pmat4::expmat Interface Reference

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

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 )

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 1728 of file pmat4.f90.

References pietc::o2, pietc::u0, pietc::u1, and pietc::u2.

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 )

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 1766 of file pmat4.f90.

References pietc::o2, pietc::u0, pietc::u1, and pietc::u2.

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 )

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 1833 of file pmat4.f90.

References pietc::o2, pietc::u0, pietc::u1, and pietc::u2.

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

• /scratch4/NCEPDEV/nems/Brian.Curtis/git/BrianCurtis-NOAA/UFS_UTILS/v1_14_0/sorc/grid_tools.fd/regional_esg_grid.fd/pmat4.f90