psym2::sqrtsym2 Interface Reference

Private Member Functions
subroutine	sqrtsym2 (em, z)
	Get the sqrt of a symmetric positive-definite 2*2 matrix. More...
subroutine	sqrtsym2d (x, z, zd)
	General routine to evaluate z=sqrt(x), and the symmetric derivative, zd = dz/dx, where x is a symmetric 2*2 positive-definite matrix. More...

Detailed Description

Definition at line 23 of file psym2.f90.

Constructor & Destructor Documentation

sqrtsym2()

subroutine psym2::sqrtsym2::sqrtsym2 ( real(dp), dimension(2,2), intent(in)  em, real(dp), dimension(2,2), intent(out)  z  )

private

Get the sqrt of a symmetric positive-definite 2*2 matrix.

Parameters

[in]	em	2*2 symmetric matrix
[out]	z	sqrt of a symmetric positive-definite 2*2 matrix

Author

R. J. Purser

Definition at line 150 of file psym2.f90.

Member Function/Subroutine Documentation

sqrtsym2d()

subroutine psym2::sqrtsym2::sqrtsym2d ( 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

General routine to evaluate z=sqrt(x), and the symmetric derivative, zd = dz/dx, where x is a symmetric 2*2 positive-definite matrix.

If the eigenvalues are very close together, extract their geometric mean for "preconditioning" a scaled version, px, of x, whose sqrt, and hence its derivative, can be easily obtained by the series expansion method. Otherwise, use the eigen-method (which entails dividing by the difference in the eignevalues to get zd, and which therefore fails when the eigenvalues become too similar).

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 177 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/sorc/grid_tools.fd/regional_esg_grid.fd/psym2.f90