LAPACK/ScaLAPACK Development

Functions c/zlarfg and c/zlarfgp have now the following formula in Purpose description
H**H * ( alpha ) = ( beta ), H**H * H = I.
( x ) ( 0 )

Should not it be
H * ( alpha ) = ( beta ), H**H * H = I.
( x ) ( 0 )

instead?

Hi Yana,

There is a difference between the real case and the complex case. In the real case, the elementary Householder reflections ("H") are symmetric. ( H = H**T.) In the complex case, the elementary Householder reflections ("H") are not Hermitian. ( H is not H**H.)

In LAPACK clarfg, H is defined as the Householder transformation such that

Code: Select all

[            ]**H * [ alpha ] = [ beta ]
[            ]      [   x1  ]   [  0   ]
[     H1     ]      [   x2  ]   [  0   ]
[            ]      [   x3  ]   [  0   ]
[            ]      [   x4  ]   [  0   ]


The **H is necessary.

Cheers,
Julien.