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| subroutine | sqrtsym2d_t (x, z, zd) |
| | Use the Taylor-series method (eigenvalues both fairly close to unity). More...
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Definition at line 25 of file psym2.f90.
| subroutine psym2::sqrtsym2d_t::sqrtsym2d_t |
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real(dp), dimension(2,2), intent(in) |
x, |
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real(dp), dimension(2,2), intent(out) |
z, |
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real(dp), dimension(2,2,2,2), intent(out) |
zd |
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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
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| [in] | x | symmetric 2*2 positive-definite matrix |
| [out] | z | sqrt(x) result |
| [out] | zd | symmetric derivative |
- Author
- R. J. Purser
Definition at line 235 of file psym2.f90.
The documentation for this interface was generated from the following file:
- /gpfs/dell2/emc/modeling/noscrub/George.Gayno/ufs_utils.git/UFS_UTILS.upstream/sorc/grid_tools.fd/regional_esg_grid.fd/psym2.f90
1.8.5