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test_linalg_norms.f90
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! Test matrix norms
module test_linalg_norms
use stdlib_linalg_interface
implicit none(type,external)
contains
!> Vector norm test: array interfaces
subroutine test_norms(error)
logical,intent(out) :: error
real :: t0,t1
call cpu_time(t0)
call test_norm_s_1d(error)
if (error) return
call test_norm_s_2d(error)
if (error) return
call test_norm_s_3d(error)
if (error) return
call test_norm_s_4d(error)
if (error) return
call test_norm_s_5d(error)
if (error) return
call test_norm_s_6d(error)
if (error) return
call test_norm_s_7d(error)
if (error) return
call test_norm_s_8d(error)
if (error) return
call test_norm_s_9d(error)
if (error) return
call test_norm_s_10d(error)
if (error) return
call test_norm_s_11d(error)
if (error) return
call test_norm_s_12d(error)
if (error) return
call test_norm_s_13d(error)
if (error) return
call test_norm_s_14d(error)
if (error) return
call test_norm2_s_2d(error)
if (error) return
call test_norm_dimmed_s_2d(error)
if (error) return
call test_norm2_s_3d(error)
if (error) return
call test_norm_dimmed_s_3d(error)
if (error) return
call test_norm2_s_4d(error)
if (error) return
call test_norm_dimmed_s_4d(error)
if (error) return
call test_norm2_s_5d(error)
if (error) return
call test_norm_dimmed_s_5d(error)
if (error) return
call test_norm2_s_6d(error)
if (error) return
call test_norm_dimmed_s_6d(error)
if (error) return
call test_norm2_s_7d(error)
if (error) return
call test_norm_dimmed_s_7d(error)
if (error) return
call test_norm2_s_8d(error)
if (error) return
call test_norm_dimmed_s_8d(error)
if (error) return
call test_norm2_s_9d(error)
if (error) return
call test_norm_dimmed_s_9d(error)
if (error) return
call test_norm2_s_10d(error)
if (error) return
call test_norm_dimmed_s_10d(error)
if (error) return
call test_norm2_s_11d(error)
if (error) return
call test_norm_dimmed_s_11d(error)
if (error) return
call test_norm2_s_12d(error)
if (error) return
call test_norm_dimmed_s_12d(error)
if (error) return
call test_norm2_s_13d(error)
if (error) return
call test_norm_dimmed_s_13d(error)
if (error) return
call test_norm2_s_14d(error)
if (error) return
call test_norm_dimmed_s_14d(error)
if (error) return
call test_norm_d_1d(error)
if (error) return
call test_norm_d_2d(error)
if (error) return
call test_norm_d_3d(error)
if (error) return
call test_norm_d_4d(error)
if (error) return
call test_norm_d_5d(error)
if (error) return
call test_norm_d_6d(error)
if (error) return
call test_norm_d_7d(error)
if (error) return
call test_norm_d_8d(error)
if (error) return
call test_norm_d_9d(error)
if (error) return
call test_norm_d_10d(error)
if (error) return
call test_norm_d_11d(error)
if (error) return
call test_norm_d_12d(error)
if (error) return
call test_norm_d_13d(error)
if (error) return
call test_norm_d_14d(error)
if (error) return
call test_norm2_d_2d(error)
if (error) return
call test_norm_dimmed_d_2d(error)
if (error) return
call test_norm2_d_3d(error)
if (error) return
call test_norm_dimmed_d_3d(error)
if (error) return
call test_norm2_d_4d(error)
if (error) return
call test_norm_dimmed_d_4d(error)
if (error) return
call test_norm2_d_5d(error)
if (error) return
call test_norm_dimmed_d_5d(error)
if (error) return
call test_norm2_d_6d(error)
if (error) return
call test_norm_dimmed_d_6d(error)
if (error) return
call test_norm2_d_7d(error)
if (error) return
call test_norm_dimmed_d_7d(error)
if (error) return
call test_norm2_d_8d(error)
if (error) return
call test_norm_dimmed_d_8d(error)
if (error) return
call test_norm2_d_9d(error)
if (error) return
call test_norm_dimmed_d_9d(error)
if (error) return
call test_norm2_d_10d(error)
if (error) return
call test_norm_dimmed_d_10d(error)
if (error) return
call test_norm2_d_11d(error)
if (error) return
call test_norm_dimmed_d_11d(error)
if (error) return
call test_norm2_d_12d(error)
if (error) return
call test_norm_dimmed_d_12d(error)
if (error) return
call test_norm2_d_13d(error)
if (error) return
call test_norm_dimmed_d_13d(error)
if (error) return
call test_norm2_d_14d(error)
if (error) return
call test_norm_dimmed_d_14d(error)
if (error) return
call test_norm_q_1d(error)
if (error) return
call test_norm_q_2d(error)
if (error) return
call test_norm_q_3d(error)
if (error) return
call test_norm_q_4d(error)
if (error) return
call test_norm_q_5d(error)
if (error) return
call test_norm_q_6d(error)
if (error) return
call test_norm_q_7d(error)
if (error) return
call test_norm_q_8d(error)
if (error) return
call test_norm_q_9d(error)
if (error) return
call test_norm_q_10d(error)
if (error) return
call test_norm_q_11d(error)
if (error) return
call test_norm_q_12d(error)
if (error) return
call test_norm_q_13d(error)
if (error) return
call test_norm_q_14d(error)
if (error) return
call test_norm2_q_2d(error)
if (error) return
call test_norm_dimmed_q_2d(error)
if (error) return
call test_norm2_q_3d(error)
if (error) return
call test_norm_dimmed_q_3d(error)
if (error) return
call test_norm2_q_4d(error)
if (error) return
call test_norm_dimmed_q_4d(error)
if (error) return
call test_norm2_q_5d(error)
if (error) return
call test_norm_dimmed_q_5d(error)
if (error) return
call test_norm2_q_6d(error)
if (error) return
call test_norm_dimmed_q_6d(error)
if (error) return
call test_norm2_q_7d(error)
if (error) return
call test_norm_dimmed_q_7d(error)
if (error) return
call test_norm2_q_8d(error)
if (error) return
call test_norm_dimmed_q_8d(error)
if (error) return
call test_norm2_q_9d(error)
if (error) return
call test_norm_dimmed_q_9d(error)
if (error) return
call test_norm2_q_10d(error)
if (error) return
call test_norm_dimmed_q_10d(error)
if (error) return
call test_norm2_q_11d(error)
if (error) return
call test_norm_dimmed_q_11d(error)
if (error) return
call test_norm2_q_12d(error)
if (error) return
call test_norm_dimmed_q_12d(error)
if (error) return
call test_norm2_q_13d(error)
if (error) return
call test_norm_dimmed_q_13d(error)
if (error) return
call test_norm2_q_14d(error)
if (error) return
call test_norm_dimmed_q_14d(error)
if (error) return
call test_norm_c_1d(error)
if (error) return
call test_norm_c_2d(error)
if (error) return
call test_norm_c_3d(error)
if (error) return
call test_norm_c_4d(error)
if (error) return
call test_norm_c_5d(error)
if (error) return
call test_norm_c_6d(error)
if (error) return
call test_norm_c_7d(error)
if (error) return
call test_norm_c_8d(error)
if (error) return
call test_norm_c_9d(error)
if (error) return
call test_norm_c_10d(error)
if (error) return
call test_norm_c_11d(error)
if (error) return
call test_norm_c_12d(error)
if (error) return
call test_norm_c_13d(error)
if (error) return
call test_norm_c_14d(error)
if (error) return
call test_norm_dimmed_c_2d(error)
if (error) return
call test_norm_dimmed_c_3d(error)
if (error) return
call test_norm_dimmed_c_4d(error)
if (error) return
call test_norm_dimmed_c_5d(error)
if (error) return
call test_norm_dimmed_c_6d(error)
if (error) return
call test_norm_dimmed_c_7d(error)
if (error) return
call test_norm_dimmed_c_8d(error)
if (error) return
call test_norm_dimmed_c_9d(error)
if (error) return
call test_norm_dimmed_c_10d(error)
if (error) return
call test_norm_dimmed_c_11d(error)
if (error) return
call test_norm_dimmed_c_12d(error)
if (error) return
call test_norm_dimmed_c_13d(error)
if (error) return
call test_norm_dimmed_c_14d(error)
if (error) return
call test_norm_z_1d(error)
if (error) return
call test_norm_z_2d(error)
if (error) return
call test_norm_z_3d(error)
if (error) return
call test_norm_z_4d(error)
if (error) return
call test_norm_z_5d(error)
if (error) return
call test_norm_z_6d(error)
if (error) return
call test_norm_z_7d(error)
if (error) return
call test_norm_z_8d(error)
if (error) return
call test_norm_z_9d(error)
if (error) return
call test_norm_z_10d(error)
if (error) return
call test_norm_z_11d(error)
if (error) return
call test_norm_z_12d(error)
if (error) return
call test_norm_z_13d(error)
if (error) return
call test_norm_z_14d(error)
if (error) return
call test_norm_dimmed_z_2d(error)
if (error) return
call test_norm_dimmed_z_3d(error)
if (error) return
call test_norm_dimmed_z_4d(error)
if (error) return
call test_norm_dimmed_z_5d(error)
if (error) return
call test_norm_dimmed_z_6d(error)
if (error) return
call test_norm_dimmed_z_7d(error)
if (error) return
call test_norm_dimmed_z_8d(error)
if (error) return
call test_norm_dimmed_z_9d(error)
if (error) return
call test_norm_dimmed_z_10d(error)
if (error) return
call test_norm_dimmed_z_11d(error)
if (error) return
call test_norm_dimmed_z_12d(error)
if (error) return
call test_norm_dimmed_z_13d(error)
if (error) return
call test_norm_dimmed_z_14d(error)
if (error) return
call test_norm_w_1d(error)
if (error) return
call test_norm_w_2d(error)
if (error) return
call test_norm_w_3d(error)
if (error) return
call test_norm_w_4d(error)
if (error) return
call test_norm_w_5d(error)
if (error) return
call test_norm_w_6d(error)
if (error) return
call test_norm_w_7d(error)
if (error) return
call test_norm_w_8d(error)
if (error) return
call test_norm_w_9d(error)
if (error) return
call test_norm_w_10d(error)
if (error) return
call test_norm_w_11d(error)
if (error) return
call test_norm_w_12d(error)
if (error) return
call test_norm_w_13d(error)
if (error) return
call test_norm_w_14d(error)
if (error) return
call test_norm_dimmed_w_2d(error)
if (error) return
call test_norm_dimmed_w_3d(error)
if (error) return
call test_norm_dimmed_w_4d(error)
if (error) return
call test_norm_dimmed_w_5d(error)
if (error) return
call test_norm_dimmed_w_6d(error)
if (error) return
call test_norm_dimmed_w_7d(error)
if (error) return
call test_norm_dimmed_w_8d(error)
if (error) return
call test_norm_dimmed_w_9d(error)
if (error) return
call test_norm_dimmed_w_10d(error)
if (error) return
call test_norm_dimmed_w_11d(error)
if (error) return
call test_norm_dimmed_w_12d(error)
if (error) return
call test_norm_dimmed_w_13d(error)
if (error) return
call test_norm_dimmed_w_14d(error)
if (error) return
call cpu_time(t1)
print 1,1000*(t1 - t0),merge('SUCCESS','ERROR ',.not. error)
1 format('Vector norm tests completed in ',f9.4,' milliseconds, result=',a)
end subroutine test_norms
!> Test several norms with different dimensions
subroutine test_norm_s_1d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**1
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:)
allocate (a(n),b(2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_1d
!> Test several norms with different dimensions
subroutine test_norm_s_2d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**2
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:)
allocate (a(n),b(2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_2d
!> Test several norms with different dimensions
subroutine test_norm_s_3d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**3
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:)
allocate (a(n),b(2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_3d
!> Test several norms with different dimensions
subroutine test_norm_s_4d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**4
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:)
allocate (a(n),b(2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_4d
!> Test several norms with different dimensions
subroutine test_norm_s_5d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**5
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_5d
!> Test several norms with different dimensions
subroutine test_norm_s_6d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**6
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_6d
!> Test several norms with different dimensions
subroutine test_norm_s_7d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**7
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_7d
!> Test several norms with different dimensions
subroutine test_norm_s_8d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**8
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_8d
!> Test several norms with different dimensions
subroutine test_norm_s_9d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**9
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_9d
!> Test several norms with different dimensions
subroutine test_norm_s_10d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**10
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_10d
!> Test several norms with different dimensions
subroutine test_norm_s_11d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**11
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_11d
!> Test several norms with different dimensions
subroutine test_norm_s_12d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**12
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_12d
!> Test several norms with different dimensions
subroutine test_norm_s_13d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**13
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_13d
!> Test several norms with different dimensions
subroutine test_norm_s_14d(error)
logical,intent(out) :: error
integer(ilp) :: j,order
integer(ilp),parameter :: n = 2_ilp**14
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:,:,:,:,:,:,:,:,:,:,:,:)
allocate (a(n),b(2,2,2,2,2,2,2,2,2,2,2,2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
do order = 1,10
error = .not. abs(norm(a,order) - norm(b,order)) < tol*max(1.0_sp,norm(a,order))
if (error) return
end do
! Infinity norms
error = .not. abs(norm(a,'inf') - norm(b,'inf')) < tol*max(1.0_sp,norm(a,'inf'))
if (error) return
! Infinity norms
error = .not. abs(norm(a,'-inf') - norm(b,'-inf')) < tol*max(1.0_sp,norm(a,'-inf'))
if (error) return
end subroutine test_norm_s_14d
!> Test Euclidean norm; compare with Fortran intrinsic norm2 for reals
subroutine test_norm2_s_2d(error)
logical,intent(out) :: error
integer(ilp) :: j,dim
integer(ilp),parameter :: ndim = 2
integer(ilp),parameter :: n = 2_ilp**ndim
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:)
intrinsic :: norm2
allocate (a(n),b(2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
error = .not. abs(norm(a,2) - norm2(a)) < tol*norm(a,2)
if (error) return
! Infinity norms
error = .not. abs(norm(b,2) - norm2(b)) < tol*norm(b,2)
if (error) return
! Test norm as collapsed around dimension
do dim = 1,ndim
error = .not. all(abs(norm(b,2,dim) - norm2(b,dim)) < tol*max(1.0_sp,norm(b,2,dim)))
if (error) return
end do
end subroutine test_norm2_s_2d
! Test norm along a dimension and compare it against individually evaluated norms
subroutine test_norm_dimmed_s_2d(error)
logical,intent(out) :: error
integer(ilp) :: j,dim,order
integer(ilp),parameter :: ndim = 2
integer(ilp),parameter :: n = 2_ilp**ndim
integer(ilp),parameter :: dims(*) = [(dim,dim=1,ndim)]
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
integer(ilp) :: coords(ndim)
real :: x(ndim)
real(sp),allocatable :: a(:),b(:,:)
real(sp),allocatable :: bnrm(:)
allocate (a(n),b(2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
do order = 1,5
do dim = 1,ndim
bnrm = norm(b,order,dim)
! Assert size
error = .not. all(shape(bnrm) == pack(shape(b),dims /= dim))
if (error) print *, 'INVALID OUTPUT SHAPE, order=',order,' dim=',dim
end do
end do
end subroutine test_norm_dimmed_s_2d
subroutine test_norm2_s_3d(error)
logical,intent(out) :: error
integer(ilp) :: j,dim
integer(ilp),parameter :: ndim = 3
integer(ilp),parameter :: n = 2_ilp**ndim
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
real(sp),allocatable :: a(:),b(:,:,:)
intrinsic :: norm2
allocate (a(n),b(2,2,2))
! Init as a range,but with small elements such that all power norms will
! never overflow, even in single precision
a = [(0.01_sp*(j - n/2_ilp),j=1_ilp,n)]
b = reshape(a,shape(b))
! Test some norms
error = .not. abs(norm(a,2) - norm2(a)) < tol*norm(a,2)
if (error) return
! Infinity norms
error = .not. abs(norm(b,2) - norm2(b)) < tol*norm(b,2)
if (error) return
! Test norm as collapsed around dimension
do dim = 1,ndim
error = .not. all(abs(norm(b,2,dim) - norm2(b,dim)) < tol*max(1.0_sp,norm(b,2,dim)))
if (error) return
end do
end subroutine test_norm2_s_3d
! Test norm along a dimension and compare it against individually evaluated norms
subroutine test_norm_dimmed_s_3d(error)
logical,intent(out) :: error
integer(ilp) :: j,dim,order
integer(ilp),parameter :: ndim = 3
integer(ilp),parameter :: n = 2_ilp**ndim
integer(ilp),parameter :: dims(*) = [(dim,dim=1,ndim)]
real(sp),parameter :: tol = 10*sqrt(epsilon(0.0_sp))
integer(ilp) :: coords(ndim)
real :: x(ndim)
real(sp),allocatable :: a(:),b(:,:,:)
real(sp),allocatable :: bnrm(:,:)
allocate (a(n),b(2,2,2))