pmat4::expmat Interface Reference

Private Member Functions
subroutine	expmat (n, a, b, detb)
	Evaluate the exponential, B, of a matrix, A, of degree n. More...
subroutine	expmatd (n, a, b, bd, detb, detbd)
	Like expmat, but for the 1st derivatives also. More...
subroutine	expmatdd (n, a, b, bd, bdd, detb, detbd, detbdd)
	Like expmat, but for the 1st and 2nd derivatives also. More...

Detailed Description

Definition at line 102 of file pmat4.f90.

Constructor & Destructor Documentation

expmat()

subroutine pmat4::expmat::expmat ( integer(spi), intent(in)  n, real(dp), dimension(n,n), intent(in)  a, real(dp), dimension(n,n), intent(out)  b, real(dp), intent(out)  detb  )

private

Evaluate the exponential, B, of a matrix, A, of degree n.

Apply the iterated squaring method, m times, to the approximation to exp(A/(2**m)) obtained as a Taylor expansion of degree L See Fung, T. C., 2004, Int. J. Numer. Meth. Engng, 59, 1273–1286.

Parameters

[in]	n	order of square matrix A
[in]	a	input matrix A
[out]	b	matrix B, the exponential of matrix A
[out]	detb	determinant of matrix B

Author

R. J. Purser

Definition at line 1729 of file pmat4.f90.

Member Function/Subroutine Documentation

expmatd()

subroutine pmat4::expmat::expmatd ( integer(spi), intent(in)  n, real(dp), dimension(n,n), intent(in)  a, real(dp), dimension(n,n), intent(out)  b, real(dp), dimension(n,n,(n*(n+1))/2), intent(out)  bd, real(dp), intent(out)  detb, real(dp), dimension((n*(n+1))/2), intent(out)  detbd  )

private

Like expmat, but for the 1st derivatives also.

Parameters

[in]	n	order of square matrix A
[in]	a	input matrix A
[out]	b	matrix B, the exponential of matrix A
[out]	bd	derivative of B wrt elements of A
[out]	detb	determinant of matrix B
[out]	detbd	derivative of detb wrt elements of A

Author

R. J. Purser

Definition at line 1767 of file pmat4.f90.

expmatdd()

subroutine pmat4::expmat::expmatdd ( integer(spi), intent(in)  n, real(dp), dimension(n,n), intent(in)  a, real(dp), dimension(n,n), intent(out)  b, real(dp), dimension(n,n,(n*(n+1))/2), intent(out)  bd, real(dp), dimension(n,n,(n*(n+1))/2,(n*(n+1))/2), intent(out)  bdd, real(dp), intent(out)  detb, real(dp), dimension((n*(n+1))/2), intent(out)  detbd, real(dp), dimension((n*(n+1))/2,(n*(n+1))/2), intent(out)  detbdd  )

private

Like expmat, but for the 1st and 2nd derivatives also.

Parameters

[in]	n	order of the matrix A
[in]	a	input matrix A
[out]	b	matrix B, exponential of matrix A
[out]	bd	derivative of B wrt elements of A
[out]	bdd	2nd derivative of B wrt elements of A
[out]	detb	determinant of matrix B
[out]	detbd	derivative of detb wrt elements of A
[out]	detbdd	2nd derivative of detb wrt elements of A

Author

R. J. Purser

Definition at line 1834 of file pmat4.f90.

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

• /scratch1/NCEPDEV/da/George.Gayno/ufs_utils.git/UFS_UTILS/sorc/grid_tools.fd/regional_esg_grid.fd/pmat4.f90