/usr/lib/petscdir/3.1/include/src/ is in libpetsc3.1-dev 3.1.dfsg-11ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/petscdir/3.1/include/src/mat/
/usr/lib/petscdir/3.1/include/src/mat/impls/
/usr/lib/petscdir/3.1/include/src/mat/impls/aij/
/usr/lib/petscdir/3.1/include/src/mat/impls/aij/mpi/
/usr/lib/petscdir/3.1/include/src/mat/impls/aij/mpi/mpiaij.h
/usr/lib/petscdir/3.1/include/src/mat/impls/aij/seq/
/usr/lib/petscdir/3.1/include/src/mat/impls/aij/seq/aij.h
/usr/lib/petscdir/3.1/include/src/mat/impls/dense/
/usr/lib/petscdir/3.1/include/src/mat/impls/dense/mpi/
/usr/lib/petscdir/3.1/include/src/mat/impls/dense/mpi/mpidense.h
/usr/lib/petscdir/3.1/include/src/mat/impls/dense/seq/
/usr/lib/petscdir/3.1/include/src/mat/impls/dense/seq/dense.h
/usr/lib/petscdir/3.1/include/src/sys/
/usr/lib/petscdir/3.1/include/src/sys/ctable.h