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module template_04_semigroup
implicit none
private
public :: semigroup, extended_semigroup, derive_extended_semigroup
requirement semigroup(T, combine)
type, deferred :: T
elemental function combine(x, y) result(combined)
type(T), intent(in) :: x, y
type(T) :: combined
end function
end requirement
requirement extended_semigroup(T, combine, sconcat, stimes)
require :: semigroup(T, combine)
pure function sconcat(list) result(combined)
type(T), intent(in) :: list(:) !! Must contain at least one element
type(T) :: combined
end function
elemental function stimes(n, a) result(repeated)
integer, intent(in) :: n
type(T), intent(in) :: a
type(T) :: repeated
end function
end requirement
template derive_extended_semigroup(T, combine)
require :: semigroup(T, combine)
private
public :: sconcat, stimes
contains
pure function sconcat(list) result(combined)
type(T), intent(in) :: list(:)
type(T) :: combined
integer :: i
if (size(list) > 0) then
combined = list(1)
do i = 2, size(list)
combined = combine(combined, list(i))
end do
else
error stop "Attempted to sconcat empty list"
end if
end function
elemental function stimes(n, a) result(repeated)
integer, intent(in) :: n
type(T), intent(in) :: a
type(T) :: repeated
integer :: i
if (n < 1) error stop "n must be > 0"
repeated = a
do i = 2, n
repeated = combine(repeated, a)
end do
end function
end template
end module
module template_04_monoid
use template_04_semigroup, only: semigroup, extended_semigroup, derive_extended_semigroup
implicit none
private
public :: monoid, extended_monoid, derive_extended_monoid
requirement monoid(T, combine, empty)
require :: semigroup(T, combine)
pure function empty()
type(T) :: empty
end function
end requirement
requirement extended_monoid(T, combine, sconcat, stimes, empty, mconcat)
require :: extended_semigroup(T, combine, sconcat, stimes)
require :: monoid(T, combine, empty)
pure function mconcat(list) result(combined)
type(T), intent(in) :: list(:)
type(T) :: combined
end function
end requirement
template derive_extended_monoid(T, combine, empty)
require :: monoid(T, combine, empty)
private
public :: stimes, mconcat
instantiate derive_extended_semigroup(T, combine), only: stimes => stimes
contains
pure function mconcat(list) result(combined)
type(T), intent(in) :: list(:)
type(T) :: combined
integer :: i
if (size(list) > 0) then
combined = list(1)
do i = 2, size(list)
combined = combine(combined, list(i))
end do
else
combined = empty()
end if
end function
end template
end module
module template_04_semiring
use template_04_monoid, only: monoid
implicit none
private
public :: semiring
requirement semiring(T, plus, zero, mult, one)
require :: monoid(T, plus, zero)
require :: monoid(T, mult, one)
end requirement
end module
module template_04_unitring
use template_04_semiring
implicit none
public :: &
unit_ring_only_minus, &
unit_ring_only_negate, &
unit_ring, &
derive_unit_ring_from_minus, &
derive_unit_ring_from_negate
requirement unit_ring_only_minus(T, plus, zero, mult, one, minus)
require :: semiring(T, plus, zero, mult, one)
elemental function minus(x, y) result(difference)
type(T), intent(in) :: x, y
type(T) :: difference
end function
end requirement
requirement unit_ring_only_negate(T, plus, zero, mult, one, negate)
require :: semiring(T, plus, zero, mult, one)
elemental function negate(x) result(negated)
type(T), intent(in) :: x
type(T) :: negated
end function
end requirement
requirement unit_ring(T, plus, zero, mult, one, minus, negate)
require :: unit_ring_only_minus(T, plus, zero, mult, one, minus)
require :: unit_ring_only_negate(T, plus, zero, mult, one, negate)
end requirement
template derive_unit_ring_from_minus(T, plus, zero, mult, one, minus)
require :: unit_ring_only_minus(T, plus, zero, mult, one, minus)
private
public :: negate
contains
elemental function negate(x) result(negated)
type(T), intent(in) :: x
type(T) :: negated
negated = minus(zero(), x)
end function
end template
template derive_unit_ring_from_negate(T, plus, zero, mult, one, negate)
require :: unit_ring_only_negate(T, plus, zero, mult, one, negate)
private
public :: minus
contains
elemental function minus(x, y) result(difference)
type(T), intent(in) :: x, y
type(T) :: difference
difference = plus(x, negate(y))
end function
end template
end module
module template_04_field
!! field is a unit_ring that also has a division or inverse operation
use template_04_unitring, only: unit_ring
implicit none
private
public :: &
field_only_division, &
field_only_inverse, &
field, &
derive_field_from_division, &
derive_field_from_inverse
requirement field_only_division(T, plus, zero, mult, one, minus, negate, divide)
require :: unit_ring(T, plus, zero, mult, one, minus, negate)
elemental function divide(x, y) result(quotient)
type(T), intent(in) :: x, y
type(T) :: quotient
end function
end requirement
requirement field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
require :: unit_ring(T, plus, zero, mult, one, minus, negate)
elemental function invert(x) result(inverse)
type(T), intent(in) :: x
type(T) :: inverse
end function
end requirement
requirement field(T, plus, zero, mult, one, minus, negate, divide, invert)
require :: field_only_division(T, plus, zero, mult, one, minus, negate, divide)
require :: field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
end requirement
template derive_field_from_division(T, plus, zero, mult, one, minus, negate, divide)
require :: field_only_division(T, plus, zero, mult, one, minus, negate, divide)
private
public :: invert
contains
elemental function invert(x) result(inverse)
type(T), intent(in) :: x
type(T) :: inverse
inverse = divide(one(), x)
end function
end template
template derive_field_from_inverse(T, plus, zero, mult, one, minus, negate, invert)
require :: field_only_inverse(T, plus, zero, mult, one, minus, negate, invert)
private
public :: divide
contains
elemental function divide_(x, y) result(quotient)
type(T), intent(in) :: x, y
type(T) :: quotient
quotient = mult(x, invert(y))
end function
end template
end module
module template_04_matrix
use template_04_monoid, only: derive_extended_monoid
use template_04_semiring, only: semiring
use template_04_unitring, only: unit_ring_only_minus, derive_unit_ring_from_minus
use template_04_field, only: field_only_division
implicit none
private
public :: matrix_tmpl
template matrix_tmpl(T, plus_t, zero_t, times_t, one_t, n)
require :: semiring(T, plus_t, zero_t, times_t, one_t)
integer :: n
private
public :: &
matrix, &
plus_matrix, &
times_matrix, &
zero, &
one, &
matrix_subtraction_tmpl
type :: matrix
type(T) :: elements(n, n)
end type
interface operator(+)
procedure :: plus_matrix
end interface
interface operator(*)
procedure times_matrix
end interface
template matrix_subtraction_t(minus_t)
require :: unit_ring_only_minus(T, plus_t, zero_t, times_t, one_t, minus_t)
private
public :: minus_matrix, gaussian_solver_tmpl
interface operator(-)
procedure minus_matrix
end interface
template gaussian_solver_tmpl(div_t)
instantiate derive_unit_ring_from_minus(T, plus_t, zero_t, times_t, one_t, minus_t), only: negate
require :: field_only_division(T, plus_t, zero_t, times_t, one_t, minus_t, negate, div_t)
contains
pure function row_eschelon(x) result(reduced)
type(matrix), intent(in) :: x
type(matrix) :: reduced
integer :: i, ii, j
type(T) :: r
reduced = x
do i = 1, n
! Assume pivot m(i,i) is not zero
do ii = i+1, n
r = div_t(reduced%elements(i,i), reduced%elements(ii,i))
reduced%elements(ii, i) = zero_t()
do j = i+1, n
reduced%elements(ii, j) = minus_t(reduced%elements(ii, j), times_t(reduced%elements(i, j), r))
end do
end do
end do
end function
pure function back_substitute(x, y) result(solved)
type(matrix), intent(in) :: x, y
type(matrix) :: solved
integer :: i, j
type(T) :: tmp(n)
solved = y
do i = n, 1, -1
tmp = zero_t()
do j = i+1, n
tmp = plus_t(tmp, times_t(x%elements(i,j), solved%elements(:,j)))
end do
solved%elements(:,i) = div_t(minus_t(solved%elements(:,i), tmp), x%elements(i,i))
end do
end function
elemental function div_matrix(x, y) result(quotient)
type(matrix), intent(in) :: x, y
type(matrix) :: quotient
quotient = back_substitute(row_eschelon(x), y)
end function
end template
contains
elemental function minus_matrix(x, y) result(difference)
type(matrix), intent(in) :: x, y
type(matrix) :: difference
difference%elements = minus_t(x%elements, y%elements)
end function
end template
contains
elemental function plus_matrix(x, y) result(combined)
type(matrix), intent(in) :: x, y
type(matrix) :: combined
integer :: i, j
! TODO: something wrong with elemental function operations
! combined%elements = plus_t(x%elements, y%elements)
do i = 1, n
do j = 1, n
combined%elements(i,j) = plus_t(x%elements(i,j), y%elements(i,j))
end do
end do
end function
pure function zero()
type(matrix) :: zero
zero%elements = zero_t()
end function
elemental function times_matrix(x, y) result(combined)
type(matrix), intent(in) :: x, y
type(matrix) :: combined
integer :: i, j, k
type(T) :: dot
do i = 1, n
do j = 1, n
! TODO: something wrong with elemental function operations
! combined%elements(i, j) = sum(times_t(x%elements(i,:), y%elements(:,j)))
dot = zero_t()
do k = 1, n
dot = plus_t(dot, times_t(x%elements(i,k), y%elements(k,j)))
end do
combined%elements(i, j) = dot
end do
end do
end function
pure function one()
type(matrix) :: one
integer :: i
one%elements = zero_t()
do concurrent (i = 1:n)
one%elements(i, i) = one_t()
end do
end function
end template
end module
module template_04_func
implicit none
private
public :: zero_integer, zero_real, one_integer, one_real
contains
pure function zero_integer() result(z)
integer :: z
z = 0
end function
pure function one_integer() result(z)
integer :: z
z = 1
end function
pure function zero_real() result(z)
real :: z
z = 0
end function
pure function one_real() result(z)
real :: z
z = 1
end function
end module
program template_04
use template_04_matrix
use template_04_func
integer, parameter :: n = 2
instantiate matrix_tmpl(integer, operator(+), zero_integer, operator(*), one_integer, n), &
only: integer_matrix => matrix, &
integer_plus_matrix => plus_matrix, &
integer_times_matrix => times_matrix, &
integer_matrix_subtraction_t => matrix_subtraction_t
instantiate integer_matrix_subtraction_t(operator(-)), &
only: integer_minus_matrix => minus_matrix, &
integer_gaussian_solver_tmpl => gaussian_solver_tmpl
instantiate integer_gaussian_solver_tmpl(operator(/)), &
only: integer_div_matrix => div_matrix
type(integer_matrix) :: m1, m2, m3, m4
m1%elements(1,1) = 1
m1%elements(1,2) = 0
m1%elements(2,1) = 0
m1%elements(2,2) = 1
m2%elements(1,1) = 1
m2%elements(1,2) = 2
m2%elements(2,1) = 2
m2%elements(2,2) = 1
m3 = integer_plus_matrix(m1, m2)
print *, m3%elements(1,1), m3%elements(1,2)
print *, m3%elements(2,1), m3%elements(2,2), achar(10)
m4 = integer_times_matrix(m3, m2)
print *, m4%elements(1,1), m4%elements(1,2)
print *, m4%elements(2,1), m4%elements(2,2), achar(10)
instantiate matrix_tmpl(real, operator(+), zero_real, operator(*), one_real, n), &
only: real_matrix => matrix, &
real_plus_matrix => plus_matrix, &
real_times_matrix => times_matrix, &
real_matrix_subtraction_t => matrix_subtraction_t
instantiate real_matrix_subtraction_t(operator(-)), &
only: real_minus_matrix => minus_matrix, &
real_gaussian_solver_tmpl => gaussian_solver_tmpl
instantiate real_gaussian_solver_tmpl(operator(/)), &
only: real_div_matrix => div_matrix
type(real_matrix) :: r1, r2, r3, r4
r1%elements(1,1) = 1.2
r1%elements(1,2) = 0
r1%elements(2,1) = 0
r1%elements(2,2) = 1
r2%elements(1,1) = 1
r2%elements(1,2) = 2.5
r2%elements(2,1) = 2
r2%elements(2,2) = 1
r3 = real_plus_matrix(r1, r2)
print *, r3%elements(1,1), r3%elements(1,2)
print *, r3%elements(2,1), r3%elements(2,2), achar(10)
r4 = real_times_matrix(r3, r2)
print *, r4%elements(1,1), r4%elements(1,2)
print *, r4%elements(2,1), r4%elements(2,2), achar(10)
end program
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