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Jacobi1D example 6

This example shows the usage of [[Jacobi1D_]] class. We test EvalGradient in this routine. the argument of EvalGradient is vector in this routine.

Modules and classes​

  • [[Jacobi1D_]]

Usage​

PROGRAM main
use easifemBase
use easifemClasses
implicit none
type(Jacobi1D_) :: obj
type(String) :: astr
integer(i4b) :: ii, n
real( dfp ), allocatable :: x(:), yexact(:), y(:)
real( dfp ), parameter :: tol=1.0E-10, alpha=0.0_DFP, beta=0.0_DFP

n=1​

  n = 1
  x = linspace(0.0_DFP, 1.0_DFP, 11_I4B)
  yexact = ones(11, 1)
  obj=Jacobi1D(varname="x", n=n, alpha=alpha, beta=beta)
  y = obj%EvalGradient( x )
  call OK( ALL( y .APPROXEQ. yexact), "test-1:" )

n=2​

  n=2
  yexact = 3.0*x
  obj=Jacobi1D(varname="x", n=n, alpha=alpha, beta=beta)
  y = obj%EvalGradient( x )
  call OK(ALL(y .APPROXEQ. yexact), "test-2:" )

n=3​

  n=3
  yexact = 2.5*3.0*x**2 - 1.5
  obj=Jacobi1D(varname="x", n=n, alpha=alpha, beta=beta)
  y = obj%EvalGradient( x )
  call OK(ALL( SOFTEQ( y, yexact, tol=tol )), "test-3:" )

n=4​

  n=4
  yexact = (35.0*4.0*x**3 - 30.0*2.0*x**1)/8.0
  obj=Jacobi1D(varname="x", n=n, alpha=alpha, beta=beta)
  y = obj%EvalGradient( x )
  call OK(ALL( SOFTEQ( y, yexact, tol=tol )), "test-4:"  )
END PROGRAM main