Structure

[[Polynomial3D_]] is a class for polynomials of argument in $R^3$.

TYPE, EXTENDS( AbstractFunction1D_ ) :: Polynomial3D_
  PRIVATE
  INTEGER( I4B ), ALLOCATABLE :: degree( :, : )
    !! power of each monomial
  REAL( DFP ), ALLOCATABLE :: coeff( : )
    !! coefficient
  TYPE( Monomial3D_ ), ALLOCATABLE :: x( : )
    !! Monomial3D

!!! note "degree" Degrees of each monomial

!!! note "coeff" Coefficient of each monomial

!!! note "x" A vector of [[Monomial3D_]]

ConstructorMethods

Polynomial3D constructor

Creates an instance of [[Polynomial3D_]].

Interface:

INTERFACE
MODULE PURE FUNCTION Polynomial3D( coeff, degree, name1, name2, name3) &
  & RESULT( ans )
  REAL( DFP ), INTENT( IN ) :: coeff( : )
  !! coefficients
  INTEGER( I4B ), INTENT( IN ) :: degree( :, : )
  !! degrees of x and y
  CHARACTER( LEN = * ), INTENT( IN ) :: name1
  !! variable x
  CHARACTER( LEN = * ), INTENT( IN ) :: name2
  !! variable y
  CHARACTER( LEN = * ), INTENT( IN ) :: name3
  !! variable z
  TYPE( Polynomial3D_ ) :: ans
END FUNCTION Polynomial3D
END INTERFACE

Example:

• [[Polynomial3D_test_1]]

Polynomial3D_Pointer

Creates a pointer to a newly created instance of [[Polynomial3D_]], the interface is same as the one given above.

Example:

• [[Polynomial3D_test_2.md]]

Deallocate

Deallocate the data.

INTERFACE
  MODULE SUBROUTINE Deallocate( obj )
    CLASS( Polynomial3D_ ), INTENT( INOUT ) :: obj
  END SUBROUTINE Deallocate
END INTERFACE

IOMethods

Display

Display the content of polynomial on the screen.

Interface:

INTERFACE
MODULE SUBROUTINE Display( obj, msg, unitno )
  CLASS( Polynomial3D_ ), INTENT( IN ) :: obj
  CHARACTER( LEN = * ), INTENT( IN ) :: msg
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: unitno
END SUBROUTINE Display
END INTERFACE

GetMethods

Eval

Evaluate the polynomial at x,y,z point.

Interface:

INTERFACE
  MODULE ELEMENTAL FUNCTION Eval( obj, x, y, z ) RESULT( ans )
    CLASS( Polynomial3D_ ), 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

Example:

• [[Polynomial3D_test_3]]

EvalGradient

Evaluate the gradient of polynomial.

Interface:

INTERFACE
  MODULE ELEMENTAL FUNCTION EvalGradient( obj, x, y, z, dim ) &
    & RESULT( ans )
    CLASS( Polynomial3D_ ), 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

!!! note "dim"

• dim=1 corresponds to $\frac{df}{dx}$
• dim=2 corresponds to $\frac{df}{dy}$
• dim=3 corresponds to $\frac{df}{dz}$

Example:

• [[Polynomial2D_test_4]]

Grad

This function returns the gradient of a polynomial as an instance of [[Polynomial3D_]]

Interface:

INTERFACE
MODULE FUNCTION Grad( obj, dim ) RESULT( ans )
  CLASS( Polynomial3D_ ), INTENT( IN ) :: obj
  INTEGER( I4B ), INTENT( IN ) :: dim
  TYPE( Polynomial3D_ ) :: ans
END FUNCTION Grad
END INTERFACE

!!! note "dim" See the above remark on dim.

Example:

• [[Polynomial2D_test_5]]

GetStringForUID

Returns the string for creating UID.

Example:

• [[Polynomial2D_test_6]]

GetDisplayString

Returns the string for display.

Example:

• [[Polynomial2D_test_6]]

GetDegree

Returns the degree.

Example:

• [[Polynomial2D_test_6]]

GetCoeff

Returns the coefficient.

Example:

• [[Polynomial2D_test_6]]

GetOrder

Returns the order of polynomial.

AddMethods

Addition operator has been overloaded. Following operation is allowed.

c = a + b

where, a, b, c are given in following table.

a	b	c
Poly3D	Poly3D	Poly3D
Poly3D	Poly3D	Mono3D
Poly3D	Mono3D	Poly3D
Poly3D	Mono3D	Mono3D
Poly3D	Mono3D	Int8
Poly3D	Mono3D	Int16
Poly3D	Mono3D	Int32
Poly3D	Mono3D	Int64
Poly3D	Mono3D	Real32
Poly3D	Mono3D	Real64
Poly3D	Int8	Mono3D
Poly3D	Int16	Mono3D
Poly3D	Int32	Mono3D
Poly3D	Int64	Mono3D
Poly3D	Real32	Mono3D
Poly3D	Real64	Mono3D
Poly3D	Poly3D	Int8
Poly3D	Poly3D	Int16
Poly3D	Poly3D	Int32
Poly3D	Poly3D	Int64
Poly3D	Poly3D	Real32
Poly3D	Poly3D	Real64
Poly3D	Int8	Poly3D
Poly3D	Int16	Poly3D
Poly3D	Int32	Poly3D
Poly3D	Int64	Poly3D
Poly3D	Real32	Poly3D
Poly3D	Real64	Poly3D

where,

• Poly3D is an instance of [[Polynomial3D_]]
• Mono3D is an instance of [[Monomial3D_]]

SubtractMethods

Subtraction operator has been overloaded. Following operation is allowed.

c = a - b

!!! note "a,b,c" a,b,c are given above.

MultiplicationMethods

Multiplication operator has been overloaded. Following operation is allowed.

c = a * b

!!! note "a,b,c" a,b,c are given above.