197 lines
6.4 KiB
Fortran
197 lines
6.4 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, KU Leuven
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!> @brief Polynomial representation for variable data.
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!--------------------------------------------------------------------------------------------------
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module polynomials
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use prec
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use IO
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use YAML_parse
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use YAML_types
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implicit none(type,external)
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private
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type, public :: tPolynomial
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real(pREAL), dimension(:), allocatable :: coef
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real(pREAL) :: x_ref = huge(0.0_pREAL)
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contains
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procedure, public :: at => eval
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end type tPolynomial
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interface polynomial
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module procedure polynomial_from_coef
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module procedure polynomial_from_dict
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end interface polynomial
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public :: &
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polynomial, &
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polynomials_init
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Run self-test.
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!--------------------------------------------------------------------------------------------------
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subroutine polynomials_init()
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print'(/,1x,a)', '<<<+- polynomials init -+>>>'; flush(IO_STDOUT)
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call selfTest()
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end subroutine polynomials_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Initialize a polynomial from coefficients.
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!--------------------------------------------------------------------------------------------------
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pure function polynomial_from_coef(coef,x_ref) result(p)
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real(pREAL), dimension(0:), intent(in) :: coef
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real(pREAL), intent(in) :: x_ref
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type(tPolynomial) :: p
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p%coef = coef
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p%x_ref = x_ref
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end function polynomial_from_coef
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!--------------------------------------------------------------------------------------------------
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!> @brief Initialize a polynomial from a dictionary with coefficients.
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!--------------------------------------------------------------------------------------------------
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function polynomial_from_dict(dict,y,x) result(p)
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type(tDict), intent(in) :: dict
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character(len=*), intent(in) :: y, x
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type(tPolynomial) :: p
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real(pREAL), dimension(:), allocatable :: coef
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real(pREAL) :: x_ref
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integer :: i, o
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character(len=1) :: o_s
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allocate(coef(1),source=dict%get_asReal(y))
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if (dict%contains(y//','//x)) then
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x_ref = dict%get_asReal(x//'_ref')
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coef = [coef,dict%get_asReal(y//','//x)]
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end if
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do o = 2,4
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write(o_s,'(I0.0)') o
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if (dict%contains(y//','//x//'^'//o_s)) then
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x_ref = dict%get_asReal(x//'_ref')
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coef = [coef,[(0.0_pREAL,i=size(coef),o-1)],dict%get_asReal(y//','//x//'^'//o_s)]
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end if
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end do
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p = Polynomial(coef,x_ref)
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end function polynomial_from_dict
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!--------------------------------------------------------------------------------------------------
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!> @brief Evaluate a polynomial.
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!> @details https://nvlpubs.nist.gov/nistpubs/jres/71b/jresv71bn1p11_a1b.pdf (eq. 1.2)
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!--------------------------------------------------------------------------------------------------
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pure function eval(self,x) result(y)
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class(tPolynomial), intent(in) :: self
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real(pREAL), intent(in) :: x
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real(pREAL) :: y
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integer :: o
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y = self%coef(ubound(self%coef,1))
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do o = ubound(self%coef,1)-1, 0, -1
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#ifndef __INTEL_LLVM_COMPILER
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y = y*(x-self%x_ref) +self%coef(o)
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#else
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y = IEEE_FMA(y,x-self%x_ref,self%coef(o))
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#endif
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end do
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end function eval
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!--------------------------------------------------------------------------------------------------
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!> @brief Check correctness of polynomical functionality.
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!--------------------------------------------------------------------------------------------------
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subroutine selfTest()
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type(tPolynomial) :: p1, p2
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real(pREAL), dimension(5) :: coef
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integer :: i
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real(pREAL) :: x_ref, x, y
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type(tDict), pointer :: dict
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character(len=pSTRLEN), dimension(size(coef)) :: coef_s
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character(len=pSTRLEN) :: x_ref_s, x_s, YAML_s
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call random_number(coef)
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call random_number(x_ref)
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call random_number(x)
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coef = coef*10_pREAL -0.5_pREAL
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x_ref = x_ref*10_pREAL -0.5_pREAL
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x = x*10_pREAL -0.5_pREAL
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p1 = polynomial([coef(1)],x_ref)
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if (dNeq(p1%at(x),coef(1))) error stop 'polynomial: eval(constant)'
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p1 = polynomial(coef,x_ref)
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if (dNeq(p1%at(x_ref),coef(1))) error stop 'polynomial: @ref'
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do i = 1, size(coef_s)
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write(coef_s(i),*) coef(i)
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end do
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write(x_ref_s,*) x_ref
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write(x_s,*) x
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YAML_s = 'C: '//trim(adjustl(coef_s(1)))//IO_EOL//&
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'C,T: '//trim(adjustl(coef_s(2)))//IO_EOL//&
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'C,T^2: '//trim(adjustl(coef_s(3)))//IO_EOL//&
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'C,T^3: '//trim(adjustl(coef_s(4)))//IO_EOL//&
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'C,T^4: '//trim(adjustl(coef_s(5)))//IO_EOL//&
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'T_ref: '//trim(adjustl(x_ref_s))//IO_EOL
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dict => YAML_parse_str_asDict(trim(YAML_s))
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p2 = polynomial(dict,'C','T')
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if (dNeq(p1%at(x),p2%at(x),1.0e-6_pREAL)) error stop 'polynomials: init'
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y = coef(1)+coef(2)*(x-x_ref)+coef(3)*(x-x_ref)**2+coef(4)*(x-x_ref)**3+coef(5)*(x-x_ref)**4
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if (dNeq(p1%at(x),y,1.0e-6_pREAL)) error stop 'polynomials: eval(full)'
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YAML_s = 'C: 0.0'//IO_EOL//&
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'C,T: '//trim(adjustl(coef_s(2)))//IO_EOL//&
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'T_ref: '//trim(adjustl(x_ref_s))//IO_EOL
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dict => YAML_parse_str_asDict(trim(YAML_s))
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p1 = polynomial(dict,'C','T')
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if (dNeq(p1%at(x_ref+x),-p1%at(x_ref-x),1.0e-10_pREAL)) error stop 'polynomials: eval(linear)'
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YAML_s = 'C: 0.0'//IO_EOL//&
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'C,T^2: '//trim(adjustl(coef_s(3)))//IO_EOL//&
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'T_ref: '//trim(adjustl(x_ref_s))//IO_EOL
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dict => YAML_parse_str_asDict(trim(YAML_s))
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p1 = polynomial(dict,'C','T')
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if (dNeq(p1%at(x_ref+x),p1%at(x_ref-x),1e-10_pREAL)) error stop 'polynomials: eval(quadratic)'
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YAML_s = 'Y: '//trim(adjustl(coef_s(1)))//IO_EOL//&
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'Y,X^3: '//trim(adjustl(coef_s(2)))//IO_EOL//&
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'X_ref: '//trim(adjustl(x_ref_s))//IO_EOL
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dict => YAML_parse_str_asDict(trim(YAML_s))
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p1 = polynomial(dict,'Y','X')
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if (dNeq(p1%at(x_ref+x)-coef(1),-(p1%at(x_ref-x)-coef(1)),1.0e-8_pREAL)) error stop 'polynomials: eval(cubic)'
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YAML_s = 'Y: '//trim(adjustl(coef_s(1)))//IO_EOL//&
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'Y,X^4: '//trim(adjustl(coef_s(2)))//IO_EOL//&
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'X_ref: '//trim(adjustl(x_ref_s))//IO_EOL
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dict => YAML_parse_str_asDict(trim(YAML_s))
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p1 = polynomial(dict,'Y','X')
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if (dNeq(p1%at(x_ref+x),p1%at(x_ref-x),1.0e-6_pREAL)) error stop 'polynomials: eval(quartic)'
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end subroutine selfTest
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end module polynomials
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