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Structure

Monomial in 1D is given by xnx^{n}. Monomial1D class is designed for this task. It is a child of AbstractBasis1D_ defined in [[AbstractBasis_]].

TYPE, EXTENDS(AbstractBasis1D_) :: Monomial1D_
  PRIVATE
  INTEGER(I4B) :: degree = 0
CONTAINS

Todo​

  • Add a zero monomial
  • Add a method to get nth derivative
  • Add integrate method
  • Add evaluate integrate method

ConstructorMethods​

Initiate​

Construct an instance of Monomial1D_.

Interface:

INTERFACE
  MODULE ELEMENTAL SUBROUTINE Initiate(obj, degree, varname)
    CLASS(Monomial1D_), INTENT(INOUT) :: obj
    INTEGER(I4B), INTENT(IN) :: degree
    CHARACTER(LEN=*), INTENT(IN) :: varname
  END SUBROUTINE Initiate
END INTERFACE

Example: [[Monomial1D_test_1.md]], You can also use the function Monomial1D as shown in this example.

CALL obj%Initiate(degree=1_I4B, varname="x")

or

obj = Monomial1D(degree=1_I4B, varname="x")

Deallocate​

Example:

  • [[Monomial1D_test_1.md]]

GetMethods​

Eval​

Evaluate the monomial at given point or points.

INTERFACE
  MODULE ELEMENTAL FUNCTION eval(obj, x) RESULT(ans)
    CLASS(Monomial1D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
  END FUNCTION eval
END INTERFACE

Example:

  • [[Monomial1D_test_3]]
ans = obj%eval(x=1.0_DFP)
ans = obj%eval(x=[1.0_DFP, 2.0_DFP])

EvalGradient​

Evaluate the gradient at given point or points.

Interface:

INTERFACE
  MODULE ELEMENTAL FUNCTION EvalGradient(obj, x) RESULT(ans)
    CLASS(Monomial1D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
  END FUNCTION EvalGradient
END INTERFACE

Example:

  • [[Monomial1D_test_4]]

OPERATOR(.Grad.)​

Returns the gradient of Monomial in terms of Monomial. For example, if the monomial is xnx^{n}, then .GRAD. operator returns monomial representing xn−1x^{n-1}.

Interface:

INTERFACE
  MODULE ELEMENTAL FUNCTION Grad(obj) RESULT(ans)
    CLASS(Monomial1D_), INTENT(IN) :: obj
    TYPE(Monomial1D_) :: ans
  END FUNCTION Grad
END INTERFACE

Example:

  • [[Monomial1D_test_4.md]]

!!! note "Grad" Note that you can also use obj%Grad() function to get the gradient.

GetStringForUID​

Returns the string for creating UID of the monomial. This method is for internal use only.

GetDegree​

Returns the degree of the monomial.

Interface:

INTERFACE
  MODULE ELEMENTAL FUNCTION GetDegree(obj) RESULT(ans)
    CLASS(Monomial1D_), INTENT(IN) :: obj
    INTEGER(I4B) :: ans
  END FUNCTION GetDegree
END INTERFACE

!!! example "Examples"

  • [[Monomial1D_test_6]]

GetDisplayString​

Returns the string for display purpose. This routine is for internal use only.

GetCoeff​

Returns the coefficient of monomial, which is always 1.0.

IOMethods​

Display​

Display the monomial on the screen.

!!! example "Examples"

  • [[Monomial1D_test_1]]
  • [[Monomial1D_test_2]]

OperatorMethods​

OPERATOR(*)​

OPERATOR(*) multiplies two Monomial.

!!! example "Examples"

  • [[Monomial1D_test_2.md]]

ASSIGNMENT(=)​

Following assignments are valid:

obj1= obj2
obj1(:) = obj2(:)

where, obj1 and obj2 are instances of Monomial1D

BasisMethods​

Monomials1D​

Generate monomials from order = 0 to N.

Interface:

INTERFACE
  MODULE PURE FUNCTION Monomials1D(order, varname) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order
    CHARACTER(LEN=*), INTENT(IN) :: varname
    !! variable varname
    TYPE(Monomial1D_), ALLOCATABLE :: ans(:)
    !! vector of monomial
  END FUNCTION Monomials1D
END INTERFACE

!!! example "Examples"

  • [[Monomial1D_test_5.md]]

EvenMonomials1D​

Generate even monomials from order = 0, 2, to 2N.

Interface:

INTERFACE
  MODULE PURE FUNCTION EvenMonomials1D(order, varname) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order
    CHARACTER(LEN=*), INTENT(IN) :: varname
    !! variable varname
    TYPE(Monomial1D_), ALLOCATABLE :: ans(:)
    !! vector of monomial
  END FUNCTION EvenMonomials1D
END INTERFACE

!!! example "Examples"

  • [[Monomial1D_test_5.md]]

OddMonomials1D​

Generate odd ordered monomials from order = 1, 2, to (2N+1)/2.

Interface:

INTERFACE
  MODULE PURE FUNCTION OddMonomials1D(order, varname) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    !! order
    CHARACTER(LEN=*), INTENT(IN) :: varname
    !! variable varname
    TYPE(Monomial1D_), ALLOCATABLE :: ans(:)
    !! vector of monomial
  END FUNCTION OddMonomials1D
END INTERFACE

!!! example "Examples"

  • [[Monomial1D_test_5.md]]