lapack-dsyevr-test

Important self-test of the famous lapack's diagonalization routine DSYEVR. It checks eigenvectors orthogonality. GNU lapack is affected with the bug, see Reference-LAPACK/lapack#151.

This small software buildup is based upon autocmake project ( https://github.com/coderefinery/autocmake ).

Quick buildup

Clone the repository, go the src/ directory and type there if you want native GNU lapack:

gfortran -fallow-argument-mismatch dsyevr_check.F90 eispack.F -llapack -lblas

Alternatively, you can utilize the openblas library:

gfortran -fallow-argument-mismatch dsyevr_check.F90 eispack.F -lopenblas

You get the a.out executable you can work with, as shown below.

Buildup examples

• Gfortran 4.7.2 and later versions, with system native libraries (/usr/lib/liblapack.so /usr/lib/libblas.so)

python setup --fc=gfortran --extra-fc-flags="-fallow-argument-mismatch" --cmake-options="-D MATH_LIB_SEARCH_ORDER='SYSTEM_NATIVE'"  build_gfortran_sysnatlibs
cd build_gfortran_sysnatlibs
make VERBOSE=1
cd src
./dsyerv_check

confirms eigenvectors nonorthogonality in the dsyevr routine:

**** LAPACK DSYEVR ****
U^{+}*A*U - eps ?= 0> norm/diag:0.1147D-14  norm/offdiag:0.1365D-05
    U^{+}*U - I ?= 0> norm/diag:0.3824D-15  norm/offdiag:0.2729D-05
    U*U^{+} - I ?= 0> norm/diag:0.8556D-05  norm/offdiag:0.5285D-05

• Gfortran (4.7.2) and the own downloaded Lapack 3.6.0

python setup --fc=gfortran --blas=off --lapack=off --cmake-options="-D EXPLICIT_LIBS='-L/u/milias/Work/qch/software/lapack/lapack-3.6.0/build/lib -llapack -lblas'"  build_gfortran_lapack3.6.0
cd build_gfortran_lapack3.6.0
make VERBOSE=1
cd src
./dsyerv_check

shows the nonorthogonality:

 **** LAPACK DSYEVR ****
U^{+}*A*U - eps ?= 0> norm/diag:0.1616D-14  norm/offdiag:0.1419D-06
    U^{+}*U - I ?= 0> norm/diag:0.3454D-15  norm/offdiag:0.2838D-06
    U*U^{+} - I ?= 0> norm/diag:0.1047D-05  norm/offdiag:0.7950D-06

• Gfortran (4.4.7) with the fresh Lapack 3.7.0

python setup --fc=gfortran --blas=off --lapack=off --cmake-options="-D EXPLICIT_LIBS='-L/home/milias/Work/qch/software/smaller_software_projects/lapack-dsyevr-test/lapack-3.7.0/build/lib  -llapack -lblas'"  build_gfortran_lapack3.7.0
cd build_gfortran_lapack3.7.0
make VERBOSE=1
cd src
./dsyerv_check

shows the nonorthogonality:

 **** LAPACK DSYEVR ****
U^{+}*A*U - eps ?= 0> norm/diag:0.1616D-14  norm/offdiag:0.1419D-06
    U^{+}*U - I ?= 0> norm/diag:0.3454D-15  norm/offdiag:0.2838D-06
    U*U^{+} - I ?= 0> norm/diag:0.1047D-05  norm/offdiag:0.7950D-06

• Intel 15.0 and the downloaded Lapack 3.6.0

python setup --fc=ifort --blas=off --lapack=off --cmake-options="-D EXPLICIT_LIBS='-L/u/milias/Work/qch/software/lapack/lapack-3.6.0/build/lib -llapack -lblas -lgfortran'"  build_ifort_lapack3.6.0
cd build_ifort_lapack3.6.0
make VERBOSE=1
cd src
./dsyerv_check

confirms eigenvectors orthogonality in the dsyevr routine:

 **** LAPACK DSYEVR ****
U^{+}*A*U - eps ?= 0> norm/diag:0.1604D-14  norm/offdiag:0.2574D-15
    U^{+}*U - I ?= 0> norm/diag:0.2961D-15  norm/offdiag:0.9328D-16
    U*U^{+} - I ?= 0> norm/diag:0.1974D-15  norm/offdiag:0.1216D-15

• Intel 15.0/16.0 with the attached MKL library

python setup --fc=ifort --cmake-options="-D MATH_LIB_SEARCH_ORDER='MKL'"  build_ifort_mkl
cd build_ifort_mkl
make VERBOSE=1
cd src
./dsyerv_check

has proper orthogonality in the dsyevr routine as we can see from the output:

  **** LAPACK DSYEVR ****
U^{+}*A*U - eps ?= 0> norm/diag:0.1684D-14  norm/offdiag:0.2746D-15
    U^{+}*U - I ?= 0> norm/diag:0.2097D-15  norm/offdiag:0.6923D-16
    U*U^{+} - I ?= 0> norm/diag:0.2467D-16  norm/offdiag:0.8681D-16