slepc4py.SLEPc.RG#

class slepc4py.SLEPc.RG#

Bases: Object

Region.

The RG package provides a way to define a region of the complex plane. This is used in various eigensolvers to specify where the wanted eigenvalues are located.

Enumerations

`QuadRule`	RG quadrature rule for contour integral methods.
`Type`	RG type.

Methods Summary

`appendOptionsPrefix`([prefix])	Append to the prefix used for searching for all RG options in the database.
`canUseConjugates`([realmats])	Half of integration points can be avoided (use their conjugates).
`checkInside`(a)	Determine if a set of given points are inside the region or not.
`computeBoundingBox`()	Endpoints of a rectangle in the complex plane containing the region.
`computeContour`(n)	Compute the coordinates of several points of the contour on the region.
`computeQuadrature`(quad, n)	Compute the values of the parameters used in a quadrature rule.
`create`([comm])	Create the RG object.
`destroy`()	Destroy the RG object.
`getComplement`()	Get the flag indicating whether the region is complemented or not.
`getEllipseParameters`()	Get the parameters that define the ellipse region.
`getIntervalEndpoints`()	Get the parameters that define the interval region.
`getOptionsPrefix`()	Get the prefix used for searching for all RG options in the database.
`getPolygonVertices`()	Get the parameters that define the interval region.
`getRingParameters`()	Get the parameters that define the ring region.
`getScale`()	Get the scaling factor.
`getType`()	Get the RG type of this object.
`isAxisymmetric`([vertical])	Determine if the region is symmetric wrt.
`isTrivial`()	Tell whether it is the trivial region (whole complex plane).
`setComplement`([comp])	Set a flag to indicate that the region is the complement of the specified one.
`setEllipseParameters`(center, radius[, vscale])	Set the parameters defining the ellipse region.
`setFromOptions`()	Set RG options from the options database.
`setIntervalEndpoints`(a, b, c, d)	Set the parameters defining the interval region.
`setOptionsPrefix`([prefix])	Set the prefix used for searching for all RG options in the database.
`setPolygonVertices`(v)	Set the vertices that define the polygon region.
`setRingParameters`(center, radius, vscale, ...)	Set the parameters defining the ring region.
`setScale`([sfactor])	Set the scaling factor to be used.
`setType`(rg_type)	Set the type for the RG object.
`view`([viewer])	Print the RG data structure.

Attributes Summary

`complement`	If the region is the complement of the specified one.
`scale`	The scaling factor to be used.

Methods Documentation

appendOptionsPrefix(prefix=None)#

Append to the prefix used for searching for all RG options in the database.

Logically collective.

Parameters:: prefix (str | None) – The prefix string to prepend to all RG option requests.
Return type:: None

Source code at slepc4py/SLEPc/RG.pyx:158

canUseConjugates(realmats=True)#

Half of integration points can be avoided (use their conjugates).

Not collective.

Used in contour integral methods to determine whether half of integration points can be avoided (use their conjugates).

Parameters:: realmats (bool) – True if the problem matrices are real.
Returns:: Whether it is possible to use conjugates.
Return type:: bool

Source code at slepc4py/SLEPc/RG.pyx:378

checkInside(a)#

Determine if a set of given points are inside the region or not.

Not collective.

Parameters:: a (Sequence[complex]) – The coordinates of the points.
Returns:: Computed result for each point (1=inside, 0=on the contour, -1=outside).
Return type:: ArrayInt

Source code at slepc4py/SLEPc/RG.pyx:291

computeBoundingBox()#

Endpoints of a rectangle in the complex plane containing the region.

Not collective.

Determine the endpoints of a rectangle in the complex plane that contains the region.

Returns:

a (float) – The left endpoint of the bounding box in the real axis
b (float) – The right endpoint of the bounding box in the real axis
c (float) – The left endpoint of the bounding box in the imaginary axis
d (float) – The right endpoint of the bounding box in the imaginary axis

Return type:

tuple[float, float, float, float]

Source code at slepc4py/SLEPc/RG.pyx:354

computeContour(n)#

Compute the coordinates of several points of the contour on the region.

Not collective.

Compute the coordinates of several points lying on the contour of the region.

Parameters:: n (int) – The number of points to compute.
Returns:: Computed points.
Return type:: list of complex

Source code at slepc4py/SLEPc/RG.pyx:323

computeQuadrature(quad, n)#

Compute the values of the parameters used in a quadrature rule.

Not collective.

Compute the values of the parameters used in a quadrature rule for a contour integral around the boundary of the region.

Parameters:

quad (QuadRule) – The type of quadrature.
n (int) – The number of quadrature points to compute.

Returns:

z (ArrayScalar) – Quadrature points.
zn (ArrayScalar) – Normalized quadrature points.
w (ArrayScalar) – Quadrature weights.

Return type:

tuple[ArrayScalar, ArrayScalar, ArrayScalar]

Source code at slepc4py/SLEPc/RG.pyx:402

create(comm=None)#

Create the RG object.

Collective.

Parameters:: comm (Comm | None) – MPI communicator; if not provided, it defaults to all processes.
Return type:: Self

Source code at slepc4py/SLEPc/RG.pyx:75

destroy()#

Destroy the RG object.

Collective.

Source code at slepc4py/SLEPc/RG.pyx:65

Return type:: Self

getComplement()#

Get the flag indicating whether the region is complemented or not.

Not collective.

Returns:: Whether the region is complemented or not.
Return type:: bool

Source code at slepc4py/SLEPc/RG.pyx:229

getEllipseParameters()#

Get the parameters that define the ellipse region.

Not collective.

Returns:

center (Scalar) – The center.
radius (float) – The radius.
vscale (float) – The vertical scale.

Return type:

tuple[Scalar, float, float]

Source code at slepc4py/SLEPc/RG.pyx:459

getIntervalEndpoints()#

Get the parameters that define the interval region.

Not collective.

Returns:

a (float) – The left endpoint in the real axis.
b (float) – The right endpoint in the real axis.
c (float) – The upper endpoint in the imaginary axis.
d (float) – The lower endpoint in the imaginary axis.

Return type:

tuple[float, float, float, float]

Source code at slepc4py/SLEPc/RG.pyx:503

getOptionsPrefix()#

Get the prefix used for searching for all RG options in the database.

Not collective.

Returns:: The prefix string set for this RG object.
Return type:: str

Source code at slepc4py/SLEPc/RG.pyx:143

getPolygonVertices()#

Get the parameters that define the interval region.

Not collective.

Returns:: The vertices.
Return type:: ArrayComplex

Source code at slepc4py/SLEPc/RG.pyx:551

getRingParameters()#

Get the parameters that define the ring region.

Not collective.

Returns:

center (Scalar) – The center.
radius (float) – The radius.
vscale (float) – The vertical scale.
start_ang (float) – The right-hand side angle.
end_ang (float) – The left-hand side angle.
width (float) – The width of the ring.

Return type:

tuple[Scalar, float, float, float, float, float]

Source code at slepc4py/SLEPc/RG.pyx:610

getScale()#

Get the scaling factor.

Not collective.

Returns:: The scaling factor.
Return type:: float

Source code at slepc4py/SLEPc/RG.pyx:276

getType()#

Get the RG type of this object.

Not collective.

Returns:: The region type currently being used.
Return type:: str

Source code at slepc4py/SLEPc/RG.pyx:107

isAxisymmetric(vertical=False)#

Determine if the region is symmetric wrt. the real or imaginary axis.

Not collective.

Determine if the region is symmetric with respect to the real or imaginary axis.

Parameters:: vertical (bool) – True if symmetry must be checked against the vertical axis.
Returns:: True if the region is axisymmetric.
Return type:: bool

Source code at slepc4py/SLEPc/RG.pyx:205

isTrivial()#

Tell whether it is the trivial region (whole complex plane).

Not collective.

Returns:: True if the region is equal to the whole complex plane, e.g., an interval region with all four endpoints unbounded or an ellipse with infinite radius.
Return type:: bool

Source code at slepc4py/SLEPc/RG.pyx:188

setComplement(comp=True)#

Set a flag to indicate that the region is the complement of the specified one.

Logically collective.