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Lagrange1D example 1

This example shows the usage of [[Lagrange1D_]] class.

Modules and classes​

  • [[Lagrange1D_]]

Usage​

PROGRAM main
use easifemBase
use easifemClasses
implicit none
type(Lagrange1D_), allocatable :: f(:)
type(Lagrange1D_) :: f1
real(dfp), allocatable :: x( : )
integer(i4b) :: ii, order

!!! note "Lagrange1D" Initiate lagrange polynomial in one dimension

l1(x)=1−xl2(x)=xl_{1}(x)=1-x \\ l_{2}(x)=x 
  x = [0.0,1.0]
  order=1
  f1=Lagrange1D( i=1, x=x, order=order, varname="x" )
  call f1%display( 'f(x)=' )
  f1=Lagrange1D( i=2, x=x, order=order, varname="x" )
  call f1%display( 'f(x)=' )

!!! example "result"

f(x)=+1x0−1x1f(x)=+1x1f(x)=+1x^0-1x^1 \\ f(x)=+1x^1

!!! note "Higher order Lagrange polynomial"

!!! note "Lagrange1D"

  order = 4_I4B
  x = linspace(0.0_DFP, 1.0_DFP, order+1)
  allocate( f(order+1) )
  do ii = 1, order+1
    f(ii) = Lagrange1D(ii, x=x, order=order, varname="x")
    call f(ii)%display("l_{"//tostring(ii)//"}=")
  end do

!!! example "result"

l1=+1x0−8.3333x1+23.333x2−26.667x3+10.667x4l2=+16x1−69.333x2+96x3−42.667x4l3=−12x1+76x2−128x3+64x4l4=+5.3333x1−37.333x2+74.667x3−42.667x4l5=−1x1+7.3333x2−16x3+10.667x4l_{1}=+1x^0-8.3333x^1+23.333x^2-26.667x^3+10.667x^4 \\ l_{2}=+16x^1-69.333x^2+96x^3-42.667x^4 \\ l_{3}=-12x^1+76x^2-128x^3+64x^4 \\ l_{4}=+5.3333x^1-37.333x^2+74.667x^3-42.667x^4 \\ l_{5}=-1x^1+7.3333x^2-16x^3+10.667x^4 
END PROGRAM main