LagrangeDegree

Returns the polynomial space for constructing the Lagrange polynomials.

A Lagrange polynomial is given by

$$p(x,y) = \sum_{a=0}^{p}\sum_{b=0}^{q} x^{a} y^{b}$$

Here span of $x^{a}y^{b}$ is called the LagrangeDegree.

• as are given by first column of ans.
• bs are given by second column of ans.

For example for order = 2, we have the following degrees:

$$x^{0}y^{0}, x, x^2, y, xy, x^{2} y, y^{2}, x y^{2}, x^{2} y^{2}$$

which is representd by:

a	b
0	0
1	0
2	0
0	1
1	1
2	1
0	2
1	2
2	2

Interface

܀ Interface

INTERFACE
  MODULE PURE FUNCTION LagrangeDegree_Quadrangle(order) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    INTEGER(I4B), ALLOCATABLE :: ans(:, :)
  END FUNCTION LagrangeDegree_Quadrangle
END INTERFACE

order

Order of Lagrange polynomial

ans

• The first col of ans denotes the exponent of x
• The second col of ans denotes the exponent of y

️܀ See example

program main
  use easifembase
  implicit none
  integer( i4b ) :: i1, i2, order
  integer( i4b ), allocatable :: ans( :, : )

  order=1
  ans = LagrangeDegree_Quadrangle( order=order )
  call display( mdencode(ans), "ans (order="//tostring(order)//")=" )
  call blankLines(nol=2)

  order=2
  ans = LagrangeDegree_Quadrangle( order=order )
  call display( mdencode(ans), "ans (order="//tostring(order)//")=" )
  call blankLines(nol=2)

  order=3
  ans = LagrangeDegree_Quadrangle( order=order )
  call display( mdencode(ans), "ans (order="//tostring(order)//")=" )
  call blankLines(nol=2)
end program main

See results

ans (order=1)=

a	b
0	0
1	0
0	1
1	1

ans (order=2)=

a	b
0	0
1	0
2	0
0	1
1	1
2	1
0	2
1	2
2	2

ans (order=3)=

a	b
0	0
1	0
2	0
3	0
0	1
1	1
2	1
3	1
0	2
1	2
2	2
3	2
0	3
1	3
2	3
3	3

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