110 lines
3.3 KiB
Plaintext
110 lines
3.3 KiB
Plaintext
! Provides a subroutine to build Pascal's triangle
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!
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! Copyright © 2021 Dynare Team
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!
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! This file is part of Dynare.
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!
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! Dynare is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! Dynare is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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module pascal
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implicit none
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type line
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integer, dimension(:), allocatable :: coeffs
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end type line
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type pascal_triangle
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integer :: d
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type(line), dimension(:), allocatable :: lines
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end type pascal_triangle
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interface pascal_triangle
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module procedure :: init_pascal_triangle
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end interface pascal_triangle
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contains
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! Fills a pascal_triangle structure with the associated coefficients up to a given order
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type(pascal_triangle) function init_pascal_triangle(d)
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integer, intent(in) :: d
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integer :: i, j
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init_pascal_triangle%d = d
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allocate(init_pascal_triangle%lines(d))
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! Initializing the first line
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allocate(init_pascal_triangle%lines(1)%coeffs(2))
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init_pascal_triangle%lines(1)%coeffs = 1
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! Iterating Pascal's triangle formula
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if (d > 1) then
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do i=2,d
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allocate(init_pascal_triangle%lines(i)%coeffs(i+1))
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init_pascal_triangle%lines(i)%coeffs(1) = 1
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init_pascal_triangle%lines(i)%coeffs(i+1) = 1
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do j=2,i
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init_pascal_triangle%lines(i)%coeffs(j) = init_pascal_triangle%lines(i-1)%coeffs(j-1) &
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+ init_pascal_triangle%lines(i-1)%coeffs(j)
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end do
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end do
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end if
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end function init_pascal_triangle
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! Returns ⎛n⎞ stored in pascal_triangle p
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! ⎝k⎠
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integer function get(k,n,p)
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integer, intent(in) :: k, n
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type(pascal_triangle), intent(in) :: p
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get = p%lines(n)%coeffs(k+1)
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end function get
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! Returns ⎛ d ⎞
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! ⎝ k₁, k₂, ..., kₙ ⎠
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integer function multinomial(k,d,p)
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integer, intent(in) :: k(:), d
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type(pascal_triangle), intent(in) :: p
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integer :: s, i
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s = d
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multinomial = 1
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i = 1
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do while (s > 0)
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multinomial = multinomial*get(k(i), s, p)
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s = s-k(i)
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i = i+1
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end do
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end function
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end module pascal
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! gfortran -o pascal pascal.f08
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! ./pascal
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! program test
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! use pascal
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! type(pascal_triangle) :: p
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! integer :: d
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! read *, d
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! p = pascal_triangle(d)
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! do n=1,d
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! do k=0,n
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! if (k < n) then
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! write (*,'(i2," ")', advance="no") get(k,n,p)
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! else
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! write (*,'(i2," ")') get(k,n,p)
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! end if
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! end do
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! end do
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! d = 3
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! p = pascal_triangle(d)
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! print '(i2)', multinomial([1,2,3], d, p) ! should print 60
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! print '(i2)', multinomial([0,0,0,3], d, p) ! should print 20
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! end program test |