DBDSDC returns non-orthogonal U and V for a specific matrix

[sergey-v-kuznetsov]

I'm attaching a Fortran code which demonstrates the problem. The code reads two diagonal matrix from a file in the binary format and call DBDSDC: CALL DBDSDC( 'U', 'I', N, S, E, U, M, VT, $ M, DUM, IDUM, WORK(INIAD), IWORK, $ INFO ) but DBDSDC returns non-orthogonal U and V. It should be noted that DBDSDC returns orthogonal matrices if we slightly change any diagonal entry.

Here are steps to reproduce:

bash-4.2$ ifort -V
Intel(R) Fortran Intel(R) 64 Compiler for applications running on Intel(R) 64, Version 18.0 Build 20180611 Copyright (C) 1985-2018 Intel Corporation. All rights reserved.

bash-4.2$ ifort reproducer.f ../lapack-3.7.1/liblapack.a ../lapack-3.7.1/librefblas.a bash-4.2$ ./a.out Check orthogonality of U Orthogonality test failed Max element in U^T * U - I 0.999872111722121
Row and column numbers of max entries 619 620 Check orthogonality of VT Orthogonality test failed Max element in U^T * U - I 0.999872111722121
Row and column numbers of max entries 619 620

If we slightly change the last diagonal entry by inserting s(n) =s(n)+1.D-15 the attached test passes: bash-4.2$ ./a.out Check orthogonality of U Orthogonality test passed Check orthogonality of VT Orthogonality test passed Repoducer.zip