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test_linalg_schur.f90
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! Test Schur form
module test_linalg_schur
use stdlib_linalg_interface
implicit none(type,external)
contains
!> SVD tests
subroutine test_schur(error)
logical,intent(out) :: error
real :: t0,t1
call cpu_time(t0)
call test_schur_api_s(error)
if (error) return
call test_schur_s(error)
call test_schur_api_d(error)
if (error) return
call test_schur_d(error)
call test_schur_api_q(error)
if (error) return
call test_schur_q(error)
call test_schur_api_c(error)
if (error) return
call test_schur_api_z(error)
if (error) return
call test_schur_api_w(error)
if (error) return
call cpu_time(t1)
print 1,1000*(t1 - t0),merge('SUCCESS','ERROR ',.not. error)
1 format('Schur tests completed in ',f9.4,' milliseconds, result=',a)
end subroutine test_schur
!> QR factorization of a random matrix
subroutine test_schur_api_s(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
complex(sp) :: eigs(n)
real(sp),dimension(n,n) :: a,t,z
real(sp),allocatable :: storage(:)
type(linalg_state) :: err
call random_number(a)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_s
subroutine test_schur_s(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 3_ilp
real(sp),parameter :: rtol = 1.0e-4_sp
real(sp),parameter :: eps = sqrt(epsilon(0.0_sp))
real(sp),dimension(n,n) :: a,t,z
type(linalg_state) :: err
call random_number(a)
! Run schur
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
error = .not. (all(abs(a - matmul(matmul(z,t),transpose(z))) <= max(rtol*abs(z),eps)))
if (error) print *, 'invalid matmul real(sp)'
if (error) print *, a - matmul(matmul(z,t),transpose(z))
end subroutine test_schur_s
subroutine test_schur_api_d(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(dp),parameter :: tol = 10*sqrt(epsilon(0.0_dp))
complex(dp) :: eigs(n)
real(dp),dimension(n,n) :: a,t,z
real(dp),allocatable :: storage(:)
type(linalg_state) :: err
call random_number(a)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_d
subroutine test_schur_d(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 3_ilp
real(dp),parameter :: rtol = 1.0e-4_dp
real(dp),parameter :: eps = sqrt(epsilon(0.0_dp))
real(dp),dimension(n,n) :: a,t,z
type(linalg_state) :: err
call random_number(a)
! Run schur
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
error = .not. (all(abs(a - matmul(matmul(z,t),transpose(z))) <= max(rtol*abs(z),eps)))
if (error) print *, 'invalid matmul real(dp)'
if (error) print *, a - matmul(matmul(z,t),transpose(z))
end subroutine test_schur_d
subroutine test_schur_api_q(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(qp),parameter :: tol = 10*sqrt(epsilon(0.0_qp))
complex(qp) :: eigs(n)
real(qp),dimension(n,n) :: a,t,z
real(qp),allocatable :: storage(:)
type(linalg_state) :: err
call random_number(a)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_q
subroutine test_schur_q(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 3_ilp
real(qp),parameter :: rtol = 1.0e-4_qp
real(qp),parameter :: eps = sqrt(epsilon(0.0_qp))
real(qp),dimension(n,n) :: a,t,z
type(linalg_state) :: err
call random_number(a)
! Run schur
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
error = .not. (all(abs(a - matmul(matmul(z,t),transpose(z))) <= max(rtol*abs(z),eps)))
if (error) print *, 'invalid matmul real(qp)'
if (error) print *, a - matmul(matmul(z,t),transpose(z))
end subroutine test_schur_q
subroutine test_schur_api_c(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
complex(sp) :: eigs(n)
complex(sp),dimension(n,n) :: a,t,z
complex(sp),allocatable :: storage(:)
real(sp) :: rea(n,n),ima(n,n)
type(linalg_state) :: err
call random_number(rea)
call random_number(ima)
a = cmplx(rea,ima,kind=sp)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_c
subroutine test_schur_api_z(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(dp),parameter :: tol = 10*sqrt(epsilon(0.0_dp))
complex(dp) :: eigs(n)
complex(dp),dimension(n,n) :: a,t,z
complex(dp),allocatable :: storage(:)
real(dp) :: rea(n,n),ima(n,n)
type(linalg_state) :: err
call random_number(rea)
call random_number(ima)
a = cmplx(rea,ima,kind=dp)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_z
subroutine test_schur_api_w(error)
logical,intent(out) :: error
integer(ilp),parameter :: n = 15_ilp
integer(ilp) :: lwork
real(qp),parameter :: tol = 10*sqrt(epsilon(0.0_qp))
complex(qp) :: eigs(n)
complex(qp),dimension(n,n) :: a,t,z
complex(qp),allocatable :: storage(:)
real(qp) :: rea(n,n),ima(n,n)
type(linalg_state) :: err
call random_number(rea)
call random_number(ima)
a = cmplx(rea,ima,kind=qp)
! Test simple API
call schur(a,t,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output transformation matrix
call schur(a,t,z,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test output eigenvalues
call schur(a,t,eigvals=eigs,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test storage query
call schur_space(a,lwork,err=err)
error = err%error(); if (error) print err%print(); if (error) return
! Test with user-defined storage
allocate (storage(lwork))
call schur(a,t,eigvals=eigs,storage=storage,err=err)
error = err%error(); if (error) print err%print(); if (error) return
end subroutine test_schur_api_w
end module test_linalg_schur