Madagascar Programming Reference Manual

Dot product test for linear operators (dottest.c)

Performs the dot product test (see p. ), to check whether the adjoint of the operator is coded incorrectly. Coding is incorrect if any of

$$\langle Lm_1,d_2\rangle = \langle m_1, L^*d_2\rangle\quad\textrm{or}\quad \langle d_1 + Lm_1,d_2\rangle = \langle m_1, m_2+L^*d_2\rangle$$

does not hold (within machine precision). $m_1$ and $d_2$ are random vectors.