matrix_exp Module Reference

Routines for calculating a complex matrix exponential. More...

Functions/Subroutines
subroutine, public	taylor_only_imaginary (exp_h, im_matrix, nsquare, ntaylor)
	specialized subroutine for purely imaginary matrix exponentials
subroutine, public	taylor_full_complex (exp_h, re_part, im_part, nsquare, ntaylor)
	subroutine for general complex matrix exponentials on input a separate cp_fm_type for real and complex part on output a size 2 cp_fm_type, first element is the real part of the exponential second the imaginary
subroutine, public	get_nsquare_norder (norm, nsquare, norder, eps_exp, method, do_emd)
	optimization function for pade/taylor order and number of squaring steps
subroutine, public	exp_pade_full_complex (exp_h, re_part, im_part, nsquare, npade)
	exponential of a complex matrix, calculated using pade approximation together with scaling and squaring
subroutine, public	exp_pade_only_imaginary (exp_h, im_part, nsquare, npade)
	exponential of a complex matrix, calculated using pade approximation together with scaling and squaring
subroutine, public	exp_pade_real (exp_h, matrix, nsquare, npade)
	exponential of a real matrix, calculated using pade approximation together with scaling and squaring
subroutine, public	arnoldi (mos_old, mos_new, eps_exp, hre, him, mos_next, narn_old)
	exponential of a complex matrix, calculated using arnoldi subspace method (directly applies to the MOs)

Detailed Description

Routines for calculating a complex matrix exponential.

Author

Florian Schiffmann (02.09)

Function/Subroutine Documentation

taylor_only_imaginary()

subroutine, public matrix_exp::taylor_only_imaginary	(	type(cp_fm_type), dimension(2)	exp_h,
		type(cp_fm_type), intent(in)	im_matrix,
		integer, intent(in)	nsquare,
		integer, intent(in)	ntaylor
	)

specialized subroutine for purely imaginary matrix exponentials

Parameters

exp_H	...
im_matrix	...
nsquare	...
ntaylor	...

Author

Florian Schiffmann (02.09)

Definition at line 68 of file matrix_exp.F.

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taylor_full_complex()

subroutine, public matrix_exp::taylor_full_complex	(	type(cp_fm_type), dimension(2)	exp_h,
		type(cp_fm_type), intent(in)	re_part,
		type(cp_fm_type), intent(in)	im_part,
		integer, intent(in)	nsquare,
		integer, intent(in)	ntaylor
	)

subroutine for general complex matrix exponentials on input a separate cp_fm_type for real and complex part on output a size 2 cp_fm_type, first element is the real part of the exponential second the imaginary

Parameters

exp_H	...
re_part	...
im_part	...
nsquare	...
ntaylor	...

Author

Florian Schiffmann (02.09)

Definition at line 164 of file matrix_exp.F.

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get_nsquare_norder()

subroutine, public matrix_exp::get_nsquare_norder	(	real(dp), intent(in)	norm,
		integer, intent(out)	nsquare,
		integer, intent(out)	norder,
		real(dp), intent(in)	eps_exp,
		integer, intent(in)	method,
		logical, intent(in)	do_emd
	)

optimization function for pade/taylor order and number of squaring steps

Parameters

norm	...
nsquare	...
norder	...
eps_exp	...
method	...
do_emd	...

Author

Florian Schiffmann (02.09)

Definition at line 243 of file matrix_exp.F.

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exp_pade_full_complex()

subroutine, public matrix_exp::exp_pade_full_complex	(	type(cp_fm_type), dimension(2)	exp_h,
		type(cp_fm_type), intent(in)	re_part,
		type(cp_fm_type), intent(in)	im_part,
		integer, intent(in)	nsquare,
		integer, intent(in)	npade
	)

exponential of a complex matrix, calculated using pade approximation together with scaling and squaring

Parameters

exp_H	...
re_part	...
im_part	...
nsquare	...
npade	...

Author

Florian Schiffmann (02.09)

Definition at line 341 of file matrix_exp.F.

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exp_pade_only_imaginary()

subroutine, public matrix_exp::exp_pade_only_imaginary	(	type(cp_fm_type), dimension(2)	exp_h,
		type(cp_fm_type), intent(in)	im_part,
		integer, intent(in)	nsquare,
		integer, intent(in)	npade
	)

exponential of a complex matrix, calculated using pade approximation together with scaling and squaring

Parameters

exp_H	...
im_part	...
nsquare	...
npade	...

Author

Florian Schiffmann (02.09)

Definition at line 446 of file matrix_exp.F.

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exp_pade_real()

subroutine, public matrix_exp::exp_pade_real	(	type(cp_fm_type), intent(in)	exp_h,
		type(cp_fm_type), intent(in)	matrix,
		integer, intent(in)	nsquare,
		integer, intent(in)	npade
	)

exponential of a real matrix, calculated using pade approximation together with scaling and squaring

Parameters

exp_H	...
matrix	...
nsquare	...
npade	...

Author

Florian Schiffmann (02.09)

Definition at line 569 of file matrix_exp.F.

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arnoldi()

subroutine, public matrix_exp::arnoldi	(	type(cp_fm_type), dimension(2)	mos_old,
		type(cp_fm_type), dimension(2)	mos_new,
		real(kind=dp), intent(in)	eps_exp,
		type(cp_fm_type), intent(in), optional	hre,
		type(cp_fm_type), intent(in)	him,
		type(cp_fm_type), dimension(2), optional	mos_next,
		integer, intent(inout)	narn_old
	)

exponential of a complex matrix, calculated using arnoldi subspace method (directly applies to the MOs)

Parameters

mos_old	...
mos_new	...
eps_exp	...
Hre	...
Him	...
mos_next	...
narn_old	...

Author

Florian Schiffmann (02.09)

Definition at line 682 of file matrix_exp.F.

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