subroutine monomial_value ( m, n, e, x, v ) !*****************************************************************************80 ! !! monomial_value() evaluates a monomial. ! ! Discussion: ! ! This routine evaluates a monomial of the form ! ! product ( 1 <= i <= m ) x(i)^e(i) ! ! where the exponents are nonnegative integers. Note that ! if the combination 0^0 is encountered, it should be treated ! as 1. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 20 April 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer M, the spatial dimension. ! ! Input, integer N, the number of points at which the ! monomial is to be evaluated. ! ! Input, integer E(M), the exponents. ! ! Input, real ( kind = rk ) X(M,N), the point coordinates. ! ! Output, real ( kind = rk ) V(N), the value of the monomial. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n integer e(m) integer i real ( kind = rk ) v(n) real ( kind = rk ) x(m,n) v(1:n) = 1.0D+00 do i = 1, m if ( 0 /= e(i) ) then v(1:n) = v(1:n) * x(i,1:n) ** e(i) end if end do return end function triangle01_area ( ) !*****************************************************************************80 ! !! triangle01_area() computes the area of the unit triangle in 2D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 January 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Output, real ( kind = rk ) TRIANGLE01_AREA, the area. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) real ( kind = rk ) triangle01_area triangle01_area = 0.5D+00 return end subroutine triangle01_monomial_integral ( e, integral ) !*****************************************************************************80 ! !! triangle01_monomial_integral(): monomial integrals in the unit triangle in 2D. ! ! Discussion: ! ! The monomial is F(X,Y) = X^E(1) * Y^E(2). ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 January 2014 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! Input, integer E(2), the exponents of X and Y in the ! monomial. Each exponent must be nonnegative. ! ! Output, real ( kind = rk ) INTEGRAL, the integral. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 2 integer e(m) integer i real ( kind = rk ) integral integer j integer k if ( any ( e(1:m) < 0 ) ) then write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TRIANGLE01_MONOMIAL_INTEGRAL - Fatal error!' write ( *, '(a)' ) ' All exponents must be nonnegative.' stop 1 end if k = 0 integral = 1.0D+00 do i = 1, m do j = 1, e(i) k = k + 1 integral = integral * real ( j, kind = rk ) / real ( k, kind = rk ) end do end do do i = 1, m k = k + 1 integral = integral / real ( k, kind = rk ) end do return end subroutine triangle01_sample ( n, x ) !*****************************************************************************80 ! !! triangle01_sample() samples points uniformly from the unit triangle in 2D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 12 January 2014 ! ! Author: ! ! John Burkardt ! ! Reference: ! ! Reuven Rubinstein, ! Monte Carlo Optimization, Simulation, and Sensitivity ! of Queueing Networks, ! Krieger, 1992, ! ISBN: 0894647644, ! LC: QA298.R79. ! ! Parameters: ! ! Input, integer N, the number of points. ! ! Output, real ( kind = rk ) X(2,N), the points. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: m = 2 integer n real ( kind = rk ) e(m+1) real ( kind = rk ) e_sum integer j real ( kind = rk ) x(m,n) do j = 1, n call random_number ( harvest = e(1:m+1) ) e(1:m+1) = - log ( e(1:m+1) ) e_sum = sum ( e(1:m+1) ) x(1:m,j) = e(1:m) / e_sum end do return end