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Contours

Summary

Numerics.Contour.Quad

Generic "contour" specified only by its nodes and weights.

Numerics.Contour.Quad.z SetObservable 

z = []

nodes

Numerics.Contour.Quad.w SetObservable 

w = []

Numerics.Contour.Quad. SetObservable

Numerics.Contour.Quad.Quad 

(z, w)

Numerics.Contour.Quad.inside 

(pt)

Determine if a point pt is inside the convex hull of the contour

Numerics.Contour.Quad.FindRandomShift 

(scale=1.25)

Returns a random point outside of the convex hull of the given contour. First, the maximum distance d between any node and the geometric center c is determined. A complex i.i.d point is chosen with distance d*scale from c.

Numerics.Contour.Circle 

flowchart TB
   Circle[Circle]
   matlab_mixin_Copyable[matlab.mixin.Copyable]
   Quad[Quad]
   matlab_mixin_Copyable --> Quad
   Quad --> Circle

Circular contour specified by a center gamma, radius rho, and number of quadrature nodes N.

Numerics.Contour.Quad.z SetObservable 

z = []

nodes

Numerics.Contour.Quad.w SetObservable 

w = []

Numerics.Contour.Circle.gamma SetObservable 

gamma

center

Numerics.Contour.Circle.rho SetObservable 

rho

Numerics.Contour.Circle. SetObservable

Numerics.Contour.Circle.N SetObservable 

N

Numerics.Contour.Circle.Circle 

(gamma=0, rho=1, N=8)

Numerics.Contour.Circle.inside 

(pt)

Numerics.Contour.Circle.interlevedshifts 

(nsw, d=1.25, mode='scale', variant='cconj')

Returns a set of left and right interleaved shifts with nsw shifts each. The shifts are placed d*\(\rho\) or d+\(\rho\) away from the center of the contour depending on setting mode=scale or mode=shift, respectively.

Input arguments:

  • nsw –
  • d –
  • mode –
  • variant –

    or 'trap'

Numerics.Contour.Circle.refineQuadrature 

(rf=2)

Scales the number of quadrature points of the contour by a factor rf and explicitly updates the contour.

Numerics.Contour.Circle.update 

()

Updates contour nodes and weights using the trapezoid rule.

Numerics.Contour.Circle.trapezoid Static 

(gamma, rho, N)

Numerics.Contour.Ellipse 

flowchart TB
   Ellipse[Ellipse]
   matlab_mixin_Copyable[matlab.mixin.Copyable]
   Quad[Quad]
   matlab_mixin_Copyable --> Quad
   Quad --> Ellipse

Ellipsoidal contour specified by a center gamma, horizontal and vertical semi-radii alpha and beta, and number of quadrature nodes N.

Numerics.Contour.Quad.z SetObservable 

z = []

nodes

Numerics.Contour.Quad.w SetObservable 

w = []

Numerics.Contour.Ellipse.gamma SetObservable 

gamma

center

Numerics.Contour.Ellipse.alpha SetObservable 

alpha

Numerics.Contour.Ellipse. SetObservable

Numerics.Contour.Ellipse.beta SetObservable 

beta

Numerics.Contour.Ellipse.N SetObservable 

N

Numerics.Contour.Ellipse.Ellipse 

(gamma=0, alpha=1, beta=1, N=8)

Numerics.Contour.Ellipse.inside 

(pt)

Numerics.Contour.Ellipse.interlevedshifts 

(nsw, d=1.25, mode='scale', variant='cconj')

Numerics.Contour.Ellipse.refineQuadrature 

(rf=2)

Numerics.Contour.Ellipse.update 

()

Numerics.Contour.Ellipse.trapezoid Static 

(gamma, alpha, beta, N)

Numerics.Contour.Ellipse.ellipquad Static 

(gamma, alpha, beta, N)