Function Mechatronix::minParabola

Function Documentation

real_type Mechatronix::minParabola(real_type f0, real_type Df0, real_type b, real_type fb, real_type smin, real_type smax)

find the minimum of a parabola passing by 2 point and 1 tangent.

The parabola \( p(x)=f_0 + f'_0 x + C x^2 \) satisfy

\[ p(0) = f_0, \qquad p(b) = f_b, \qquad p'(x) = f'_0 \]
The minimum is searched in the interval
\[ [s_{\min}b,s_{\max}b] \]
and thus satisfy

\[ x = \arg\min \{p(z) \,|\, z\in[s_{\min}b,s_{\max}b] \} \]
Parameters

  • f0 – the value \( f_0 \)

  • Df0 – the value \( f'_0 \)

  • b – the value \( b \)

  • fb – the value \( f_b \)

  • smin – the value \( s_{\min} \)

  • smax – the value \( s_{\max} \)