psym2::sqrtsym2d_t Interface Reference

Private Member Functions
subroutine	sqrtsym2d_t (x, z, zd)
	Use the Taylor-series method (eigenvalues both fairly close to unity). More...

Detailed Description

Definition at line 25 of file psym2.f90.

Constructor & Destructor Documentation

sqrtsym2d_t()

subroutine psym2::sqrtsym2d_t::sqrtsym2d_t ( real(dp), dimension(2,2), intent(in)  x, real(dp), dimension(2,2), intent(out)  z, real(dp), dimension(2,2,2,2), intent(out)  zd  )

private

Use the Taylor-series method (eigenvalues both fairly close to unity).

For a 2*2 positive definite symmetric matrix x, try to get both the z=sqrt(x) and dz/dx using the binomial-expansion method applied to the intermediate matrix,

r = (x-1). ie z=sqrt(x) = (1+r)^{1/2} = I + (1/2)*r -(1/8)*r^2 ...
  + [(-)^n *(2n)!/{(n+1)! * n! *2^{2*n-1}} ]*r^{n+1}

Parameters

[in]	x	symmetric 2*2 positive-definite matrix
[out]	z	sqrt(x) result
[out]	zd	symmetric derivative

Author

R. J. Purser

Definition at line 236 of file psym2.f90.

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The documentation for this interface was generated from the following file:

• /lfs/h2/emc/global/noscrub/George.Gayno/ufs_utils.git/UFS_UTILS.upstream/sorc/grid_tools.fd/regional_esg_grid.fd/psym2.f90