"Samples in Fortran are not acceptable."

I think ORNL believes that scientific computing will move away from Fortran, and it is hiring accordingly.

Jack Dongarra is a well-known figure in numerical linear algebra, involved in EISPACK, LINPACK, LAPACK, BLAS etc. He is affiliated with Oak Ridge and the University of Tennesee. (Oak Ridge is in Tennesee). He is one of the authors, along with UT colleagues, of a 2020 Lapack working note

Prospectus for the Next LAPACK and ScaLAPACK Libraries:
Basic ALgebra LIbraries for Sustainable Technology with
Interdisciplinary Collaboration (BALLISTIC)

BALLISTIC will be in C:

For historic reasons, the existing software base for Sca/LAPACK is
written in Fortran and uses archaic software engineering techniques.
Most scientific software written today is not based in Fortran, and a
recent study of programming languages ranks Fortran 38th, with the
top-3 programming languages listed as Python, Java, and C [129]. As
part of the BALLISTIC effort, we plan to develop a new prototype
library in C. We will involve the community at large (open source,
industry, users, contributors) in the design of the interfaces and the
library as a whole.

but Fortran compatible

We will follow language standards for all future development and will
strive to make all existing codes standards compliant. Specifically,
all C/C++ codes will be compliant with C11 (with C18 corrections) and
C++11 standards and their contemporary replacements, and all Fortran
interfaces will be compliant with Fortran 2003’s ISO C binding which
will serve the newer Fortran compilers.

It’s good that Fortran has recently climbed in the TIOBE rankings. The quote above shows how published language rankings influence the choice of programming language (although they use IEEE rankings, not TIOBE). Yes, LAPACK does use “archaic software engineering techniques”, because the people behind it have not really moved it beyond FORTRAN 77, although it is officially a Fortran 90 package. It uses fixed source form and no argument INTENTs, for example.

The classical FORTRAN libraries at Netlib were often developed at U.S. national labs. Modernization of those libraries is up to communities like this.

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