Data Types
interface	simplex_dos

interface	simplex_t

interface	simplex_weights

Functions/Subroutines
pure subroutine	simplex_sort_2 (values, idx)
	Sort two real values in ascending order while permuting indices. More...

pure subroutine	simplex_sort_3 (values, idx)
	Sort three real values in ascending order while permuting indices. More...

pure subroutine	simplex_sort_4 (values, idx)
	Sort four real values in ascending order while permuting indices. More...

pure subroutine	simplex_compare_swap (a, b, ia, ib)
	Swap two value-index pairs if they are out of ascending order. More...

type(simplex_t) function, pointer, public	simplex_init (dim, naxis, nshifts, shift, kpoints, equiv, opt)
	Constructor for linear simplex methods. More...

subroutine, public	simplex_end (this)
	Destructor for linear simplex methods. More...

subroutine	simplex_weights_single (rdim, esimplex, eF, weights, dos)
	Get the weights and DOS contribution of a single simplex. More...

subroutine	simplex_weights_array (rdim, esimplex, eFs, weights, dos)
	Get the weights and DOS contribution of a single simplex for multiple reference energies. More...

subroutine	simplex_dos_single (rdim, esimplex, eF, dos)
	Get only the DOS contribution of a single simplex. More...

subroutine	simplex_dos_array (rdim, esimplex, eFs, dos)
	Get only the DOS contribution of a single simplex for multiple reference energies. More...

subroutine	simplex_weights_1d (esegment, eFs, weights, dos)
	Get the weights and DOS contribution of a single segment. More...

subroutine	simplex_dos_1d (esegment, eFs, dos)
	Get only the DOS contribution of a single segment. More...

subroutine	simplex_weights_2d (etriangle, eFs, weights, dos)
	Get the weights and DOS contribution of a single tetrahedron. More...

subroutine	simplex_dos_2d (etriangle, eFs, dos)
	Get only the DOS contribution of a single triangle. More...

subroutine	simplex_weights_3d (etetra, eFs, weights, dos)
	Get the weights and DOS contribution of a single tetrahedron. More...

subroutine	simplex_dos_3d (etetra, eFs, dos)
	Get only the DOS contribution of a single tetrahedron. More...

Function/Subroutine Documentation

◆ simplex_sort_2()

pure subroutine simplex_oct_m::simplex_sort_2	(	real(real64), dimension(2), intent(inout)	values,
		integer, dimension(2), intent(inout)	idx
	)

private

Sort two real values in ascending order while permuting indices.

Uses an optimal sorting network in number of comparisons to avoid the overhead of calling a foreign sorting routine for very small arrays. The sorting is unstable.

Parameters

[in,out]	values	Values to sort in place
[in,out]	idx	Indices permuted together with `values`

Definition at line 170 of file simplex.F90.

◆ simplex_sort_3()

pure subroutine simplex_oct_m::simplex_sort_3	(	real(real64), dimension(3), intent(inout)	values,
		integer, dimension(3), intent(inout)	idx
	)

private

Sort three real values in ascending order while permuting indices.

Uses an optimal sorting network in number of comparisons to avoid the overhead of calling a foreign sorting routine for very small arrays. The sorting is unstable.

Parameters

[in,out]	values	Values to sort in place
[in,out]	idx	Indices permuted together with `values`

Definition at line 185 of file simplex.F90.

◆ simplex_sort_4()

pure subroutine simplex_oct_m::simplex_sort_4	(	real(real64), dimension(4), intent(inout)	values,
		integer, dimension(4), intent(inout)	idx
	)

private

Sort four real values in ascending order while permuting indices.

Uses an optimal sorting network in number of comparisons to avoid the overhead of calling a foreign sorting routine for very small arrays. The sorting is unstable.

Parameters

[in,out]	values	Values to sort in place
[in,out]	idx	Indices permuted together with `values`

Definition at line 202 of file simplex.F90.

◆ simplex_compare_swap()

pure subroutine simplex_oct_m::simplex_compare_swap	(	real(real64), intent(inout)	a,
		real(real64), intent(inout)	b,
		integer, intent(inout)	ia,
		integer, intent(inout)	ib
	)

private

Swap two value-index pairs if they are out of ascending order.

Parameters

[in,out]	a	First value
[in,out]	b	Second value
[in,out]	ia	Index associated with `a`
[in,out]	ib	Index associated with `b`

Definition at line 219 of file simplex.F90.

◆ simplex_init()

type(simplex_t) function, pointer, public simplex_oct_m::simplex_init	(	integer, intent(in)	dim,
		integer, dimension(1:dim), intent(in)	naxis,
		integer, intent(in)	nshifts,
		real(real64), dimension(:,:), intent(in)	shift,
		real(real64), dimension(:,:), intent(in)	kpoints,
		integer, dimension(:), intent(in), optional	equiv,
		logical, intent(in)	opt
	)

Constructor for linear simplex methods.

At the moment this performs a dumb tetrahedrization of the BZ by converting the coordinates of k-points back into integer triples. This only works for a two- and three-dimensional BZ and if there is only a single shift. Both of these conditions are ASSERTed.

Parameters

[in]	dim	Dimension of the system
[in]	naxis	Number of k-points along each dimension
[in]	nshift	Number of shifts
[in]	shift	Shifts along each dimension
[in]	kpoints	Grid of k-points in the unreduced BZ
[in]	equiv	Mapping of k-point indices in the full BZ to the reduced BZ
[in]	opt	Whether to use the improved tetrahedron method

Returns: New linear simplex method instance

Definition at line 252 of file simplex.F90.

◆ simplex_end()

subroutine, public simplex_oct_m::simplex_end ( type(simplex_t), intent(inout) this )

Destructor for linear simplex methods.

Parameters

[in,out] this Linear simplex method instance

Definition at line 486 of file simplex.F90.

◆ simplex_weights_single()

subroutine simplex_oct_m::simplex_weights_single	(	integer, intent(in)	rdim,
		real(real64), dimension(:), intent(in)	esimplex,
		real(real64), intent(in)	eF,
		real(real64), dimension(:), intent(out)	weights,
		real(real64), dimension(:), intent(out)	dos
	)

private

Get the weights and DOS contribution of a single simplex.

Parameters

[in]	rdim	Reduced dimension of the problem (non-zero dimensions in k-space)
[in]	esimplex	Eigenenergies on the corner points of a simplex
[in]	eFs	Reference energies
[out]	weights	Integration weights for each corner of the segment, indexed as (vertex, energy)
[out]	dos	Contribution to the DOS by the segment, indexed as (vertex, energy)

Definition at line 500 of file simplex.F90.

◆ simplex_weights_array()

subroutine simplex_oct_m::simplex_weights_array	(	integer, intent(in)	rdim,
		real(real64), dimension(:), intent(in)	esimplex,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	weights,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get the weights and DOS contribution of a single simplex for multiple reference energies.

Parameters

[in]	rdim	Reduced dimension of the problem (non-zero dimensions in k-space)
[in]	esimplex	Eigenenergies on the corner points of a simplex
[in]	eFs	Reference energies
[out]	weights	Integration weights for each corner of the simplex, indexed as (vertex, energy)
[out]	dos	Contribution to the DOS by the simplex, indexed as (vertex, energy)

Definition at line 523 of file simplex.F90.

◆ simplex_dos_single()

subroutine simplex_oct_m::simplex_dos_single	(	integer, intent(in)	rdim,
		real(real64), dimension(:), intent(in)	esimplex,
		real(real64), intent(in)	eF,
		real(real64), dimension(:), intent(out)	dos
	)

private

Get only the DOS contribution of a single simplex.

Parameters

[in]	rdim	Reduced dimension of the problem (non-zero dimensions in k-space)
[in]	esimplex	Eigenenergies on the corner points of a simplex
[in]	eF	Reference energy
[out]	dos	Contribution to the DOS by the simplex

Definition at line 555 of file simplex.F90.

◆ simplex_dos_array()

subroutine simplex_oct_m::simplex_dos_array	(	integer, intent(in)	rdim,
		real(real64), dimension(:), intent(in)	esimplex,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get only the DOS contribution of a single simplex for multiple reference energies.

Parameters

[in]	rdim	Reduced dimension of the problem (non-zero dimensions in k-space)
[in]	esimplex	Eigenenergies on the corner points of a simplex
[in]	eFs	Reference energies
[out]	dos	Contribution to the DOS by the simplex, indexed as (vertex, energy)

Definition at line 575 of file simplex.F90.

◆ simplex_weights_1d()

subroutine simplex_oct_m::simplex_weights_1d	(	real(real64), dimension(:), intent(in)	esegment,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	weights,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get the weights and DOS contribution of a single segment.

Parameters

[in]	esegment	Eigenenergies on the corner points of a segment
[in]	eF	Reference energy
[out]	weights	Integration weights for each corner of the tetrahedron (including Bloechl correction)
[out]	dos	Contribution to the DOS by the tetrahedron

Definition at line 604 of file simplex.F90.

◆ simplex_dos_1d()

subroutine simplex_oct_m::simplex_dos_1d	(	real(real64), dimension(:), intent(in)	esegment,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get only the DOS contribution of a single segment.

Parameters

[in]	esegment	Eigenenergies on the corner points of a segment
[in]	eFs	Reference energies
[out]	dos	Contribution to the DOS by the segment, indexed as (vertex, energy)

Definition at line 688 of file simplex.F90.

◆ simplex_weights_2d()

subroutine simplex_oct_m::simplex_weights_2d	(	real(real64), dimension(:), intent(in)	etriangle,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	weights,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get the weights and DOS contribution of a single tetrahedron.

The expressions for the weights and the DOS are given in S. I. Kurganseii, et al., phys. stat. sol. (b) 129, 293 (1985).

The expression for the Bloechl-type correction is given in Eq. 4 of J.-H. Lee, et al., Phys. Rev. B 66, 233102 (2002).

Parameters

[in]	etriangle	Eigenenergies on the corner points of a triangle
[in]	eFs	Reference energies
[out]	weights	Integration weights for each corner of the triangle, indexed as (vertex, energy)
[out]	dos	Contribution to the DOS by the triangle, indexed as (vertex, energy)

Definition at line 760 of file simplex.F90.

◆ simplex_dos_2d()

subroutine simplex_oct_m::simplex_dos_2d	(	real(real64), dimension(:), intent(in)	etriangle,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get only the DOS contribution of a single triangle.

The expressions for the DOS are given in S. I. Kurganseii, et al., phys. stat. sol. (b) 129, 293 (1985).

Parameters

[in]	etriangle	Eigenenergies on the corner points of a triangle
[in]	eFs	Reference energies
[out]	dos	Contribution to the DOS by the triangle, indexed as (vertex, energy)

Definition at line 871 of file simplex.F90.

◆ simplex_weights_3d()

subroutine simplex_oct_m::simplex_weights_3d	(	real(real64), dimension(:), intent(in)	etetra,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	weights,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get the weights and DOS contribution of a single tetrahedron.

The expressions for the weights are given in Appendix C of P. E. Bloechl, et al., Phys. Rev. B 49, 16223 (1994).

The expressions for the DOS are given in A. H. MacDonald, et al., J. Phys. C: Solid State Phys. 12, 2991 (1979).

The expressions for the weights of the improved tetrahedron method are given in Eq. (18)-(21) of M. Kawamura, et al., Phys. Rev. B 89, 094515 (2014).

Parameters

[in]	etetra	Eigenenergies on the corner points of a tetrahedron
[in]	eFs	Reference energies
[out]	weights	Integration weights for each corner of the tetrahedron, indexed as (vertex, energy)
[out]	dos	Contribution to the DOS by the tetrahedron, indexed as (vertex, energy)

Definition at line 962 of file simplex.F90.

◆ simplex_dos_3d()

subroutine simplex_oct_m::simplex_dos_3d	(	real(real64), dimension(:), intent(in)	etetra,
		real(real64), dimension(:), intent(in)	eFs,
		real(real64), dimension(:,:), intent(out)	dos
	)

private

Get only the DOS contribution of a single tetrahedron.

The expressions for the DOS are given in A. H. MacDonald, et al., J. Phys. C: Solid State Phys. 12, 2991 (1979).

The expressions for the weights of the improved tetrahedron method are given in Eq. (18)-(21) of M. Kawamura, et al., Phys. Rev. B 89, 094515 (2014).

Parameters

[in]	etetra	Eigenenergies on the corner points of a tetrahedron
[in]	eFs	Reference energies
[out]	dos	Contribution to the DOS by the tetrahedron, indexed as (vertex, energy)

Definition at line 1137 of file simplex.F90.

Data Types

Functions/Subroutines

Function/Subroutine Documentation

◆ simplex_sort_2()

◆ simplex_sort_3()

◆ simplex_sort_4()

◆ simplex_compare_swap()

◆ simplex_init()

◆ simplex_end()

◆ simplex_weights_single()

◆ simplex_weights_array()

◆ simplex_dos_single()

◆ simplex_dos_array()

◆ simplex_weights_1d()

◆ simplex_dos_1d()

◆ simplex_weights_2d()

◆ simplex_dos_2d()

◆ simplex_weights_3d()

◆ simplex_dos_3d()