fortran - How to control lapack solver presion -

i'm trying use lapack zhesv subroutine in fortran solve linear system, precision seems not good.

here code:

program main implicit none  integer,parameter::n=4 integer::lda=n,ipiv(n),ldb=n,lwork=n*n,info,i complex*16::a(n,n),b(n),work(n,n),x(n)   a=reshape( (/(1.,0.),(0.,0.),(0.,-6.94908e-13),(0.,-6.94908e-13),&           &(0.,0.),(1.,0.0352595),(0.,-4.51893e-11),(0.,-4.51893e-11),&           &(0.,-6.94908e-13),(0.,-4.51893e-11),(1.,0.0376938),(0.,0.),&           &(0.,-6.94908e-13),(0.,-4.51893e-11),(0.,0.),(1.,0.0378932)/),shape(a))  a=transpose(a)  b=(/(1.,0.),(0.,0.),(0.,6.94908e-13),(0.,6.94908e-13)/) x=b  write(*,*) "--------------b----------------" write(*,99999) b   call zhesv('upper',n,1,a,lda,ipiv,x,n,work,lwork,info)  write(*,*) "--------------x----------------" write(*,99999) x write(*,*) "-------------info--------------" write(*,*) info  write(*,*) "-------------error-------------" write(*,99999) matmul(a,x)-b  99999 format ((3x,4(' (',e15.8,',',e15.8,')',:))) end program main 

the outputs are

 --------------b----------------     ( 0.10000000e+01, 0.00000000e+00) ( 0.00000000e+00, 0.00000000e+00) ( 0.00000000e+00, 0.69490800e-12) ( 0.00000000e+00, 0.69490800e-12)  --------------x----------------     ( 0.10000000e+01, 0.00000000e+00) ( 0.00000000e+00, 0.00000000e+00) ( 0.00000000e+00, 0.00000000e+00) ( 0.00000000e+00, 0.00000000e+00)  -------------info--------------            0  -------------error-------------     ( 0.00000000e+00, 0.00000000e+00) ( 0.00000000e+00, 0.00000000e+00) ( 0.00000000e+00,-0.13898160e-11) ( 0.00000000e+00,-0.13898160e-11) 

the error quite large compare element of b.

in contrary, tried solve in mathematica, , error quite small.

a.linearsolve[a, b] - b  {0. + 0. i, 0. + 3.67342*10^-40 i, 4.13609*10^-34 + 0. i, 4.13609*10^-34 + 0. i} 

so how can control precision of lapack solver achieve same precision of mathematica's linearsolver?

zhesv computes solution complex system of linear equations a * x = b, a n-by-n hermitian matrix , x , b n-by-nrhs matrices.

but, matrix a not hermitian matrix.