the square root. @f[
-         *      c \cdot c = c \overline c = a^2 + b^2
+         *      c \cdot c = a^2 + b^2
          * @f]
          * @see dot(const Complex&, const Complex&)
          */
         inline T dot() const {
-            return _real*_real + _imaginary*_imaginary;
+            return dot(*this, *this);
         }
 
         /**
          * @brief %Complex number length
          *
          * See also dot() const which is faster for comparing length with other
          * values. @f[
-         *      |c| = \sqrt{c \overline c} = \sqrt{a^2 + b^2}
+         *      |c| = \sqrt{c \cdot c}
          * @f]
          */
         inline T length() const {
@@ -318,7 +318,7 @@ template<class T> class Complex {
          *
          * See invertedNormalized() which is faster for normalized
          * complex numbers. @f[
-         *      c^{-1} = \frac{\overline c}{c \overline c} = \frac{\overline c}{a^2 + b^2}
+         *      c^{-1} = \frac{\overline c}{|c|^2} = \frac{\overline c}{c \cdot c}
          * @f]
          */
         inline Complex<T> inverted() const {

diff --git a/src/Math/Test/ComplexTest.cpp b/src/Math/Test/ComplexTest.cpp
@@ -183,7 +183,7 @@ void ComplexTest::dot() {
     Complex a(5.0f,  3.0f);
     Complex b(6.0f, -7.0f);
 
-    CORRADE_COMPARE(Complex::dot(a, b), Complex(9.0f, 53.0f));
+    CORRADE_COMPARE(Complex::dot(a, b), 9.0f);
 }
 
 void ComplexTest::dotSelf() {