negf_integr_utils Module Reference

Helper functions for integration routines. More...

Data Types
interface	equidistant_nodes_a_b

Functions/Subroutines
subroutine, public	rescale_normalised_nodes (nnodes, tnodes, a, b, shape_id, xnodes, weights)
pure real(kind=dp) function, public	get_arc_radius (a, b)
	Compute arc radius.
pure real(kind=dp) function, public	get_arc_smallest_angle (a, b)
	Compute the angle phi.
subroutine, public	rescale_nodes_arc (nnodes, tnodes_angle, a, b, xnodes)
	Rescale nodes [pi, phi] -> arc[a, b] .
subroutine, public	rescale_nodes_cos (nnodes, tnodes)
	Rescale nodes tnodes(i) = cos(pi/2 * (1-tnodes(i))); tnodes \in [-1 .. 1] .
subroutine, public	rescale_nodes_linear (nnodes, tnodes, a, b, xnodes)
	Rescale nodes [-1, 1] -> [a, b] .
subroutine, public	rescale_nodes_pi_phi (a, b, nnodes, tnodes)
	Rescale nodes [-1, 1] -> [pi, phi] .

Variables
integer, parameter, public	contour_shape_linear = 0
integer, parameter, public	contour_shape_arc = 1

Detailed Description

Helper functions for integration routines.

History

• 06.2017 created [Sergey Chulkov]

Function/Subroutine Documentation

rescale_normalised_nodes()

subroutine, public negf_integr_utils::rescale_normalised_nodes	(	integer, intent(in)	nnodes,
		real(kind=dp), dimension(nnodes), intent(in)	tnodes,
		complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b,
		integer, intent(in)	shape_id,
		complex(kind=dp), dimension(nnodes), intent(out), optional	xnodes,
		complex(kind=dp), dimension(nnodes), intent(out), optional	weights
	)

Definition at line 86 of file negf_integr_utils.F.

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get_arc_radius()

pure real(kind=dp) function, public negf_integr_utils::get_arc_radius	(	complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b
	)

Compute arc radius.

Parameters

a	lower bound
b	upper bound

Returns

radius

History

• 05.2017 created [Sergey Chulkov]

Note

Assuming Re(a) < Re(b) and Im(a) < Im(b)

Definition at line 152 of file negf_integr_utils.F.

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get_arc_smallest_angle()

pure real(kind=dp) function, public negf_integr_utils::get_arc_smallest_angle	(	complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b
	)

Compute the angle phi.

Parameters

a	lower bound
b	upper bound

Returns

angle

History

• 05.2017 created [Sergey Chulkov]

Note

Assuming Re(a) < Re(b) and Im(a) < Im(b)

Definition at line 182 of file negf_integr_utils.F.

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rescale_nodes_arc()

subroutine, public negf_integr_utils::rescale_nodes_arc	(	integer, intent(in)	nnodes,
		real(kind=dp), dimension(:), intent(in)	tnodes_angle,
		complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b,
		complex(kind=dp), dimension(:), intent(out)	xnodes
	)

Rescale nodes [pi, phi] -> arc[a, b] .

Parameters

nnodes	number of nodes
tnodes_angle	parametrically-defined nodes to rescale
a	lower bound
b	upper bound
xnodes	rescaled nodes (initialised on exit)

History

• 05.2017 created [Sergey Chulkov]

Note

Assuming Re(a) < Re(b) and Im(a) < Im(b)

Definition at line 222 of file negf_integr_utils.F.

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rescale_nodes_cos()

subroutine, public negf_integr_utils::rescale_nodes_cos	(	integer, intent(in)	nnodes,
		real(kind=dp), dimension(nnodes), intent(inout)	tnodes
	)

Rescale nodes tnodes(i) = cos(pi/2 * (1-tnodes(i))); tnodes \in [-1 .. 1] .

Parameters

tnodes

parametrically-defined nodes to rescale / rescaled nodes (modified on exit)

History

• 05.2017 created [Sergey Chulkov]

Note

Assuming Re(a) < Re(b) and Im(a) < Im(b)

Definition at line 247 of file negf_integr_utils.F.

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rescale_nodes_linear()

subroutine, public negf_integr_utils::rescale_nodes_linear	(	integer, intent(in)	nnodes,
		real(kind=dp), dimension(nnodes), intent(in)	tnodes,
		complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b,
		complex(kind=dp), dimension(nnodes), intent(out)	xnodes
	)

Rescale nodes [-1, 1] -> [a, b] .

Parameters

nnodes	number of nodes
tnodes	parametrically-defined nodes to rescale
a	lower bound
b	upper bound
xnodes	rescaled nodes (initialised on exit)

History

• 05.2017 created [Sergey Chulkov]

Definition at line 264 of file negf_integr_utils.F.

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rescale_nodes_pi_phi()

subroutine, public negf_integr_utils::rescale_nodes_pi_phi	(	complex(kind=dp), intent(in)	a,
		complex(kind=dp), intent(in)	b,
		integer, intent(in)	nnodes,
		real(kind=dp), dimension(nnodes), intent(inout)	tnodes
	)

Rescale nodes [-1, 1] -> [pi, phi] .

Parameters

nnodes	number of nodes
a	lower bound
b	upper bound
tnodes	parametrically-defined nodes to rescale / rescaled nodes (modified on exit)

History

• 05.2017 created [Sergey Chulkov]

Note

Assuming Re(a) < Re(b) and Im(a) < Im(b)

Definition at line 288 of file negf_integr_utils.F.

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Variable Documentation

contour_shape_linear

integer, parameter, public negf_integr_utils::contour_shape_linear = 0

Definition at line 27 of file negf_integr_utils.F.

contour_shape_arc

integer, parameter, public negf_integr_utils::contour_shape_arc = 1

Definition at line 27 of file negf_integr_utils.F.