AbstractFunction

To handle analytical functions following abstract functions have been defined in EASIFEM.

• AbstractFunction_ all functions are children of this.
• AbstractFunction1D_ abstract function in one variable
• AbstractFunction2D_ abstract function of two variables
• AbstractFunction3D_ abstract function of three variables
• AbstractFunctionND_ abstract function of N variables

Structure

TYPE, ABSTRACT :: AbstractFunction_
CONTAINS
  PROCEDURE, PUBLIC, PASS(Obj) :: Deallocate => func_Deallocate
END TYPE AbstractFunction_

AbstractFunction

TYPE, ABSTRACT :: AbstractFunction_
CONTAINS
  PROCEDURE, PUBLIC, PASS(Obj) :: Deallocate => func_Deallocate
END TYPE AbstractFunction_

AbstractFunction1D

TYPE, ABSTRACT, EXTENDS(AbstractFunction_) :: AbstractFunction1D_
  TYPE(String) :: varname
END TYPE AbstractFunction1D_

AbstractFunction2D

TYPE, ABSTRACT, EXTENDS(AbstractFunction_) :: AbstractFunction2D_
  TYPE(String) :: varname(2)
END TYPE AbstractFunction2D_

AbstractFunction3D

TYPE, ABSTRACT, EXTENDS(AbstractFunction_) :: AbstractFunction3D_
  TYPE(String) :: varname(3)
END TYPE AbstractFunction3D_

AbstractFunctionND

TYPE, ABSTRACT, EXTENDS(AbstractFunction_) :: AbstractFunctionND_
  TYPE(String), ALLOCATABLE :: varname(:)
END TYPE AbstractFunctionND_

note

Following classes are children of Abstract1D_

• Polynomial1D_

Methods

AbstractFunctions are equipied with following methdods:

• Deallocate() To deallocate/ destroy the instance/variable.
• Eval Evaluate the function
• EvalGradient Evaluate the first gradient.
• GetVarName return the name of agrumnets of the function.

Eval

Eval method evaluates the function. For AbstractFunction1D,2D,3D it is an ELEMENTAL function. In case of AbstractFunctionND it is only PURE.

AbstractFunction1D

Eval method for AbstractFunction1D_

ABSTRACT INTERFACE
  RECURSIVE PURE FUNCTION Eval(obj, x) RESULT(ans)
    IMPORT AbstractFunction1D_, DFP
    CLASS(AbstractFunction1D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
  END FUNCTION Eval
END INTERFACE

AbstractFunction2D

Eval method for AbstractFunction2D_

ABSTRACT INTERFACE
  ELEMENTAL FUNCTION Eval(obj, x, y) RESULT(ans)
    IMPORT AbstractFunction2D_, DFP
    CLASS(AbstractFunction2D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP), INTENT(IN) :: y
    REAL(DFP) :: ans
  END FUNCTION Eval
END INTERFACE

AbstractFunction3D

Eval method for AbstractFunction3D_

ABSTRACT INTERFACE
  ELEMENTAL FUNCTION Eval(obj, x, y, z) RESULT(ans)
    IMPORT AbstractFunction3D_, DFP
    CLASS(AbstractFunction3D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP), INTENT(IN) :: y
    REAL(DFP), INTENT(IN) :: z
    REAL(DFP) :: ans
  END FUNCTION Eval
END INTERFACE

AbstractFunctionND

Eval method for AbstractFunctionND_

ABSTRACT INTERFACE
  PURE FUNCTION Eval(obj, x) RESULT(ans)
    IMPORT AbstractFunctionND_, DFP
    CLASS(AbstractFunctionND_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x(:)
    REAL(DFP) :: ans
  END FUNCTION Eval
END INTERFACE

EvalGradient

EvalGradient computes the first derivative of the function at given argument.

AbstractFunction1D

ABSTRACT INTERFACE
  RECURSIVE PURE FUNCTION EvalGradient(obj, x) RESULT(ans)
    IMPORT AbstractFunction1D_, DFP
    CLASS(AbstractFunction1D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP) :: ans
  END FUNCTION EvalGradient
END INTERFACE

info

EvalGradient method for AbstractFunction1D_

AbstractFunction2D

ABSTRACT INTERFACE
  ELEMENTAL FUNCTION EvalGradient(obj, x, y, dim) RESULT(ans)
    IMPORT AbstractFunction2D_, DFP, I4B
    CLASS(AbstractFunction2D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP), INTENT(IN) :: y
    INTEGER(I4B), INTENT(IN) :: dim
    REAL(DFP) :: ans
  END FUNCTION EvalGradient
END INTERFACE

info

Here, dim denotes the argument with respect to which the derivative is computed.

AbstractFunction3D

ABSTRACT INTERFACE
  ELEMENTAL FUNCTION EvalGradient(obj, x, y, z, dim)  &
    & RESULT(ans)
    IMPORT AbstractFunction3D_, DFP, I4B
    CLASS(AbstractFunction3D_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x
    REAL(DFP), INTENT(IN) :: y
    REAL(DFP), INTENT(IN) :: z
    INTEGER(I4B), INTENT(IN) :: dim
    REAL(DFP) :: ans
  END FUNCTION EvalGradient
END INTERFACE

info

Here, dim denotes the argument with respect to which the derivative is computed.

AbstractFunctionND

ABSTRACT INTERFACE
  PURE FUNCTION EvalGradient(obj, x, dim) RESULT(ans)
    IMPORT AbstractFunctionND_, DFP, I4B
    CLASS(AbstractFunctionND_), INTENT(IN) :: obj
    REAL(DFP), INTENT(IN) :: x(:)
    INTEGER(I4B), INTENT(IN) :: dim
    REAL(DFP) :: ans
  END FUNCTION EvalGradient
END INTERFACE

info

Here, dim denotes the argument with respect to which the derivative is computed.

GetVarName

GetVarName returns the variable name as an instance of String.