rpa_rescale_eigval Function

public function rpa_rescale_eigval(x, dxr) result(xr)

Rescale eigenvalues $x$ of the RPA matrix $\mathbf{AT}$ to tame the spurious divergence of $\log(1+x)$ as $x\to-1$. Non-negative eigenvalues are left intact.

$$x_\mathrm r=\begin{cases}x & x\ge0\\ -\operatorname{erf}\!\big(\tfrac{\sqrt\pi}2 x^4\big)^\frac14 & x<0 \end{cases},\qquad \frac{\mathrm dx_\mathrm r}{\mathrm dx}=\begin{cases}1 & x\ge0\\ \big(\tfrac x{x_\mathrm r}\big)^3 \mathrm e^{-(\frac{\sqrt\pi}2 x^4)^2} & x<0\end{cases}$$

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp),	intent(in)			::	x(:)
real(kind=dp),	intent(out),	optional		::	dxr(:)

Return Value real(kind=dp), (size(x))