linint_Grow

subroutine linint_Grow(x, left, right, growth, n, il, ir, phi)

Description:

This subroutine calculates nodes and weights for the linear interpolation of data that is located on an grid of nodes with growing distance , see grid_Cons_Grow. It therefore calculates the indices of a left and right gridpoints and as well as an interpolation weight , so that we can calculate the linear interpolant as

Input arguments:

• real*8 :: x    or    real*8 :: x(:)
  The point(s) where to evaluate the interpolating polynomial. This can be either a scalar or a one-dimensional array of arbitrary size. In the latter case, the polynomial is evaluated at each point supplied in the array x.
• real*8 :: left
  The left interval endpoint of the growing grid of points .
• real*8 :: right
  The right interval endpoint of the growing grid of points .
• real*8 :: growth
  The growth rate of gridpoints of the growing grid of points .
• integer :: n
  The number of gridpoints the growing grid of points is made up of.

Output arguments:

• integer :: il    or    integer :: il(:)
  The left interpolation node(s) . If the input value x is a scalar, this needs to be a scalar. If x is a one-dimensional array, this also needs to be a one-dimensional array with exactly the same length.
• integer :: ir    or    integer :: ir(:)
  The right interpolation node(s) . If the input value x is a scalar, this needs to be a scalar. If x is a one-dimensional array, this also needs to be a one-dimensional array with exactly the same length.
• real*8 :: phi    or    real*8 :: phi(:)
  The interpolation weight(s) . If the input value x is a scalar, this needs to be a scalar. If x is a one-dimensional array, this also needs to be a one-dimensional array with exactly the same length.

References

• For further reading refer to:
  • Süli, E. & Mayers, D. F. (2003). An Introduction to Numerical Analysis. Cambridge: Cambridge University Press.
  • Powell, M.J.D. (1996). Approximation Theory and Methods. Cambridge: Cambridge University Press.
• This routine is used in the following programs:
  • prog09_08m.f90
  • prog09_09m.f90
  • prog09_10.f90
  • prog09_10m.f90
  • prog10_01.f90
  • prog10_01m.f90
  • prog10_02.f90
  • prog10_02m.f90
  • prog10_03.f90
  • prog10_03m.f90
  • prog10_04.f90
  • prog10_04m.f90
  • prog10_05.f90
  • prog10_05m.f90
  • prog10_06.f90
  • prog10_06m.f90
  • prog11_01.f90
  • prog11_01m.f90
  • prog11_02.f90
  • prog11_02m.f90
  • prog11_03.f90
  • prog11_03m.f90