How to find optimal block size and LWORK in LAPACK - fortran

Question

I am trying to find inverse and eigenfunctions of nxn Hermitian matrices using Fortran with lapack.
How do I choose the optimal values for parameters like lda, lwork, liwork and lrwork. I browse through some example and find these choices
integer,parameter::lda=nh
integer,parameter::lwork=2*nh+nh*nh
integer,parameter::liwork=3+5*nh
integer,parameter::lrwork=1 + 5*nh + 2*nh*nh
where nh is the dimension of the matrix. I also find another example with lwork=16*nh. How can I determine the best choice? At this point, I am dealing with 500x500 Hermitian matrices (maximum).
I found this documentation which suggests
WORK
(workspace) REAL array, dimension (LWORK)
On exit, if INFO = 0, then WORK(1) returns the optimal LWORK.
LWORK
(input) INTEGER
The dimension of the array WORK. LWORK  max(1,N).
For optimal performance LWORK  N*NB, where NB is the optimal block size returned by ILAENV.
Is it possible to find out the optimal block size using WORK or ILAENV for a given matrix dimension?
I am using both gfortran and ifort with mkl.
EDIT
Based on the comment by #percusse and #kvantour's answer here is a sample code
character,parameter::jobz="v",uplo="u"
integer, parameter::nh=15
complex*16::m(nh,nh),m1(nh,nh)
integer,parameter::lda=nh
integer::ipiv(nh),info
complex*16::work(1)
real*8::rwork(1), w(nh)
integer::iwork(1)
real*8::x1(nh,nh),x2(nh,nh)
call random_seed()
call random_number(x1)
call random_number(x2)
m=cmplx(x1,x2)
m1=conjg(m)
m1=transpose(m1)
m=(m+m1)/2.0
call zheevd(jobz,uplo,nh,m,lda,w,work,-1,rwork,-1,iwork, -1,info)
print*,"info : ", info
print*,"lwork: ", int(work(1)) , 2*nh+nh*nh
print*,"lrwork:", int(rwork(1)) , 1 + 5*nh + 2*nh*nh
print*,"liwork:", int(iwork(1)) , 3+5*nh
end
info : 0
lwork: 255 255
lrwork: 526 526
liwork: 78 78

Answer 1

I'm not sure what you are implying with "Is it possible to find out the optimal block size using WORK or ILAENV for a particular machine architecture?". You can however find the optimal values for a particular problem.
Eg. If you want to find the eigenvalues of a complex Hermitian matrix, using cheev, you can ask the routine to return you the value :
subroutine CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
character , intent(in) :: JOBZ
character , intent(in) :: UPLO
integer , intent(in) :: N
complex, dimension(lda,*), intent(inout) :: A
integer , intent(in) :: LDA
real , dimension(*) , intent(out) :: W
complex, dimension(*) , intent(out) :: WORK
integer , intent(in) :: LWORK
real , dimension(*) , intent(out) :: RWORK
integer , intent(out) :: INFO
Then the documentation clearly states (be advised, in the past this was easier to read):
WORK is COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK is INTEGER
The length of the array WORK. LWORK >= max(1,2*N-1).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for CHETRD returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
So all you need to do is
call cheev(jobz, uplo, n, a, lda, w, work, -1, rwork, info)
lwork=int(work(1))
dallocate(work)
allocate(work(lwork))
call cheev(jobz, uplo, n, a, lda, w, work, lwork, rwork, info)